Part A
What are the possible outcomes of rolling a six-sided dle?

Using the proportional relationship, it is found that the radius of the pipe that would allow the sink to drain completely in 14 seconds is of 1.25 cm.

A proportional relationship is a function in which the output variable is given by the input variable multiplied by a constant of proportionality, that is:

[tex]y = kx[/tex]

In which k is the constant of proportionality.

If they are inverse proportional, the relationship is:

[tex]y = \frac{k}{x}[/tex]

In this problem, the amount of time is inversely proportional to the square of the radius of the pipe, hence:

[tex]t = \frac{k}{r^2}[/tex]

A pipe of radius 1 cm can empty a sink in 22 seconds, hence k = 22.

The radius for 14 seconds is:

[tex]t = \frac{k}{r^2}[/tex]

[tex]14 = \frac{22}{r^2}[/tex]

[tex]r^2 = \frac{22}{14}[/tex]

[tex]r = \sqrt{\frac{22}{14}}[/tex]

[tex]r = 1.25[/tex]

The radius of the pipe that would allow the sink to drain completely in 14 seconds is of 1.25 cm.

More can be learned about proportional relationships at https://brainly.com/question/25890103

Answer:

3217.00

Step-by-step explanation:

V=πr^2h=π·8^2·16≈3216.99088

Answer:

804.2 or 803.8

Step-by-step explanation:

volume = π · r2 · h

π · [tex]4^{2}[/tex] · 16 = 804.2

3.14 · [tex]4^{2}[/tex] · 16 = 803.8

Answer:

x=-8

Step-by-step explanation:

5x-3x=-2-14

2x=-16

x=-8

Answer:

0.92 cm

Step-by-step explanation:

Do not pick 0.920 as it is the same as 0.92 but 0.92 is always the preferable option

The accurate measurement for the length of the green box is indeed 0.92 cm.

To measure the length of the green box accurately, we must carefully analyze the given image. By comparing the green box to the provided scale, we can deduce the correct measurement.

Upon examination, the green box appears to span almost the entirety of the "0.1 cm" scale division and extends slightly beyond it. Given that the box reaches around 9 divisions on the scale, it is reasonable to deduce that its length is 0.92 cm. This is because it's covering 9 divisions of 0.1 cm each, and considering the small extension.

Hence, the accurate measurement for the length of the green box is indeed 0.92 cm. This value takes into account its coverage of 0.9 cm (9 divisions) and a slight extension, aligning with the provided options.

To know more about measurement:

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Answer:

X= 5/18

Step-by-step explanation:

Answer:

68 degrees

Step-by-step explanation:

EHD and CHF are vertical angles, meaning their angle measures are the same.

Answer:

m<CHF = 68°

Step-by-step explanation:

Angles EHD and CHF are vertical angles, so their measures are equal.

m<CHF = m<EHD = 68°

Answer:

[tex]\sf x < \dfrac{16}{7} ,x > \dfrac{16}{7}[/tex]

Step-by-step explanation:

Given function:

[tex]\sf f[g(x)]=\dfrac{-6+23}{7x-16}[/tex]

The domain will be values of x that do NOT make the denominator zero:

[tex]\sf \implies 7x-16=0[/tex]

[tex]\sf \implies 7x=16[/tex]

[tex]\sf \implies x=\dfrac{16}{7}[/tex]

Therefore, the domain is [tex]\sf x\neq \dfrac{16}{7}[/tex] so

[tex]\sf x < \dfrac{16}{7} ,x > \dfrac{16}{7}[/tex]

Total Amount on principal 7000dollars  at the rate of interest 3%  for time period 7years is equals to $8470.

" Simple interest is a method of calculating interest on the amount of money deposited for fixed period on fixed rate of interest."

Formula used

[tex]Amount = P ( 1+ rt) \\P= Principal\\r= Rate of interest\\t= time period[/tex]

According to the question,

Given,

Principal 'P' = $7000

Rate of interest 'r'= 3%

Time period 't' = 7years

Substitute the value in the formula to get total amount with interest,

[tex]Amount = 7000 [ 1+ (\frac{3}{100} )(7)][/tex]

             [tex]=7000[ 1+ (0.03)(7)]\\=7000(1.21)\\=8470 dollars[/tex]

Hence, the total Amount on principal 7000dollars  at the rate of interest 3%  for time period 7years is equals to $8470.

Learn more about simple interest here

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The length of one of the legs  of an isosceles right triangle and has a hypotenuse length of seven times the square root of two is 7 units.

Isosceles triangles are triangles that has two of it sides equal to each other. The base angles of an isosceles triangle are equal.

The  isosceles triangle is also a right angle triangle. The hypotenuse is the longest side of a right angle triangle.

Therefore,

hypotenuse = 7(√2)

let the length of the other legs = x

Therefore, using Pythagoras theorem

c² = a² + b²

(7(√2))² = x² + x²

49 × 2 = 2x²

98 = 2x²

x² = 98 / 2

x = √49

x = 7 units

learn more on isosceles triangle here: https://brainly.com/question/10412877

Hello !

_______

[tex]\huge {\boxed {\underline{Explanation :}}}[/tex]

[tex]\sf{5 \: x \: \frac{3}{4}[/tex]

_______

[tex]\sf{Apply \: the \: fraction \: rule :} \: a \: ^. \: \frac{b}{c} = \frac{a \: ^. \: b}{c}[/tex]

[tex]\sf{\frac{5x \: ^. \: 3}{4}[/tex]

_______

[tex]\sf{Multiply \: the \: numbers:} \: 5 \: ^. \: 3 = 15[/tex]

[tex]\sf{= \frac{15x}{x}[/tex]

Hopefully This Helps ! ~

#LearnWithBrainly

[tex]\underline{Answer :}[/tex]

Dollixna ~

Answer:

4.57894737

Step-by-step explanation:

261 divided by 57 = 4.57894737

or 4.6 to 1 decimal place

If you need further explanation, let me know!

-profparis

Answer: 4.57894736842

Answer/Step-by-step explanation:

 All of the solutions to the equation 3x^2 - 12 = 0 are x = 12 and x = -2

Answer: False

Explanation:

[tex]3x^2-12+12=0+12[/tex]

[tex]3x^2=12[/tex]

[tex]\frac{3x^2}{3}=\frac{12}{3}[/tex]

[tex]x^2=4[/tex]

[tex]\mathrm{For\:}x^2=f\left(a\right)\mathrm{\:the\:solutions\:are\:}x=\sqrt{f\left(a\right)},\:\:-\sqrt{f\left(a\right)}[/tex]

[tex]x=\sqrt{4},\:x=-\sqrt{4}[/tex]

[tex]x=2,\:x=-2[/tex]

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

There are two unique solutions to the equations (x-3)^2 = 16

Note: Each variable in the matrix can have only one possible value, and this is how you know that this matrix has one unique solution.

Answer: True

Explanation:

[tex]\mathrm{For\:}\left(g\left(x\right)\right)^2=f\left(a\right)\mathrm{\:the\:solutions\:are\:}g\left(x\right)=\sqrt{f\left(a\right)},\:\:-\sqrt{f\left(a\right)}[/tex]

[tex]x=7,\:x=-1[/tex]

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Ths solutions for the equation 2(x-3)^3 - 18 = 0 are x = 6 and x = 0

Answer: False

Explanation:

[tex]2\left(x-3\right)^3-18+18=0+18[/tex]

[tex]2\left(x-3\right)^3=18[/tex]

[tex]\frac{2\left(x-3\right)^3}{2}=\frac{18}{2}[/tex]

[tex]\left(x-3\right)^3=9[/tex]

[tex]\mathrm{For\:}g^3\left(x\right)=f\left(a\right)\mathrm{\:the\:solutions\:are\:}g\left(x\right)=\sqrt[3]{f\left(a\right)},\:\sqrt[3]{f\left(a\right)}\frac{-1-\sqrt{3}i}{2},\:\sqrt[3]{f\left(a\right)}\frac{-1+\sqrt{3}i}{2}[/tex]

[tex]=\sqrt[3]{9}+3,\:x=\frac{6-\sqrt[3]{9}}{2}+i\frac{\sqrt[3]{9}\sqrt{3}}{2},\:x=\frac{6-\sqrt[3]{9}}{2}-i\frac{\sqrt[3]{9}\sqrt{3}}{2}[/tex]

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~The solutions for the equation 2(x-5)^2-8=0 are x = 7 and x = -7

Answer: False

Explanation:

[tex]2\left(x-5\right)^2-8+8=0+8[/tex]

[tex]2\left(x-5\right)^2=8[/tex]

[tex]\frac{2\left(x-5\right)^2}{2}=\frac{8}{2}[/tex]

[tex]\left(x-5\right)^2=4[/tex]

[tex]\mathrm{For\:}\left(g\left(x\right)\right)^2=f\left(a\right)\mathrm{\:the\:solutions\:are\:}g\left(x\right)=\sqrt{f\left(a\right)},\:\:-\sqrt{f\left(a\right)}[/tex]

[tex]x=7,\:x=3[/tex]

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

The solutions for the equation (x + 3)^2-25 = -8 are x = 2 and x = -8

Answer: False

Explanation:

[tex]\left(x+3\right)^2-25+25=-8+25[/tex]

[tex]\left(x+3\right)^2=17[/tex]

[tex]\mathrm{For\:}\left(g\left(x\right)\right)^2=f\left(a\right)\mathrm{\:the\:solutions\:are\:}g\left(x\right)=\sqrt{f\left(a\right)},\:\:-\sqrt{f\left(a\right)}[/tex]

[tex]x=\sqrt{17}-3,\:x=-\sqrt{17}-3[/tex]

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

The solutions for the equation 2(2x-1)^2=18 are x = 5 and x = -4

Answer: False

Explanation:

[tex]\frac{2\left(2x-1\right)^2}{2}=\frac{18}{2}[/tex]

[tex]\left(2x-1\right)^2=9[/tex]

[tex]\mathrm{For\:}\left(g\left(x\right)\right)^2=f\left(a\right)\mathrm{\:the\:solutions\:are\:}g\left(x\right)=\sqrt{f\left(a\right)},\:\:-\sqrt{f\left(a\right)}[/tex]

[tex]x=2,x=-1[/tex]

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

The only solution for equation (2x-1)^2-49=0 is x = 4

Answer: False
Explanation:

[tex]\left(2x-1\right)^2-49+49=0+49[/tex]

[tex]\left(2x-1\right)^2=49[/tex]

[tex]\mathrm{For\:}\left(g\left(x\right)\right)^2=f\left(a\right)\mathrm{\:the\:solutions\:are\:}g\left(x\right)=\sqrt{f\left(a\right)},\:\:-\sqrt{f\left(a\right)}[/tex]

[tex]x=4,\:x=-3[/tex]

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

The solutions for the equation 3(x+2)^2 - 3 = 0 are x = -3 and x = -1

Answer: True
Explanation:

[tex]3\left(x+2\right)^2-3+3=0+3[/tex]

[tex]3\left(x+2\right)^2=3[/tex]

[tex]\frac{3\left(x+2\right)^2}{3}=\frac{3}{3}[/tex]

[tex]\left(x+2\right)^2=1[/tex]

[tex]\mathrm{For\:}\left(g\left(x\right)\right)^2=f\left(a\right)\mathrm{\:the\:solutions\:are\:}g\left(x\right)=\sqrt{f\left(a\right)},\:\:-\sqrt{f\left(a\right)}[/tex]

[tex]x=-1,\:x=-3[/tex]

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

The solutions for the equation 5x^2 - 180 = 0 are x = 6 and x  = -6

Answer: True

Explanation:

[tex]5x^2-180+180=0+180[/tex]

[tex]5x^2=180[/tex]

[tex]\frac{5x^2}{5}=\frac{180}{5}[/tex]

[tex]x^2=36[/tex]

[tex]\mathrm{For\:}x^2=f\left(a\right)\mathrm{\:the\:solutions\:are\:}x=\sqrt{f\left(a\right)},\:\:-\sqrt{f\left(a\right)}[/tex]

[tex]x=\sqrt{36},\:x=-\sqrt{36}[/tex]

[tex]x=6,\:x=-6[/tex]

~Lenvy~

Answer:

make the n in side and join together

Answer:

C)  y = -2x - 5

Step-by-step explanation:

[tex]\sf let \ (x_1,y_1)=(-3,1)\\\\let \ (x_2,y_2)=(0,-5)[/tex]

[tex]\sf slope=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{-5-1}{0-(-3)}=-2[/tex]

Point-slope formula: [tex]\sf y-y_1=m(x-x_1)[/tex]

[tex]\sf \implies y-1=-2(x-(-3))[/tex]

[tex]\sf \implies y=-2x-5[/tex]

Slope:-

Equation in point slope form

Answer:

A

Step-by-step explanation:

tanΘ = [tex]\frac{\sqrt{3} }{3}[/tex] , then

Θ = [tex]tan^{-1}[/tex] ( [tex]\frac{\sqrt{3} }{3}[/tex] ) = [tex]\frac{\pi }{6}[/tex]

since tanΘ > 0 then Θ is in first / third quadrants

Θ = π + [tex]\frac{\pi }{6}[/tex] = [tex]\frac{7\pi }{6}[/tex]

solution is { [tex]\frac{\pi }{6}[/tex] , [tex]\frac{7\pi }{6}[/tex] } in the interval 0 < Θ < 2π

Answer:

9/7

Step-by-step explanation:

2+2+1+3+4+6+8+1/10+4+3+4

Hope this helps!!!

Answer:

Step-by-step explanation:

Assuming you can use any digit from 0-9

You can do 5% of 260 = 13 . All of which are different digits and not the same

This is true because 260 x .05 = 13

Answer:

66

Step-by-step explanation:

Lacrosse: 33

Tennis: 33

0.25 x 132 = 33

Basket ball:?

33 + 33 + b = 132

66 + b = 132

132 - 66 = 66

b = 66

Have a great day!

Please rate and mark brainliest!!

Answer:

D.  66

Step-by-step explanation:

Total number of students = 132

If 25% of 132 students play tennis:

⇒ 0.25 × 132 = 33

So 33 students play tennis

Number of students who play basketball is: total number of students minus students play tennis minus students play lacrosse:

= basketball = 132 - 33 - 33 = 66

Answer:

b) one quarter hour

Step-by-step explanation:

every section is worth 5 minutes, there are three sections, which equals 15 minutes, 15 minutes is a one-quarter hour. hope this helps :)

Answer:

B

Step-by-step explanation:

it Is one quarter of an hour because they are exactly 15 minutes

Answer:

y = -1/2x + 1

Step-by-step explanation:

We find slope using rise-over-run and by counting I got 1/2 but the slope is also negative. The y-intercept is 1 because the points are counting by 1/2 and the line goes through where half of 2 is on the y-axis. Hope this helps!

Answer:

140

Step-by-step explanation:

5t + 10 = 4t + 22

t + 10 = 22

t = 12

5(12) + 10 = 70

4(12)+ 22 = 70

70 + 70 = 140

CP + PK = CK

Edit:

I'm not sure if the solution is correct , but there is at least something.

Now

CK

well, we know that he makes $60 weekly, that'd be the 100%, we also know that he saves 30% of that and the rest, well, 100% - 30% = 70%, so 70% he spends it on food.

if we take 60 to be the 100%, what is 70% of it?

[tex]\begin{array}{ccll} amount&\%\\ \cline{1-2} 60 & 100\\ x& 70 \end{array} \implies \cfrac{60}{x}=\cfrac{100}{70}\implies \cfrac{60}{x}=\cfrac{10}{7} \\\\\\ 420=10x\implies \cfrac{420}{10}=x\implies 42=x[/tex]

Answer:

B. y = 5x-1

Step-by-step explanation:

B. y = 5x-1 is not an exponential function.

Answer:

{- 1, 0, 4 }

Step-by-step explanation:

the range is the y- coordinates of the plotted points

the coordinates of the points are

(- 4, - 1 ) , (1, 0 ) , (1, 4 ) with y- coordinates - 1, 0, 4

then range is { - 1, 0, 4 }

The 100th term of the sequence is -273

Arithmetic sequence is one derived from addition/subtraction of a constant term to find the next term. the constant term is usually called the common difference

first term a = 222

common difference, d = -5

nth term of an Arithmetic sequence. Tn = a + ( n - 1 ) d

T100 = a + ( 100 - 1 ) d

T100 = 222 + 99 * -5

T100 = -273

Read more on Arithmetic sequence here:

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Answer:

Option C :- 7.5x + 8.1

Step-by-step explanation:

Let's simplify step-by-step.

4.5x+3.1−(−3x−5)

Distribute the Negative Sign:

=4.5x+3.1+−1(−3x−5)

=4.5x+3.1+−1(−3x)+(−1)(−5)

=4.5x+3.1+3x+5

Combine Like Terms:

=4.5x+3.1+3x+5

=(4.5x+3x)+(3.1+5)

=7.5x+8.1

Answer:

=7.5x+8.1

Answer:

90 students

Step-by-step explanation:

So, if you have 100 students to start and it decreases by 10% then take the 100 and multiply it by .10. You should get 10. Then, subtract 10 from 100 and you end up with 90.

Answer:

hello

2010 = 100 students

2011 = 100 x 0.9 = 90

2012 =  90 x 1.1 =  99  

Step-by-step explanation:

Answer: (2,1)

Step-by-step explanation:

The two equations given are:

           y = 3 -x

           y = x - 1

The question is asking to determine the point of intersection for two linear functions aka two lines.

Step #1: Both functions must be in slope intercept form which is y = mx+b. In this case, this step can be skipped because both functions are in slope form. At an intersection, x and y must have the same value for each equation. This means that the equations are equal to each other. Therefore, we can set both equations equal to each other to solve for x.

Step #2: We found the x-coordinate, but we need to find the y-coordinate. We know that the x-coordinate is 2, so substitute the number 2 into any of the given equations. So, either into y = 3 - x or y = x - 1.

The point of intersection is (2,1).

Hope this helps ^_^