MATHEMATICS HIGH SCHOOL

5 students participated in a push-up competition.The amount of push-ups each student completed is listed: 12, 7, 10, 11,5
What was the mean number of push-ups?

Answers

Answer 1
Answer:

Answer: 9

Step-by-step explanation:

Formula : Mean = \frac{\text{Sum of observations}}{\text{Number of observaions}}

Given: 5 students participated in a push-up competition.

The amount of push-ups each student completed is listed: 12, 7, 10, 11,5.

Mean = (12+7+10+77+5)/(5)

=(45)/(5)=9

Hence, the mean number of push-ups = 9

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a dog weighs 44 pounds and the veterinarian thinks i needs to lose 7 pounds. Milkala wrote the equation x+7 to represent the situation. Kirk wrote the equation 44- x = 7. Which equation is correct? can you write another equation that represents the situation?

Answers

so assuming that you meant that the dog needs to lose 7 pounds
the equation should be
44-7=x
where x represents the dog's ideal weight

x+7 means 7 more pounds
44-x=7 means that 44 minus the ideal weight is 7
this can be reweiten as 44-7=x so this is correct


Kirk is correct
another equation is 44-7=x

Hmmm I don't think either is correct.

So he weighs 44 pounds, and needs to lose 7 pounds

44 - 7 = x

where x is the dog's new weight.

One year the attendance at the SuperBowl was 79,401 the following year, the attendance was 89,916 .Use words to explain the relationship between the digit 9 in 79,401 and the digit 9 in 85,916.

Answers

The 9 in 79,401 is in the thousands place and the 9 in 85,916 is in the hundreds place
The 9 in the 79 401 is in the thousand digit place value while the 9 in the 85 916 is in the hundred digit place value.

Is a square a cross section of a rectangular and triangular prism?

Answers

Answer:

No, a square is NOT the cross section of a rectangular and triangular prism.

Step-by-step explanation:

Prisms have a uniform cross-section and are named after their cross-section. Hence, the cross-section of a rectangular prism is a rectangle and the cross-section of a triangular prism is a triangle. The only prism with a square cross-section is a cube.

Please someone help me to prove this. ​

Answers

Answer:  see proof below

Step-by-step explanation:

Use the Power Reducing Identity:  sin² Ф = (1 - cos 2Ф)/2

Use the Double Angle Identity:  sin 2Ф = 2 sin Ф · cos Ф

Use the following Sum to Product Identities:

\sin x - \sin y = 2\cos \bigg((x+y)/(2)\bigg)\sin \bigg((x-y)/(2)\bigg)\n\n\n\cos x - \cos y = -2\sin \bigg((x+y)/(2)\bigg)\sin \bigg((x-y)/(2)\bigg)

Proof LHS →  RHS

\text{LHS:}\qquad \qquad \qquad (\sin^2A-\sin^2B)/(\sin A\cos A-\sin B \cos B)

\text{Power Reducing:}\qquad (\bigg((1-\cos 2A)/(2)\bigg)-\bigg((1-\cos 2B)/(2)\bigg))/(\sin A \cos A-\sin B\cos B)

\text{Half-Angle:}\qquad \qquad (\bigg((1-\cos 2A)/(2)\bigg)-\bigg((1-\cos 2B)/(2)\bigg))/((1)/(2)\bigg(\sin 2A-\sin 2B\bigg))

\text{Simplify:}\qquad \qquad (1-\cos 2A-1+\cos 2B)/(\sin 2A-\sin 2B)\n\n\n.\qquad \qquad \qquad =(-\cos 2A+\cos 2B)/(\sin 2A - \sin 2B)\n\n\n.\qquad \qquad \qquad =(\cos 2B-\cos 2A)/(\sin 2A-\sin 2B)

\text{Sum to Product:}\qquad \qquad (-2\sin \bigg((2B+2A)/(2)\bigg)\sin \bigg((2B-2A)/(2)\bigg))/(2\cos \bigg((2A+2B)/(2)\bigg)\sin \bigg((2A-2B)/(2)\bigg))

\text{Simplify:}\qquad \qquad (-2\sin (A + B)\cdot \sin (-[A - B]))/(2\cos (A + B) \cdot \sin (A - B))

\text{Co-function:}\qquad \qquad (2\sin (A + B)\cdot \sin (A - B))/(2\cos (A + B) \cdot \sin (A - B))

\text{Simplify:}\qquad \qquad \quad (\cos (A+B))/(\sin (A+B))\n\n\n.\qquad \qquad \qquad \quad =\tan (A+B)

LHS = RHS:    tan (A + B) = tan (A + B)    \checkmark

Answer:

We know that,

\dag\bf\:sin^2A=(1-cos2A)/(2)

\dag\bf\:sin2A=2sinA\:cosA

___________________________________

Now, Let's solve !

\leadsto\:\bf(sin^2A-sin^2B)/(sinA\:cosA-sinB\:cosB)

\leadsto\:\sf((1-cos2A)/(2)-(1-cos2B)/(2))/((2sinA\:cosA)/(2)-(2sinB\:cosB)/(2))

\leadsto\:\sf(1-cos2A-1+cos2B)/(sin2A-sin2B)

\leadsto\:\sf(2sin(2A+2B)/(2)\:sin(2A-2B)/(2))/(2sin(2A-2B)/(2)\:cos(2A+2B)/(2))

\leadsto\:\sf(sin(A+B))/(cos(A+B))

\leadsto\:\bf{tan(A+B)}

Alex has 48 stickers. This is 6 times the 4. Number of stickers Max has. How many stickers does Max have?

Answers

Assuming you mean:


Alex has 48 stickers. This is 6 times number of stickers Max has. How many stickers does Max have?


48 divided by 6 gives you 8.

Find the measure of each interior angle of a regular decagon.The measure of each interior angle is
°.

Answers

Answer:

The measure of each interior angle is 144°

Step-by-step explanation:
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