All categories

3 years ago

A can of tomatoes has a 4 in. diameter and is 4.5 in. high. What is the area of the paper label that goes around the can

Mathematics

1 answer:

Luden [163]3 years ago

3 0

Answer:

56.5

Step-by-step explanation:

The length of the paper around the can is equal the circumference of the base.

Circumference = πd

Circumference = 3.14 * 4

Circumference = 12.56

And since the height is 4.5 (which is also the width of the paper if you unwrap it), Multiply the circumference by 4.5.

12.56 * 4.5

= 56.52

You might be interested in

How much do I pay for the loan

Natali5045456 [20]

500 / 100 = 5 5 x 15 = 75 75 x 4 = 300 300 + 500 = 800
After the loan, you will pay $800. Hope this helps :)

4 0

2 years ago

Find the product of all real values of r for which 1/2x=r-x/7

Dahasolnce [82]

Answer:

$r = \±\sqrt{14$

$Product = -14$

Step-by-step explanation:

Given

$\frac{1}{2x} = \frac{r - x}{7}$

Required

Find all product of real values that satisfy the equation

$\frac{1}{2x} = \frac{r - x}{7}$

Cross multiply:

$2x(r - x) = 7 * 1$

$2xr - 2x^2 = 7$

Subtract 7 from both sides

$2xr - 2x^2 -7= 7 -7$

$2xr - 2x^2 -7= 0$

Reorder

$- 2x^2+ 2xr -7= 0$

Multiply through by -1

$2x^2 - 2xr +7= 0$

The above represents a quadratic equation and as such could take either of the following conditions.

(1) No real roots:

This possibility does not apply in this case as such, would not be considered.

(2) One real root

This is true if

$b^2 - 4ac = 0$

For a quadratic equation

$ax^2 + bx + c = 0$

By comparison with $2x^2 - 2xr +7= 0$

$a = 2$

$b = -2r$

$c =7$

Substitute these values in $b^2 - 4ac = 0$

$(-2r)^2 - 4 * 2 * 7 = 0$

$4r^2 - 56 = 0$

Add 56 to both sides

$4r^2 - 56 + 56= 0 + 56$

$4r^2 = 56$

Divide through by 4

$r^2 = 14$

Take square roots

$\sqrt{r^2} = \±\sqrt{14$

$r = \±\sqrt{14$

Hence, the possible values of r are:

$\sqrt{14$ or $-\sqrt{14$

and the product is:

$Product = \sqrt{14} * -\sqrt{14}$

$Product = -14$

8 0

2 years ago

Consider the probability that no less than 96 out of 145 people will not get the flu this winter. Assume the probability that a

dsp73

Answer:

0.1324 = 13.24% probability that no less than 96 out of 145 people will not get the flu this winter.

Step-by-step explanation:

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

Can be approximated to a normal distribution, using the expected value and the standard deviation.

The expected value of the binomial distribution is:

$E(X) = np$

The standard deviation of the binomial distribution is:

$\sqrt{V(X)} = \sqrt{np(1-p)}$

Normal probability distribution

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

When we are approximating a binomial distribution to a normal one, we have that $\mu = E(X)$ , $\sigma = \sqrt{V(X)}$ .

In this problem, we have that:

$n = 145, p = 0.61$

$\mu = E(X) = np = 145*0.61 = 88.45$

$\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{145*0.61*0.39} = 5.87$

Consider the probability that no less than 96 out of 145 people will not get the flu this winter.

More than 95 people, which is the same as 1 subtracted by the pvalue of Z when X = 95. So

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{95 - 88.45}{5.87}$

$Z = 1.115$

$Z = 1.115$ has a pvalue of 0.8676

1 - 0.8676 = 0.1324

0.1324 = 13.24% probability that no less than 96 out of 145 people will not get the flu this winter.

6 0

2 years ago

Ryan estimates the measurements of the volume of a container to be 36 cubic inches. the original volume of the popcorn container

PolarNik [594]

Answer:

difference: -4 cubic inches
% change: -10%

Step-by-step explanation:

The difference between the new volume and the original volume is ...

(new volume) - (original volume) = (36 in³) - (40 in³) = -4 in²

The percentage change is figured with respect to the original volume:

% change = (difference)/(original volume) × 100% = (-4 in³)/(40 in³) × 100%

= -1/10 × 100% = -10%

4 0

3 years ago

Solve<br><br> 6x + 8 = 2x + 11<br><br> Thanks

hammer [34]

The equation given in the question should be written down first and then the process should start for solving and finding the value of the unknown variable "x".
6x + 8 = 2x + 11
6x - 2x = 11 - 8
4x = 3
x = 3/4
The value of the unknown variable "x" comes out to be 3/4. I hope the procedure for solving this equation is clear enough for you to understand. In future you can always use this procedure to get to the solution of similar problems.

6 0

2 years ago

Read 2 more answers