The solution to the problems are given below:
n + e = 14 + 5 = 19t - j = 20 - 10 = 10d x e = 4 x 5 = 20p / b = 16 / 2 = 8How to solveGiving each of the letters numbers based on their numerical position on the English alphabet, we can solve below:
n (14) + e (5) = 14 + 5 = 19
t (20) - j (10) = 20 - 10 = 10
d (4) x e (5) = 4 x 5 = 20
p (16) / b (2) = 16 / 2 = 8
It can be seen that with the letter e for example is the 5th letter of the alphabet and the value is used to compute the addition of the problem.
Read more about addition here:
https://brainly.com/question/778086
#SPJ1
I NEED HELP PLEASE!
1. 3 statements about limiting frictional force between two surfaces are given below.
A - Nature of surfaces in contact affects to limiting frictional force.
B - Normal reaction between them affects to limiting frictional force.
C - Area of surfaces in contact affects to limiting frictional force.
Correct statement / statements from above A, B, C is/ are,
(1) A
(2) B
(3) A and C
(4) A, B and C
The limiting frictional force depends only on:
A. The nature of surfaces in contact: Rough and irregular surfaces have higher friction than smooth surfaces. C. The area of surfaces in contact: Larger the contact area, higher is the friction between the surfaces.(3) A and C is the right optionHooke's Law says that the force exerted by the spring in a spring scale varies directly with the distance that the spring is stretched. If a 39 pound mass suspended on a spring scale stretches the spring 10 inches, how far will a 48 pound mass stretch the spring? Round your answer to one decimal place if necessary
48 pound mass will stretch the spring approximately 12.31 inches.
To solve this problemIf the spring's force is directly proportional to how far it is stretched, we can express this relationship mathematically as follows:
F = kx
Where
F is the force exerted by the springx is the distance that the spring is stretchedk is the proportionality constantWe can use the first value of the spring scale to determine k:
39 = k(10)
k = 3.9
Now, using this value of k, we can calculate how far the spring is stretched when a 48-pound mass is applied:
F = kx
48 = 3.9x
x = 48/3.9
x = 12.31
Therefore, a 48 pound mass will stretch the spring approximately 12.31 inches.
Learn more about Hooke's Law here : brainly.com/question/14477435
#SPJ4
The volume of a cylinder is 336m3 . what is the volume of a cone with the same radius and height?
12. Julie is buying a house for $225,000. She obtains a mortgage in the amount of $156,000 at a
4. 5% fixed rate. The bank offers a 4. 25% interest rate if julie pays 2. 25 points. What is the cost
of points for this mortgage rounded to the nearest dollar?
$3,510
$5,063
$6,630
$7,020
The cost of points for this mortgage is $3,510 rounded to the nearest dollar if Julie pays 2.25 points.
Cost of house = $225,000.
Mortgage amount = $156,000
Fixed-rate = 4.5%
Bank offer rate = 4.25%
Points to pay = 2.25 points
If we assume that one point is equal to 1%, then 2.25 points are equal to 2.25% of the loan amount.
The cost of points for the mortgage can be calculated by the product of the loan amount by 2.25%.
Cost of points = 0.0225 × $156,000
Cost of points = $3,510
Therefore, we can conclude that the cost of points for this mortgage is $3,510 rounded to the nearest dollar.
To learn more about Mortgage Loan
https://brainly.com/question/28772433
#SPJ4
Find the following integral results a. So to dz b. C2+ IT x'sir. 'o 1+cos? dx A solid is obtained by rotating the shaded region about the specified line such as the x-axis or the y-axis. Find the volume of the solid
V = ∫2πx f(y) dy volume of the solid
a. The integral of dz is simply z + C, where C is the constant of integration. So the result of integrating dz is:
∫ dz = z + C
b. To find the integral of (C^2 + I∫sin(x))/(1+cos(x)) dx, we can use the substitution u = 1 + cos(x), du/dx = -sin(x), and dx = du/(-sin(x)). Then we have:
∫(C^2 + I∫sin(x))/(1+cos(x)) dx = ∫(C^2 + I∫sin(x))/u (-du/sin(x))
= -I∫(C^2 + I∫sin(x))/u du
= -I(C^2ln|u| + I∫ln|u| sin(x) dx) + C'
= -I(C^2ln|1+cos(x)| - I∫ln|1+cos(x)| sin(x) dx) + C'
where C' is the constant of integration.
c. To find the volume of the solid obtained by rotating the shaded region about the x-axis or the y-axis, we need to use the method of cylindrical shells or disks, respectively.
If we rotate the region about the x-axis, we can use the formula:
V = ∫2πy f(x) dx
where f(x) is the distance from the x-axis to the function y(x) that defines the region. If we have a function y(x) = g(x) - h(x) that defines the region between two curves, then f(x) = g(x) - h(x) and the limits of integration are the x-values where the two curves intersect.
If we rotate the region about the y-axis, we can use the formula:
V = ∫2πx f(y) dy
where f(y) is the distance from the y-axis to the function x(y) that defines the region. If we have a function x(y) = g(y) - h(y) that defines the region between two curves, then f(y) = g(y) - h(y) and the limits of integration are the y-values where the two curves intersect.
To learn more about function click here
brainly.com/question/12431044
#SPJ11
Dinah is driving on the highway. She must drive at a speed of at least
60 miles per hour and at most70 miles per hour. Based on this information, what is a possible amount of time, in hours, that it could take Dinah to drive 420 miles?
The possible amount of time for Dinah to drive 420 miles on the highway is between 6 & 7 hours.
What time can Dinah use to drive 420 miles?To get the possible time, we need to consider the range of speeds she can drive at.
Because she must drive at least 60 miles per hour and at most 70 miles per hour, we can calculate the possible time ranges using "Time = Distance / Speed"
At 60 miles per hour:
= 420 miles / 60 miles per hour
= 7 hours
At 70 miles per hour:
= 420 miles / 70 miles per hour
= 6 hours.
Read more about time
brainly.com/question/26046491
#SPJ1
not all summer blockbusters are cinematic breakthroughs. subject term: summer blockbusters predicate term: cinematic breakthroughs which of the following statements is true of this categorical proposition? it is a standard-form categorical proposition because it is a substitution instance of this form: some s are not p. it is a standard-form categorical proposition because it is a substitution instance of this form: no s are p. it is a standard-form categorical proposition because it is a substitution instance of this form: some s are p. it is a standard-form categorical proposition because it is a substitution instance of this form: all s are p. it is not a standard-form categorical proposition.
The statements is true of this categorical proposition is: It is a standard-form categorical proposition because it is a substitution instance of this form: some s are not p option A.
A proposition or statement that is categorically affirmed or denied of all or part of the topic is known as a categorical proposition in syllogistic or classical logic. Hence, there are four fundamental types of categorical propositions: "Every S is P," "No S is P," "Some S is P," and "Some S is not P."
Every man is mortal, for instance, is an A-proposition since these forms are denoted by the letters A, E, I, and O, respectively. In particular, being declarations of reality rather than logical connections, they contrast significantly with hypothetical propositions, such as "If every man is mortal, then Socrates is mortal," which categorical propositions are to be differentiated from and enter into as integral words.
Learn more about categorical proposition:
https://brainly.com/question/30874385
#SPJ4
Various doses of an experimental drug, in milligrams, were injected into a patient. The patient's
change in blood pressure, in millimeters of mercury, was recorded in the table below.
40 50
Dose (mg)
Change in Blood Pressure
(mmHg)
10
2
20
9
30
12
14 16
Use the model to find the expected change in blood pressure for a 100 mg dose.
10
Using the linear model, we can predict that a 100 mg dose of the experimental drug would cause a change in the patient's blood pressure of 540 mmHg.
What is equation?An equation is a mathematical statement that expresses the equality of two expressions. It consists of two expressions, one on the left side and one on the right side, which are connected by an equals sign (=). Equations are fundamental to mathematics, and are used to solve many problems. In addition, equations can also be used to describe physical laws, such as Newton's law of gravity.
10 + 2(20) + 3(30) + 4(100)
= 10 + 40 + 90 + 400
= 540 mmHg
The linear model suggests that a 100 mg dose of the experimental drug would cause a change in the patient's blood pressure of 540 mmHg. This can be seen by using the linear equation 10 + 2x + 3x + 4x. Here, the first coefficient of 10 represents the change in blood pressure for a 10 mg dose, the second coefficient of 2 represents the change in blood pressure for each additional 10 mg dose, the third coefficient of 3 represents the change in blood pressure for each additional 20 mg dose, and the fourth coefficient of 4 represents the change in blood pressure for each additional 30 mg dose.
For example, if the patient was given a 40 mg dose, the equation would be 10 + 2(20) + 3(30), which would yield a change in blood pressure of 140 mmHg. Similarly, if the patient was given a 50 mg dose, the equation would be 10 + 2(20) + 3(30) + 4(10), which would yield a change in blood pressure of 190 mmHg.
Therefore, using the linear model, we can predict that a 100 mg dose of the experimental drug would cause a change in the patient's blood pressure of 540 mmHg.
To know more about equation click-
http://brainly.com/question/2972832
#SPJ1
The linear model predicts that a 100 mg dose of the investigational drug will raise the patient's heart rate by 540 mmHg.
What is equation?A mathematical statement that expresses the equality of two expressions is known as an equation. It comprises of two expressions that are joined together by the equals sign (=), one on the left side and one on the right. Equations are essential to mathematics and are frequently used to resolve issues. Moreover, equations can be utilised to explain natural laws like Newton's law of gravity.
10 + 2(20) + 3(30) + 4(100)
= 10 + 40 + 90 + 400
= 540 mmHg
The linear model predicts that a 100 mg dose of the investigational drug will raise the patient's heart rate by 540 mmHg.
Using the linear equation 10 + 2x + 3x + 4x, this may be observed. In this case, the first coefficient of 10 denotes the change in blood pressure for a dose of 10 mg, the second coefficient of 2, the change for each additional dose of 10 mg, the third coefficient of 3, the change for each additional dose of 20 mg, and the fourth coefficient, the change for each additional dose of 30 mg.
For instance, if the patient received a dose of 40 mg, the equation would be 10 + 2(20) + 3(30), resulting in a 140 mmHg change in blood pressure. The calculation would be 10 + 2(20) + 3(30) + 4(10) if the patient received a 50 mg dose, which would result in a 190 mmHg change in blood pressure.
As a result, we can infer from the linear model that a 100 mg dose of the experimental medication would result in a 540 mmHg change in the patient's blood pressure.
To know more about equation, click-
brainly.com/question/2972832
#SPJ9
The spinner has 8 congurent sections it is spun 24 times what is a reasonable prediction for the number of times the spinner will land on the number 3.
A reasonable prediction for the number of times the spinner will land on the number 3 is 3 times.
Since the spinner has 8 congruent sections and is spun 24 times, we can use probability to make a reasonable prediction for the number of times it will land on the number 3.
1. Calculate the probability of landing on the number 3 for a single spin:
Since there are 8 congruent sections, the probability of landing on the number 3 is 1/8.
2. Determine the expected number of times the spinner will land on the number 3:
To do this, multiply the probability of landing on the number 3 (1/8) by the total number of spins (24).
Expected number of times = (1/8) * 24
3. Simplify the expression:
Expected number of times = 3
So, a reasonable prediction for the number of times the spinner will land on the number 3 is 3 times.
Learn more about probability,
https://brainly.com/question/24756209
#SPJ11
A group of friends wants to go to the amusement park. They have $100. 25 to spend
on parking and admission. Parking is $17. 75, and tickets cost $13. 75 per person,
including tax. Which equation could be used to determine p, the number of people
who can go to the amusement park?
100. 25 = 13. 75p + 17. 75
Op=
100. 25-13. 75
17. 75
Submit Answer
13. 75(p+17. 75) = 100. 25
O p =
17. 75-100. 25
13. 75
The correct equation to determine the number of people (p) who can go to the amusement park is: 100.25 = 13.75p + 17.75.
Here's the step-by-step explanation:
1. The total amount they have to spend is $100.25.
2. The cost of parking is $17.75, which is a one-time expense.
3. The cost of admission per person is $13.75.
To find out how many people can go, you need to account for both the parking cost and the cost of tickets for each person. Therefore, the equation is:
100.25 (total amount) = 13.75p (cost per person times the number of people) + 17.75 (cost of parking)
To learn more about Equations
https://brainly.com/question/29174899
#SPJ11
Suppose 45% of all students at aiden's school brought a can of food to contribute to a canned food drive. aiden picks a representative sample of 25 students and determines the samples percentage he expects the percentage for this sample will be 45% do you agree? explain your reasoning
A z-score of 0 means that the sample proportion is equal to the population proportion. Therefore, after using sampling distribution we can conclude that we agree with Aiden's expectation that the percentage for this sample will be 45%.
Based on the given information, we can assume that the population proportion of students who brought a can of food to contribute to the canned food drive is 0.45. Aiden picks a representative sample of 25 students, and he expects the percentage for this sample will be 45%.
We can use the sampling distribution formula to calculate the expected sample proportion:
SE = sqrt[p(1-p) / n]
where p is the population proportion, n is the sample size, and SE is the standard error.
Plugging in the values, we get:
SE = sqrt[0.45(1-0.45) / 25] = 0.0984
Next, we can use the normal distribution to find the z-score corresponding to a sample proportion of 0.45:
z = (0.45 - 0.45) / 0.0984 = 0
A z-score of 0 means that the sample proportion is equal to the population proportion. Therefore, we can conclude that we agree with Aiden's expectation that the percentage for this sample will be 45%.
To know more about sampling distribution, visit:
https://brainly.com/question/29375938#
#SPJ11
A set of data is represented in the stem plot below.
Key: 315= 35
Part A: Find the mean of the data. Show each step of work. (2 points)
Part B: Find the median of the data. Explain how you determined the median. (2 points)
Part C: Find the mode of the data. Explain how you determined the mode. (2 points)
Part A: The mean of the data is approximately 5.79. Part B: The median is 6.5. Part C: The mode of the data is the set of values {5, 9}.
Describe Mean?In statistics, mean is a measure of central tendency that represents the average of a set of numbers. The mean is calculated by adding up all the values in a data set and dividing by the total number of values.
The formula for calculating the mean of a set of n numbers is:
mean = (x1 + x2 + ... + xn) / n
where x1, x2, ..., xn are the individual values in the data set.
Part A:
To find the mean of the data, we need to add up all the values and divide by the total number of values:
3 + 4 + 4 + 5 + 5 + 5 + 6 + 7 + 7 + 8 + 8 + 9 + 9 + 9 = 81
There are 14 values in the data set, so we divide the sum by 14 to get:
81/14 ≈ 5.79
Therefore, the mean of the data is approximately 5.79.
Part B:
To find the median of the data, we need to arrange the values in order from lowest to highest:
3, 4, 4, 5, 5, 5, 6, 7, 7, 8, 8, 9, 9, 9
There are 14 values, so the median is the middle value. Since there is an even number of values, we need to find the average of the two middle values, which are 6 and 7. Thus, the median is:
(6 + 7)/2 = 6.5
Therefore, the median of the data is 6.5.
Part C:
To find the mode of the data, we need to look for the value(s) that occur most frequently. From the stem plot, we can see that the values 5 and 9 occur three times each, while all other values occur either once or twice. Therefore, the mode of the data is:
5 and 9
Thus, the mode of the data is the set of values {5, 9}.
To know more about mode visit:
https://brainly.com/question/27827306
#SPJ1
help pls rlly fast i will give good points
Answer: less than
Step-by-step explanation:
find an expression which represents the difference when
(7x−10) is subtracted from (−5x+6) in simplest terms.
Answer: -12x + 16
Step-by-step explanation:
To find the difference between (−5x+6) and (7x−10), we need to subtract the second expression from the first. So we have:
(−5x+6) - (7x−10)
To subtract the second expression, we can distribute the negative sign to all the terms inside the parentheses:
-5x + 6 - 7x + 10
Then we can combine the like terms:
-12x + 16
Therefore, the difference between (−5x+6) and (7x−10) is -12x + 16.
A tailor charges set amounts for alterations on dresses and suits.
One customer has
2
dresses and
1
suit altered for a total of
$
80
.
Another customer has
1
dress and
3
suits altered for a total of
$
115
The cost to alter each dress is $25 and each suit is $30 based on the given set of relations.
Let us represent the dresses as x and suit as y. Forming the equation for both customers.
Cost of one dress × number of dress +
Cost of one suit × number of suit = total cost
2x + y = 80 : equation 1
x + 3y = 115 : equation 2
Multiply equation with 1
6x + 3y = 240 : equation 3
Subtract equation 2 from equation 3
6x + 3y = 240
- x + 3y = 115
5x = 125
x = 125/5
x = $25
Keep the value of x in equation 2 to find the value of y
25 + 3y = 115
3y = 115 - 25
3y = 90
y = 90/3
y = $30
Hence, the altering cost of each is $25 and $30.
Learn more about equation -
https://brainly.com/question/2972832
#SPJ4
The complete question is -
A tailor charges set amounts for alterations on dresses and suits. One customer has 2 dresses and 1 suit altered for a total of $80. Another customer has 1 dress and 3 suits altered for a total of $115. How much does it cost to alter each dress?
Find the slope of the line represented by the data below
Answer:
m = -3
Step-by-step explanation:
We Know
Slope = rise/run or (y2 - y1) / (x2 - x1)
Pick 2 points (0,15) (2,9)
We see the y decrease by 6, and the x increase by 2, so the slope is
m = -6/2 = -3
So, the slope of the line representing the data is -3.
Determine the product of 23.5 and 2.3
Answer:
Therefore, the product of 23.5 and 2.3 is 54.05.
Step-by-step explanation:
To determine the product of 23.5 and 2.3, we can use the following steps:
Align the numbers vertically with the ones digit of the second factor (2.3) under the tenths digit of the first factor (3 in 23.5).
23.5
x 2.3
-----
Multiply the ones digit of the second factor by the first factor and write the result below, shifted one place to the right.
23.5
x 2.3
-----
71
Multiply the tenths digit of the second factor by the first factor and write the result below, shifted two places to the right.
23.5
x 2.3
-----
71
470
Add the two partial products together.
23.5
x 2.3
-----
71
470
-----
54.05
Therefore, the product of 23.5 and 2.3 is 54.05.
Please help and solve this! Have a blessed day!
Answer: 8
Step-by-step explanation:
CF looks like the radius of the circle.
ED looks like the diameter.
.: ED = 2 x CF = 2 x 4 = 8
.: ED = 8
Answer:
The length of ED, or the diameter, is 8
Step-by-step explanation:
As the other person explained, CF is the radius, as the radius is from the centermost point to the edge. I also see that ED is the diameter, as the diameter is from edge to edge, going through the centermost point. Therefore, since the diameter is double the radius, we can solve this with the following equation:
2 * r = d, where r is radius and d is diameter.
2 * 4 = d
8 = d
Let X be the number of screws delivered to a box by an automatic filling device.
Assume = 1000 and
2 = 25. There are problems with too many screws going
into the box or too few screws going into the box.
a. How many units to the right of is 1009? (5 marks)
b. What X value is 2. 6 units to the left of ? (4 marks
There are approximately 0.1480 standard deviations (or 3.7 screws) to the right of the mean when there are 1009 screws in the box. When the automatic filling device delivers 1065 screws to the box, there are approximately 2.6 standard deviations (or 65 screws) to the left of the mean.
To answer this question, we need to use the normal distribution formula.
a. To find how many units to the right of 1000 is 1009, we need to calculate the z-score:
z = (X - μ) / σ
where X = 1009, μ = 1000, and σ = 25.
z = (1009 - 1000) / 25 = 0.36
Using a standard normal distribution table or calculator, we can find that the probability of getting a z-score of 0.36 or higher is 0.3520.
To convert this probability to units to the right of the mean, we subtract it from 0.5 (which represents the area to the left of the mean):
units to the right = 0.5 - 0.3520 = 0.1480
Therefore, there are approximately 0.1480 standard deviations (or 3.7 screws) to the right of the mean when there are 1009 screws in the box.
b. To find the X value that is 2.6 units to the left of the mean, we can rearrange the formula:
X = μ - zσ
where z = -2.6 (since we want units to the left of the mean) and μ and σ are the same as before.
X = 1000 - (-2.6) * 25 = 1065
Therefore, when the automatic filling device delivers 1065 screws to the box, there are approximately 2.6 standard deviations (or 65 screws) to the left of the mean.
To know more about standard deviations refer here:
https://brainly.com/question/23907081
#SPJ11
BRAIN-COMPATIBLE
Directions: Arrange the sentences in the box to form a problem. Then solve each problem.
Write your answer in your activity notebook.
1. If she leaves home at 6:00 in the morning
What time will she arrive?
Zaira goes to her grandmother's house
She cycles 30 km at a steady speed of 10 km
Problem
Solution
2. I had an average speed of 55 kph for 2 hours in the afternoon
What was the total distance covered by the bus
A bus had an average speed of 65 kph for 1. 5 hours in the morning.
Problem:
Solution:
3 What was the average speed of the train?
The distance between the two stations is 14 km
A train left Station X at 9:00 a. M. And arrived station Y ay 9:30 a. M.
The correct arrangement of problem is explained below and their solution are as follows:
(1) Zaira will arrive at her grandmother's house at 9:00 am.
(2) The total distance covered by bus is 207.5 km.
(3) The average-speed of the train was 28 km/h.
Part (1) : The Problem is : Zaira goes to her grandmother's house. If she leaves home at 6:00 in the morning, she cycles 30 km at a steady speed of 10 km. What time will she arrive?
Solution:
Zaira cycles at a steady speed of 10 km, she will cover the distance of 30 km in 30/10 = 3 hours.
So, she will arrive at her grandmother's house at 6:00 + 3:00 = 9:00 am.
Part (2) : Problem : A bus had an average speed of 65 kph for 1.5 hours in the morning. It had average speed of 55 kph for 2 hours in afternoon. What was total distance covered by bus?
Solution:
The distance covered by the bus in the morning can be calculated as:
Distance = Speed × Time = 65 kph × 1.5 hours = 97.5 km,
The distance covered in the afternoon can be calculated as:
Distance = Speed × Time = 55 kph × 2 hours = 110 km
So, total-distance covered by bus is = 97.5 km + 110 km = 207.5 km.
Part (3) : Problem : A train left Station X at 9:00 a.m. and arrived station Y at 9:30 a.m. The distance between the two stations is 14 km. What was average speed of train?
Solution:
The time taken by the train to cover the distance of 14 km can be calculated as:
Time = Arrival Time - Departure Time = 9:30 am - 9:00 am = 0.5 hours
The average speed of the train = Distance/Time = 14 km/0.5 hours = 28 km/h;
Therefore, the average speed of the train was 28 km/h.
Learn more about Speed here
https://brainly.com/question/25422377
#SPJ4
The given question is incomplete, the complete question is
Directions: Arrange the sentences in the box to form a problem. Then solve each problem.
(1) If she leaves home at 6:00 in the morning
What time will she arrive?
Zaira goes to her grandmother's house
She cycles 30 km at a steady speed of 10 km
(2) I had an average speed of 55 kph for 2 hours in the afternoon
What was the total distance covered by the bus
A bus had an average speed of 65 kph for 1. 5 hours in the morning.
(3) What was the average speed of the train?
The distance between the two stations is 14 km
A train left Station X at 9:00 a.m. and arrived station Y at 9:30 a.m.
Find the derivative of the given function.
y= (4x² – 9x) e⁻⁴
ˣy' = ... (Type an exact answer.)
The derivative of the given function is:
y' = (8x – 9) e⁻⁴ - 16x (4x - 9) e⁻⁴
Find the derivative?
To find the derivative of the given function y= (4x² – 9x) e⁻⁴, we need to use the product rule of differentiation. The formula for the product rule is:
(fg)' = f'g + fg'
Where f and g are two differentiable functions. Applying this formula, we get:
y' = (4x² – 9x)' e⁻⁴ + (4x² – 9x) (e⁻⁴)'
The first term on the right-hand side can be simplified using the power rule and the constant multiple rule of differentiation:
(4x² – 9x)' = 8x – 9
The second term on the right-hand side requires the chain rule of differentiation. Let u = -4x, then we have:
(e⁻⁴)' = (e^u)' = e^u (-4) = -4e⁻⁴x
Substituting these results back into the expression for y', we get:
y' = (8x – 9) e⁻⁴ + (4x² – 9x) (-4e⁻⁴x)
Simplifying this expression, we get:
y' = (8x – 9) e⁻⁴ - 16x (4x - 9) e⁻⁴
Therefore, the derivative of the given function is:
y' = (8x – 9) e⁻⁴ - 16x (4x - 9) e⁻⁴
Learn more about chain rule of differentiation.
brainly.com/question/27072366
#SPJ11
The area of a rectangle is 72.8cm? if one side of the length is 6.52cm. find the length of the other two to two decimal places
Answer:
11.17, my answer needs to be 20+ characters soooooooo
25) When (x + 1)2 is divided by x - 2, the quotient is 16 and the remainder is x - 3. Find the possible values of x.
Answer:
x = 3 or x = 12
Step-by-step explanation:
You want the possible values of x that make it true that ...
(x +1)²/(x -2) = 16 +(x -3)/(x -2)
Division expressionThe given division expression can be written in terms of quotient and remainder as ...
p/q = a +r/q ⇒ p = aq +r
ApplicationHere, this means ...
(x +1)² = 16(x -2) +(x -3)
x² +2x +1 = 16x -32 +x -3
x² -15x = -36
x² -15x +56.25 = 20.25 . . . . . complete the square
(x -7.5)² = 4.5²
x = 7.5 ± 4.5 . . . . . . . . . . . . . take the square root, add 7.5
x = 3 or 12
__
Additional comment
The given quotient-remainder equation has a vertical asymptote at x = 2. When we write it as f(x) = 0, the graph of f(x) is symmetrical about the point (2, -11).
Find the area of the following shape. You must show all work to recive credit.
this is a writting question
The total area of the given figure is 12 units²
In the given figure, we have 3 shapes. One is rectangle and the other two are triangles. We can find areas of all three shapes and add to find the total area.
Finding area of the triangle ABC,
base of the triangle ABC = 4 units
height of the triangle ABC = 4 units
Area of the triangle ABC = 1/2 x base x height = 1/2 x 4 x 4 = 8 units²
Finding area of the triangle CDE,
base of the triangle CDE = 2 units
height of the triangle CDE = 2 units
Area of the triangle CDE = 1/2 x base x height = 1/2 x 2 x 2 = 2 units²
Finding area of the rectangle,
length of the rectangle = 2 units
breadth of the rectangle = 1 unit
Area of the rectangle = length x breadth = 2 x 1 = 2 units²
So, total area of the given figure = 8 units² + 2 units² + 2 units² = 12 units²
To know more about area,
https://brainly.com/question/21735282
#SPJ1
Allison is cleaning the windows on her house. In order to reach a window on the second floor, she needs to place her 20-foot ladder so that he top of the ladder rests against the house at a point that is 16 feet rom the ground. How far from the house should she place the base of her ladder?
The base of her ladder should be 12 feet from the house.
Pythagorean theorem.A Pythagorean theorem is a useful theorem which can be applied so as to determine the length of the missing side of a right angled triangle. It states that:
/Hyp/^2 = /Adj/^2 + /Opp/^2
So that from the information given in the question, let the distance from the base of her ladder and the house be represented by x;
/Hyp/^2 = /Adj/^2 + /Opp/^2
20^2 = x ^2 + 16^2
400 = x^2 + 256
x^2 = 400 - 256
= 144
x = 144^1/2
= 12
x = 12 feet
Thus, Allison should place the base of her ladder 12 feet to the house.
Learn more about Pythagorean theorem at https://brainly.com/question/15249087
#SPJ1
Suppose the horses in a large stable have a mean weight of 807lbs, and a variance of 5776. what is the probability that the mean weight of the sample of horses would differ from the population mean by greater than 18lbs if 41 horses are sampled at random from the stable?
The probability that the mean weight of the sample of horses would differ from the population mean by greater than 18lbs if 41 horses are sampled at random from the large stable is approximately 0.131 or 13.1%.
Suppose the horses in a large stable have a mean weight of 807lbs and a variance of 5776. We want to find the probability that the mean weight of a sample of 41 horses would differ from the population mean by greater than 18lbs.
Step 1: Calculate the standard deviation of the population.
Standard deviation (σ) = √variance = √5776 = 76lbs.
Step 2: Calculate the standard error of the mean.
Standard error (SE) = σ / √n = 76 / √41 ≈ 11.88lbs, where n is the sample size (41 horses).
Step 3: Calculate the z-score for the difference of 18lbs.
z = (difference - 0) / SE = (18 - 0) / 11.88 ≈ 1.51
Step 4: Find the probability corresponding to the z-score.
Using a z-table, we find that the probability corresponding to a z-score of 1.51 is approximately 0.9345.
Step 5: Calculate the probability of the mean weight differing by more than 18lbs.
Since we are looking for the probability of the mean weight differing by more than 18lbs (in either direction), we need to consider both tails of the distribution.
P(z > 1.51) = 1 - 0.9345 = 0.0655
P(z < -1.51) = 0.0655 (since the distribution is symmetric)
Total probability = P(z > 1.51) + P(z < -1.51) = 0.0655 + 0.0655 = 0.1310
So, the probability that the mean weight of the sample of horses would differ from the population mean by greater than 18lbs if 41 horses are sampled at random from the large stable is approximately 0.131 or 13.1%.
To know more about probability, visit:
https://brainly.com/question/30034780#
#SPJ11
Here is another one sorry there will be a lot
Answer:
2 7/24 gallons
(sorry if its wrong)
Show that the two straight lines through the origin which make an angle 45° with the line px + qy + r = 0 are given by the equation (p²-q)(x² - y²) + 4pqxy = 0.
The equation of the two straight lines through the origin making an angle of 45° with the line px + qy + r = 0 is (p²-q)(x² - y²) + 4pqxy = 0.
How to show the equation for the two straight lines passing through the origin and making a 45° angle with the line px + qy + r = 0?To prove that the equation of the two straight lines through the origin, making an angle of 45° with the line px + qy + r = 0, is given by (p²-q)(x² - y²) + 4pqxy = 0, we can use the concept of slopes and trigonometric identities.
Let's consider the line px + qy + r = 0. The slope of this line is given by -p/q.
Now, the lines making an angle of 45° with this line will have slopes equal to tan(45°), which is 1.
Using the formula for the tangent of the sum of angles, we have:
tan(45°) = (m - (-p/q))/(1 + m(-p/q)), where m represents the slope of one of the lines.
Simplifying the equation, we get:
1 = (mq + p)/(q - mp)
Cross-multiplying and rearranging the terms, we obtain:
(p² - q)(m² - 1) + 2pqm = 0
Since these lines pass through the origin (0,0), we can replace m with y/x. Substituting y/x for m in the equation above, we get:
(p² - q)(x² - y²) + 2pqxy = 0
Further simplifying the equation, we arrive at:
(p² - q)(x² - y²) + 4pqxy = 0
Hence, we have proven that the equation of the two straight lines through the origin, making an angle of 45° with the line px + qy + r = 0, is given by (p²-q)(x² - y²) + 4pqxy = 0.
Learn more about origin
brainly.com/question/28490920
#SPJ11
A cuboid is placed on top of a cube, as shown in the diagram, to form a solid.
2 cm
3 cm
The cube has edges of length 7 cm.
The cuboid has dimensions 2 cm by 3 cm by 5 cm.
Work out the total surface area of the solid.
Optional working
Ansv
cm²
+
5 cm
7 cm
Answer: 344cm²
Step-by-step explanation:
7x7=49
49x5=245
3x2=6
49-6=43
245+43=288
5x2=10 10x2=20
5x3=15 15x2=30
288+30+20+6=344
Can you explain to me how to solve this?????
√19x^5
The final step when solving the given math problem is:
Take the fifth root of both sides: x = [tex]((y^2)/19)^(^1^/^5)[/tex]
How to solveTo solve √19x^5 for x, follow these steps:
Isolate the square root term: [tex]\sqrt{19x^5}[/tex] = y (Let y be the other side of the equation)
Square both sides: [tex](y^2) = 19x^5[/tex]
Divide both sides by 19: [tex](y^2)/19 = x^5[/tex]
Take the fifth root of both sides: x = [tex]((y^2)/19)^(^1^/^5^)[/tex]
The square root of a number is a value that, when multiplied by itself, gives the original number. It is denoted by the symbol √ and can be found using mathematical operations.
Read more about square roots here:
https://brainly.com/question/428672
#SPJ1