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3 years ago

Which are vertical angles?

Mathematics

2 answers:

vichka [17]3 years ago

7 0

Answer:

You should republish this question but with a picture because this doesnt really make sense

Arisa [49]3 years ago

7 0

Answer:

Its A.

Step-by-step explanation:

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Frank practiced basketball on 4 different days last week for 1 3/4 hours each time. How many hours did he practice last week?

GrogVix [38]

4 3/4 hours he practiced last week

3 0

3 years ago

A rectangular storage container with an open top is to have a volume of 10 m3 . then length of its base is twice the width. mate

katrin [286]

Answer:

The cost of materials for the cheapest such container is $163.54.

Step-by-step explanation:

A rectangular storage container with an open top is to have a volume of 10 m³.

The volume of the rectangle is

$\text{Volume} =\text{Length} \times \text{Width} \times \text{Height}$

Length of its base is twice the width.

Let Width be 'w'.

Length is l=2w.

Height be 'h'.

$10 =2w\times w\times h$

$10=2w^2h$

The height in terms of width is represented as,

$h=\frac{10}{2w^2}$

$h=\frac{5}{w^2}$

According to question,

The cost is 10 times the area of the base and 6 times the total area of the sides.

i.e. Cost is given by,

$C=10(L\times W)+6(2\times L\times H+2\times W\times H)$

$C=10(2w\times w)+6(2\times 2w\times \frac{5}{w^2}+2\times w\times \frac{5}{w^2})$

$C=20w^2+\frac{120}{w}+\frac{60}{w}$

$C(w)=20w^2+\frac{180}{w}$

To get the minimum value,

Differentiate the cost w.r.t 'w',

$C'(w)=20\frac{d(w^2)}{dw}+180\frac{d(w^{-1})}{dw}$

$C'(w)=20\times 2w-180 w^{-2}$

$C'(w)=40w-\frac{180}{w^2}$

To find critical points put derivate =0,

$40w-\frac{180}{w^2}=0$

$40w=\frac{180}{w^2}$

$w^3=\frac{180}{40}$

$w=\sqrt[3]{4.5}$

$w=1.65$

We find the second derivative to minimize,

$C''(w)=40\frac{d(w)}{dw}-180\frac{d(w^{-2})}{dw}$

$C''(w)=40+360(w^{-3})$

$C''(w)>0$

As $C''(w)>0$ it is the minimum cost.

The cost is minimum at w=1.65.

Substitute the values in the cost function,

$C(1.65)=20(1.65)^2+\frac{180}{1.65}$

$C(1.65)=54.45+109.09$

$C(1.65)=163.54$

Therefore, the cost of materials for the cheapest such container is $163.54.

7 0

3 years ago

Preston works in a bakery where he puts muffins in boxes. He makes the following table to remind himself how many blueberry muff

Natasha_Volkova [10]

It is being multiplied by 3. blueberry muffins ×3 = total # of muffins,so the answer would be 12

8 0

3 years ago

Read 2 more answers

The mayor of a town has proposed a plan for the construction of an adjoining community. A political study took a sample of 900 v

Aleks04 [339]

Answer:

P-value = 0.0367

Step-by-step explanation:

This is a hypothesis test for a proportion.

The claim is that the percentage of residents who favor construction is significantly over 42%.

Then, the null and alternative hypothesis are:

$H_0: \pi=0.42\\\\H_a:\pi>0.42$

The sample has a size n=900.

The sample proportion is p=0.45.

The standard error of the proportion is:

$\sigma_p=\sqrt{\dfrac{\pi(1-\pi)}{n}}=\sqrt{\dfrac{0.42*0.58}{900}}\\\\\\ \sigma_p=\sqrt{0.000271}=0.016$

Then, we can calculate the z-statistic as:

$z=\dfrac{p-\pi-0.5/n}{\sigma_p}=\dfrac{0.45-0.42-0.5/900}{0.016}=\dfrac{0.029}{0.016}=1.79$

This test is a right-tailed test, so the P-value for this test is calculated as:

$\text{P-value}=P(z>1.79)=0.0367$

4 0

3 years ago

Select ALL the intervals where f(x)= -x^3 + 3x^2 +1 is only decreasing.

Sphinxa [80]

Answer:

5 < x < ∞

-∞ < x < 0

2 < x < ∞

Step-by-step explanation:

Given function is $-x^{3}$ + 3 $x^{2}$ + 1.

To, Calculate where the function is increasing or decreasing,

we have to calculate the derivative of the function,

so,

f'(x) = -3 $x^{2}$ + 6x.

Equating the f'(x)= 0 , we get

x(-3x + 6) = 0

So, f'(x) will be zero at x = 0 and x = 2.

f(x) will be decreasing in the interval where f'(x) will be negative.

now as the coefficient of f'(x) is negative it will be negative between

the interval -∞ < x < 0 and 2 < x < ∞.

Options which lie in these intervals only are

5 < x < ∞

-∞ < x < 0

2 < x < ∞

3 0

3 years ago