If I don't read carefully, I often make mistakes on my work.

help an ogre out- A toy designer is creating a basketball plushy. The designer has fabric that measures 171.9 sq. in. What is th

trapecia [35]

Answer: 3.7 in.

Step-by-step explanation:

Given, A toy designer is creating a basketball plushy. The designer has fabric that measures 171.9 sq. in.

To find: The maximum radius of the basketball that the designer can create.

For this, Surface area of basketball = area of fabric

Formula: Surface area of sphere = $4\pi r^2$ , where r is the radius.

Then, $4\pi r^2=171.9$

$r^2=\dfrac{171.9}{4\pi}=\dfrac{171.9}{4\times3.14}\\\\\Rightarrow\ r=13.6863057325\\\\\Rightarrow\ r=\sqrt{13.6863057325}=3.69950074098\approx3.7$

Hence, the maximum radius of the basketball that the designer can create is 3.7 in.

4 0

3 years ago

Read 2 more answers

Y varies directly as x. If x = 15 when y = 20, find x when y = 30.

Goryan [66]

Answer:

22.5

Step-by-step explanation:

y=kx

20=k15

k=1•33

30=1•33x

x=22•5

5 0

3 years ago

What is the product of -3 and 5

weeeeeb [17]

Answer:

45 is the correct answer

6 0

3 years ago

Read 2 more answers

Consider the following problem: A farmer with 750 ft of fencing wants to enclose a rectangular area and then divide it into four

gregori [183]

Answer and step-by-step explanation:

For any rectangle, the one with the largest area will be the one whose dimensions are as close to a square as possible.

However, the dividers change the process to find this maximum somewhat.

Letting x represent two sides of the rectangle and the 3 parallel dividers, we have 2x+3x = 5x.

Letting y represent the other two sides of the rectangle, we have 2y.

We know that 2y + 5x = 750.

Solving for y, we first subtract 5x from each side:

2y + 5x - 5x = 750 - 5x

2y = -5x + 750

Next we divide both sides by 2:

2y/2 = -5x/2 + 750/2

y = -2.5x + 375

We know that the area of a rectangle is given by

A = lw, where l is the length and w is the width. In this rectangle, one dimension is x and the other is y, making the area

A = xy

Substituting the expression for y we just found above, we have

A = x(-2.5x+375)

A = -2.5x² + 375x

This is a quadratic equation, with values a = -2.5, b = 375 and c = 0.

To find the maximum, we will find the vertex. First we find the axis of symmetry, using the equation

x = -b/2a

x = -375/2(-2.5) = -375/-5 = 75

Substituting this back in place of every x in our area equation, we have

A = -2.5x² + 375x

A = -2.5(75)² + 375(75) = -2.5(5625) + 28125 = -14062.5 + 28125 = 14062.5

6 0

3 years ago

Ksju [112]

Answer:

We conclude that the mean contents of cola bottles is more than or equal to the advertised 300 ml.

Step-by-step explanation:

We are given that Bottles of a popular cola drink are supposed to contain 300 ml of cola. The distribution of the contents is normal with standard deviation of 3 ml.

A student who suspects that the bottler is under-filling measures the contents of six bottles. The results are: 299.4, 297.7, 301.0, 298.9, 300.2, 297.0

Let $\mu$ = mean contents of cola bottles.

SO, Null Hypothesis, $H_0$ : $\mu \geq$ 300 ml {means that the mean contents of cola bottles is more than or equal to the advertised 300 ml}

Alternate Hypothesis, $H_A$ : $\mu$ < 300 ml {means that the mean contents of cola bottles is less than the advertised 300 ml}

The test statistics that will be used here is One-sample z test statistics as we know about the population standard deviation;

T.S. = $\frac{\bar X -\mu}{\frac{\sigma}{\sqrt{n} } }$ ~ N(0,1)

where, $\bar X$ = sample mean contents of cola bottle = $\frac{\sum X}{n}$ = 299.03 ml

$\sigma$ = population standard deviation = 3 ml

n = sample of bottles = 6

So, test statistics = $\frac{299.03-300}{\frac{3}{\sqrt{6} } }$

= -0.792

Now at 5% significance level, the z table gives critical value of -1.6449 for left-tailed test. Since our test statistics is more than the critical value of z as -0.792 > -1.6449, so we have insufficient evidence to reject our null hypothesis as it will not fall in the rejection region due to which we fail to reject our null hypothesis.

Therefore, we conclude that the mean contents of cola bottles is more than or equal to the advertised 300 ml.

8 0

3 years ago