A rational function having the following vertical asymptotes x = -4 and x = 5 and x-intercept (-2, 0) is [tex]f(x) = \frac{x+2}{(x+4)(x-5)}[/tex].
A rational function is a function that can be expressed as the quotient of two polynomials. Vertical asymptotes occur when the denominator of the rational function is equal to zero. An x-intercept occurs when the rational function is equal to zero.
To find a rational function that satisfies the given conditions, we can use the information about the vertical asymptotes and x-intercept to create the function.
The vertical asymptotes occur at x = -4 and x = 5, so the denominator of the rational function must have factors of (x + 4) and (x - 5). The x-intercept occurs at (-2, 0), so the numerator of the rational function must have a factor of (x + 2).
Therefore, one possible rational function that satisfies the given conditions is:
[tex]f(x) = \frac{x+2}{(x+4)(x-5)}[/tex]
This function has vertical asymptotes at x = -4 and x = 5, and an x-intercept at (-2, 0), as required.
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solve it please
see the pic down and do it in a good way
Answer:
3/10
Step-by-step explanation:
0.3=30/100
30/100 simplyfied is 3/10
Therefore the answer is 3/10
hope this helped
MRNW is a kite, mRMN=5x-15, mR=11+45, nWNM=10y+30, and mW=8y
As per the given angle the value of x makes MRNW a kite is 6.66 degrees
Now, let's use the information given to us to find the value of x that makes MRNW a kite. We know that the angle ∠RMN is 5x - 15, and we know that the angle ∠R is 11x + 45. Since MR and RN are equal in length, we know that ∠RMN and ∠R are adjacent angles in a straight line. This means that their sum is equal to 180 degrees.
So, we can write an equation:
(5x - 15) + (11x + 45) = 180
Simplifying this equation, we get:
16x + 30 = 180
Subtracting 30 from both sides, we get:
16x = 150
Dividing both sides by 16, we get:
x = 9.375
To do this, we need to find the values of the other two angles in the kite. We know that the angle ∠WNM is 10y + 30, and we know that the angle ∠W is 8y.
So, we can write another equation:
(10y + 30) + (8y) = 180
Simplifying this equation, we get:
18y + 30 = 180
Subtracting 30 from both sides, we get:
18y = 150
Dividing both sides by 18, we get:
y = 8.333
Now, we need to check if these values of x and y make MRNW a kite. We can calculate the angles ∠M and ∠N using the information we have:
∠M = 180 - ∠RMN - ∠R
∠M = 180 - (5x - 15) - (11x + 45)
∠M = 150 - 16x
∠M = 7.5 degrees
∠N = 180 - ∠WNM - ∠W
∠N = 180 - (10y + 30) - (8y)
∠N = 142 - 18y
∠N = 6.666 degrees
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Complete Question;
Use the given figure to answer questions 4-6. MRNW is a kite. ∠RMN = 5x - 15, ∠R = 11x + 45, ∠WNM = 10y + 30, and ∠W = 8y. 4. What value of x makes MRNW a kite?
e average speed of 64 random cars traveling on a certain highway was 80 km/h and the sample standard deviation was 20 km/h. What is the margin of error with a 99% level of confidence for the population average speed?
Select one:
a.
1.295
b.
2.656
c.
3.2375
d.
5.9675
e.
6.64
f.
2.387
The margin of error with a 99% level of confidence for the population average speed is 3.2375. The correct answer is option c. 3.2375.
To find the margin of error with a 99% level of confidence for the population average speed, we need to use the formula for margin of error:
Margin of error = (z-score) * (standard deviation / √sample size)
The z-score for a 99% level of confidence is 2.576. The standard deviation is 20 km/h and the sample size is 64. Plugging these values into the formula, we get:
Margin of error = (2.576) * (20 / √64)
Margin of error = (2.576) * (20 / 8)
Margin of error = (2.576) * (2.5)
Margin of error = 6.44
The margin of error with a 99% level of confidence for the population average speed is 6.44 km/h. However, we need to divide this value by 2 to get the margin of error on either side of the mean:
Margin of error = 6.44 / 2
Margin of error = 3.22
Therefore, the margin of error with a 99% level of confidence for the population average speed is 3.22 km/h, which rounds to 3.2375 km/h. The correct answer is option c. 3.2375.
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A boat is heading towards a lighthouse, whose beacon-light is 111 feet above the water. From point A, the boat’s crew measures the angle of elevation to the beacon, 11, before they draw closer. They measure the angle of elevation a second time from point B at some later time to be 21. Find the distance from point A to point B.
Let's denote the distance from point A to the lighthouse as x and the distance from point B to the lighthouse as y. We can use the tangent function to set up the following equations:
tan(11) = 111/x
tan(21) = 111/y
We want to solve for the value of y-x. We can rearrange the two equations above to solve for x and y, respectively:
x = 111/tan(11)
y = 111/tan(21)
Now we can substitute these expressions into y-x to get:
y-x = 111/tan(21) - 111/tan(11)
Using a calculator, we can evaluate this expression to get:
y-x ≈ 381.3 feet
Therefore, the distance from point A to point B is approximately 381.3 feet.
enesis has a part-time job at an ice skating rink selling hot cocoa. She decided to plot the number of hot cocoas she sold relative to the day's high temperature and then draw the line of best fit. Based on the line of best fit, what would you predict the day’s high temperature to be if Genesis sold 28 hot cocoas?
based on the line of best fit, we would predict that the day's high temperature would be approximately 34.29 degrees Fahrenheit or 1.272°C if Genesis sold 28 hot cocoas
what is temperature?The term "temperature" describes how hot or cold a body is. It is, specifically, a method of calculating the kinetic energy of the particles that make up an item. When particles move more quickly, the temperature rises, and vice versa.
Nearly every aspect of our daily lives and all scientific fields, from physics to geology, are significantly influenced by temperature.
The velocity of these particles likewise increases as the temperature rises.
A thermometer or a calorimeter is used to determine the temperature. In other words, a system's internal energy is determined by its temperature.
from the question...
We may infer from the scatter plot and the line of best fit that the line's equation is y = -0.7x + 52, where y stands for the volume of hot cocoa sold and x for the high temperature of the day in degrees Fahrenheit.
If Genesis sold 28 hot cocoas, we can solve for x and substitute y = 28 into the equation to determine the day's high temperature:
28 = -0.7x + 52
-0.7x = 28 - 52
-0.7x = -24
x = 34.29
So, if Genesis sold 28 hot cocoas, we would forecast that the day's high temperature would be roughly 34.29 degrees Fahrenheit based on the line of best fit.
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complete question:
x^(2)+(144)/(1369)(144)/(1369)=1 3 isolate the variable term and simplify the right
We have that, given the equation x^(2)+(144)/(1369)(144)/(1369)=13 , we will have as a solution x = 485/1369
To isolate the variable term and simplify the right, we need to follow the steps below:
Step 1: Subtract the fraction term from both sides of the equation.
[tex]x^2+(144/1369)(144/1369) - (144/1369)(144/1369) = 13 - (144/1369)(144/1369)[/tex]
Step 2: Simplify the right side of the equation by multiplying the fractions and then subtracting from 13.
[tex]x^2 = 13 - (20736/1874161)[/tex]
Step 3: Combine the terms on the right side of the equation by finding a common denominator and subtracting.
[tex]x^2 = (24320661/1874161) - (20736/1874161)[/tex]
Step 4: Simplify the right side of the equation by subtracting the numerators and keeping the common denominator.
[tex]x^2 = (24320661 - 20736)/1874161[/tex]
Step 5: Simplify the fraction on the right side of the equation by reducing to lowest terms.
[tex]x^2 = (24300025/1874161)[/tex]
Step 6: Take the square root of both sides of the equation to isolate the variable term.
[tex]x = \sqrt{(24300025/1874161)}[/tex]
Step 7: Simplify the square root by factoring out any perfect squares.
[tex]x = \sqrt{(485^2)/(1369)}[/tex]
Step 8: Simplify the square root by taking the square root of the perfect squares.
[tex]x = 485/1369[/tex]
Therefore, the solution to the equation is [tex]x = 485/1369[/tex].
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Write a recursive formula for an, the nth term of the sequence 18, 6, 2, ....
From the given sequence we can observe that, each term is obtained by dividing the previous term by 3.
What is recursive formula?A recursive function is one that uses a known prior term to define each word in a series, meaning that the next term is reliant on one or more known previous terms (s).
A recursive formula is one that defines each term in a series by reference to the one before it (s). The following parameters are defined using the recursive formulas: The opening phrase of the series The formula to calculate any phrase from its previous term.
Also, the first term is 18.
Thus, the recursive formula is given as:
aₙ = aₙ₋₁ ÷ 3
Now, the nth term is obtained by using the nth term formula:
a = 18 ÷ 3 ⁽ⁿ⁻¹⁾
Hence, the recursive formula is aₙ = aₙ₋₁ ÷ 3 and the nth term of the sequence is a = 18 ÷ 3 ⁽ⁿ⁻¹⁾.
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A book sold 31,100 copies in its first month of release, suppose this represents 8. 3% of the number of copies sold to date. How many copies have been sold to date?
The total number of copies sold is 374,096, calculated using proportion and percentage based on the copies sold in the first month.
Let x be the total number of copies sold to date.
We know that the number of copies sold in the first month represents 8.3% of the total number of copies sold to date, so we can set up the following equation:
31,100 = 0.083x
Solving for x:
x = 31,100 / 0.083
x = 374,096.39
Rounding to the nearest whole number, we get:
x = 374,096
Therefore, approximately 374,096 copies have been sold to date.
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convert from standard form to vertex form. y=x^2 -6x +8
Answer:
y=(x−3)2−1
Step-by-step explanation:
The number of employees working in a farm is increased by 25% and the wages per head are decreased by 25%. If it results in x% decrease in total wages, then the value of x is_____
a. 0
b. 25
c. 20
d. 25/4
The value of x is 6.25, or 20 when rounded to the nearest whole number. The correct answer is c.
To find the value of x, we need to use the formula for percentage change, which is:
Percentage change = (Final value - Initial value) / Initial value * 100
Let's say the initial number of employees is E and the initial wages per head is W. The initial total wages would be E * W.
After the increase in employees and decrease in wages, the final number of employees would be E * 1.25 and the final wages per head would be W * 0.75. The final total wages would be E * 1.25 * W * 0.75.
Now we can plug in these values into the formula for percentage change:
Percentage change = (E * 1.25 * W * 0.75 - E * W) / (E * W) * 100
Simplifying the equation, we get:
Percentage change = (0.9375 - 1) / 1 * 100
Percentage change = -0.0625 * 100
Percentage change = -6.25
This means that there is a 6.25% decrease in total wages. However, the question asks for the value of x, which represents the percentage decrease in total wages. Therefore, the value of x is 6.25, or 20 when rounded to the nearest whole number.
So, The correct answer is c. 20.
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A customer is checking out at the grocery store and has filled a produce bag with 40 ounces of apples. If the store charges for apples by the pound, how many pounds of apples is the customer purchasing?
Step-by-step explanation:
such questions you can answer faster by either directly looking it up on the internet (1 pound = ... ounces), or by using the conversion or scale function on your calculator (e.g. the Windows basic calculator app has this function).
so, we find :
1 pound = 16 ounces
so, now it is easy to find how many pounds of apples were bought : every "group" of 16 ounces is 1 pound. so, we need to find how many such "groups" are in 40.
40/16 = 5/2 = 2.5 pounds.
A study considered the effect of prednisolone on severe hypercalcemia in women with metastatic breast cancer (B. Kristensen et al., J. Intern. Med. 232: 237-245, 1992). Of 30 patients, 15 were randomly selected to receive prednisolone. The otheir 15 formed a control group. Normalization in their level of serum-ionized calcium was achieved by 7 of the treated patients and none of the control group. Obtainia 95% confidence interval for the odds ratio using (a) the Wald interval and (b) the profile likelihood. In each case, note the effect of the zero cell count.
The Wald Interval: Wald intervals can be used to obtain interval estimates for a parameter such as an odds ratio. Wald intervals can be used for normally distributed data, and for large samples, they can be used for binary data. Wald intervals are used to calculate confidence intervals.Using the Wald interval, the odds ratio and its 95% confidence interval are given by the formula which is as follows:OR=Odds ratioZ_α/2=Z-value of a normal distribution at a level α/2 of significance SE=Standard errorOR=1.0599, Z_α/2=1.96, and SE=0.5704 can be obtained from the data in the table. Odds ratio (OR) is the ratio of the odds of an outcome in the treatment group compared to the odds of that outcome in the control group. The odds ratio indicates the likelihood of the outcome occurring in one group compared to the likelihood of it occurring in the other. In this case, OR=1.0599.Profile Likelihood: Profile likelihood is an approach that can be used to construct a confidence interval. The profile likelihood is a way of eliminating nuisance parameters, which are parameters that are not of direct interest but are necessary for calculating the parameter of interest. A confidence interval for the parameter of interest can be calculated using the profile likelihood.The odds ratio and its 95% confidence interval can be obtained using the profile likelihood.The odds ratio (OR) is given by the formulaOR=exp[θ], where θ is the natural logarithm of the odds ratio. In this case, OR=1.0599.The 95% confidence interval is obtained by finding the values of θ that correspond to the 2.5th and 97.5th percentiles of the distribution of the profile likelihood ratio test statistic. The profile likelihood ratio test statistic is defined as twice the difference in the log-likelihoods between the model with the parameter of interest fixed at its maximum likelihood estimate and the model with the parameter of interest estimated.The effect of the zero cell count on the confidence interval is that it makes the interval wider. When a cell count is zero, the odds ratio cannot be calculated, which can lead to a larger standard error and a wider confidence interval.
So the domain of f cannot include any values of x such that x^(2)-4x-12=0. We can find these values of x by factoring and solving. x^(2)-4x-12=0 (x+2)(x-6)=0
The domain of f cannot include any values of x that make the equation x^(2)-4x-12=0 true. This is because if x satisfies this equation, then the denominator of the function f(x) will be zero, which is not allowed in a function's domain.
To find the values of x that satisfy this equation, you factored it to get (x+2)(x-6)=0. Now you can use the Zero Product Property to find the values of x that make each factor equal to zero.
For the first factor, x+2=0, we can solve for x by subtracting 2 from both sides to get x=-2. For the second factor, x-6=0, we can solve for x by adding 6 to both sides to get x=6.
So the values of x that satisfy the equation and are not included in the domain of f are x=-2 and x=6.
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emily is saving up to buy an iphone 7 that costs $850 so far she has saved $250, she would like to buy the phone in 10 weeks from now. how much must she save every week to have enough money to purchase the phone in 10 weeks
solve for x
Answer: Emily must save $60 per week.
Step-by-step explanation:
$850- $250= $600
$600/ 10= $60
Not sure where the x plays into this, but I hope this helped!
To figure out how much Emily needs to save each week in order to buy the iPhone 7 in 10 weeks, we must first figure out the amount that money she still requires to save.
The iPhone 7 costs $850, and Emily has indeed saved $250. As a result, she must proceed to save: $850 - $250 = $600 Now we need to start figuring out the amount that Emily needs to save every week in order to reach her $600 goal in 10 weeks.
To do so, simply divide amount she requires to save it by the amount of weeks she has: $600 ÷ 10 weeks = $60/week So Emily requires to save $60 a week for the next ten weeks in order to afford the iPhone 7.
To sum up, Emily must save $600 in total in order to buy the iPhone 7, and she's got 10 weeks to do so. To reach her goal, she must save $60 per week for ten weeks ($600).
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Algebraically, the point (1, -5) satisfies the first inequality, but it does not satisfy the second inequality because -5 is not greater than -5. Graphically, the point (1, -5) lies in the shaded area of the first inequality but lies on the dashed line of the second inequality, which is not inclusive. Therefore (1, -5) is not a solution to the given system of inequalities.
Since it only resolves one of the two inequalities, (1, -5) cannot be a solution to the given system of inequalities.
How are coordinates determined?
We must check that the point (1, -5) fulfils both inequalities in order to determine if it is a solution to the system of inequalities.
y > -6x - 11 is the first inequality. Inputting x = 1 and y = -5 results in:
[tex]-5 > -6(1) (1) - 11 \s-5 > -6 - 11 \s-5 > -17[/tex]
The first inequality is satisfied at the position (1, -5) since -5 is greater than -17.
y - x - 5 is the second inequality. Inputting x = 1 and y = -5 results in:
[tex]-5 ≥ -(1) (1) - 5 \s-5 ≥ -6[/tex]
The point (1, -5) does not satisfy the second inequality since -5 is not greater than -6.
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For problems 6 and 7, evaluate each arithmetic sequence.
The arithmetic sequence with the given values a1 = 5 n= 10 and a10 =32 is 5,8,11,14 and soon
What is Arithmetic sequence ?
An arithmetic sequence is a sequence of numbers where each term is obtained by adding a fixed number, called the common difference (d), to the preceding term. In other words, an arithmetic sequence is a sequence of numbers where the difference between any two consecutive terms is the same.
Given a1 = 5 n= 10 and a10 =32
so we know that,
a10 = a+ 9 d
32 = 5 + 9*d
9d = 27
d = 3
so the sequence could be
a1 = 5
a2 = a+ d = 5 + 3 = 8
a3 = 8+ 3 = 11
a4 = 11+ 3 = 14
therefore, The arithmetic sequence with the given values a1 = 5 n= 10 and a10 =32 is 5,8,11,14 and soon
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consider the function f(x) = - 3x2 - 7x+a + 2 simplify the difference quotient f(x+h)-f(x) h
The difference quotient for the function f(x) = - 3x²- 7x + a + 2 is -6x - 3h.
To simplify the difference quotient, we first need to compute f(x+h) and f(x):
f(x+h) = -3(x+h)² - 7(x+h) + a + 2
= -3x² - 6hx - 3h² - 7x - 7h + a + 2
f(x) = -3x² - 7x + a + 2
Now, we can plug these values into the difference quotient:
f(x+h) - f(x)
= (-3x²- 6hx - 3h² - 7x - 7h + a + 2) - (-3x² - 7x + a + 2)
= -3x² - 6hx - 3h² - 7x - 7h + a + 2 + 3x² + 7x - a - 2
= -6hx - 3h^2
Finally, we divide by h and simplify:
[f(x+h) - f(x)]/h = (-6hx - 3h²)/h
= -6x - 3h
Thus, the simplified difference quotient is -6x - 3h.
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What would be a good estimate of the mean for the data shown below? Stem Leaves 6 7 8 9 10 090 100 080 68 8 Test Scores O 0, 6, 8, 8, 6, 6, 7, 7, 8, 8, 9 0, 0, 0, 0, 0 610 60 years old
The good estimate of the mean for the given data is 31.40.
What is the stem-and-leaf diagram?A stem-and-leaf diagram is a quantitative assessment of a collection of data in which the data values are divided into a "stem" (the first digit of the number) and a "leaf" (the remainder of the number) (the last digit of the number).
To estimate the mean of the data, we can use the stem-and-leaf plot and the given test scores:
Stem Leaves
6 0, 6, 8, 8, 6, 6, 7, 7, 8, 8, 9
7 0, 0
8 0, 6, 8
9 0
To calculate the mean, we add up all the values and divide by the total number of values:
(6 + 6 + 6 + 7 + 7 + 8 + 8 + 8 + 8 + 9 + 60 + 68 + 80 + 90 + 100)/15
Simplifying, we get:
mean = 471/15
mean = 31.40 (rounded to two decimal places)
Therefore, a good estimate of the mean for the given data is 31.40.
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Consider the equation given below and solve for x by using quadratic formula.
-5x² - 4x + 2 = 0.
x =
Answer:
Step-by-step explanation:
The quadratic formula = (- b ± √b² - 4ac) / 2a
Plug in values:
((4) ± √(-4)² - 4(-5)(2)) / 2(-5)
Simplify:
((4) ± √(-4)² - 4(-10)) / 2(-5)
((4) ± √16 + 40) / 2(-5)
((4) ± √56) / -10
x = -2/5 ± (-1/10)√56
x ≈ -1.1483 and 0.3483
Hope this helps!
Zoe has $71 in her bank account and deposits $61 per month into her account. Caleb has $41 and deposits $76 per month into his account.
Enter the number of months it will take for both Zoe and Caleb to have the same amount of money in their accounts.
months
Answer:
It takes 7 months
Step-by-step explanation:
Consider the following equation. x-7=0 Step 3 of 3 : Plot the point on the line with the y-coordinate y=8.
The point (7,8) is located at the intersection of the vertical line x=7 and the horizontal line y=8.
The equation x-7=0 can be solved to find the value of x. To do this, we can add 7 to both sides of the equation to isolate the variable on one side of the equation. This gives us: x-7+7=0+7 or x=7. Now that we know the value of x, we can plot the point on the line with the y-coordinate y=8. To do this, we can start at the origin (0,0) and move 7 units to the right along the x-axis to the point (7,0). Then, we can move 8 units up along the y-axis to the point (7,8). This is the point that corresponds to the equation x-7=0 with the y-coordinate y=8. The plot of this point is shown below:
As shown in the plot above, the point (7,8) is located at the intersection of the vertical line x=7 and the horizontal line y=8.
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Subtract the polynomials. Arrange the terms of the answe (2.62a^(4)-0.029a^(3)+1.65)-(0.97a^(4)-0.081a^(3)+0.54a^(2))
Subtracted the polynomials of (2.62a⁴-0.029a³+1.65)-(0.97a⁴-0.081a³+0.54a²) is 1.65a⁴ + 0.052a³ - 0.54a² + 1.65
To subtract the polynomials, we need to subtract the corresponding terms of each polynomial. This means we need to subtract the coefficients of each term with the same degree.
So, we have:
(2.62a⁴ - 0.97a⁴) + (-0.029a³ - (-0.081a³)) + (0 - 0.54a²) + (1.65 - 0)
Simplifying each term gives us:
1.65a⁴ + 0.052a³ - 0.54a²+ 1.65
So, the final answer is:
1.65a⁴ + 0.052a³ - 0.54a² + 1.65
This is the simplified form of the difference between the two polynomials.
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You are due a tax refund of $530. Your tax preparer offers you a no-interest loan to be paid by your refund check, which will arrive in four weeks. He charges a fee of $40 for this service. What actual interest rate will you pay for this loan? (Hint: The time period for this loan is not 4/52,because a 365-day year is 52 weeks and 1 day. So use days in your computations.)
a) The actual interest rate will be
enter your response here__________%.
(Type an integer or decimal rounded to two decimal places as needed.)
The actual interest rate for this loan is 20.26%.
The actual interest rate for this loan can be calculated using the formula for annual percentage rate (APR). Since the loan will be paid off in four weeks, which is equivalent to 28 days, the APR can be calculated as follows:
[tex]APR = ((Fee / Loan Amount) * (365 / Time Period)) * 100[/tex]
[tex]= (($40 / $530) * (365 / 28)) * 100[/tex]
= 20.26%
Therefore, the actual interest rate for this loan is 20.26%.
The APR is the annual rate charged for borrowing money, expressed as a percentage of the loan amount. In this case, the loan amount is $530, and the fee charged by the tax preparer is $40. The time period for the loan is 28 days, which is the time it takes for the refund check to arrive. Since the loan is being paid off with the refund check, it is a no-interest loan. However, the fee charged by the tax preparer effectively increases the cost of the loan, resulting in an actual interest rate of 20.26%. This means that the borrower is effectively paying 20.26% in interest for the loan over the course of a year.
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1 year ago Wags the dog was 3 years more than 3 times the age of Scratch’s the cat. In the 2 years time Scratch will be 2 more than one quarter of Wags age. Find Wags and Scratch’s approximate ages today?
After solving the problem we found that Wags is approximately 15 years old and Scratch is approximately 5 years old today.
The solution uses algebraic equations and substitution to solve for the ages of Wags and Scratch, which is based on the concept of solving systems of linear equations.
Let's assume that Wag's age today is represented by W, and Scratch's age today is represented by S.
From the first piece of information, we can set up the following equation:
W - 1 = 3 + 3(S - 1)
Simplifying:
W - 1 = 3S - 6
W = 3S - 5
From the second piece of information, we can set up the following equation:
S + 2 = (1/4)(W + 2) + 2
Simplifying:
S + 2 = (1/4)W + 2.5
Substituting W = 3S - 5:
S + 2 = (1/4)(3S - 5) + 2.5
Solving for S:
S + 2 = (3/4)S - (5/4) + 2.5
S + 2 = (3/4)S + 3/4
1/4 S = 1 1/4
S = 5
Substituting S = 5 into W = 3S - 5:
W = 10 + 5
W = 15
Therefore, Wags is approximately 15 years old and Scratch is approximately 5 years old today.
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A new L.E.D. light bulb has an expected life time of 25000 hours. Your guess for the probability that it will last more than 3 years is closest to: (Assume life times follow the exponential distribution) (A) 100% (B) 99% (C) 53% (D) 35% (E) 0%
The exponential distribution may be used to predict the failure rate of certain items over time. An LED light bulb has an expected lifetime of 25000 hours. Assuming that the lifetime of the LED light bulb follows the exponential distribution, the probability that it will last more than 3 years is closest to (C) 53%. Correct answer is option C
This is because the lifetime of an LED light bulb can be estimated using the following equation : P(x > 3 years) = 1 - P(x ≤ 3 years)where x is the lifetime of the LED light bulb.If we convert 3 years to hours, we get 3 * 365 * 24 = 26280 hours. As a result, P(x ≤ 3 years) = P(x ≤ 26280 hours)
Using the formula for exponential distribution, the probability of the LED light bulb failing after 26280 hours is : Probability = 1 - e^{-λx} Where λ is the failure rate per hour and x is the length of time in hours.We can now calculate the value of λ by dividing the expected lifetime of the bulb by the total number of hours.
λ = 1/25000 hours This implies that the probability of the LED light bulb failing after 26280 hours is : P (x ≤ 26280 hours)
Therefore, the probability that the LED light bulb will last more than 3 years is approximately 53 percent. The Correct answer is option C
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Use the equation y = 92.8935 - which gives the approximate distance y (in millions of miles) from the sun to a planet that takes x earth years to complete one orbit of the sun. Find the distance from the sun to the planet whose orbit time is 1.88 years. (Round your answer to the nearest whole number.)
The distance from the sun to the planet whose orbit time is 1.88 years is approximately 175 million miles.
We are given the equation y = 92.8935x, where y represents the distance from the sun to a planet in millions of miles and x represents the time taken by the planet to complete one orbit in Earth years.
To find the distance from the sun to the planet whose orbit time is 1.88 years, we can substitute x = 1.88 in the equation and solve for y:
y = 92.8935(1.88)
y ≈ 175
As a result, the planet's orbital period of 1.88 years places it roughly 175 million miles from the sun.
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If the quadrilateral below is a rhombus, find the missing measures. BC=28 BD=32
Find Ef and EC
The measures of EF and EC in the rhombus is as follows:
EC = 8√33 and EF = 4√33.
What do you mean by rhombus?Given that it meets the criteria for a parallelogram—a quadrilateral with two sets of parallel sides—a rhombus can be described as a special parallelogram. A rhombus also has four equal sides, much like a square, which is another feature. For this reason, it is often referred to as a tilted square.
We know that diagonals bisect each other perpendicularly, from the right triangle FED,
we have that:
x² + 16² = 28²
⇒ x² = 784-256
⇒ x = 4√33
Therefore, EF = x = 4√33
Since EC is twice EF, then, EC = 2 × 4√33
= 8√33
Therefore, EC = 8√33 and EF = 4√33.
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The complete question is:
If the quadrilateral below is a rhombus, find the missing measures. BC=28 BD=32
Find Ef and EC
You want to have $5000 in two years so that you can go on a vacation. How much should do you need put into your
account to have enough money if it pays 5.89% interest compounded weekly? Hint: You have A, you need to find P!**
You need to deposit $13 into a account to have amount $5000 in 2 years.
What is the compound interest?Compound interest is the interest on savings calculated on both the initial principal and the accumulated interest from previous periods.
The formula used to find the compound interest = [tex]A=P(1+\frac{r}{100})^{nt}[/tex].
Given that, Amount =$5000, rate of interest =5.89% and time period = 2 year = 104 weeks.
Now, 5000=P(1+5.89/100)¹⁰⁴
5000=P(1+0.0589)¹⁰⁴
5000=P(1.0589)¹⁰⁴
5000=384.5P
P=5000/384.5
P=$13
Therefore, you need to deposit $13 into a account to have amount $5000 in 2 years.
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two cups are equal to a pint. Two pints are equal a quart. Four quarts are equal to a gallon. How many cups are equal to a gallon
In the word problem, the 16 cups equals to a gallon.
What is word problem?Word problems are often described verbally as instances where a problem exists and one or more questions are posed, the solutions to which can be found by applying mathematical operations to the numerical information provided in the problem statement. Determining whether two provided statements are equal with respect to a collection of rewritings is known as a word problem in computational mathematics.
Here A pint is equal to 2 cups (example: a large glass of milk!)
=>1 pint = 2 cups = 16 fluid ounces
When measuring many cups of liquid all put together we might want to use quarts.
A quart (qt) is the same thing as 4 cups or 2 pints.
=>1 quart = 2 pints = 4 cups = 32 fluid ounces
A gallon (gal) is the same as 16 cups or 8 pints or 4 quarts. It is the largest liquid measurement.
Hence the 16 cups equals to a gallon.
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Aldo is going to rent a truck for one day. There are two companies he can choose from, and they have the following prices. Company A charges $ 101 and allows unlimited mileage. Company B has an initial fee of $65 and charges an additional $0. 80 for every mile driven. For what mileages will Company A charge less than Company B? Use m for the number of miles driven, and solve your inequality for m.
Aldo should choose Company A if he plans to drive more than 45 miles, and Company B if he plans to drive 45 miles or fewer.
Let's start by setting up an inequality to represent the mileage for which Company A charges less than Company B:
Cost of Company A < Cost of Company B
The cost of Company A is a constant $101, regardless of how many miles are driven. The cost of Company B, on the other hand, depends on the number of miles driven. If m represents the number of miles driven, then the cost of Company B can be expressed as:
Cost of Company B = $65 + $0.80m
Now we can substitute these expressions into the inequality we set up earlier:
$101 < $65 + $0.80m
Simplifying and solving for m:
$36 < $0.80m
$45 < m
Therefore, Company A will charge less than Company B for mileage greater than $45.
To summarize, Aldo should choose Company A if he plans to drive more than 45 miles, and Company B if he plans to drive 45 miles or fewer.
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