The record for the boston marathon's weelchair division is 1 hour, 18 minutes, and 27 seconds.The boston Marathon is 26.2 miles long.What's the average speed of the record winner of the weelchair division? At this rate about how long would it take this competitor to complete a 30-mile race?

Final answer:

To multiply 6 and 42 using the distributive property, you break down 42 into 40 and 2, then multiply each part by 6 and add them together to get 252.

Explanation:

The distributive property in mathematics allows us to multiply a sum by multiplying each addend separately and then adding the products. April wants to multiply 6 by 42 using the distributive property. The correct way to do this using the distributive property is to break down 42 into 40 and 2, then multiply each by 6 and add the results. Therefore, the correct number sentence using the distributive property is:

6 × (40 + 2) = (6 × 40) + (6 × 2)

This simplifies to:

(6 × 40) + (6 × 2) = 240 + 12 = 252

So, 6 × 42 equals 252 when applied through distributive property.

Final answer:

The height of the plane above the ground after traveling 3,000 meters at a 15° angle of elevation is approximately 776.4 meters. This is calculated using the sine function: height = 3,000 m × sin(15°).

Explanation:

To find the height of the plane above the ground after taking off at an angle of elevation of 15° and traveling for 3,000 meters, we can use trigonometric functions. Specifically, the sine function relates the opposite side of a right-angled triangle (in this case, the height above ground) to the hypotenuse (the distance traveled by the plane).

The sine of an angle in a right triangle is equal to the length of the opposite side divided by the length of the hypotenuse. The formula is:

height = hypotenuse × sin(angle)

Here, the hypotenuse is the distance traveled by the plane (3,000 m), and the angle is 15°. Thus, the calculation would be:

height = 3,000 m × sin(15°)

We can calculate the sine of 15° using a calculator.

height = 3,000 m × 0.2588 (approximately)

height = 776.4 m (approximately)

Therefore, the plane is approximately 776.4 meters above the ground.

The value of the digit 5 in the number 75 is 5. This is because in the number 75, 5 is in the ones place and thus represents 5.

The value of the digit 5 in the number 75 is actually 5 itself. In any two-digit number like 75, the place values are tens and ones. The first digit represents the tens place and the second represents the ones place. Therefore, in 75, the digit 7 represents 70 (as it is in the tens place) and the digit 5 represents 5 (as it is in the ones place). Hence, the value of the digit 5 in the number 75 is 5.

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Answer:

The remainder is 100.

Step-by-step explanation:

The divisor is [tex]x^2-8[/tex].

Dividend is [tex]x^4+36[/tex].

We have to find the remainder of

[tex]\frac{x^4+36}{x^2-8}[/tex]

It can be written as

[tex]\frac{x^4+36}{x^2-8}=\frac{x^4-64+64+36}{x^2-8}[/tex]

[tex]\frac{x^4+36}{x^2-8}=\frac{(x^4-64)+100}{x^2-8}[/tex]

[tex]\frac{x^4+36}{x^2-8}=\frac{(x^4-64)}{x^2-8}+\frac{100}{x^2-8}[/tex]

[tex]\frac{x^4+36}{x^2-8}=\frac{(x^2-8)(x^2+8)}{x^2-8}+\frac{100}{x^2-8}[/tex]       [tex][\because a^2-b^2=(a-b)(a+b)][/tex]

[tex]\frac{x^4+36}{x^2-8}=x^2+8+\frac{100}{x^2-8}[/tex]

Therefore the remainder is 100.

Answer:

the answer is actually is $2,258.33

Step-by-step explanation:

Answer x= 32

Imagine math

The result is g'(x) = -2x.

Given g(x) =[tex]7 - x^2.[/tex]

Evaluate g(x+h)
=[tex]7 - (x+h)^2[/tex]
= [tex]7 - x^2 - 2xh - h^2.[/tex]

Compute g(x+h) - g(x)
=[tex][7 - x^2 - 2xh - h^2] - [7 - x^2][/tex]
= [tex]-2xh - h^2.[/tex]

Divide by h:
(g(x+h) - g(x)) / h
= [tex](-2xh - h^2) / h[/tex]
= -2x - h.

Take the Limit as h Approaches 0: As h approaches 0, the expression -2x - h approaches -2x.
Therefore, g'(x) = -2x.

So, the derivative of g(x) when h = 0 is -2x.

Answer:

(C)The two triangles may be congruent, but additional measurements are needed.

Step-by-step explanation:

It is given that QRS and FGH each have two sides that are 9 mm long that is QR=QS=9mm and FG=FH=9mm.

Thus, both the triangles that are QRS and FGH becomes the isosceles triangles.

Now, in order to prove that ΔQRS≅ΔFGH, we require more measurements as congruency can be proved only by SAS, SSS, ASA or AAA that is by using all the three sides of triangle or by using two sides one angle or by using two angles and one side or by using all the three angles.

Therefore, we need remaining side or angle in order to prove that ΔQRS is congruent to ΔFGH.

Hence,  option (C) is correct.

To find out how much carpet Maria needs for her square-shaped bedroom with each side measuring 12 feet, we can calculate the area of the room by using the exponential expression 12².

To find out how much carpet Maria needs for her square-shaped bedroom, we need to calculate the area of the room. Since each side of the square is 12 feet, we can use an exponential expression to find the area. The exponential expression is 12², which simplifies to 144 square feet.

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Answer:

25,35

Step-by-step explanation:

Part A: There are five buttons in all in all in the given item. The item above can be answered through the fundamental principles of counting.  

There are 5 items to choose from during the first pick. Because the shape can be returned and picked again, there are also 5 items to choose from in the second pick. Multiplying them,

                              n = 5 x 5 = 25

Therefore, the sample size for the compound event is equal to 25.

Part B: The same concept can be used in this part of the item; however, instead of 5 there are 6 buttons to choose from.

                             n = 6 x 6 = 36

Hence, the sample size of this picking process is 36.

Answer:2,2,2

Step-by-step explanation: I just took the test and got it right.

 tax gets added to the price of the camera

 so the equation is:

x + 0.07x = 45; x = $42.06

The coordinates of point P that partitions the segment AB in the ratio 1:1 are (4, -1). The calculation is done using the segment partition formula.

To solve this problem, we use the formula for finding the point that divides a line segment into a given ratio. The formula is P(x, y) = ((x1*m2 + x2*m1)/(m1+m2), (y1*m2 + y2*m1)/(m1+m2)). Here, points A and B are (13,1) and (-5,-3) respectively, and the ratio m1:m2 is 1:1.

So applying the formula, we have P(x, y) = ((13*1 + -5*1) / (1+1), (1*1 + -3*1) / (1+1)) = (8/2, -2/2) = (4, -1).

So, the coordinates of point P that partitions the segment AB in the ratio 1:1 are (4, -1).

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To find the coordinates of point P that bisects the segment AB in the ratio 1:1, we use the midpoint formula. Substituting the values of points A(13,1) and B(-5,-3) into the formula gives us P(4,-1).

The student wants to find the coordinates of point P that would bisect the line segment AB in a 1:1 ratio. Since the ratio is 1:1, point P is the midpoint of the segment. To find the coordinates of the midpoint P, we need to calculate the average of the x-coordinates and the y-coordinates of points A and B.

Using the formula of a midpoint, M(x, y) = [ (x1+x2)/2 , (y1+y2)/2 ], let's substitute the coordinates of points A(13,1) and B(-5,-3).

P(x, y) = [ (13-5)/2 , (1-3)/2 ]

Therefore, the coordinates of point P that partitions the segment AB in the ratio 1:1 is P(4, -1).

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Answer:

[tex]cos(tan^{-1}(0))=1[/tex]

Step-by-step explanation:

Evaluate cos(tan^-1 0)

[tex]cos(tan^{-1}(0))[/tex]

We know that tan(0)=0

tan (0 degree)=0

[tex]tan^{-1}(0)=0[/tex]

Replace it in our problem

[tex]cos(tan^{-1}(0))[/tex]

[tex]cos(0)[/tex]

At 0 degree the cos value is 1

So co(0)=1

[tex]cos(tan^{-1}(0))=1[/tex]

Answer:

the correct answer is 1

2.50 / 1.00 = 250% gross margin percentage

1.00 + 0.25 = 1.25

1.25 x 250% = 1.25 x 2.5 = 3.125

 the unit selling price needs to be increased by 0.63 cents  to $3.13

Answer:

D infinitely many  

Step-by-step explanation:

They lines never cross

The rate of change of the function f(x)=(-4/5)x+8 is -4/5, as this is the slope of the linear function which is constant.

To find the rate of change of the function f(x)=-4/5x+8, we can identify the coefficient of the x term, which in this case is -4/5. This coefficient represents the slope of the line, which is the rate of change of the function.

Hence, the rate of change of the function f(x) is -4/5. No additional calculations are needed because the function is linear, and its rate of change is constant.

In terms of calculus, for linear functions, the rate of change is equal to the derivative, which for f(x)=-4/5x+8 is -4/5.

Total hours= 2.2+3.5=5.7

Total earned = 5.7 x $7.50= $42.75