Members of a soccer team raised $2143.50 to go to a tournament. They
rented a bus for $888.50 and budgeted $62.75 per player for meals. Write
and solve an equation which can be used to determine x, the number of
players the team can bring to the tournament.

Answer: 9.900

The explicit rule for the sequence in the graph is f(n) = 9.5 + 2(n - 1)

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

The graph

In the graph, we can see that 2 is added to the previous term to get the new term

This means that

First term, a = 9.5

Common difference, d = 2

The nth term is then represented as

f(n) = a + (n - 1) * d

Substitute the known values in the above equation, so, we have the following representation

f(n) = 9.5 + 2(n - 1)

Hence, the explicit rule is f(n) = 9.5 + 2(n - 1)

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-1

We can solve in this way,

-3x-5x+8=16

-8x=16-8

-8x=8

x= -8/8

x= -1

Therefore for this equation, x= -1.

The temperature at 8:00 A.M. was 15°C.

Using the given information:
1. At 7:00 P.M., the temperature was 16°C.
2. This temperature was 9°C less than the temperature at 2:00 P.M.

We can use this information to find the temperature at 2:00 P.M.:
Temperature at 2:00 P.M. = 16°C (temperature at 7:00 P.M.) + 9°C
Temperature at 2:00 P.M. = 25°C

3. The temperature at 2:00 P.M. was 10°C higher than the temperature at 8:00 A.M.

Now, we can find the temperature at 8:00 A.M.:
Temperature at 8:00 A.M. = 25°C (temperature at 2:00 P.M.) - 10°C
Temperature at 8:00 A.M. = 15°C

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Answer:

(x+2)(4x-1)

For this problem, use the FOIL (first, outside, inside, last) method

You have x, 2, 4x, and -1. Start by multiplying x by 4x and -1. Then multiply 2 by 4x and -1. You should have four separate values to add together.

(x*4x)+(x*(-1))+(2*4x)+(2*(-1)) = 4x^2+(-x)+8x+(-2)

Once you have this, order each value by their exponents and combine like terms. The highest exponents always go to the left and lowest exponents go to the right.

4x^2+7x-2

The answer to the equation −0.22x + x − 0.33x is 0.11x.

The answer is 0.11x. To solve this, we can start by rearranging the terms of the equation. The equation can be written as:

−0.22x + x − 0.33x = −0.22 + 0.33x

We then subtract x from both sides of the equation, resulting in:

−0.22x − x = −0.22 + 0.33x − x

We then combine like terms on the left side of the equation, resulting in:

−1.22x = −0.55

Finally, we divide both sides of the equation by -1.22 to solve for x, resulting in:

x = 0.11

Therefore, the answer is 0.11x.

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Complete question

What is the value of -0.22+−0.33−0.22x+x−0.33x?

Answer:

10

Step-by-step explanation:

After hour, pay increases by 10.

When 1,493,600 is divided by 8 the quotient is 186,700.

To divide 1,493,600 by 8, you can follow these steps:

We have to write down the dividend (1,493,600) and the divisor (8).

Now start with the largest place value in the dividend (the leftmost digit) and perform the division.

Divide 1 by 8. Since 1 is smaller than 8, you move to the next digit.

Bring down the next digit (4) and combine it with the previous quotient (0). This gives you 04.

Divide 4 by 8. Since 4 is smaller than 8, you move to the next digit.

Bring down the next digit (9) and combine it with the previous quotient (0). This gives you 09.

Divide 9 by 8. The quotient is 1, and the remainder is 1.

Bring down the next digit (3) and combine it with the remainder (1). This gives you 13.

Divide 13 by 8. The quotient is 1, and the remainder is 5.

Bring down the next digit (6) and combine it with the remainder (5). This gives you 56.

Divide 56 by 8. The quotient is 7, and there is no remainder.

Bring down the next digit (0) and combine it with the quotient (7). This gives you 70.

Divide 70 by 8. The quotient is 8, and there is no remainder.

There are no more digits to bring down, and the division is complete.

The quotient is the result of the division. In this case, 1,493,600 divided by 8 is equal to 186,700.

Therefore, the result of 1,493,600 ÷ 8 is 186,700.

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a) The algebraic fraction \(\frac{{x + 2}}{{(x - 1)^2}}\) is proper. b) The algebraic fraction \(\frac{{4x^2 - 31x + 59}}{{(x - 4)^2}}\) can be expressed as \(-\frac{{31}}{{x - 4}} - \frac{{25}}{{(x - 4)^2}}\).

Let's solve each part step by step and determine whether the fraction is proper or improper, and then express it accordingly.

a) \(\frac{{x + 2}}{{(x - 1)^2}}\):

Step 1: Determine the degree of the numerator and the denominator:

  - Degree of the numerator = 1 (linear term)

  - Degree of the denominator = 2 (quadratic term)

Since the degree of the numerator is less than the degree of the denominator, the fraction is proper.

Step 2: Express the proper fraction in partial fractions:

\(\frac{{x + 2}}{{(x - 1)^2}} = \frac{A}{{x - 1}} + \frac{B}{{(x - 1)^2}}\).

Step 3: Find the values of A and B:

Multiply both sides of the equation by \(((x - 1)^2)\) to eliminate the denominators:

  (x + 2) = A(x - 1) + B.

Expand the equation and collect like terms:

  x + 2 = Ax - A + B.

Equate the coefficients of like terms:

  Coefficient of x: 1 = A.

  Constant term: 2 = -A + B.

Solve the system of equations to find the values of A and B:

From the coefficient of x, A = 1.

Substituting A = 1 into the constant term equation: 2 = -1 + B, we find B = 3.

Therefore, the partial fraction decomposition is:

  \(\frac{{x + 2}}{{(x - 1)^2}} = \frac{1}{{x - 1}} + \frac{3}{{(x - 1)^2}}\).

b) \(\frac{{4x^2 - 31x + 59}}{{(x - 4)^2}}\):

Step 1: Determine the degree of the numerator and the denominator:

  - Degree of the numerator = 2 (quadratic term)

  - Degree of the denominator = 2 (quadratic term)

Since the degree of the numerator is equal to the degree of the denominator, the fraction is proper.

Step 2: Express the proper fraction in partial fractions:

  \(\frac{{4x^2 - 31x + 59}}{{(x - 4)^2}} = \frac{A}{{x - 4}} + \frac{B}{{(x - 4)^2}}\).

Step 3: Find the values of A and B:

Multiply both sides of the equation by \(((x - 4)^2)\) to eliminate the denominators:

  (4x^2 - 31x + 59) = A(x - 4) + B.

Expand the equation and collect like terms:

  4x^2 - 31x + 59 = Ax - 4A + B.

Equate the coefficients of like terms:

Coefficient of \(x^2\): 4 = 0 (No \(x^2\) term on the right side).

Coefficient of x: -31 = A.

Constant term: 59 = -4A + B.

Solve the system of equations to find the values of A and B:

From the coefficient of x, A = -31.

Substituting A = -31 into the constant term equation: 59 = 4(31) + B, we find B = -25.

Therefore, the partial fraction decomposition is:

  \(\frac{{4x^2 - 31x + 59}}{{(x - 4)^2}} = -\frac{{31}}{{x - 4}} - \frac{{25}}{{(x - 4)^2}}\).

The above steps provide the solution for each part, including determining if the fraction is proper or improper and expressing it in partial fractions.

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Answer:

The slope-intercept equation of the line that goes through the points (1, 5) and (2, 8) is​ \(\mathbf{y=\frac{3}{2}x+\frac{7}{2} }\)

Step-by-step explanation:

We need to find the slope-intercept equation of the line that goes through the points (1, 5) and (2, 8)

The general equation for slope intercept form is ​ \(y=mx+b\) where m is slope and b is y-intercept

Finding slope

Slope can be found using formula \(Slope=\frac{y_2-y_1}{x_2-x_1}\)

We have \(x _1=1, y_1=5, x_2=2, y_2=8\)

Putting values and finding slope

\(Slope=\frac{y_2-y_1}{x_2-x_1}\\Slope=\frac{8-5}{2-1}\\Slope=\frac{3}{2}\)

So, we get slope \(m=\frac{3}{2}\)

Finding y-intercept

y-intercept can be found using slope \(m=\frac{3}{2}\) and point (1,5)

\(y=mx+b\\5=\frac{3}{2}(1)+b\\b=5- \frac{3}{2}\\b=\frac{10-3}{2}\\b=\frac{7}{2}\\\)

So, we get y-intercept \(b=\frac{7}{2}\)

Equation of line

So, equation of line having slope \(m=\frac{3}{2}\) and y-intercept \(b=\frac{7}{2}\) is:

\(y=mx+b\\y=\frac{3}{2}x+\frac{7}{2}\)

The slope-intercept equation of the line that goes through the points (1, 5) and (2, 8) is​ \(\mathbf{y=\frac{3}{2}x+\frac{7}{2} }\)

Answer:

i think it might be a correct me if i am wrong

Step-by-step explanation:

Answer:

20/100 * 80=16

80_16=64$

Step-by-step explanation:

Answer:

a rate

Step-by-step explanation:

Answer:

y=1x-6

Step-by-step explanation:

First we find the slope by using rise over run. So you can either count up and over(rise/run) or use the slope formula y2-y1/x2-x1. You will find that the slope is 1, so plug that into the equation for mx. So we have y=1x so far. Then we find the y-intercept by looking where the graph intersects the y-axis. As you can see it intersects at -6, so plug -6 into the equation for b. No we have our full equation of y=1x-6.

-Hope this helped

Answer:f(x) = (x-10)^2-49

f(x) = (x-10+7)(x-10-7)

f(x) = (x-3)(x-17)

The zeros of the function are 3 and 17.

Step-by-step explanation:

Answer:

b

Step-by-step explanation:

Answer:

Step-by-step explanation:

mean=(88+72+85+76)/4=321/4=80.25

x      |x-mean|

88     7.75  (88-80.25)

72     8.25  (80.25-72)

85     4.75   (85-80.25)

76      4.25  (80.25-76)

         --------

       25.00

      ______

mean absolute deviation=25/4=6.25

Answer:

4608

Step-by-step explanation:

answer is 4,608

6+2 = 8, 8^3 = 512, 512*9 = 4608

a) A formula that describes aₙ is; aₙ = 30(⁶/₇)^(n - 1)

b) The arc length of the tire on the 11th swing is; 6.422 feet

c) The number of swings it takes for the arc length to be less than one is; 21

The general formula for the nth term of a geometric progression is;

aₙ = ar^(n - 1)

where;

a is first term

r is common ratio

a) We are given the initial arc length is 30 ft. Thus

a = 30

It swings with 6/7th of the previous length and so; r = 6/7. Thus;

A formula that describes aₙ is;

aₙ = 30(⁶/₇)^(n - 1)

b) The arc length of the tire on the 11th swing is;

a₁₁ = 30(⁶/₇)^(11 - 1)

a₁₁ = 6.422 feet

c) The number of swings it takes for the arc length to be less than one foot is expressed as;

30(⁶/₇)^(n - 1) = 1

(⁶/₇)^(n - 1) = 1/30

(n - 1) In (6/7) = In 30

Solving gives gives n = 21

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Answer:

AB> sorry if I'm incorrect

Answer

24*108=x

Step-by-step explanation:

Lets say x is the total amount. and you need to find it for 24 and 85+23= 108 dollars. and so you multiplay 108 with 24. hope it helped

We substitute -1+1/6y for x in the second equation (bottom equation) in order to solve the system by the substitution method.

The given system of equations are 2x-1/3y = -2...(1)

3x+y=1...(2)

We solve this system of equations by using substitution method.

Let us solve for x in equation to substitute it in equation (2).

2x=-2+1/3y

Divide both sides of equation by 2.

x=-1+1/6y

Now plug in the value of x in equation 2.

Hence, we substitute -1+1/6y for x in the second equation (bottom equation) in order to solve the system by the substitution method.

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Your chances of being killed or injured in such a crash are 5 times greater when you are thrown from your car than when you are buckled up

The safest decision that drivers and passengers can make is to use their seatbelts.

The national seat belt use rate was 90.4% in 2021, indicating that many Americans are aware of the life-saving benefits of seat belts.

In 2017, it is projected that 14,955 lives were saved by seat belt use in passenger automobiles.

Recognize the potentially devastating repercussions of not using a seat belt and discover how to always buckle up properly for you and your family.

Buckling up keeps you safe and secure within your car, whereas not doing so increases your chance of being completely ejected from the vehicle in an accident, which is virtually always fatal.

You need more protection than air bags.

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The standard deviation of the sample is 0.63

What is standard deviation?

A random variable, sample, statistical population, data set, or probability distribution's standard deviation is equal to the square root of its variance.

To find the standard deviation of the sample, we need to first find the mean of the distribution. The mean of a distribution is given by the expected value of the random variable, which can be calculated as follows:

       \(E[X] = \int\limits {xf(x)dx}\)

Substituting the given pdf for f(x), we get:

     \(E[X] = \int\limits {x(x2 + Źosxs1)dx}\)

Evaluating the integral, we get:

   \(E[X] = (x3/3) + (Źosxs2/2) |0\\\\ E[X] = (1/3) + (0/2)\\\\ E[X] = 1/3\)

Next, we need to find the variance of the distribution. The variance of a distribution is given by the expected value of the squared deviation of the random variable from its mean, which can be calculated as follows:

\(Var[X] = E[(X - E[X])2]\)

Substituting the value of E[X] that we just found, we get:

Var[X] = E[(X - (1/3))2]

Var[X] = ∫((x - (1/3))2)(x2 + Źosxs1)dx

Evaluating the integral, we get:

Var[X] = ((x - (1/3))2)(x2 + Źosxs1) |0

Var[X] = ((1 - (1/3))2)(1 + 0) - ((0 - (1/3))2)(0 + 0)

Var[X] = (4/9)(1) - (1/9)(0)

Var[X] = 4/9

Finally, the standard deviation of the distribution is the square root of the variance, which is:

\(Std\ Dev[X] = \sqrt{Var[X]}\\\\ Std\ Dev[X] = \sqrt{(4/9) } \\\\Std\ Dev[X] = 0.63\)

Rounding off to the second decimal place, the standard deviation of the sample is 0.63.

Hence, The standard deviation of the sample is 0.63

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The equation of the line is x = -9 , Option  is the correct answer

The equation of a line is given by y = mx+c

where m is the slope and c is the intercept

It is given that

A line passes through (-9,-6) and has an undefined slope.

undefined slope means it is a vertical line at -9

Therefore the equation of the line is x = -9 , Option  is the correct answer

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Answer:

2 forms

Step-by-step explanation:

hope this helps <3

\( \sf \longrightarrow \: \frac{8}{5} \div 6 \\ \)

\( \sf \longrightarrow \: \frac{5}{8} \times 6 \\ \)

\( \sf \longrightarrow \: \frac{5 \times 6}{8} \\ \)

\( \sf \longrightarrow \: \frac{30}{8} \\ \)

\( \sf \longrightarrow \: \frac{8}{30} \\ \)

\( \sf \longrightarrow \: 0.26 \\ \)

_____________________________

B. Yes; The numbers are combine to zero

is additive inverses because the sum is 0

The value for the unknown side length, x in simplest radical form is \(\sqrt{65}\).

Based on the figure that is been provided , it can be deduced that the length of the line separating the two triangles is 4 which an be found using the Pythagoras theorem as

\(5^{2} = 3^{2} + y^{2} \\\\y^{2} = 25 -9\\\\y^{2} =16\\y=\sqrt{16} \\y=4\)

Then the line dividing the triangle is been named y and it is 4., then we calculate the value of x as;

\(x^{2} = 7^{2} + 4^{2} \\x^{2} = 49 + 16\\ x^{2} = 65\\x=\sqrt{65}\)

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Answer:

1278.8 ft^3

Step-by-step explanation:

radius of cylinder = r = 5.8 ft

height of cylinder = h = 8.9 ft

radius of cone = r = 5.8 ft

height of cone = H - h = 18.5 ft - 8.9 ft = 9.6 ft

volume = volume of cylinder + volume of cone

V = (pi)(r^2)h + (1/3)(pi)(r^2)(H - h)

V = (3.14159)(5.8^2 ft^2)(8.9 ft) + (1/3)(3.14159)(5.8^2 ft^2)(9.6 ft)

V = 1278.8 ft^3

Answer:

If you use 3.14 for pi

1278.1 ft^2

Using the pi button on the calculator

1278.8 ft^2

Step-by-step explanation:

First find the volume of the cylinder

V = pi r^2 h where r is the radius and h is the height of the cylinder

V = pi ( 5.8) ^2 ( 8.9)

V = pi *33.64 * 8.9

V = 299.396 pi

The find the volume of the cone

V= 1/3 pi r^2h

The height of the cone is  18.5- 8.9 =9.6

V= 1/3 ( pi ) ( 5.8)^2 ( 9.6)

V= 1/3 ( pi ) 33.64 ( 9.6)

V = 107.648 pi

Add the two volumes together

299.396 pi + 107.648 pi

407.044 pi

If you use 3.14 for pi

1278.11816 ft^2

Rounding to the nearest tenth

1278.1 ft^2

Using the pi button on the calculator

1278.76644

Rounding to the nearest tenth

1278.8 ft^2