Jenny has 4 feet of yarn. She cuts<br> the yarn into 4 equal pieces. How<br> long is each piece?

According the the U.S. Department of Education, full-time graduate students receive an average salary of $15,000 with a standard

Firdavs [7]

Answer:

Step-by-step explanation:

Given that :

population Mean = 15000

standard deviation= 1200

sample size n = 100

sample mean = 16000

The null and the alternative hypothesis can be computed as follows:

$\mathtt{H_o : \mu = 15000 }\\ \\ \mathtt{H_1 : \mu > 15000}$

Using the standard normal z statistics

$z = \dfrac{\overline X - \mu}{\dfrac{\sigma }{\sqrt{n}}}$

$z = \dfrac{16000 -15000}{\dfrac{1200 }{\sqrt{100}}}$

$z = \dfrac{1000}{\dfrac{1200 }{10}}$

$z = \dfrac{1000\times 10}{1200}$

z = 8.333

degree of freedom = n - 1 = 100 - 1 = 99

level of significance ∝ = 0.05

P - value from the z score = 0.00003

Decision Rule: since the p value is lesser than the level of significance, we reject the null hypothesis

Conclusion: There is sufficient evidence that the Dean claim for his graduate students earn more than average salary of $15,000

5 0

3 years ago

Can someone please hep me with this question Jordan is proofreading his personal narrative.

charle [14.2K]

Answer:

When proofreading, you should make sure all details are accurate and writing mechanics are correctly used.

7 0

4 years ago

Part of the graph of the function f(x) = (x – 1)(x + 7) is shown below. Which statements about the function are true? Select thr

devlian [24]

Answer:

The vertex of the function is at (–3,–16)

The graph is increasing on the interval x > –3

The graph is positive only on the intervals where x < –7 and where x > 1

Step-by-step explanation:

The roots of this function are the values that make f(x) = 0. As the equation is already factored, we can see that the roots are x1 = 1 and x2 = -7

The x-coordinate of the vertix can be calculated as:

x_v = (x1 + x2)/2 = -6/2 = -3

So the first statement: "The vertex of the function is at (–4,–15)" is wrong.

The y_coordinate of the vertex is:

f(x_v) = (x_v - 1)*(x_v + 7) = (-3 -1) * (-3 +7) = (-4) * (4) = -16

So the second statemente: "The vertex of the function is at (–3,–16)" is correct.

for values of x greater than x_v = -3, the graph increases, as the equation represents a parabola with concavity upwards. So the third statement is correct.

As the roots are 1 and -7 and the concavity is upwards, the parabola have positive values for x<-7 and x>1. So the fourth statement is correct.

For values of x< -4, the parabola can have both positive or negative values (it has positive values for x < -7) so the fifth statement is wrong.

4 0

4 years ago

Read 2 more answers

What is the sum of the solutions of x2 + 9x + 20 = 0?

ZanzabumX [31]

Answer:

Sum of the solutions of $x^2+9x+20=0$ is -9.

Product of the solutions of $6x^2+7x=3$ is $-0.50$

Step-by-step explanation:

1. $x^2+9x+20=0$

Given:

The expression whose sum of the solution is required is given as:

$x^{2} +9x+20=0$

For a quadratic equation of the form $ax^2+bx+c=0$ the sum of the solutions is given as:

Sum = $\frac{-b}{a}$

Here, $a=1,b=9,c=20$

Therefore, the sum of the solutions = $-\frac{9}{1}=-9$

2. $6x^2+7x=3$

Rewriting the above equation in a standard quadratic equation, we get:

$6x^2+7x-3=0$

For a quadratic equation of the form $ax^2+bx+c=0$ the product of the solutions is given as:

Product = $\frac{c}{a}$

Here, $a=6,b=7,c=-3$

Therefore, the product of the solutions = $\frac{-3}{6}=-0.50$

6 0

3 years ago

Fernando has been saving money to buy an e-book reader. A store has just marked down the price of its readers by 40%. Each reade

murzikaleks [220]

Answer:

Fernado saves $90.

Step-by-step explanation:

40% of $150 ( original price ) = $60

$150 - $60 ( original price - discounted price ) = $90 ( savings )

The question asks about the 40% markdown only, so I'd assume you wouldn't reduce it by $25.

But if you did Fernando would save $115 :

40% of $150 ( original price ) = $60

$60 - $25 ( mail-in rebate ) = $35

$150 - $35 ( original price - discounted price ) = $115 ( savings )

6 0

3 years ago

Jenny has 4 feet of yarn. She cuts the yarn into 4 equal pieces. How long is each piece?