What is the sum of the first 20 terms of the arithmetic sequence 3,9,15,21,27

The numbers of runners that are 50 and above are 3000.

Using the pie chart,

If there are 1500 runners that are under 20, therefore,

1500 = 10 / 100 × x

where

x = total number of runners

10x = 150000

x = 15000

Therefore,

the number of runners that are 50 and above = 20 / 100 × 15000 = 3000

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Answer:

8x + 16

Step-by-step explanation:

(f - g)(x) = f(x) - g(x)

g(x) = -(x+4)(x+4)

= -(x² + 4x + 4x + 16)

= -(x² + 8x + 16)

= -x² - 8x - 16

1) Subtract the two functions.

= (-x²) - (-x² - 8x - 16)

= -x² + x² + 8x + 16

= 8x + 16

The distance between (-2, 3) and (-5, 1) is √13.

or, the distance between (-2, 3) and (1, 1) is √13.

We know that the length of the line segment connecting any two points represents the distance between them. There is just one line that connects the two points. Therefore, by measuring the length of the line segment that connects the two points, the distance between them can be determined. If (a, b) and (c, d) be two points, then the distance between them is [tex]\sqrt[]{(b - a)^{2} +(d- c)^{2} }[/tex].

Here, one point is (-2, 3).

Let the other point be (x, 1).

Given that the distance is √13.

Now, [tex]\sqrt[]{(x - (-2))^{2} +(1 - 3)^{2} } = \sqrt{13}[/tex]  

i.e. [tex]\sqrt[]{(x + 2)^{2} +( - 2)^{2} } =\sqrt{13}[/tex]

i.e. [tex]\sqrt[]{x^{2}+4x +4 +4 }=\sqrt{13}[/tex]

i.e. [tex]x^{2}+4x +8 =13[/tex]

i.e. [tex]x^{2}+4x + 8- 13=0[/tex]

i.e.[tex]x^{2}+4x -5=0[/tex]

i.e. [tex]x^{2} +5x - x -5=0[/tex]

i.e. [tex]x(x+5)-1(x+5)=0[/tex]

i.e. [tex](x+5)(x-1)=0[/tex]

i.e. [tex]x=-5,1[/tex]

So, the point is either (-5, 1) or (1, 1).

Therefore, the required point is either (-5, 1) or (1, 1).

i.e. the distance between (-2, 3) and (-5, 1) is √13.

or, the distance between (-2, 3) and (1, 1) is √13.

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Answer:

0.4 : 0.04

Step-by-step explanation:

4 ÷ 10 = 0.4

1 ÷ 25 = 0.04

The best description of the car's motion as shown in the graph is: A. It travels for 1 hour, then stops for 1 hour, and finally travels again for 3 hours.

In a distance-time graph, an horizontal line implies no distance was covered within that time frame, meaning there was a stop.

Thus, in the graph given, the stop occurred 1 and 2, which is equivalent to an hour. From 2 to 5 on the x-axis means there was movement for up to 3 hours.

Therefore, the best description is: A. It travels for 1 hour, then stops for 1 hour, and finally travels again for 3 hours.

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Answer:

Step-by-step explanation:

The theorem of similarity implies that the line segment divided the triangle into the proportional segment.

It should be noted that the theorem of similarity states that the line segment splits two sides of a triangle into proportional segments.

This occurs when the side is parallel to the third side of the triangle.

These three theorems, known as Angle-Angle (AA), Side-Angle-Side (SAS), and Side-Side-Side are foolproof methods for determining similarity in triangles.

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Answer:

[tex]\large \boxed{\checkmark}} \quad \textsf{has four right angles}[/tex]

[tex]\large \boxed{\checkmark}} \quad \textsf{opposite sides are congruent}[/tex]

[tex]\large \boxed{\checkmark}} \quad \textsf{diagonals bisect each other}[/tex]

[tex]\large \boxed{\checkmark}} \quad \textsf{opposite sides are parallel}[/tex]

[tex]\large \boxed{\checkmark}} \quad \textsf{opposite angles are congruent}[/tex]

[tex]\large \boxed{\checkmark}} \quad \textsf{diagonals are congruent to each other}[/tex]

Step-by-step explanation:

Properties of a rectangle:

Therefore, the correct answer options are:

The equation of the line is y = -11x + 232

The given parameters are:

Slope (m)= -11

Point (x1, y1) = (31, -109)

The linear equation is then calculated as:

y = m(x - x1) + y1

This gives

y = -11(x - 31) - 109

Evaluate the product

y = -11x + 341 - 109

Evaluate the like terms

y = -11x + 232

Hence, the equation of the line is y = -11x + 232

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Answer:

that is all I could do. hope you have gotten your answer.good day.

Answer:  -1/9  which is choice B

Explanation:

The term "zeros" refers to the x intercepts.

Plug in y = 0 and solve for x.

y = -9x-1

0 = -9x - 1

9x = -1

x = -1/9

Your answers for (a) and (c) are correct.

(b) Salt flows into the tank at a rate of

[tex]\left(0.025 \dfrac{\rm kg}{\rm L}\right) \left(5 \dfrac{\rm L}{\rm min}\right) = 0.125 \dfrac{\rm kg}{\rm min} = \dfrac18 \dfrac{\rm kg}{\rm min}[/tex]

If [tex]A(t)[/tex] is the amount of salt (in kg) in the tank at time [tex]t[/tex] (in min), then the salt flows out of the tank at a rate of

[tex]\left(\dfrac{A(t)}{1000+(5-5)t} \dfrac{\rm kg}{\rm L}\right) \left(5 \dfrac{\rm L}{\rm min}\right) = \dfrac{A(t)}{200} \dfrac{\rm kg}{\rm min}[/tex]

The net rate of change in the amount of salt in the tank at any time is then governed by the linear differential equation

[tex]\dfrac{dA}{dt} = \dfrac18 - \dfrac{A(t)}{200}[/tex]

[tex]\dfrac{dA}{dt} + \dfrac{A(t)}{200} = \dfrac18[/tex]

I'll solve this with the integrating factor method. The I.F. is

[tex]\mu = \exp\left(\displaystyle \int \frac{dt}{200}\right) = e^{t/200}[/tex]

Distributing [tex]\mu[/tex] on both sides of the ODE gives

[tex]e^{t/200} \dfrac{dA}{dt} + \dfrac1{200} e^{t/200} A(t) = \dfrac18 e^{t/200}[/tex]

[tex]\dfrac d{dt} \left(e^{t/200} A(t)\right) = \dfrac18 e^{t/200}[/tex]

Integrate both sides.

[tex]\displaystyle \int \frac d{dt} \left(e^{t/200} A(t)\right) \, dt = \frac18 \int e^{t/200} \, dt[/tex]

[tex]e^{t/200} A(t) = \dfrac{200}8 e^{t/200} + C[/tex]

[tex]A(t) = 25 + Ce^{-t/200}[/tex]

Given that [tex]A(0)=50\,\rm kg[/tex], we find

[tex]50 = 25 + Ce^0 \implies C = 25[/tex]

so that

[tex]A(t) = 25 + 25e^{-t/200}[/tex]

Then the amount of salt in the tank after 1 hr = 60 min is

[tex]A(60) = 25 + 25e^{-60/200} = \boxed{25 \left(1 + e^{-3/10}\right)}[/tex]

Answer:

refer to the above attachment

Step-by-step explanation:

4×sin(4t) = 4×sin(2t + 2t) =

= 4×(sin(2t)cos(2t) + cos(2t)sin(2t)) =

= 4×2×sin(2t)cos(2t) = 8×sin(2t)cos(2t)

but that did not lead anywhere near to any of the answer options.

so, i guess, you made typos in the description and in the answer options.

did you mean maybe

4×sin⁴(t) ?

sin⁴(t) = (3 - 4×cos(2t) + cos(4t))/8

4×sin⁴(t) = 4×(3 - 4×cos(2t) + cos(4t))/8 =

= (3 - 4×cos(2t) + cos(4t))/2 =

= 3/2 - 2×cos(2t) + 1/2 × cos(4t)

is that the real answer option 2 ?

then that is the correct answer.

Answer:

$325

Step-by-step explanation:

Let the dryer price be x, then the washer price would be x-78

x+x-78 = 572

2x = 650

x = 325

The probability that a randomly selected male college student gains 15 lb or more during their freshman year is 11.6%

Probability is defined as the likeliness of an event to happen.

Let X be a random variable that shows the term "freshman 15" that claims that students typically gain 15lb during their freshman year at college.

It is given that

X follows is a normal distribution with a mean of 2.1 lb (μ) and a standard deviation (σ)  of 10.8 lb.

Population Mean (μ) = 2.1

Population Standard Deviation (σ) = 10.8

We need to compute Pr(X≥15). The corresponding z-value needed to be computed is:

[tex]\rm Z_{lower} = \dfrac{ X_1 -\mu }{\sigma}\\\\Z_{lower} = \dfrac{ 15-2.1 }{10.8}\\\\\\Z_{lower} = 1.19[/tex]

Then the probability is given as

[tex]\rm Pr(X \geq 16 ) = Pr (\dfrac{X -21}{10.8} \geq \dfrac{15-21}{10.8})\\\\= Pr (Z \geq \dfrac{15-2.1}{10.8}\\\\= Pr (Z\geq 1.19)\\\\ = 0.1162[/tex]

Pr(X≥15)=0.1162. (11.6%)

The probability that a randomly selected male college student gains 15 lb or more during their freshman year is 11.6%

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The probability that exactly 8 individuals do not cover their mouth is 0.0037.

It should be noted that the probability will be solved by using the binomial distribution.

From the information, the probability that a randomly selected individual will not cover his or her mouth when sneezing is 0.267.

Therefore, the probability that thee person will not cover their mouth will be:

= 1 - 0.267

= 0.733

This will be:

= 12C8 × (0.267)^8 × (1 - 0.267)⁴

= 12C8 × (0.267)^8 × 0.733⁴

= 495 × 0.00002582 × 0.28867

= 0.0037

In conclusion, the probability is 0.0037.

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Answer:

Step-by-step explanation:

Function values and the extent of the graph can be determined by reading the graph.

The domain of the function is the set of values for which the function is defined. It is the horizontal extent of the graph. The graph shows the function is defined for all real numbers.

  The domain is -∞ < x < ∞.

The range of the function is the set of output values the function may have. It is the vertical extent of the graph. The graph shows the function can have any value no greater than -1.

  The range is -∞ < y ≤ -1.

Function values can be read from the graph by locating the x-value on the x-axis, and following the vertical line to its intersection with the function graph. The y-value of that point is the function value.

  f(-5) = -2

  f(-1) = -4

Or, we can write the function definition based on the graph, and use that definition to find the values at specific points. The graph is of the absolute value function reflected over x and translated <-4, -1>.

  f(x) = -|x+4| -1

  f(-5) = -|-5 +4| -1 = -1 -1 = -2

  f(-1) = -|-1 +4| -1 = -3 -1 = -4

Answer:

abcdefghijklmnopqrstuvwxyz

Step-by-step explanation:

these are the alphabets

The equation of the parabola is y = 2/25x^2 + 2

The complete question is in the image

The given parameters are:

Vertex, (h, k) = (0,2)

Point (x,y) = (-5, 4)

The parabola is represented as;

y = a(x - h)^2 + k

Substitute (h, k) = (0,2)

y = a(x - 0)^2 + 2

This gives

y = ax^2 + 2

Substitute (x, y) = (-5,4)

4 = a(-5)^2 + 2

This gives

4 = 25a + 2

Subtract 2 from both sides

25a = 2

Divide by 25

a = 2/25

Substitute a = 2/25 in y = ax^2 + 2

y = 2/25x^2 + 2

Hence, the equation of the parabola is y = 2/25x^2 + 2

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Answer:

x+10

Step-by-step explanation:

So they did a bet, and placed 5 cents each. George lost the bet that gives Joyce 5 points plus 5 more that make 10.

After the bet George has: x cents

Before the bet George had: x + 5 cents

Before the bet Joyce had also x + 5 cents

Since Joyce won 5 cents, after the bet she has x + 5 + 5 = x + 10 cents.

The coordinates of R is (1.2, 0.4)

The points are given as:

P= (6, -5)

Q = (-2, 4)

The ratio is given as:

m : n = 3 : 2

The location of R is calculated as:

[tex]R = \frac{1}{m + n}* (mx_2 + nx_1, my_2 + ny_1)[/tex]

So, we have:

[tex]R = \frac{1}{3 + 2}* (3 * -2 + 2 * 6, 3 * 4 + 2 * -5)[/tex]

Evaluate the products

[tex]R = \frac{1}{5}* (6, 2)[/tex]

This gives

R = (1.2, 0.4)

Hence, the coordinates of R is (1.2, 0.4)

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Answer:

27

Step-by-step explanation:

[tex] - 4 = \frac{ - 9 + x}{2} \\ - 8 = - 9 + x \\ x = 1[/tex]

[tex]1 = \frac{5 + y}{2} \\ 2 = 5 + y \\ y = - 3[/tex]

Answer:

16

Step-by-step explanation:

he missed 25%

if 4 = 25% then 16 questions total

4*4=16 and 25% * 4 = 100%

Answer: 16 problems

Step-by-step explanation:

First find out how many John got wrong. 100%-75%=25%. Then do cross multiplication: 4*100=25x; 400=25x. Divide 25 on both sides and... BOOM! you get 16 problems.

The permutation shows that when one has been cast yet, the different ways that are there to cast Fantine from the 28 women is 28.

The different ways that are there to cast Fantine from the 28 women will be:

= 28!/(28 - 1)!

= 28!/27!

= 28

When Fantine has already been cast, the number of ways that are there to cast adult Cosette from the remaining women will be:

= 27!(27 - 1)!

= 27!/26!

= 26

When Fantine and adult Cosette have already been cast, the different ways that are there to cast Éponine from the remaining women is:

= (28 - 2)!/(28 - 2 - 1)!

= 26!/25!

= 25

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Answer:

Step-by-step explanation:

Answer:

-22

Step-by-step explanation:

-14+(-12）+4

=-14-12+4

=-26+4

=-22

Answer:

18

Step-by-step explanation:

We want to find the composite function at a specific value (-5).

Thus, we can write and think of the function like this:

f[g(-5)]

So we substitue the -5 for every x in the g(x) function:

g(x) = -5 + 7 = 2

Then we substitute this 2 for every x in the f(x) function:

f(x) = 2^2+7(2) = 4 + 14 = 18