A child's bank contains 143 coins consisting of nickels and quarters. If the total amount of money is $18.35, find the number of nickels and quarters in the bank.

Answer:

x = 4

Step-by-step explanation:

x + 8 = 3x

8 = 2x

x = 4

So, the answer is x = 4

The area of the triangle is approximately 6.4936 square centimeters.

We can use Heron's formula to find the area of a triangle given the lengths of its sides. Heron's formula states that the area (A) of a triangle with sides a, b, and c is:

A = √[s(s-a)(s-b)(s-c)]

where s is the semi-perimeter of the triangle, defined as:

s = (a + b + c) / 2

Using the values given in the problem, we have:

a = 7 cm, b = 3 cm, c = 5 cm

The semi-perimeter is:

s = (a + b + c) / 2 = (7 + 3 + 5) / 2 = 7.5 cm

Substituting these values into Heron's formula, we get:

A = √[s(s-a)(s-b)(s-c)]

= √[7.5(7.5-7)(7.5-3)(7.5-5)]

= √[7.5(0.5)(4.5)(2.5)]

= √[42.1875]

= 6.4936 cm² (rounded to 4 decimal places)

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Answer: 42

Step-by-step explanation:

We start by looking at the 49 degree angle. A common method of solving geometric problems is to bring things together. To follow this concept, we can say that the 49 degree angle has a vertical angle inside the triangle, which means that angle is 49 degrees. We now work with the 91 degree angle. We can see the 91 degree angle falls on a line, so the other side of the angle equals 180-91=89. All angles in a triangle add up to 180 degrees, so x + 49 + 89 = 180, so x=180 - 138 = 42.

Answer:

F(x)=x^3+2x^2+15

Step-by-step explanation:

a)  E

b)  C

c) p-value 0.03 significant difference in two procedures

A. No, neither procedure A appears to be normal nor procedure B appears to be normal

B. There appears to be more variation in the 1st procedure than in the 2nd.

C. The p-value of the test is 0.03, which indicates that there is a statistically significant difference in the variances of the two procedures.

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A basketball court takes the shape of a rectangle and the perimeter of a rectangle is =88m

The area encircling a two-dimensional figure is known as its perimeter. Whether it is a triangle, square, rectangle, or circle, it specifies the length of the shape. The two primary characteristics of a 2D shape are area and perimeter.

Each form has a different perimeter depending on its measurements. The perimeter is only ever stated as the circle's diameter when referring to a circle. So we must add all of the sides of each polygon to determine its perimeter, which is the same for all polygons.

A basketball court takes the shape of a rectangle and the perimeter of a rectangle is calculated by the formula:

= Length + Length + Width + Width

Slotting the figures in will give:

= 27 + 27 + 17 + 17

= 88 m

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Answer:

meaning the computer is $1246

Step-by-step explanation:

$1895-$649=$1246

The first term in the given sequence is 5

From the question, we have the following parameters that can be used in our computation:

Rule:

The sequence starting at 5 and following the given rule is:

The first term in the sequence is simply the starting number, which is 5.

Hence, the value of the first term in the sequence is 5.

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Therefore , the solution of the given problem of expressions comes out to be 3x³ - 8x²+ 2x + 3 is the abbreviated expression in standard form.

With shifting variables, estimates that mix joining, deactivating, and random division should be made. They could accomplish the following if they united: A math problem, some facts, and software. Formulas, parts, and arithmetic operations like additions, subtractions, omissions, and groupings can all be found in a declaration of truth. Both words and sentences can be evaluated and analysed.

Here,

The distributive property of multiplication must be used to multiply the two factors jointly in order to simplify the expression:

=> (x-1)(3x²-5x-3) = x(3x²) - x(5x) - x(3) - 1(3x²) + 1(5x) + 1 (3)

Condensing each term:

=> 3x³ - 5x²- 3x - 3x² + 5x + 3

=> 3x³ - 8x²+ 2x + 3

Therefore, 3x³ - 8x²+ 2x + 3 is the abbreviated expression in standard form.

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Answer: 10/36 or 5/8

Step-by-step explanation:

Let’s start by solving how many pens Rohan has left. 36-11-15=36-26=10. Rohan has 10 pens left. Now to solve the fraction of pens Rohan has left, we divide our 10 by 36, or 10/36. Another fraction of this could be 5/18, because both the denominator and numerator have 2 as a factor.

Answer:

Below

Step-by-step explanation:

Area of a triangle = 1/2  base * height

  this triangle has base = 4 ( 3 in) = 12 in    and height = 3 (3 in) = 9 in

 area = 1/2 * 12 * 9 = 54 in^2

54 in^2 *  $ 2.75 /in^2 = $ 148.50

If the window is scaled down by .5 then the dimensions would be

  base = 6 in   height = 4.5 in

    area = 1/2 * 6 * 4.5 = 13.5 in^2

      cost would be    13.5 in^2   *  $ 2.75/in^2  =~ $37.13

The simplified expression with only positive exponents is 729 / 19^7.

We can simplify the expression as follows, using the exponent rules:

19 to the -3rd power = 1 / (19^3)

19×19 to the -4th power = (19^2)^-2 = 1 / (19^2)^2 = 1 / (19^4)

nine to the third power = 9^3

Therefore, the expression can be written as:

(1 / (19^3)) × (1 / (19^4)) × (9^3)

To simplify further, we can combine the two terms with powers of 19 into a single term:

(1 / (19^3 × 19^4)) × (9^3) = (1 / 19^7) × (9^3)

Finally, we can evaluate 9^3 to get the final answer:

(1 / 19^7) × (9^3) = (1 / 19^7) × 729 = 729 / 19^7

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The given question is incomplete, the complete question is:

19 to the -3rd power times 19×19 to the -4th power times nine to the third power. Simplify the expression using only positive exponents

Step-by-step explanation:

1) 12×5=60

8×4=32

32÷2=16

60+16=82

2) 12×14=168

10×2=20

20÷2= 10

168+10+10=188

3) 4×4= 16

4×11=44

4×5=20

16+44+20=80

4) 8×4=32

3×3= 9

9÷2= 4.5

32+4.5=36.5

Answer:

2.05 yards, Fredic and Fioana's answers are in the same range.

The true statements based on the shape in the given image are:

The result of flipping a triangle on a coordinate system based on a line of reflection is a figure known as a triangle reflection.

Let's say we wish to mirror the triangle A B C over the -axis or the line. The image that results from reflecting the triangle, if A B C is the pre-image, is A ′ B ′ C ′. When using triangle reflections, the final image will keep the triangle's shape.

With this explanation in mind and from the image provided, C'Q = QC because they are parallel to each other.

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Answer: 61 degrees

Step-by-step explanation:

just trust me

Answer:

You must know the value of x

Answer:

Sale Price-$48  What Percent Represents the reg. Price?-%100

Step-by-step explanation:

20% of 60 is 12, so if supplies are 20% off, they are $12 off, so 60 - 12 =48.

And if the regular price is $60, then $60 is the whole price, a.k.a. 100% of the price. So, the percent that represents the regular price of supplies is 100%.

Answer:

Quadratic Function, Second Difference

it takes 6 hοurs fοr the sleighs tο be 390 miles apart.

velοcity is a unit οf measurement fοr the Distance an οbject travels in a

the predetermined periοd οf time. Here is a wοrd equatiοn that illustrates the cοnnectiοn between space, speed, and time: velοcity is calculated by

dividing the tοtal Distance traveled by the jοurney time.

Since the sleighs are traveling in οppοsite directiοns, their distances frοm each οther are increasing at a cοmbined rate οf 20 mph + 45 mph = 65 mph. We can use the fοrmula:

distance = rate x time

Let's call the time it takes fοr the sleighs tο be 390 miles apart "t". Then we can write:

390 = 65t

Sοlving fοr "t", we can divide bοth sides by 65:

t = 6

Therefοre, it takes 6 hοurs fοr the sleighs tο be 390 miles apart.

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Answer:

Stephanie Mary and Nicole

Step-by-step explanation:

Option B, 18 million, is the answer to this question.

In September 1998, the population of West Goma in millions was modeled by the function f(x) = 17.9e0.002x, and the population of East Goma in millions was modeled by the function g(x) = 13.6e0.017x. Here, x represents the year, with x=0 corresponding to September 1998.

To find out the point of intersection where the populations are equal, we equate both formulas and solve for x:

17.9e0.002x = 13.6e0.017x

Taking the natural logarithm of both sides of the equation gives:

x ln(17.9) + 0.002x = x ln(13.6) + 0.017x

Simplifying and rearranging terms, we get:

ln(17.9) - ln(13.6) = (0.017 - 0.002)x

0.079 = 0.015x

Solving for x, we get:

x = 5.27 years

Since x is the year, when x = 5.27, it corresponds to the year 1998 + 5.27 ≈ 2003.

When the populations are equal, the population will be f(5.27) ≈ 18 million for West Goma.

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The system of equations that represents the number of each type of basket Jake scored is  given by:

x  + y = 13

2x +  3y = 28

A system of equations is   when two or more variables are related, and equations are built to find   the values of each variable.

In this problem,   the variables are:

Variable x: Number of  2-point shots.

Variable y: Number of 3-point shots.

Jake scored 28 points in his   basketball game   by shooting only 2-point and 3-point   shots, hence:

2x  +  3y = 28.

He scored a total   of 13 baskets, hence:

x  + y  = 13.

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Answer:

3.44827586

Step-by-step explanation:

1450:10,000::x:2

=10,000x=2900

x= 10,000

----------

2900

x=3.44827586 km

The cοst each οf οne apple pie is $8 and οne lemοn meringue pie is $20.

Apples serve as the primary filling in fruit pies, which are knοwn as apple pies. Apple pies are cοmmοnly served with whipped cream, cheddar cheese, custard, ice cream, οr custard. The upper crust οften has pastry abοve and belοw the filling and may be sοlid οr latticed. The bοttοm crust can be baked separately tο prevent it frοm becοming sοggy. Deep dish apple pies typically just feature the tοp crust. The tarte tatin's crust is baked οn tοp, even thοugh it is placed οn the bοttοm when it is served.

Suppοse the cοst οf each apple pie is x and οne lemοn meringue pie is y.

Eimy sοld 6 apple pies and 8 lemοn meringue pies fοr a tοtal οf $208.

Then, 6x+8y= 208

Or, 6x=208-8y…………(1)

Enerlyn sοld 6 apple pies and 2 lemοn meringue pies fοr a tοtal οf $88.

Then, 6x+2y=88……………(2)

Putting the value οf 6x in equatiοn nο 2

208-8y+2y=88

Or, -6y=88-208

Or,y=120/6=20

Putting the value οf y in equatiοn 1

6x= 208-8*20

Or, x= 48/6

Or, x= 8

Hence the cοst each οf οne apple pie is $8 and οne lemοn meringue pie is $20.

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The solution to the system of inequalities is the region enclosed in the triangle

An equation is an expression that shows the relationship between numbers and variables using mathematical operators such as addition, subtraction, exponent, multiplication and division.

Let x denote the time (in hours) that Shen spends doing cardiovascular work. Let y denote the time (in hours) he spends on weight training.

Each week, he exercises for at least 12 hours, hence:

x + y ≥ 12   (1)

He spends at most 9 hours on weight training. Therefore:

x ≤ 6      (3)

He spends at most 6 hours doing cardiovascular work. Hence:

y ≤ 9    (3)

The solution to the system of inequalities is the darker region shown in the graph.

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In the triangle , the cοrrect οptiοn is  B) b = CD sin(A) and a = CD sin(B).

A triangle is a fοrm οf pοlygοn with three sides; the intersectiοn οf the twο lοngest sides is knοwn as the triangle's vertex. There is an angle created between twο sides. One οf the crucial elements οf geοmetry is this.

Certain fundamental ideas, including the Pythagοrean theοrem and trigοnοmetry, rely οn the characteristics οf triangles. The angles and sides οf a triangle determine its kind.

Here the given triangle CD is altitude.

According to the given statement table , in 4th statement we have definition of sine , Then

=> Sin(A) = [tex]\frac{CD}{b}[/tex] and Sin(B) = [tex]\frac{CD}{a}[/tex]

Here simplifying this sine equation for a and b then,

=> b = CD sin(A) and a = CD sin(B).

Hence the correct option is B) b = CD sin(A) and a = CD sin(B).

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Answer:

To find the best line model for the data, we will use linear regression analysis.

First, we need to calculate the mean of x and y:

mean of x = (0 + 2 + 4 + 6 + 8 + 10 + 12 + 24 + 14) / 9 = 8

mean of y = (9 + 9 + 10 + 11 + 11 + 12 + 13 + 13 + 14) / 9 = 11

Next, we need to calculate the deviations of x and y from their respective means:

deviation of x = x - mean of x

deviation of y = y - mean of y

x y deviation of x deviation of y (deviation of x)^2 deviation of x * deviation of y

0 9 -8 -2 64 16

2 9 -6 -2 36 12

4 10 -4 -1 16 4

6 11 -2 0 4 0

8 11 0 0 0 0

10 12 2 1 4 2

12 13 4 2 16 8

24 13 16 2 256 32

14 14 6 3 36 18

Then, we can calculate the slope (b) of the best-fit line using the formula:

b = sum of (deviation of x * deviation of y) / sum of (deviation of x)^2

b = (16 + 12 + 4 + 0 + 0 + 2 + 8 + 32 + 18) / (64 + 36 + 16 + 4 + 0 + 4 + 16 + 256 + 36) = 0.190

Next, we can calculate the y-intercept (a) of the best-fit line using the formula:

a = mean of y - b * mean of x

a = 11 - 0.190 * 8 = 7.48

Therefore, the equation of the best-fit line is:

y = 0.190x + 7.48

Finally, we can calculate the correlation coefficient (r) using the formula:

r = sum of (deviation of x * deviation of y) / (sqrt(sum of (deviation of x)^2) * sqrt(sum of (deviation of y)^2))

r = (16 + 12 + 4 + 0 + 0 + 2 + 8 + 32 + 18) / (sqrt(64 + 36 + 16 + 4 + 0 + 4 + 16 + 256 + 36) * sqrt(16 + 16 + 1 + 0 + 0 + 1 + 4 + 4 + 1)) = 0.905

Therefore, the best-fit line for the given data is y = 0.190x + 7.48, and the correlation coefficient is r = 0.905.

Step-by-step explanation: