The marginal cost function, in dollars per item, for producing the x th item of a certain brand of bar stool is given by MC(x)=20−0. 5 x , 0≤ x≤ 100. The fixed cost is $200. Estimating the total cost of producing 100 bars tools using the left-rectangle approximation with five rectangles, we conclude that the total cost is approximately $

Courtney rides for two hours on a bicycle, traveling 24 miles from her home. She has ridden for nine hours and is now 101 miles away. Courtney travels at a speed of 6 mph.

Let x represent the duration in hours and y the distance in miles.

Courtney travels 24 miles from her home after a two-hour ride.

She has traveled 101 miles after riding for nine hours.

rate is the slope

We divide the change in hours by the change in miles to find the rate.

\(Slope=\frac{y_{2} - y_{1} }{x_{2}-x_{1} } \\Slope=\frac{101-24}{9-2} \\Slope= \frac{77}{7} \\Slope=11\)

Therefore, Courtney's speed is 11 mph.

The speed of something or someone is shown to us. If you know how far and how long it took, you can find the average speed of an object.

The distance covered in a given amount of time would also double if one were to speed up. We need to know how far an object has traveled in order to determine its speed, and the slowest speeds are measured over the longest time periods.

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Answer:

k=192

Step-by-step explanation:

switch sides

\(\frac{k}{12} =16\)

multiply both sides by 12

\(\frac{k}{12x12}\)= \(16x12\)

12x12 would get cancelled out and 16x12 is 192

\(k=192\)

hope this makes sense

The average line shows the average of the data for a particular graph by drawing a line across the chart at the mean value points on the y-axis. By default, the average line label is displayed as a combination of line value and line title. 

Graph is a collection of data from several tables that will be presented or also displayed in the form of images, such as squares, circles, tubes, triangles, beams, cones or others. Graphics are also usually also interpreted as a framework or image that will be used to create a visualization object from data in tables with the aim of being able to provide information about a data from the material presenter to the recipient of the material.

In addition, graphs are also often interpreted as a description of the ups and downs of an existing data, or depicted by lines or pictures. The data used to create graphics can be in the form of numbers, letters, symbols, pictures, symbols, sayings, or paintings.

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Answer:

(-4,-1)

Step-by-step explanation:

The solution to a system of linear equations is simply where the two lines intersect.

From the graph, we can see that they intersect at (-4,-1).

Therefore, the solution to the system graphed below is (-4,-1).

And we're done!

Answer:

b) P(mean weight > 176) = 1 - P(mean weight ≤ 176) = 1 - 0.9332 = 0.0668

c) P(mean weight > 176) = 1 - P(mean weight ≤ 176) = 1 - 0.9997 = 0.0003

it is possible that options (A) and (D) are both true, but without seeing the graph, it is difficult to say for sure.

If the graph shows a straight line with a constant slope, then the angular speed of the object is constant. If the graph shows a horizontal line, then the angular speed of the object is zero, which means the object is not rotating.

If the graph shows a straight line with a constant slope, then the angular acceleration of the object is zero because the angular speed is not changing. If the graph shows a straight line with a constant non-zero slope, then the angular acceleration of the object is constant because the angular speed is changing at a constant rate.

If the graph shows a horizontal line, then the angular position of the object is constant because the object is not rotating.

The net torque applied to an object is equal to the rate of change of its angular momentum. If the graph shows a straight line with a constant slope, then the angular momentum is changing at a constant rate, which means the net torque applied to the object is constant.

Based on the above information, it is possible that options (A) and (D) are both true, but without seeing the graph, it is difficult to say for sure.

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The most appropriate choice for permutation and combination will be given by

Number of sequences obtained by drawing three balls = 8000

Number of sequences obtained by drawing four balls = 16000

What is permutation and combination?

When there is a case of ordering, the number of arrangements that can be made in a set is called permutation

When there is no case of ordering, the number of arrangements that can be made in a set is called combination.

Here,

For three balls

Total number of balls = 20

Number of balls drawn = 3

This problem is same as the problem for drawing of r balls from n balls with replacement

So number of choices for first place = 20

Number of choices for second place = 20

Number of choices for third place = 20

Total number of sequences obtained = \(20 \times 20 \times 20\)

                                                              = 8000

For four balls

So number of choices for first place = 20

Number of choices for second place = 20

Number of choices for third place = 20

Number of choices for fourth place = 20

Total number of sequences obtained = \(20 \times 20 \times 20 \times 20\)

                                                              = 16000

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Using sampling concepts, it is found that the correct option is:

This is a convenience sample and likely overestimates support for raising funds.

Samples may be classified as:

In this problem, people at the pool were surveyed, hence it is a convenience sampling.

Also, since it only involved pool users, the proportion may be overestimated, hence the correct option is:

This is a convenience sample and likely overestimates support for raising funds.

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Answer:

2334

Step-by-step explanation:

Answer:

120 calories

Step-by-step explanation:

If 1/4 of a cup is 90 calories we can find that 1 cup is 4*90=360 calories. If you wanted to find the amount of calories in 1/3 of a cup, we can divide the amount of calories in 1 cup by 3. So, 360/3=120 calories.

We know that this is accurate as 1/3>1/4 so the amount of calories should also be bigger, as 120>90.

The amount of calories in 1/3 cup is 120.

The function which is in format f(x) =aˣ where x is variable and a is constant,  the domain of this exponential function lies   (-∞, ∞).

Given, a function  Y=500(1.067)^x

For calculating the y-intercept x will be 0

Thus  y-intercept of the given exponential function  = 500 (1.067)^0 = 500

As we can show in the attached graph the function is exponential growth.

In the attached image an equation is given that is \(\frac{(3g^3m^4)^{-3}}{(g^5 m^{-5})^ {-2}}\)

When we will simplify this using the only condition if the base is the same then power can be equal.

Thus the simplified version of the given function is \(\frac{g}{3 m^{22} }\).

In the third question,

A certain car depreciates at a rate of 15% a year,

The price is $26,000,

Expression of the depreciating price is given as,

= 26000(1 - 0.15)⁶

= 26000(0.85)⁶

= $9805.88

Thus, the required depreciated cost of the car is $9805.88 in 6 years.

Given a line  2x+y=6 that has another parallel line passing through the point (0, -1).

The equation of the parallel Line is 2x + y = c

Since, it goes through the point (0, -1)

value of c = 2*0 -1 = -1

Thus, the equation of the line parallel to 2x+y=6 and passing through the point (0,-1) is 2x +y  + 1 = 0

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Step-by-step explanation:

180-46 = 134

180 - 13 = 177

177-134 = 43

? = 43

The expression to represent the change in elevation would be 13 - 150.

The change in elevation would be - 137 feet.

The change in elevation refers to the difference between the elevation that a person ends up in, from the elevation that they started out at.

The change in elevation for the goat would therefore be:

= Ending elevation - Starting elevation

= 13 - 150

= - 137 feet

In conclusion, the change in elevation of the goat in its travels was - 137 feet.

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The angles between 0° and 360° that satisfy the equation sin θ=1/2 are θ = 30° + k x 360° or θ = 150° + k x 360°
where k is any integer

If sin θ=1/2, we can use two ways to find all the angles between 0° and 360° that satisfy this equation. They are described below.

Method 1: Use the inverse sine function.  
We know that sin θ=1/2. It is also known that sin 30°=1/2. Therefore, we can say that θ=30°. However, this is only one solution.  We can use the inverse sine function to get the other solutions. The inverse sine function is denoted by sin⁻¹. Therefore, we can write:
θ = sin⁻¹(1/2) + k x 360°
where k is any integer.
Using a calculator, we get:
sin⁻¹(1/2) = 30°

Therefore, the solutions are:
θ = 30° + k x 360°
where k is any integer.

Method 2: Use the unit circle
We know that sin θ=1/2. This means that θ is an angle whose terminal side intersects the unit circle at a point with a y-coordinate 1/2. We can draw the unit circle and locate the points whose y-coordinate is 1/2. These points are at angles of 30° and 150°.

However, we can go around the circle multiple times and get more solutions. The solutions are separated by an angle of 360°. Therefore, we can say that the solutions are:
θ = 30° + k x 360° or θ = 150° + k x 360°
where k is any integer.

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Answer:

\( \large \boxed{x = 4}\)

Step-by-step explanation:

Goal

Given

\(7x - 2 = 26\)

Step 1

\(7x - 2 + 2 = 26 + 2 \\ 7x + 0 = 28 \\ 7x = 28 \\ x = \frac{28}{7} \\ x = 4\)

Step 2 (Optional)

\(7x - 2 = 26 \\ 7(4) - 2 = 26 \\ 28 - 2 = 26 \\ 26 = 26\)

The equation is true for x = 4. Hence, the solution is x = 4.

Answer:

3398.1761

Step-by-step explanation:

Using compound interest relation:

A = P(1 + r/n)^nt

5.2 / 100 = 0.052

n = 365 * 12 = 4380

6000 = P(1 + 0.052/4380)^4380*11

6000 = P(1.0000118)^48180

6000 = 1.7656530P

P = 6000/ 1.7656530

P = 3398.1761

Answer:

98086

Step-by-step explanation:

Out of the five options provided, Joe should choose the dimensions of the enlarged photo that have the same ratio as the dimensions of the original photo. The correct options in this case are 9 inches by 15 inches and 30 inches by 50 inches.

To determine which dimensions have the same ratio as the original photo, we need to compare the ratios of the lengths and widths of the original and enlarged photos. The ratio of the length to width for the original photo is 3:5.

Let's calculate the ratios for each of the options:

9 inches by 15 inches: The ratio of the length to width is 9:15, which simplifies to 3:5. This option has the same ratio as the original photo.

13 inches by 15 inches: The ratio of the length to width is 13:15, which does not match the original ratio of 3:5.

9 inches by 25 inches: The ratio of the length to width is 9:25, which does not match the original ratio of 3:5.

15 inches by 25 inches: The ratio of the length to width is 15:25, which simplifies to 3:5. This option has the same ratio as the original photo.

30 inches by 50 inches: The ratio of the length to width is 30:50, which simplifies to 3:5. This option has the same ratio as the original photo.

Therefore, the dimensions of the enlarged photo that will have the same ratio as the original photo are 9 inches by 15 inches and 30 inches by 50 inches.

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To test the hypothesis H₁: μx = μy versus Hoxy, where μx and μy represent the means of X and Y respectively, we can perform a two-sample t-test. The test compares the means of two independent samples to determine if they are significantly different from each other.

The given information provides the sample means (X = 33.8, Y = 32.5) and the sample standard deviations (Sx = 3.9, Sy = 5.1). The sample sizes for both X and Y are n = m = 25.

Using this information, we can calculate the test statistic, which is given by:

t = (X - Y) / sqrt((Sx^2 / n) + (Sy^2 / m))

Plugging in the values, we get:

t = (33.8 - 32.5) / sqrt((3.9^2 / 25) + (5.1^2 / 25))

Next, we need to determine the degrees of freedom for the t-distribution. Since the sample sizes are equal (n = m = 25), the degrees of freedom for the test is given by (n + m - 2).

Using the t-distribution table or software, we can find the critical value corresponding to a significance level of α = 0.05 and the degrees of freedom.

Finally, we compare the calculated test statistic with the critical value. If the test statistic falls within the rejection region (i.e., the absolute value of the test statistic is greater than the critical value), we reject the null hypothesis. The p-value can also be calculated, which represents the probability of observing a test statistic as extreme or more extreme than the calculated value, assuming the null hypothesis is true.

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The values of x when the diagram is solved using vertically opposite angles is 10 .67°.

Vertically opposite angles are angles that are opposite one another at a specific vertex and are created by two straight intersecting lines.

To calculate the value of X, we use the formula of a vertically opposite angles.

As shown in the diagram,

Solve for x in the equation 1

Hence, the values of x is 10 .67°.

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Hence, the total surface area of the rectangular prism is 736 in².

A 3D object's surface area is calculated as the total of all of its faces. For instance, if we wanted to figure out how much paint we would need to paint a cube, we would use the cube's surface area.

To calculate the total surface area of the rectangular prism, we need to find the area of each of its six faces and add them together.

The area of the top and bottom faces, which are identical, is:

Length x Breadth = 16 in x 8 in = 128 in².

The area of the front and back faces, which are also identical, is:

Height x Breadth = 10 in x 8 in = 80 in².

The area of the left and right faces, which are also identical, is:

Height x Length = 10 in x 16 in = 160 in².

Therefore, the total surface area of the rectangular prism is:

2(Length x Breadth) + 2(Height x Breadth) + 2(Height x Length)

= 2(16 in x 8 in) + 2(10 in x 8 in) + 2(10 in x 16 in)

= 256 in² + 160 in² + 320 in²

= 736 in²

Hence, the total surface area of the rectangular prism is 736 in².

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Answer:

There are total 50 teachers, 30% are male, 70% are female

Step-by-step explanation:

There is no specific question, but I just put the percentage of each gender teacher. Hope this is the question you were trying to find!

Answer:

\(12.5(x + 20) = 460 \\ x + 20 = 460 \div 12.5 \\ x + 20 = 36.8 \\ x = 36.8 - 20 \\ x = 16.8\)

Hence, 16.8 miles is your answer

The statistical techniques of analysis of variance (ANOVA) and analysis of covariance (ANCOVA) are used to test the validity of the hypothesis regarding the comparison of group mean values.

The term "parametric approach" refers to a statistical technique used to compare the means of two normally distributed continuous variables.

In contrast to ANOVA, which is used to compare the means among three or more groups, the Student's t test (also known as the T test) is used to compare the means between two groups.An ANOVA test with a significant P value identifies at least one pair in which the mean difference was statistically significant.

The post-hoc test (multiple comparisons) is utilized to determine whether pair(s) are significant. When at least one covariate (continuous variable) in an ANOVA test is altered to eliminate confounding variables from the outcome, the procedure is known as an ANCOVA. Because inferences about means are made by analyzing variance, the ANOVA test (F test) is referred to as "Analysis of Variance" rather than "Analysis of Means."

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No, events a and b are not disjoint if if the p(a) = 0.25 and the p(b) = 0.5.

Two events are considered disjoint if they cannot occur at the same time, meaning their intersection is equal to zero. Mathematically, if A and B are disjoint events, then P(A ∩ B) = 0.

In this case, we do not know whether events a and b are independent or dependent. Therefore, we cannot determine whether they are disjoint based on the given probabilities alone.

To determine whether events a and b are disjoint, we need to know whether they share any common outcomes. If there are any outcomes that belong to both events, then the events are not disjoint.

Without further information, we cannot determine whether events a and b are disjoint.

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The velocity of the boat when it reaches the buoy is approximately 17.32 m/s. This is found using the equation v² = u² + 2as, where u is the initial velocity, a is the acceleration, and s is the displacement.

To solve this problem, we can use the equations of motion. The initial velocity of the boat, u, is 30 m/s, the acceleration, a, is -3.0 m/s² (negative because the boat is slowing down), and the displacement, s, is 100 m. We need to find the final velocity, v, when the boat reaches the buoy.

We can use the equation: v² = u² + 2as

Substituting the given values, we have:

v² = (30 m/s)² + 2(-3.0 m/s²)(100 m)

v² = 900 m²/s² - 600 m²/s²

v² = 300 m²/s²

Taking the square root of both sides, we find:

v = √300 m/s

v ≈ 17.32 m/s

Therefore, the velocity of the boat when it reaches the buoy is approximately 17.32 m/s.

The problem provides the initial velocity, acceleration, and displacement of the boat. By applying the equation v² = u² + 2as, we can find the final velocity of the boat. This equation is derived from the kinematic equations of motion. The equation relates the initial velocity (u), final velocity (v), acceleration (a), and displacement (s) of an object moving with uniform acceleration.

In this case, the boat is decelerating with a constant acceleration of -3.0 m/s². By substituting the given values into the equation and solving for v, we find that the velocity of the boat when it reaches the buoy is approximately 17.32 m/s.

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Based on this statement "Suppose at a point P that the gradient ∇f of a scalar function f exists and is nonzero. Which of the following, if any, is false?" There is no unit vector u such that |fu(P)| > |∇f(P)|. Option C is false.

A scalar function can be defined as a function that only returns one value per row unlike aggregate function that return one value per group of rows.  

Since the gradient ∇f at point P is nonzero, a direction exist in which the function f increases the most. This direction is given by the unit vector u = ∇f/|∇f|. T

Hence,  fu(P) = |∇f(P)| > 0, since u is the direction of maximum increase for f at point P.

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To solve this equation you need to follow the BODMAS rule and also the rules of algebraic expressions as there is an x.

So the equation to be solved is 5(7-x)+32=106-1. 5(4x+18). Here the sign '.' is taken to be multiplication and not decimal, as there is space between '1' and '5'.

Forwarding with the sum: First solve L.H.S. 5(7-x)+32, = 35 - 5x + 32, = 67 - 5x. Now doing R.H.S. 106-1. 5(4x+18), = (105) (20x + 90), = 2100x + 9450.

Now, find the value of x. L.H.S. = R.H.S.

67 - 5x = 2100x + 9450.

-5x - 2100x = 9450 - 67

- 2105x = 9383. So we have the value of x. Where x= 9383+2105. Therefore x= 11488.

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Answer:

yes you're right it is 14 + 28p = 315

Answer:

C

Step-by-step explanation:

I had this question edge 2021

Answer:

A

Step-by-step explanation:

short cut, it has 5 dashes/ point markings