The sum of a number times 6 and 5 equals 4 translate the sentence into an equation

Which points satisfy the following system of linear inequalities? Show all your work. -5y+4x<18 -15y-9x>117

raketka [301]

The lines intersect on the graph at (-3, -6). The solution set falls within the domain of negative infinity to positive infinity and a range of y is greater than or equal to -6. Without having the capabilities of graphing it to show you, that's the best I can do. Graph the lines (dotted, I presume) and see if you can follow those guidelines for the solution set.

3 0

3 years ago

A bag of chips states that it contains 24 oz of chips. A sample of 40 bags finds a mean of 23.7 and a standard deviation of 0.2.

PIT_PIT [208]

Answer:

a) Null hypothesis: $\mu \geq 24$

b) Alternative hypothesis: $\mu < 40$

c) $t=\frac{23.7-24}{\frac{0.2}{\sqrt{40}}}=-9.487$

d) $df=n-1=40-1=39$

$p_v =P(t_{39}$

e) Since the p value is almost 0 we have enough evidence to reject the null hypothesis at the significance level of 0.05

f) Since we reject the null hypothesis we have enough evidence to conclude the true mean is significantly less than 24 ounces

Step-by-step explanation:

Information provided

$\bar X=23.7$ represent the sample mean for the weigth in ounces

$s=0.2$ represent the standard deviation

$n=40$ sample size

$\mu_o =24$ represent the value to verify

$\alpha=0.05$ represent the significance level

t would represent the statistic

$p_v$ represent the p value

Part a

For this case the null hypothesis is:

Null hypothesis: $\mu \geq 24$

Part b

And the alternative would be given by the claim:

Alternative hypothesis: $\mu < 40$

Part c

We don't know the population deviation so then the statistic would be given by:

$t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}$ (1)

And replacing the data given we got:

$t=\frac{23.7-24}{\frac{0.2}{\sqrt{40}}}=-9.487$

Part d

The degrees of freedom are given by:

$df=n-1=40-1=39$

And the p value for this case would be:

$p_v =P(t_{39}$

Part e

Since the p value is almost 0 we have enough evidence to reject the null hypothesis at the significance level of 0.05

Part f

Since we reject the null hypothesis we have enough evidence to conclude the true mean is significantly less than 24 ounces

5 0

3 years ago

A sphere has volume 463.01 cm^3. What is the radius of the sphere? A second sphere has a radius half as long as this radius. Wha

Mumz [18]

Answer:

1: r = 2.4 cm

2: V = 57.8765 cm^3

Step-by-step explanation:

1:

The volume of a sphere is given by V = (4/3) * pi * (r^3), being 'r' its radius.

So if the volume is 463.01 cm^3, we have that:

463.01 = (4/3) * pi * (r^3)

463.01 * 3 = 4 * 3.14 * r^3

r^3 = 463.01 * 3 / (4 * 3.14) = 110.59156

r = 4.8 cm

2:

The radius of the second sphere is 4.8/2 = 2.4 cm, so its volume is:

V = (4/3) * 3.14 * (2.4^3) = 57.8765 cm^3

6 0

3 years ago

Read 2 more answers

780000= <br> Rename the number

Monica [59]

Sevenhundred and eighty thousand

3 0

3 years ago

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Solve for x<br> 1(x-2) = -5.5

Dafna1 [17]

Answer:

x = -3.5

Step-by-step explanation:

Divide both sides by 1 to get rid of the 1

x - 2 = -5.5

Add 2 on both sides

x = -3.5

6 0

3 years ago

Read 2 more answers