Find the value of x in a triangle . If the hypotenuse of the triangle is 10 , the opposite is x+2 and the adjacent is x.​

Answer:

Rational, Real

Hope this helps!

The performance of a thermocouple is displayed in the scatterplot is

Explanatory variable: Temperature

Response variable: Voltage

Given that,

The performance of a thermocouple is displayed in the scatterplot below.

We have to find which of the following choices accurately identifies the explanatory and response variables for the scatterplot.

We know that,

Dots are used to indicate the values for two different numerical variables in a scatter plot (also known as a scatter chart or scatter graph). The positions of each dot on the horizontal and vertical axes represent the values of a single data point. To see how different variables relate to one another, utilize scatter plots.

Explanatory variable: Temperature

Response variable: Voltage

So, we can see the scatterplot in the picture.

Therefore, Explanatory variable: Temperature

Response variable: Voltage when the performance of a thermocouple is displayed in the scatterplot

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Answer:

Explanatory variable: Temperature

Response variable: Voltage

Step-by-step explanation:

Got it right on the test.

Answer:

THE COMMENT IS CORRECT

Step-by-step explanation:

Thanks, man.

Answer:

Use the given information to complete the sentences.

The constant of the polynomial expression represents the

daily earnings of the amusement park before any $2 increases

in the price of a ticket.

The binomial is a factor of the polynomial expression and represents the

number of tickets sold after x increases of $2

in the price of a ticket.

Step-by-step explanation:

Answer:

tan N = 0.73

Step-by-step explanation:

\(ML^{2}\) = \(\sqrt{77}^{2}\\\) - \(6^{2}\)  = 41

\(ML^{2}\) = 77 - 36  = 41

ML = \(\sqrt{41}\)

tan N = opp/adj

tan N = \(\sqrt{41}\) /  \(\sqrt{77}\)

tan N = 0.729703729240527

Rounded

tan N = 0.73

Part A: The reasonable domain for the growth function is d ≥ 0, allowing for positive days and future growth.

Part B: The y-intercept is 7, indicating the initial radius of the algae when the study began.

Part C: The average rate of change from d = 4 to d = 11 is approximately 0.55 mm/day, representing the daily increase in radius during that period.

Part A: To determine a reasonable domain to plot the growth function, we need to consider the context of the problem. The biologist's equation for the radius of the algae is given by f(d) = 7(1.06)^d, where d represents the number of days.

Since time (d) cannot be negative or non-existent, the domain for the growth function should be restricted to positive values.

Additionally, we can assume that the growth function is applicable within a reasonable range of days that align with the biologist's study. It's important to note that the given equation does not impose any upper limit on the number of days.

Based on the information given, a reasonable domain for the growth function would be d ≥ 0, meaning the number of days should be greater than or equal to zero.

This allows us to include the starting point of the study and extends the domain indefinitely into the future, accommodating any potential growth beyond the conclusion of the study.

Part B: The y-intercept of a function represents the value of the dependent variable (in this case, the radius of the algae) when the independent variable (days, d) is zero. In the given equation, f(d) = 7(1.06)^d, when d = 0, the equation becomes:

f(0) = 7(1.06)^0

f(0) = 7(1)

f(0) = 7

Therefore, the y-intercept of the graph of the function f(d) is 7. In the context of the problem, this means that when the biologist started her study (at d = 0), the radius of the algae was approximately 7 mm.

Part C: To calculate the average rate of change of the function f(d) from d = 4 to d = 11, we need to find the slope of the line connecting the two points on the graph.

Let's evaluate the function at d = 4 and d = 11:

f(4) = 7(1.06)^4

f(4) ≈ 7(1.26)

f(4) ≈ 8.82 mm

f(11) = 7(1.06)^11

f(11) ≈ 7(1.81)

f(11) ≈ 12.67 mm

The average rate of change (slope) between these two points is given by the difference in y-values divided by the difference in x-values:

Average rate of change = (change in y) / (change in x)

= (12.67 - 8.82) / (11 - 4)

= 3.85 / 7

≈ 0.55 mm/day

The average rate of change of the function f(d) from d = 4 to d = 11 is approximately 0.55 mm/day. This represents the average daily increase in the radius of the algae during the period from day 4 to day 11.

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We square the residuals when using the least-squares line method to find the line of best fit because we believe that huge negative residuals (i.e., points well below the line) are just as harmful as large positive residuals (i.e., points that are high above the line).

We treat both positive and negative disparities equally by squaring the residual values.  We cannot discover a single straight line that concurrently minimizes all residuals. The average (squared) residual value is instead minimized.

We might also take the absolute values of the residuals rather than squaring them. Positive disparities are viewed as just as harmful as negative ones under both strategies.

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Answer:

5/12

Step-by-step explanation:

I used a calculator

89.086 milliliters of juice will be in a glass with 7 ice cubes.

A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.

Variables are the name given to these symbols because they lack set values.

In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.

Given:

Equation of line: y = -29 202x + 293.5.

So, for 7 ice cubes i.e., x= 7

The amount of juice is

y= -29.202 (7)+ 293.5

y= -204.414+ 293.5

y= 89.086

Hence, the juice is 89.086 milliliters

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Answer:

y=-2/3-2

Step-by-step explanation:

The closest point on the sphere x^2 + y^2 + z^2 = 4 to the point (3, 1, -1) is (-0.46, 1.38, -1.38), and the farthest point is (1.85, -0.55, 0.55).

To find the points on the sphere that are closest and farthest from the given point, we need to minimize and maximize the distance between the points on the sphere and the given point. The distance between two points (x1, y1, z1) and (x2, y2, z2) can be calculated using the distance formula: √((x2-x1)^2 + (y2-y1)^2 + (z2-z1)^2).

To find the closest point, we want to minimize the distance between the point (3, 1, -1) and any point on the sphere x^2 + y^2 + z^2 = 4. This is equivalent to minimizing the squared distance, which is given by the equation (x-3)^2 + (y-1)^2 + (z+1)^2.

To minimize this equation subject to the constraint x^2 + y^2 + z^2 = 4, we can use Lagrange multipliers. Solving the equations, we find that the closest point is approximately (-0.46, 1.38, -1.38).

To find the farthest point, we want to maximize the distance between the point (3, 1, -1) and any point on the sphere. This is equivalent to maximizing the squared distance (x-3)^2 + (y-1)^2 + (z+1)^2 subject to the constraint x^2 + y^2 + z^2 = 4.

Using Lagrange multipliers, we find that the farthest point is approximately (1.85, -0.55, 0.55). These points represent the closest and farthest points on the sphere x^2 + y^2 + z^2 = 4 to the given point (3, 1, -1).

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The 90% confidence interval for the difference in the population means is -2.51 to 0.31

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

xˉ₁ = −17.1

s₁² = 8.4

n₁ = 22

​xˉ₂ = −16.0

s₂² = 8.7

n₂ = 24

Calculate the pooled variance using

P = (df₁ * s₁² + df₂ * s₂²)/df

Where

df₁ = 22 - 1 = 21

df₂ = 24 - 1 = 23

df = 22 + 24 - 2 = 44

So, we have

P = (21 * 8.4 + 23 * 8.7)/44

P = 8.56

Also, we have the standard error to be

SE = √(P/n₁ + P/n₂)

So, we have

SE = √(8.56/22 + 8.56/24)

SE = 0.86

The z score at 90% CI is 1.645, and the CI is calculated as

CI =  (x₁ - x₂) ± z * SE

So, we have

CI = (-17.1 + 16.0) ± 1.645 * 0.86

This gives

CI = -1.1 ± 1.41

Expand and evaluate

CI = (-2.51, 0.31)

Hence, the confidence interval is -2.51 to 0.31

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If utility function is given then we set up U(45) = p2 * U(-20) + (1 - p2) * U(110) and solve for p2.

(a) To find the probabilities p1 and p2, we set up the equation U(45) = p1 * U(20) + (1 - p1) * U(150) and solve for p1. Similarly, we set up U(45) = p2 * U(-20) + (1 - p2) * U(110) and solve for p2.

(b) The selling price of a lottery is the amount at which an individual is willing to sell the lottery. We compare the expected utility of the lottery to the utility of the certain amount. The risk premium is the difference between the selling price and the expected value of the lottery.

(c) The buying price is the amount an individual is willing to pay for a lottery. We set up the equation U(45) = p * U(150) + (1 - p) * U(45) and solve for p to find the buying price.

Note: The specific calculations for parts (a), (b), and (c) require the values of U(X) for each corresponding X value in the utility function.

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If your friend went to bed at 1:00am on Friday and woke up at 1:00pm on Friday, she slept for 12 hours.

To see why, you can count the number of hours between 1:00am and 1:00pm:

1:00am to 2:00am = 1 hour

2:00am to 3:00am = 1 hour

...

11:00am to 12:00pm = 1 hour

12:00pm to 1:00pm = 1 hour

The total number of hours between 1:00am and 1:00pm is 12 hours.

Answer:

C) 324 cm^3

Step-by-step explanation:

So you know the volume and 2 side lengths. 360 divided by 12 divided by 5 to find the third side. The third side is 360 / 60 (answer of 12x5), which is 6. Surface area of prism is 324 (c)

The value of ∠WXY = 20.

What is Exterior angle theorem?

The exterior angle theorem describes the connection between the two remote angles in a triangle and the external angle created by an extended side outside the triangle.

Given: Measure of angle YWX = (3x + 17) °

Measure of angle WXY = (3x + 2) °

Measure of angle XYZ = (10x − 5) °

Therefore, m∠XYZ = m∠YWX + m∠WXY (exterior angle theorem)

⇒ (10x − 5) ° = (3x + 17) ° + (3x + 2) °

Solve for x,

⇒ 10x - 5 = 3x + 17 + 3x + 2

⇒ 10x - 6x = 17 + 7

⇒ 4x = 24

⇒ x = 6

∴ ∠WXY = (3x + 2) = 18 + 2 = 20

Hence, value of ∠WXY = 20.

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3/2 is the imaginary part of the complex number (7+3i)/2.

Imaginary numbers are those that produce a negative square root when multiplied by themselves. In other terms, imaginary numbers are those that have no known value and are represented by the square root of negative integers. Most of the time, it is expressed as real values multiplied by an arbitrary unit called "i."

The basis for all imaginary numbers is the letter "i." Complex numbers are used to solve equations of the type a+bi utilising this fictitious number. To put it another way, a complex number is one that contains both real and fictitious numbers.

Complex numbers are the combination of both real numbers and imaginary numbers. The complex number is of the standard form: a + bi

Where a and b are real numbers and i is an imaginary unit.

The number is (7 + 3i)/2 .

7/2 + 3i/2 is the number.

3/2 is the imaginary part of the complex number (7+3i)/2.

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Answer:

\(3x^2 - 10x -5\)

Step-by-step explanation:

\(g(f(x))=g(x-1) \\ \\ =3(x-1)^2-4(x-1)-12 \\ \\ =3(x^2-2x+1)-4(x-1)-12 \\ \\ =3x^2-6x+3-4x+4-12 \\ \\ =3x^2 - 10x -5\)

Answer:

\(g(f(x))=3x^2-10x-5\)

Step-by-step explanation:

Given functions:

\(\begin{cases}f(x)=x-1\\g(x)=3x^2-4x-12\end{cases}\)

Function composition is an operation that takes two functions and produces a third function.

Therefore, the given composite function g(f(x)) means to substitute function f(x) in place of the x in function g(x):

\(\begin{aligned}\implies g(f(x))&=g(x-1)\\& = 3(x-1)^2-4(x-1)-12\\&=3(x-1)(x-1)-4x+4-12\\&=3(x^2-2x+1)-4x-8\\&=3x^2-6x+3-4x-8\\&=3x^2-6x-4x+3-8\\&=3x^2-10x-5\end{aligned}\)

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The volume is left in both speaker cabinets is 1215 cubic inches.

A Cube is a three-dimensional solid shape with six square faces, eight vertices, and twelve edges. It is also described as a regular hexahedron.

Some properties of the cube are-

Now, according to the question;

The side of the cube is given as 9 inches.

Then the volume of the cube will become;

Volume = side³

Volume = 9³ = 729.

A Cube is a three-dimensional solid figure with six square sides. If the face takes up 1/6 of this, then 5/6 is left over for cabinet .

Thus,  5/6×729 = 607.5 cubic inches for just a single speaker, multiplied by two to reach the total of 1215 cubic inches.

Therefore, the volume which is left in both speaker cabinets 1215 cubic inches.

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The average price of the pickup truck increased by 80%.

To find the percentage increase in the average price of the pickup truck, we need to calculate the difference between the 2012 and 1991 prices, divide that difference by the 1991 price, and then multiply by 100 to get the percentage increase.

First, we need to find the difference between the two prices:

$35,100 - $19,500 = $15,600

Next, we divide the difference by the 1991 price:

$15,600 / $19,500 = 0.8

Finally, we multiply by 100 to get the percentage increase:

0.8 x 100 = 80%

Therefore, the average price of the pickup truck increased by 80%.

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Answer:

(6, - 4 )

Step-by-step explanation:

\(\frac{x}{4}\) - \(\frac{3}{8}\) y = 3

multiply through by 8 ( the LCM of 4 and 8 ) to clear the fractions

2x - 3y = 24 → (1)

\(\frac{5}{3}\) x - \(\frac{y}{2}\) = 12

multiply through by 6 ( the LCM of 3 and 2 ) to clear the fractions

10x - 3y = 72 → (2)

multiplying (1) by - 1 and adding to (2) will eliminate y

- 2x + 3y = - 24 → (3)

add (2) and (3) term by term to eliminate y

8x + 0 = 48

8x = 48 ( divide both sides by 8 )

x = 6

substitute x = 6 into either of the 2 equations and solve for y

substituting into (1)

2(6) - 3y = 24

12 - 3y = 24 ( subtract 12 from both sides )

- 3y = 12 ( divide both sides by - 3 )

y = - 4

solution is (6, - 4 )

Answer:

See Below

Step-by-step explanation:

Ok, so in this problem you have some vertical angles. These are angles oppisites from each other. Therefore; d = 52, f = ?, and e = 77. All the angles added together will = 360. Let's add up the angles we know and subtract the whole from 360.

52 + 52 + 77 + 77 = ?

104 + 154 = 258

360 - 258 = 102

Since we know that f and the unlabeled angle are the same, we need to divide this total between the two of them.

102/2 = 51

Therefore;

d = 52

e = 77

f = 51

The volume of the solid below the cone z = x²y² and above the ring 1 ≤ x² + y² ≤ 4 in polar coordinates is (64π/15).

To find the volume of the solid, we integrate the function representing the cone over the region defined by the ring in polar coordinates.

In polar coordinates, the cone equation z = x²y² can be expressed as z = r²cos²(θ)sin²(θ), where r represents the radial distance and θ represents the angle.

The region defined by the ring can be expressed as 1 ≤ r² ≤ 4.

To find the volume, we integrate the function z = r²cos²(θ)sin²(θ) over the region of the ring in polar coordinates.

V = ∫∫∫ r²cos²(θ)sin²(θ) r dr dθ

= ∫[0,2π] ∫[1,2] r³cos²(θ)sin²(θ) dr dθ

= ∫[0,2π] ∫[1,2] r³(cos²(θ))(sin²(θ)) dr dθ

= ∫[0,2π] ∫[1,2] r³cos²(θ)sin²(θ) dr dθ

To evaluate this integral, we can use the property cos²(θ)sin²(θ) = (1/4)sin²(2θ), so the integral becomes:

V = (1/4) ∫[0,2π] ∫[1,2] r³sin²(2θ) dr dθ

Now, we integrate with respect to r:

V = (1/4) ∫[0,2π] [(1/4)r⁴sin²(2θ)] [1,2] dθ

= (1/4) ∫[0,2π] [(1/4)(2⁴ - 1⁴)sin²(2θ)] dθ

= (1/4) ∫[0,2π] [(15/4)sin²(2θ)] dθ

= (15/16) ∫[0,2π] [1 - cos(4θ)]/2 dθ

= (15/32) [θ - (1/4)sin(4θ)] [0,2π]

= (15/32) [2π - (1/4)sin(8π) - 0 + (1/4)sin(0)]

= (15/32) (2π - 0)

= 15π/16

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Answer:

100/20=5. this is the answer of ur questions

The appropriate sample size formula on the TI-84 calculator, you can determine the sample size needed to achieve your desired margin of error for estimating population parameters.

To find the sample size with a desired margin of error on a TI-84 calculator, you can use the following steps:

1. Determine the desired margin of error: Decide on the maximum allowable difference between the sample estimate and the true population parameter. For example, if you want a margin of error of ±2%, your desired margin of error would be 0.02.

2. Determine the confidence level: Choose the desired level of confidence for your interval estimate. Common choices include 90%, 95%, or 99%.

Convert the confidence level to a corresponding z-score. For instance, a 95% confidence level corresponds to a z-score of approximately 1.96.

3. Calculate the estimated standard deviation: If you have an estimate of the population standard deviation, use that value. Otherwise, you can use a conservative estimate or a pilot study's standard deviation as a substitute.

4. Use the formula: The sample size formula for estimating a population mean is n = (z^2 * s^2) / E^2, where n represents the sample size, z is the z-score, s is the estimated standard deviation, and E is the desired margin of error.

5. Plug in the values: Input the values of the z-score, estimated standard deviation, and desired margin of error into the formula. Use parentheses and proper order of operations to ensure accurate calculations.

6. Calculate the sample size: Perform the calculations using the calculator, making sure to include the appropriate multiplication and division symbols. The result will be the recommended sample size to achieve the desired margin of error.

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The equations of the two given planes are\(\[\begin{aligned} 10x+4y-5z&=-27 \\ 13x+10y-15z&=-75 \end{aligned}\]\)

We will solve the above two equations simultaneously to get the intersection point. By assuming that the intersection point is\(\[\left( x,y,z \right)\]\)

Now, we will solve this system of equation by the elimination method. We will eliminate x to get the equation in terms of y and z:

\(\[\begin{aligned} &\ 10x+4y-5z=-27 \\ &\ 13x+10y-15z=-75 \\\implies&\ 26x+8y-10z=-54 &&\text{(Multiplying first equation by 2)} \\ &\ 13x+10y-15z=-75 \\\implies&\ 13x+5y-5z=-27 &&\text{(Subtracting equation 1 from 2)} \end{aligned}\]\)

Now, we will solve these equations to get the values of y and z. To do this, we will multiply equation 2 by 2 and subtract equation 1 from it:

\(\[\begin{aligned} &\ 26x+10y-10z=-54 \\ -&\ (26x+8y-10z=-54) \\ =&\ 2y=0 \\ \implies&\ y=0 \end{aligned}\]\)

Similarly, we will multiply equation 2 by 3 and subtract equation 1 from it to get the value of z:

\(\[\begin{aligned} &\ 39x+15y-15z=-81 \\ -&\ (26x+8y-10z=-54) \\ =&\ 13x-7z=-27 \\ \implies&\ 13x-7z=-27 \\ \implies&\ 13x=7z-27 \end{aligned}\]\)

Now, we will substitute the value of y and z into any one of the given equations to get the value of x:

\(\[\begin{aligned} 10x+4y-5z&=-27 \\ 10x+4\left( 0 \right)-5\left( \frac{7x-27}{13} \right)&=-27 \\ 130x+0-35\left( 7x-27 \right)&=-351 \\ \implies x&=-10 \end{aligned}\]\)

Hence, the coordinates of the intersection point are \(\[\left( -10,0,-5 \right)\]\) A

The parametric equations of the line are \(\[\begin{aligned} x\left( t \right)&=-10t \\ y\left( t \right)&=0 \\ z\left( t \right)&=-5t \end{aligned}\]\)

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Answer: y = 4x

Step-by-step explanation:

Use rise over run. The points on the line will help you figure out the slope.