A rectangular aquarium is 1.5 ft wide, 6ft long, and 2 ft tall. If 1 ft^3 = 7.5 gallons, how much water can the aquarium hold?

Answer:

  24π cubic units

Step-by-step explanation:

Using the formula for the volume of a cylinder, you find it to be ...

  V = πr²h

  V = π(2²)(6)

  V = 24π . . . . cubic units

Answer:

y intercept (0,-32)

x intercept (3.2,0)

Step-by-step explanation:

To find the y intercept set x = 0 and solve for y

y = 10x -32

y = 0-32

y = -32

(0,-32)

To find the x intercept set y = 0 and solve for x

y = 10x -32

0 = 10x -32

Add 32 to each side

32 = 10x

Divide by 10

32/10 = x

(3.2,0)

Answer:

[tex]y-intercept(0,-32)\\\\x-intercept(\frac{16}{5},0)[/tex]

Step-by-step explanation:

The y-intercept happens where x is 0, and the x-intercept if where y is 0. You can use this knowledge to find the intercepts.

This equation is written in slope-intercept form:

[tex]y=mx+b[/tex]

where b is the y-intercept, so the y-intercept is -32.

To find the x intercept, insert 0 as the value of y:

[tex]0=10x-32[/tex]

Solve for x. Add 32 to both sides:

[tex]0+32=10x-32+32\\\\32=10x[/tex]

Divide both sides by 10:

[tex]\frac{32}{10}=\frac{10x}{10} \\\\x=\frac{32}{10} =\frac{16}{5}[/tex]

The x-intercept is at [tex]\frac{16}{5}[/tex] or [tex]3.2[/tex] .

Find the points:

[tex]y-intercept(0,-32)\\x-intercept(\frac{16}{5},0)[/tex]

Finito.

Answer:

Length = 13

Width = 9

Step-by-step explanation:

The equation to find the perimeter is 2l+2w=44. The second equation is 2w-5=l since the length is 5 less than double the width.

2l+2w=44,2w-5=l (write equations)

use the equation for length, the second equation, and subtitute it into the first equation's l. Since all l is the same and 2w-5 is equal to l, we can use that equation for the l in 2l+2w=p

2(2w-5)+2w=44 (subtitute)

4w-10+2w=44

6w-10=44 (simplify)

6w=54 (add 10 to both sides)

w=9

use the width to find the length by plugging it into any original equation

2w-5=l

2(9)-5=l

18-5=l

13=l

Answer:

The length is 13.

The width is 9.

Step-by-step explanation:

length = x

width = w

1) x = 2w - 5

2) 44 = 2x + 2w

3) 44 = 2(2w - 5) + 2w

4) 44 = 4w - 10 + 2w

5) 44 = 6w - 10

6) 54 = 6w

7) w = 9

8) x = 2(9) - 5

9) x = 18 - 5

10) x = 13

Multiply the amount he sold by the percent of commission:

4500 x 0.13 = 585

he made $585 last week.

There are 52 weeks in a year, multiply the amount of commission by 52:

585 x 52 = 30,420

he made $30,420 in 2011.

Alexander made $585 in commission last week. In 2011, he made $30,420 in commission.

To calculate Alexander's commission, we can multiply the value of the stocks he sold by the commission rate.

$4,500  imes 0.13 = $585

Therefore, Alexander made $585 in commission last week.

To calculate how much he made in commission in 2011, we need to know the number of weeks in 2011. Assuming there are 52 weeks in a year, we can multiply Alexander's weekly commission by the number of weeks in 2011:

$585  imes 52 = $30,420

Answer:

B. red, blue, green

Using the sample space concept, it is found that for this situation, it is given by:

B. {red, blue, green}

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

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Answer:

Isosceles and Scalene

Step-by-step explanation:

I did some research and plus we learned about angles and triangles in Geometry.

Plz click the Thanks button!

<Jayla>

Answer:

Isosceles and Scalene

Step-by-step explanation:

Answer:

4

Step-by-step explanation:

Trust me

Answer:

2 + 2 = 4

Step-by-step explanation:

Are you sure?  Is this a trick?  Or is the "+"  a different kind of plus?

Answer: A the member can tolerate a temp of 173 fahrenheit for 0 minutes

The true statement is (a) The member can tolerate a temperature of 173∘ Fahrenheit for 0 minutes.

The equation of the line of best fit for the data is given as:

y = -1.5x + 173

Set x to 0, to calculate the y-intercept

y = -1.5 * 0 + 173

Evaluate the product

y = 0 + 173

Evaluate the sum

y = 173

This means that initial temperature is 173

Hence, the true statement is (a) The member can tolerate a temperature of 173∘ Fahrenheit for 0 minutes.

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We have been a right triangle. We are asked to find the missing length of the given triangle.

We can see that our given triangle is 30-60-90 triangle.

We know that the lengths of the sides of a 30-60-90 triangle are in the ratio [tex]1:\sqrt{3}:2[/tex].

If the side opposite to 30 degree is [tex]n[/tex], then the side opposite to 60 degree angle will be [tex]\sqrt{3}n[/tex] and side opposite to hypotenuse will be [tex]2n[/tex].

We can see that side corresponding to hypotenuse is 6 that is [tex]2n=6[/tex].

Let us solve for n.

[tex]\frac{2n}{2}=\frac{6}{2}[/tex]

[tex]n=3[/tex]

The side corresponding to 30 degree angle will be half of 6 that is 3. Therefore, the value of y is 3.

The value of x will be [tex]3\sqrt{3}[/tex] as it is side corresponding to 60 degree angle.

Answer:

2

x

,

2

,

11

x

+

12

2x,2,11x+12

Answer:

0

Step-by-step explanation:

Answer:

6  7/12

Step-by-step explanation:

-7 2/3 +(5 1/2) + 8 3/4

Get a common denominator of 12

-7 2/3 * 4/4 +(5 1/2 +6/6) + 8 3/4*3/3

-7 8/12    + 5 6/12     + 8 9/12

Subtract the  first two terms first

They have opposite signs so subtract and take the sign of the larger

-7 8/12    + 5 6/12    = -2 2/12

-2  2/12 + 8 9/12

They have opposite signs so subtract and take the sign of the larger

-2  2/12 + 8 9/12 = 6 7/12

Answer:

C

Step-by-step explanation:

The solution is: quadratic; y = 2.5x^2, this function best models the data.

Option (1)

Function, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable.

here, we have,

given that,

x               -2              -1                 0                    1                   2

y               10            2.5                0                  2.5                3.0

Ist difference,

d_1 = -7.5  

d_2= -2.5

d_3 = 2.5

d_4 = 7.5

2nd difference,

x_1  = 5

x_2 = 5

x_3 = 5

Since 2nd difference is common, given table represents a quadratic equation.

Let the equation is,

y = ax²+ bx + c

For a point (0, 0) passing through the quadratic equation,

0 = c

Therefore, quadratic equation is y = ax² + bx

Since ordered pair (-1, 2.5) passes through the graph of the function,

2.5 = a(-1)² + b(-1)

a - b = 2.5 ------(1)

For another point (1, 2.5)

2.5 = a(1)² + b(1)

a + b = 2.5 ------(2)

By adding equations (1) and (2),

2a = 5

a = 2.5

and from equation (2)→ y = 0

Therefore, equation of the quadratic function given in the table is y = 2.5x²

Option (1) is the answer.

Hence, The solution is: quadratic; y = 2.5x^2, this function best models the data. i.e. Option (1)

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Complete question:

Graph the data in the table. Which kind of function best models the data? Write an equation to model the data. quadratic; y = 2.5x2 linear; y = 2.5x quadratic; y = –2.5x2 exponential; y = 2.5x

Answer:

11 pens weigh 53.43 grams.

2 pens weigh X grams.

We have:

11/53.43 = 2/X

=> X = 2 x 53.43/11 = 9.72 grams

Hope this helps!

:)

Answer: A. 169.65 mi^3

Step-by-step explanation:

The volume of a cylinder is formula  is   v= π *r^2 *h  where  r is radius and h is the height being multiplied pie.

V= 3.14 * 3^2 * 6

v= 3.14 * 9 * 6

v =169.6460  to the nearest hundredth is 169.65

Answer: Infinite solutions.

x could be equal to anything, and you can't solve for x since there is no equation on the other side of an equal sign for you to solve it. Hope that helps.

The answer is A on USA test prep

Step-by-step explanation:

Answer:

380 different ways

Step-by-step explanation:

We can solve this problem using a permutation formula, as the order in a group of two students matter.

So, for this problem, we have 20 students and want to form groups of 2, so we have a permutation of 20 choose 2:

P(20,2) = 20! / (20-2)! = 20! / 18! = 20 * 19 = 380 different ways

Another way to solve this problem is:

For the first student being chose, we have 20 students available, and for the second student, we have just 19, as one was already chose, so the number of ways to choose these two students is 20 * 19 = 380

Answer:

23. Length = 21 feet, Width = 3 feet

24. Larger Angle = 162 degrees, Smaller Angle = 18 degrees

Step-by-step explanation:

23.

Let us say:                                                                                                      l ⇒ length of the rectangular pool, w ⇒ width of the rectangular pool

According to the problem we could formulate two equations as such:

2l + 2w = 48,

l = 15 + 2w

Now let us solve for the dimensions;

First convert the two equations to standard form:

2l + 2w = 48,

l - 2w = 15

Using process of elimination:

  2l + 2w = 48

+   l  - 2w = 15

Simplify:

3l = 63,

length = 21 feet

Substitute this value of length into the second equation.....:

21 - 2w = 15

.......And simplify:

-2w = -6,

width = 3 feet

24.

Let us say:                                                                                                      L ⇒ larger angle, S ⇒ smaller angle,

According to the problem we could formulate two equations as such:

L + S = 180,

L = 9S

Now let us solve for the angles;

Let us here use substitution:

(9S) + S = 180

Simplify:

10S = 180,

Smaller Angle = 18 degrees

Substitute this value of the smaller angle into the second equation.....:

L = 9(18)

.......And simplify:

Larger Angle = 162 degrees

Answer:

a) [tex] df =n_1 +n_2 -2 =15 +17-2 =30[/tex]

And then since we want to conduct a two tailed test we need to llok in the t distribution with 30 degrees of freedom a value who accumulate 0.05 of the area and we got:

[tex] t_{\alpha/2} =\pm 1.697[/tex]

b)[tex]S^2_p =\frac{(15-1)(12)^2 +(17 -1)(15)^2}{15 +17 -2}=187.2[/tex]

[tex]S_p=13.682[/tex]

c) [tex]t=\frac{(350 -342)-(0)}{13.682\sqrt{\frac{1}{15}+\frac{1}{17}}}=1.65[/tex]

d) For this case the statistic calculated is lower than the critical value so then we FAIL to reject the null hypothesis at the significance level given.

e) The p value for this case would be given by:

[tex]p_v =2*P(t_{30}>1.65) =0.1094[/tex]

Step-by-step explanation:

We are assuming that the two population deviations are equal:

[tex]\sigma^2_1 =\sigma^2_2 =\sigma^2[/tex]

And the statistic is given by this formula:

[tex]t=\frac{(\bar X_1 -\bar X_2)-(\mu_{1}-\mu_2)}{S_p\sqrt{\frac{1}{n_1}+\frac{1}{n_2}}}[/tex]

Where t follows a t distribution with [tex]n_1+n_2 -2[/tex] degrees of freedom and the pooled variance [tex]S^2_p[/tex] is given by this formula:

[tex]\S^2_p =\frac{(n_1-1)S^2_1 +(n_2 -1)S^2_2}{n_1 +n_2 -2}[/tex]

Part a

For this case we need to find the degrees of freedom given by:

[tex] df =n_1 +n_2 -2 =15 +17-2 =30[/tex]

And then since we want to conduct a two tailed test we need to llok in the t distribution with 30 degrees of freedom a value who accumulate 0.05 of the area and we got:

[tex] t_{\alpha/2} =\pm 1.697[/tex]

Part b

The pooled deviation can be founded with this formula:

[tex]S^2_p =\frac{(15-1)(12)^2 +(17 -1)(15)^2}{15 +17 -2}=187.2[/tex]

And the deviation would be:

[tex]S_p=13.682[/tex]

Part c

The system of hypothesis on this case are:

Null hypothesis: [tex]\mu_1 = \mu_2[/tex]

Alternative hypothesis: [tex]\mu_1 \neq \mu_2[/tex]

Replacing the info given we got:

[tex]t=\frac{(350 -342)-(0)}{13.682\sqrt{\frac{1}{15}+\frac{1}{17}}}=1.65[/tex]

Part d

For this case the statistic calculated is lower than the critical value so then we FAIL to reject the null hypothesis at the significance level given.

Part e

The p value for this case would be given by:

[tex]p_v =2*P(t_{30}>1.65) =0.1094[/tex]

The question refers to hypothesis testing for difference in population means. The null hypothesis is rejected both by using the critical value approach and the p-value approach, indicating a significant difference in population means at the 0.10 significance level.

This question deals with hypothesis testing for difference in population means with a given significance level.

(a) The decision rule for this two-tailed test is: Reject the null hypothesis if the absolute value of the test statistic is greater than the critical value at the 0.10 significance level, or if the p-value is less than the significance level.

(b) The pooled estimate of the population variance is calculated using the formula: [(n1-1)s1^2 + (n2-1)s2^2] / (n1+n2-2) = [(15-1)*12^2 + (17-1)*15^2] / (15+17-2) = 196.77.

(c) The test statistic is calculated as: (x1 - x2) / sqrt[(pooled variance)*(1/n1 + 1/n2)] = (350 - 342) / sqrt[(196.77)*(1/15 + 1/17)] = 1.87.

(d) With degrees of freedom of (15+17-2)=30, the critical values for a two-tailed test at the 0.10 significance level are approximately ±1.697. As our test statistic is greater than the critical value, we reject the null hypothesis.

(e) The p-value associated with the test statistic of 1.87 is approximately 0.07, which is less than the significance level of 0.10. Hence, we again reject the null hypothesis. Therefore, we conclude that there is a significant difference in the population means at the 0.10 significance level.

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Answer:

f(x)=1200(1.04)^n

Step-by-step explanation:

Answer:

(-4, 0) and (5/2, 0)

Step-by-step explanation:

f(x) = –2x2 – 3x + 20

factor  using the diamond method

-2*20 = -40

so  -8 * 5 = -40  and   -8 + 5 = -3  so...

f(x) = -2x^2 - 8x + 5x  + 20

f(x) = -2x (x + 4) + 5 *(x + 4)

f(x) = (-2x + 5)*(x + 4)

x-intercepts are   x = 5/2  and x =-4

(-4, 0) and (5/2, 0)

Answer:

(-4, 0) and (5/2, 0)

Step-by-step explanation:

Answer:

The smallest number is 23

Step-by-step explanation:

Let x be the first number

x+1 is the next consecutive number

x+2 is the next consecutive number

The sum is

x+ x+1 + x+2 = 72

Combine like terms

3x+3 = 72

subtract 3 from each side

3x+3-3 = 72-3

3x = 69

Divide each side by 3

3x/3 = 69/3

x = 23

x+1 = 24

x+2 =25

The numbers are

23,24,25

Answer:

x=123

Step-by-step explanation:

x is across from the angle that measures 123 degrees. Therefore, they are vertical angles, and are congruent.

x=123

Additionally, 57 and x are on a straight line. This means they are supplementary and add to 180 degrees

57*x=180

Subtract 57 from both sides to get x by itself.

x=123

Answer:

2.

Step-by-step explanation:

Take the surface area and divide it by pi. Then take that value, and square root it. Then, divide by two. In this case, you get two.

The radius of a sphere with a surface area of 16pi is calculated using the formula for the surface area of a sphere, resulting in a radius of 2 units.

To find the radius of a sphere with a surface area of 16π, you can use the formula for the surface area of a sphere which is surface area = 4 π (r)². By setting the surface area to 16π and solving for r, you have:

16π = 4πr²

Dividing both sides by 4π leaves you with r² = 4, and taking the square root of both sides gives you r = 2. Therefore, the radius of the sphere is 2 units.

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Answer:

3% simple interest

Step-by-step explanation:

Simple interest formula is:

I = P*r*t

P = $2000

r = ?

t = 4

I = $240

240 = 2000 * r * 4

60 = 2000r

r = 60/2000

r = 3/100 = 0.03  = 3%

m=-2-4/3-4=-6/-1=6

y-4=6(x-4)

y=6x-20

Answer:

113.1

there u go

Answer:

The answer will be number 3

8.917

Answer:

i think 3

Step-by-step explanation:

Answer:

A' = (6, 15)

Step-by-step explanation:

We consider the center point of dilation to be the origin (0,0)

so  point A(-2, -5)  to A'  by scale factor N = -3 means

A' = (-2*(-3),  -5*(-3)) = (6, 15)