The absolute value inequality in form |x-b| < c that has the solution set x<-5 or x>7 is |x-1| < 7
To write an absolute value inequality in the form |x-b| < c, we need to think about what this form means.
The expression |x-b| represents the distance between x and b on the number line. Therefore, |x-b| < c means that the distance between x and b is less than c.
Now, let's consider the given solution set: x < -5 or x > 7. We can see that the midpoint between -5 and 7 is 1, so we choose b = 1. Then, we need to determine c, which is the maximum distance between b and any of the solutions.
If we take x = -6 (which is less than -5), then |x-b| = |-6-1| = 7. Similarly, if we take x = 8 (which is greater than 7), then |x-b| = |8-1| = 7. Therefore, the maximum distance is 7.
Putting it all together, we get the absolute value inequality:
|x-1| < 7
To learn more about inequality click on,
https://brainly.com/question/31505158
#SPJ1
It is claimed that 75% of puppies are house-trained by the time they are 6 months old. To investigate this claim, a random sample of 50 puppies is selected. It is discovered that 42 are house-trained by the time they are 6 months old. A trainer would like to know if the data provide convincing evidence that greater than 75% of puppies are house-trained by the time they are 6 months old. The standardized test statistic is z = 1. 47 and the P-value is 0. 708. What conclusion should be made using the Alpha = 0. 05 significance level?
Because the P-value is greater than Alpha = 0. 05, there is convincing evidence that 75% of puppies are house-trained by the time they are 6 months old.
Because the P-value is greater than Alpha = 0. 05, there is not convincing evidence that 75% of puppies are house-trained by the time they are 6 months old.
Because the P-value is greater than Alpha = 0. 05, there is convincing evidence that greater than 75% of puppies are house-trained by the time they are 6 months old.
Because the P-value is greater than Alpha = 0. 05, there is not convincing evidence that greater than 75% of puppies are house-trained by the time they are 6 months old
The conclusion should be made using the Alpha = 0. 05 significance level is because the P-value is greater than Alpha = 0.05, there is not convincing evidence that greater than 75% of puppies are house-trained by the time they are 6 months old. The correct answer is B.
The given null hypothesis is that 75% of puppies are house-trained by the time they are 6 months old. The alternative hypothesis is that greater than 75% of puppies are house-trained by the time they are 6 months old.
The test statistic is a z-score, which is calculated by subtracting the hypothesized proportion (0.75) from the sample proportion (42/50 = 0.84), dividing by the standard error of the sample proportion, and then standardizing with respect to the standard normal distribution. The resulting z-score is 1.47.
The P-value is the probability of observing a test statistic as extreme or more extreme than the calculated z-score, assuming the null hypothesis is true. A P-value of 0.708 means that there is a 70.8% chance of observing a sample proportion as extreme or more extreme than 0.84, assuming that 75% of puppies are house-trained by the time they are 6 months old.
Since the P-value is greater than the significance level (alpha) of 0.05, we fail to reject the null hypothesis. In other words, there is not convincing evidence to suggest that greater than 75% of puppies are house-trained by the time they are 6 months old.
Learn more about hypothesis at https://brainly.com/question/30461126
#SPJ11
Kyra has 2 plates, 2 cups, and 2 bowls. If she chooses one of each randomly, what is the probability that the plate, cup, and bowl she chooses will all be blue?
0.167
0.333
0.125
0.083
The probability is 0.125
To solve this problemThere are a total of 2 × 2 x 2 = 8 possibilities of one plate, one cup, and one bowl that Kyra can select if she has two plates, two cups, and two bowls.
We need to figure out how many combinations fit this requirement because we are interested in the likelihood that all three objects are blue. There are 2 × 2 x 2 = 8 potential color combinations if we assume that each item can be either blue or not blue.
There is only one of these eight color pairings in which all three components are blue. P(all three are blue) = 1/8 = 0.125 is the likelihood that Kyra will select one blue plate, one blue cup, and one blue bowl.
So, the probability is 0.125.
Learn more about probability here : brainly.com/question/29280399
#SPJ1
Americans consume on average 32. 3 lbs of cheese per year with a standard deviation of 8. 7 lbs. Assume that the amount of cheese consumed each year by an American is normally distributed. An American in the middle 70% of cheese consumption consumes per year how much cheese?
An American in the middle 70% of cheese consumption consumes per year between 23.252 and 41.348 lbs of cheese.
To find the amount of cheese consumed by an American in the middle 70%, we need to find the range of values that contain the middle 70% of the distribution.
First, we need to find the z-scores corresponding to the lower and upper boundaries of the middle 70% of the distribution. We can use the standard normal distribution for this, by converting the raw score of 32.3 lbs to a z-score:
z = (x - μ) / σ = (32.3 - 32.3) / 8.7 = 0
The z-score for the mean is zero, which means the mean is the midpoint of the normal distribution.
Next, we need to find the z-scores that correspond to the lower and upper boundaries of the middle 70% of the distribution. We can use the standard normal distribution table or calculator to find the z-scores. For a middle 70% range, the z-scores are approximately -1.04 and 1.04.
Finally, we can use the z-scores and the formula z = (x - μ) / σ to find the corresponding values of x, which represent the range of cheese consumption that contains the middle 70% of the distribution:
Lower boundary: z = -1.04
-1.04 = (x - 32.3) / 8.7
x - 32.3 = -9.048
x = 23.252 lbs
Upper boundary: z = 1.04
1.04 = (x - 32.3) / 8.7
x - 32.3 = 9.048
x = 41.348 lbs
Learn more about normal distribution at https://brainly.com/question/29509087
#SPJ11
y varies inversely as x. y= 27 when x=5 Find y when x=3
As y varies inversely as x, the value of y when x = 3 is 45.
What is the value of y when x = 3?Inverse proportionality is expressed as:
y ∝ 1/x
Hence:
y = k/x
Where k is the constant of proportionality.
First, we determine the constant of proportionality.
Using the information given in the problem.
When x = 5, y = 27
Substituting these values into the formula, we get:
y = k/x
27 = k/5
k = 135
Now that we have found the value of k, we can use the formula to find y when x = 3. Substituting x = 3 and k = 135, we get:
y = k/x
y = 135/3
y = 45
Therefore, the value of y is 45.
Learn more about proportionality here: https://brainly.com/question/27530069
#SPJ1
Babacar has a coupon for 20% off, after tax, at Burger Beast Restaurant. When Babacar and Arturo eat dinner at Burger Beast restaurant, their bill is $36. 00 after tax. They use Babacar’s coupon, and they decide to leave a tip that is 20% of the discounted price. How much did Babacar and Arturo pay in total?
The total amount Babcar and Arutro paid in the Burger Beast Restaurant is $ 34.56.
Total bill = $36
Discount coupon = 20 %
The price paid after the discount coupon = 36 - (20% of 36 )
Price paid = 36 - (36 × 20/100)
The price paid = 36 - 7.2
Price paid = 28.8
The tip paid is 20 % the discounted price
The tip paid = 20% of 28.8
The tip paid = 28.8 × 20/100
The tip paid = 5.76
The total price paid = price paid after discount coupon + Tip paid
The total price paid = 28.8 + 5.76
The total price paid = 34.56
To know more about amount click here :
https://brainly.com/question/28970975
#SPJ4
4+5x > 19
how to do
Answer:
x>3
Step-by-step explanation:
i assume you're solving for x so,
1) rearrange terms,
5x+4>19
2)subtract 4 from both sides
5x+4-4>19-4
3) Simplify
5x>15
4) divide both sides by 5, because they are same factor
\frac{5x}{5} > \frac{15}{5}
5) Finally, the answer is
x>3
The hottest day of the year in Buenos Aires, Argentina, on average, is January 7, when the average high temperature is 37° C. The coolest day of the year has an average high temperature of 17° C. Use a trigonometric function to model the temperature in Buenos Aires, Argentina using 365 days as the length of a year. Remember that January 7 is in the summer in Buenos Aires
The temperature in Buenos Aires can be modeled using the equation T(t) = 5 sin(2π(t - 182.5)/365) + 27, where t is the number of days since January 1.
How to model temperature in Buenos Aires?To model the temperature in Buenos Aires using a trigonometric function, we can use the sine function.
First, we need to find the amplitude, period, phase shift, and vertical shift.
Amplitude: The difference between the maximum and minimum temperatures is (37 - 17) / 2 = 10 degrees, so the amplitude is 10/2 = 5 degrees.Period: The period of the function is 365 days, which is the length of a year.Phase shift: January 7 is in the summer, so we want to shift the function to the right by half a year (182.5 days).Vertical shift: The average temperature over the year is (37 + 17) / 2 = 27 degrees, so the vertical shift is 27 degrees.Putting it all together, the equation for the temperature in Buenos Aires as a function of time is:
T(t) = 5 sin(2π(t - 182.5)/365) + 27
Where t is the number of days since January 1 and T(t) is the temperature in degrees Celsius.
Learn more about trigonometric function
brainly.com/question/6904750
#SPJ11
Pls help
a polynomial function is represented by the data in the table
x 0 i 1 i 2 i 3 i 4 i
f(x) -24 i -21¾ i -14 i ¾ i 24 i
choose the function represented by the data.
1. f(x) = x3 − x2 − 24
2. f(x) [tex]\frac{x}{4}^{3}[/tex] + 2[tex]x^{2}[/tex] -24
3. f(x)= -2[tex]\frac{1}{4} x^{2}[/tex] + 24
4. f(x)= [tex]\frac{3}{4} x^{2}[/tex] -3x + 24
The function represented by the data is f(1/4)x³ + 2x² - 24. The correct option is 2.
In the given table, we have the values of x and f(x) for x=0,1,2,3, and 4. We need to find a polynomial function that satisfies these data points.
Looking at the table, we can see that f(x) is negative for x=0,1,2 and positive for x=3,4. This suggests that the polynomial has a root or a zero between x=2 and x=3.
To find the degree of the polynomial, we count the number of data points given. Since we have 5 data points, we need a polynomial of degree 4.
We can use interpolation to find the coefficients of the polynomial. One way to do this is to set up a system of equations using the data points:
f(0) = -24 = a(0)⁴ + b(0)³ + c(0)² + d(0) + e
f(1) = -21.75 = a(1)⁴ + b(1)³ + c(1)² + d(1) + e
f(2) = -14 = a(2)⁴ + b(2)³ + c(2)² + d(2) + e
f(3) = 0.75 = a(3)⁴ + b(3)³ + c(3)² + d(3) + e
f(4) = 24 = a(4)⁴ + b(4)³ + c(4)² + d(4) + e
Solving this system of equations gives us the polynomial function:
f(x) = -0.25x⁴ + 2x³ - 2.75x² - 0.5x + 24
Therefore, the correct option is 2. f(x) = (1/4)x³ + 2x² - 24.
Learn more about polynomials function at https://brainly.com/question/9482448
#SPJ11
Sarah wants to attend a private college with a yearly tuition of $31,000. Room and board costs are estimated to be $12,000 per year, and the cost of books and supplies is estimated to be $2,000. Assuming she receives no financial aid, how much will it cost her to get a four-year degree from this college?
Sarah wants to attend a private college with a yearly tuition of $31,000. Room and board costs are estimated to be $12,000 per year, and the cost of books and supplies is estimated to be $2,000. To calculate the total cost of her four-year degree, follow these steps:
1. Add the yearly costs together: $31,000 (tuition) + $12,000 (room and board) + $2,000 (books and supplies) = $45,000 per year.
2. Multiply the yearly cost by the number of years in the degree program: $45,000 * 4 = $180,000.
Assuming she receives no financial aid, it will cost Sarah $180,000 to get a four-year degree from this private college.
To know more about total cost refer here
https://brainly.com/question/21662065#
#SPJ11
Anne's Road Paving Company mixed 16 1/4 tons of cement. They used 6 3/4 tons of the cement to pave a street downtown. How much cement did they have left?
Answer is 9.5 tons of cement
Anne's Road Paving Company initially mixed 16 1/4 tons of cement. They used 6 3/4 tons for paving a street downtown. To find the remaining amount of cement, subtract the used amount from the initial amount:
16 1/4 - 6 3/4 = 15 1/4 - 5 3/4 = 9 1/2 tons.
So, they had 9 1/2 tons of cement left.
To know more about subtraction calculations:
https://brainly.com/question/28669193
#SPJ11
2. A scientist placed 100 bacteria in a petri dish. The number of bacteria triples every 12 hours. What is the equivalent hourly rate?
Let's call the initial number of bacteria in the petri dish as $N_0 = 100$. After 12 hours, the number of bacteria triples, which means there are now $3N_0$ bacteria. After another 12 hours, the number of bacteria triples again, which means there are now $3(3N_0) = 9N_0$ bacteria.
We can see a pattern here that after every 12 hours, the number of bacteria is multiplied by 3. Let's calculate the number of bacteria after 1 hour:
$\sf\implies\:N_1 = N_0 \times 3^{1/12}$
After simplifying:
$\sf\implies\:N_1 = 100 \times 3^{1/12}$
Using a calculator, we can find that $\sf\:3^{1/12} \approx 1.1548$. Therefore:
$\sf\implies\:N_1 \approx{\boxed{115.48}}$
So the equivalent hourly rate at which the number of bacteria is increasing is approximately 15.48% per hour.
In general, if the number of bacteria triples every $t$ hours, the equivalent hourly rate can be calculated as:
$\sf\implies\:r = 3^{1/t} - 1$
where $r$ is the hourly rate expressed as a decimal.
[tex]\begin{align}\huge\colorbox{black}{\textcolor{yellow}{\boxed{\sf{I\: hope\: this\: helps !}}}}\end{align}[/tex]
[tex]\begin{align}\colorbox{black}{\textcolor{white}{\underline{\underline{\sf{Please\: mark\: as\: brillinest !}}}}}\end{align}[/tex]
[tex]\textcolor{lime}{\small\textit{If you have any further questions, feel free to ask!}}[/tex]
[tex]\huge{\bigstar{\underline{\boxed{\sf{\color{red}{Sumit\:Roy}}}}}}\\[/tex]
Consider the function f(x)=x(x-4).
If the point (2+c,y) is on the graph of f(x), the following point will also be on the graph of f(x):
The point (c-2, y) will also be on the graph of f(x) if the point (2+c, y) is on the graph. The correct option is (c-2, y).
If the point (2+c, y) is on the graph of f(x) = x(x-4), we can determine the x-value of the following point on the graph by substituting the given x-value into the function.
1. Start with the given point (2+c, y).
2. Substitute the x-value into the function f(x) = x(x-4):
f(2+c) = (2+c)((2+c)-4)
= (2+c)(c-2)
= c(c-2) + 2(c-2)
= c² - 2c + 2c - 4
= c² - 4
So, the y-value of the point (2+c, y) on the graph of f(x) is y = c² - 4.
Now, let's determine the x-value of the following point on the graph by considering the options provided.
If we select the value (c-2) as the x-value of the following point, we can substitute it into the function f(x) to find the corresponding y-value.
f(c-2) = (c-2)((c-2)-4)
= (c-2)(c-2-4)
= (c-2)(c-6)
= c(c-6) - 2(c-6)
= c² - 6c - 2c + 12
= c² - 8c + 12
So, the y-value of the point (c-2, y) on the graph of f(x) is y = c² - 8c + 12.
To learn more about the function;
brainly.com/question/28303908
#SPJ12
The complete question:
Consider the function f(x)=x(x-4).
If the point (2+c,y) is on the graph of f(x), the following point will also be on the graph of f(x):
Select a Value
(c-2,y)
(2-c,y)
A pitcher contains 13 cups of iced tea. You drink 1. 75 cups of the tea each morning
and 1. 5 cups of the tea each evening. When will you run out of iced tea?
You will run out of iced tea in 5.33 days.
To calculate this, we need to first determine how much tea you drink each day:
1.75 cups in the morning + 1.5 cups in the evening = 3.25 cups per day.
Then, we can divide the total amount of tea by the amount you drink per day to find out how many days the tea will last:
13 cups ÷ 3.25 cups per day ≈ 4 days.
However, we need to account for the fact that you won't run out of tea at the end of the day, so we need to round up to the nearest day:
ceil(4 days) = 5 days.
Finally, we need to account for the partial day on the fifth day, which we can calculate by finding how much tea you drink in the morning before running out:
1.75 cups in the morning - (5 days x 3.25 cups per day) = 0.5 cups.
So, you will run out of iced tea on the fifth day in the evening, after drinking 1.5 cups. Therefore, you will run out of iced tea in 5.33 days.
To know more about iced tea, refer here:
https://brainly.com/question/28531302#
#SPJ11
Omar Cuts A Piece Of Wrapping Paper with the shape and dimensions as shown .Find the area of the wrapping paper. Round your answer to the nearest tenth if needed
The area of the wrapping paper would be = 72.5in².
How to calculate the area of the wrapping paper?To calculate the area of the wrapping paper, the figure is first divided into two leading to the formation of a triangle and a rectangle.
For the triangle, the formula use to calculate it's area is given as follows;
Area = 1/2 base × height
base = 15-10 = 5 in
height = 9-4 = 5 in
area = 1/2×5 × 5
= 25/2 = 12.5 in²
Area of a rectangle = length× width
width = 4 in
length = 15 in
area = 4×15 = 60in²
Therefore the area of the wrapping paper = 12.5+60 = 72.5in²
Learn more about area here:
https://brainly.com/question/28470545
#SPJ1
THE PUZZLE
This problem gives you the chance to
Solve and reason abxut equations
A magazine contains a puzzle.
Each symbol represents a
number
>
28
>
24
Different symbols have
different values.
N
42
The sum of each row is given
at the side of the table.
>
36
Try to find out the value for each symbol:
heart-. Spade - 1. Club - 4 diamond
The value for each symbol is: Heart - 9, Spade - 3, Club - 6, Diamond - 8.
How to determine symbol values?To solve the puzzle and find the value for each symbol, we can use the given information.
First, we observe that the sum of each row is provided on the side of the table. Therefore, we can use this information to find the value for each symbol.
Let's assign variables to each symbol: heart (H), spade (S), club (C), and diamond (D).
From the first row, we have H + S + C = 28.
From the second row, we have H + D = 24.
From the third row, we have H + S + C + D = 36.
We can solve this system of equations to find the value for each symbol. By substituting the values, we can deduce that heart (H) is equal to 10, spade (S) is equal to 7, club (C) is equal to 11, and diamond (D) is equal to 14.
Learn more about value
brainly.com/question/10416781
#SPJ11
Greg, Harry and Ian share their electricity bill in the ratio 2:4:5.
how much dies each of them pay when their electricity bill are 1) 110$ 2) 165$ 3) 352$
pls answer quickly
The amount each of them pays when their electricity bill is $110, $165, and $352 respectively, in the ratio 2:4:5, are:
1) $20, $40, $50
2) $30, $60, $75
3) $64, $128, $160
1. How much do they pay for a $110 electricity bill?To find out how much each of them pays, we'll use the given ratio of 2:4:5 and divide the total bill among them accordingly.
Total bill: $110
The total ratio is 2+4+5=11.
Greg's share: (2/11) * $110 = $20
Harry's share: (4/11) * $110 = $40
Ian's share: (5/11) * $110 = $50
Therefore, Greg pays $20, Harry pays $40, and Ian pays $50.
2. How much do they pay for a $165 electricity bill?Total bill: $165
The total ratio is still 2+4+5=11.
Greg's share: (2/11) * $165 = $30
Harry's share: (4/11) * $165 = $60
Ian's share: (5/11) * $165 = $75
Therefore, Greg pays $30, Harry pays $60, and Ian pays $75.
3. How much do they pay for a $352 electricity bill?Total bill: $352
The total ratio remains the same: 2+4+5=11.
Greg's share: (2/11) * $352 = $64
Harry's share: (4/11) * $352 = $128
Ian's share: (5/11) * $352 = $160
Therefore, Greg pays $64, Harry pays $128, and Ian pays $160.
Learn more about ratio
brainly.com/question/13419413
#SPJ11
Jane completed 8 homework problems in class. The function p(m) relates the
time (in minutes) Jane spent on her homework at home to the total number
of problems she completed. The input is the number of minutes worked. The
output is the number of problems completed.
p(m)= m/5+8
Which equation represents the inverse function m(p), which uses problems
completed as the input and gives minutes worked as the output?
Answer:
Step-by-step explanation:
5p-40
All the 4-digit numbers you could make using seven square tiles numbered 2, 3, 4, 5, 6, 7, and 8
Using the seven square tiles numbered 2, 3, 4, 5, 6, 7, and 8, we can make 1260 different 4-digit numbers.
To create a 4-digit number using these seven square tiles, we have to consider the following:
- The first digit cannot be 2 because then the number would only have three digits.
- We can choose any of the remaining six tiles for the first digit, which means there are 6 choices.
- We can choose any of the seven tiles for the second digit, which means there are 7 choices.
- We can choose any of the remaining six tiles for the third digit, which means there are 6 choices.
- We can choose any of the remaining five tiles for the fourth digit, which means there are 5 choices.
Therefore, the total number of 4-digit numbers we can make is:
6 x 7 x 6 x 5 = 1260
So, using the seven square tiles numbered 2, 3, 4, 5, 6, 7, and 8, we can make 1260 different 4-digit numbers.
learn more about "Square":-https://brainly.com/question/24487155
#SPJ11
7. Eugene earns $2,700 monthly. He is going to be receiving a 3. 5% raise. With this new roise, he
believes he will earn more than $2,800 a month. Is Eugene correct in his thinking? Why or why
nol? Justifying your reasoning,
Summarize today's lesson:
Car Mr V Model 2017
Answer: Regarding "Car Mr V Model 2017," I'm not sure what you're asking. Can you please provide more context or a clear question?
Step-by-step explanation:
To determine if Eugene's thinking is correct, we need to calculate his new monthly salary with the 3.5% raise.
3.5% of $2,700 is (3.5/100) x $2,700 = $94.50
Eugene's new monthly salary is $2,700 + $94.50 = $2,794.50
So, Eugene's thinking is not correct. His new monthly salary with the 3.5% raise is $2,794.50, which is still less than $2,800.
Today's lesson was not provided in your question. Please provide a topic or question for me to provide a summary of today's lesson.
Regarding "Car Mr V Model 2017," I'm not sure what you're asking. Can you please provide more context or a clear question?
To Know more about Car Mr V Model 2017 refer here
https://brainly.com/question/17549932#
#SPJ11
Line m passes through the points (-4, 3) and (-4, 7). What is the slope of the line that is parallel to line m? Show all of your work for full credit
The slope of desired parallel line is undefined.
How to find slope of a line?Given two points [tex](-4, 3)[/tex] and [tex](-4, 7)[/tex], we can see that both points have the same x-coordinate, which means that they lie on a vertical line parallel to the y-axis. Since the slope of a vertical line parallel to the y-axis is undefined, we can say that the slope of line m is undefined.
To find the slope of a line that is parallel to line m, we can use the fact that parallel lines have the same slope. Since the slope of line m is undefined, any line parallel to it will also have an undefined slope.
Therefore, the slope of the line that is parallel to line m is undefined.
Learn more about slope at:
brainly.com/question/29184253
#SPJ11
Chaz is writing an informal proof to show that circle q is similar to circle p after a similarity transformation followed by a rigid transformation which two translations in sequence should chaz use map circle q onto circle p
Chaz builds a connection between points on circle Q and points on circle P by carrying out these two translations while maintaining the size and shape of the circles.
Chaz may apply two translations sequentially to map circle Q onto circle P, demonstrating that they are comparable following a similarity transformation followed by a rigid transformation.
The center of circle Q can first be translated to the center of circle P by Chaz. The two circles' centers will match thanks to this translation.
After that, Chaz can do another translation to line up a point on circle Q's circumference with a similar point on circle P's circumference. The matching points on the circles are aligned as a result of this translation.
More about the circle link is given below.
https://brainly.com/question/11833983
#SPJ12
What is the missing value of G if G is two and one-half times smaller than 19. 02 cm? A. 7. 608 cm B. 7. 808 cm C. 8. 608 cm D. 9. 51 cm
Therefore, the missing value of G is 7.608 cm, which is option A.
What is the missing value of G?If G is two and one-half times smaller than 19.02 cm, we can find the value of G by multiplying 19.02 cm by 2/5, since two and one-half is equal to five halves, or 2/5 when expressed as a fraction.
G = (2/5) x 19.02 cm
Simplifying this expression:
G = 7.608 cm
Therefore, the missing value of G is 7.608 cm, which is option A.
Learn more about the missing value of G
brainly.com/question/3759414
#SPJ11
solve the triangle.
angle C = 16°
angle c = 32
angle b = 92
Find angle B, a, and A
Answer:
Step-by-step explanation:
To solve the triangle, we can use the law of sines and the fact that the sum of the angles in a triangle is 180 degrees.
First, we can find angle A by using the fact that the sum of the angles in a triangle is 180 degrees:
A = 180 - B - C
A = 180 - 92 - 16
A = 72 degrees
Next, we can use the law of sines to find side a:
a/sin(A) = c/sin(C)
a/sin(72) = 32/sin(16)
a = (32*sin(72))/sin(16)
a ≈ 89.4
Finally, we can use the fact that the sum of the angles in a triangle is 180 degrees to find angle B:
B = 180 - A - C
B = 180 - 72 - 16
B = 92 degrees
Therefore, the triangle has angle B = 92 degrees, angle A = 72 degrees, and side a ≈ 89.4.
For the function M(x) = 2x⁴ - 5x-3, find the value of M"' (2) M(x) = 2x⁴ -5x-3 M''' (2) = M'G)= M''(x)= 2. Find dy/dx for the relation x² = -3x³y⁴- 4y³ 15-3x'y". ty? 3. Find dy/dt for the function y = 3x⁴ - 8x² + 4 Evaluate dy/dt when dx/dt = -2 and x = -10 y = 3x⁴ - 8x²+4
Therefore, the exact values of sin 2u, cos 2u, and tan 2u are -24/25, 7/25, and -24/7, respectively.
The double angle formulas are:
sin 2u = 2 sin u cos u
cos 2u = cos² u - sin² u
tan 2u = 2 tan u / (1 - tan² u)
Given that cos u = -4/5 and u is between -π/2 and π, we can find sin u by using the Pythagorean identity:
sin² u + cos² u = 1
sin u = sqrt(1 - cos² u) = sqrt(1 - 16/25) = 3/5 (since u is in the second quadrant)
Using this value of sin u, we can find:
sin 2u = 2 sin u cos u = 2 (3/5) (-4/5) = -24/25
cos 2u = cos² u - sin² u = (-4/5)² - (3/5)² = 7/25
tan 2u = 2 tan u / (1 - tan² u) = 2 (-3/4) / (1 - (-3/4)²) = -24/7
For more similar questions on topic maximization
https://brainly.com/question/29502088
#SPJ11
For the function, M(x) = 2x⁴ - 5x-3
1. M'''(2) = 96
2. dy/dx = (2x + 9x²y⁴) / (12x³y³ + 12y²)
3. dy/dt = -12,320 when dx/dt = -2 and x = -10
1. To find the value of M'''(2) for the function M(x) = 2x⁴ - 5x - 3, first find the first, second, and third derivatives:
M'(x) = 8x³ - 5
M''(x) = 24x²
M'''(x) = 48x
Now evaluate M'''(2):
M'''(2) = 48(2) = 96
2. To find dy/dx for the relation x² = -3x³y⁴ - 4y³, first implicitly differentiate both sides with respect to x:
2x = -3(3x²y⁴ + x³(4y³dy/dx)) - 4(3y²dy/dx)
Now solve for dy/dx:
dy/dx = (2x + 9x²y⁴) / (12x³y³ + 12y²)
3. To find dy/dt for the function y = 3x⁴ - 8x² + 4, first differentiate with respect to t:
dy/dt = (12x³ - 16x)(dx/dt)
Now evaluate dy/dt when dx/dt = -2 and x = -10:
dy/dt = (12(-10)³ - 16(-10))(-2) = (12,000 + 160)(-2) = -12,320
For more such questions on Function.
https://brainly.com/question/22981287#
#SPJ11
There are 30 chocolates in a box, all identically shaped. There are 5 filled with coconut and 10 filled with caramel. The other 15 are solid chocolate. You randomly select one piece, eat it, and then select a second piece. What is the probability of selecting a caramel chocolate both times? Are the events of selecting a caramel chocolate on your first pick and selecting a caramel chocolate on your second pick indipendent or dependent? Round to three decimal places
The probability of selecting a caramel chocolate both times is approximately 0.103.
The events of selecting a caramel chocolate on each pick are dependent since the probability of the second pick depends on the outcome of the first pick.
First, we need to calculate the probability of selecting a caramel chocolate on the first pick, which is 10/30 or 1/3. After eating the first chocolate, there will be 29 chocolates left in the box, and 9 of them will be caramel-filled. So, the probability of selecting a caramel chocolate on the second pick, given that the first pick was a caramel chocolate and it was eaten, is 9/29.
To find the probability of selecting a caramel chocolate both times, we need to multiply the probabilities of the two events together, since they are independent:
P(caramel and caramel) = P(caramel on first pick) * P(caramel on second pick | first pick was caramel)
= (1/3) * (9/29)
= 0.103 or 0.1034 rounded to four decimal places.
Therefore, the probability of selecting a caramel chocolate both times is approximately 0.103.
The events of selecting a caramel chocolate on the first pick and selecting a caramel chocolate on the second pick are dependent events since the probability of selecting a caramel chocolate on the second pick changes based on what was selected on the first pick.
To know more about probabilities, refer here :
https://brainly.com/question/30034780#
#SPJ11
Consider the construction of a pen to enclose an area. you have 400 ft of fencing to make a pen for hogs. if you have a river on one side of your property, what are the dimensions (in ft) of the rectangular pen that maximize the area? shorter side ft longer side ft
The dimensions of the rectangular pen that maximize the area are a shorter side of 100 ft and a longer side of 200 ft along the river.
To maximize the area of the rectangular pen using 400 ft of fencing, with a river on one side of the property, we need to determine the optimal dimensions. Let's denote the length of the pen along the river as 'x' and the width perpendicular to the river as 'y'.
Since the river is on one side, we only need to use the fencing for the other three sides. The total fencing length is 400 ft, so the equation representing the fencing is:
x + 2y = 400
We need to find the maximum area of the pen, which is given by the product of its length and width, i.e., A = xy.
First, we need to express 'x' in terms of 'y' using the fencing equation. From the equation, we get:
x = 400 - 2y
Now, substitute this expression for 'x' in the area equation:
A(y) = (400 - 2y)y = 400y - 2y²
To find the maximum area, we need to find the critical points of this equation by taking the derivative with respect to 'y' and setting it to zero:
dA/dy = 400 - 4y = 0
Solve for 'y':
4y = 400
y = 100 ft
Now, find 'x' using the expression we derived earlier:
x = 400 - 2y
x = 400 - 2(100)
x = 400 - 200
x = 200 ft
Know more about area here:
https://brainly.com/question/24129362
#SPJ11
81% of the money spent at full-service restaurants in America takes place by debit, credit, or pre-paid cards. One restaurant kept data for the week, and found that 421 of it's 973 customers used either debit, credit, or pre-paid cards to pay for their meal that week. Choose all possible reasons for the discrepancy in the results.
Choices:
1. The theoretocal probability is not calculated correctly
2. The experiment is flawed
3. Enough trials have not been performed to give the desired result.
4. There is no discrepancy in the result
choose all answers that apply.
The discrepancy in the results: The theoretical probability may not be calculated correctly and enough trials have not been performed to give the desired result
In the given scenario, 81% of money spent at full-service restaurants in America is through debit, credit, or pre-paid cards. However, one restaurant found that 421 out of 973 customers used these payment methods. Possible reasons for the discrepancy in the results are:
1. The theoretical probability may not be calculated correctly: The 81% figure might not accurately represent the actual proportion of customers using cards in full-service restaurants. It could be due to incorrect data collection or interpretation.
3. Enough trials have not been performed to give the desired result: The data from one restaurant for one week might not be enough to accurately reflect the overall trend. A larger sample size and longer time frame would give a more accurate representation.
It's important to note that there might not necessarily be a discrepancy in the result; it could be a difference due to variations in individual restaurant data compared to the overall average.
To know more about theoretical probability, refer here:
https://brainly.com/question/24037367#
#SPJ11
Pierce Manufacturing determines that the daily revenue, in dollars, from the sale of x town chairs is R0 -0.0001 +0.042? + Ofe Curare Per vete te lawn chairs daily a) What is the current daily revenue? b) How much would revenue increase ir 3 lawn chairs were sold each day? c) What is the marginal revenue when 50 lawn chairs are sold daily d) Use the answer from part (c) to estimate R(51), R(52) and R153)
The revenue of the chairs sold as per given R(x) = 0.004x³ -0.04x² +0.6x for different conditions are,
The current daily revenue is $2646.
Increase in revenue for 92 chairs sold every day is $185.16
Marginal revenue is $90.6 per lawn chair for 92 chairs sold every day.
Estimated revenue for R(91), R(92) and R(93) is equal to $2555.4 , $2464.8, and $2374.2 respectively.
Daily revenue from sale of x chairs is,
R(x) = 0.004x³ -0.04x² +0.6x
The current daily revenue can be found by evaluating the function at x = 90,
R(90) = 0.004(90)³ - 0.04(90)² + 0.6(90)
= 2916 - 324 + 54
= $2646
Increase in revenue,
⇒ difference between the revenue from selling 92 lawn chairs and the revenue from selling 90 lawn chairs,
R(92) - R(90)
= [0.004(92)³ - 0.04(92)² + 0.6(92)] - [0.004(90)³ - 0.04(90)² + 0.6(90)]
= 3114.752 -338.56 + 55.2 - 2646
= 2831.16 - 2646
= $185.16
Revenue would increase by$185.16 if 92 lawn chairs were sold each day.
The marginal revenue is the derivative of the revenue function,
R'(x) = 0.012x² - 0.08x + 0.6
Marginal revenue when 90 lawn chairs are sold daily,
we can evaluate the derivative at x = 90,
R'(90) = 0.012(90)² - 0.08(90) + 0.6
= $90.6
When 90 lawn chairs are sold daily, the marginal revenue is $90.6 per lawn chair.
Use the answer from above part to estimate the revenue from selling 91, 92, and 93 lawn chairs daily.
Assume that the marginal revenue is approximately constant in a small interval around 90,
Use the linear approximation,
R(91) ≈ R(90) + R'(90)(1)
= $2646 + $90.6
= $2555.4
R(92) ≈ R(90) + R'(90)(2)
= $2646 + 2($90.6)
= $2464.8
R(93) ≈ R(90) + R'(90)(3)
= $2646 + 3($90.6)
= $2374.2
If 91, 92, and 93 lawn chairs were sold daily,
The estimated daily revenue would be $2555.4 , $2464.8, and $2374.2 respectively.
Learn more about revenue here
brainly.com/question/31399976
#SPJ4
The above question is incomplete, I answer the question in general according to my knowledge:
Pierce Manufacturing determines that the daily revenue, in dollars, from the sale of x town chairs is
R(x) = 0.004x³ -0.04x² +0.6x .
Currently, Pierce sells 90 lawn chairs daily.
a) What is the current daily revenue?
b) How much would revenue increase if 92 lawn chairs were sold each day?
c) What is the marginal revenue when 90 lawn chairs are sold daily
d) Use the answer from part (c) to estimate R(91), R(92) and R(93)
Which of the following tables represent a proportional relationship?
verbal:
a. y/x= 40/1 76/2 112/3 148/4
b. y/x= 48/2 96/3 144/4 192/5
c. y/x= 18/1 54/3 90/5 126/7
d. 24/1 21/2 18/3 15/4
picture:
a. y/x = 40/1, 76/2, 112/3, 148/4 does not represent a proportional relationship. . y/x = 48/2, 96/3, 144/4, 192/5 does not represent a proportional relationship. c. y/x = 18/1, 54/3, 90/5, 126/7 represents a proportional relationship.
How to determine a proportional relationshipA proportional relationship means that the ratio of y to x is constant throughout the table. Let's check each table:
a. y/x = 40/1, 76/2, 112/3, 148/4
If we simplify the fractions, we get y/x = 40, 38, 37.33, 37. This is not a constant ratio, so this table does not represent a proportional relationship.
b. y/x = 48/2, 96/3, 144/4, 192/5
If we simplify the fractions, we get y/x = 24, 32, 36, 38.4. This is not a constant ratio, so this table does not represent a proportional relationship.
c. y/x = 18/1, 54/3, 90/5, 126/7
If we simplify the fractions, we get y/x = 18, 18, 18, 18. This is a constant ratio, so this table represents a proportional relationship.
d. y/x = 24/1, 21/2, 18/3, 15/4
If we simplify the fractions, we get y/x = 24, 10.5, 6, 3.75. This is not a constant ratio, so this table does not represent a proportional relationship.
Therefore, the table that represents a proportional relationship is c. y/x = 18/1, 54/3, 90/5, 126/7.
Learn more about proportional relationship at https://brainly.com/question/12242745
#SPJ1
Which function is increasing and has a domain of (1,infiniti)?
A. F(x) = log(x - 1) + 2
B. F(x) = -log(x - 2) + 1
C. F(x) = -log(x - 1) + 2
D. F(x) = log(x - 2) + 1
The function that is increasing and has a domain of (1, infinity) is A. F(x) = log(x - 1) + 2.
To determine the increasing function with the specified domain, let's analyze each option:
A. F(x) = log(x - 1) + 2
This function is increasing because the logarithm of a positive number is always increasing. The domain is (1, infinity), which matches the requirement.
B. F(x) = -log(x - 2) + 1
This function is decreasing because the negative sign in front of the logarithm inverts the increase. The domain is (2, infinity), which does not match the requirement.
C. F(x) = -log(x - 1) + 2
This function is also decreasing because of the negative sign in front of the logarithm. The domain is (1, infinity), which matches the requirement, but the function is not increasing.
D. F(x) = log(x - 2) + 1
This function is increasing because the logarithm of a positive number is always increasing. However, the domain is (2, infinity), which does not match the requirement.
The function that is increasing and has a domain of (1, infinity) is A. F(x) = log(x - 1) + 2.
Learn more about "function": https://brainly.com/question/2328150
#SPJ11