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3 years ago

15

Internet prices for glasses are often considerably lower than those at the brick and mortar stores but quality is another questi

on. To address that issue, some optometrists ordered 154 adult pairs of spectacles from various online stores. Of the 154 pairs of spectacles, 44 pairs of eye wear contained at least one lens that did not pass optical analysis testing.
Required:
a. Conduct a test of hypotheses with the intent of establishing that the probability of not passing the optical analysis testing is greater than 0.20. Use level of significance 0.05.
b. Calculate the p-value and comment.

1 answer:

FinnZ [79.3K]3 years ago

3 0

The answer would be B hope I could help (: next time try to make it more explained (:

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There are 364 first-grade students in Park Elementary School. If there are 26 more girls than boys, how many girls are there?

wlad13 [49]

Answer:

195

Step-by-step explanation:

If there are x boys, then there are x+26 girls. Hence, we write the equation,

x+(x+26)=364

Solve for x:

2x+26=364

2x-338

x=169

So there are 169+26 =195 girls

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3 years ago

Need help!! What is the slope of the line through (2,-2) and (9,3)?

In-s [12.5K]

Finding the slope using two points:

The formula for slope is

$\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

In this case...

$y_{2} =3\\y_{1} =-2\\x_{2} =9\\x_{1} =2$

^^^Plug these numbers into the formula for slope...

$\frac{3 - (-2) }{9 - 2}$

A) $\frac{5}{7}$

^^^This is your slope

Hope this helped!

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2 years ago

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What is the prime factorization of 18?<br> 2x3<br> 2x9<br> 2x3x3<br> 2x3x9

liraira [26]

Answer: 2 × 3 × 3 or we can also write them as 2 × 32, where 2 and 3 both are prime numbers.

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2 years ago

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Otis plans to make 3 batches of sidewalk chalk How much plaster of paris does he need

den301095 [7]

Answer:

$4\frac{1}{2}$ cups plaster of paris.

Step-by-step explanation:

Given:

for one batch of sidewalk chalk = $1\frac{1}{2}$ cup plaster of paris.

Number of bathes = 3

We need to find quantity of plaster of paris.

Solution:

For making 1 batch of sidewalk chalk = $1\frac{1}{2}$ cup plaster of paris.

For making 3 batches of sidewalk chalk = $3\times 1\frac{1}{2}$ cup plaster of paris.

$= 3\times \frac{2\times 1+1}{2}$

$= 3\times \frac{2+1}{2}$

$= 3\times \frac{3}{2}$

$= \frac{3\times 3}{2}$

$= \frac{9}{2}$

$=4\frac{1}{2}$

Therefore, he needed $4\frac{1}{2}$ cups plaster of paris.

5 0

3 years ago

A box has a volume of 192 cubic inches, a length that is twice as long as its width, and a height that is 2 inches greater than

ruslelena [56]

Answer:

Therefore the dimension of the cuboid is 8 inches×4 inches ×6 inches.

Step-by-step explanation:

Cuboid : A cuboid is a three dimension shape. The length ,breadth and height of a cuboid are not same.

A cuboid has 6 faces.
A cuboid contains 8 vertices.
A cuboid contains 12 edges .
The total surface area of a cuboid is

= 2(length×breadth+breadth×height+length×height) square units

The dimension of a cuboid is written as length×breadth×height.

The volume is( length×breadth×height) cubic units

Given that the volume of the box is 192 cubic inches.

Let x inches be the width of the cuboid.

Since the length is twice as long as its width.

Then length = 2x inches

Again height is 2 inches longer than width.

Then height = (x+2) inches.

Therefore the volume of the cuboid is

$=[x\times 2x\times (x+2)]$ cubic inches

$=[2x^2(x+2)]$ cubic inches

$=(2x^3+4x^2)$ cubic inches

According to the problem,

$2x^3+4x^2=192$

$\Rightarrow 2x^3+4x^2-192=0$

$\Rightarrow 2(x^3+2x^2-96)=0$

$\Rightarrow (x^3+2x^2-96)=0$

$\Rightarrow x^3-4x^2+6x^2-24x+24x-96=0$

$\Rightarrow x^2(x-4) +6x(x-4)+24(x-4)=0$

$\Rightarrow (x-4)(x^2+6x+24)=0$

Therefore x=4

Since the all zeros of x²+6x+24 =0 is negative.

Therefore breadth = 4 inches

length=(2×4) inches=8 inches

and height = (4+2)inches = 6 inches.

Therefore the dimension of the cuboid is 8 inches×4 inches ×6 inches.

8 0

3 years ago