Calculate the value of 3√216
by using prime

factors

Answer:

[tex]14\text{ liters}[/tex]

Step-by-step explanation:

Let the total amount of water the container can hold be [tex]t[/tex]. Currently, there are [tex]n[/tex] liters in the container. If Ito adds 10 liters of water, the container will be 60% full. We can express this statement in the following mathematical equation:

[tex]n+10=0.6t[/tex]

Next, we're given that if we add 6 more liters to this, the container will be 75% full.

Therefore, we have:

[tex]n+10+6=0.75t,\\n+16=0.75t[/tex]

This is a system of equations:

[tex]\begin{cases}n+10=0.6t,\\ n+16=0.75t\end{cases}[/tex]

Subtract both equations to conveniently get rid of [tex]n[/tex]:

[tex]10-16=0.6t-0.75t,[/tex]

Combine like terms:

[tex]-6=-0.15t[/tex]

Divide both sides by -0.15:

[tex]t=\frac{-6}{-0.15}=40[/tex]

Now substitute [tex]t=40[/tex] into any equation (I'll choose the first):

[tex]n+10=0.6(40),\\n+10=24[/tex]

Subtract 10 from both sides:

[tex]n=24-10=\boxed{14\text{ liters}}[/tex]

Hello!

[tex] \bf 5 \sqrt{37} + \sqrt{98} - 3 \sqrt{147} [/tex]

[tex] \bf 5 \sqrt{37} + 7 \sqrt{2} - 21 \sqrt{3} [/tex]

I removed the factors from under the radical.

Good luck! :)

Answer:

hello,

answer C

Step-by-step explanation:

As |a| ≥0,

f(|a|)=|a|+5

Answer:

copy and paste...

Step-by-step explanation:

As in the picture.hope it helps.......

Plzzzz mark brainlist if correct.....

A square pyramid has 4 triangles and the square base.

Calculate the area of one triangle, multiply that by 4 then add the area of the base.

Area of triangle = 1/2 x base x height = 1/2 x 5 x 12 = 30 square yards.

30 x 4 = 120 square yards

Area of base = 5 x 5 = 25 square yards

Total = 120 + 25 = 145 square yards.

Answer:

4

Step-by-step explanation:

64^1/3

cube root of 64 is

4

Answer:

C

Step-by-step explanation:

Using the rule of exponents

[tex]a^{\frac{1}{3} }[/tex] ⇔ [tex]\sqrt[3]{a}[/tex] , then

[tex]64^{\frac{1}{3} }[/tex] = [tex]\sqrt[3]{64}[/tex] = 4 → C

Answer:

Step-by-step explanation:

o find the unit rate , divide the numerator and denominator of the given rate by the denominator of the given rate.

start with the rate of miles to gallons . then divide , write as a rate.

hope this helps.

where are the following vehicles name

[tex]mean = \frac{sum \: of \: all \: observations}{number \: of \: observations} \\ = > mean = \frac{8 + 12 + 16 + 10 + 18 + 15 + 22 + 16 + 14 + 17}{10} \\ = > mean = \frac{148}{10} \\ = > mean = 14.8[/tex]

This is the answer.

Given:

The data set is:

0, 1, 1, 1, 2, 3, 4, 4, 6, 6, 9

To find:

The correct statement that represents the box plot of the data correctly.

Solution:

We have,

0, 1, 1, 1, 2, 3, 4, 4, 6, 6, 9

Divide the data in 2 equal parts.

(0, 1, 1, 1, 2), 3, (4, 4, 6, 6, 9)

Divide each parenthesis in 2 equal parts.

(0, 1), 1, (1, 2), 3, (4, 4), 6, (6, 9)

Here,

Minimum value = 0

First quartile = 1

Median = 3

Third quartile = 6

Maximum value = 9

A number line goes from 0 to 10. The whiskers range from 0 to 9, and the box ranges from 1 to 6. A line divides the box at 3.

Therefore, the correct option is D.

Answer:

its d

Step-by-step explanation: my yt Tray Clayps

Answer:

-0.5

Step-by-step explanation:

Answer:

552

Step-by-step explanation:

I'm almost certain this is correct. Only one step is rounded.

Answer:  942 - 225*sqrt(3)

This is roughly equivalent to 552.29

The unit for the area is in square cm, or cm^2.

The two area values above are based on pi = 3.14, so they are approximations.

============================================================

Explanation:

The radius of the circle is r = 30 because OA = 30.

The full circle has area A = pi*r^2 = 3.14*30^2 = 2826 cm^2 approximately

However, we only want 120/360 = 1/3 of this full area to get the area of the pizza slice. So the area of the pizza slice is approximately (1/3)*2826 = 942 cm^2

This is not the final answer, but helps get us there.

What we just calculated was the approximate area of the entire figure: the yellow area plus the white triangle.

If we can find the area of the white triangle, and subtract it off, then we'll find just the area of the yellow region only.

-----------------------

The SAS (side angle side) area formula for a triangle is

Area = 0.5*p*q*sin(R)

where p,q are the sides and angle R is between those sides.

Here we have p = q = 30, which are sides OA and OB, and we have R = 120 degrees as the central angle.

So the area of triangle AOB is...

Area = 0.5*p*q*sin(R)

Area = 0.5*30*30*sin(120)

Area = 450*sqrt(3)/2

Area = 225*sqrt(3)

This value is exact.

-----------------------

The area of the yellow region is therefore

(area of full figure) - (area of triangle)

(942) - (225*sqrt(3))

942 - 225*sqrt(3)

This is approximate because we used pi = 3.14 as an approximation earlier.

You could then use your calculator to say

942 - 225*sqrt(3) = 552.288568

This rounds to 552.29

Answer:

d. Cannot be determined with the information provided.

Step-by-step explanation:

Z-score:

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

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 p-value, we get the probability that the value of the measure is greater than X.

Finding the better relative position:

The score with the better relative position is the one with a higher z-score.

To find the z-score, the mean and the standard deviation is needed, and in this question, the standard deviation is not given, and thus, the correct answer is given by option d.

Answer:

Solution given:

note=diameter=2*radius

1:

Area of circle =πr²=22/7*(21/2)²=346.5cm²

2:

radius (r)= 3 ½=7/2cm

Area of circle =πr²=22/7*(7/2)²=38.5cm²

3;

radius (r)=14/2=7cm

Area of circle =πr²=22/7*(7)²=154cm²

note:

π=3.14 or 22/7

Answer:

3/4

Step-by-step explanation:

Let's say that r is the radius of the large circle or the diameter of the small circle.

Area of the big circle is [tex]\pi r^{2}[/tex] .

Area of the small circle is [tex]\pi \frac{r}{2} ^{2} = \pi \frac{r^{2}}{4}[/tex].

The ratio of these 2 circles is 1/4 (calculation in the comments).

So the shaded part represent 1 - 1/4 = 3/4.

Answer:

25

Step-by-step explanation:

5 cents = 0.05

1.25 / 0.05 = 25

let me know if i'm wrong

Answer:

25

Step-by-step explanation:

$1.25=125cents

125/5 = 25

$\sf\underline\bold\blue{Information\:given\:in\:the\:question:}$

$\space$

$\sf\underline\bold\blue{What\:we\:have\:to\:find?}$

$\space$

$\sf\underline\bold\blue{Answer:}$

$\space$

$\sf\underline\bold\blue{Calculations:}$

Here we have the value of the circle's diameter that is 20inches. So, first we have to calculate the radius of the circle using the formula :

$\mapsto$ $\sf\bold{Radius=}$ $\sf\dfrac{Diameter}{2}$

$\space$

$\sf\underline\bold\blue{Calculating\:the\:required\:values:}$

$\mapsto$ $\sf\bold{Radius=}$ $\sf\dfrac{20}{2}$

$\sf{Convert \: to \: the\:lowest\:term(Divide),}$

$\mapsto$ $\sf\underline\bold{Radius=10}$

☆Now we know the value of the radius . So now let's calculate the area of the circle.

$\space$

$\sf\bold{Area\:of\:circle:}$ π$\sf{ r \: ^{2} }$

$\sf\bold{Evaluating \: the\:required\:values:}$

$\sf\bold{Area\:of\:circle=3.1415(10)^2}$

$\space$

$\sf\bold{Area\:of\:the\:circle=3.1415\times10\times10}$

$\sf\bold{Now,}$

$\sf\bold{Area\:of\:the\:circle:3.1415\times100}$

$\space$

$\sf\underline\bold\green{Thus,Area\:of\:the\:circle\: is \: 314.15}$

____________________________

Answer:

[tex]\displaystyle x = \sqrt{y^2 + z^2}[/tex]

General Formulas and Concepts:

Pre-Algebra

Algebra i

Step-by-step explanation:

Step 1: Define

Identify

[tex]\displaystyle x^2 = y^2 + z^2[/tex]

Step 2: Solve for x

Answer:

124

Step-by-step explanation:

Answer:

[tex]\bar x_{girls} = 46.25[/tex]

Step-by-step explanation:

Given

[tex]Boys = 7\\Girls = 16[/tex]

[tex]\bar x = 49[/tex]

Required

Mean of girls

The mean of the boys and girls is calculated as:

[tex]\bar x = \frac{\sum x}{n}[/tex]

This gives:

[tex]\bar x = \frac{\sum(boys) + \sum(girls)}{boys + girls}[/tex]

So, we have:

[tex]49= \frac{42+85+47+29+58+54+ 72 + \sum(girls)}{7 + 16}[/tex]

[tex]49= \frac{387 + \sum(girls)}{23}[/tex]

Cross multiply

[tex]23 * 49=387 + \sum(girls)[/tex]

[tex]1127=387 + \sum(girls)[/tex]

Subtract by 387

[tex]1127-387 = \sum(girls)[/tex]

[tex]740= \sum(girls)[/tex]

[tex]\sum(girls) = 740[/tex]

The mean of girls is:

[tex]\bar x_{girls} = \frac{\sum(girls)}{girls}[/tex]

[tex]\bar x_{girls} = \frac{740}{16}[/tex]

[tex]\bar x_{girls} = 46.25[/tex]

Answer:

-11/6

Step-by-step explanation:

To find the slope, we use the formula

m = ( y2-y1)/(x2-x1)

   = ( 8- -3)/( -6 - 0)

   = (8+3)/(-6-0)

  = 11 / -6

 = -11/6

Step-by-step explanation:

is that really all ?

to simplify 12/2 and 12/3 ?

well, 12 can be divided by 2 and by 3 without remainder.

and so we get

12/2 = 6/1 = 6

12/3 = 4/1 = 4

Answer:

what should we be finding?

What is your question? if it is arranging in descending order, the answer is as follows:

25,23,20,16

Answer:

y = -x + 1

Step-by-step explanation:

eqn of line: y=mx+c

perpendicular, m1 x m2 = -1

m × 1 = -1

m = -1

y=-x+c

sub x=-5, y=6

6 = -(-5) +c

6 = 5 + c

c = 1

y = -x + 1

Answer:

she baked 3 times as many cranberry than blueberry muffins

Step-by-step explanation:

i think that because 9×3=27

the amount of the cranberry muffins are 9

Answer:

x = 10             x = -16

Step-by-step explanation:

(x+3)^2 - 169 = 0

Add 169 to each side

(x+3)^2 - 169+169 = 0+169

(x+3)^2 =169

Take the square root of each side

sqrt((x+3)^2) =sqrt(169)

x+3 =±13

x+3 = 13    x+3 = -13

Subtract 3 from each side

x+3-3 = 13-3    x+3-3 = -13

x = 10             x = -16

Answer:

D

Step-by-step explanation:

The first 3 are perfect squares and have 2 equal zeros

j(x) = x² + 6x + 9 = (x + 3)² with zeros x = - 3 , multiplicity of 2

k(x) = x² - 8x + 16 = (x - 4)² with zeros x = 4 , multiplicity of 2

h(x) = x² + 2x + 1 = (x + 1)² with zeros x = - 1 , multiplicity of 2

g(x)

x² - 64 is a difference of squares

(x - 8)(x + 8) = 0

with zeros x = - 8, x = 8 ← 2 different zeros

Answer:

-5 since he only had 80 in his checking