At a candy store, 3 giant lollipops sell for $7.59 and 2 small packets of bubblegum cost $4.82. Which is a better buy?

Answer:

a) We have evidence of the " center stage effect" pair number 3 was selected 34 times almost double the probability of random process

b) probability of ocurrency in random case is 20 %

Step-by-step explanation:

To answer this question we first look at the probability of chossing a pair in case of random selection

P = successful event / total outcomes

P₁ = 1/5

P₁ = 0,2    or   P₁ = 20 %

Then if the central pair was selected  34 times from 100 participants          ( almost the double ) we have evidence of the center stage effect

P₂  = 34/100   or   P₂  = 0,34

In this experiment, the data showing 34 subjects choosing the center pair of socks out of 100 participants does indicate evidence of the "center stage effect" as the observed frequency surpasses the expected frequency under randomness.

To determine if the data provided is evidence of the "center stage effect," we need to analyze whether the subjects' choices align with randomness or if there is a noticeable bias towards the center socks.

1. Calculate the expected frequency of selecting the center pair of socks under the assumption of randomness:
- Since there are 5 pairs of socks, the chance of randomly selecting the center pair would be 1 out of 5.
- This gives us a probability of 1/5  or 0.2.

2. Determine the expected number of subjects choosing the center pair out of 100 participants:
- Expected frequency = Probability of selection x Total number of participants
- Expected frequency = 0.2 x 100 = 20

3. Compare the expected frequency (20) with the actual frequency observed in the data (34):
- If the observed frequency significantly exceeds the expected frequency, it suggests a bias towards selecting the center pair of socks, supporting the "center stage effect" hypothesis.

Therefore, in this experiment, the data showing 34 subjects choosing the center pair of socks out of 100 participants does indicate evidence of the "center stage effect" as the observed frequency surpasses the expected frequency under randomness.

Answer:

-3

Step-by-step explanation:

i know because i took the test

Answer:

-3 a)

Step-by-step explanation:

bc

Answer:

4.17

Step-by-step explanation:

Answer:

4.17 is greater than 4.085

Step-by-step explanation:

Answer:

The mean and standard deviation of the number preferring the incumbent is mean = 330, standard deviation = 10.59.

Step-by-step explanation:

We are given that From previous polls, it is believed that 66% of likely voters prefer the incumbent.

A new poll of 500 likely voters will be conducted. In the new poll the proportion favoring the incumbent has not changed.

Let p = probability of voters preferring the incumbent = 66%

n = number of voters polled = 500

So, the mean of the number preferring the incumbent is given by;

         Mean = [tex]n \times p[/tex] = [tex]500 \times 0.66[/tex]

                                = 330 voters

And, standard deviation of the number preferring the incumbent is given by;

          Variance =  [tex]n \times p\times (1-p)[/tex]  

                          =  [tex]500 \times 0.66 \times (1-0.66)[/tex]

                          =  112.2

So, Standard deviation =  [tex]\sqrt{Variance}[/tex]

                                       = [tex]\sqrt{112.2}[/tex]  = 10.59

Based on the binomial distribution and the probability of 66%, the mean number of likely voters favoring the incumbent is 330, and the standard deviation is approximately 18.17.

In this scenario, we are working with a binomial distribution where we have a fixed number of trials, each trial has two possible outcomes (in this case, favoring the incumbent or not), the probability of success is constant, and the trials are independent. Here, a success is a likely voter favoring the incumbent.

To find the mean of the number preferring the incumbent, we use the formula μ = np, where n is the number of trials (or voters), and p is the probability of a success. Thus, the mean is 500 voters times 66%, which gives us:

μ = 500 * 0.66 = 330.

The formula for the standard deviation (σ) of a binomial distribution is σ = √npq, where q is the probability of failure (1 - p). Therefore, standard deviation is:

σ = √(500 * 0.66 * (1 - 0.66)) = 18.17.

The correct answer is: mean = 330, standard deviation = 18.17

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Answer: The weekly demand equation would  be

[tex]p=-0.2m+84.8[/tex]

Step-by-step explanation:

Since we have given that

Number of units of their portable media player = 109 units per week

Cost per unit = $63.00

At unit price of $12.80, consumer are buying 360 units per week.

So, here, p = $63.00 and x = 109 units

Here, price and quantity are linearly related by

[tex]p=mx+b\\\\63=109m+b\\\\63-109m=b-----------------(1)[/tex]

If p = $12.80, x= 360

So, the equation of price would be

[tex]12.80=360m+b\\\\12.80-360m=b-------------(2)[/tex]

From eq(1) and (2), we get that

[tex]63-109m=12.80-360m\\\\63-12.80=-360m+109m\\\\50.20=-251m\\\\\dfrac{50.2}{251}=-m\\\\-0.2=m[/tex]

So, the value of b would be

[tex]63=109m+b\\\\63-109(-0.2)=b\\\\63+21.8=b\\\\84.8=b[/tex]

So, the weekly demand equation would  be

[tex]p=-0.2m+84.8[/tex]

Answer:

Radius = 6.5cm

Diameter = 13cm (given)

Step-by-step explanation:

The diameter is the length of one side of a circle to the other. It's already given in the diagram as 13cm.

The radius is half of the diameter. 13 divided by 2 is 6.5cm.

The correct answer are as follows

Radius = 6.5 cm

Diameter = 13 cm

So , The diameter is 13cm

and The radius is 1/2 x diameter = 1/2 x13 = 6.5cm

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Approximately 215 samples are needed for a 95% confidence interval estimating the mean breakdown voltage with a 2 kV width and a 1 kV margin of error, assuming the range is 40 to 70 kV.

To determine the required sample size for estimating the mean breakdown voltage with a 95% confidence interval (CI) width of 2 kV and an estimated margin of error (m) of 1 kV, you can use the formula:

[tex]\[ n = \left(\frac{{Z^2 \cdot \sigma^2}}{{m^2}}\right) \][/tex]

Where:

- n is the required sample size,

- Z is the Z-score corresponding to the desired confidence level (for 95%, it's approximately 1.96),

- [tex]\( \sigma \)[/tex] is the estimated standard deviation of the population.

Since you mentioned the investigator believes breakdown voltage is between 40 and 70, assuming a uniform distribution, you might consider using [tex]\( \sigma = \frac{{\text{{range}}}}{4} \)[/tex] as an approximation. Therefore,

[tex]\[ \sigma = \frac{{70 - 40}}{4} = 7.5 \][/tex]

Now plug these values into the formula:

[tex]\[ n = \left(\frac{{1.96^2 \cdot 7.5^2}}{{1^2}}\right) \][/tex]

Let's calculate the required sample size n:

[tex]\[ n = \frac{{(1.96)^2 \cdot (7.5)^2}}{{1^2}} \]\[ n = \frac{{3.841 \cdot 56.25}}{{1}} \]\[ n \approx \frac{{214.6}}{{1}} \]\[ n \approx 214.6 \][/tex]

So, the required sample size for the 95% confidence interval to have a width of 2 kV (with a margin of error of 1 kV) is approximately 215.

Therefore, the investigator would need a sample size of about 215 to estimate the mean breakdown voltage with the desired level of confidence and precision.

Answer:

[tex]t=\frac{180-175}{\frac{4}{\sqrt{15}}}=4.84[/tex]    

[tex]df=n-1=15-1=14[/tex]  

[tex]p_v =P(t_{(14)}>4.84)=0.000131[/tex]  

We got a very low value for the p value so then we have enough evidence to reject the null hypothesis at any significance level commonly used. And the best conclusion based on the possible options are:

None of the above are true

Step-by-step explanation:

Data given

[tex]\bar X=180[/tex] represent the sample mean

[tex]s=4[/tex] represent the sample standard deviation

[tex]n=15[/tex] sample size  

[tex]\mu_o =175[/tex] represent the value that we want to test

[tex]\alpha=0.1[/tex] represent the significance level for the hypothesis test.  

t would represent the statistic (variable of interest)  

[tex]p_v[/tex] represent the p value for the test (variable of interest)  

System of hypothesis

We need to conduct a hypothesis in order to check if the true mean is above the limit of 175 degrees, the system of hypothesis would be:  

Null hypothesis:[tex]\mu \leq 175[/tex]  

Alternative hypothesis:[tex]\mu > 175[/tex]  

The statistic is given by:

[tex]t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex]  (1)  

And replacing we got:

We can replace in formula (1) the info given like this:  

[tex]t=\frac{180-175}{\frac{4}{\sqrt{15}}}=4.84[/tex]    

P-value

The degrees of freedom are given by:

[tex]df=n-1=15-1=14[/tex]  

Since is a one sided test the p value would be:  

[tex]p_v =P(t_{(14)}>4.84)=0.000131[/tex]  

We got a very low value for the p value so then we have enough evidence to reject the null hypothesis at any significance level commonly used. And the best conclusion based on the possible options are:

None of the above are true

The carnivores mammals are (1/2) of the total animals in the natural park.

Step-by-step explanation:

Let the total no. of animals be 'a'

The amount of mammals = (3/5)a

The amount of carnivores= (5/6) (3/5) a

= (1/2) a

So, the carnivores mammals are (1/2) of the total animals in the natural park.

Answer:

(a) The variance decreases.

(b) The variance increases.

Step-by-step explanation:

According to the Central Limit Theorem if we have a population with mean μ and standard deviation σ and we take appropriately huge random samples (n ≥ 30) from the population with replacement, then the distribution of the sample mean will be approximately normally distributed.

Then, the mean of the sample mean is given by,

[tex]\mu_{\bar x}=\mu[/tex]

And the standard deviation of the sample mean is given by,

[tex]\sigma_{\bar x}=\frac{\sigma}{\sqrt{n}}[/tex]

The standard deviation of sample mean is inversely proportional to the sample size, n.

So, if n increases then the standard deviation will decrease and vice-versa.

(a)

The sample size is increased from 64 to 196.

As mentioned above, if the sample size is increased then the standard deviation will decrease.

So, on increasing the value of n from 64 to 196, the standard deviation of the sample mean will decrease.

The standard deviation of the sample mean for n = 64 is:

[tex]\sigma_{\bar x}=\frac{\sigma}{\sqrt{n}}=\frac{5.6}{\sqrt{64}}=0.7[/tex]

The standard deviation of the sample mean for n = 196 is:

[tex]\sigma_{\bar x}=\frac{\sigma}{\sqrt{n}}=\frac{5.6}{\sqrt{196}}=0.4[/tex]

The standard deviation of the sample mean decreased from 0.7 to 0.4 when n is increased from 64 to 196.

Hence, the variance also decreases.

(b)

If the sample size is decreased then the standard deviation will increase.

So, on decreasing the value of n from 784 to 49, the standard deviation of the sample mean will increase.

The standard deviation of the sample mean for n = 784 is:

[tex]\sigma_{\bar x}=\frac{\sigma}{\sqrt{n}}=\frac{5.6}{\sqrt{784}}=0.2[/tex]

The standard deviation of the sample mean for n = 49 is:

[tex]\sigma_{\bar x}=\frac{\sigma}{\sqrt{n}}=\frac{5.6}{\sqrt{49}}=0.8[/tex]

The standard deviation of the sample mean increased from 0.2 to 0.8 when n is decreased from 784 to 49.

Hence, the variance also increases.

Variance has decreased in first case and Variance has increased in second case.

What information do we have?

Mean tensile stength = 78.3 kilograms

Standard variance = 5.6 kilogram

Variance = sigma² / n

A.

Variance of sample mean with sample size 64 = 5.6² / 64

Variance of sample mean with sample size 64 = 0.49

Variance of sample mean with sample size 196 = 5.6² / 196

Variance of sample mean with sample size 196 = 0.16

Variance has decreased.

B.

Variance of sample mean with sample size 784 = 5.6² / 784

Variance of sample mean with sample size 784 = 0.04

Variance of sample mean with sample size 49 = 5.6² / 49

Variance of sample mean with sample size 49 = 0.64

Variance has increased.

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Answer:

30

Step-by-step explanation:

6*5= 30

3*10= 30

5*6= 30

The Lowest Common Multiple of 3, 5, and 6. is 30

The lowest common multiple of a group of numbers is the smallest number that is a multiple of all the numbers.

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Answer:

n= - 11/3

Step-by-step explanation:

3(n+8)=13

3n+24=13

3n=13-24

3n-11

n= - 11/3

Answer:

A Non-Bank Financial Institution (NBFI)

Step-by-step explanation:

A Non-Bank Financial Institution (NBFI) can be described as any institution without full banking license but offers loans and other financial services.

They are able to provide low cost loans due to the fact that they are privately owned and operated by individuals, as a result of this, they're mostly used by small and medium-sized enterprise.

A Non-Bank Financial Institution (NBFI) includes;

- Insurance companies.

- Pension funds.

- Pawn shops.

- Thrift or mutual credit societies.

- Credit unions.

Answer:

[tex]2t^3+15t^2+19t+6[/tex]

Step-by-step explanation:

Height of the Rectangle[tex]=t^2+7t+6[/tex]

Width of the Rectangle[tex]=2t+1[/tex]

Area of the Rectangle = Height X Width

[tex]=(2t+1)(t^2+7t+6)\\=2t(t^2+7t+6)+1(t^2+7t+6)\\=2t^3+14t^2+12t+t^2+7t+6\\$Collect like terms\\=2t^3+14t^2+t^2+12t+7t+6\\Area=2t^3+15t^2+19t+6\\[/tex]

The area of the rectangle is [tex]2t^3+15t^2+19t+6[/tex]

The height of the rectangle is[tex]t^4 + 26t^3 + 169t^2 + 7t + 6,[/tex] and the width is 26t + 1.

It seems there might be some confusion in the way the dimensions of the rectangle are presented. To clarify, let's break down the height and width of the rectangle:

Height:

The height of the rectangle is given as [tex](t^2 + 7t + 6t)^2[/tex] + 7t + 6.

To simplify the expression inside the parentheses:

[tex](t^2 + 7t + 6t)^2[/tex] = [tex](t^2 + 13t)^2[/tex]= [tex]t^4 + 26t^3 + 169t^2[/tex]

So, the height of the rectangle is[tex]t^4 + 26t^3 + 169t^2 + 7t + 6.[/tex]

Width:

The width of the rectangle is given as 2t + 12t + 12t + 1.

Combine like terms in the width expression:

2t + 12t + 12t + 1 = 26t + 1

So, the width of the rectangle is 26t + 1.

Now you have the height and width of the rectangle expressed as functions of "t":

Height = [tex]t^4 + 26t^3 + 169t^2 + 7t + 6.[/tex]

Width = 26t + 1

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Answer:

- There is enough evidence to support the claim that the heart rate level lower than 120 bpm  (P-value=0.002).

- The 95% confidence interval for the population mean weight control heart rate of 20-year-olds is (98.07, 115.93).

Step-by-step explanation:

This is a hypothesis test for the population mean.

The claim is that the heart rate level lower than 120 bpm

Then, the null and alternative hypothesis are:

[tex]H_0: \mu=120\\\\H_a:\mu< 120[/tex]

The significance level is 0.05.

The sample has a size n=100.

The sample mean is M=107.

As the standard deviation of the population is not known, we estimate it with the sample standard deviation, that has a value of s=45.

The estimated standard error of the mean is computed using the formula:

[tex]s_M=\dfrac{s}{\sqrt{n}}=\dfrac{45}{\sqrt{100}}=4.5[/tex]

Then, we can calculate the t-statistic as:

[tex]t=\dfrac{M-\mu}{s/\sqrt{n}}=\dfrac{107-120}{4.5}=\dfrac{-13}{4.5}=-2.889[/tex]

The degrees of freedom for this sample size are:

[tex]df=n-1=100-1=99[/tex]

This test is a left-tailed test, with 99 degrees of freedom and t=-2.889, so the P-value for this test is calculated as (using a t-table):

[tex]P-value=P(t<-2.889)=0.002[/tex]

As the P-value (0.002) is smaller than the significance level (0.05), the effect is  significant.

The null hypothesis is rejected.

There is enough evidence to support the claim that the heart rate level lower than 120 bpm .

Confidence interval:

We have to calculate a 95% confidence interval for the mean.

The population standard deviation is not known, so we have to estimate it from the sample standard deviation and use a t-students distribution to calculate the critical value.

The sample mean is M=107.

The sample size is N=100.

When σ is not known, s divided by the square root of N is used as an estimate of σM:

[tex]s_M=\dfrac{s}{\sqrt{N}}=\dfrac{45}{\sqrt{100}}=\dfrac{45}{10}=4.5[/tex]

The t-value for a 95% confidence interval is t=1.984.

The margin of error (MOE) can be calculated as:

[tex]MOE=t\cdot s_M=1.984 \cdot 4.5=8.929[/tex]

Then, the lower and upper bounds of the confidence interval are:

[tex]LL=M-t \cdot s_M = 107-8.929=98.07\\\\UL=M+t \cdot s_M = 107+8.929=115.93[/tex]

The 95% confidence interval for the population mean weight control heart rate of 20-year-olds is (98.07, 115.93).

Using the t-distribution, it is found that the 95% confidence interval for the population mean weight control heart rate is (98.07, 115.93). Since the entire interval is lower than 120 bpm, it is evidence to conclude that the expected level is actually lower than 120 bpm.

We are given the standard deviation for the sample, which is why the t-distribution is used to solve this question.

The information given is:

The confidence interval is:

[tex]\overline{x} \pm t\frac{s}{\sqrt{n}}[/tex]

The critical value, using a t-distribution calculator, for a two-tailed 95% confidence interval, with 100 - 1 = 99 df, is t = 1.984.

Hence:

[tex]\overline{x} - t\frac{s}{\sqrt{n}} = 107 - 1.984\frac{45}{\sqrt{100}} = 98.07[/tex]

[tex]\overline{x} + t\frac{s}{\sqrt{n}} = 107 + 1.984\frac{45}{\sqrt{100}} = 115.93[/tex]

The 95% confidence interval for the population mean weight control heart rate is (98.07, 115.93). Since the entire interval is lower than 120 bpm, it is evidence to conclude that the expected level is actually lower than 120 bpm.

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Answer:

70%

Step-by-step explanation:

Answer:

0.10

Step-by-step explanation:

The experimental likelihood of getting a 50% coupon is thus 2/20, or 0.1 to the decimal place.

The likelihood of rolling any one of the number cube's 6 equally likely results is 1/6. We must roll the number cube 20 times and tally how many times we receive a 50% discount in order to determine the experimental chance of doing so.

Assume that rolling a 1, 2, or 3 means you won't receive a coupon, a 4 means you'll receive a 25% coupon, a 5 means you'll receive a 50% coupon, and a 6 means you'll receive a 75% coupon.

The following outcomes are possible after 20 rolls of the number cube:

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Answer: 4/25

Step-by-step explanation:

answer

graph a

speeds up from (0,1) U (2,3) and slows down from (1,2)

if it marks (2,3) incorrectly, it may be from (2,∞) instead

graph b

speeds up from (1,2) U (3,4) and slows down from (0,1) U (2,3)

if it marks (3,4) incorrectly, it may be from (3,∞) instead

step-by-step explanation

looking at the velocity graphs, when the absolute value of velocity is increasing (moving away from the x axis), the particle must be speeding up. we say absolute value because while velocity has direction, speed only has magnitude, so we need to take the absolute value of velocity to get speed.

for graph a, we can see the velocity moving away from the x axis during the interval (0,1), moving towards the x axis during the interval (1,2) and then moving away again during the interval (2,3)

so it speeds up from (0,1) U (2,3) and slows down from (1,2)

if it marks (2,3) incorrectly, it may be from (2,∞) instead since this is at an endpoint

repeat for graph b where it moves toward the x axis from (0,1), moves away from (1,2), moves towards from (2,3), and moves away again from (3,4)

so it speeds up from (1,2) U (3,4) and slows down from (0,1) U (2,3)

if it marks (3,4) incorrectly, it may be from (2,∞) instead since this is at an endpoint

Answer:

The probability is 0.9583

Step-by-step explanation:

First, we have 2 possibilities, Bob's outcome is heads or Bob's outcome is tails.

If Bob's outcome is heads, the probability that Chuck doesn't get a king is equal 1, because there aren't kings in the poker deck. it means that if Bob's outcome is heads, the probability that David raises a green flag is 1.

On the other hand, if Bob's outcome is tails, the probability that Chuck doesn't get a king is equal to:

[tex]\frac{44}{48}=0.9166[/tex]

Because there are 48 cards in the poker deck (without the 4 aces) and 44 of them aren't kings. So, if Bob's outcome is Tails, the probability that David raises a green flag is 0.9166.

Now, the probability that David raises a green flag is calculated as:

[tex]P=0.5(1)+0.5(0.9166)=0.9583[/tex]

Because there is a probability of 0.5 that Bob's outcome is heads and there is a probability of 0.5 that Bob's outcome is Tails.

Answer:

Each friend would get 100000000

Step-by-step explanation:

1000000000 ÷ 10 = 100000000

Answer:

$100,000,000

Step-by-step explanation:

divide 1,000,000,000 by 10, be sure to count your zeros.

Answer:

Check the explanation

Step-by-step explanation:

(a) Best decision based on maximax criterion= large facility

maximum in the two facilities is $300 and $800 of which $800 is the maximum, So larger facility satisfies maximax.

(b) Best decision based on maximin criterion= small facility

minimum in the two facilities is $100 and -$200 of which $100 is the maximum, So smaller facility satisfies maximin.

(c) Best decision based on minimax regret= large facility

maximum in the two facilities is $300 and $800 of which $300 is the minimum, So larger facility satisfies minimax regret.

Final answer:

Explanation of maximax, maximin, and minimax regret criteria for decision-making in uncertain scenarios.

Explanation:

Maximax criterion: This criterion involves selecting the decision with the maximum possible payoff under each possible outcome. In this case, the manager would choose the large facility due to the potential high payoff of $800 in case of high demand.

Maximin criterion: This criterion involves selecting the decision with the maximum possible payoff under the worst-case scenario. Here, the manager would choose the small facility to minimize the loss to -$200 in case of low demand.

Minimax regret: This criterion involves minimizing the maximum regret that could be incurred based on the wrong decision. The manager would need to calculate regrets for each decision and choose the one with the least possible regret

Step-by-step explanation:

[tex](7g + 3)( - g - 3) \\ = 7g( - g - 3) + 3( - g - 3) \\ = - 7 {g}^{2} - 21g - 3g - 9 \\ \red{ \bold{ = - 7 {g}^{2} - 24g - 9 }} \\ is \: in \: the \: standard \: form.[/tex]

-7g² - 24g - 9 is the polynomial in standard form.

In equations like the quadratic equation, cubic equation, etc., a polynomial function is a function that only uses non-negative integer powers or only positive integer exponents of a variable.

Given an equation (7g+3)(−g−3) to convert it into the polynomial form we need to simplify it. Hence,

(7g+3)(−g−3) => -7g² - 21g- 3g -9

=>  -7g² - 24g - 9

Therefore, for the given problem -7g² - 24g - 9 is the polynomial in standard form.

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Answer:

it would have to be a 99

The solution is, the measure of angle A is 79°.

In Plane Geometry, a figure which is formed by two rays or lines that shares a common endpoint is called an angle. The two rays are called the sides of an angle, and the common endpoint is called the vertex.

here, we have,

we know that

the law of cosines establish

c²=a²+b²-2*a*b*cos C------> cos C=[a²+b²-c²]/[2*a*b]

in this problem

a=11 units

b=11 units

c=14 units

C=angle A

so, we get,

cos C=[11²+11²-14²]/[2*11*11]

-----> cos C=0.19008

C=arc cos (0.19008)

------> C=79.04°

the answer is

the measure of angle A is 79°.

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Answer:

16 apples.

Step-by-step explanation:

[tex]U(x, y) = x^2y^8[/tex]

[tex]MU_x =\frac{\partial U}{\partial x} = 2xy^8\\MU_y = \frac{\partial U}{\partial x} = 8x^2y^7\\[/tex]

Price of apples, Px=$4

Price of tomatoes,  Py=$3

Ratio of their Marginal Utilities

[tex]\frac{MU_x}{MU_y} = \frac{Px}{Py}[/tex]

[tex]\frac{y}{4x} = \frac{4}{3}[/tex]

[tex]y=\frac{16x}{3}[/tex]

Since Natalie’s income is $320

320 = xPx+yPy

[tex]320=4x + 3*\frac{16x}{3} \\320= 4x+16x = 20x\\x=\frac{320}{20} = 16\\Also\\y=\frac{16x}{3}=\frac{16X16}{3}=\$85.33[/tex]

Since x=16, Natalie will consume 16 apples.

Given Natalie's budget and the prices of apples and tomatoes, plus the fact that her utility function indicates she consumes two as many tomatoes as apples, we determined that Natalie will consume up to 32 apples under these conditions.

To determine how many apples Natalie will consume, we first need to solve the utility maximization problem where she chooses 'x' and 'y' to maximize her utility subject to her budget constraint. This problem is typically solved using calculus, but here is a simplified way of solving it:

Firstly, let's consider Natalie's budget constraint. With $320, the prices of apples and tomatoes being $4 and $3 respectively, her budget constraint is $4x + $3y ≤ $320.

Due to the nature of Natalie's utility function U(x, y) = x 2y 8, it's clear that for every apple she buys, she consumes twice as many tomatoes (since y=2x). Replacing 'y' in the budget constraint yields to $4x + $3(2x) ≤ $320, or $10x ≤ $320.

x ≤ 32, that is, Natalie will consume up to 32 apples.

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Rewrite the percent as a decimal by moving the decimal point 2 places to the left:

97% = 0.97

Now multiply:

698.04 x 0.97 = 677.0988

Round to 2 decimal places= 677.10

To find 97% of £698.04, you simply multiply £698.04 by 0.97. This gives you an answer of £677.30, rounded to 2 decimal places.

The question is asking for 97% of £698.04. To find this, you would need to multiply £698.04 by 0.97 (which is the decimal equivalent of 97%). Let's do this calculation:

£698.04 * 0.97 = £677.30

Here, the result (rounded to 2 decimal places) is £677.30. So, 97% of £698.04 is £677.30.

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Answer:

  2³n²

Step-by-step explanation:

An exponent signifies the number of times the base is a factor in the product. Here, 2 is a factor 3 times; n is a factor 2 times. Their exponents will be 3 and 2, respectively:

  2•2•2•n•n = 2³n²

To find the surface area of ANY prism you need to find the area of individual shape first.

To find 2 faces of the prism, you will need to do bxh. As there is 2 of the same rectangle , you need to multiply it by 2. Therefore, the first number you need is 16m squared.

To find the next part of the prism, you will need to do 2m x 3m which is 6m. You need the area so 6m squared (The units are important). There are also 2 of these, so multiply it by 2 to get 12m squared.

For the final part of the prism, you will need to do 4m x 3m which is 12m squared. There are 2 of these so the it is 24m squared.

Finally, you will need to add all these figures up.

16m squared + 12m squared + 24m squared = 52m squared

Answer:

52 m

Step-by-step explanation:

Her weekly allowance is $20

Step-by-step explanation:

Let her weekly allowance be 'a'

Given that,

She spent half of the allowance (a/2)

So,

Money left with her = (a/2)

She earned $6 by washing the car

She has $16 at the end.

So,

(a/2) + 6 = 16

(a/2) = 16 - 6

(a/2) = 10

a = 10 x 2

a = 20

So, her weekly allowance is $20