The legs of a right triangle measure 39 and 80 units. What is the measure of the
hypotenuse? Answer as a number only.

Answer:

∠A=∠P, AC = PR

Step-by-step explanation:

Because triangles ABC and PQR are congruent their corresponding angles and sides are congruent.

So

∠A=∠P

∠B=∠Q

∠C=∠R

Also

Side AB = Side PQ

Side BC = Side QR

Side AC = Side PR

They should mix 16 pounds of City Roast Columbian coffee with 4 pounds of French Roast Columbian coffee to make their blend.

Let x be the number of pounds of City Roast Columbian coffee.

Let y be the number of pounds of French Roast Columbian coffee.

The total cost of the blend is 7.80x + 8.10y

The total weight is x + y = 20.

We can write an equation for the cost per pound:

(7.80x + 8.10y) / 20 = 7.86.

We will multiply both sides by 20 which gives:

7.80x + 8.10y = 157.20.

We can use this equation along with the total weight equation to solve for x and y:

x + y = 20

y = 20 - x (subtract x from both sides)

7.80x + 8.10(20 - x) = 157.20 (substitute y = 20 - x into the cost equation)

7.80x + 162 - 8.10x = 157.20 (distribute)

-0.30x = -4.80

x = 16

Solve for the equation (x + y = 20):

y = 20 - x

y = 20 - 16

y = 4.

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The function that models the total amount of money Julia has after x weeks is f(x) = 27x + 254

An equation is an expression that uses mathematical operations to show how numbers and variables are related to each other.

Let f(x) represent the total amount of money Julia has after x weeks.

Julia has $254 and saves $27 each week, hence:

f(x) = 27x + 254

The function is f(x) = 27x + 254

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If you use the normal distribution to estimate the probability that score exceeds 100, the answer would be zero.

This is because a normal distribution is a continuous probability distribution, and the probability of any individual score, no matter how high or low, is always zero.

However, this answer contradicts the assumption of a normal distribution for scores because it implies that scores cannot exceed 100, which is not true. Scores can theoretically range from negative infinity to positive infinity, and in practice, there may be some scores above 100, especially if the measurement instrument is imprecise or the test is very difficult.

Therefore, if we observe scores that are higher than 100, it suggests that the assumption of a normal distribution may not be appropriate for the data, and we may need to use a different distribution or statistical model to estimate probabilities or make inferences about the scores.

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Answer:the first one

Step-by-step explanation:

Answer:

x= 64/ 7

Step-by-step explanation:

3/8x - 6 = 1/2(4 - x)

3/8x - 6 = 2- 1/2 x

3/8x - 8 = - 4/8 x

so 7/8 x = 8

x = 64/7

Answer:

I'm guessing A

Step-by-step explanation:

175 is the only multiple of 5 so it has to be that also there's no option for zero

Required value of cosy is 12/13.

What is Complementary angle?

Two angles are said to be complementary if their addition is 90°.Let if one angle is x then the other angle will be 90° – x. Hence, we use these complementary angles for trigonometry ratios, where one ratio is complementary to another ratio by 90 degrees such as,

[tex]sin(x) = \cos(\frac{\pi}{2} - x) \\ \tan(x) = \cot(\frac{\pi}{2} - x) \\ \sec(x) = \csc(\frac{\pi}{2} - x) \\ \cos(x) = \sin(\frac{\pi}{2} - x) \\ \cot(x) = \tan(\frac{\pi}{2} - x) \\ \csc(x) = \sec(\frac{\pi}{2} - x)[/tex]

Given, here x and y are complementary.

So, we can say that

[tex]x + y = {90}^{o} \\ y = {90}^{o} - x[/tex]

So,

[tex] \sin( x) = \frac{12}{13} \\ \sin( {90}^{o} - y) = \frac{12}{13} \\ \cos(y) = \frac{12}{13} [/tex]

Therefore, required value of cosy is 12/13.

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Answer: Without additional information about the study and the definition of "high level of satisfaction," we cannot determine the probability that a randomly chosen customer did not have a high level of satisfaction with the company.

The probability would depend on the specific criteria used to define a high level of satisfaction, as well as the distribution of satisfaction levels among the customers in the study.

If we have access to this information, we could use it to calculate the probability that a randomly chosen customer did not have a high level of satisfaction using the appropriate formulas or statistical techniques.

Step-by-step explanation:

The true statements are:

A. The graph of function f(x) = -√(√(√x)) will look like the graph of f(x)=√x but will reflect it about the x-axis and shrink it vertically by a factor of 1/2.

D. f(x) = √x has the same domain but a different range as f(x) = -√x.

A graph is a visual representation of a mathematical relationship or data. It consists of points or vertices connected by edges or lines to show the relationship between them.

A function is a mathematical concept that relates an input value to an output value, such that for each input, there is exactly one output. It can be represented as a set of ordered pairs, a graph, or an equation.

According to the given information:

A. The statement A is true. The graph of function f(x) = -√(√(√x)) is a transformation of the function f(x) = √x. The negative sign outside the square roots will reflect the graph of f(x) = √x about the x-axis, and the multiple square roots will shrink the graph vertically by a factor of 1/2.

B. The statement B is false. The graph of function f(x) = -√(√x) is also a transformation of the function f(x) = √x, but it will only reflect the graph about the x-axis. It will not shrink the graph vertically.

C. The statement C is false. The graph of function |f(x)| = √(√(√x)) is not a transformation of f(x) = √x. The absolute value bars will make the graph symmetric about the y-axis, but it will not shrink it horizontally.

D. The statement is true. The graph of function f(x) = √x and f(x) = sqrt(x) are equivalent, and have the same domain (all non-negative real numbers) but different ranges. The range of f(x) = √x is [0, infinity) while the range of f(x) = sqrt(x) is (0, infinity).

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The amount of fabric that should be used to build a kite with the above given dimensions would be = 2,285.125cm²

To calculate the area of a kite the formula that should be used would be = 1/2 d1d2

where d1 = 50½cm

d2 = 90½cm

The area of the kite;

= 1/2 × 50.5×90.5b

= 4570.25/2

= 2,285.125cm²

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Answer:

(9,8)

Step-by-step explanation:

Solve the first equation

then solve the second equation with the substitute number from the first equation.  

The correct transformation is - "a is a stretch by a factor of 5, while h moves the graph to the left by 6, and k moves the graph up by 7".

A point, line, or geometric figure can be transformed in one of four ways, each of which affects the shape and/or location of the object. Pre-Image refers to the object's initial shape, and Image, after transformation, refers to the object's ultimate shape and location. Every point in a reflection is equally spaced from a fixed line

The line of symmetry is another name for this curve. The Image and Pre-Image share the same size in a reflection.

General form for the member of the reciprocal family:

y = a /(x - h) + k  ..eq 1

For the given function:

y = 5/(x + 6) + 7 ...eq 2

On comparing eq 1 and eq 2

a = 5

h = -6

k = 7

Now,

Thus, the correct transformation is - "a is a stretch factor of 5, while h moves the graph to the left by 6, and k moves the graph up by 7".

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The required equilibrium quantity is 80 units and equilibrium price is 5600 in monetary units for the supply function p = 70q and the demand function p= -q^2+12000.

The supply function of a commodity is given as, p= 70q

The demand function of the commodity is given as, p= -q^2+12000

We know at equilibrium condition of market,

Supply of a commodity is equal to its demand in the market.

Therefore,

70q = p = -q^2+12000

⇒ 70q = -q^2+12000

⇒ q^2+ 70q -12000 = 0

⇒ q^2+ 150q - 80q -12000 = 0

⇒ q( q + 150) - 80( q + 150) = 0

⇒ (q -80) ( q + 150) = 0

⇒q = 80 ad q = -150

We ignore the negative value of q, that is - 150 , as quantity of a commodity can not in negative.

Therefore, the equilibrium quantity of the commodity is 80 units.

Thus, p = 70(80) = 5600 (in monetary units)

Therefore, equilibrium price of the commodity is 5600 (in monetary units).

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Kalani deposited $200 into her checking account every week and $400 into her savings account every month.

A group of equations that must be solved simultaneously is referred to as a system of equations. Typically, a system of equations involves multiple variables, and the goal is to find the values of those variables that satisfy all of the equations in the system.

Let's start by using the given information to write equations for the total amount deposited in each account over the course of the year.

For the checking account, Kalani deposited x dollars every week for 52 weeks, so the total amount deposited for the year is:

52x

For the savings account, Kalani deposited y dollars every month for 12 months, so the total amount deposited for the year is:

12y

We are also told that each checking account deposit was half the amount of each savings account deposit, so we can write:

x = (1/2)y

Finally, we are given that the total of all deposits for the year was $15,200, so we can write:

52x + 12y = 15200

A system of two equations with two variables is now available:

x = (1/2)y

52x + 12y = 15200

We can solve this system to determine the values of x and y. The result of putting the first equation into the second equation is:

52(1/2)y + 12y = 15200

Simplifying:

26y + 12y = 15200

38y = 15200

y = 400

Substituting y = 400 into the first equation, we get:

x = (1/2)y = (1/2)(400) = 200

Therefore, Kalani deposited $200 into her checking account every week and $400 into her savings account every month.

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The electrician needs approximately 296.26 feet of wire.

The links between triangle's sides and angles are studied in the mathematic discipline known as trigonometry. It entails an examination of triangle's angles, lengths, and areas as well as their angles' mathematical properties (such as sine, cosine, and tangent).

The situation described can be modeled as a right triangle, where the wire from the electric box to the pole is the hypotenuse, and the angle of elevation is one of the acute angles. Let x be the length of the wire needed in feet.

Using trigonometry, we can write:

sin(17°) = opposite / hypotenuse

where the opposite side is the height of the connection on the pole above the ground. We can solve for the hypotenuse (the length of wire needed) as follows:

hypotenuse = opposite / sin(17°)

To find the opposite side, we can use the fact that the angle of elevation is 17° and the distance from the pole to the point on the ground directly beneath the connection is 85 feet. This distance is the adjacent side of the triangle, so we can write:

tan(17°) = opposite / 85

Solving for the opposite side, we get:

opposite = 85 tan(17°)

Substituting this into the formula for the hypotenuse, we get:

hypotenuse = (85 tan(17°)) / sin(17°)

hypotenuse ≈ 296.26 feet

Therefore, the electrician needs approximately 296.26 feet of wire.

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Line JN = line AE = 22ft

Line DC = Line LM = 17ft

Line KL = line BC = 12 ft

< D = <M = 158°

< K = <B = 135°

Two shapes are said to be congruent when they both have the same length size and same angle measurements.

From the given shapes, polygon ABCDE = JKLMN.

Therefore the corresponding angles and lengths is as follows:

Line JN = line AE = 22ft

Line DC = Line LM = 17ft

Line KL = line BC = 12 ft

< D = <M = 158°

< K = <B = 135°

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A shop is open 9 am - 7 pm. the function r(t), graphed above, gives the rate at which customers arrive (in people/hour) at time t, the line will vanish at 9 am + 2.5 hours = 11:30 am.

Since the salespeople can serve customers at a rate of 75 people per hour, the net rate at which customers are added to the line is given by:

Net rate = R(t) - 75

where R(t) is the rate at which customers arrive.

The line will vanish when the net rate becomes zero, which means that the rate at which customers are added to the line is equal to the rate at which they are served. Thus, we have:

R(t) - 75 = 0

Solving for t, we get:

R(t) = 75

Looking at the graph, we can see that R(t) is equal to 75 at approximately 2.5 hours after 9 am. Therefore, the line will vanish at 9 am + 2.5 hours = 11:30 am.

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The solutions to the system of equations f(x) = x² + x - 6 and g(x) = -2x² - 2x + 12 are (-3, 0) and (2, 0). So, correct option is 1.

To graph the functions f(x) and g(x) using a calculator, we can enter the equations into the calculator's graphing function and choose an appropriate window to display the graph. Once the graphs are displayed, we can look for the points of intersection to find the solution to the system of equations.

Using a graphing calculator, we can see that the graphs of f(x) and g(x) intersect at two points: (-3, 0) and (2, 0). These points represent the x-coordinates of the solutions to the system of equations.

To verify that these points are indeed the solutions, we can substitute each of them into both equations and check that they satisfy both equations simultaneously.

For point (-3, 0):

f(-3) = (-3)² + (-3) - 6 = 0

g(-3) = -2(-3)² - 2(-3) + 12 = 0

Therefore, (-3, 0) is a solution to the system of equations.

For point (2, 0):

f(2) = 2² + 2 - 6 = 0

g(2) = -2(2)² - 2(2) + 12 = 0

Therefore, (2, 0) is also a solution to the system of equations.

The point (0, -6) and (0, 12) are not the points of intersection and (-6, 12) is not a solution to the system of equations.

Therefore, the answer is option 1.

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Answer:

81

Step-by-step explanation:

for the volume you just multiple length, height, and depth

Answer: 81.

Step-by-step explanation:

9 x 3 x 3 . LxWxH  brother!

The Unit-Price for first-bag is $1.72/kg and for second-bag is $1.86/kg, then the first-bag is cheaper compared to the second-bag with a unit-price.

The "Unit-Price" refers to the cost of dog food per kilogram. It is calculated by dividing the "total-cost" of the bag of dog-food by its weight in kilograms.

⇒ For the first bag of dog food:

The Cost is = $10.47,

The Weight is = 6.08 kg,

So, the Unit-Price is = Cost/Weight = $10.47/6.08 kg ≈ $1.72/kg,

⇒ For the second bag of dog food:

The Cost is = $13.88,

The Weight is = 7.48 kg,

So, the Unit Price will be = Cost/Weight = $13.88/7.48 kg ≈ $1.86/kg,

Based on the "unit-prices" calculated, the first bag of dog food has a unit price of $1.72 per kilogram, and the second bag has a unit price of $1.86 per kilogram.

Therefore, the first bag of dog food is the better-buy as it is cheaper compared to the second bag.

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The given question is incomplete, the complete question is

Justin paid $10.47 for a 6.08-Kg bag of dog food.  A few weeks later, he paid $13.88 for a 7.48-kg bag at a different store. Find the unit price for each bag. Then state which bag is the better buy based on the unit price.

The solution for the equation -x² + 2x + x - 3x = -9 + 2 + 6 is derived to be x = 1

We shall solve for x by simplifying the equation and making x the subject as follows:

-x² + 2x + x - 3x = -9 + 2 + 6

-x² + 3x - 3x = 8 - 9

-x² = -1

multiply both sides by -1 we have;

x² = 1

take square root of both sides

x = √1

x = 1

Therefore, the equation -x² + 2x + x - 3x = -9 + 2 + 6 will have a solution for the value of x = 1

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Answer:

22

i took this one

Answer:

17.5

Step-by-step explanation:

94 divided by 4 is 23.5 and I subtracted 6 from 23.5

As a result, they would pay: 5/6 x $36 = $30 as Kendie's family would shell out 1/6 less than the standard admission price.

In mathematics, the linear approach is a way when resolving issues with direct or negative proportion. It entails figuring out the value of one unit of a quantity and utilising that value to figure out the value of any given quantity divided by that number of units. For instance, using the unitary technique, if we know that 5 oranges cost $10, we may calculate the price of 10 apples by first dividing $5 by 5 to get $2 per apple, multiplying $two by 10 to get $20 for 10 apples, and then using the result to get the price of 5 apples. In industries where proportional correlations are regularly found, like banking, business, and science, the unitary technique is frequently employed.

given

On Sunday, Kendie's family would shell out 1/6 less than the standard admission price, or 5/6 of the standard admission price.

As a result, they would pay: 5/6 x $36 = $30 as Kendie's family would shell out 1/6 less than the standard admission price.

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Answer: tan 47/1 = x/.5 = x = .53618

Step-by-step explanation:

Answer:

∠ ABC = 90°

Step-by-step explanation:

∠ ABC is the angle on the circle subtended by the diameter AC

it is the angle in a semicircle and is 90°

To find a reasonable estimate for the total time of the album, we can add the times of the shortest and longest songs and divide by 2 to find the average time per song, and then multiply by the total number of songs on the album.

The shortest song on the album is 1 minute and 14 seconds, which is equivalent to 74 seconds.

The longest song on the album is 5 minutes and 54 seconds, which is equivalent to 354 seconds.

Therefore, the average time per song is:

(74 + 354) / 2 = 214 seconds

And the total time of the album is approximately:

13 songs x 214 seconds/song = 2,782 seconds

Converting this to minutes and seconds, we get:

2,782 seconds = 46 minutes and 22 seconds

So a reasonable estimate for the total time of the album is about 46 minutes and 22 seconds.

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using trignometric ratio of sine thee measure of the angle x to the nearest degree is 28 degrees

Trigonometric ratios are ratios of the sides of a right triangle, such as sine, cosine, and tangent, that are used to find missing side lengths or angles.

An angle is a geometric figure formed by two rays or line segments that share a common endpoint, known as the vertex. It is typically measured in degrees or radians.

According the given information:

We can use the trigonometric ratio of sine to find the measure of the angle x.

sin(x) = opposite/hypotenuse

In this case, the opposite side is the height of the triangle, which is 13, and the hypotenuse is the length of the diagonal line connecting the base and the top of the triangle. We can use the Pythagorean theorem to find the length of the hypotenuse.

hypotenuse² = base² + height²

hypotenuse² = 22² + 13²

hypotenuse² = 769

hypotenuse ≈ 27.73

Now we can substitute the values into the sine ratio:

sin(x) = 13/27.73

x ≈ 28 degrees

Therefore, the measure of the angle x to the nearest degree is 28 degrees.

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