Anthony's sink is shaped like a half-sphere, and it has a volume of 512π cubic inches. It is completely full of water, and he has two different cylindrical cups he can use to scoop it out.

The blue cup has a diameter of 4 in. and a height of 8 in., and the green cup has a diameter of 8 in. and a height of 8 in.. How many cupfuls of water will it take for him to empty his sink using each cup?

In your answer, give the number of cupfuls it will take to empty the sink using each cup, and then explain how you calculated it.

Explanation:

The first column is nothing but "2"s.

The second column has the sequence 2, 1, 0 from top to bottom. If the pattern keeps up, then the next value in the second column should be -1 since we're counting down by 1. Use a number line to see this.

So we have 2-(-1) = 2+1 = 3 or 2-(-1) = 3 as the next line. I think keeping it as 2-(-1) rather than 2+1 is beneficial so that the minus signs line up.

The result of 3 helps confirm that the final column of values (0,1,2) is incrementing by 1.

Answer: 200

Step-by-step explanation:

The initial value is 200, since this is the population before conservation efforts began.

Answer:

The equation of the line is y = 2x + 2

Step-by-step explanation:

Equation of a linear line can be placed in the format:

Formula for finding the slope(m):

[tex] \sf{}m = \frac{x- x_1}{y - y_1} = \frac{y_2 - y_1}{x_2 - x_1} \\ \\ \sf{}m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]

[tex] \sf{}m = \frac{8 - 4}{5 - 3} = \cancel \frac{4}{2} = 2[/tex]

Form the intermediate equation:

y = mx + c

[tex] \mathtt{y = 2x + c}[/tex]

Find the y-intercept:

Substitute (3,4) into the equation

[tex] : \longrightarrow \: \mathtt{y = 2x + c} \\ \\ : \longrightarrow \:\mathtt{4 = 2(3) + c} \\ \\ : \longrightarrow \: \mathtt{4 = 6 + c} \\ \\ : \longrightarrow \: \mathtt{c = 6 - 4} \\ \\ : \longrightarrow \: \mathtt{c = 2}[/tex]

Form the equation:

[tex]: \longrightarrow \: \mathtt{y = 2x + c} \: \\ \\ \mathtt{putting \: values \: of \: c} \\ \\ : \longrightarrow \: \mathtt{y = 2x + 2}[/tex]

The equation of the line is [tex]\underline\mathfrak\red{{{y = 2x + 2}}}[/tex]

Using the t-distribution, as we have the standard deviation for the sample, it is found that the p-value is of 0.0009.

At the null hypothesis, it is tested if the students study 20 hours, that is:

[tex]H_0: \mu = 20[/tex].

At the alternative hypothesis, it is tested if they study less than 20 hours, that is:

[tex]H_1: \mu < 20[/tex].

The test statistic is given by:

[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]

The parameters are:

In this problem, the values of the parameters are given as:

[tex]\overline{x} = 17.7, \mu = 20, s = 3.9, n = 33[/tex].

Hence, the value of the test statistic is:

[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]

[tex]t = \frac{17.7 - 20}{\frac{3.9}{\sqrt{33}}}[/tex]

[tex]t = -3.39[/tex]

Using a t-distribution calculator, considering a left-tailed test, as we are testing if the mean is less than value, the p-value is of 0.0009.

More can be learned about the t-distribution at https://brainly.com/question/13873630

Answer:

slope: 2

slope:

[tex]\sf \dfrac{y_2-y_1}{x_2-x_1}[/tex]

[tex]\rightarrow \sf \dfrac{12-4}{6-2}[/tex]

[tex]\rightarrow \sf \dfrac{8}{4}[/tex]

[tex]\rightarrow 2[/tex]

2

x-9 = -5

2=x 2+x + 4-2=2 2-6+

-4

2

X

Answer:

The scale factor is 2.

Step-by-step explanation:

From the coordiante plane, we can see that:

Point H(4) has been expanded to 4 {4 · 2 = 8}

Point G(1) has been expanded to 2 {1 · 2 = 2}

Point I(-2) has been expanded to -4 {-2 · 2 = -4}

hope this helps!

Answer:

38.5

Step-by-step explanation:

to find the area of the triangle, you can do 11 x 3 ÷ 2 = 16.5

then you find the area of the triangles: 3 x 3 = 9

and 3 × 11 = 33

then you add them all to find a total area of 38.5

Answer:

Hope the picture will help you......

[tex]\huge\fbox\purple{ANSWER} [/tex]

[tex] \mathsf\pink{v = l \times w \times h}[/tex]

[tex] \mathsf \purple{{72in}^{3} = c \times 4in \times 3in}[/tex]

[tex] \mathsf \pink{ {72in}^{3} = c \times 12 {in}^{2} }[/tex]

[tex] \mathsf \purple{ \frac{72 {in}^{3} }{ {12in}^{2} } = c \times \frac{12 {in}^{2} }{ {12in}^{2} } }[/tex]

[tex] \mathsf \pink{6in = c}[/tex]

[tex] \huge \tt \color{pink}{A}\color{blue}{n}\color{red}{s}\color{green}{w}\color{grey}{e}\color{purple}{r }[/tex]

[tex] \boxed{ \pink✠\underline{ \boxed{ \sf{Volume \: of \: Rectangular \: prism=length × width × height.}}} \pink✠}[/tex]

[tex]\rule{80mm}{2.5pt}[/tex]

[tex] \qquad \sf \: ➛ 72 = c \times 4 \times 3 \\ \qquad \sf \: ➛72 = c \times 12 \\ \qquad \sf \: ➛transporting \: 12 \: in \: divide \\ \qquad \sf \: ➛ \frac{72}{12} = c \\ \qquad \sf \: ➛ \cancel\frac{72}{12} = c \\ \qquad \sf \: ➛6 = c[/tex]

[tex]\rule{80mm}{2.5pt}[/tex]

★ Hence "c" (length) of Rectangular prism (shipping carton) is

[tex]\boxed{ \blue✜\underline{ \boxed{ \sf{length(c)= 6inch \green✓}}} \blue✜}[/tex]

Hope it helps !

Using an exponential function, it is found that the approximate number of crimes in the year of 2016 was of 2502.

An increasing exponential function is modeled by:

[tex]A(t) = A(0)(1 + r)^t[/tex]

In which:

In this problem, there were 550 crimes in the initial year observed, and the growth rate is of 6%, hence the parameters are A(0) = 550, r = 0.06, and the equation is given by:

[tex]A(t) = A(0)(1 + r)^t[/tex]

[tex]A(t) = 550(1 + 0.06)^t[/tex]

[tex]A(t) = 550(1.06)^t[/tex]

2016 is 26 years after 1990, hence:

[tex]A(26) = 550(1.06)^{26} \approx 2502[/tex]

The approximate number of crimes in the year of 2016 was of 2502.

More can be learned about exponential functions at https://brainly.com/question/25537936

Answer: [tex]Y=-3[/tex]

Step-by-step explanation:

[tex]Y=5x-3[/tex]

[tex]Y=5 * (x) -3[/tex]

Then replace x by 0

[tex]Y=5 * (0) -3[/tex] or [tex]Y= 5(0) -3[/tex]

[tex]Y=0 -3[/tex]

[tex]Y=-3[/tex]

Answer:

12×3=36

Step-by-step explanation:

hope ththis helped :))

Step-by-step explanation:

common ratio is usually used for geometric sequences.

every term is created by multiplying the previous term by a certain constant factor (= common ratio).

this factor or common ratio is in our case 4.

such a sequence is a function f(x) for x being whole numbers.

a0 = 1

a1 = a0×4 = 1×4 = 4

a2 = a1×4 = 4×4 = 16

...

an = 4^n

as general function that is then

f(x) = 4^x

a horizontal shift right by 6 units means that now the functional value of x is the same as it was for (x-6) before the shift.

e.g. f_new(6) = f_old(0)

so, the function is

f(x) = 4^(x - 6) or (4^x)/4⁶

Answer:

more girls than boys.

Step-by-step explanation:

because there is 95 girls compared to 65 boys, so whatever random numbers of both are pulled, girls will have the higher ratio.

Answer:

2/15

Step-by-step explanation:

Given:

A box contains 4 white balls and 6 yellow balls. A ball is drawn at random from the box and is not replaced. What is the probability that both balls are white?

8/45

3/25

4/25

2/15

Solve:

Knowing that total = 10 { 4 white balls and 6 yellow balls}

P(first white)=4/10=2/5 { 4 out of 10 balls are white}

P(second white)=3/9=1/3 { 3 out of 9 balls are white; Since no replaced}

P(both white)=2/5 × 1/3=2/15

Hence, Answer = 2/15

Lenvy~

Original price = $7200

But he bought it for 65%

So it is just 65% of $7200

0.65 * $7200 = $4680

Answer:

just practice alot . .. ...........

Answer:

you could do all your work and try to ask the teacher for help

Step-by-step explanation:

Answer:

240 feet

Step-by-step explanation:

The formula for finding the area of a triangle is: [tex]\frac{1}{2}bh[/tex], where [tex]b[/tex] stands for the base and [tex]h[/tex] stands for the height.

In this case, 20 is our height, and 24 is our base. Let's plug that into the formula.

[tex]1/2(20)(24)\\1/2(480)\\240[/tex]

Therefore, the area of the triangle is 240 feet.

#LearnWithBrainly

Answer:

Average velocity

Step-by-step explanation:

The average speed is only different from average velocity because it has direction.

The average speed will be calculated with the hypotenuse A_C, but average velocity will be calculated with the two directions AB_BC.

The equation that can be used to determine the volume of the sphere is 4/3π10³

A sphere is a three-dimensional object in which points from its center to its circumference is equidistant.

Volume of a sphere = 4/3πr³

Where:

To learn more about the volume of a sphere, please check: https://brainly.com/question/13705125

Answer:

The answer is [tex]13\pi[/tex] or 40.84

Step-by-step explanation:

We are given the diamater so

[tex]r=\frac{d}{2}[/tex]

[tex]r=\frac{13}{2}[/tex]

[tex]r=6.5[/tex]

Formula for circumference.

Take note.

C = circumference

r = radius

[tex]C=2\pi r[/tex]

You want your answer in terms of Pi.

So we can write another equation.

[tex]2\pi r=\pi x[/tex]

x stands for the number in terms of Pi.

Now we can solve for x.

[tex]x=\frac{2\pi r}{\pi }[/tex]

Now lets plug in what we know.

[tex]x=\frac{2*\pi*6.5 }{\pi }[/tex]

[tex]x=13[/tex]

Answer:

11/30

Step-by-step explanation:

Do you need an explanation?

Answer:

51 total items

Step-by-step explanation:

210 Magazine : 300 Books

21 Magazine : 30 Books

If She wants to sell 21 magazines, she would have to sell  another 30 books in order to maintain the ratio.

21 + 30 = 51

Answer: x = 4ooo sin 340 x = 223627 ft.

Step-by-step explanation: The angle between the waterline and the submarine is 34°. How deep is the submarine?

Answer:

92.9

Step-by-step explanation:

8.90 times 6 equals 53.40

7.90 times 5 equals 39.50

39.50 plus 53.40 equals 92.9

The area of the considered 3 triangles is given by: Option B: 13 sq. units.

Suppose the vertices of the considered triangle ABC are on [tex]A(A_x,A_y), B(B_x,B_y), C(C_x,C_y)[/tex], then, the area of the triangle is given by:

[tex]Area = \dfrac{|A_x(B_y-C_y) + B_x(C_y-A_y) + C_x(A_y-B_y)|}{2}[/tex]

For this case, the missing image is attached below.

The second and third triangle are easy as their base and height are parallel to x or y axis.

We will find area of third triangle by coordinates of its vertices.

Getting area of first triangle:

Thus, we get:

[tex]Area_{ABC} = \dfrac{|4(7-8) + 5(8-10) + 7(10-7)|}{2} = \dfrac{7}{2} = 3.5 \: \rm unit^2[/tex]

Area of second triangle = [tex]\dfrac{|RS| \times h}{2}[/tex]base, and h is the perpendicular line connecting from line RS and the vertex T

From figure we see:

|RS| = 3 units, h = 3 units

Thus, area of second triangle = [tex]3 \times 3 /2 = 4.5 \: \rm unit^2[/tex]

Area of third triangle = [tex]\dfrac{|XY| \times h}{2}[/tex] where XY is base, and h is the perpendicular line connecting from line XY and the vertex Z

From figure we see:

|XY| = 5 units, h = 2 units

Thus, Area of third triangle = [tex]5 \times 2 /2 = 5 \: \rm unit^2[/tex]

Total area = 3.5 + 4.5 + 5  = 13 sq. units

Thus, the area of the considered 3 triangles is given by: Option B: 13 sq. units.

Learn more about area of a triangle from its vertices' coordinates here:

https://brainly.com/question/2532574

Answer:

13

Step-by-step explanation:

Answer: 6. this is like 3rd grade math just multiply 1/3 and 1/6 to see

Answer:

1/2

Step-by-step explanation:

1/6/1/3=1/2or2

I the not understand the question properly