4. For each babysitting job, Adam charges a fee for his bus fare plus an hourly rate. The graph shows how he calculates the cost of a babysitting job. Write a linear function in the form
y = mx + b to represent the situation.
Ay = 3x+2
B. y = 3x+1
C. y = 6x+2
D. y = -6× + 2

Answer: y = 550x

Step-by-step explanation:

Answer:

V = (4/3) × 3.14 × 14³ = 11,310.08 cubic feet

Work Shown:

d = diameter = 28

r = radius = d/2 = 28/2 = 14

V = volume of a sphere

V = (4/3)*pi*r^3

V = (4/3)*3.14*(14)^3

V = 11,488.2133 cubic feet approximately

The info "weighs almost 8 tons" is never used. It is likely an intended distraction. All we need is the radius of the sphere to get its volume.

Answer:

Step-by-step explanation:

Median:  List numbers from smallest to largest.  Median is middle number

2       2        3         5        6          8           10

                               |

5 is in the middle

Median = 5

The cubic model that fits the given data is: y ≈ 0.00006204x³ + 0.00231059x² - 0.10811757x + 18.2

Let's set up a system of equations using the given data points:

For x = 0 (year 1950):

18.2 = a(0)³ + b(0)² + c(0) + d ==> d = 18.2

For x = 10 (year 2000):

65.5 = a(10)³ + b(10)² + c(10) + 18.2

For x = 20 (year 2010):

75.3 = a(20)³ + b(20)² + c(20) + 18.2

For x = 25 (year 2015):

78.1 = a(25)³ + b(25)² + c(25) + 18.2

For x = 30 (year 2020):

78.5 = a(30)³ + b(30)² + c(30) + 18.2

For x = 40 (year 2030):

80.5 = a(40)³ + b(40)² + c(40) + 18.2

For x = 50 (year 2040):

86.6 = a(50)³ + b(50)² + c(50) + 18.2

For x = 60 (year 2050):

91.5 = a(60)³ + b(60)² + c(60) + 18.2

Simplifying these equations, we have: d = 18.2

1000a + 100b + 10c + 18.2 = 65.5

8000a + 400b + 20c + 18.2 = 75.3

15625a + 625b + 25c + 18.2 = 78.1

27000a + 900b + 30c + 18.2 = 78.5

64000a + 1600b + 40c + 18.2 = 80.5

125000a + 2500b + 50c + 18.2 = 86.6

216000a + 3600b + 60c + 18.2 = 91.5

We can solve this system of equations to find the coefficients a, b, and c.

Using a cubic regression calculator or a matrix solver, the solution is:

a ≈ 0.00006204

b ≈ 0.00231059

c ≈ -0.10811757

Therefore, the cubic model that fits the given data is: y ≈ 0.00006204x³ + 0.00231059x² - 0.10811757x + 18.2

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Answer:

d

Step-by-step explanation:

Answer:

Expected winnings = $1.33

Expected profit or loss = -$2.67

Step-by-step explanation:

Winning Probability Prize Value

Yes   1/150         $200

No         149/150         $0

Expected winnings of one raffle ticket:

Expected winnings = (Probability of winning x Prize value) + (Probability of losing x Prize value)

Expected winnings = (1/150 x $200) + (149/150 x $0)

Expected winnings = $1.33

If a raffle ticket costs $4, the expected profit or loss of one raffle ticket can be calculated as:

Expected profit or loss = Expected winnings - Cost of ticket

Expected profit or loss = $1.33 - $4

Expected profit or loss = -$2.67

The width, w, of the opening between x and y, is 6.9 ft.

We have,

From the diagram,

We have the radius of the circle and the angle subtended by the chord at the center of the circle.

So,

We can also use the formula.

= 2 x radius x sin(angle/2)

This is the length of the chord.

Now,

radius = 4 ft

angle = 360/3 = 120

Substituting the values.

= 2 x radius x sin(angle/2)

= 2 x 4 x sin (120/2)

= 2 x 4 x sin 60

= 2 x 4 x √3/2

= 4 x √3

= 4 x 1.732

= 6.928

Rounding to the nearest tenth.

= 6.9 ft

Thus,

The width, w, of the opening between x and y, is 6.9 ft.

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Answer:

I love math

Step-by-step explanation:

The formula for simple interest is:

I = P * r * t

where:

I = interest earned

P = principal amount

r = interest rate (as a decimal)

t = time (in years)

In this case, we know that:

P = $1,264

r = 2.75% = 0.0275 (as a decimal)

t = 2.5 years

So, we can plug in these values and solve for I:

I = 1,264 * 0.0275 * 2.5 = $87.55

Therefore, the interest earned over 2.5 years is $87.55. To find the ending balance, we need to add the interest earned to the principal:

Ending balance = $1,264 + $87.55 = $1,351.55

So, Quentin's account balance will be $1,351.55 at the end of 2.5 years.

a) The mean of the random variable is 2.610 (rounded to 2 decimal places).

b) The variance of the random variable is 1.880 (rounded to 3 decimal places).

c) The standard deviation of the random variable is 1.372 (rounded to 3 decimal places).

d) The probability that a randomly selected student has a parent involved in 4 activities is 0.260 (rounded to 3 decimal places).

To compute the variance of the random variable, we need to calculate the squared deviation of each value from the mean, weighted by their respective probabilities, and then sum them up.

b) Variance [tex](\sigma^2)[/tex] of the random variable:

Variance is given by the formula[tex]Var(X) = \sum [(X - \mu)^2 \times P(X)],[/tex] where X represents the values of the random variable, μ is the mean, and P(X) is the probability.

Using the given data:

X: 0 1 2 3 4

P(X): 0.053 0.117 0.258 0.312 0.26

μ (mean): 2.610

Calculating the squared deviations for each value:

[tex](0 - 2.610)^2 \times 0.053 = 14.152[/tex]

[tex](1 - 2.610)^2 \times 0.117 = 0.291[/tex]

[tex](2 - 2.610)^2 \times 0.258 = 0.148[/tex]

[tex](3 - 2.610)^2 \times 0.312 = 0.122[/tex]

[tex](4 - 2.610)^2 \times 0.26 = 1.429[/tex]

Summing up the squared deviations:

Var(X) = 14.152 + 0.291 + 0.148 + 0.122 + 1.429 = 16.142

Therefore, the variance of the random variable is 16.142.

c) Standard deviation (σ) of the random variable:

The standard deviation is the square root of the variance.

Taking the square root of the variance calculated above:

Standard deviation (σ) = √(16.142) ≈ 4.020 (rounded to 3 decimal places)

d) Probability of a randomly selected student having a parent involved in 4 activities:

The probability of a specific value occurring in a discrete probability distribution is given by the corresponding probability value.

From the given data:

P(X = 4) = 0.26

Therefore, the probability that a randomly selected student has a parent involved in 4 activities is 0.26 (rounded to 3 decimal places).

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The stem display for the data, given the monthly rent and the apartment building is:

$14 | 10 15 35

$15 | 15 55 75 95

$16 | 40 90

To create a stem display, we first divide the data into groups of tens. The first group is $ 1400  -$ 1499, the second group is  $ 1500 - $1599 , and so on. Next, we write the units digit of each number in the appropriate group.

For example, the number 1,710 is in the $ 1500 - $ 1599 group, so we write a 1 in the 15 column. Finally, we count the number of numbers in each group. There are three numbers in the $ 1400 - $ 1499 group, two numbers in the $ 1500 - $ 1599 group, and three numbers in the $ 1600 - $ 1699 group.

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The domain for the square root function is the set of all whole numbers

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

Function type = square root function

Equation: square root of x

This means that

f(x) = √x

The domain for x in the function is the set of input values the function can take

In this case, the square root function can take any whole number as its input

This means that the domain for f(x) is the set of all whole number

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Answer:

[tex]\huge\boxed{\sf x = 5}[/tex]

Step-by-step explanation:

20x + 30 = 28x - 10 (Corresponding angles)

20x + 30 + 10 = 28x

20x + 40 = 28x

40 = 28x - 20x

40 = 8x

5 = x

OR

[tex]\rule[225]{225}{2}[/tex]

The number that belongs in the green box is given as follows:

D.  2.

A quadratic function is given according to the following rule:

y = ax² + bx + c

The solutions are given as follows:

In which the discriminant is given as follows:

[tex]\Delta = b^2 - 4ac[/tex]

The number that goes into the green box is then given as follows:

2a = 2(1) = 2.

Meaning that option D is the correct option in the context of this problem.

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The ratios that are equivalent to the ratio 12:3 are 4:1 and 120:30.

We have,

To determine the ratios that are equivalent to the ratio 12:3, we need to find ratios that have the same value when simplified.

The ratio 12:3 can be simplified by dividing both numbers by their greatest common divisor (GCD), which in this case is 3.

Dividing 12 by 3 gives us 4, and dividing 3 by 3 gives us 1. Therefore, the simplified ratio is 4:1.

Now let's check the given options:

6:1 - This ratio is not equivalent because it is different from the simplified ratio 4:1.

1:4 - This ratio is not equivalent because the order of the numbers is reversed, and it is different from the simplified ratio 4:1.

4:1 - This ratio is equivalent to the original ratio 12:3. When simplified, both ratios result in 4:1.

246 - This is not a ratio and cannot be compared to the original ratio 12:3.

15:6 - This ratio is not equivalent because it is different from the simplified ratio 4:1.

120:30 - This ratio can be simplified by dividing both numbers by their GCD, which is 30.

Dividing 120 by 30 gives us 4, and dividing 30 by 30 gives us 1.

Therefore, the simplified ratio is 4:1, which is equivalent to the original ratio 12:3.

Thus,

The ratios that are equivalent to the ratio 12:3 are 4:1 and 120:30.

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Answer:

y = 3x + 3

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2} -x_{1} }[/tex]

with (x₁, y₁ ) = (- 1, 0) and (x₂, y₂ ) = (0, 3) ← 2 points on the line

m = [tex]\frac{3-0}{0-(-1)}[/tex] = [tex]\frac{3}{0+1}[/tex] = [tex]\frac{3}{1}[/tex] = 3

the line crosses the y- axis at (0, 3 ) ⇒ c = 3

y = 3x + 3 ← equation of line

The consumer surplus for the price of the dog food is given as follows:

$1.

The consumer surplus is defined as the difference between the amount a consumer is willing to pay for a product and the actual price they pay.

The parameters in the context of this problem are given as follows:

Hence the consumer surplus for the price of the dog food is given as follows:

5 - 4 = $1.

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The calculated area of the triangle is 38.30 square units

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

The triangle

The area of the triangle is calculated as

Area = 1/2absin(c)

Where

a = b = 10

c = 50 degrees

Using the above as a guide, we have the following:

Area = 1/2 * 10 * 10 * sin(50 degrees)

Evaluate

Area = 38.30

Hence, the area of the triangle is 38.30 square units

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The function g(x) is increasing exponentially because it eventually exceeds f(x).

The table shows that as x increases, the values of g(x) increase at a much faster rate compared to the values of f(x).

In fact, the values of g(x) are growing exponentially, as each subsequent value is significantly larger than the previous one.

Therefore, the function g(x) is most likely increasing exponentially.

Thus, g(x) is increasing exponentially because it eventually exceeds f(x).

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The inequality that represents the number sentence is given as follows:

w + 4.6 > 6.

The four most common inequality symbols, and how to interpret them, are presented as follows:

A number w plus 4.6 is represented as follows:

w + 4.6.

The amount is more than 6, hence the inequality is given as follows:

w + 4.6 > 6.

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Answer:

The x-intercepts are (-3, 0) and (2, 0).

Answer:

y=8

Step-by-step explanation:

Answer:

  125/384 ≈ 0.32552

Step-by-step explanation:

You want the area between the curves y = 5x and y = 8x².

The difference between the curves is ...

  f(x) = 5x -8x² = x(5 -8x)

This difference is zero when ...

  x = 0

  5 -8x = 0   ⇒   x = 5/8

The area will be the integral of f(x) with the limits 0 and 5/8:

  [tex]\displaystyle \text{area}=\int_0^\frac{5}{8}{(5x-8x^2)}\,dx=\dfrac{5}{2}\cdot\left(\dfrac{5}{8}\right)^2-\dfrac{8}{3}\cdot\left(\dfrac{5}{8}\right)^3\\\\\\\text{area}=\left(\dfrac{5}{8}\right)^2\left(\dfrac{5}{2}-\dfrac{8}{3}\cdot\dfrac{5}{8}\right)=\dfrac{25}{64}\cdot\dfrac{5}{6}=\boxed{\dfrac{125}{384}}[/tex]

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Answer: if it's true that 10 > 7 (P), then it's also true that 10 > 5 (Q).

Step-by-step explanation: In the context of logic and truth tables, p → q can be read as "if p then q." You've provided the truth values for the combinations of p and q, which I'll summarize here:

If p and q are both False (F), then p → q is True (T).

If p is True (T) and q is False (F), then p → q is False (F).

If p is False (F) and q is True (T), then p → q is True (T).

If p and q are both True (T), then p → q is True (T).

Given your propositions:

P: 10 > 7

Q: 10 > 5

P is True because 10 is indeed greater than 7. Q is also True because 10 is greater than 5.

Therefore, we're in the fourth case of your truth table: both p and q are True, so p → q is also True.

The value of the side labelled x is equal to 3.8 to the nearest tenth using the trigonometric ratio of sine.

The trigonometric ratios is concerned with the relationship of an angle of a right-angled triangle to ratios of two side lengths.

The basic trigonometric ratios includes;

sine, cosine and tangent.

Considering the sine of angle 41°

sin 41° = 2.5/x {opposite/hypotenuse}

x = 2.5/sin 41° {cross multiplication}

x = 3.8106

Therefore, the value of the side labelled x is equal to 3.8 to the nearest tenth using the trigonometric ratio of sine.

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Answer:

Kendra's Tea Shop served 87 caffeinated teas and 13 decaffeinated teas. This means that 87 out of 100 teas served were caffeinated. Therefore, 87% of the teas served were caffeinated.

1)

The measure of angle A is 45° .

Given,

a= 60

b = 60√2

c = 60

Now the given sides with the dimension is of right angled triangle.

So,

Angle B = 90°

Angle A = 45°

Angle C = 45°

2)

All the six trigonometric functions:

SinФ = 60/60√2

cosФ = 60/60√2

tanФ = 60/60

cosecФ = 60√2/60

secФ = 60√2 /60

cotФ = 60/60

3)

Area of triangle = 1/2 × b× h

Area of triangle = 1/2 *60*60

Area of triangle = 1800 in²

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Answer: C: (-4,-3)

Step-by-step explanation:

You have the correct answer selected!

The solution of a system of equations is where the graphs of the two lines intersect. we can read that point to be (-4,-3), so thats the answer :)

The rate of the decay of the given function is 75 percent.

The given function is y=12,500(3/4)ˣ

This function represents exponential decay with a base of (3/4). The rate of decay, "r", is equal to 3/4. This means that the value of the function decreases by a factor of 3/4 every time the independent variable increases by 1. Thus, the rate of decay is 3/4 or 75%.

Therefore, the rate of the decay of the given function is 75 percent.

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Answer: Inflation is the rise in general level of prices which is determined by the Consumer Price Index (CPI).