A student has a monthly budget of $800. She can spend her budget on two items, X and Y. Each unit of X costs $20 and each unit of Y costs $10. If the student has a utility function of U = 348X + 100Y + 6X2 + 4Y2 + 2XY, what is the optimal amount of X and Y for her to consume to have the maximum utility? What is this total utility? What is the value of lambda and what does this mean?

Answer:

The y-intercept is y = 2

Step-by-step explanation:

A linear function has the following format:

[tex]y = mx + b[/tex]

In which m is the slope and b is the y-intercept, which is the value of y when x = 0.

We are given these three points:

(-28, -54)

(-21, -40)

(-14, -26)

We use two of them to build a system, to find values for m and b.

(-28, -54)

This means that when [tex]x = -28, y = -54[/tex]

So

[tex]y = mx + b[/tex]

[tex]-54 = -28m + b[/tex]

[tex]28m = b + 54[/tex]

[tex]m = \frac{b + 54}{28}[/tex]

(-21, -40)

This means that when [tex]x = -21, y = -40[/tex]

So

[tex]y = mx + b[/tex]

[tex]-40 = -21m + b[/tex]

[tex]-40 = -21\frac{b + 54}{28} + b[/tex]

[tex]-40 = \frac{-21b - 1134 + 28b}{28}[/tex]

[tex]7b - 1134 = -40*28[/tex]

[tex]7b = 14[/tex]

[tex]b = \frac{14}{7}[/tex]

[tex]b = 2[/tex]

The y-intercept is y = 2

Answer:

y = (0,2)

Step-by-step explanation:

Answer:

7

Step-by-step explanation:

Answer:

Claim is rejected

Step-by-step explanation:

Solution:-

- The claim was made on the effectiveness of medication on the market of Parkinson's disease to be p = 75%.

- A random sample was taken of N = 150 individuals and n = 100 number of people reported that it was effectively.

- We are to test the claim made by the manufacturer of the medication based on the statistics available for the sample N.

- State the hypothesis for the effectiveness of medication:

          Null Hypothesis: p = 0.75   ... Claim

          Alternate hypothesis: p < 0.75   .... Test

- The conditions of standard normality:

Hence, the standard normal test is applicable. Assuming the population proportion to be normally distributed.

- We will estimate the population proportion with the sample proportion ( p* ):

                          p* = n / N

                          p* = 100 / 150

                          p* = 2/3 = 0.667

- Testing against the claimed population proportion ( p ) = 0.75. The standard normal statistic value is given by:

                         [tex]Z-test= \frac{(p^* - p)}{\sqrt{p(1-p) / N} } \\\\Z-test= \frac{(0.6667 - 0.75)}{\sqrt{0.75(0.25) / 150} } \\\\Z-test= \frac{-0.0833}{\sqrt{0.00125} } \\\\Z-test= -2.35607 \\[/tex]

- We will see whether the Z-test statistic falls in the rejection region defined by the critical value of Z at significance level ( α ) of 0.05.

- The rejection region is defined by the Alternate hypothesis which is less than the claimed value. So, the rejection region defined by the lower tail of the standard normal.

- So for lower tailed test the critical value of statistics is:

                       P ( Z < Z-critical ) = α = 0.05

                       Z-critical = - 1.645

- The rejected values all lie to the left of the Z-critical value -1.645          

- The claim test value is compared the rejection region:

                      -2.35607 < -1.645

                       Z-test < Z-critical

Hence, Null hypothesis rejected because test lies in the rejection region.

Conclusion:

The Null hypothesis or claim made by the manufacturer of Parkinson's disease medication of 75% effectiveness is without sufficient evidence. Hence, the claim made is false or has no statistical evidence.

By calculating the Z-score and corresponding p-value for the statistical test, we found that there is significant evidence at the 0.05 level to suggest that the medication's effectiveness is less than the 75% claimed.

The subject we're dealing with here is hypothesis testing in statistics, where we have a claim (the effectiveness of the medication is 75%) and we are testing whether the observations (effectiveness in 100 out of 150 individuals) support this claim.

Firstly, the parameter of interest here is the proportion (p) of individuals for whom the medication is effective. Our null hypothesis (H0) is that p = 0.75 and our alternate hypothesis (Ha) is that p < 0.75.

To conduct the hypothesis test, let's check the conditions:

The sample proportion (p-hat) = 100/150 = 0.67

Next, we calculate the Z score, which is (p-hat - p) / sqrt[p(1-p)/n] = (0.67 - 0.75) / sqrt[0.75 * (0.25) / 150] = -1.65. The p-value associated with a Z score of -1.65 is 0.0495.

Since the p-value is less than the significance level of 0.05, we reject H0 and conclude that there is statistically significant evidence at the 0.05 level that the effectiveness of medication is less than 75% as claimed by the manufacturer.

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Answer:

-1

Step-by-step explanation:

The weight of the cell phone is given by:

[tex]W=2.8*10^n[/tex]

The options provided for 'n' are:

a. -3

b. -1

c. 0

d. 1

Applying the possible values:

[tex]W_a=2.8*10^{-3}\\W_a = 0.0028\ pounds\\\\W_b=2.8*10^{-1}\\W_b = 0.28\ pounds\\\\W_c=2.8*10^{0}\\W_c = 2.8\ pounds\\\\W_d=2.8*10^{1}\\W_d = 28\ pounds[/tex]

A cellphone could not possibly weigh as little as 0.0028 or as much as 2.8 or 28 pounds. Therefore, the most reasonable value for n is -1.

Answer:

(B)-1

Step-by-step explanation:

Let us plug in the given values into [tex]2.8X10^n[/tex][tex]2.8X10^{-3}=2.8X 0.001=0.0028\:Pounds\\2.8X10^{-1}=2.8X 0.1=0.28\:Pounds\\2.8X10^{0}=2.8X 1=2.8\:Pounds\\2.8X10^{1}=2.8X 10=28\:Pounds[/tex]

A reasonable value for the weight of a cell phone will be 0.28 Pounds.

Therefore, n=-1

Answer:

360

Step-by-step explanation:

Divide by two on both numbers to get how many out of 100, or a percentage.

72 / 2 = 36

200 / 2 = 100

Multiply times ten to get 1000

100 x 10 = 1000

36 x 10 = 360

Answer:

14%

Step-by-step explanation:

you divide 35 by 245 to get 0.14285714285 than you round

Answer:

Bruh i got correlation hw that i posted on here too and nobody helped lol.

Step-by-step explanation:

The comparison of the slopes is accurate: the slope of the line for Car 1 is greater than the slope of the line for Car 2.

Step 1:

The comparison of the slopes of the two lines can be made by calculating the slope of each line. Let's calculate the slopes:

For Car 1:

The coordinates are (2, 50) and (4, 100).

Using the slope formula [tex]\( m = \frac{y_2 - y_1}{x_2 - x_1} \)[/tex]:

[tex]\[ m = \frac{100 - 50}{4 - 2} = \frac{50}{2} = 25 \][/tex]

For Car 2:

The coordinates are (2, 40) and (4, 80).

Using the slope formula:

[tex]\[ m = \frac{80 - 40}{4 - 2} = \frac{40}{2} = 20 \][/tex]

Step 2:

Comparing the slopes:

- The slope of the line for Car 1 is 25.

- The slope of the line for Car 2 is 20.

Therefore, the comparison of the slopes is accurate: the slope of the line for Car 1 is greater than the slope of the line for Car 2.

The surface area of a square pyramid is found by adding the area of the square base to the area of the four triangular faces. If the side of the square base is 's' and the length of the slant height of the triangles is 'l', the formula is: Surface [tex]Area = s^2 + 2 * s * l.[/tex]

The net described in the question would form a square pyramid. To calculate the surface area of a square pyramid, you add the area of the square base to the combined areas of the four triangular faces. If the side of the square is 's' and the length of the slant height of the triangular faces is 'l', the formula is: Surface [tex]Area = s^2 + 2 * s * l.[/tex] The surface area is expressed in square units. For example, if the side of the square is 4 units and the slant height is 6 units, the surface area of the pyramid is [tex]4^2 + 2 * 4 * 6 = 16 + 48 = 64[/tex] square units.

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Answer:

8 to 20 1 to 4 4 to 10

Step-by-step explanation:

it was easy

Answer:

840cm³

Step-by-step explanation:

devide them into 2 shapes.

a×b×h

a×b×h

V=720cm³+120cm³=840cm³

Answer:

840 cm^3

Step-by-step explanation:

L x W x H = V

Split the prism into 2 different prisms.

6 is constant throughout the figure, so all we have to do is find the L and H of the two prisms and multiply them by 6.

15 x 8 = 120

The height of the higher prism can be determined by subtracting the bottom height from the total height.

12 - 8 = 4

5 x 4 = 20

Add the two side areas together.

20 + 120 = 140

Multiply by the width, 6.

140 x 6 = 840

Answer:

Check the explanation

Step-by-step explanation:

b ) [tex]P(s^2<p\sigma^2)=0.05[/tex]

or , [tex]P\left (\frac{(n-1)s^2}{\sigma^2}<(n-1)p \right )=0.05[/tex]

or , [tex]P\left (\chi^2_5<5p \right )=0.05=P(\chi^2_5< 1.145476 )[/tex]

or , 5p =1.145476

or , [tex]p =\frac{1.145476}{5}= 0.2290952[/tex]

Required percentage = 22.91

Answer:

Step-by-step explanation:

A 90° CCW rotation makes the transformation ...

  (x, y) ⇒ (-y, x)

A translation 3 left and 2 down makes the transformation ...

  (x, y) ⇒ (x -3, y-2)

The two transformations together are ...

  (x, y) ⇒ (-y-3, x -2)

Then the given points are transformed to ...

 A'(-6, -8)

  B'(-7, -6)

  C'(-6, -4)

  D'(-5, -6)

The student asked about the simple interest earned on an investment. The simple interest can be calculated using the formula I = PRT. For a principal of $21,500 at a 9% APR for 16 years, the interest earned is $30,960.

To calculate simple interest, you can use the formula I = PRT, where I is the interest, P is the principal amount (the initial amount of money), R is the rate of interest per period, and T is the time the money is invested for.

In this case, we have:

Plugging these values into the formula, we get:

I = PRT

I = $21,500 × 0.09 × 16

I = $30,960

The simple interest earned after 16 years is $30,960.

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Final answer:

The simple interest on $21,500 at 9% APR over 16 years is calculated using the formula I = PRT, which gives us a total interest of $30,960.

Explanation:

To calculate the simple interest earned on a sum of money, we can use the formula I = PRT, where I stands for interest, P for principal amount, R for the annual interest rate (in decimal form), and T for the time in years. In this case, the student wants to determine the interest earned on $21,500 at 9% APR for 16 years.

First, convert the interest rate from a percentage to a decimal by dividing by 100:

R = 9% / 100 = 0.09

Next, apply the values to the simple interest formula:

I = PRT

I = $21,500 × 0.09 × 16

I = $30,960

Therefore, the total simple interest earned after 16 years is $30,960.

Answer:20000ft^3

Step-by-step explanation:

volume of triangular prism:

Base area x height

1/2 x 20 x 20 x40

(1x20x20x40) ➗ 2

16000 ➗ 2=8000ft^3

Volume of rectangular prism:

Length x width x height

40 x 15 x 20=12000ft^3

Total volume=8000+12000

Total volume=20000ft^3

The total amount of volume inside the parking garage = 20,000 cu. ft.

The volume of the triangular prism = base area × height

V = l × b × h, where 'l' represents the length, 'w' represents the width and 'h' represents the height of the rectangular prism

For given example,

Let V1 represents the volume of the triangular prism and V2 represents the volume of the rectangular prism.

Dimensions of the triangular prism are:

Base - 20 feet by 20 feet and Height - 40 feet

The base of the triangular prism is a triangle.

So, the area of the base would be,

⇒ A = 1/2 × 20 × 20

⇒ A = 200 sq. ft.

The volume of the triangular prism would be,

⇒ V1 = base area × height

⇒ V1 = 200 × 40

⇒ V1 = 8,000 cubic feet

Now, the dimensions of the rectangular prism are:

Base - 15 feet by 40 feet and Height - 20 feet

⇒ l = 40ft., w = 15 ft., h = 20 ft.

The volume of the rectangular prism would be,

⇒ V2 = l × w × h

⇒ V2 = 40 × 15 × 20

⇒ V2 = 12,000 cu. ft.

So, the total amount of volume inside the parking garage would be,

⇒ V = V1 + V2

⇒ V = 8000 + 12000

⇒ V = 20,000 cu. ft.

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Answer:

Part a

For the given study, the explanatory variable or independent variable is given as regularity or frequency of exercise. This variable is classify as categorical variable because variable is divided into two categories such as whether participant exercise 5 or more days a week or not.

Part b

For the given study, the response variable or dependent variable is given as frequency of colds. This variable is classified as quantitative variable because we measure the quantities or frequency of number of colds.

Part c

A confounding variable for this research study is given as incidence of upper respiratory tract infections that provides an alternative explanation for the lower frequency of colds among those who exercised 5 or more days per week, compared to those who were largely sedentary. This confounding variable is categorical in nature.

Under a normal distribution with a mean of 16 ounces and a standard deviation of 0.5 ounce, there's a 15.87% probability that a randomly selected can will have less than 15.5 ounces of soda.

This question is related to probability within the field of statistics. Particularly, it's about the normal distribution, a common statistical distribution that shows the spread of data around the mean. In this specific case, the amount of soda in a 16-ounce can is normally distributed with a mean (µ) of 16 ounces and a standard deviation (σ) of 0.5 ounce.

We're asked to calculate the probability that a randomly selected can will have less than 15.5 ounces. This requires us to standardize the score of 15.5, meaning we use the formula (X - µ) / σ, where X is the value we are assessing. So, (15.5 - 16) / 0.5 equals -1.

This standardized score is known as a z-score, and tells us how many standard deviations a value is from the mean. In this case, 15.5 is one standard deviation below the mean. We then look up this z-score in a z-table, which gives us the probability associated with this z-score. For a z-score of -1, the probability is 0.1587, or 15.87%.

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The probability that a randomly selected can will have less than 15.5 ounces is approximately 0.1587.

To find the probability that a randomly selected can will have less than 15.5 ounces, we can use the standard normal distribution.

First, we need to calculate the z-score for 15.5 ounces using the formula:

where:

Plugging in the values:

Next, we look up the z-score of -1 in the standard normal distribution table to find the probability. The probability that a randomly selected can will have less than 15.5 ounces is the area to the left of the z-score of -1.

Using the standard normal distribution table, the area to the left of -1 is approximately 0.1587.

Therefore, the probability that a randomly selected can will have less than 15.5 ounces is approximately 0.1587.

The length of the L of the ramp, which the builder makes with a base to height ratio of 12 to 1 is 9.63 meter.

Pythagoras theorem states that, right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

A builder makes all the ramps with a base to height ratio of 12 to 1 to be wheelchair accessible.

Let p is the factor of ratio. Thus, the height and base is,

h = p

b = 12p

According to Pythagoras theorem,

unknown side (say l) is hypotenuse

l² = (12p)² + p²

[tex]l^2=144p+p^2[/tex]

[tex]l = \sqrt{144p+p^2}[/tex]

[tex]l = \sqrt{145} p[/tex]

A ramp needs to cover a height of 0.8 m. Height is equal to the factor p.

Thus, the value of p is,

p = h

p = 0.80

Thus, the length of the l is,

[tex]l = \sqrt{145} p[/tex]

[tex]l = \sqrt{145} {(0.8)}[/tex]

[tex]l=(12.041)(0.8)[/tex]

[tex]l=9.63m[/tex]

Hence, the length of the L of the ramp, which the builder makes with a base to height ratio of 12 to 1 is 9.63 meter.

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The correct question has in the image below

Answer:

-0.71828

Step-by-step explanation:

2 + e(6-7)

2 + e(-1)

2 -e

e is approximately 2.718281828459045235360287471352662497757247093699959574966

2 - 2.71828.....

-0.71828

Answer:

2.37 (3 sf)

Step-by-step explanation:

2 + e^(6-7)

2 + e^(-1)

2 + 1/e (exact)

Roughly, 2.367879441

Angle: [tex]\( 60^\circ \)[/tex], complementary angle: [tex]\( 30^\circ \)[/tex]. Angle is 30° more than its complementary angle.

Let's denote the measure of the angle as [tex]\( x \)[/tex] degrees.

The complementary angle would be [tex]\( 90^\circ - x \)[/tex] degrees.

Given that the angle measures 30° more than its complementary angle, we can write the equation:

[tex]\[ x = (90^\circ - x) + 30^\circ \][/tex]

Now, let's solve for [tex]\( x \)[/tex]:

[tex]\[ x = 90^\circ - x + 30^\circ \][/tex]

[tex]\[ 2x = 90^\circ + 30^\circ \][/tex]

[tex]\[ 2x = 120^\circ \][/tex]

Dividing both sides by 2:

[tex]\[ x = \frac{120^\circ}{2} \][/tex]

[tex]\[ x = 60^\circ \][/tex]

So, the angle measures [tex]\( 60^\circ \)[/tex] and its complementary angle measures:

[tex]\[ 90^\circ - 60^\circ = 30^\circ \][/tex]

Therefore, the measure of the angle is [tex]\( 60^\circ \)[/tex] and the measure of its complementary angle is [tex]\( 30^\circ \)[/tex].

Answer:

Point Estimate for different between population means = - 0.99

Step-by-step explanation:

We are given data of two samples and we have to find the best point estimate of the true difference between two population means. Remember that in absence of data about population the best estimator is the sample data. So, we will find the means of both sample data and find the difference of that means. This difference between the means of sample data will be the best point estimate for the true difference between the population means.

Formula to calculate the mean is:

[tex]Mean=\frac{\text{Sum of Values}}{\text{Number of Values}}[/tex]

Mean of Sample 1:

[tex]Mean=\frac{1414}{11}=128.55[/tex]

Mean of Sample 2:

[tex]Mean=\frac{1684}{13}=129.54[/tex]

Therefore the best point estimate for difference between two population means would be = Mean of Sample 1 - Mean of Sample 2

= 128.55 - 129.54

= - 0.99

Final answer:

The point estimate for the true difference between the given population means is -1.028.

Explanation:

The point estimate for the true difference between the given population means can be found by subtracting one sample mean from the other. Let's calculate it:

Sample 1: 129, 127, 129, 129, 128, 130, 127, 129, 128, 131, 127
Sample 2: 131, 126, 132, 129, 128, 131, 131, 130, 128, 129, 126, 132, 131

Sample mean of Sample 1 = (129+127+129+129+128+130+127+129+128+131+127)/11 = 128.818

Sample mean of Sample 2 = (131+126+132+129+128+131+131+130+128+129+126+132+131)/13 = 129.846

Point estimate for the difference = Sample mean of Sample 1 - Sample mean of Sample 2 = 128.818 - 129.846 = -1.028

Answer:

114 square meters

Step-by-step explanation:

formula:1/2×h(a+b)

1/2×12{(12+5)+12}

1/2×12(17+12)

=6×19

=114m^2

Answer:

The way you worded this he should buy at either store because the price is 20 at both and he won't have any savings because they have the same price.

Step-by-step explanation:

Answer:

Well correct me if I am wrong but I think something is missing in this problem because I do not see another number to compare $20 to...

Answer:

The objective of the confidence interval is to give a range in which the real mean of the population is placed, with a degree of confidence given by the level of significance.

The conclusion we can make is that there is 95% of probability that the mean of the population (professor's average salary) is within $99,881 and $171,172.

Step-by-step explanation:

This is a case in which, from a sample os size n=16, a confidence interval is constructed.

The objective of the confidence interval is to give a range in which the real mean of the population is placed, with a degree of confidence given by the level of significance. In this case, the probability that the real mean is within the interval is 95%.

Answer:

25 miles per gallon x 7 gallons used=175 miles driven

175/7=25

NOTE: THIS IS AN EXAMPLE

Answer:

7

Step-by-step explanation:

67ururiierururf8fucicififfifig

Answer:

the answer is a it increases

Step-by-step explanation:

Answer:

(A)-  It increases

Step-by-step explanation:

Good luck with your unit test for Kahn!!

Answer:

We showed that if we have the position of the particle [tex]x(t)= \frac{t^2 - 9}{3t^2 + 8}[/tex] the velocity of the particle at time t is given by [tex]v(t)=\frac{70t}{\left(3t^2+8\right)^2}[/tex].

Step-by-step explanation:

Velocity is defined as the rate of change of position with respect to time.

                                                  [tex]v(x)=\frac{dx}{dt}[/tex]

To find velocity, we take the derivative of the position function [tex]x(t)= \frac{t^2 - 9}{3t^2 + 8}[/tex]

[tex]\mathrm{Apply\:the\:Quotient\:Rule}:\quad \left(\frac{f}{g}\right)'=\frac{f\:'\cdot g-g'\cdot f}{g^2}[/tex]

[tex]\frac{d}{dt}\left(\frac{t^2-9}{3t^2+8}\right)=\frac{\frac{d}{dt}\left(t^2-9\right)\left(3t^2+8\right)-\frac{d}{dt}\left(3t^2+8\right)\left(t^2-9\right)}{\left(3t^2+8\right)^2}[/tex]

Next, we find the values of [tex]\frac{d}{dt}\left(t^2-9\right)[/tex] and [tex]\frac{d}{dt}\left(3t^2+8\right)[/tex]

[tex]\frac{d}{dt}\left(t^2-9\right)=\frac{d}{dt}\left(t^2\right)-\frac{d}{dt}\left(9\right)=2t-0=2t[/tex]

[tex]\frac{d}{dt}\left(3t^2+8\right)=\frac{d}{dt}\left(3t^2\right)+\frac{d}{dt}\left(8\right)=6t+0=6t[/tex]

So,

[tex]\frac{d}{dt}\left(\frac{t^2-9}{3t^2+8}\right)=\frac{2t\left(3t^2+8\right)-6t\left(t^2-9\right)}{\left(3t^2+8\right)^2}[/tex]

Next, we expand [tex]2t\left(3t^2+8\right)-6t\left(t^2-9\right)[/tex]

[tex]2t\left(3t^2+8\right)-6t\left(t^2-9\right)=6t^3+16t-6t\left(t^2-9\right)=6t^3+16t-6t^3+54t=70t[/tex]

Therefore,

[tex]v(t)=\frac{d}{dt}\left(\frac{t^2-9}{3t^2+8}\right)=\frac{70t}{\left(3t^2+8\right)^2}[/tex]

This question lies in high school level Mathematics, more specifically in calculus. The process includes finding the derivative of a function x(t) to get v(t), which is the velocity of the particle. There appears to be an error in the provided equations in the question.

The subject of this question falls under calculus, a branch of Mathematics, and the grade level would most likely be High School. The equation for the particle's position in terms of time x(t)=(t^2 - 9)/(3t^2 + 8) indicates the focus is on particle motion.

To find the velocity of a particle moving along a line at a given time, we find the derivative of the position function. This principle comes from the fact that velocity is the rate of change of position with respect to time. In this case, the derivative of the position function x(t) gives the velocity function v(t).

However, it seems there might be a mistake in the question because the derivative of x(t) is not v(t)=70t/(30t^2 + 8)^2. Please double-check the original problem to ensure the equations are correctly provided.

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