A swimming pool can be emptied in 6 hours using a 10-horsepower pump along with a 6-horsepower pump. The 6-horsepower pump requires 5 hours more than the 10-horsepower pump to empty the pool when working by itself. How long will it take to empty the pool using just the 10-horsepower pump?

Answer:

[tex]24 units^2[/tex]

Step-by-step explanation:

Well we can divide the given polygon into smaller triangles.

The triangle on the upper right corner has a base of 4 units and a height of 3 units.

So we use the following formula,

[tex]\frac{b*h}{2}[/tex]

4*3 = 12

12 / 2 = 6 units^2

Now we can do the bottom triangle.

It has a base of 4 units and a height of 1 unit.

So 4*1 = 4

4 / 2 = 2 units^2

Now for the top left triangle.

It has a base of 4 units and a height of 2 units.

So 4*2 = 8

8 / 2 = 4 units^2

Now all we have is the middle part.

Its a triangle with a base of 4 units and a height of 2 units.

So 4*2 = 8

8 / 2 = 4 units^2

6 + 2 + 4 + 4 = 16 units^2

Thus,

after adding everything up the total area of the polygon is 16 units^2.

Hope this helps :)

Answer:

b

Step-by-step explanation:

you need to round 2.51 to 3 because it was the correct answer

Answer:

The x value of the point 1/4 the distance from point C to point D is -0.25

Step-by-step explanation:

The given information are;

The location of point C = (1, 2)

The location of point D = (-4, -2)

The point 1/4 from point C to point D is the point 3/4 from point D to point C

Which gives;

The coordinate at point D + 3/4× The difference between the coordinates of point C and point D

Which is (-4 + 3/4×(1 - (-4),  - 2 + 3/4×(2 - (-2))

Which gives;

(-4 + 3.75, -2 + 3)  and (-0.25, 1)

The coordinates of the point 1/4 the distance from point C to point D is (-0.25, 1)

Therefore, the x value of the point 1/4 the distance from point C to point D = -0.25.

Answer:

There is no price difference between the two stores.

Step-by-step explanation:

The dependent t-test (also known as the paired t-test or paired samples t-test) compares the two means associated groups to conclude if there is a statistically significant difference amid these two means.

In this case a paired t-test is used to determine if there is a price difference between the two stores.

The hypothesis for the test can be defined as follows:

H₀: There is no price difference between the two stores, i.e. d = 0.

Hₐ: There is a price difference between the two stores, i.e. d ≠ 0.

From the information provided the sample mean and standard deviation are:

 [tex]\bar d=-0.464\\\\S_{d}=1.019[/tex]

Compute the test statistic value as follows:

 [tex]t=\frac{\bar d}{S_{d}/\sqrt{n}}=\frac{-0.464}{1.019/\sqrt{10}}=-1.4399\approx -1.44[/tex]

The test statistic value is -1.44.

Decision rule:

If the p-value of the test is less than the significance level then the null hypothesis will be rejected and vice-versa.

The degrees of freedom is:

n - 1 = 10 - 1 = 9

Compute the p-value of the test as follows:

[tex]p-value=2\cdot P(t_{\alpha/2, (n-1)}>-1.44)[/tex]

               [tex]=2\cdot P(t_{0.10/2, 9}>-1.44)\\=2\times 0.092\\=0.184[/tex]  

*Use a t-table.

The p-value of the test is 0.184.

p-value= 0.184 > α = 0.10

The null hypothesis was failed to be rejected.

Thus, it can be concluded that there is no price difference between the two stores.

Answer:

B and D

Step-by-step explanation:

I think this is the answer

See the answer in attachment

Answer:

(x-2)(x+1)(x+1)

Step-by-step explanation:

x³-3x-2=

(x-2)(x+1)(x+1)

Answer:

B. x > 3

Step-by-step explanation:

Well we first simplify the following inequality,

3(8 - 4x) < 6(x - 5)

Distribute

24 - 12x < 6x - 30

Communicative property

-6x

24 - 18x < -30

-24

-18x < -54

Divide -18x by both sides

Which flips the < to a >.

x > 3

Thus,

the answer is B. x > 3.

Hope this helps :)

Answer:

this. question is not clear please send clear question

We can conclude that -

The general equation of a straight line is -

[y] = [m]x + [c]

where -

[m] is slope of line which tells the unit rate of change of [y] with respect to [x].

[c] is the y - intercept i.e. the point where the graph cuts the [y] axis.

y = mx also represents direct proportionality. We can write [m] as -

m = y/x

OR

y₁/x₁ = y₂/x₂

We have the following two functions -

y = -x

AND

y = x

Refer to the graphs attached for both the functions -

y = - x     and     y = x

The graphs as seen pass through the origin. One graph (y = x) has a slope of +1 while the other one (y = - x) has a slope of -1. The y - intercept of both the graphs will be 0.

We can conclude that -

To solve more questions on straight line, visit the link below-

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Answer: B. $16.13

Step-by-step explanation:

Formula : Sum of n observations = Mean x n

Given, 82 seniors earned an average $26.75 per student, 74 juniors earned an average $12.25 per student, 96 sophomores earned an average $15.50 per student, and 99 freshmen earned an average $10.85 per student.

Total students = 82+74+96+99 =351

Sum of earnings of 82 seniors  = $26.75  x 82= $2193.5

Sum of earnings of 74 juniors  = $12.25 x 74 = $906.5

Sum of earnings of 96 sophomores  = $15.50  x 96 = $1488

Sum of earnings of 99 freshmen  =  $10.85 x 99 = $1074.15

Total earnings =  $2193.5  + $906.5+  $1488 +$1074.15

= $5662.15

Average collection = (Total earnings) ÷ (Total students )

= $5662.15÷ 351

≈ $16.13

Hence, the  average collection for a student in this school = 16.31

So, the correct option is B.

Answer:

c. (3x^2-1)(x-7)

Step-by-step explanation:

=(3x^3-21x^2)+(-x+7)

=-(x-7)+3x^2(x-7)

=(3x^2-1)(x-7)

Answer:

B. The Dress Shop.

Step-by-step explanation:

To find the best deal, we want to find the cost for one dress.

Lara's Boutique: $64 for 4 dresses.

x / 1 = 64 / 4

x = 64 / 4

x = $16 per dress.

The Dress Shop: $75 for 5 dresses.

x / 1 = 75 / 5

x = 75 / 5

x = $15 per dress.

Marge's Dresses: $160 for 8 dresses.

x / 1 = 160 / 8

x = 160 / 8

x = $20 per dress.

The boutique with the best deal will have the cheapest dresses. So, the best deal would be at B. The Dress Shop.

Hope this helps!

Answer:

hey! it's A and X on edge :)

Answer:

for exapmle:  (2, 5)          {5=2•2.5}

                       (8, 20)        {20=8•2.5}  

                       (-5,  -12.5}    {-12.5=-5•2.5}

Step-by-step explanation:

    -3y+3x    -3y+3x

            ÷2     ÷2

Answer:

neither

Step-by-step explanation:

Answer:

[tex]\angle BAC = 141\frac{3}{7} ^{\circ}[/tex]

Step-by-step explanation:

The interior angle of a regular heptagon = = 900/7° = 128.57°

Therefore, angle DAB = 128.57°

The interior angle of the square = 90°

Therefore, angle DAC = 90°

Therefore, we have

angle DAB+ angle DAC + angle BAC = 360° (sum of angles at a point (A))

Angle BAC = 360° - angle DAB - angle DAC =  360° - 900/7° - 90° = 990/7°

Angle BAC = 141.43°

Expressing 141.43° as a common fraction gives;

[tex]141.43 ^{\circ}= \dfrac{990}{7} ^{\circ}=141\frac{3}{7} ^{\circ}[/tex]

[tex]\angle BAC = 141\frac{3}{7} ^{\circ}[/tex]

 The degree measure of exterior angle BAC is [tex]141\frac{3}{7}^\circ[/tex]

Given, A square and a regular heptagon are coplanar as shown in below figure attached.

We have find the exterior angle of BAC.

We know that, The formula that gives the interior angle measure for a regular polygon with any number of sides is,

[tex]\frac{180(n-2)}{n}[/tex]  where n is the number of sides.  

Since the heptagon has 7 no. of sides.

So regular heptagon's interior angle measures,

[tex]\frac{180(7-2)}{7}=128\frac{4}{7}[/tex]

Hence [tex]\angle A[/tex] will be[tex]128\frac{4}{7}[/tex] degrees.

We know that a square's interior angle is 90 degrees and a heptagon's interior angle is  128.57 degrees. We will subtract those from 360 degrees to find angle BAC.

[tex]\angle BAC = 360 - (\angle A + 90)\\[/tex]

[tex]\angle BAC = 360 - (128\frac{4}{7} + 90)\\\angle BAC=141\frac{3}{7} ^\circ[/tex]

Hence the degree measure of exterior angle BAC is [tex]141\frac{3}{7}^\circ[/tex].

For more details on Exterior angle follow the link:

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Answer: The systems are solved by solving for one variable in one of the equations, then substituting that equation into the second equation. Solve for a in the second equation, then substitute the second equation into the first. The Elimination Method: Both equations are in standard form:            Ax + By = C.

Answer:

Length 1 - Width = 19, Area = 19

Length 2 - Width = 18, Area = 36

Length 3 - Width = 17, Area = 51

Length 4 - Width = 16, Area = 64

Length 5 - Width = 15, Area = 75

Step-by-step explanation:

Area Formula: A = lw

Since we only have a combined total of 20 m to use, we have to subtract the number of length in order to find length:

Length 1 = 20 - 1 = Width 19 m

Length 2 = 20 - 2 = Width 18 m

Length 3 = 20 - 3 = Width 17 m

Length 4 = 20 - 4 = Width 16 m

Length 5 = 20 - 5 = Width 15 m

Then we simply plug in our l values and w values into the area formula:

A = 1(19) = 19 m²

A = 2(18) = 36 m²

A = 3(17) = 51 m²

A = 4(16) = 64 m²

A = 5(15) = 75 m²

width from 1-5 =

when lem

length=1, width=19

length=2,width=18

length=3,width=17

length=4,width=16

length=5,width=15

length =1,Area=19

length=2,Area=36

length=3,area=51

length=4,area=64

length=5,area=75.

Step-by-step explanation:

to get our width, we minus each length from the given value which is 20m.

e.g.

when length =1 our width becomes 20-1=19.

and you do same for the rest.

the formula for the area was given to us in the question so we use that to find the area.

A=Length×Width.

e.g when length=1, width =19

so the area becomes 1×19=

[tex] {19m}^{2} [/tex]

please note that your area should be in

[tex] {m}^{2} [/tex]

Answer:

10

Step-by-step explanation:

12 ÷ 1 1/5

Change to an improper fraction

12 ÷ ( 5*1+1)/5

12 ÷ 6/5

Copy dot flip

12 * 5/6

12/6 * 5

2*5

10

Answer:

10

Step-by-step explanation:

12 ÷ 1 1/5

Change into an improper fraction.

12 ÷ 6/5

Reciprocal and it becomes multiplication.

12 × 5/6

60/6

= 10

Answer:

Step-by-step explanation:

4 solids cubes A, B, C and D have been made with the same material.

Since material is same density of the material (grams per cm³) will be same.

It shows that the weight of the cubes will vary in the ratio of their volumes.

Volume of cube A = 6³ = 216 cm³

Volume of cube B = 8³ = 512 cm³

Volume of cube C = 10³ = 1000 cm³

Volume of cube D = 12³ = 1728 cm³

Therefore, weights of these cubes will be in the same proportion.

Since, Volume of D = Volume of (A + B + C)

1728 = (216 + 512 + 1000)

1728 = 1728

Therefore, weights of A, B, C, D will be arranged in the same way to balance the plates of a scale.

On one side of the scale cubes A, B, and C should be placed and on the the other side of the scale cube D should be placed to balance the scale.

Answer:

(-15,3)

Step-by-step explanation:

Answer:

No, Beth is not correct. The function g(x) has an h value of 5 and a k value of 1. This would be a horizontal translation of the square root function of 5 units to the right, rather than the left. Beth was correct about the vertical translation of the square root function of 1 unit up. The point (0, 0) from the square root function would be translated to the point (5, 1) on the graph of g(x).

Step-by-step explanation:

This came right from Edg

Answer: $310.31

Step-by-step explanation:

Invested amount (P) = $302

Interest rate (r) = 3.3% per year

Period = 10 months

Recall, simple interest formula :

A = P(1 + rt) where ; A = final amount

Interest = 3.3% = 3.3/ 100 = 0.033

A = $302 ( 1 + 0.033(10/12))

A = $302 (1 + 0.033(0.8333333))

A = $302 ( 1 + 0.0275)

A = $302 ( 1. 0275)

A = $310.305

A = $310.31

Answer:B

Step-by-step explanation: x is less than 1 so it is a open circle on the graph and x is greater than or equal to -1 so it is a closed circle on -1, B has both of these so B is the answer

Answer:

7.5kilometer

Step-by-step explanation:

for 30mins semin runs 5kilometer

then for 1min: (1min×5kilometer)÷30mins,

therefore, for 45mins: (45mins×5kilometer)÷30mins=7.5kilometer

From the given information:

We are being informed that Samin can run for 5 kilometers in 30 minutes;

If Samin can run such a kilometer in 30 minutes;

5 kilometers = 30 minutes

∴

In x kilometers = 45 minutes

By cross multiplying;

(x × 30 minutes) = 5 kilometers × 45 minutes

30x = 225 kilometer/minutes

[tex]x = \dfrac{225 \ kilometer/minutes}{30 minutes}[/tex]

[tex]\mathbf{x = 7.5 \ kilometers}[/tex]

Therefore, we can conclude that the Samin can run 7.5 kilometers in 45 minutes.

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Answer: w=5

Step-by-step explanation:

Answer:

see explanation

Step-by-step explanation:

Using the translation rule (x, y ) → (x - 2, y + 4 )

Subtract 2 from the original x- coordinate and add 4 to the original y- coordinate, thus

A(0, 3 ) → A'(0 - 2, 3 + 4 ) → A'(- 2, 7 )

B(- 2, - 4 ) → B'(- 2 - 2, - 4 + 4 ) → B'(- 4, 0 )

C(1, 5 ) → C'(1 - 2, 5 + 4 ) → C'(- 1, 9 )

Answer:

X=6/11

Step-by-step explanation:

8-(5x-2)=6-2(3x+1)

8-5x+2=6-6x-2

10-5x=4-6x

6=11x

x=6/11

Answer:

8-5x-2=6-6x+2

8-2-6-2=5x-6x

-10+8=-x

-2 =-x

x=2 ........×-1

x=2

Answer:

1 Pound of Rock = .01 cubic feet

OR 100 pounds per cubic foot

A) Company needs 500,000 pounds of rock

Volume of Rock to be transported: = 500,000 * .01 =

5,000 cubic feet

B) Volume of each truck 12 * 9 * 8 = 864 cubic feet

C) Trucks needed for entire shipment:

= 5,000 / 864 = 5.78

So, we'll need 6 trucks.

Step-by-step explanation:

Answer:

210 students

Step-by-step explanation:

The total number of students surveyed was

19+14+30+23+14 = 100

The fraction that picked Yosemite is 14/100

Multiply that fraction by the total number of students

1500* 14/100 = 210

Answer:

210 students

Step-by-step explanation:

vote me brainliest plz

Answer:

A.

Step-by-step explanation:

We need to find the equation where, if x is equal to 3, g(x) is equal to 1, because g(x) passes through the point (3,1)

Then, replacing x by 3 on every option we get:

[tex]g(x)=(\frac{1}{3}x)^2= (\frac{1}{3}3)^2=1\\g(x)=(\frac{1}{9}x)^2= (\frac{1}{9}3)^2=\frac{1}{9}\\g(x)= \frac{1}{3}x^2= \frac{1}{3}3^2=3\\g(x)=3x^2=3*3^2=27[/tex]

So, the answer is A. because g(x) is equal to 1

Answer:

5 < 10x – 3

Step-by-step explanation:

The inequality is 5 - 2x < 8x - 3.

5 < 6x – 3 is incorrect because 8x + 2x = 10x, not 6x.

3x < 8x – 3 is incorrect because 5 - 2x is not 3x, you can't subtract those terms as they are not like terms.

5 < 10x – 3 is correct because 8x + 2x = 10x.

2 – 2x < 8x is incorrect because 5 + 3 = 8, not 2.

Answer:

C on edg

Step-by-step explanation:

Answer:

(1.5,-3) and (4.5,-3)

Step-by-step explanation: