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Arada [10]
3 years ago
12

Substitute the values of x and y into the expression -3x 2 + 2y 2 + 5xy - 2y + 5x 2 - 3y 2. Match that value to one of the numbe

rs.
1. x = 2, y = -1

9.17

2. x = 0, y = 2.5

1.665

3. x = -1, y = -3

-11.25

4. x = 0.5, y =

14

5. x = , y =

-1

6. x = √2, y = √2

0.44
Mathematics
1 answer:
seropon [69]3 years ago
5 0
X = 2, y = -1  Answer = -1
x = 0, y = 2.5  Answer = -11.25
x = -1, y = -3   Answer = 14
x = 0.5, y = -0.1 (one tenths)  Answer = 0.44
x = 0.75 (three quarters), y = 0.4 (two fifths)  Answer = 1.665
x = 1.41 (sqareroot of 2), y = 1.41 (sqareroot of 2)  Answer = 9.17

I hope this helps!
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The mean amount purchased by a typical customer at Churchill's Grocery Store is $26.00 with a standard deviation of $6.00. Assum
Vadim26 [7]

Answer:

a) 0.0951

b) 0.8098

c) Between $24.75 and $27.25.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean \mu and standard deviation \sigma, the zscore of a measure X is given by:

Z = \frac{X - \mu}{\sigma}

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value 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. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean \mu and standard deviation \sigma, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \mu and standard deviation s = \frac{\sigma}{\sqrt{n}}.

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

In this problem, we have that:

\mu = 26, \sigma = 6, n = 62, s = \frac{6}{\sqrt{62}} = 0.762

(a)

What is the likelihood the sample mean is at least $27.00?

This is 1 subtracted by the pvalue of Z when X = 27. So

Z = \frac{X - \mu}{\sigma}

By the Central Limit Theorem

Z = \frac{X - \mu}{s}

Z = \frac{27 - 26}{0.762}

Z = 1.31

Z = 1.31 has a pvalue of 0.9049

1 - 0.9049 = 0.0951

(b)

What is the likelihood the sample mean is greater than $25.00 but less than $27.00?

This is the pvalue of Z when X = 27 subtracted by the pvalue of Z when X = 25. So

X = 27

Z = \frac{X - \mu}{s}

Z = \frac{27 - 26}{0.762}

Z = 1.31

Z = 1.31 has a pvalue of 0.9049

X = 25

Z = \frac{X - \mu}{s}

Z = \frac{25 - 26}{0.762}

Z = -1.31

Z = -1.31 has a pvalue of 0.0951

0.9049 - 0.0951 = 0.8098

c)Within what limits will 90 percent of the sample means occur?

50 - 90/2 = 5

50 + 90/2 = 95

Between the 5th and the 95th percentile.

5th percentile

X when Z has a pvalue of 0.05. So X when Z = -1.645

Z = \frac{X - \mu}{s}

-1.645 = \frac{X - 26}{0.762}

X - 26 = -1.645*0.762

X = 24.75

95th percentile

X when Z has a pvalue of 0.95. So X when Z = 1.645

Z = \frac{X - \mu}{s}

1.645 = \frac{X - 26}{0.762}

X - 26 = 1.645*0.762

X = 27.25

Between $24.75 and $27.25.

3 0
3 years ago
Which expressions represents the simplified version of the following expression? ​
elixir [45]

Answer:

7x³y² - 3x²y² + xy - 5

Step-by-step explanation:

Add like terms.

5x³y² + 2x³y² = 7x³y²

-3x²y² = -3x²y²

-3xy + 4xy = xy

2 - 7 = -5

Put them all together.

7x³y² - 3x²y² + xy - 5

8 0
3 years ago
Please help with the last equation on the bottom.
Alisiya [41]

Answer:

0.5

Step-by-step explanation:

4 0
3 years ago
A plastic ball is filled with gel to make a stress ball. If the ball has a radius of 4 cm, how much
Dafna1 [17]

Answer:

267.947 cm^{3} of gel is required to fill the plastic ball.

Step-by-step explanation:

<em>The radius of the ball is given as 4 cm.</em>

<em>The gel is filled in the plastic ball, that means the gel occupies the volume of the radius.</em>

The volume of the sphere is given by the formula,

V = \frac{4}{3}(\pi)R^{3} , the R is the radius of sphere.

V = \frac{4}{3}(\pi)(4)^{3} = 267.947 cm^{3}

Thus, the volume of gel required to fill the plastic ball to make it stress ball is

267.947 cm^{3} of gel.

3 0
3 years ago
Only answer if you are 100% sure about the answer.
hram777 [196]

Answer:

180

Step-by-step explanation:

3 0
3 years ago
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