The mean of the data set is 40 and one standard deviation is 5. About what percent of the numbers fall between 35 and 50?

Note:

Images with coordinates or original and translated triangles are attached.

Answer:

The coordinates for the given triangle are A(6,3), B(6,-3) and C(-2,-3), respectively.

Let us translate this triangle by -6 units along the x-axis and +3 units along the y-axis. This means that 6 will be subtracted from each of the abcissas (x-points) and 3 will be added to each ordinates (y-points). Hence, our translated triangle will have the following coordinates: A'(0,6), B'(0,0) and C'(-8,0), respectively.

Now to prove that both triangles are congruent, we use the SSS postulate, which states that:

"If three sides of one triangle are congruent to three sides of another triangle, then the triangles are congruent."

Distance between two point P1 and P2 will be:

[tex]|P_1P_2|=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

Now using distance formula to find sides of triangle ABC and triangle A'B'C'.

For Triangle ABC:

|AB| = [tex]\sqrt{(6-6)^2+(-3-3)^2} =\;6\;units[/tex]

|AC| = [tex]\sqrt{(-2-6)^2+(-3-3)^2} =\;10\;units[/tex]

|BC| = [tex]\sqrt{(-2-6)^2+[-3-(-3)]^2} =\;8\;units[/tex]

For Triangle A'B'C':

|A'B'| = [tex]\sqrt{(0-0)^2+(0-6)^2} =\;6\;units[/tex]

|A'C'| = [tex]\sqrt{(-8-0)^2+(0-6)^2} =\;10\;units[/tex]

|B'C'| = [tex]\sqrt{(-8-0)^2+(0-0)^2} =\;8\;units[/tex]

Hence, as the distances are equal, the two triangles are congruent by SSS postulate.

Final answer:

To find the amount for the monthly payments for a plasma-screen TV, subtract the down payment from the total cost and divide by the number of installments. The equation is: Monthly Payment = (Total Cost - Down Payment) / Number of Installments, which calculates to $195.75.

Explanation:

The student is seeking to find an equation that represents the cost of a plasma screen television being paid off with a down payment and equal monthly installments. Given the total cost of the television is $5250 and the down payment is $552, we can start by calculating the remaining balance after the down payment, which will be paid in 24 equal monthly payments.

First, subtract the down payment from the total cost to find the balance that needs to be paid in installments:

Next, we divide the balance by the number of monthly payments to find the amount of each payment:

Therefore, the equation that represents the monthly payment after the down payment is:

Monthly Payment = (Total Cost - Down Payment) / Number of Installments

Applying the given numbers we get:

Monthly Payment = ($5250 - $552) / 24

Plugging in the values:

Monthly Payment = $4698 / 24 = $195.75

Answer: B is on bottom, C is on the left

Step-by-step explanation:

A is on top and B is opposite of A. Therefore, it's on bottom and C is on the left as E is on the right.

The bottom of the rectangular prism is side C, and the left side is side B.

To determine which side is the bottom and which side is on the left of the rectangular prism, we need to visualize how the paper was cut and folded. Let's assume that the original piece of paper had the letters A, B, C, D, E, and F on it. After folding, the side with the letter C will be the bottom of the rectangular prism, and the side with the letter B will be on the left. So, the correct answer is A. C is on the bottom, B is on the left.

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Answer:

The answer is:  [tex]x^3-9x^2+14x+24[/tex]

Step-by-step explanation:

The given expression is:  [tex](x-4)(x^2-5x-6)[/tex]

For getting the product, we need to distribute [tex](x-4)[/tex] with each term in the second parenthesis. So.....

[tex](x-4)(x^2-5x-6)\\ \\ =x^2(x-4)-5x(x-4)-6(x-4)\\ \\ =x^3-4x^2-5x^2+20x-6x+24 \ [using\ distribution\ rule]\\ \\ =x^3-9x^2+14x+24\ [combining\ like\ terms][/tex]

So, the answer is:  [tex]x^3-9x^2+14x+24[/tex]

Answer:

7x = 6(x+15)

Step-by-step explanation:

a pex

Answer:

Solution is (2,1)

Step-by-step explanation:

In order to graph both lines ,we need to find the X and Y intercepts for both equations

Lets take equation  y =2x -3

               To find y intercept ,we plug x =0 ,we get y =2(0)-3 = 0-3 =-3

                         Y intercept is (0,-3) Which is point  'C' in the graph

              To find X intercept ,we plug y =0 ,we get 0 = 2x-3 or x = 3/2 or 1.5

                        X intercept is (1.5,0) Which is point D in the graph.

Lets take equation y =-2x+5

                   To find y intercept ,we plug x =0 ,we get y = -2(0)+5 = 0+5 = 5

                       Y intercept is (0,5) which is point A in the graph .

              To find X intercept ,we plug y =0 ,we get 0 =-2x+5 or x = 5/2 or 2.5

                     X intercept is (2.5,0) which is point B on the graph

         After getting intercept of both lines ,we plot both lines

In the graph Blue line shows  y=2x-3 and Red line shows y =-2x+5

both lines intersect at point E which is called the solution of both equation

which is given to be (2,1)

Answer: No, the line through points P(–8, –10) and Q(–5, –12) is not perpendicular to the line through points R(9, –6) and S(17, –5).

Step-by-step explanation:

Two lines are called perpendicular to each other if the product of their slope is -1.

Since, the slope of a line having end points [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] is,

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

Thus, the slope of line Joining points P(–8, –10) and Q(–5, –12),

[tex]m_1=\frac{-12+10}{-5+8}=\frac{-2}{3}=-\frac{2}{3}[/tex]

While, The slope of line Joining points R(9, –6) and S(17, –5),

[tex]m_2=\frac{-5+6}{17-9}=\frac{1}{8}[/tex]

Since,

[tex]m_1\times m_2=-\frac{2}{3}\times \frac{1}{8}=-\frac{1}{12}\neq -1[/tex]

Thus, the line through points P(–8, –10) and Q(–5, –12) is not perpendicular to the line through points R(9, –6) and S(17, –5).

The distance between -3.1 and -5.7 on the number line is 2.6 units.

The distance between two points on the number line is the absolute difference between those two points.

So, the distance between -3.1 and -5.7 is:

[tex]|-3.1 - (-5.7)| = |-3.1 + 5.7| = |2.6| = 2.6[/tex]

Therefore, the distance between -3.1 and -5.7 on the number line is 2.6 units.

Answer:

Step-by-step explanation:

its answer C !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

There are 22,764 possible cones.

To calculate the number of possible cones, we need to consider the number of flavors and the number of scoops. Since a customer can order a single-, double-, or triple-scoop cone, we will consider each case separately.

For a single-scoop cone, the customer can choose one flavor out of the 28 available flavors. Therefore, there are 28 possible single-scoop cones.

For a double-scoop cone, the customer can choose two flavors for the two scoops. Since the order of the flavors matters and repetition is allowed, we can think of this as selecting two flavors with replacement. Using the formula n^r, where n is the number of flavors and r is the number of scoops, there are a total of 28^2 = 784 possible double-scoop cones.

For a triple-scoop cone, the customer can choose three flavors for the three scoops. Again, using the formula n^r, there are a total of 28^3 = 21,952 possible triple-scoop cones.

Therefore, the total number of possible cones is 28 + 784 + 21,952 = 22,764.

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Answer:b

Step-by-step explanation:

Answer:

In Total=560

Step-by-step explanation:

216/6=36

36*10=360

216+360=560

To convert 15°C to Fahrenheit, we use the formula °F = (9/5 x °C) + 32, which will give us 59°F as the equivalent temperature. The formula is based on the freezing and boiling points of water in the two scales.

To convert a temperature given in degrees Celsius to Fahrenheit, we use the formula °F = (9/5 × °C) + 32. In this case, where the Celsius temperature (x) is 15, we substitute 15 into the formula: °F = (9/5 * 15) + 32. The calculation then becomes °F = 27 + 32 = 59°F, meaning 15°C is equivalent to 59°F on a Fahrenheit scale.

The formula is derived from the fact that the freezing point of water is 0°C (32°F) and the boiling point is 100°C (212°F). On the Fahrenheit scale, that's a range of 180 (212 - 32), and on the Celsius scale, it's 100 (100 - 0), which gives us the ratio 180/100 or 9/5.

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Answer:

Step-by-step explanation:

Given that there is a cone and cylinder with equal radius and height.

Recall volume formula for cone and cylinder as

Volume of cone = [tex]\frac{1}{3} \pi r^2 h[/tex]

Volume of cylinder =[tex]\pi r^2 h[/tex]

Thus we find that cylinder has a greater volume and ratio is 3:1

Hence 3 times if filled up with a cone the cylinder will be completely full

The student can match each slice of the surface 2x^2+5y^2+z^2=4 with its correct plot by substituting the slice values into the equation, resulting in a set of new equations each representing a different conic section centered at the origin.

To understand the shapes or plots of the resulting slices when the surface given by 2x^2+5y^2+z^2=4 is sliced by planes of the form x=a, y=b or z=c, you must substitute values of a, b, and c into the equation of the surface to reveal new equations describing the slices.

By comparing these resulting equations with the standard forms of conic sections (circle, ellipse), you can match them with their correct plots.

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The equation relating W to T is W = 600 + 25T.

Given:

The initial amount of water in the pond is 600 liters.

The water is being added at a rate of 25 liters per minute.

As time (T) increases, the amount of water in the pond (W) will increase due to the constant addition of 25 liters per minute.

The equation can be written as follows:

W = 600 + 25T

In this equation, 600 represents the initial amount of water in the pond (at T = 0), and 25T represents the additional water added for each minute of time (T).

Learn more about Linear Equation here:

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The Answer:

356+56y=-832

To maximize revenue for John Deere's heavy-duty tractors, the optimal unit price is found by determining the vertex of the provided quadratic revenue function R(p). Using the vertex formula, the unit price p that maximizes revenue is $1520.

Maximizing Revenue for John Deere Heavy-Duty Tractors

To find the unit price that maximizes revenue for John Deere heavy-duty tractors, we need to analyze the revenue function R(p) provided, which follows a quadratic format:

R(p) = [tex](-1/2)p^2[/tex]  + 1520p

To find the maximum revenue, we can use the fact that the vertex of a parabola described by a quadratic equation y = ax^2 + bx + c provides the maximum or minimum value of the function. Since our equation is in the form of a parabola opening downwards (because the coefficient of p^2 is negative), the vertex will give us the maximum revenue point.

The formula for the p-coordinate (horizontal axis) of the vertex of a parabola is given by -b/(2a). In this case, a = -1/2 and b = 1520, therefore:

p = -b/(2a) = -1520/(2 * (-1/2)) = -1520/(-1) = 1520

Hence, the unit price p should be set at $1520 to maximize revenue for the sale of heavy-duty tractors. This value is already an integer, so rounding to the nearest dollar is not necessary.

Final answer:

The probability that both marbles chosen by Linda are blue is 2/15, calculated by multiplying the probability of selecting a blue marble on each draw without replacement.

Explanation:

To calculate the probability that Linda selects two blue marbles in a row without replacement, we need to consider the number of blue marbles and the total number of marbles in the bag during each draw. Initially, there are 10 marbles in total with 4 blue marbles. The probability of drawing a blue marble on the first draw is therefore 4/10.

Upon successfully drawing a blue marble the first time, the marble is not replaced, meaning there are now only 9 marbles left with 3 being blue. The probability of drawing a second blue marble is now 3/9, which simplifies to 1/3.

To find the total probability of both events occurring in sequence (both draws resulting in blue marbles), we multiply the probabilities of each individual event occurring:

(4/10) × (3/9) = (2/5) × (1/3) = 2/15.

Therefore, the probability that both marbles Linda chooses are blue is 2/15.

Answer:

89; the mode

Step-by-step explanation:

Final answer:

The best measure of central tendency for the student's test scores is the mode, which is 89. The mean and median are 86 and 87 respectively, but the mode gives the highest score, hence it is the most favorable for determining the student's final grade.

Explanation:

The question asks for the most favorable measure of central tendency for a student's test scores to determine their final grade. The test scores provided are 89, 81, 85, 82, 89, and 89.

To find the most favorable measure, we need to calculate the mean (average), median, and mode of the test scores. The mean is calculated by adding all the scores together and dividing by the number of tests. The median is the middle number when the scores are listed in order, and the mode is the number that appears most frequently.

Calculating the mean: (89 + 81 + 85 + 82 + 89 + 89) / 6 = 85.83, which we round to the nearest whole number as 86.

To find the median, we order the scores: 81, 82, 85, 89, 89, 89. Since there are an even number of scores, the median is the average of the two middle numbers, in this case, 85 and 89. Thus, the median is (85 + 89) / 2 = 87.

The mode is the most frequent score, which is 89.

Out of the mean, median, and mode, the mode is the highest and most favorable measure of central tendency for the student, resulting in a final grade of 89 when rounded to the nearest whole number.

Answer:

The correct answer is most definitely A. $ 500 credit

Step-by-step explanation:

I am 100% Positive