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3 years ago

A bicycle wheel has a diameter of 62cm. The wheel makes 80 complete

Mathematics

1 answer:

Varvara68 [4.7K]3 years ago

5 0

Answer:

<em>The bicycle traveled 77.9 m</em>

Step-by-step explanation:

<u>Circumference of a Circle</u>

Given a circle of radius r, the circumference or perimeter is calculated as follows:

$C =2\pi r$

The radius of the bicycle wheel has a radius of r=62 cm. Converting to meters r=62/100=0.62 m.

Calculate the circumference:

$C =2\pi \ 0.62$

$C=3.8956\ m$

Given the wheel makes 80 complete revolutions, the total distance covered by the bicycle is:

$D=20*3.8956\ m$

D = 77.9 m

The bicycle traveled 77.9 m

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Solve the following system of equations. What is one x-value of a solution?

gulaghasi [49]

Answer:

There is some mistake in the question, because the solutions are x = -1.445 and x = -34.555

Step-by-step explanation:

Given the functions:

f(x) = x² + 4x + 10

g(x) = -32x - 40

we want to find the points at which f(x) = g(x).

x² + 4x + 10 = -32x - 40

x² + 4x + 10 + 32x + 40 = 0

x² + 36x + 50 = 0

Using quadratic formula:

$x = \frac{-b \pm \sqrt{b^2-4(a)(c)}}{2(a)}$

$x = \frac{-36 \pm \sqrt{36^2-4(1)(50)}}{2(1)}$

$x = \frac{-36 \pm 33.11}{2}$

$x_1 = \frac{-36 + 33.11}{2}$

$x_1 = -1.445$

$x_2 = \frac{-36 - 33.11}{2}$

$x_2 = -34.555$

5 0

3 years ago

A machine that fills beverage cans is supposed to put 12 ounces of beverage in each can. The standard deviation of the amount in

erica [24]

Answer:

$\chi^2 =\frac{10-1}{0.0144} 0.0217 =13.54$

The degrees of freedom are:

$df=n-1=10-1=9$

Now we can calculate the p value using the alternative hypothesis:

$p_v =2*P(\chi^2 >13.54)=0.279$

Since the p value is higher than the signficance level assumed of 0.05 we have enough evidence to FAIL to reject the null hypothesis and there is no evidence to conclude that the true deviation differs from 0.12 ounces

Step-by-step explanation:

Assuming the following data:"12.14 12.05 12.27 11.89 12.06

12.14 12.05 12.38 11.92 12.14"

We can calculate the sample deviation with this formula:

$s =\sqrt{\frac{\sum_{i=1}^n (X_i -\bar X)^2}{n-1}}$

$n=10$ represent the sample size

$\alpha=0.05$ represent the confidence level

$s^2 =0.0217$ represent the sample variance

$\sigma^2_0 =0.12^2= 0.0144$ represent the value to verify

Null and alternative hypothesis

We want to determine whether the standard deviation differs from 0.12 ounce, so the system of hypothesis would be:

Null Hypothesis: $\sigma^2 = 0.0144$

Alternative hypothesis: $\sigma^2 \neq 0.0144$

The statistic can be calculated like this;

$\chi^2 =\frac{n-1}{\sigma^2_0} s^2$

$\chi^2 =\frac{10-1}{0.0144} 0.0217 =13.54$

The degrees of freedom are:

$df=n-1=10-1=9$

Now we can calculate the p value using the alternative hypothesis:

$p_v =2*P(\chi^2 >13.54)=0.279$

7 0

3 years ago

Solve for d: 0.5(2d-6)=0.2(4x-10)

Law Incorporation [45]

Answer:d=0.8x+1

Step-by-step explanation:

To solve 0.5(2d-6)=0.2(4x-10)

Open the brackets

We get

d-3=0.8x-2

To make d the subject of formular

d=0.8x-2+3

d=0.8x+1

7 0

3 years ago

Please help WILL MARK BRAIN LEST 5 STAR RATING THANKS ON YOUR PAGE

kotegsom [21]

Part A

So the coefficient would be the number that is with a variable. The coefficient of 7.50h is 7.50. The variable is h, variables can be a letter or symbol that stands for something in a equation. For this question, h stands for the number of hours Corinne works. The constant is the number that is alone in the equation. That doesn't have a variable with it. In this equation the constant would be the number 40.

Part B

To solve this I will plug in 25 into "h" in and 300 for "s" in the equation 7.50h + 0.20s + 40 and then solve.

1. 25 * 7.50 = $187.5.

2. 0.20 * 300 = $60

3. Add it all together: $187.50 + $60 = $247.50 + $40 = $287.50

Part C

If Corrine gets a raise and earns $9 an hour the coefficient would change. It would be 9h instead of 7.50h.

5 0

3 years ago

Read 2 more answers

Caitlin has cut out a square piece of graph paper that contains a total of 81 blocks.How many blocks are there along one side of

FinnZ [79.3K]

Answer:

9 squares on each side of the square.

Step-by-step explanation:

$\sqrt{81}=\sqrt{9\times 9}=\sqrt{9^2}=9$

There are 9 equally sized blocks on one side of square piece of graph paper.

Best Regards!

5 0

3 years ago