One pump can fill a reservoir in 60 hours. Another pump can fill the same reservoir in 80 hours. a third can empty the reservoir in 90 hours. If all three pumps are operating at the same time, how long will it take to fill the reservoir?

Answer:

  infinitely fast

Step-by-step explanation:

To have double the average speed, he must complete the two laps in the same amount of time that he spent completing the first lap. That is, he must complete the second lap in zero time.

Hamilton's average speed for the second lap should be infinite. (He needs to finish it in zero time.)

_____

  speed = distance/time

Multiplying by 2, we get ...

  2×speed = 2×distance/time . . . . . the time hasn't changed

Hey there! :)

Answer:

m∠θ = 69°.

Step-by-step explanation:

If sin (21°) = 0.36 and cos θ = 0.36, the two angles are complementary because the sine and cosine values are equivalent. Therefore:

90 - 21 = 69°.

The correct answer is D) m∠θ = 69°.

Answer:

Step-by-step explanation:

x=✓64*36=✓8^2*6^2

x=8*6

x=48

Answer:

We decreased by 37%

Step-by-step explanation:

Let x be the starting temperature

We decrease by 10 percent which means we are left with 100-10 =90 percent

.90 x

Then we decrease by 30 percent, 100 - 30 = 70

( .90x) * .70

.63x

We  have .63 of the original left or 63%

100 -63 = 37

We decreased by 37%

Answer:

37% and it decreased

Step-by-step explanation:

Answer:

(5a^2-4)*(25a^4+20a^2+16)

Step-by-step explanation:

Answer:

Its B, (5a^2-4)(25a^4+20a^2+16)

Step-by-step explanation:

Edge 2020

Answer:

B. The variable s represents the number of students in each class.

C. The coefficient 14 represents the number of classes in the 9th grade.

Step-by-step explanation:

The total number can be found by multiplying the number of the things with the number of people producing it. For example if 5 boys make 5  colored ropes the total number of ropes will be 5*5= 25.

In this question the combinations rule is used for variuos number of classes which are 14. Now we have to find the number of students which are s (s-1). Suppose s= 6 so the number of students would be 6(6-1) = 6(5) = 30

We will multiply the number of classes 14 with the number of students s(s-1) to get the total number of cards produced.

Answer:

a) x = 128 degrees

b) Angle APD is the arc angle, which is equal to the central angle x subtended by the arc.  Therefore angle APD = 128 degrees (and not 116 degrees)

Step-by-step explanation:

Given:

attached diagram

ABC is a straight line

Solution:

a) Find x

ABC is a straight line

angle ABD = supplement of CBD = 180-CBD = 180-116 = 64 degrees.

x is the central angle of the arc APD

so angle ABD is the inscribed angle which equals half of the arc angle =>

angle ABD = x/2 = 64 degrees

Solve for x

x/2 = 64

x = 2*64

x = 128 degrees

b.

Angle APD is the arc angle, which is equal to the central angle x subtended by the arc.  Therefore angle APD = 128 degrees (and not 116 degrees)

Answer:

the amount of fuel consumed every 100 kilometers is 62.5 litres.

Step-by-step explanation:

To determine the amount of fuel consumed every 100 kilometers.

Note: since the graph is a straight line graph (linear graph) the amount of fuel consumed every 100 kilometers is constant (i.e the same for every 100 kilometers). So, we only need to derive the amount of fuel consumed any 100 kilometers on the graph.

From the graph, the amount of fuel consumed for the first 100 kilometers is;

[tex]F = F_0 - F_{100} .........................1[/tex]

[tex]F_0 = 500\\F_{100} \simeq 437.5\\[/tex]

substituting into equation 1.

[tex]F = F_0 - F_{100} \\F = 500 - 437.5\\ F = 62.5 litres\\[/tex]

Therefore, the amount of fuel consumed every 100 kilometers is 62.5 litres.

Answer:500

Step-by-step explanation:got it on Kahn

Answer.

Step-by-step explanation:

Answer:

2.35 m²

Step-by-step explanation:

Divide the shape into shapes you can calculate the area of: a rectangle with a semi-circle on top, minus a square.

1. Calculate the area of the rectangle. Formula for area of a rectangle is length · width

1 m · 2 m = 2 m²

2. Calculate the area of the semi-circle. Formula for a semi-circle is [tex]\frac{\pi r^{2} }{2}[/tex] (use 3.14 for π) (radius is equal to half the diameter)

3.14(0.5)² = 0.785

0.785 ÷ 2 = 0.3925 m²

3. Combine the total area

2 + 0.3925 = 2.3925

4. Calculate the area of the square that will not be painted. Formula for area of a square is s² (side · side)

0.2² = 0.04 m²

5. Subtract the area of the square from the total area

2.3925 - 0.04 = 2.3525

2.3525 rounds to 2.35 m²

Answer:

5/3

Step-by-step explanation:

it should be y/x

you can count 5 up and 3 over

Answer:

8/5

Step-by-step explanation:

You can use the formula [tex]\frac{y_{1}-y_{2}}{x_{1}-x_{2}}[/tex] with a pair of points [tex](x_{1},y_{1})[/tex][tex](x_{2},y_{2})[/tex]. We can use points (1,4) and (-4,-4). Plugging in the equation we get (4-(-4))/(1-(-4)), which simplifies to 8/5, which is the slope.

Answer:

1 zero:  Answer C

Step-by-step explanation:

Keep in mind that the polynomial value is zero at any root.  Therefore each point that is a root must lie precisely on the x-axis (where y = 0).  In the graph given there is only one such point  (Answer C)

Answer:

B) 122 degrees.

Step-by-step explanation:

Consider the kite :- the 2 angles at the tangents are 90 degrees so we have:

9x - 5 + 14x + 24 + 90 + 90 = 360

9x - 5 + 14x + 24  = 180

23x + 19 = 180

23x = 161

x = 7

So the obtuse angle = 14(7) + 24

= 98 + 24

= 122 degrees.

Answer:

C

Step-by-step explanation:

It is an iscoceles triangle because there are 180 degrees in a triangle and the right angle plus the 45 degree equals 135 and 180 minus 135 is 45.

Since it is an iscoceles triangle that means that n = 3 and the pythagorean theorom says that a^2 + b^2 = c^2 which means that m = 3^2 plus 3^2 with a root.

3^2 is 9 so you get 18

the root of 18 is infinite, however can be simplified to 3 root to 2 because 3 times 3 equals 9 times 2 equals a root of 18

Hope this helps!

Answer:

WHAT

Step-by-step explanation:

Answer:

x = 3

Inverse matrix:

[tex]A^{-1} = \begin{pmatrix} \frac{1}{9} & \frac{2}{9} \\ \frac{1}{3} & -\frac{1}{3} \end{pmatrix} \quad[/tex]

Step-by-step explanation:

Determinant: ad - bc

a = 3, b = 2, c = 3, d = -1

3 * (-1) - (2 * x) = -9

-3 - 2x = -9

-2x = -6

x = 3

For matrix

[tex]A = \begin{pmatrix}a & b\\c & d\end{pmatrix} \quad[/tex]

the inverse is

[tex]A^{-1} = \dfrac{1}{ad - bc}\begin{pmatrix}d & -b \\-c & a\end{pmatrix}\quad[/tex]

Here we have: det = -9

a = 3, b = 2, c = 3, d = -1

Inverse matrix:

[tex]A^{-1} = \dfrac{1}{-9}\begin{pmatrix} -1 & -2 \\ -3 & 3 \end{pmatrix}\quad[/tex]

[tex]A^{-1} = \begin{pmatrix} \frac{-1}{-9} & \frac{-2}{-9} \\\frac{-3}{-9} & \frac{3}{-9}\end{pmatrix} \quad[/tex]

[tex]A^{-1} = \begin{pmatrix} \frac{1}{9} & \frac{2}{9} \\\frac{1}{3} & -\frac{1}{3}\end{pmatrix}\quad[/tex]

Answer:

radius

Step-by-step explanation:

That "fixed distance" is the 'radius' of the circle.

Answer:

The expressions are not equivalent.

Step-by-step explanation:

The answers would be 196 and 193 for t = 8

The answers would be 76  and 73 for t = 3

[tex]\mathfrak{\huge{\pink{\underline{\underline{AnSwEr:-}}}}}[/tex]

Actually Welcome to the Concept of the Quadrilaterals.

Basically we know that, the sum of opposite angles of a quadrilateral inscribed in a circle is always 180°.

so applying this law here, we get as,

2X + (3X-10) = 180°

=> 5X - 10° = 180°

=> 5X = 190°

=> X = 190°/5

=> X = 38°

thus the angle X= 38°.

Answer:

The length of the missing segment is 36

Step-by-step explanation:

Given

The figure above

Required

Determine the missing segment

Let the missing segment be represented with x

Given that, there exist parallel lines between the two triangles;

The relationship between the sides of the triangles is as follows;

[tex]\frac{20}{24} = \frac{30+20}{24+x}[/tex]

[tex]\frac{20}{24} = \frac{50}{24+x}[/tex]

Cross Multiply

[tex]20 * (24 + x) = 24 * 50[/tex]

[tex]20 * (24 + x) = 1200[/tex]

Divide both sides by 20

[tex]\frac{20 * (24 + x)}{20} = \frac{1200}{20}[/tex]

[tex](24 + x)= \frac{1200}{20}[/tex]

[tex]24 + x= 60[/tex]

Subtract 24 from both sides

[tex]24 - 24 + x = 60 - 24[/tex]

[tex]x = 60 - 24[/tex]

[tex]x = 36[/tex]

Hence, the length of the missing segment is 36

Answer:

B) 128.3 square yards

Step-by-step explanation:

A = (n/360 deg)(pi)r^2

where n = central angle of sector.

A = (75/360)(3.14159)(14 yd)^2

A = 128.3 yd^2

Answer:

B. 128.3 yards

Step-by-step explanation:

Area of a Sector Formula: A = ∅/360πr²

Simply plug in our variables:

A = 75/360(π)(14)²

A = 5π/24(196

A = 128.3

Answer:

m=2

Step-by-step explanation:

When you put a number into the inverse of a function (f^-1) you get the original number back.

Ex: f^-1(11) = (11-3)/2 = 4

f(4) = 2×4+3 = 11

So, f(-5)=-2

So, when x is -5,

f(x) = -2

f(x)=m(-5)+8

-2=m(-5) + 8

m=2

Answer:

A

Step-by-step explanation:

The zeroes of the function are the x values when f(x) = 0 so we can write:

0 = x² + x - 30

0 = (x + 6)(x - 5) (To factor this we need to find 2 numbers that have a sum of 1 and a product of -30; these numbers are 6 and -5)

x + 6 = 0 or x - 5 = 0 (Use Zero Product Property)

x = -6, 5

Hey there! :)

Answer:

A. x = -6 and x = 5.

Step-by-step explanation:

Given:

f(x) = x² + x - 30

Factor the equation by finding two numbers that sum up to 1 and multiply into -30. We get:

-5, 6

Use these to express this quadratic function in factored form:

f(x) = (x - 5) (x + 6)

Set each factor equal to 0 to solve for the zeros of the equation:

0 = x - 5

x = 5

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

0 = x + 6

x = -6

Therefore, the correct answer is A. x = -6 and x = 5.

Answer:

Greater than the original = 2, 4

Less than the original = 5

Same as the original = 1, 3

Step-by-step explanation:

Let the original value be x.

1. A $30 increase followed by a $30 decrease.

New value [tex]=x+30-30=x[/tex], it is same as original value.

2. A 20% decrease followed by a 40% increase.

Afer 20% decrease.

New value [tex]=x-\dfrac{20}{100}x=x-0.2x=0.8x[/tex]

Afer 40% increase.

New value [tex]=0.8x+\dfrac{40}{100}(0.8x)=0.8x+0.32x=1.12x[/tex], it is greater than original value.

Similarly check the other values.

3. A 100% increase followed by a 50% decrease.

New value [tex]=x+\dfrac{100}{100}x-\dfrac{50}{100}(x+x)=x[/tex], it is same as original value.

4. A 75% increase followed by a 33% decrease

New value [tex]=x+\dfrac{75}{100}x-\dfrac{33}{100}(x+0.75x)=1.1725x[/tex], it is greater than the original value.

5. 55% decrease followed by a 25% increase

New value [tex]=x-\dfrac{55}{100}x+\dfrac{25}{100}(x-0.55x)=0.5625x[/tex], it is less than the original value.

Therefore, Greater than the original = 2, 4, Less than the original = 5, Same as the original = 1, 3 .

A 100% increase followed by a 50% decrease

A $30 increase followed by a $30 decrease

55% decrease followed by a 25% increase

A 20% decrease followed by a 40% increase

A 75% increase followed by a 33 1/3% decrease

Answer:

A. Interquartile

Step-by-step explanation:

Answer:

A: interquartile range

Step-by-step explanation:

edg2020

Answer:

15

Step-by-step explanation:

Try 1, 2, 3, or 4 blue pencils. Then green is 6 times as many. Red must be the rest to make up 20 total.

No. of blue        No. of green      No. of red

1                          6                           13

2                        12                           6

3                        18                           -1

You can't have 3 blue pencils because 3 blue + 18 green = 21 pencils, and there are only 20.

If you have 1 blue and 6 green, then there must be 13 red, but red must be less than green, and 13 is not less than 6.

The only possibility is

2 blue, 12 green, 6 red

If you start taking out pencils, when you take out the first 14 they may be all blues or green, so only when you take out the 15th pencil do you know for sure there must be 1 green pencil.

Answer:

Simplifying

41 = 12d + -7

Reorder the terms:

41 = -7 + 12d

Solving

41 = -7 + 12d

Solving for variable 'd'.

Move all terms containing d to the left, all other terms to the right.

Add '-12d' to each side of the equation.

41 + -12d = -7 + 12d + -12d

Combine like terms: 12d + -12d = 0

41 + -12d = -7 + 0

41 + -12d = -7

Add '-41' to each side of the equation.

41 + -41 + -12d = -7 + -41

Combine like terms: 41 + -41 = 0

0 + -12d = -7 + -41

-12d = -7 + -41

Combine like terms: -7 + -41 = -48

-12d = -48

Divide each side by '-12'.

d = 4

Simplifying

d = 4

Answer:

The number of subsets of a set containing 10 elements is 2^10=1024.

Step-by-step explanation: