there are 500 seventh grade students at heritage middle school. sixty percent of them play a musical instrument. how many seventh grade students play a musical instrument

To compare 29 feet and 9 yards, convert 9 yards to feet, which equals 27 feet. Since 29 feet is greater than 27 feet, 29 feet is longer.

To determine which length is longer between 29 feet and 9 yards, we need to convert one of the measurements to the same unit. We know that 1 yard is equal to 3 feet. Therefore, to convert 9 yards to feet:

Comparing the two lengths, 29 feet is longer than 27 feet.

Thus, 29 feet is the longer length.

The probability that your flight will arrive on time is 0.6, or 60%.

To calculate the probability that your flight will arrive on time, we can use the concept of conditional probability. Let A represent the event of good weather and B represent the event of the flight arriving on time. We know P(A) = 0.6, P(B|A) = 0.8, and P(B|A') = 0.3 (where A' represents bad weather). We can use the formula for conditional probability: P(B) = P(A) * P(B|A) + P(A') * P(B|A'). Substituting the given values, we have P(B) = 0.6 * 0.8 + 0.4 * 0.3 = 0.48 + 0.12 = 0.6. Therefore, the probability that your flight will arrive on time is 0.6, or 60%.

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Answer:

92/27 and 58/27 for n=3 and 13/4 and 9/4 for n=4

Step-by-step explanation:

n = 3: First let’s find ∆x:

∆x = (b − a)/n = 1 − (−1)3 = 2/3

We will have three intervals: −1 ≤ x ≤ −1/3, −1/3 ≤ x ≤1/3, 1/3 ≤ x ≤ 1.

Upper sum: On the first interval, the highest point occurs at f(−1) = 2. On the second interval, the highest point occurs at f(1/3) = f(−1/3) = 1 + ( 1/3)^2=1 + 1/9 = 10/9

On the third interval, the highest point occurs at f(1) = 2. So A ≈ A upper = 3Σ i=1 f(xi)∆x = [f(−1) + f (1/3)+ f(1)]∆x = (2 +10/9+ 2)*2/3 = 92/27

Lower sum: On the first interval, the lowest point occurs at f(−1/3) = 10/9

On the second interval, the lowest point occurs at f(0) = 1. On the third interval, the lowest point occurs at f(1/3) = 10/9. SoA ≈ A lower =3Σ i=1 f(xi)∆x = f(−1/3) + f(0) + f(1/3) . ∆x = (10/9+ 1 +10/9)· 2/3= 58/27

Apply the same technique for n=4

its 1, 3, and 5 I think

Answer:

1) False

2) True

3) True

4) False

5) True

Step-by-step explanation:

We are given the following information in the question:

1) False

The sum of measures of interior angle is given by:

[tex](n-2)\times 180^\circ\\\text{where n is the number of sides in regular polygon}[/tex]

Putting n = 5

Sum of interior\r angle = [tex](5-2)\times 180 = 3\times 180 = 540^\circ[/tex]

2) True

Each interior angle measure =

[tex]\displaystyle\frac{\text{Sum of interior angles}}{\text{Number of sides}} = \frac{540}{5} = 108^\circ[/tex]

3) True

All the angles in a regular polygon are equal.

4) False

The polygon is a regular pentagon.

5) True

The sum of measures of interior angle is given by:

[tex]180^\circ(5-2)[/tex]

Answer:

so on the fourth bounce the ball will reach a height of 8 feet

Step-by-step explanation:

There is a common ratio of 2/3 between the height of the ball at each bounce so the bounce height from a geometric sequence 27,18,12 two-thirds of 12 is 8 so on the fourth bounce the ball will reach a height of 8 feet

The original volume equation looks like this: V = 1/3 * h * (x^2) 
After the side is reduced by 0.002, the new volume would look like V1 = 1/3 * h * (x-0.002) ^ 2 

Then we have: 
V-V1 = 1/3*h*(x^2) - 1/3*h*(x – 0.002) ^2 

= 1/3 * h *(x^2 - (x – 0.002) ^2) 

= 1/3 * h * (0.004x - 0.00004) 

The rate of decreasing is computed by:

(V-V1)/V * 100% = [1/3 * h *(0.004x - 0.00004)] / [1/3 * h * (x ^ 2)] * 100% this would be equal to (0.004x - 0.00004) / (x^2) * 100% 

So replace x by 200, you’ll get:

(0.004(200) - 0.00004) / (200^2) * 100% 

= 0.001999% is the rate of decreasing.

Answer:

10°

Step-by-step explanation:

To find this, we look at the sides of the triangle that we are given and their position in relation to ∠C.

AB is opposite ∠C and AC is adjacent to ∠C.

The ratio of opposite/adjacent is the ratio of tangent.  This gives us the equation

tan C = 2/11

To solve this for C, we take the inverse tangent of each side:

tan⁻¹(tan C) = tan⁻¹(2/11)

C = 10.305 ≈ 10°

The measure of the angle ∠c will be 10°.

The branch of mathematics that sets up a relationship between the sides and the angles of the right-angle triangle is termed trigonometry.

The trigonometric functions, also known as circular, angle, or goniometric functions in mathematics, are real functions that link the angle of a right-angled triangle to the ratios of its two side lengths.

To find this, we look at the sides of the triangle that we are given and their position in relation to ∠C.

AB is opposite ∠C and AC is adjacent to ∠C.

The ratio of opposite/adjacent is the ratio of a tangent.  This gives us the equation

tan C = 2/11

To solve this for C, we take the inverse tangent of each side:

tan⁻¹(tan C) = tan⁻¹(2/11)

C = 10.305 ≈ 10°

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The value of c such that the line y = 9/4 x + 9 is tangent to the curve y = c x is 9/4. This is because a line is tangent to a curve when it touches the curve at exactly one point, hence the slope of the given line (9/4) will be equal to the value of c, which is the slope of the curve.

The problem asks us to find the value of c such that the line y = 9/4 x + 9 is tangent to the curve y = c x. A line is tangent to a curve when it touches the curve at exactly one point. In this context, the slope of the given line (9/4) will be equal to the value of c since in the line equation y = c x, c is the slope. So the value of c is 9/4.

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The x-coordinate of the point is changing at a rate of [tex]\( 6 \text{ cm/s} \)[/tex].

To determine how fast the x-coordinate of the particle is changing at the instant it reaches the point (4, 2), we start with the equation of the hyperbola and apply the related rates method.

Given:

[tex]\[ xy = 8 \][/tex]

Differentiate both sides of the equation with respect to time [tex]\( t \)[/tex]:

[tex]\[ \frac{d}{dt}(xy) = \frac{d}{dt}(8) \][/tex]

Using the product rule on the left side:

[tex]\[ x \frac{dy}{dt} + y \frac{dx}{dt} = 0 \][/tex]

We need to find [tex]\(\frac{dx}{dt}\)[/tex] when the particle is at the point [tex]\((4, 2)\)[/tex] and [tex]\( \frac{dy}{dt} = -3 \text{ cm/s} \)[/tex] (since the y-coordinate is decreasing).

Substitute [tex]\( x = 4 \)[/tex], [tex]\( y = 2 \)[/tex], and [tex]\( \frac{dy}{dt} = -3 \)[/tex] into the differentiated equation:

[tex]\[ 4 \left( -3 \right) + 2 \frac{dx}{dt} = 0 \][/tex]

Simplify and solve for [tex]\( \frac{dx}{dt} \)[/tex]:

[tex]\[ -12 + 2 \frac{dx}{dt} = 0 \][/tex]

[tex]\[ 2 \frac{dx}{dt} = 12 \][/tex]

[tex]\[ \frac{dx}{dt} = 6 \][/tex]

Answer:

30

Step-by-step explanation:

A bundle of 3 adult tickets and 1 child ticket sells for $32.80, so there were ...

... $984/$32.80 = 30 . . . . bundles sold.

The number of child tickets sold was 30.

_____

Using an equation

Let c represent the number of child tickets sold. Then 3c is the number of adult tickets sold. The total revenue is ...

... 5.80c + 9.00·(3c) = 984.00

... 32.80c = 984.00 . . . . . . . . . . simplify

... c = 984.00/32.80 = 30 . . . . . divide by the coefficient of c

The required simplified value of the g(h(3)) is given as 59.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
g(x) = x³ - 5 and h(x) = 2x - 2

h(3) = 2(3) - 2
h(3) = 4

g(h(3)) = 4³ - 5
         = 64 - 5
         = 59

Thus, the required simplified value of the g(h(3)) is given as 59.

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85 divided by 5 equals 17.

To find the answer to 85 divided by 5 using the distributive property, we break 85 into simpler numbers that are easier to divide by 5. For example:

Step 1: Write 85 as a sum of numbers that can easily be divided by 5:
85 = 50 + 35

Step 2: Divide each part by 5:
50 ÷ 5 = 10
35 ÷ 5 = 7

Step 3: Add the results:
10 + 7 = 17

Therefore, 85 divided by 5 equals 17.

Final answer:

The baseball team needs to play 7 more games to exceed its goal of 84 home runs, based on their current average of 7 home runs per game.

Explanation:

The baseball team has hit 35 home runs and wants to hit more than 84. To find how many more games it will take, we first calculate the total number of home runs needed to surpass 84, which is 84 - 35 = 49 home runs. Since the team averages 7 home runs per game, we divide the remaining home runs needed by the average per game to find x, the number of games needed: 49 home runs / 7 home runs per game = 7 games.

Therefore, the baseball team needs to play 7 more games to reach its goal, assuming the average stays constant.

Answer:2/3

Step-by-step explanation:

The speed of thirty-four thousand centimeters per second in scientific notation is 3.4  x 10^2 meters per second, after converting centimeters to meters.

The speed of thirty-four thousand centimeters per second can be expressed in scientific notation by first converting it to the base unit of meters per second (since one meter is equal to one hundred centimeters) and then expressing it in the form of a significant figure followed by the power of 10.

First, convert centimeters to meters:

Now, express this in scientific notation:

This shows the speed in scientific notation with the unit meters per second, which is a combination of two SI units.