A rectangle has a base of 5 cm and a height of (x + 2)cm. Its area is 20 cm ^ 2. What is the value of x?

The manager of Petco, a nationwide chain of pet supply stores, wants to study characteristics of the customers, particularly the

shutvik [7]

Answer:

The 95% confidence interval would be given by (19.141;23.538)

Step-by-step explanation:

1) Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

$\bar X=21.34$ represent the sample mean for the sample

$\mu$ population mean (variable of interest)

s=9.22 represent the sample standard deviation

n=70 represent the sample size

2) Confidence interval

The confidence interval for the mean is given by the following formula:

$\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}$ (1)

In order to calculate the critical value $t_{\alpha/2}$ we need to find first the degrees of freedom, given by:

$df=n-1=70-1=69$

Since the Confidence is 0.95 or 95%, the value of $\alpha=0.05$ and $\alpha/2 =0.025$ , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.025,69)".And we see that $t_{\alpha/2}=1.994$

Now we have everything in order to replace into formula (1):

$21.74-1.994\frac{9.22}{\sqrt{70}}=19.141$

$21.74+1.994\frac{9.22}{\sqrt{70}}=23.538$

So on this case the 95% confidence interval would be given by (19.141;23.538)

3 0

3 years ago

The volume of a pyramid is 1/3 the volume of a prism ? True False

marissa [1.9K]

Answer: True

Step-by-step explanation:

Prism volume = lwh

Pyramid Volume = lwh/3

6 0

3 years ago

Solve by elimination:

Pie

Answer:

B (5, 13)

Step-by-step explanation:

9x + 4y = 97

9x + 6y = 123

To solve by elimination, we want to eliminate a variable. To do this, we must make one variable cancel out.

First, we can see that both equations have 9x. To cancel out x, we must make one of the 9x's negative. To do this, multiply each term in the equation by -1.

-1(9x + 6y = 123)

-9x - 6y = -123

This is one of your equations. Set it up with your other given equation.

9x + 4y = 97

-9x - 6y = -123

Imagine this is one equation. Since every term is negative, you will be subtracting each term.

9x + 4y = 97

-9x - 6y = -123

___________

0x -2y = -26

-2y = -26

To isolate y further, divide both sides by -2.

y = 13

Now, to find x, plug y back into one of the original equations.

9x + 4(13) = 97

Multiply.

9x + 52 = 97

Subtract.

9x = 45

Divide.

x = 5

Check your answer by plugging both variables into the equation you have not used yet.

-9(5) - 6(13) = -123

-45 - 78 = -123

-123 = -123

Your answer is correct!

(5, 13)

Hope this helps!

6 0

3 years ago

You are given a line that has a slope of 4 and passed through the point (3/8, 1/2). Which statements about the question of the l

alexgriva [62]

Answer:

Statement 1, 2 and 4 are true where as statement 3 is not true.

Step-by-step explanation:

Statement 1: The y-intercept is -1

Point (3/8, 1/2)

Slope = m = 4

y = mx + c

1/2 = 4(3/8) + c

1/2 = 3/2 + c

1/2 = 3/2 + 2c/2

-2 = 2c

c = -1

This statement is true as the y-intercept is -1.

Statement 2: The slope intercept equation is y= 4x - 1

slope = m = 4

y-intercept = c = -1

y = mx + c

y = 4x - 1

This statement is true as the slope intercept equation is y= 4x -1

Statement 3: The point slope equation is y - 3/8 = 4 (x - 1/2)

Point slope equation: y - y1 = m (x - x1)

Points: (x, y) (3/8, 1/2)

y1 = 1/2

x1 = 3/8

Slope = m = 4

y - 1/2 = 4 (x - 3/8)

This statement is not true as the slope intercept equation is y - 1/2 = 4 (x - 3/8) instead of y - 3/8 = 4 (x - 1/2).

Statement 4: The point (3/8, 1/2) corresponds to (x1, y1) in the point slope form of the equation

This statement is true as shown in statement 3's explanation where x1 = 3/8 and y1 = 1/2

!!

6 0

3 years ago

A coat at a store is originally priced at $54.99. The store marks the price down to $32.99. To the nearest percent, what is the

Dmitry_Shevchenko [17]

Answer:

66.6%

Step-by-step explanation:

Step one

given

A coat at a store is originally priced at $54.99

The store marks down the price down to $32.99

Required

the percent decrease

Step two:

the percent decrease= change in price/ old price*100

the percent decrease= 54.99-32.99/54.99*100

the percent decrease= 22/ 32.99*100

the percent decrease= 0.666*100

the percent decrease= 66.6%

6 0

3 years ago