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The US Department of Energy reported that 49% of homes were heated by natural gas. A random sample of 338 homes in Oregon found

Furkat [3]

Answer:

$z=\frac{0.438 -0.49}{\sqrt{\frac{0.49(1-0.49)}{338}}}=-1.912$

The p value for this case would be given by:

$p_v =2*P(z$

For this case the p value is higher than the significance level so then we have enough evidence to FAIL to reject the null hypothesis and we can conclude that the true proportion is not significantly different from 0.49 or 49%

Step-by-step explanation:

Information given

n=338 represent the random sample taken

X=148 represent the homes in Oregon were heated by natural gas

$\hat p=\frac{148}{338}=0.438$ estimated proportion of homes in Oregon were heated by natural gas

$p_o=0.49$ is the value that we want to test

represent the significance level

z would represent the statistic

$p_v$ represent the p value

Hypothesis to test

We want to check if the true proportion of interest is 0.49, then the system of hypothesis are.:

Null hypothesis: $p=0.49$

Alternative hypothesis: $p \neq 0.49$

The statitic is given by:

$z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}$ (1)

Replacing we got:

$z=\frac{0.438 -0.49}{\sqrt{\frac{0.49(1-0.49)}{338}}}=-1.912$

The p value for this case would be given by:

$p_v =2*P(z$

For this case the p value is higher than the significance level so then we have enough evidence to FAIL to reject the null hypothesis and we can conclude that the true proportion is not significantly different from 0.49 or 49%

8 0

4 years ago

Complete the square to rewrite y = x2 + 8x – 4 in vertex form, and then identify the minimum y-value of the function

babunello [35]

Answer:

The vertex form is (x + 4)² - 20

The minimum value of the function is -20

Step-by-step explanation:

* Lets write the general form and the vertex form of the

quadratic function

- General form ⇒ ax² + bx + c, where a , b , c are constant

- Vertex form ⇒g(x - h)² + k, where g , h , k are constant and

(h , k) is the vertex point (minimum or maximum)

- By equating them we can find the vertex point

* Lets do that in the problem

∵ y = x² + 8x - 4

∴ x² + 8x - 4 = g(x - h)² + k ⇒ solve the bracket

∴ x² + 8x - 4 = g(x² - 2xh + h²) + k ⇒ open the bracket

∴ x² + 8x - 4 = gx² - 2ghx + gh² + k

* Now lets equate the like terms

- Let x² = gx²

∴ g = 1

- Let 8x = -2ghx ⇒ -2gh = 8 ⇒ -2(1)h = 8 ⇒ -2h = 8 ⇒ ÷ -2 for both sides

∴ h = -4

- let -4 = gh² + k ⇒ -4 = (1)(-4)² + k ⇒ 16 + k = -4 ⇒ -16 for both sides

∴ k = -4 - 16 = -20

* Substitute these values in the equation

∴ x² + 8x - 4 = (x - -4)² + -20

* The vertex form is (x + 4)² - 20

∵ The vertex point is (h , k)

∴ The vertex point is (-4 , -20)

* The minimum value of the function is the value of y

of the vertex point

∴ The minimum value of the function is -20

6 0

3 years ago

Read 2 more answers

For the following, find the missing values.

vitfil [10]

Y=12, and X=18, it’s a 30 60 90 triangle

8 0

3 years ago

Sue wants to plan a meal with 71 grams of fat and 1755 calories. If hot dogs have 13 grams of fat and 145 calories each and if b

Lena [83]

Answer:

Sue must use 3 hotdogs and 4 half-cup serving of baked beans.

Step-by-step explanation:

Let the number of hot dogs be represented by h

Let the number of baked beans be represented by b

Hot dogs have 13 grams of fat and 145 calories each

Baked beans have 8 grams of fat and 330 calories per half cup serving

Sue wants to plan a meal with 71 grams of fat and 1755 calories.

Grams of Fat from Hotdog + grams of fat from baked beans=71

13h+8b=71....(I)

Similarly,

Calories from hot dog + Calories from baked beans=1755

145h+330b=1755....(II)

We then solve Equations (I) and (II) simultaneously.

13h+8b=71....(I)

145h+330b=1755....(II)

Multiply equation 1 by 145 and equation 2 by 13

1885h+1160b=10295

1885h+4290b=22815

Subtracting

-3130b=-12520

b=4

Substitute b=4 into (I)

13h+(8X4)=71

13h=71-32

13h=39

h=3

Sue must use 3 hotdogs and 4 half-cup serving of baked beans.

4 0

4 years ago

Find the solutions to (x, y) y = -0.5x + 2 y = 0.5x + 6

Marat540 [252]

Answer:

y=-0.5x+2 (-4,0) (0,2) y=0.5x+6 (0,6)(12,0)

Step-by-step explanation:

Desmos

3 0

3 years ago