The decomposition of 713 × 49 has been provided below
How to decompose the problemTo multiply 713 and 49, we can use the distributive property and decompose the second number as follows:
49 = 40 + 9
Then, we can multiply each part of the sum by 713:
713 × 40 + 713 × 9
To calculate this, we can use the multiplication table and then add the results:
713
x 40
28520
713
x 9
6417
Then, we add the two results:
713 × 40 = 28520
713 × 9 = 6417
34997
Therefore, the multiplication 713 × 49, decomposed as 713 × 40 + 713 × 9, equals 34,997.
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Triangle A′B′C′ is a dilation of triangle ABC about point P with a scale factor of 1/2. Is the dilation a reduction or an enlargement? reduction enlargement
Triangle A′B′C′ is a dilation of triangle ABC about point P with a scale factor of 1/2. The dilation is a reduction.
A dilation is a transformation that changes the size of a figure, but not its shape. It can be either an enlargement or a reduction depending on the value of the scale factor.
If the scale factor is greater than 1, then the image will be larger than the original figure. This is called an enlargement.
If the scale factor is between 0 and 1, then the image will be smaller than the original figure. This is called a reduction.
In this case, the scale factor is 1/2, which is less than 1. Therefore, the image of triangle ABC is smaller than the original triangle, and the dilation is a reduction.
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Two water balloons were launched into the air at different moments and collided. The water balloons were modeled by the quadratic functions: y = −7x2 + 26x + 3 and y = −6x2 + 23x + 5, where y represents the height in meters and x represents the time in seconds after the launch. What is the time, in seconds, that the balloons collided at the highest point?
The height at x = 2 seconds is greater (25 meters), the balloons collided at the highest point at 2 seconds. We can use quadratic functions to solve this.
To find the time in seconds that the balloons collided at the highest point, we will first find the points where the balloons have the same height (y) by setting the two quadratic functions equal to each other:
-7x² + 26x + 3 = -6x² + 23x + 5
Next, we will solve for x:
x² - 3x - 2 = 0
Now, factor the quadratic equation:
(x - 2)(x - 1) = 0
The solutions for x are 1 and 2 seconds. To find the highest point of collision, we need to determine which of these times results in a greater height. Plug each value of x into one of the original equations and compare the y values:
For x = 1:
y = -7(1)² + 26(1) + 3 = 22
For x = 2:
y = -7(2)² + 26(2) + 3 = 25
The balloons collided at the highest point at 2 seconds.
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N equation for the depreciation of a car is given by y = A(1 – r)t , where y = current value of the car, A = original cost, r = rate of depreciation, and t = time, in years. The value of a car is half what it originally cost. The rate of depreciation is 10%. Approximately how old is the car?
3. 3 years
5. 0 years
5. 6 years
6. 6 years
the car is approximately 6.6 years old. The closest option provided is 6 years, so the answer is (C) 6 years.
A car's original value depreciates by 10% per year. If the current value of the car is half of its original value, approximately how old is the car?Given:
y = A(1 – r)t
The value of a car is half what it originally cost, which means:
y = 1/2 A
The rate of depreciation is 10%, which means:
r = 0.1
Substituting these values in the equation, we get:
1/2 A = A(1 – 0.1)t
Simplifying, we get:
1/2 = 0.9t
Solving for t, we get:
t = ln(1/2) / ln(0.9) ≈ 6.6 years
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Draw a rectangle that is 4 squares long and
1/2 of a square wide.
then add up the partial squares to find the area.
multiply to check your answer
The exact area of our rectangle is 2 square units
The total area of the rectangle can be found by adding up the area of each square. We have four unit squares and one half-square, which can be represented as 4 + 1/2. To add these two values, we need to find a common denominator, which is 2.
Thus, we can represent the area of the rectangle as
=> 8/2 + 1/2 = 9/2 square units.
We know that the area of a rectangle is calculated by multiplying its length by its width. Thus, we can represent the area of our rectangle as follows:
A = lw
where A is the area, l is the length, and w is the width.
Now, we need to differentiate this equation with respect to the width w. This means we are finding the rate of change of the area with respect to the width. Using the product rule of differentiation, we get:
dA/dw = l * dw/dw + w * dl/dw
Since the width is constant (it does not change), the second term on the right-hand side of the equation is zero. Thus, we are left with:
dA/dw = l
To calculate the exact area of our rectangle, we can use the concept of limits. We can start by approximating the area of our rectangle with a width of 1 square unit. In this case, the area of the rectangle would be 4 square units.
We can then approach the width of 1/2 of a square unit by taking the limit as the width approaches 1/2. Using the derivative we calculated earlier, we can represent this limit as follows:
lim(w→1/2) A = lim(w→1/2) lw = l * lim(w→1/2) w = 4 * (1/2) = 2 square units
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What adds to +10 and multiplys to 290
Michael is using a rotating
sprinkler to water his lawn. The
sprinkler rotates in a complete
circle. It sprays water at most 8
feet. Find the area of the lawn
that is watered. Use 3. 14 for π. Show Your Work
The area of the lawn that is watered by the sprinkler is approximately 200.96 square feet.
The area of the field that's doused by the sprinkler is a sector of a circle with a compass of 8 bases and a central angle of 360 degrees.
To find the area of the sector, we can use the formula
Area = ( θ/ 360) x πr2
where θ is the central angle in degrees,
r is the radius of the circle,
and π is the constant pi.
Substituting the given values,
we get Area = (360/360) x3.14 x 82
Area = 3.14 x 64 Area = 200.96
Thus, the area of the field that's doused by the sprinkler is roughly 200.96 square feet.
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The complete question is as follows:
Michael is using a rotating sprinkler to water his lawn. The sprinkler rotates in a complete circle. It sprays water at most 8 feet. Find the area of the lawn that is watered.
down 9 units and left 2 units what coordinates would you end up at? What quadrant would you be in?
So, depending on the original coordinates, moving down 9 units and left 2 units will end up in either the third or fourth quadrant of the coordinate plane.
What is coordinate?A coordinate is a set of values that specifies the position of a point or an object in a geometric space. In a two-dimensional space, such as the Cartesian plane, a coordinate is typically represented by a pair of numbers (x, y), where x represents the horizontal position (or abscissa) of the point and y represents the vertical position (or ordinate) of the point.
Here,
Starting from an arbitrary point (x, y), if we move down 9 units and left 2 units, we will end up at the point with coordinates (x - 2, y - 9). The new x-coordinate is obtained by subtracting 2 from the original x-coordinate, since we moved 2 units to the left. The new y-coordinate is obtained by subtracting 9 from the original y-coordinate, since we moved 9 units down.
The quadrant we end up in depends on the original coordinates (x, y) and the direction of the movement. If we start in the first quadrant (x > 0, y > 0) and move down and left, we will end up in the third quadrant (x < 0, y < 0).
If we start in the second quadrant (x < 0, y > 0) and move down and left, we will also end up in the third quadrant (x < 0, y < 0).
If we start in the third quadrant (x < 0, y < 0) and move down and left, we will end up in the fourth quadrant (x > 0, y < 0).
If we start in the fourth quadrant (x > 0, y < 0) and move down and left, we will still end up in the fourth quadrant (x > 0, y < 0).
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To the nearest hundredth, what is the relative frequency of boys who want to go to the water park
To find the relative frequency of boys who want to go to the water park, we need to divide the number of boys who want to go to the water park by the total number of boys in the sample:
Relative frequency = Number of boys who want to go to the water park / Total number of boys
Assuming you have the necessary data, you can compute this value by dividing the number of boys who want to go to the water park by the total number of boys and rounding the result to the nearest hundredth.
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A water sample shows 0.063 grams of some trace element for every cubic centimeter of water. Tariq uses a container in the shape of a right cylinder with a radius of 7.6 cm and a height of 17 cm to collect a second sample, filling the container all the way. Assuming the sample contains the same proportion of the trace element, approximately how much trace element has Tariq collected? Round your answer to the nearest tenth.
Therefore, Tariq has collected 201.09 g trace element.
We are given that Tariq uses a container that is in the shape of a cylinder. The radius of the cylinder is 7.6 cm and the height of the cylinder is 17 cm.
Firstly, we will find the volume of the cylinder by applying the formula
The volume of the cylinder = [tex]\pi r^{2} h[/tex]
As we know the values of r and h, we will substitute these values in the given formula
The volume of cylinder = 3.14 * 17.6 * 7.6 *7.6
The volume of cylinder = 55.264 * 57.76
Volume = 3192.04 [tex]cm^{3}[/tex]
We are given that the water sample shows 0.063 grams of some trace element for every cubic centimeter of water. Therefore, we will multiply the volume of the cylinder by 0.063 to calculate the number of trace elements collected.
= 3192.04 * 0.063
= 201.09
Therefore, a total of 201.09 g of trace elements was collected by Tariq.
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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 $
The total cost of producing 100 bar stools using the left-rectangle approximation with five rectangles is approximately $200.
The marginal cost function for producing the x-th item of a certain brand of bar stool is given by MC(x) = 20 - 0.5x, where 0 ≤ x ≤ 100. To estimate the total cost of producing 100 bar stools using the left-rectangle approximation with five rectangles, we first need to calculate the width of each rectangle.
The width of each rectangle is (100 - 0) / 5 = 20.
Now, we will evaluate the marginal cost function at the left endpoints of each rectangle:
MC(0) = 20 - 0.5(0) = 20
MC(20) = 20 - 0.5(20) = 10
MC(40) = 20 - 0.5(40) = 0
MC(60) = 20 - 0.5(60) = -10
MC(80) = 20 - 0.5(80) = -20
Next, multiply each value by the width (20) and sum the results to approximate the variable cost:
Variable cost ≈ 20(20) + 10(20) + 0(20) + (-10)(20) + (-20)(20) = 400 + 200 - 200 - 400 = 0
Finally, add the fixed cost of $200 to the variable cost:
Total cost ≈ $200 + $0 = $200
So, the total cost of producing 100 bar stools using the left-rectangle approximation with five rectangles is approximately $200.
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The enrollment of students at a school is decreasing at a constant rate of 5 % per year what percent remains after one year
Answer: depends but just subtract 5 from the original rate
Step-by-step explanation:
example
100 to 95 to 90 to 85 to 80 and etc.
22. Your choir is taking a trip. The trip has an initial cost of $500, plus $150 for
each student.
a. Estimate how many students must go on the trip for the average cost
per student to fall to $175.
b. What happens to the average cost as more students go on the trip?
a. There would be at least 20 students must go on the trip for the average cost per student to fall to $175.
b. As more students go on the trip, the total cost of the trip increases, but the cost per student decreases.
a. To find out how many students must go on the trip for the average cost per student to fall to $175, we can use the formula:
Total Cost = $500 + $150 x Number of Students
Average Cost per Student = Total Cost / Number of Students
Setting the average cost per student to $175 and solving for the number of students, we get:
$175 = ($500 + $150 x Number of Students) / Number of Students
Multiplying both sides by Number of Students, we get:
$175 x Number of Students = $500 + $150 x Number of Students
Simplifying, we get:
$25 x Number of Students = $500
Number of Students = $500 / $25 = 20
Therefore, at least 20 students must go on the trip for the average cost per student to fall to $175.
b. As more students go on the trip, the total cost of the trip increases, but the cost per student decreases. This is because the fixed cost of $500 is spread over more students, making the cost per student lower. So, as more students go on the trip, the average cost per student will continue to decrease.
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In the diagram below, quadrilateral HIJK is inscribed in circle L. Solve for x and y.
The values of the variables x and y area 42 and 12 respectively
How to determine the valuesWe can see that the quadrilateral that is inscribed in the circle is a parallelogram.
The properties of a parallelogram includes;
The opposite sides of a parallelogram are equalThe opposite angles of a parallelogram are equalThere are adjacent and non- adjacent anglesThen, from the information given, we have that;
x + 35 = 77
Now. collect the like terms, we get;
x = 77 - 35
subtract the values, we have;
x = 42
Also,
4y + 46 = 94
collect the like terms
4y = 94 - 46
4y = 48
Divide by the coefficient of y, we have;
y = 12
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find the area of the circle
with steps pls
x = 3/8.
Starting from the left side of the equation:
2(x+1) - 3(x-2) = 7x + 5
Simplify the expressions in parentheses:
2x + 2 - 3x + 6 = 7x + 5
Combine like terms:
x + 8 = 7x + 5
Subtract 7x from both sides:
-8x + 8 = 5
Subtract 8 from both sides:
-8x = -3
Divide both sides by -8:
x = 3/8
Therefore, the solution to the equation is x = 3/8.
Answer: M=3
Step-by-step explanation:
Given:
tangent =4cm
secant outside of circle = 2 cm
Find:
M is secant inside of circle
Theorem:
Tangent-Secant Theorem => tangent² =(secant outside)(full secant)
Solution and Set up:
4²=(2)(2+M) >Set up from theorem, square 4 and distribute
16=4+4M >subtract 4 from both sides
12 = 4M >divide both sides by 4
M=3
PLEASE HELP ASAP (BRAINLIEST) 39 POINTS
Answer:
3x + 5 = 4x - 40
x = 45
5y - 50 = y
4y = 50
y = 25/2
4. Use a graphing calculator to determine the linear, quadratic, or exponential equation that best represents the d
integer. For exponential, round a to the nearest integer and b to the nearest tenth.
Day Snow Depth (inches)
1
47
234567
Oy=-88e0.5x
Oy=88e 0.5%
Oy 47e 5
Sa
Oy=-47e
29
20
10
7
5
1.5
Mrs. Thomas has two rolls of garden edging that are each 96 inches long.
She wants to make two new flower beds in her back yard. Each flower bed
will be bordered by one roll of the edging. One flower bed will be in the
shape of a quadrilateral. The other will be in the shape of a triangle.
Mrs. Thomas decides to make a scale drawing of each flower bed using a
scale of 1 centimeter = 5 inches. What will be the total length of each roll
of edging in her scale drawings?
The total length of each roll of edging in Mrs. Thomas's scale drawings will be 19.2 cm.
How to find the total length ?To find the total length of each roll of edging in her scale drawings, we need to convert the length from inches to centimeters using the given scale.
To convert the length to centimeters:
( Length in cm ) / ( Length in inches ) = ( 1 cm ) / ( 5 inches )
x / 96 inches = 1 cm / 5 inches
x 5 inches = 96 inches x 1 cm
5x = 96 cm
x = 96 cm / 5
x = 19.2 cm
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Martin collected data from students about whether they played a musical Instrument. The table shows his
results.
Instrument
No Instrument TOTAL
Boys
42
70
112
Girls
48
88
TOTAL
90
110
200
Of the students surveyed, how many played an instrument?
The number of students surveyed who played an instrument is
Out of the students surveyed, 90 played a musical instrument.
To find the total number of students who played a musical instrument, we need to look at the table provided and sum up the number of boys and girls who played an instrument.
From the table, we can see the following:
- Boys who played an instrument: 42
- Girls who played an instrument: 48
To find the total number of students who played a musical instrument, simply add the number of boys and girls together:
Total students who played an instrument = (Number of boys who played an instrument) + (Number of girls who played an instrument)
Total students who played an instrument = 42 (boys) + 48 (girls)
Total students who played an instrument = 90
So, of the students surveyed, 90 played a musical instrument.
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A sequence can be generated by using an=an−1+7, where a1=4 and n is a whole number greater than 1. What are the first 3 terms in the sequence? 7, 11, 15 7, 28, 112 4, 11, 18 4, 28, 196
To generate the sequence, we start with a1 = 4, and then use the formula an = an-1 + 7 for n > 1.
So, to find the first 3 terms of the sequence, we can use the formula:
a2 = a1 + 7 = 4 + 7 = 11
a3 = a2 + 7 = 11 + 7 = 18
The first 3 terms of the sequence are 4, 11, and 18.
So, the answer is 4, 11, 18, which corresponds to the third option.
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The quantity of a substance can be modeled by the function R(t) that satisfies the differential equation dR/dt= -1/5(R – 20). One point on this function is R(2) = 35. Based on this model, use a linear approximation to the graph of Rat t = 2 to estimate the quantity of the substance at t 1.9. \
The estimated quantity of the substance at t = 1.9 is approximately 35.3 units.
To estimate the quantity of the substance at t = 1.9 using linear approximation, we can use the formula:
ΔR ≈ dR/dt * Δt
Given the point R(2) = 35 and the differential equation dR/dt = -1/5(R – 20), we can first find the value of dR/dt at t = 2.
dR/dt(2) = -1/5(R(2) – 20) = -1/5(35 – 20) = -1/5(15) = -3
Now, we can calculate Δt, which is the difference between the given t-value (2) and the desired t-value (1.9):
Δt = 1.9 - 2 = -0.1
Next, we can calculate ΔR using the linear approximation formula:
ΔR ≈ dR/dt * Δt ≈ -3 * (-0.1) = 0.3
Finally, we can estimate the quantity of the substance at t = 1.9 by adding ΔR to the given value of R(2):
R(1.9) ≈ R(2) + ΔR ≈ 35 + 0.3 = 35.3
Therefore, the estimated quantity of the substance at t = 1.9 is approximately 35.3 units.
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The rectangular model is made up of squares each square is a equal size what percent of the model shaded
The percentage of the model is shaded is 45% if the total number of square is 80 option (H) is correct.
What is the percentage?It is defined as the ratio of two numbers expressed in the fraction of 100 parts. It is the measure to compare two data, the % sign is used to express the percentage.
Total No. of squares = 10×8 = 80
Total No. of squares shaded = 36
Percentage of the model is shaded = (36/80)×100
= 0.45×100
= 45%
Thus, the percentage of the model is shaded is 45% if the total number of square is 80 option (H) is correct.
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Full Question:
Although part of your question is missing, you might be referring to this full question:
See attached image.
The table shows the number of beads used to make a necklace.
Ginger wants to make a smaller necklace using the same ratio of pink to white beads.
How many different necklaces could Ginger make?
How do you know?
Answer:
The Answer is 5
Step-by-step explanation:
Pink beads : White beads
30 : 35
( 30 / 5 ) : ( 35 / 5 )
6 : 7
To find the number of beads, You divide the number of pink beads available by the number of pink beads in the ratio:
= 30 / 6
= 5 necklaces
hope this helps :)
you start new workings.
It takes 30 minutes for 5 old printers to produce a batch of comic books.
It takes 18 minutes for 4 new printers to produce an identical batch of
comic books.
a) Which of the following would produce a batch of comic books in less
time:
6 old printers or 2 new printers?
b) How much less time would this take?
It should be noted that with the equations 6 old printers would produce a batch of comic books in less time.
Using 2 new printers is 27 minutes faster than using 6 old printers.
How to solve the information6 old printers would produce 6*(1/150) = 2/75 of a batch per minute.
2 new printers would produce 2*(1/72) = 1/36 of a batch per minute.
(5/6) * t = 30
(4/2) * t' = 18
Solving for t and t', we get:
t = 36 minutes
t' = 9 minutes
Therefore, using 6 old printers would take 36 minutes to produce a batch of comic books, while using 2 new printers would take only 9 minutes. Using 2 new printers is 27 minutes faster than using 6 old printers.
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Casey is going to wear a gray sportscoat and is trying to decide what tie he should wear to work. In his closet, he has 22 ties, 13 of which he feels go well with the sportscoat. If Casey selects one tie at random, determine the probability and the odds of the tie going well or not going well with the sportscoat.
The probability the tie goes well with the jacket is?
The probability the tie will not go well with the jacket is?
The odds against the tie going well with the jacket is?
(Simplify your answer. Type an integer or a fraction.)
The odds in favor of the tie going well with the jacket is?
(Simplify your answer. Type a ratio using a colon.)
This is absolute value so if u dont know just leave if u steal points im reporting
Answer:
k = - 1/3------------------------
We know the property of an absolute value: it is never negative.
Hence the given inequality is equivalent to below equation:
(3k + 1)/74 = 03k + 1 = 03k = - 1k = - 1/3This is the only solution.
When we solve for K in the inequality, 0 ≥ |(3K + 1) / 74|, the result obtained is -1/3
How do i solve 0 ≥ |(3K + 1) / 74|?We can solve the expression 0 ≥ |(3K + 1) / 74| as illustrated below:
0 ≥ |(3K + 1) / 74|
Remove the absolute sign
0 ≥ (3K + 1) / 74
Cross multiply
0 ≥ (3K + 1) / 74
0 × 74 ≥ 3K + 1
0 ≥ 3K + 1
Collect like terms
0 - 1 ≥ 3K
-1 ≥ 3K
Divide both sides by 3
-1/3 ≥ K
K = -1/3
Thus, we can conclude from the above calculation that the value of K in the inequality, 0 ≥ |(3K + 1) / 74| is -1/3
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Find the Zeros of each quadratic equation below by graphing
bro idrk but I think
Answer: The correct option is
(A) {-1, -5}.
Step-by-step explanation: We are given to find the zeroes of the quadratic function graphed in the figure shown.
We know that
the zeroes of a quadratic function f(x) are the value of x for which f(x) is equal to zero.
That is, the points on the graph where the curve crosses the X-axis.
From the graph, we note that the curve of the function crosses the X-axis at the points x = 1 and x = -5.
Therefore, the zeroes of the given function are x = -1 an x = -5.
Thus, option (A) is CORRECT.
In an isosceles triangle, the measure of a base angle is 65. Find the number of degrees in the measure of the vertex angle
The number of degrees in the measure of the vertex angle is 50 degrees.
An isosceles triangle has two equal sides and two equal base angles. In your question, the measure of a base angle is 65 degrees. To find the measure of the vertex angle, we'll use the fact that the sum of angles in any triangle is always 180 degrees.
Since both base angles are equal, their combined measure is 2 * 65 = 130 degrees. Now, we subtract the sum of the base angles from the total angle measure of the triangle:
180 degrees (total angle measure) - 130 degrees (sum of base angles) = 50 degrees.
So, the measure of the vertex angle in the isosceles triangle is 50 degrees. In summary, when given the measure of a base angle in an isosceles triangle, we can use the triangle's angle sum property to find the measure of the vertex angle.
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Does anyone know how to finish the coding section on lesson 4 unit 7 parameter and return investigate for 2 and 3? (code. org) (number crunch)
In the coding section of Lesson 4, Unit 7 on Code.org, you will be working with parameters and return statements to create a Number Crunch function for 2 and 3. To complete this task, follow these steps:
1. Define a function called 'numberCrunch' that takes two parameters: 'num1' and 'num2'.
2. Inside the function, perform the desired calculations using 'num1' and 'num2' (e.g., addition, multiplication, etc.).
3. Use a return statement to return the result of the calculation.
4. Call the 'numberCrunch' function with the values 2 and 3 as arguments, and store the result in a variable (e.g., 'result').
5. Display the result using a console.log or any other preferred method.
Here's an example using addition as the operation:
```javascript
function numberCrunch(num1, num2) {
return num1 + num2;
}
var result = numberCrunch(2, 3);
console.log(result);
```
Modify the code according to the specific requirements of the lesson and the desired operation.
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trapezoid ABCD is similar to trapezoid EFGH what is the value of M
The value of M is 4.
The value of M represents the length of the segment that connects the midpoints of the non-parallel sides of trapezoid ABCD. To find the value of M, we can use the fact that the trapezoids are similar.
Now, let's label the points where MN intersects sides BC and FG as P and Q, respectively. We can use the fact that MN is parallel to sides BC and FG to show that triangles BMP and FQN are similar to trapezoids ABCD and EFGH, respectively.
Therefore, we can write:
BM/AB = MP/CD = k
and
FQ/EF = QN/GH = k
Since we know that AB/EF = k, we can substitute this into the first equation to get:
BM/EF = MP/GH
Similarly, we can substitute FQ/EF = k into the second equation to get:
FQ/EF = QN/GH
Now, let's combine these two equations to get:
(BM + FQ)/EF = (MP + QN)/GH
But we know that BM + FQ = EF, and MP + QN = GH. Therefore, we can simplify the equation to get:
EF/EF = GH/GH
Or simply:
1 = 1
This means that our calculations are correct, and that we can use the ratio k to find the value of M. Specifically, since MN is parallel to AB and CD, we know that the length of MN is equal to half the difference between the lengths of AB and CD. Therefore, we can write:
M = (1/2)(AB - CD)/k
When we apply the values on it, then we get,
M = (1/2) (56 - 48) / 1
M = (1/2) x 8 = 4
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The table shows the average cost of gasoline in the United States in dollars per gallon for the given years.
Year
1995 1996 2000 2001 2005 2006 2010 2011 2013 2014
Price per gallon ($) ( 1. 13) (1. 14) (1. 33) (1. 49) (1. 88) (2. 36) (2. 77) (3. 15) (3. 39) (3. 40)
(a) Write the least squares regression equation that models the data. Let x = time in years since
1995 and let y = price per gallon.
(b) Use the equation to estimate the price per gallon in 2030. Show your Work
(a) The least squares regression equation that models the data is: y = 0.091x + 1.125, where x is the time in years since 1995 and y is the price per gallon.
(b) To estimate the price per gallon in 2030, we need to find the value of y when x = 35 (2030 - 1995). Substituting x = 35 in the equation, we get: y = 0.091(35) + 1.125 = 4.22 dollars per gallon. Therefore, the estimated price per gallon in 2030 is 4.22 dollars.
(a) The least squares regression equation is used to model the relationship between two variables, in this case, time and gasoline price. It calculates the line that best fits the data points and can be used to estimate the value of the dependent variable (gasoline price) for any given value of the independent variable (time).
(b) To estimate the price per gallon in 2030, we simply need to substitute the value of x = 35 in the equation and solve for y. The equation shows that the price per gallon increases by 9.1 cents every year since 1995.
However, this is just an estimate based on the data available, and other factors such as changes in supply and demand, government policies, and global events can also influence gasoline prices in the future.
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