A race car driver won a 200 mile race with a speed of 159.5 miles per hour. Find the driver's time.

Cinnamon tea costs $1.50 per pound, and spice tea costs $2.75 per pound.

To solve this problem, we can set up a system of equations based on the given information.

Let's denote the cost per pound of the cinnamon tea as C, and the cost per pound of the spice tea as S.

From the first mixture, we know that the total weight is 17 pounds, so we can write the equation:

12C + 5S = 28 ----(Equation 1)

From the second mixture, we know that the total weight is 20 pounds, so we can write the equation:

14C + 6S = 33 ----(Equation 2)

To solve this system of equations, we can use a method like substitution or elimination.

Let's use the elimination method to eliminate the variable C:

Multiply Equation 1 by 2 and Equation 2 by -3 to eliminate the C terms:

24C + 10S = 56 ----(Equation 3)

-42C - 18S = -99 ----(Equation 4)

Add Equation 3 and Equation 4:

-18C - 8S = -43

Solve for S:

8S = 43 - 18C

S = (43 - 18C)/8 ----(Equation 5)

Now substitute Equation 5 into Equation 1:

12C + 5((43 - 18C)/8) = 28

Multiply through by 8 to eliminate the fraction:

96C + 215 - 90C = 224

6C = 9

C = 9/6 = 1.5

Substitute the value of C back into Equation 5 to find S:

S = (43 - 18(1.5))/8 = 2.75

Therefore, the cost per pound of the cinnamon tea is $1.50, and the cost per pound of the spice tea is $2.75.

In summary, the cost per pound of the cinnamon tea is $1.50, and the cost per pound of the spice tea is $2.75.

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the answer is D

The figure can be divided into a rectangle and 2 triangles

Answer:

y = (-1/6)x represents a proportional relationship.

Answer: 102 dollars/4.5x+75

Step-by-step explanation: Your question isn't really straightforward, x x snacks for everybody to share? Please elaborate, and are they talking about the total cost, or just the cost of 6 snacks?

First, we have to take into account that if SADIE is taking her FOUR kids, there will be 5 people.

Cost of tickets is equal to $15 per one, and

5x (where x=15, per 5)

5(15)=75, and now onto the snacks

4.5x2=9, and 6/2=3, so 9x3=27, or 4.5x6=27

75+27=102

then for x snacks, if 1 snack costs 4.5 dollars than it'd be 4.5x (x number of snacks)+75 to find the total cost with tickets and all.

a.  The investment to double in value take about 14 years for the funding to double in value.

b.  The genuine time it will take for the funding to double in fee is about 13.86 years.

(a) To estimate the time it takes for an funding to double in cost the use of the rule of 70, we want to decide the increase rate. In this case, the increase price is given as 5% per 12 months compounded continuously.

Using the rule of 70, we can calculate the estimated doubling time:

Time to double ≈ 70 / boom rate

Time to double ≈ 70 / 5

Simplifying, we have:

Time to double ≈ 14 years

Therefore, it would take about 14 years for the funding to double in value.

(b) To decide the genuine time it will take for the funding to double in value, we can use the formulation for non-stop compounding:

Doubling time (exact) = ln(2) / (ln(1 + r))

where r is the increase fee as a decimal.

In this case, the increase charge is 5% per year, or 0.05 as a decimal.

Doubling time (exact) = ln(2) / (ln(1 + 0.05))

Doubling time (exact) ≈ 13.86 years (rounded to two decimal places)

Therefore, the genuine time it will take for the funding to double in fee is about 13.86 years.

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Answer:

1 1/8 of a mile.

Step-by-step explanation:

The distance around the track is one quarter of a mile. Therefore, if you run around the track 4 times, you will have ran 1 mile, as 4 * 1/4 = 1. You would also run the other 1/2 of the lap, and to find that distance, you would multiply 1/2 * 1/4, because you only ran 1/2 of a lap and not one whole lap, which would come out to 1/8 of a mile. So, your final answer would be 1 + 1/8 of a mile, which comes out to 1 and 1/8 of a mile.

Rounding the given value to the nearest tenth would be 1020.5

The tenth value is the first digit after the decimal point. Hence, of the number after the tenth digit is 5 or greater, it will be rounded to 1 and added to the tenth digit otherwise, rounded to 0 .

Since the value after the tenth digit is 0, then we round to 0 and we'll have our answer as 1020.5.

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Answer:

The area of the complex figure is approximately 210.92 square units.

Step-by-step explanation:

Let's calculate the area of the complex figure with the given information.

We can break the figure down into three components: an equilateral triangle, a right triangle, and a rectangle.

1. Equilateral Triangle:

The height of the equilateral triangle is given as 4.33 units. We can calculate the area using the formula:

Area of Equilateral Triangle = (base^2 * √3) / 4

In this case, the base of the equilateral triangle is also the length of side d, which is given as 13 units.

Area of Equilateral Triangle = (13^2 * √3) / 4

Area of Equilateral Triangle ≈ 42.42 square units

2. Right Triangle:

The right triangle has two sides with lengths a (5 units) and b (5 units), and its hypotenuse has a length of side c (also 5 units).

Area of Right Triangle = (base * height) / 2

In this case, both the base and height of the right triangle are the same and equal to a or b (5 units).

Area of Right Triangle = (5 * 5) / 2

Area of Right Triangle = 12.5 square units

3. Rectangle:

The rectangle has a length equal to side d (13 units) and a width equal to side e (12 units).

Area of Rectangle = length * width

Area of Rectangle = 13 * 12

Area of Rectangle = 156 square units

Now, to get the total area of the complex figure, we add the areas of each component:

Total Area = Area of Equilateral Triangle + Area of Right Triangle + Area of Rectangle

Total Area = 42.42 + 12.5 + 156

Total Area ≈ 210.92 square units

Therefore, the area of the complex figure is approximately 210.92 square units.

a.The Industry Average Salary is $55,680. b.The Firm A's Average Salary is $51,718.40 .c. Firm B's average salary is approximately 112.27% of Firm A's average salary.

a. To determine the industry average salary, we can use the information that the industry average salary is 96% of Firm B's average salary. Firm B's average salary is $58,000. Therefore, we can calculate the industry average salary as follows:

Industry Average Salary = 96% of Firm B's Average Salary

= 0.96 * $58,000

= $55,680

b. Firm A's average salary is stated as 93% of the industry average salary. To calculate Firm A's average salary, we can multiply the industry average salary by 93%:

Firm A's Average Salary = 93% of Industry Average Salary

= 0.93 * $55,680

= $51,718.40

c. To express Firm B's average salary as a percentage of Firm A's average salary, we can divide Firm B's average salary by Firm A's average salary and multiply by 100:

Percentage = (Firm B's Average Salary / Firm A's Average Salary) * 100

= ($58,000 / $51,718.40) * 100

≈ 112.27%

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Answer: 12

Step-by-step explanation:

Answer:

Therefore, the correct answer is: x < 23.

Step-by-step explanation:

To solve the inequality x - 5 + 2 < 20, we can simplify it step by step:

x - 5 + 2 < 20

Combine like terms:

x - 3 < 20

Add 3 to both sides of the inequality:

x - 3 + 3 < 20 + 3

Simplify:

x < 23

The solution to the inequality is x < 23.

Therefore, the correct answer is: x < 23.

Answer and Step-by-step explanation:

Please see the photo for the solution :)

Answer$535.50

Step-by-step explanation:

15% is equal to .15

So, multiply 600.00x .15=90

                   600.00 - 90.0=510.
                   510. 00x .05=25.50

                   510.00+25.50=535.50

                   Your answer is $535.5

Answer:

πr^2 h

π(11)^2 (15)

= 1815π or = 5701

(3a) The equation that can be used to determine the cost, C is C = 2.55 + 1.85x.

(3b) The cost of 3 miles taxi ride is $8.1.

(3a) The equation that can be used to determine the cost, C is calculated by applying the following equation as follows;

C = f + nx

where

C = 2.55 + 1.85x

(3b) The cost of 3 miles taxi ride is calculated as follows;

C = 2.55 + 1.85x

where;

C = 2.55 + 1.85 (3)

C = $8.1

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The Math Club raised $400.

To find out how much money the Math Club raised, we need to determine the percentage of the total amount raised that corresponds to the Math Club's portion.

Let's assume the Math Club raised "x" amount of money. The total amount raised by all five clubs is $2000.

According to the incomplete circle graph, the Math Club's percentage is missing, but we know the percentages for the other clubs: Computer Club raised 15%, Gardening Club raised 18%, Art Club raised 30%, and Spanish Club raised 17%.

To find the missing percentage for the Math Club, we subtract the percentages of the other clubs from 100%:

Missing percentage = 100% - (15% + 18% + 30% + 17%) = 100% - 80% = 20%

Now we can set up a proportion to determine the amount raised by the Math Club:

(x / $2000) = 20% / 100%

Cross-multiplying:

x = ($2000 * 20%) / 100%

Simplifying:

x = $400

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Answer:

-6 and 7.

Step-by-step explanation:

If we have a function called g, and we know that it has two factors: (x - 7) and (x + 6), then we can find the values of x that make g equal to zero. We call those values the "zeros" of the function g. To find the zeros, we just need to solve the equation (x - 7)(x + 6) = 0. The answer is that the zeros of g are -6 and 7.

After 300 trials, the experimental probabilities may not align perfectly with the theoretical probabilities. However, with more trials, the experimental probabilities tend to converge towards the theoretical probabilities for closer alignment.

To examine whether experimental probabilities after 300 trials align closely with theoretical probabilities, let's consider an example of flipping a fair coin.

Theoretical probability: When flipping a fair coin, the theoretical probability of obtaining heads or tails is 0.5 each. This assumes that the coin is unbiased and has an equal chance of landing on either side.

Experimental probability: After conducting 300 trials of flipping the coin, we record the outcomes and calculate the experimental probabilities. Let's assume that heads occurred 160 times and tails occurred 140 times.

Experimental probability of heads: 160/300 = 0.5333

Experimental probability of tails: 140/300 = 0.4667

Comparing the experimental probabilities to the theoretical probabilities, we can observe that the experimental probability of heads is slightly higher than the theoretical probability, while the experimental probability of tails is slightly lower.

In this particular example, the experimental probabilities after 300 trials do not align perfectly with the theoretical probabilities. However, it is important to note that these differences can be attributed to sampling variability, as the experimental outcomes are subject to random fluctuations.

To draw a more definitive conclusion about the alignment between experimental and theoretical probabilities, a larger number of trials would need to be conducted. As the number of trials increases, the experimental probabilities tend to converge towards the theoretical probabilities, providing a closer alignment between the two.

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The question probable may be:

Do experimental probabilities after 300 trials tend to align closely with theoretical probabilities? Consider an example scenario and calculate both the theoretical and experimental probabilities to determine if they are close.

The linear function for this case is:

f(x) = 5,000*x + 7,000

The general linear function is written as:

f(x) = a*x + b

Where a is the slope and b is the y-intercept.

Here we want a linear function for the given scenario, we know that the initial population is 7,000, then we can write:

f(x)= a*x + 7,000

Then we know that the population increases by 5,000 per year for 5 years, so the slope is 5,000, then we can write the function as:

f(x) = 5,000*x + 7,000

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Answer:

w(25) = 96

There are 96 wolves in the year 2020

Step-by-step explanation:

Given:

[tex]w(x)=14\cdot 1.08^{x}[/tex]

w(25) =

[tex]w(25)=14\cdot 1.08^{25}\\\\= 14 * (6.848)\\\\=95.872\\\\\approx 96[/tex]

Number of years : 1995 + 25 = 2020

In 2020, there are 96 wolves

Answer:

f(x)=5x

g(x)=1/x-5

f(g)=5(1/x-5)

f(x)=5/x- 25

therefore domain is x=0

The radius of the circle is 25 inches. The length of arc with a central angle of 138° is 115π/6 in

An equation is an expression that shows how numbers and variables are related to each other using mathematical operators.

The length of an arc with a central angle Ф with circle radius (r) is given by:

Length of arc = (Ф/360) * 2πr

Given the length of arc as 115π/6 in and angle of 138°, hence:

Length of arc = (Ф/360) * 2πr

Substituting:

115π/6 = (138/360) * 2πr

r = 25 inches

The radius of the circle is 25 inches.

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a. The distribution of X is X ~ N(68, 14).

b. The corresponding area to the right of 0.9286, which is approximately 0.1772.

c. The longest amount of time a patron can spend and still receive the discount is approximately 48.5654 minutes.

d. The Inter Quartile Range (IQR) for time spent at the hot springs is approximately 21.373 minutes.

a. The distribution of X is X ~ N(68, 14), where X represents the amount of time a person spends at Grover Hot Springs, 68 is the mean, and 14 is the standard deviation.

b. To find the probability that a randomly selected person stays longer than 81 minutes, we need to calculate the area under the normal curve to the right of 81.

Using the z-score formula: z = (x - μ) / σ, where x is the value (81), μ is the mean (68), and σ is the standard deviation (14).

Plugging in the values, we have z = (81 - 68) / 14 = 0.9286.

Using a standard normal distribution table or a calculator, we can find the corresponding area to the right of 0.9286, which is approximately 0.1772.

c. To find the longest amount of time a patron can spend at the hot springs and still receive the discount, we need to find the value that corresponds to the lowest 8% of the distribution.

Using a standard normal distribution table or a calculator, we can find the z-score that corresponds to the 8th percentile, which is approximately -1.4051.

Using the z-score formula, we can calculate the longest amount of time: x = μ + z [tex]\times[/tex] σ = 68 + (-1.4051) [tex]\times[/tex] 14 = 48.5654 minutes.

Therefore, the longest amount of time a patron can spend and still receive the discount is approximately 48.5654 minutes.

d. The Inter Quartile Range (IQR) is a measure of the spread of the data and represents the range between the first quartile (Q1) and the third quartile (Q3).

To find Q1 and Q3, we can use the z-score formula and the standard normal distribution table.

For Q1, we find the z-score corresponding to the 25th percentile, which is approximately -0.6745.

Using the formula Q1 = μ + z [tex]\times[/tex] σ, we have Q1 = 68 + (-0.6745) [tex]\times[/tex] 14 = 57.053.

Therefore, Q1 is approximately 57.053 minutes.

For Q3, we find the z-score corresponding to the 75th percentile, which is approximately 0.6745.

Using the formula Q3 = μ + z [tex]\times[/tex] σ, we have Q3 = 68 + (0.6745) [tex]\times[/tex] 14 = 78.426.

Therefore, Q3 is approximately 78.426 minutes.

Finally, we can calculate the IQR by subtracting Q1 from Q3: IQR = Q3 - Q1 = 78.426 - 57.053 = 21.373 minutes.

Therefore, the Inter Quartile Range (IQR) for time spent at the hot springs is approximately 21.373 minutes.

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Answer:

19, 14, 38

Step-by-step explanation:

Let x, y, and z be each number respectively:

[tex]x+y+z=71\\z=2x\\y=x-5\\\\x+y+z=71\\x+(x-5)+2x=71\\2x-5+2x=71\\4x-5=71\\4x=76\\x=19\\\\y=x-5\\y=19-5\\y=14\\\\z=2x\\z=2(19)\\z=38[/tex]

Therefore, the three numbers are 19, 14, and 38.

The statements that are true about the system of equations are: Options C, D, and E.

Let's analyze each statement and determine whether it is true or false for the given systems of equations:

System A

2x - 3y = 4

4x - y = 18

System B

3x - 4y = 5

y = 5x + 3

System C

2x - 3y = 4

12x - 3y = 54

A. All three systems have different solutions.

To determine if the systems have different solutions, we need to solve them. Solving system A gives the solution x = 5 and y = -6. Solving system B gives the solution x = -1 and y = -2. Solving system C gives the solution x = 5 and y = -6. Therefore, this statement is false because systems A and C have the same solution.

B. Systems B and C have the same solution.

As mentioned above, solving system B gives the solution x = -1 and y = -2. Solving system C gives the solution x = 5 and y = -6. Therefore, this statement is false because systems B and C have different solutions.

C. System C simplifies to 2x-3y=4 and 4x-y=18 by dividing the second equation by three.

To simplify system C, we can divide the second equation by 3, resulting in:

2x - 3y = 4

4x - y = 18

This is exactly the same as system A. Therefore, this statement is true.

D. Systems A and B have different solutions.

As mentioned earlier, solving system A gives the solution x = 5 and y = -6. Solving system B gives the solution x = -1 and y = -2. Therefore, this statement is true.

E. Systems A and C have the same solution.

As mentioned earlier, solving system A gives the solution x = 5 and y = -6. Solving system C gives the solution x = 5 and y = -6. Therefore, this statement is true.

In summary:

A. False

B. False

C. True

D. True

E. True

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Complete Question:

Select all the statements that are true for the following systems of equations.

System A

2x - 3y = 4

4x - y = 18

System B

3x - 4y = 5

y = 5x +3

System C

2x - 3y = 4

12x - 3y = 54

A. All three systems have different solutions.

B. Systems B and C have the same solution.

C. System C simplifies to 2x-3y=4 and 4x-y=18 by dividing the second equation by three.

D. Systems A and B have different solutions.

E. Systems A and C have the same solution.

The equation of the line parallel to the line passing through (1, -2) and (-4, 3) and passing through the point (-4, -5) is y = -x - 9 in slope-intercept form.

To find the equation of a line parallel to a given line, we need to determine the slope of the given line and then use it to construct the equation of the parallel line.

First, let's calculate the slope of the given line passing through points (1, -2) and (-4, 3). The slope, denoted as m, can be found using the slope formula:

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

Substituting the coordinates, we have:

m = (3 - (-2)) / (-4 - 1) = 5 / (-5) = -1

Now that we have the slope, we can use it to construct the equation of the parallel line.

We'll use the point-slope form of a linear equation, which is:

y - y1 = m(x - x1)

where (x1, y1) represents the coordinates of a point on the line.

We'll use the point (-4, -5) on the parallel line:

y - (-5) = -1(x - (-4))

y + 5 = -1(x + 4)

Simplifying further:

y + 5 = -x - 4

y = -x - 9

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Answer:

A scale is just another way of saying what we want to count by on our graph.

Step-by-step explanation:

A "scale" is just another way of saying what we want to count by on our graph. The scale is the range of values that are shown on the axis of a graph. It helps to determine the size and spacing of the intervals or ticks on the axis. The scale can be in different units, such as time, distance, weight, or any other measurable quantity depending on the type of data being represented in the graph.

Answer:

The answer is 2400 cm^3

Step-by-step explanation:

You just need to multiply the dimensions

Answer:

2400 cm³

Step-by-step explanation:

Volume of cuboid = length × width × height

Volume = 8 cm × 15 cm × 20 cm

Volume = 2400 cm³

So, the volume of the cuboid is 2400 cm³

y" = cos(y) * dy/dx - sin(x) + sin(y) by implicit differentiation.

To find the second derivative (y") by implicit differentiation, we will differentiate the equation with respect to x twice.

Equation: cos(y) + sin(x) = 1

Differentiating once with respect to x using the chain rule:

-sin(y) * dy/dx + cos(x) = 0

Now, differentiating again with respect to x:

Differentiating the first term:

-d/dx(sin(y)) * dy/dx - sin(y) * d^2y/dx^2

Differentiating the second term:

-d/dx(cos(x)) = -(-sin(x)) = sin(x)

The equation becomes:

-d/dx(sin(y)) * dy/dx - sin(y) * d^2y/dx^2 + sin(x) = 0

Now, let's isolate the second derivative, d^2y/dx^2:

-d^2y/dx^2 = d/dx(sin(y)) * dy/dx - sin(x) + sin(y)

Substituting the previously obtained expression for d/dx(sin(y)) = cos(y):

-d^2y/dx^2 = cos(y) * dy/dx - sin(x) + sin(y)

Thus, the second derivative (y") by the equation:

y" = cos(y) * dy/dx - sin(x) + sin(y)

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