find the exact value of z.

Answer:

48 adult tickets were sold.

Step-by-step explanation:

Let's use algebra to solve this problem:

Let's define:

From the problem statement, we know:

We can use the first equation to solve for x in terms of y:

x = 320 - y

Substituting this expression for x into the second equation, we get:

3(320 - y) + 8y = 1200

Expanding the left side, we get:

960 - 3y + 8y = 1200

Simplifying, we get:

5y = 240

Solving for y, we get:

y = 48

Therefore, 48 adult tickets were sold.

Additional:

To find the number of student tickets sold, we can substitute y=48 into the first equation:

x + 48 = 320

x = 272

Therefore, 272 student tickets were sold.

An exponential function in terms of x is [tex]P(x) = 140,000(1.05)^x[/tex]

The population would be 291049.95 after 15 years.

In Mathematics, a population that increases at a specific period of time represent an exponential growth. This ultimately implies that, a mathematical model for any population that increases by r percent per unit of time is an exponential function of this form:

[tex]P(x) = I(1 + r)^x[/tex]

Where:

By substituting given parameters, we have the following:

[tex]P(x) = 140,000(1 + 0.05)^x\\\\P(x) = 140,000(1.05)^x[/tex]

After 15 years, we have:

[tex]P(15) = 140,000(1.05)^{15}[/tex]

P(15) = 291049.95 units.

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The interest accrued after one month at a rate of 15.5% on a principal amount of $1,000 is $12.92.

To use the formula I=Prt to calculate the interest accrued after one month at a rate of 15.5%, we need to know the principal amount (P) and the time period (t) in years.

Assuming that the principal amount is $1,000, and the time period is one month, which is equivalent to 1/12 of a year, we can calculate the interest as follows:

[tex]I = Prt[/tex]

[tex]I[/tex] [tex]= 1000 x 0.155 x (1/12)[/tex]

[tex]I = $12.92[/tex]

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Answer:

C. The distributive property

A set of data points could be modeled by a decreasing linear function include the following: C. {(0, 50), (1, 42), (2, 33), (3, 25), (4, 16)}.

In Mathematics, a linear function is a type of function whose equation is graphically represented by a straight line on the cartesian coordinate.

For any given function, y = f(x), if the output value (range or y-value) is decreasing when the input value (domain or x-value) is increased, then, the function is generally referred to as a decreasing function.

By critically observing the set of data points, we can reasonably infer and logically deduce that it set C is decreasing as follows 50, 42, 33, 25, 16.

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The value of the test statistic z is approximately -2.12. The Option D is correct.

To test the hypothesis that the mean wrist breadth of men is equal to 9 cm, we will use a one-sample z-test.

The null hypothesis is: H0: µ = 9 cm

The alternative hypothesis is: Ha: µ ≠ 9 cm

We are given a sample of n = 72 men with a sample mean of x = 8.91 cm and a population standard deviation = 0.36 cm.

The test statistic for a one-sample z-test is given by: z = (x - µ) / (o / sqrt(n))

Substituting the given values, we get:

= (8.91 - 9) / (0.36 / sqrt(72))

z = -2.119

At a significance level of a = 0.01, the critical values for a two-tailed test are ±2.576.

Since our test statistic (-2.119) falls outside of this range, we reject the null hypothesis and conclude that there is sufficient evidence to suggest that the mean wrist breadth of men is not equal to 9 cm.

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a. The initial height of the bouncing ball is 15 feet.

b. The percent rate of change is 85%.

c. The height of the bouncing ball after 5 seconds is approximately 6.79 feet (rounded to the nearest hundredth).

In mathematics, a function is a rule that assigns each element in a set (the domain) to a unique element in another set (the range). The domain and range can be any sets, but they are typically sets of real numbers.

The function f(x) = 15 (0.85)ˣ models the height, in feet, of a bouncing ball after x seconds.

a. The initial height of the bouncing ball is given by f(0). Plugging in x = 0, we get:

f(0) = 15*1

f(0) = 15(1)

f(0) = 15

Therefore, the initial height of the bouncing ball is 15 feet.

b. The percent rate of change is given by the coefficient of the base, which is 0.85 in this case. To convert this decimal to a percentage, we can multiply by 100:

0.85 × 100 = 85

Therefore, the percent rate of change is 85%.

c. The height of the bouncing ball after 5 seconds is given by f(5). Plugging in x = 5, we get:

f(5) = 15

f(5) ≈ 6.79

Therefore, the height of the bouncing ball after 5 seconds is approximately 6.79 feet (rounded to the nearest hundredth).

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1) If Amy deposits $2,300 in an account that pays 8.5% interest, after 4 years, the future value will be $3,187.48.

2) If Andres deposits $10,000 in an account that pays 8% interest, after 4 years, the future value will be A. $13,604.89.

3) If Kara deposits $500 in an account that pays 5% interest, after 2 years, the future value will be C. $551.25.

The future values represent the present investment compounded at an interest rate.

The future values can be determined using an online finance calculator as follows:

1) N (# of periods) = 4 years

I/Y (Interest per year) = =8.5%

PV (Present Value) = $2,300

PMT (Periodic Payment) = $0

Results:

Future Value (FV) = $3,187.48

Total Interest = $887.48

2) N (# of periods) = 4 years

I/Y (Interest per year) = =8%

PV (Present Value) = $10,000

PMT (Periodic Payment) = $0

Results:

Future Value (FV) = $13,604.89

Total Interest = $3,604.89

3) N (# of periods) = 2 years

I/Y (Interest per year) = 5%

PV (Present Value) = $500

PMT (Periodic Payment) = $0

Results:

Future Value (FV) = $551.25

Total Interest = $51.25

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The expression 0.85(1.4s) represents the final selling price of the jacket after two price changes: an initial 15% decrease in price, followed by another 15% decrease in price.

The expression 0.85(1.4s) represents the final selling price of the jacket after two price changes. We can break it down into its constituent parts to understand what happened to the price.

Factor 1.4s represents the original selling price of the jacket. This means that the store owner started with a price of 1.4s dollars.

The factor 0.85 represents the first price change. When the store owner lowered the price by 15%, the new price became 0.85 times the original price.

The second factor of 0.85 represents the second price change. After the first price change, the new price was 0.85(1.4s) dollars. When the store owner lowered the price again by 15%, the final selling price became 0.85 times the price after the first price change.

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The probability of a bulb lasting for at most 624 hours is 0.9861, rounded to four decimal places.

The standard deviation of the lifetime is a measure of how spread out the lifetimes are. In other words, it tells us how much the lifetimes of bulbs vary from the mean. In this case, the standard deviation of the lifetime is 20 hours.

Now, let's get to the question at hand. We want to find the probability of a bulb lasting for at most 624 hours. To do this, we need to use the properties of the normal distribution.

First, we need to calculate the z-score, which tells us how many standard deviations a value is from the mean. We can use the formula z = (x - mu) / sigma, where x is the value we are interested in, mu is the mean, and sigma is the standard deviation. In this case, x = 624, mu = 580, and sigma = 20.

Plugging these values into the formula, we get z = (624 - 580) / 20 = 2.2.

Next, we need to find the probability of a bulb lasting for at most 624 hours, which is the same as finding the area under the normal curve to the left of z = 2.2. We can use a standard normal distribution table or a calculator to find this probability.

Using a calculator, we can use the normal cdf function with the values -9999 (a very large negative number) and 2.2 to find the probability. This gives us a probability of 0.9861.

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The problem involves finding the radius of a cylindrical can that will minimize the cost of the metal to make the can, given that the can must hold one liter of oil.

Specifically, we need to find the radius of the can that will minimize the surface area, and hence the cost, of the metal required to make the can.

To solve the problem, we need to first write an expression for the surface area of the can in terms of its radius, and then differentiate this expression with respect to the radius to find the critical point. We then need to check that the critical point corresponds to a minimum value of the surface area, which will give us the optimal radius for the can. Optimization problems like this one are used in many fields, including engineering, economics, and physics, to find the best course of action given certain constraints and objectives.

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Answer:

Step-by-step explanation: Solution:

Total cost: 150
150-30=120
120 divided by  5   = 24
They visited 24 times in a month.

To move triangle KLM so that point K lies on the Y-axis, you need to apply a translation that shifts the entire triangle horizontally. By translating triangle KLM using the vector (-4, 0), point K now lies on the Y-axis.

To move the triangle so that point K lies on the Y axis, we need to perform a translation. First, we need to determine how far point K is from the Y axis. We can do this by finding the x-coordinate of point K, which is 4. This means that point K is 4 units away from the Y axis.

Next, we need to determine the direction of the translation. Since we want to move point K onto the Y axis, we need to move the triangle in the negative x direction. Therefore, the translation that will move the triangle so that point K lies on the Y axis is a horizontal translation of -4 units. We can express this translation as follows:

T(-4, 0)

This means that we need to move each point of the triangle 4 units to the left (negative x direction) to achieve the desired position of point K on the Y axis.

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Answer:

(2,-4)

Step-by-step explanation:

In order to solve by elimination, coefficients of one of the variables must be the same in both equations so that the variable will cancel out when one equation is subtracted from the other.

2x+3y=−8,3x+y=2

To make 2x and 3x equal, multiply all terms on each side of the first equation by 3 and all terms on each side of the second by 2. Then simplify

6x+9y=−24,6x+2y=4

Add 6x to −6x. Terms 6x and −6x cancel out, leaving an equation with only one variable that can be solved, add 9y to −2y, add −24 to −4, and divide both sides by 7.

y=−4

Substitute −4 for y in 3x+y=2. Because the resulting equation contains only one variable, you can solve for x directly. Add 4 to both sides of the equation and divide both sides by 3.

x=2

If Kayla can pay off up to $175 monthly for the purchase of a new television for $487.89, the interest she will pay at 23.5% compounded monthly is D. $18.87.

The compound interest payable on the credit card for the purchase of a new television can be computed using an online finance calculator as follows:

N (# of periods) = 3 months

I/Y (Interest per year) = 23.5%

PV (Present Value) = $487.89

PMT (Periodic Payment) = $-175

Results:

FV = $18.23

Sum of all periodic payments = $525.00

Total Interest = $18.87

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The maximum height of the arrow is 105 feet. To find the maximum height of the arrow, we need to determine the vertex of the quadratic function h = -16[tex]t^{2}[/tex] + 80t + 25.

The vertex is the highest point on the graph of the function, which represents the maximum height of the arrow.

To find the t-value at the vertex, we use the formula t = -b/2a, where a = -16 and b = 80. Plugging these values into the formula gives us t = -80/(2(-16)) = 2.5 seconds.

To find the maximum height, we plug t = 2.5 into the equation to get h = -16[tex](2.5)^{2}[/tex] + 80(2.5) + 25 = 105 feet. Therefore, the maximum height of the arrow is 105 feet.

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There are several steps a consumer market can take to become more knowledgeable like research and asking questions.

Research The first step is to  probe the product or service that you're interested in. This involves looking at reviews, product descriptions, and comparing prices. You can also look for information from  dependable sources  similar as consumer reports or government websites.   Ask questions If you have any  dubieties or  enterprises, don't  vacillate to ask the  dealer or service provider.

Ask them about their experience and qualifications, and make sure to clarify any terms or conditions that are unclear.   Get a alternate opinion If you're  doubtful about a product or service, seek the advice of someone you trust or who has  moxie in that area. They can help you make an informed decision grounded on their knowledge and experience.

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The minimum surface area of fabric needed for the sleeve is approximately 628.32 cm².

Based on the given model arm, a right circular cylinder would best represent the model for the sleeve.

To calculate the minimum surface area of fabric needed for the sleeve, we need to find the lateral surface area of the right circular cylinder.

The lateral surface area of a right circular cylinder is given by the formula:

Lateral surface area = 2πrh

where r is the radius of the cylinder, h is the height of the cylinder.

In this case, the height of the cylinder needs to be 20 cm (to cover the distance from the shoulder to the elbow), and the radius can vary depending on the desired fit. Let's assume a radius of 5 cm for the purposes of this calculation.

Plugging in the values, we get:

Lateral surface area = 2π(5 cm)(20 cm)

= 628.32 cm²

Therefore, the minimum surface area of fabric needed for the sleeve is approximately 628.32 cm².

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As a result, the angle formed by Luis's backpack and the ground is roughly 53 degrees (rounded to the nearest degree).

A function in mathematics is a relationship between a set of potential outputs and a number of potential inputs, with the feature that each input is associated to only one possible output. It is a principle or set of guidelines that allots a different output value towards each input value. Equations, graphs, and tables are frequently used to depict functions in order to explain how the output changes as the input does. They are employed to express relationships between various quantities, such as the length of time it takes for an automobile to drive a certain distance or the height of an object in relation to its weight. The concept of a function is crucial to many departments of science and math, and it is widely applied in areas like engineering,

given

We can use trigonometry to determine the angle that Luis's backpack creates with the ground.

Consider the backpack's handle to represent the hypotenuse of a right triangle, with the vertical leg being Luis's hand's distance from the ground (3 feet) and the horizontal leg being the backpack's height (3.5 feet).

The angle can be determined using the inverse tangent function (tan-1):

53.13 degrees at tan-1(3.5/3)

As a result, the angle formed by Luis's backpack and the ground is roughly 53 degrees (rounded to the nearest degree).

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The training program with the least rate of change is Rachel's, with an increase of 3 minutes per day.

Rachel:
Starting minutes: 30
Increase in rate: 3 minutes per day
Equation: f(x) = 3x + 30

Nicole:
Starting minutes: 30 (since f(0) = 5(0) + 30 = 30)
Increase in rate: 5 minutes per day
Equation: f(x) = 5x + 30

To find the training program with the least rate of change, we need to find the derivative of each equation and set it equal to zero:

f'(x) = 3 for Rachel's equation
f'(x) = 5 for Nicole's equation

Since 3 is less than 5, Rachel's training program has the least rate of change. Therefore, the rate of change in minutes per day for Rachel's training program that has the least rate of change is 3 minutes per day.

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In this scenario, the dependent variable is "how many jumps I can do," while the independent variable is "how long I am jumping (2 minutes)."

The relationship between these variables can be described as follows: The number of jumps completed depends on the duration of time spent jumping, with a specific focus on a 2-minute interval.

When we say the dependent variable is "how many jumps I can do," it means that the number of jumps completed is determined by or depends on the independent variable, which is the duration of time spent jumping.

This suggests that as the duration of time increases or decreases, it will likely have an impact on the number of jumps performed.

In this particular case, you have specified a 2-minute interval as the focus. It suggests that you are examining the relationship between the number of jumps completed and the specific duration of 2 minutes.

This implies that you are interested in understanding how the number of jumps varies within this fixed time frame.

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A store has 25 VCRs in stock, but 2 of these are defective he answer is the probability that the second person to buy a VCR gets a defective one and the first customer's VCR was not defective is .077.

The probability that the first customer's VCR is not defective is 23/25, as there are 23 working VCRs out of the total 25.

Since one VCR has already been sold, there are 24 VCRs left and 1 defective VCR. Thus, the probability that the second customer gets a defective VCR is 1/24.

To find the probability that both events occur, we multiply the individual probabilities:

P = (23/25) x (1/24)

P = 0.077 or 0.0778 when rounded to the nearest thousandth.

Therefore, A store has 25 VCRs in stock, but 2 of these are defective he answer is the probability that the second person to buy a VCR gets a defective one and the first customer's VCR was not defective is .077.

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The measure of each labeled angles in the rhombus are  ∠1 = 49°, ∠2 = 90°, ∠3 = 49° and ∠4 = 41°

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

The rhombus

By corresponding angles, we have

∠3 = 49°

∠1 = 49°

The diagonals of a rhombus bisect each other at right angles

So, we have

∠2 = 90°

Ths sum fo angles in a triangle is 180

So, we have

∠4 = 180 - 90 - 49°

Evaluate

∠4 = 41°

Hence, the measure of the angles in the rhombus are  ∠1 = 49°, ∠2 = 90°, ∠3 = 49° and ∠4 = 41°

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Answer:

50, positive

Step-by-step explanation:

(-5) * (-10) = 50

When a negative multiplies by another negative, the answer is positive

So, the answer is 50 and the sign is positive

Answer:

60

Step-by-step explanation:

((sum of frequency of even numbers)/(total number of tries))(150)

If Sam needs 2/5 pound turkey to make one sandwich, then to make 7 sandwiches, he will need:

(2/5) x 7 = (2 x 7)/5 = 14/5 = 2.8 pounds of turkey

Therefore, Sam needs 2.8 pounds of turkey to make 7 sandwiches.

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The area of sector is 14π/3 square inches for a circle having a radius of 7 inches and measures an angle of 4π/15 radians.

Radius of circle =  7 inches

Angle of circle =  4π/15 radians

The area of a sector of a circle can be calculated by using the formula:

A = (θ/2) × [tex]r^2[/tex]

A =  The area of the sector

θ = central angle in radians

r = radius of the circle.

Substituting the given values in the formula:

Area = (θ/2) × [tex]r^2[/tex]

Area = (4π/15 × 1/2) × [tex]7^2[/tex]

Area= (2π/15) × 49

Area = 14π/3

Therefore, we can conclude that the area of the sector is 14π/3 square inches.

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Answer:

25%

Step-by-step explanation:

The total number of 7th grade students = 9 + 11 + 11 + 13 = 44

Out of the 44 students 11 play bass

Probability that a seventh grader chosen at random will play the base is:

11/44 = 1/4 = 0.25

As a percentage, this would be 0.25 x 100 = 25%