Answer:
- The number of t-shirts he needs to print to obtain maximum profit = 2.79 (in thousand), that is, 2790 t-shirts.
- The maximum profit for this number of shirts is then = 12.208761 (in thousand dollars) = $12209
Step-by-step explanation:
Complete Question
Keegan is printing and selling his original design on t-shirts. He has concluded that for x shirts, in thousands sold his total profits will be p(x) = -x³ + 4x² + x dollars, in thousands will be earned. How many t-shirts (rounded to the nearest whole number) should he print in order to make maximum profits? What will his profits rounded to the nearest whole dollar be if he prints that number of shirts?
The profit function is given as
p(x) = -x³ + 4x² + x
The maximum profit will be obtained by investigating the maximum value of the profit function
At the maximum value of the function,
(dp/dx) = 0 and (d²p/dx²) < 0
p(x) = -x³ + 4x² + x
(dp/dx) = -3x² + 8x + 1
at maximum point
(dp/dx) = -3x² + 8x + 1 = 0
Solving the quadratic equation
x = -0.12 or 2.79
(d²p/dx²) = -6x + 8
at x = -0.12
(d²p/dx²) = -6(0.12) + 8 = 7.28 > 0 (not a maximum point)
At x = 2.79
(d²p/dx²) = -6(2.79) + 8 = -8.74 < 0 (this corresponds to a maximum point!)
So, the maximum of the profit function exists when the number of shirts, x = 2.79 (in thousand).
So, the maximum profits that corresponds to this number of t-shirts is obtained from the profit function.
p(x) = -x³ + 4x² + x
p(x) = -(2.79)³ + 4(2.79²) + 2.79
p(x) = -21.717639 + 31.1364 + 2.79
p(x) = 12.208761 (in thousand dollars) = $12209 to the mearest whole number.
Hope this Helps!!!
Keegan should print around 2,000 shirts to maximize his profits, resulting in approximately $12,000 in earnings
To find the number of t-shirts Keegan should print to maximize his profits, we need to find the critical points of the profit function p(x) = -x^3 + 4x^2 + x.
Taking the derivative, we get p'(x) = -3x^2 + 8x + 1. Setting this equal to zero and solving for x gives:
0 = -3x^2 + 8x + 1
Using the quadratic formula, we find two potential values for x: x ≈ 2.37 and x ≈ -0.12. Since x must be a positive value representing the number of shirts, we discard the negative root.
Next, we need to determine whether this value of x corresponds to a maximum or minimum. We can do this by examining the second derivative, p''(x) = -6x + 8. Since p''(2.37) > 0, we conclude that x ≈ 2.37 corresponds to a local minimum.
However, since we're dealing with a cubic function, we need to consider behavior as x approaches infinity. As x gets very large, the -x^3 term dominates, making the function tend toward negative infinity. This means there is no global maximum, but rather a local maximum.
To find the approximate number of shirts Keegan should print, we take the nearest whole number, which is 2. The maximum profit can be found by plugging this value back into the profit function:
p(2) ≈ -2^3 + 4(2)^2 + 2 ≈ 12 (in thousands).
So, Keegan should print around 2,000 shirts to maximize his profits, which will be approximately $12,000 (rounded to the nearest whole dollar).
Complete question:
Keegan is printing and selling his original design on t-shirts. He has concluded that for x shirts, in thousands sold his total profits will be p(x) = -x³ + 4x² + x dollars, in thousands will earned. How many t-shirts (rounded to the nearest whole number) should he print in order to make maximum profits? What will his profits rounded to the nearest whole dollar be if he prints that number of shirts?
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If Zoe paints the visible outside faces of her shed, what is the total surface area that she paints? Alternative Text A. 48 ft2 B. 64 ft2 C. 96 ft2 D. 112 ft2
The total surface area that she paints will be 96 square feet. Thus, the correct option is C.
What is the area of the rectangle?Let W be the rectangle's width and L its length. The area of the rectangle is the multiplication of the two different sides of the rectangle. Then the rectangle's area will be given as,
Area of the rectangle = L × W square units
Given that:
Length, L = 12 ft
Width, W = 8 ft
The area of the rectangle is given as,
A = 12 x 8
A = 96 square feet
Thus, the correct option is C.
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The missing diagram is given below.
Sketch the region of integration and evaluate the following integral. ModifyingBelow Integral from nothing to nothing Integral from nothing to nothing With Upper R StartFraction 1 Over 3 plus StartRoot x squared plus y squared EndRoot EndFraction dA , RequalsStartSet (r comma theta ): 0 less than or equals r less than or equals 2 comma StartFraction pi Over 2 EndFraction less than or equals theta less than or equals StartFraction 3 pi Over 2 EndFraction EndSet
Answer:
[tex]\frac{10\pi}{3}[/tex]
Step-by-step explanation:
According to the information of the problem we have to compute the following integral.
[tex]{\displaystyle \int\limits \int} \frac{1}{3} + \sqrt{x^2 + y^2} \, dA[/tex]
Where the region of integration is
[tex]R = \Big\{ (r,\theta) : 0 \leq r \leq 2 , \,\,\,\, \frac{\pi}{2} \leq \theta \leq \frac{3\pi}{2} \Big\}[/tex]
If you plot, that is just a circle between [tex]\pi/2[/tex] and [tex]3\pi/2[/tex], which is just half of the circle on the negative part of the plane.
When you switch coordinates
[tex]{\displaystyle \int\limits \int} \frac{1}{3} + \sqrt{x^2 + y^2} \, dA = {\displaystyle \int\limits_{0}^{2} \int\limits_{\pi/2}^{3\pi/2}} \bigg(\frac{1}{3} + r \bigg)r \, d\theta\, dr = \frac{10\pi}{3}[/tex]
One hundred volunteers who suffer from severe depression are available for a study. Fifty are selected at random and are given a new drug that is thought to be particularly effective in treating severe depression. The other 50 are given an existing drug for treating severe depression. A psychiatrist evaluates the symptoms of all volunteers after 4 weeks in order to determine if there has been substantial improvement in the severity of the depression. Suppose volunteers were first divided by gender, and then half of the men were randomly assigned to the new drug and half of the women were assigned to the new drug. The remaining volunteers received the other drug. What is this an example of
Answer:
This is an example of placebo testing.
Step-by-step explanation:
This is an example of placebo testing in which, the two groups are given two substances that are said to have an effect on the condition that is being treated but one of them is the actual medicine that is being tested while the other one has no real effect over the medical condition. But the volunteers are not given information on which of the medicines is real and which is not, so that this does not affect the outcome of the experiment.
I hope this answer helps.
Which exponential expressions are equivalent to the one below? Check all
that apply.
(5x9)^12
Answer:D
Step-by-step explanation:
(5x9)^12
5^12 x 9^12
Area =
22ft for diameter
Here is your answer! uwu
Which of the following has a constant of proportionality of 2?
A) y = 2 x
B) 2 y = x
C) y = x + 2
D) y + 2 = 2 x
Answer:
A) y = 2 x
Step-by-step explanation:
The equation for direct variation is
y = kx where the constant of proportionality is k
y = 2x
Kelly walks 4/5 of a mile each day. How many miles does Kelly walk after three days?
Answer:
Kelly walks 4/5 of a mile each day.
After 3 days, Kelly walks a distance: D = 3 x 4/5 = 12/5 = 2.4 miles
Hope this helps!
:)
Kelly walks 4/5 of a mile each day, and after three days, she would have walked 2 and 2/5 miles.
Kelly walks 4/5 of a mile each day. To find out how many miles Kelly walks after three days, we simply multiply the daily distance by three.
Calculation:
4/5 mile/day * 3 days = 12/5 miles
To convert 12/5 miles into a mixed number, we divide 12 by 5. The quotient is 2 with a remainder of 2, so Kelly walks 2 and 2/5 miles after three days.
observe as seguintes situações e sua representação em linguagem matematica dois numeros x e y são tais 2x y=6 x-y=3
Answer:
We have two relations
2*x*y = 6 (2 times x times y is equal to six)
x - y = 3 ( the difference between x and y is trhe)
Where whe have two variables, x and y.
To solve this system, the first step is isolation one of the variables in one of the equations, let's isolate x in the second equation.
x - y = 3
x = 3 + y
now we can replace this in the other equation and then solve it for y.
2*x*y = 6
2*(3 + y)*y = 6
6y + 2y^2 = 6
now we have the quadratic equation:
2y^2 + 6y - 6 = 0
the solutions are:
[tex]y = \frac{-6 + -\sqrt{6^2 - 4*2*(-6)} }{2*2} = \frac{-6 +- 9.2}{4}[/tex]
the solutions are:
y = (-6 + 9,2)/4 = 0.8
y = (-6 - 9.2)/4 = -3.8
if y = 0.8, then:
x = 3 + y = 3.8
if y = -3.8
x = 3 + y = 3 - 3.8 = -0.8
so we have two possible solutions:
(-0.8, -3.8) and (3.8, 0.8)
A random sample of 400 Michigan State University (MSU) students were surveyed recently to determine an estimate for the proportion of all MSU students who had attended at least three football games. The estimate revealed that between .372 and .458 of all MSU students attended. Given this information, we can determine that the confidence coefficient was approximately: a. .92 b. .95 c. .88 d. .90 e. .99
Answer:
a. .92
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].
The margin of error of the interval is:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
The lower bound is the point estimate [tex]\pi[/tex] subtracted by the margin of error.
The upper bound is the point estimate [tex]\pi[/tex] added to the margin of error.
Point estimate:
The confidence interval is symmetric, so it is the mean between the two bounds.
In this problem:
[tex]\pi = \frac{0.372 + 0.458}{2} = 0.415[/tex]
Sample of 400, which means that [tex]n = 400[/tex]
Margin of error is the estimate subtracted by the lower bound. So [tex]M = 0.415 - 0.372 = 0.043[/tex]
We have to find z.
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
[tex]0.043 = z\sqrt{\frac{0.415*0.585}{400}}[/tex]
[tex]z = \frac{0.043\sqrt{400}}{\sqrt{0.415*0.585}}[/tex]
[tex]z = 1.745[/tex]
[tex]z = 1.745[/tex] has a pvalue of 0.96.
This means that:
[tex]1 - \frac{\alpha}{2} = 0.96[/tex]
[tex]\frac{\alpha}{2} = 1 - 0.96[/tex]
[tex]\frac{\alpha}{2} = 0.04[/tex]
[tex]\alpha = 0.08[/tex]
Confidence level:
[tex]1 - \alpha = 1 - 0.08 = 0.92[/tex]
So the correct answer is:
a. .92
To determine the confidence coefficient for the proportion of MSU students who attended at least three football games, the margin of error is calculated from the given interval range and related to the Z-value of a standard normal distribution. The coefficient that matches the margin of error from the calculation is approximately 0.95, indicating a 95% confidence level.
The confidence interval for the proportion of Michigan State University (MSU) students who attended at least three football games is given as (0.372, 0.458). To determine the confidence coefficient used to calculate this interval, we need to look at the width of the interval and how it relates to the standard error of the proportion.
The width of the confidence interval is 0.458 - 0.372 = 0.086. Since we know that the total width of the interval spans the range of twice the margin of error, one margin of error is then 0.086 / 2 = 0.043.
Using the Z-table for the normal distribution, we can find which confidence coefficient corresponds to a Z-value that gives a margin of error of 0.043, considering that the formula for the margin of error in this case would be: Z * sqrt((p*(1-p))/n). For a sample size of 400, and approximating p by the midpoint of the confidence interval (0.372 + 0.458)/2 = 0.415, the computation would look roughly like this:
Z * sqrt((0.415*(1-0.415))/400) = 0.043
After solving this equation for Z, we can then locate the corresponding confidence level on the standard normal (Z) distribution table. This process would lead to finding that the closest confidence coefficient that would generate the margin of error of 0.043 with the given sample size and point estimate proportion is approximately 0.95, or 95%.
Therefore, the confidence coefficient is 0.95, which corresponds to option b. 0.95.
A manufacturing company is ready to introduce a new product with a national sales campaign. After extensive test marketing, the market research department estimates that sales (in millions of dollars) will increase at the monthly rate of S'(t) = 10 - 10e-0.2t for 0 ≤ t ≤ 24, t months after the national campaign has started. What will the total sales be five months after the beginning of the campaign if we assume zero sales at the beginning of the campaign? (Round the answer to the nearest million.)
Final answer:
The total sales five months after the beginning of the campaign is approximately 72 million dollars.
Explanation:
To find the total sales five months after the beginning of the campaign, we need to calculate the definite integral of the sales rate function from t=0 to t=5. The sales rate function can be expressed as S'(t) = 10 - 10e^(-0.2t).
First, let's find the antiderivative of the sales rate function. The antiderivative of 10 is 10t, and the antiderivative of -10e^(-0.2t) is 50e^(-0.2t). Therefore, the indefinite integral of S'(t) is S(t) = 10t - 50e^(-0.2t) + C, where C is the constant of integration.
Next, we evaluate the definite integral over the interval t=0 to t=5. Substituting the upper and lower limits into the antiderivative, we get S(5) - S(0) = (10(5) - 50e^(-0.2(5))) - (10(0) - 50e^(-0.2(0))) = (50 - 50e^(-1)) - (0 - 50e^0) = 50 - 50e^(-1) + 50 = 100 - 50e^(-1) million dollars.
Rounding the answer to the nearest million, the total sales five months after the beginning of the campaign is approximately 72 million dollars.
Product A requires 9 minutes of milling, 7 minutes for inspection, and 6 minutes of drilling per unit; product B requires 10 minutes of milling, 5 minutes for inspection, and 8 minutes of drilling per unit; product C requires 7 minutes of milling, 3 minutes for inspection, and 15 minutes of drilling. The department has 20 hours available during the next period for milling, 15 hours for inspection, and 24 hours for drilling. Product A contributes $2.0 per unit to profit, product B contributes $2.3 per unit, and product C contributes $4.0 per unit. a. How many constraints are there in the Linear Programming Formulation of this problem
Answer:
The Linear programming problem has 3 constraints :- Milling time, Inspection time, Drilling time constraints.
Step-by-step explanation:
Product A : 9 minutes milling, 7 minutes inspection, 6 minutes drilling Product B : 10 minutes milling, 5 minutes inspection, 8 minutes drilling Product C : 7 minutes milling, 3 minutes inspection, 15 minutes drilling
Total milling time available = 20 hours = (20 x 60) i.e 1200 minutes Total inspection time available = 15 hours = (15 x 60) i.e 900 minutes Total drilling time available = 24 hours = (24 x 60) i.e 1440 minutes
Let QA, QB, QC be quantities of product A, B, C respectively
Milling time constraint : 9QA + 10QB + 7QC = 1200 Inspection time constraint : 7QA + 5QB + 3QC = 900Drilling time constraint : 6QA + 8QB + 15QC = 1440What is the lateral surface area of the square pyramid below?
a
48 in²
b
105 in²
c
96 in²
d
57 in²
Answer:
lateral surface area = 48 inches²
Step-by-step explanation:
The picture below is the square base pyramid you are referring. The lateral area is adding the area of the 4 triangles in the pyramid.
area of a triangle = 1/2 × b × h
The slant height of the triangle is gotten using Pythagoras theorem
lateral surface area = 4 × (1/2 × 3 × 8)
lateral surface area = 4 × 24/2
lateral surface area = 4 × 12
lateral surface area = 48 inches²
Answer:
48 in
Step-by-step explanation:
<3 hoped this helped <3
Which represents a quadratic function?
f(x) = −8x3 − 16x2 − 4x
f (x) = three-quarters x 2 + 2x − 5
f(x) = StartFraction 4 Over x squared EndFraction minus StartFraction 2 Over x EndFraction + 1
f(x) = 0x2 − 9x + 7
Answer:[tex]f(x)=\frac{3}{4}x^2+2x-5[/tex]
Step-by-step explanation:
Answer:
b
Step-by-step explanation:
b
How many possible outcomes exist when Louisa spins the spinner below twice? A spinner with 8 equal sections labeled 1 through 8. 8 10 16 64
Answer:
64
Step-by-step explanation:
The spinner has 8 equal sections numbered from 1 to 8
Each time she spinns the spinner has 8 possible outcomes.
To know the number of possible results when spinning two times, you must multiply the possible results for the first spin (8 possible outcomes) by the possible results for the second spin (also 8 possible outcomes).
And because each spin has the same number of outcomes:
[tex]8*8=64[/tex]
the answer is that there are 64 possible outcomes
Answer:
64
Step-by-step explanation:
Awnser this please.
Answer:
1.5 hours
Step-by-step explanation:
make each half hour represent t
Cost C(t) = 24 + 14t
66 = 24 + 14t
42 = 14t
t = 3
3 half hours = 1.5 hours
Answer:
1 and a half hours of work
Step-by-step explanation:
You minus 66 and 24 to get 42. Then you divide 42 and 14
Write a verbal description for each algebraic expression 100-5n
Step-by-step explanation:
One hundred minus five n
You are in charge of buying office supplies for your business. Your workers use red and black pens. Red pens cost $5 per box and black pens cost $3 per box. You need at least 10 boxes of pens. You want no more than 7 boxes of black pens and no more than 6 boxes of red pens. You want to minimize the cost to your business.
The objective function for this situation is C = 5x + 3y. What (x, y) pair minimizes cost?
image
(6, 7)
(0, 7)
(3, 7)
(6, 4)
Answer:
C. (3, 7)
Step-by-step explanation:
plug all the numbers into all of the coordinates and (3, 7) is the lowest number :) pls rate 5 stars and thank me
The option of buying 6 boxes of red pens and 4 boxes of black pens minimizes the cost to the business, based on the objective function C = 5x + 3y and the given constraints of at least 10 boxes in total, no more than 7 boxes of black pens, and no more than 6 boxes of red pens.
Explanation:To minimize the cost of buying office supplies, particularly red and black pens, we need to use the given objective function C = 5x + 3y where x represents the number of boxes of red pens and y represents the number of boxes of black pens. We have the following constraints: at least 10 boxes of pens in total, no more than 7 boxes of black pens, and no more than 6 boxes of red pens.
By applying these constraints, we can determine the combinations of x and y that meet the criteria:
x + y ≥ 10 (at least 10 boxes of pens)x ≤ 6 (no more than 6 boxes of red pens)y ≤ 7 (no more than 7 boxes of black pens)Looking at the choices provided, (6, 4) meets all our constraints, and when plugged into the objective function:
C = 5(6) + 3(4) = 30 + 12 = $42
This results in the lowest cost when compared to the other presented options. Therefore, buying 6 boxes of red pens and 4 boxes of black pens minimizes the cost to the business.
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Suppose Kristen is researching failures in the restaurant business. In the city where she lives, the probability that an independent restaurant will fail in the first year is 32 % . She obtains a random sample of 72 independent restaurants that opened in her city more than one year ago and determines if each one had closed within a year. What are the mean and standard deviation of the number of restaurants that failed within a year? Please give your answers precise to two decimal places.
Answer:
The mean of the number of restaurants that failed within a year is 23.04 and the standard deviation is 3.96.
Step-by-step explanation:
For each restaurant, there are only two possible outcomes. Either it fails during the first year, or it does not. The probability of a restaurant failling during the first year is independent of other restaurants. So we use the binomial probability distribution to solve this question.
Binomial probability distribution
Probability of exactly x sucesses on n repeated trials, with p probability.
The expected value of the binomial distribution is:
[tex]E(X) = np[/tex]
The standard deviation of the binomial distribution is:
[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]
The probability that an independent restaurant will fail in the first year is 32%.
This means that [tex]p = 0.32[/tex]
72 independent restaurants
This means that [tex]n = 72[/tex]
Mean:
[tex]E(X) = np = 72*0.32 = 23.04[/tex]
Standard deviation:
[tex]\sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{72*0.32*0.68} = 3.96[/tex]
The mean of the number of restaurants that failed within a year is 23.04 and the standard deviation is 3.96.
Final answer:
The mean number of independent restaurants in the sample expected to fail within the first year is 23.04, and the standard deviation is approximately 4.28.
Explanation:
To find the mean and standard deviation of the number of restaurants that failed within a year in Kristen's research, we can use the properties of the binomial distribution. The probability of a single restaurant failing (success in this context) is 0.32 (32%). Given a sample size of 72 restaurants, the mean number of restaurants that fail within a year is the product of the sample size and the probability of failure.
The formula for the mean (μ) of a binomial distribution is μ = n * p, where n is the sample size and p is the probability of success. Therefore, the mean number of failed restaurants is 72 * 0.32 = 23.04.
The formula for the standard deviation (σ) of a binomial distribution is σ = √(n * p * (1 - p)). Thus, the standard deviation of failed restaurants is √(72 * 0.32 * (1 - 0.32)) = √(72 * 0.32 * 0.68) ≈ 4.28.
Therefore, the mean number of restaurants that failed within a year is 23.04, and the standard deviation is approximately 4.28.
Juan Pablo demora 7 minutos en dar una vuelta a la cancha de fútbol y Pedro demora 2 minutos más corriendo a la misma velocidad que Juan Pablo. ¿Cuánto tiempo demorará Pedro en dar 12 vueltas?
Answer: 108 minutes
Step-by-step explanation:
This translates to:
Juan Pablo takes 7 minutes to do a full lap on a football field, Pedro needs 2 more minutes ruuning at the same speed thanJuan Pablo.
How much time does Pedro need to do 12 laps?
The fact that Pedro runs at the same speed than Juan Pablo, and needs more time, may mean that the radius of the laps of Pedro are a little bit bigger than the ones of Juan Pablo (which means that the total distance that pedro runs is bigger)
If Juan Pablo does a lap in 7 minutes, then Pedro does a lap in 7 minutes + 2 minutes = 9 minutes.
Then to do 12 laps, he needs 12 times that amount of time, this is:
12*9 min = 108 minutes
Jasmine has 3 and 3/8 pound of Turkey meat she is making 1/3 pound Turkey burgers does Jasmine have enough meat to make 12 Turkey burgers
Answer:
No
Step-by-step explanation:
To answer this you have to divide 3 and 3/8 by 1/3. The easiest way to do this without a calculator is to do this separately. First divide 3 by 1/3. When dividing fractions, the second number is flipped upside down and the two numbers are multiplied. From 3 pounds, Jasmine will be able to make nine 1/3 pound burgers.
3 ÷ 1/3 = 3 × 3/1 = 9
Next, divide 3/8 by 1/3. From 3/8 pounds, Jasmine will be able to make 1 1/8 burgers
3/8 ÷ 1/3 = 3/8 × 3/1 = 9/8 = 1 1/8
Add the two numbers together.
9 + 1 1/8 = 10 1/8
This is less than 12.
To make 12 Turkey burgers Jasmine needs 4 pounds thus 3 and 3/8 are not enough to make 12 Turkey burgers.
What are the ratio and proportion?The ratio is the division of the two numbers.
For example, a/b, where a will be the numerator and b will be the denominator.
Proportion is the relation of a variable with another. It could be direct or inverse.
Given that,
Jasmine has 3 and 3/8 pounds of turkey meat
Amount in pounds needed to make 1 burger = 1/3 pound
Number of burgers in 3 3/8 ⇒
(3 3/8)/(1/3) = 10 1/8
For making 12 Turkey burgers ⇒
Amount of meat required = 12 × 1/3 = 4 pounds
Hence "To make 12 Turkey burgers Jasmine needs 4 pounds thus 3 and 3/8 are not enough to make 12 Turkey burgers".
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Which expressions are solutions to the equation (3/4)x = 15? Select all that apply.
The expressions that are solutions to the equation [tex]\( \frac{3}{4}x = 15 \)[/tex] are A and C
as [tex]\( \frac{15}{\frac{3}{4}} = 20 \)[/tex] - This is a solution and [tex]\( \frac{4}{3} \times 15 = 20 \)[/tex] - This is a solution.
Let's solve the equation [tex]\( \frac{3}{4}x = 15 \)[/tex] and then check each expression to see if it is a solution:
1. Solve the equation:
[tex]\[ x = \frac{15}{\frac{3}{4}} \][/tex]
To divide by a fraction, we can multiply by its reciprocal:
[tex]\[ x = 15 \times \frac{4}{3} = 20 \][/tex]
Now, let's check each expression:
A. [tex]\( \frac{15}{\frac{3}{4}} = 20 \)[/tex] - This is a solution.
B. [tex]\( \frac{15}{\frac{4}{3}} \)[/tex] - This expression is equivalent to [tex]\( \frac{15 \times 3}{4} = \frac{45}{4} \)[/tex], not equal to 20.
C. [tex]\( \frac{4}{3} \times 15 = 20 \)[/tex] - This is a solution.
D. [tex]\( \frac{3}{4} \times 15 = 11.25 \)[/tex] - This is not equal to 20.
E. [tex]\( \frac{15}{\frac{3}{4}} \)[/tex] - This is equivalent to expression A, which is a solution.
Therefore, the expressions that are solutions to the equation[tex]\( \frac{3}{4}x = 15 \)[/tex] are A and C.
Complete Question: Which expressions are solutions to the equation 3/4 x=15 ? Select all that apply.
A. frac 15 3/4
B. frac 15 4/3
C. 4/3 · 15
D. 3/4 · 15
E. 15/ 3/4
A package has dimensions 10x10x6 inches mrs James wants to gift a wrap it for her grandson what is the total surface area to be wrapped?
Answer:
440 square inches
Step-by-step explanation:
10x10x2=200
10x6x4=240
240+200=440
Two angles are complementary. Angle 1 measures 33.5 degrees. What is the measure of Angle 2? *
A broken thermometer reads 33° F, but Kira knows that the temperature is at least 33° F, if not even colder. Which of the following inequalities, shows the possible temperatures? t ≤ 33° F t ≥ 33° F t > 33° F t < 33° F
Answer:
t ≤ 33
Step-by-step explanation:
The answer can be 33 or below.
The per capita electric power consumption level in a recent year in Ecuador is normally distributed, with a mean of 471.5 kilo-watt hours and a standard deviation of 187.9 kilowatt-hours. Random samples of size 35 are drawn from this population. Find (a) the mean and (b) the standard deviation of the sampling distribution of sample means. Round the answer from part (b) to the third decimal place.
Answer:
a) 471.5 kilo-watt hours.
b) 31.76 kilo-watt hours
Step-by-step explanation:
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
For the population:
Mean 471.5 kilo-watt hours.
Standard deviation of 187.9 kilowatt-hours.
For the sample:
Sample size of 35, by the Central Limit Theorem:
a) Mean
471.5 kilo-watt hours.
b) Standard deviation
[tex]s = \frac{187.9}{\sqrt{35}} = 31.76[/tex]
31.76 kilo-watt hours
Final answer:
The mean of the sampling distribution of sample means is 471.5 kilo-watt hours, and the standard deviation (or standard error) of the sampling distribution, rounded to the third decimal place, is 31.749 kilo-watt hours.
Explanation:
The question concerns the concept of sampling distribution and its parameters, namely the mean and standard deviation, within the field of statistics. Given that the per capita electric power consumption level in Ecuador is normally distributed with a mean of 471.5 kilo-watt hours and a standard deviation of 187.9 kilo-watt hours, and considering samples of size 35, we are to find the mean and standard deviation of the sampling distribution of sample means.
(a) The mean of the sampling distribution of sample means is equal to the population mean. Therefore, the mean is:
471.5 kilo-watt hours
(b) The standard deviation of the sampling distribution of sample means, also known as the standard error (SE), is calculated using the following formula:
SE = σ / √n
where σ is the population standard deviation and n is the sample size. In this case:
SE = 187.9 / √35 ≈ 31.749 kilo-watt hours (rounded to the third decimal place)
A shipment to a warehouse consists of 500 PS4. The manager chooses a random sample of 50 PS4 and finds that 3 are defective. How many PS4 in the shipment are likely to be defective?
Answer:
30 PS4 in the shipment are likely to be defective
Step-by-step explanation:
We take the estimate from the sample and estimate to all the PS4 in store. This means that we can solve this question using a rule of 3.
From the sample of 50 PS4, 3 are defective. How many are expected to be defective out of 500?
50PS4 - 3 defective
500 PS4 - x defective
[tex]50x = 3*500[/tex]
[tex]x = \frac{1500}{50}[/tex]
[tex]x = 30[/tex]
30 PS4 in the shipment are likely to be defective
Answer:
don't take my word but I think 150
Step-by-step explanation:
Select the correct answer.
Which value of x makes the equation true?
x + 7 = -9
A. -16
B. -2
C. 2
D. 16
The value of x makes the equation true is -16. Therefore, option A is the correct answer.
The given equation is x+7=-9.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
The given equation can be solved as follows:
x+7=-9
Transpose 7 to RHS of the equation, we get
x=-9-7
=-16
The value of x makes the equation true is -16. Therefore, option A is the correct answer.
To learn more about an equation visit:
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Which is the graph of the linear equation y= -1/3x +5
Answer:
x=-3(y-5)
Step-by-step explanation:
Mrs. Braddock has a bag containing 6 lipsticks, 4 eye shadows, 6 eye liners, and 5 mascaras. She will randomly choose one item from the bag.What is the probability that she will pull NOT lipstick? p(NOT lipstick). Round percents to nearest whole number
Answer:
The probability that she will not pull lipstick is 71%.
Step-by-step explanation:
The probability of an event E is the ratio of the favorable number of outcomes to the total number of outcomes.
[tex]P(E)=\frac{n(E)}{N}[/tex]
Here,
n (E) = favorable number of outcomes
N = total number of outcomes
The contents in Mrs. Braddock's bag are:
Number of lipsticks = n (L) = 6
Number of eye shadows = n (S) = 4
Number of eye liners = n (E) = 6
Number of mascaras = n (M) = 5
Total number of items in the bag = N = 21
Consider that the probability of an event occurring is P. Then the probability of the given event not taking place is known as the complement of that event.
Complement of the given event is, 1 – P.
Compute the probability of selecting a lipstick as follows:
[tex]P(L)=\frac{n(L)}{N}\\\\=\frac{6}{21}\\\\=\frac{2}{7}[/tex]
Compute the probability of not selecting a lipstick as follows:
[tex]P(L^{c})=1-P(L)[/tex]
[tex]=1-\frac{2}{7}\\\\=\frac{7-2}{7}\\\\=\frac{5}{7}[/tex]
Convert this probability into percentage as follows:
[tex]\frac{5}{7}\times 100 = 71.4286\approx 71\%[/tex]
Thus, the probability that she will not pull lipstick is 71%.
Which equation represents an exponential function with an initial value of 500?
Answer:
the fourth one
Step-by-step explanation:
Answer:
Answer: f(x) = 500(2)^x
Step-by-step explanation:
Just took the test .