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4 years ago

Jessie's daughter went to Target and bought $1 or $2 items from the One Spot area. She wants to spend less than $20 at Target

Mathematics

2 answers:

jenyasd209 [6]4 years ago

6 0

She can buy 20 $1 items or 10 $2 items or a mixture of both.

OverLord2011 [107]4 years ago

5 0

She can buy 20 1$ items, or 10 $2 items, at most

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Natalie consumes only apples and tomatoes. Her utility function is U(x, y) = x 2y 8 , where x is the number of apples consumed a

Kamila [148]

Answer:

16 apples.

Step-by-step explanation:

$U(x, y) = x^2y^8$

$MU_x =\frac{\partial U}{\partial x} = 2xy^8\\MU_y = \frac{\partial U}{\partial x} = 8x^2y^7\\$

Price of apples, Px=$4

Price of tomatoes, Py=$3

Ratio of their Marginal Utilities

$\frac{MU_x}{MU_y} = \frac{Px}{Py}$

$\frac{y}{4x} = \frac{4}{3}$

$y=\frac{16x}{3}$

Since Natalie’s income is $320

320 = xPx+yPy

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

Since x=16, Natalie will consume 16 apples.

6 0

3 years ago

in the unted states, the height of men are normally distributed with the mean 69 inches and standard deviation 2.8 inches. If 16

yaroslaw [1]

Answer:

Probability that their mean height is less than 68 inches is 0.0764.

Step-by-step explanation:

We are given that in the united states, the height of men are normally distributed with the mean 69 inches and standard deviation 2.8 inches.

Also, 16 men are randomly selected.

Let $\bar X$ = sample mean height

The z-score probability distribution for sample mean is given by;

Z = $\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }$ ~ N(0,1)

where, $\mu$ = population mean height = 69 inches

$\sigma$ = population standard deviation = 2.8 inches

n = sample of men = 16

The Z-score measures how many standard deviations the measure is away from the mean. After finding the Z-score, we look at the z-score table and find the p-value (area) associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X.

So, probability that the mean height of 16 randomly selected men is less than 68 inches is given by = P( $\bar X$ < 68 inches)

P( $\bar X$ < 68 inches) = P( $\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }$ < $\frac{68-69}{\frac{2.8}{\sqrt{16} } }$ ) = P(Z < -1.43) = 1 - P(Z $\leq$ 1.43)

= 1 - 0.9236 = 0.0764

Now, in the z table the P(Z x) or P(Z < x) is given. So, the above probability is calculated by looking at the value of x = 1.43 in the z table which has an area of 0.92364.

Therefore, probability that their mean height is less than 68 inches is 0.0764.

3 0

4 years ago

9) What 2 numbers have a total of 28 and a difference of 6?

Vedmedyk [2.9K]

Answer:

Sum: 17 + 11 = 28

Difference: 17 - 11 = 6

Step-by-step explanation:

The sum of x and y is 28. In other words, x plus y equals 28 and can be written as equation A:

x + y = 28

The difference between x and y is 6. In other words, x minus y equals 6 and can be written as equation B:

x - y = 6

Now solve equation B for x to get the revised equation B:

x - y = 6

x = 6 + y

Then substitute x in equation A from the revised equation B and then solve for y:

x + y = 28

6 + y + y = 28

6 + 2y = 28

2y = 22

y = 11

Now we know y is 11. Which means that we can substitute y for 11 in equation A and solve for x:

x + y = 28

x + 11 = 28

X = 17

Summary: The sum of two numbers is 28 and their difference is 6. What are the two numbers? Answer: 17 and 11 as proven here:

Sum: 17 + 11 = 28

Difference: 17 - 11 = 6

8 0

3 years ago

Read 2 more answers

10 orange sodas, 15 cream sodas and 7 cherry sodas are in an ice chest. How many sodas must be removed from the chest to guarant

Inessa [10]

Answer:

25 sodas if the type of soda chosen is cherry sodas

5 0

3 years ago

Factorize 2^x+7 + 2^x+6

joja [24]

Answer:

Step-by-step explanation:

$2^{(x+ 7)} + 2^{(x+ 6 )} = 2^{x} * 2^{7} + 2^{x}*2^{6}\\\\=2^{x} *(2^{7} + 2^{6})$

$= 2^{x} * 2^{6} ( 2+ 1)\\\\= 2^{x} * 2^{6} * 3$

8 0

3 years ago