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3 years ago

Determine whether 42 is divisible by 2,3,5,and/or 10

Mathematics

2 answers:

Trava [24]3 years ago

6 0

42 is only evenly divisible by 1 2 3 6 7 14 21 42. Therefore it is divisible by 2.

Pie3 years ago

3 0

42 is divisible by 2 and 3

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Find an equation to the line perpendicular to 4x + 36y =80 an goes through the point (3,6) write answer in form y= Mx+b

Veronika [31]

Answer:

$\textbf{y = 9x + 21 }\\$

Step-by-step explanation:

$\textup{Given equation is: $4x + 36y = 80 $}\\\textup{This can be written in the form of $y = mx + a$ as follows}\\$ 36y = -4x + 80 $\\$ \implies y = \frac{80}{36} - \frac{4}{36}x $\\$ \implies y = \frac{-1}{9}x + \frac{20}{9} $\\\textup{This means that the slope of this line is $m = \frac{-1}{9}$}\\$

$\textup{Then the slope of the line perpendicular to this line would be \textbf{negative reciprocal of m}.}\\$i.e.,$ \textup{Slope of the perpendicular line would be $m_1 = \frac{-1}{\frac{-1}{9}}$}\\$\implies m_1 = 9$\\$

$\textup{The perpendicular line passes through the point $(3,6)$}\\\textup{Using the \textbf{point-slope formula}, we get:}\\$

$$$ y - y_1 = m(x - x_1) $$$ \implies y - 6 = 9(x - 3) $\\\textup{After solving this reduces to $y = 9x + 21$ }$

8 0

3 years ago

Use a whole number, a fraction, one plus sign, and four 2's to make 23.

alexira [117]

22+2/2=23

22 is whole number
one plus sign
and 2/2 is the fraction
4 digits are 2

6 0

3 years ago

Bert and Ernie are missing each other and their friend Big Bird They want to meet at Big Bird's nest which is halfway from their

algol [13]

Answer:

The distance between Bert and Ernie's apartments from Big Bird's nest

is 21 miles

Step-by-step explanation:

* Lets change the story problem to an equation to solve the problem

- The information i the story problem is

# The Big Bird's nest is halfway from there apartments

# The distance between Bert's apartment and Big Bird's nest is (5x + 4)

# The distance between Ernie's apartment and Big Bird's nest is (15x - 30)

* Now lets solve

∵ The Big Bird's nest is halfway from there apartments

∴ The distance between Bert's apartment and Big Bird's nest = The

distance between Ernie's apartment and Big Bird's nest

∴ 5x + 4 = 15x - 30

- Collect the variable terms in one side and the numerical terms

in th other side

∴ 15x - 5x = 30 + 4 ⇒ add

∴ 10x = 34

∴ x = 34 ÷ 10 = 3.4

* Now lets find the distance between Bert and Ernie's apartments

from the Big Bird's nest

- We can use any relation to find the distance

∵ The distance = 5x + 4

∵ x = 3.4

∴ The distance = 5(3.4) + 4 = 17 + 4 = 21 miles

You can check the answer by using second equation

∵ The distance = 15x - 30

∵ x = 3.4

∴ The distance = 15(3.4) - 30 = 51 - 30 = 21 miles

4 0

3 years ago

There are 2,000 eligible voters in a precinct. A total of 500 voters are randomly selected and asked whether they plan to vote f

Ann [662]

Answer:

$0.7 - 2.58 \sqrt{\frac{0.7(1-0.7)}{500}}=0.647$

$0.7 + 2.58 \sqrt{\frac{0.7(1-0.7)}{500}}=0.753$

And the 99% confidence interval would be given (0.647;0.753).

So the correct answer would be:

a. 0.647 and 0.753

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The population proportion have the following distribution

$p \sim N(p,\sqrt{\frac{p(1-p)}{n}})$

Solution to the problem

The estimated population proportion for this case is:

$\hat p = \frac{350}{500}=0.7$

The confidence interval would be given by this formula

$\hat p \pm z_{\alpha/2} \sqrt{\frac{\hat p(1-\hat p)}{n}}$

For the 99% confidence interval the value of $\alpha=1-0.99=0.01$ and $\alpha/2=0.005$ , with that value we can find the quantile required for the interval in the normal standard distribution.

$z_{\alpha/2}=2.58$

And replacing into the confidence interval formula we got:

$0.7 - 2.58 \sqrt{\frac{0.7(1-0.7)}{500}}=0.647$

$0.7 + 2.58 \sqrt{\frac{0.7(1-0.7)}{500}}=0.753$

And the 99% confidence interval would be given (0.647;0.753).

So the correct answer would be:

a. 0.647 and 0.753

7 0

3 years ago

A chocolate company makes chocolate malt balls that have a radius of 0.34

IceJOKER [234]

Answer:

<h2>Approximately 141 malt balls</h2>

Step-by-step explanation:

this problem is on the mensuration of solids shapes.

first we need to calculate the volume of the rectangular prism

volume of prsim= l*b*h

given that

length= 1.5 in

breath=2.5 in

hieght= 6 in

volume= 1.5*2.5*6

volume=22.5 in^3

secondly we then calculate the volume of a malt ball

given that

raduis r= 0.34

volume of sphere = 4/3πr^3

volume of sphere = 4/3*3.124*(0.34)^3

volume of sphere = 1.33*3.142*0.039

volume of sphere = 0.16 in^3

now we can calculate the amount of sphere that can fit into the prism as

= volume of prism/volume of sphere

= 22.5/0.16

=140.6

approximately 141 malt balls

3 0

3 years ago