The double number lines show the ratio of yards to miles.How many yards are in 4 miles?

The completed equations are:

2x + 3y = 80 equation 1

x + y = 37 equation 2

In order to determine the number of each type of shots made, two equations would be derived based on the information provided in the question. These equations would be solved simultaneously in order to determine the required values.

[(type of basket made)x ]+ [(type of baskets made)y] = total number of points

2x + 3y = 80

x + y = total number of baskets

x + y = 37

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Answer:

29, 21, 84

Step-by-step explanation:

Let the first number be x.

The second number is x - 8.

The third number is 4(x - 8).

Their sum is 134.

x + (x - 8) + 4(x - 8) = 134

x + 5(x - 8) = 134

x + 5x - 40 = 134

6x = 174

x = 29

x - 8 = 29 - 8 = 21

4(x - 8) = 4(29 - 8) = 4(21) = 84

The interpretation of the slope is that (b) the volume of helium in the balloon decreases at a rate of 0.1 cubic per minute

Linear equations are equations that have constant average rates of change, slope or gradient

From the table of values, we have the following points

(x, y) = (5, 5.5) and (10, 5)

The slope of the table of values is calculated as:

m = (y2 - y1)/(x2 - x1)

Substitute the known values in the above equation

m = (5 - 5.5)/(10 -5)

Evaluate the difference

m = -0.5/5

Evaluate the quotient

m = -0.1

This means that the slope is -0.1

From the table of values, we have

x represents the elapsed time and y represents the volume of helium

So, the interpretation of the slope is that (b) the volume of helium in the balloon decreases at a rate of 0.1 cubic per minute

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Answer:

180

Step-by-step explanation:

If she received requests for 150 tickets, and that is 120% of what they have, you would find 20% of 150. You would do this because 100% of 150 is 150, now you need to add the other 20%, so you have to find 20% of 150. Which is 30. You would then add that to 150 sine it is 120% of what they have. So, they have 180 tickets

The number of $1, $5 and $10 are 49, 44 and 22 respectively.

There are 3 denominations of bills in a wallet: $1, $5, and $10.

There are 5 fewer $5-bills than $1-bills.

let

x = number of $1 bills

Hence,

number of $5 bills = x - 5

There are half as many $10-bills as $5-bills.

number of $10 bills = 1 / 2 (x - 5)

Therefore,

x + x - 5 + 1 / 2 (x - 5) = 115

2x - 5  + 1 / 2 x - 5 / 2 = 115

2x + 1 / 2 x - 5 - 5 / 2 = 115

5 / 2 x  - 7.5 = 115

2.5x  = 115 + 7.5

x = 122.5 / 2.5

x = 49

Number of $1 bills = 49

Number of $5 bills = 49 - 5 = 44

Number of $10 bills = 1 / 2 (49 - 5) = 22

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The car will be worth $20467 in 2017

The given parameters are:

Initial value, a = 38000

Depreciation rate, r = 6%

The value of the car after x years is represented by the following exponential equation

V(x)= a(1 - r)^x

Substitute the known values in the above equation

V(x) = 38000 * (1 - 6%)^x

2017 is 10 years from 2007

This means that x = 10

So, we have:

V(x) = 38000 * (1 - 6%)^10

Evaluate

V(x) = 20467

Hence, the car will be worth $20467 in 2017

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Answer:

6 children passes

Step-by-step explanation:

a = adult and c = children

25a + 15c = 440           and          a + c = 20

                                                     c = 20 - a

25a + 15(20-a) = 440

25a + 300 - 15a = 440

25a - 15a = 440 - 300

10a = 140

a = 140/10

a = 14 and this is 14 adult tickets

Now we plug the a value into the equation to find the c value

14 + c = 20

c = 20 - 14

c = 6

Verify answer:

25(14) = 15(6) = 440

350 + 90 = 440

440 = 440

It looks like you have

[tex]f(x) = \begin{cases} 3 & \text{if } -4 \le x \le 0 \\ 4 - x^2 & \text{if } 0 < x \le 3\end{cases}[/tex]

and the integral you want to compute is

[tex]\displaystyle \int_{-4}^3 f(x) \, dx[/tex]

Split the integral up at [tex]x=0[/tex]. Then

[tex]\displaystyle \int_{-4}^3 f(x) \, dx = \int_{-4}^0 f(x)\,dx + \int_0^3 f(x)\,dx \\\\ ~~~~~~~~~~~~ = \int_{-4}^0 3 \, dx + \int_0^3 (4 - x^2) \, dx \\\\ ~~~~~~~~~~~~ = 3(0 - (-4)) + \left(4\cdot3 - \frac{3^3}3\right) = \boxed{15}[/tex]

After evaluating the integral we get 15

Integral is the representation of the area of a region under a curve. We approximate the actual value of an integral by drawing rectangles. A definite integral of a function can be represented as the area of the region bounded by its graph of the given function between two points in the line.

Given,

f(x) = 3         if   - 4 ≤ x ≤ 0

f(x) = 4 - [tex]x^{2}[/tex]  if   0 < x ≤ 3

Then,

[tex]f(x) = \left \{ {{3} \atop {4-x^{2} }}[/tex]

We need to solve the integral -[tex]\int\limits^3_4 {f(x)} \, dx[/tex]

Elaborate the integral with x = 0

                                             -[tex]\int\limits^3_4 {f(x)} \, dx[/tex]

                                          = -[tex]\int\limits^0_4 {f(x)} \, dx + \int\limits^3_0 {f(x)} \, dx[/tex]

                                          = -[tex]\int\limits^0_4 {3} \, dx + \int\limits^3_0 {4-x^{2} } \, dx[/tex]

                                          = 3 ( 0 - (-4)) + (4.3 - [tex]\frac{3^{3} }{3}[/tex])

                                          = 15

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Answer:

16482 this is the answer

A number line can be defined as a type of graph with a graduated straight line which contains both positive and negative numerical values that are placed at equal intervals along its length.

A line plot can be defined as a type of graph that is used to graphically represent a data set above a number line, while using crosses, dots, or any other mathematical symbol.

A mean is also referred to as an arithmetic average and it can be defined as a ratio of the sum of the total number in a data set (population) to the frequency of the data set.

Mathematically, the distance between the means of both classes A and B is given by:

Distance = Mean of class A - Mean of class B

Distance = 12 - 4

Distance = 8.

The mean absolute deviation (MAD) for class A is given by:

MAD A = 1/9[2(9 - 12) + (10 - 12) + (11 - 12) + (12 - 12) + (13 - 12) + (14 - 12) + 2(15 - 12)]

MAD A = 1/9[2(3) + (2) + (1) + 0 + (1) + (2) + (1) + 2(3)]

MAD A = 1/9[6 + 2 + 1 + 1 + 2 + 1 + 6]

MAD A = 1/9 × [18]

MAD A = 18/9

MAD A = 2.

Also, the mean absolute deviation (MAD) for class B is given by:

MAD B = 1/9[2(1 - 4) + (2 - 4) + (3 - 4) + (4 - 4) + (5 - 4) + (6 - 4) + 2(7 - 4)]

MAD B = 1/9[2(3) + 2(2) + (1) + (0) + (1) + (2) + 2(3)]

MAD B = 1/9[6 + 4 + 1 + 0 + 1 + 2 + 6]

MAD B = 1/9 × [18]

MAD B = 18/9

MAD B = 2.

Therefore, distance between the means = four (4) times the MAD.

Distance = Means × MAD

8 = 4 × 2.

In conclusion, we can infer and logically deduce that there is no overlap and the distance between the means of both players A and B is between one (1) times the MAD and five (5) times the MAD.

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Answer:

748.23 in^2.

Step-by-step explanation:

Area = 1/2 * apothem * perimeter

        = 1/2 * 14.7 * 101.8

        =  748.23 in^2.

Answer:

748.23

Step-by-step explanation:

If the pth term of an arithmetic progression is q and qth term is p then the (p+q) th term is 0.

Given that the p th term of an A.P is q aand q th term is p.

We are required to find the (p+q) th term of that A.P.

Arithmetic progression is a sequence in which all the terms have common difference between them.

N th term of an A.P.=a+(n-1)d

p th term=a+(p-1)d

q=a+(p-1)d-------1

q th term=a+(q-1)d

p=a+(q-1)d---------2

Subtract equation 2 by 1.

q-p==a+(p-1)d-a-(q-1)d

q-p=pd-qd-d+d

q-p=d(p-q)

d=(p-q)/(q-p)

d=-(p-q)/(p-q)

d=-1

Put the value of d in 1.

q=a+(p-1)(-1)

q=a-p+1

a=q+p-1

(p+q) th term=a+(n-1)d

=q+p-1+(p+q-1)(-1)

=q+p-1-p-q+1

=0

Hence if the pth term of an A.P is q and qth term is p then the (p+q) th term is 0.

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Answer:

s - c over c = m   or  (s-c)/c = m

Step-by-step explanation:

s = c * mc

s -c = mc

(s - c) / c = m

Answer:

A ) m=s-c/c

Step-by-step explanation:

Canceling units is also called unit analysis.

This is also called dimensional analysis.

What is a unit of analysis in statistics?

For example -

1 ft = 12 in

3 ft =  [tex]3 ft * \frac{12 in }{1 ft}[/tex]

3 ft = ( 3 * 12 )  in ⇒ 36 in

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Answer:

$329.00

Step-by-step explanation:

Let the original price be $x, then

x - 0.30x - 0.10(x - 0.30x) =  207.27

x - 0.30x - 0.10x + 0.03x = 207.27

0.63x = 207.27

x = 329.00.

The value of s for the given conditions is 9/2.

Any equation that can be rewritten in standard form as where x represents an unknown, a, b, and c represent known numbers, and where a 0 is true is a quadratic equation. As there is no ax2 term when a = 0, the equation is linear rather than quadratic.

r = k*s*t

k = constant of proportionality

r = 8

s = 6

t = 5

Putting the value in the equation:

8 = k x (6) x (4)

8 = 24k

k = 8 /24

k = 1/3

Now,

t = 16

r = 24

Putting the value in the equation:

r = k*s*t

24 = 1/3( x (s) x (16))

((24) x (3) )/ 16  = s

((3) x (3))/2 = s

s = 9/2

The value of s for the given conditions is 9/2.

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Answer:

   [tex]\frac{2}{6}[/tex] or [tex]\frac{1}{3}[/tex]

Step-by-step explanation:

To find a fraction of a fraction simply multiply the numerators and denominators into another fraction:

[tex]\frac{1}{2}*\frac{2}{3} = \frac{2}{6} = \frac{1}{3}[/tex]

Answer:

1/3.

Step-by-step explanation:

'of' means multiply. so

1/2 of 2/3

= 1/2 * 2/3

= 1*2  /  2*3

= 2/6

= 1/3.

Answer:

7

Step-by-step explanation:

The length of the arc can be calculated via a simple proportion:

2 pi r : 360° = x : 45°

Where r is the radius of the circumference and x the length of the arc we want to know. Isolating the x:

x = (2 pi r : 360) * 45 = (2 pi * 9 : 180) * 45 = 18 pi : 360 * 45 = 18pi : 8 = 7

If we suppose a researcher conducts an A-B-A-B study. She records baseline observations and then administers a treatment and records behavior during treatment. Her next step would be administering the treatment again.

Reason Behind the Next Step of the Study

It is given the the researcher conducts an A-B-A-B study.

Her first step was recording the baseline observations.

Hence, first A indicates the first step here that is, recording the observations

In the next step of the study, she administers a treatment.

Thus, B denotes the administering treatment step.

Again, for the third step of the study, she again records behavior during the treatment.

This is again denoted by A.

Hence, we can conclude that in the A-B-A-B study, A denotes recording observation or behavior, B denotes administering a treatment.

Now, since, A, B, and A steps of the study have already been followed, the next phase is B which is concerned with reintroducing or re-administering the treatment.

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The parent function of the function represented in the table is exponential.

If function f was translated down 4 units, the f(x) values would be decreased by 4.

A point on the table for the transformed function would be (4, 87).

Answer:

  C.  5

Step-by-step explanation:

The product of chord segment lengths is the same for the two crossing chords.

One chord has segment lengths 4 and 10; the other has segment lengths x and 8.

  (4)(10) = (x)(8)

  40/8 = x = 5 . . . . . . . divide by the coefficient of x

The value of x is 5, making option C the right choice, using the chord theorem.

The chord theorem, also known as the intersecting chords theorem, is a statement in basic geometry that explains the relationship between the four line segments formed by two intersecting chords inside of a circle. According to this statement, the products of the line segment lengths on each chord are equal.

In the question, we are asked to find the value of x.

Using the chord property, we know that:

8*x = 4*10,

or, 8x = 40,

or, x = 40/8,

or, x = 5.

Thus, the value of x is 5, making option C the right choice, using the chord theorem.

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Answer:

120

Step-by-step explanation:

My choices are: 1, 3, 5, 7, 9.  I cannot repeat any of the numbers.

The first spot, I have 5 choices.  The second spot, I have 4 choices, the third spot, I have 3 choices and the final spot has only 2 choices.

5x4x3x2 = 60

Answer:

42

Step-by-step explanation:

One angle of a regular pentagon = 108°

One angle of a regular hexagon = 120°.

One angle of a square = 90°

∴ ∠BAC = 360 – (108 + 20 + 90) 360 – 318 = 42°

According to the ratio criterion, the rational series presented in the picture converges as x < 1. The limit L was 4 /5.

Herein we have a series in rational form, whose convergence can be proved by the ratio criterion, whose defintion is shown below:

x = lim (n → ∞) |aₙ/aₙ₊₁|   (1)

The series converges if x < 0 and diverges when x > 1. If x = 1, the criterion cannot be used and another criterion must be used instead. Now we proceed to apply it on the expression behind the series:

|aₙ/aₙ₊₁| = [(2 · n + 1) · (2 · n + 2)] / [5 · (n + 1)²]

|aₙ/aₙ₊₁| = [4 · n² + 5 · n + 2] / [5 · n² + 10 · n + 5]

Then, by applying the limit property for rational equations we find that limit of the expression within the series is:

L = 4 / 5

According to the ratio criterion, the rational series presented in the picture converges as x < 1. The limit L was 4 /5.

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By the ratio test, the series diverges.

[tex]\displaystyle \lim_{k\to\infty} \left| \frac{5^{k+1} ((k+1)!)^2}{(2(k+1))!} \cdot \frac{(2k)!}{(5^k (k!)^2}\right| = 5 \lim_{k\to\infty} \frac{(k+1)^2}{(2k+2)(2k+1)} = \frac54 > 1[/tex]

The height is 2 units.

Find the area of the base of the square pyramid:

The volume of the square pyramid is equal to [tex]V=\frac{1}{3} BH[/tex]

B is the area of the base, and H is the height of the pyramid

[tex]H= 6 units[/tex]

[tex]V=70 units^{3}[/tex]

Solve: B

[tex]70=\frac{1}{3} B(6)\\ \\ B=\frac{70}{2} \\ \\ = 35units[/tex]

To find the height of the square prism:

The volume of the square prism is equal: [tex]V=Bh[/tex]

B is the area of the base and h is the height of the prism

[tex]B=35 units^{2}[/tex]

[tex]V=70units^{3}[/tex]

Solve: h

[tex]70=\frac{35}{h}[/tex]

[tex]h=2units.[/tex]

The height is 2 units.

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The height of the square pyramid exists 2 units.

Volume of the square pyramid

[tex]$V = \frac{1}{3}BH[/tex]

where B exists in the area of the base  H lives at the height of the pyramid

we have H = 6 [tex]$$unit^3[/tex]

V = 70 [tex]$$unit^3[/tex]

substitute in the formula and solve for B, we get

[tex]$70 = \frac{1}{3}B(6)[/tex]

B = [tex]$\frac{70}{2}[/tex]

= 35 [tex]$$unit^3[/tex]

To estimate the height of the square prism

Volume of the square prism = Bh

Where B exists the area of the base

h exists the height of the prism

we have B = 35 and V = 70

substitute in the formula and solve for h

70 = (35)h

h = 2 units.

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Answer:

480

Step-by-step explanation:

Answer:

See below

Step-by-step explanation:

REMEMBER  sec = 1/cos ...so the left side is

[1/cos -1]   /  [1/cos  +1 ]    

  get common denominator for numerator and denominator

[ (1 -cos) /cos  ]  /  [ (1+cos) / cos ]    

 now flip the bottom fraction and multiply to get

[(1-cos/cos) ]  *  [ cos / (1+cos) ]    which simplifies to   ( the 'cos' term cancels)

(1-cos) / (1+cos)              done !