The cafeteria at Midtown Middle School surveyed 575 students about their favorite food. Find the number of students that responded for each of the following.

Fruit = 24%

Write your answer like this
Answer __________

tan(41π/36) can be written in terms of the tangent of a positive acute angle as (tan((1/9)π) + tan((37/36)π)) / (1 - tan((1/9)π)tan((37/36)π))

To express tan(41π/36) in terms of the tangent of a positive acute angle, we need to find an angle within the range of 0 to π/2 that has the same tangent value.

First, let's simplify 41π/36 to its equivalent angle within one full revolution (2π):

41π/36 = 40π/36 + π/36 = (10/9)π + (1/36)π

Now, we can rewrite the angle as:

tan(41π/36) = tan((10/9)π + (1/36)π)

Next, we'll use the tangent addition formula, which states that:

tan(A + B) = (tan(A) + tan(B)) / (1 - tan(A)tan(B))

In this case, A = (10/9)π and B = (1/36)π.

tan(41π/36) = tan((10/9)π + (1/36)π) = (tan((10/9)π) + tan((1/36)π)) / (1 - tan((10/9)π)tan((1/36)π))

Now, we need to find the tangent values of (10/9)π and (1/36)π. Since tangent has a periodicity of π, we can subtract or add multiples of π to get equivalent angles within the range of 0 to π/2.

For (10/9)π, we can subtract π to get an equivalent angle within the range:

(10/9)π - π = (1/9)π

Similarly, for (1/36)π, we can add π to get an equivalent angle:

(1/36)π + π = (37/36)π

Now, we can rewrite the expression as:

tan(41π/36) = (tan((1/9)π) + tan((37/36)π)) / (1 - tan((1/9)π)tan((37/36)π))

Since we are looking for an angle within the range of 0 to π/2, we can further simplify the expression as:

tan(41π/36) = (tan((1/9)π) + tan((37/36)π)) / (1 - tan((1/9)π)tan((37/36)π))

Therefore, tan(41π/36) can be written in terms of the tangent of a positive acute angle as the expression given above.

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Answer

well first u put it as 2/2 which is 2 then you have to times it by 69 which is 138 then divide that by 6.5 which is 21

Step-by-step explanation:

actual answer is 4 if you were serious about this

Answer: 4

Step-by-step explanation:

Use your hands:

2 on one hand

2 on the other hand

Put them together which is 4

To find the volume of the given solid using polar coordinates, we integrate the function over the appropriate range of values for the radial coordinate and the angle.

The given solid consists of a cone and a ring in the xy-plane. The cone is defined by the equation z = √(x² + y²), which represents a right circular cone with its vertex at the origin and opening upwards. The ring is defined by the inequality 1 ≤ x² + y² ≤ 64, which represents a circular region centered at the origin with an inner radius of 1 unit and an outer radius of 8 units.

To evaluate the volume using polar coordinates, we can express the equations in terms of the radial coordinate (r) and the angle (θ). In polar coordinates, the cone equation becomes z = r, and the ring equation becomes 1 ≤ r² ≤ 64. To set up the integral, we need to determine the range of values for r and θ. For the radial coordinate, r ranges from 1 to 8, as that corresponds to the region defined by the ring. For the angle θ, we can integrate from 0 to 2π, covering a full revolution around the origin.

The volume integral is then given by V = ∫∫∫ r dz dr dθ over the region defined by 1 ≤ r² ≤ 64 and 0 ≤ θ ≤ 2π. By evaluating this triple integral, we can find the volume of the solid.

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We would expect to roll an even number (2, 4, or 6) approximately 75 times in 150 trials,

Assuming that the rolls are random and fair, the probability of rolling an even number (2, 4, or 6) on a single roll is 1/2, since there are three even numbers out of six possible outcomes. Therefore, the number of times we would expect to roll an even number in 150 trials can be calculated using the expected value formula:

Expected value = probability of success * number of trials

In this case, the probability of rolling an even number in a single trial is 1/2, and the number of trials is 150. Therefore, the expected number of times we would roll an even number is:

Expected value = (1/2) * 150

Expected value = 75

assuming that the rolls are random, fair, and independent of each other. It is important to note that this is an expected value and the actual number of times we roll an even number may vary from this value due to the randomness of the process.

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let the pounds be 12

the cost = 12× 6

= 72 dollars

Step-by-step explanation:

\((A-B) = ( - 2, \: - 2, \: - 2, \: - 2)\)

Answer:

-850 m

Step-by-step explanation:

New position = - 1300 +450 = - 850 m

Answer:

- 850 m

Step-by-step explanation:

a submarine is positioned 1300 m below sea level => - 1300 m

it ascends 450 m =>

- 1300 m + 450 m =

= - (1300 - 450)

= - 850 m

y=-5x-44

Step-by-step explanation:

5x+y=13 passes through (15,31)

rearrange the equation to y=mx+c

5x+y=13

y=-5x+13

substitute the points (15,31)

y=5x+c

31=5(15)+c

31=75+c

-44=c

y=-5x-44

Can be written as 5x+y=-44

Since, m and n are prime positive number. Therefore,

               m + n = 18 + 19 =037

The polynomial we are given is rather complicated, so we could use Rational Root Theorem to turn the given polynomial into a degree-2 polynomial. With Rational Root Theorem, x = 1, -1, 2, -2 are all possible rational roots. Upon plugging these roots into the polynomial, x = -2 and x = 1 make the polynomial equal 0 and thus, they are roots that we can factor out.

The polynomial becomes:

(x - 1)(x + 2)(x^2 + (2a - 1)x + 1)

Since we know 1 and -2 are real numbers, we only need to focus on the quadratic.

We should set the discriminant of the quadratic greater than or equal to 0.

(2a - 1)^2 - 4 ≥ 0.

This simplifies to:

a ≥ 3/2

or,

a ≤ - 1/2

This means that the interval (- 1/2 ,3/2) is the "bad" interval. The length of the interval where a can be chosen from is 38 units long, while the bad interval is 2 units long. Therefore, the "good" interval is 36 units long.

36/38 = 18/19

18+ 19 = 037

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Answer:

c) 5.9%

Step-by-step explanation:

whats the question? or like the answer choices

Answer:

gwgwg

Step-by-step explanation:

Answer:

40%

Step-by-step explanation:

1 and 3/5 as a fraction is 8/5 which as a percent is 160%.

25% of 16 is 4

160%/4 = 40%

Answer:

8x^3y

Step-by-step explanation:

The area of a rectangle is length * width.

area = 4x^2y * 2x =

= 4 * 2 * x^2 * x * y

area = 8x^3y

The value of the constant of proportionality, k, in the equation r = ksv/p^3, is determined to be 1036.8 when given specific values for s, v, p, and r.

To express the statement as a formula, we have:

r = ksv / p^3

To determine the value of k, we can substitute the given values of s, v, p, and r into the formula and solve for k.

Given:

s = 2

v = 5

p = 6

r = 48

Substituting these values into the formula, we have:

48 = k * 2 * 5 / 6^3

Simplifying further:

48 = 10k / 216

To isolate k, we can cross-multiply and solve for k:

48 * 216 = 10k

10368 = 10k

k = 10368 / 10

k = 1036.8

Therefore, the value of k is 1036.8.

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Answer:

23.6 m

Step-by-step explanation:

In a right-angled triangle, a ² + b ² = c ²

b² = 10² - 8.8²

100 - 77.44

b = 4.75

perimeter = 4.75 + 8.8 + 10 = 23.55 = 23.6 m to nearest tenth

Answer:

The answer is 23.5m to 1 d.p

Step-by-step explanation:

c²=a²+b²

b²=c²-a²

b²=10²-8.8²

b²=100-77.44

b²=22.56

√b²=√22.56

b=4.7m

Perimeter =a+b+c

P=8.8+4.7+10

P=23.5

P=23.5m to 1 d.p

By using the concept of testing of hypothesis, it can be calculated that

The required test statistic is t = 0.918

What is testing of hypothesis?

Suppose, there is a hypothesis and there is a data at hand. Testing of hypothesis is a method of inferencing which is used to decide whether the given hypothesis is true or not based on the statistical data given

From the table attached here, it can be calculated that

\(\bar{x}_{2012}=365.4667\\s^{2}_{2012}=27133.66364\\\bar{x}_{2013}=331.775\\s^{2}_{2013}=29750.53782\\n_{2012}=45\\n_{2013}=40\\\)

So the test statistic t is

\(\large t=\frac{\bar{x}_{2012}-\bar{x}_{2013}}{\sqrt{\frac{s^{2}_{2012}}{n_{2012}}+\frac{s^{2}_{2013}}{n_{2013}}}}\)

\(t=\frac{365.4667-331.775}{\sqrt{\frac{27133.66364}{45}+\frac{29750.53782}{40}}}\)

\(t \large =\frac{33.6917}{36.6978711}\)

t = 0.918

The value of the test statistic is 0.918

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The Trapezoidal rule and Simpson's rule are two methods used to approximate the value of a definite integral. The Trapezoidal rule approximates the integral by dividing the region between the lower and upper limits of the integral into n trapezoids, each with a width h. The approximate value of the integral is then calculated as the sum of the areas of the trapezoids. The Simpson's rule is similar, except the region is divided into n/2 trapezoids and then the integral is approximated using the weighted sum of the area of the trapezoids.

For the given integral 4 x x2 1 0 dx, with n = 200, the Trapezoidal rule and Simpson's rule approximate the integral to be 7.4528 and 7.4485 respectively, rounded to four decimal places. The exact value of the integral is 7.4527. The difference between the exact and approximate values is very small, thus indicating that both the Trapezoidal rule and Simpson's rule are accurate approximations.

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Answer:

\({ \tt{p(x) : {y}^{2} = 4ax}} \\ { \tt{f(x) : {(y')}^{2} = 4a {x}'}} \\ { \tt{g(x) : {(y'')}^{2} = 4ax''}} \\ { \bf{since \: they've \: a \: common \: root}} : \\ {y}^{ 2} = {(y')}^{2} = {(y'')}^{2} \\ = > { \tt{4ax + 4ax' + 4ax''}} \\ = 4a(x + x' + x'') \\ common \: root \: is \: 4a \\ { \tt{ \infin {}^{ - } \leqslant 4a \leqslant \infin {}^{ + } }}\)

Answer:

\(\boxed {m = -7}\)

Step-by-step explanation:

Solve for the value of \(m\):

\(-98 = 14m\)

-Switch:

\(14m = -98\)

-Divide both sides by \(14\):

\(\frac{14m}{14} = \frac{-98}{14}\)

\(\boxed {m = -7}\)

Therefore, the value of \(m\) is \(-7\).

Answer:

x=8

Step-by-step explanation:

2x + 5 = 21

Subtract 5 from each side

2x+5-5 = 21-5

2x= 16

Divide each side by 2

2x/2 = 16/2

x = 8

Answer:8

Step-by-step explanation:

2 times eight plus five is 21

Answer:

Option d is the ryt answer.

Point slope form:

y-y1 = m(x-x1)

Slope intercept form:

y = mx+b

According to the information, the group of people over 60 who use the camping is 28.1% (option C).

To find the percentage that corresponds to the group of people over 60 years of age who used the park camping, we must consider the total number of people 60 years of age or older who were included in the survey. In this case we can infer that there were 21,000 people. On the other hand, the group that used the camping was 5,900. So the percentage would be:

Based on the above, we can infer that the correct answer is B.

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Answer:

24, 48, 72, 96

Step-by-step explanation:

Least Common Multiple (LCM)

It's the smallest positive number that is a multiple of two or more numbers. For example, let's find the LCM of 15 and 25:

Multiples of 15: 15,30,45,60,75,90,...

Multiples of 25: 25,50,75,100,...

Note 75 is a common multiple of both and is also the smallest possible.

Lin puts a snowflake sticker every 6 lockers and a snowman sticker every 8 lockers. To find the lockers where both stickers are places, we must find the LCM of 6 and 8:

6 = 2*3

8 = 2*2*2

Multiplying the common factors the maximum number of times it appears:

LCM = 2*2*2*3 = 24

Thus, every 24 lockers there are two stickers until Lin reaches the last 100th locker along the halfway.

The sequence of lockers is:

24, 48, 72, 96

we can conclude that the last digit of the product of all the numbers between 11 and 29 is 0.

Here we want to find the last digit of the product between all the whole numbers larger than 11 and smaller than 29.

Then we have the product:

P = 12*13*14*15*16*17*18*19*20*21*22*23*24*25*26*27*28

Now, notice that there is a 20 there.

Any number times 20 will end with a zero, then:

P = 20*(12*13*14*15*16*17*18*19*21*22*23*24*25*26*27*28)

Only with that, we can conclude that the last digit of the product of all the numbers between 11 and 29 is 0.

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SOLUTIION

The given equations are

This further gives

Therefore the solutions are:

From the option considering the value q=8, it follows

And

Therefore the solution is

Answer:

Step-by-step explanation:

factors of 8

Answer:

F- of a 8* i think

Step-by-step explanation:

To find the y-coordinate of point P on the unit circle, given that its x-coordinate is 5/13, we can utilize the Pythagorean identity for points on the unit circle.

The Pythagorean identity states that for any point (x, y) on the unit circle, the following equation holds true:

x^2 + y^2 = 1

Since we are given the x-coordinate as 5/13, we can substitute this value into the equation and solve for y:

(5/13)^2 + y^2 = 1

25/169 + y^2 = 1

To isolate y^2, we subtract 25/169 from both sides:

y^2 = 1 - 25/169

y^2 = 169/169 - 25/169

y^2 = 144/169

Taking the square root of both sides, we find:

y = ±sqrt(144/169)

Since we are dealing with points on the unit circle, the y-coordinate represents the sine value. Therefore, the y-coordinate of point P is:

y = ±12/13

So, the y-coordinate of point P can be either 12/13 or -12/13.

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♥️ \(\large{\underline{\textcolor{red}{\mathcal{SUMIT\:\:ROY\:\:(:\:\:}}}}\)

Answer:

B) 5%

Step-by-step explanation:

the slope of the linear equation is 2.25, which means that the third option is the correct one.

Remember that a linear equation is a function of the form:

y = a*x + b

Where a is the slope and b is the y-intercept.

If the linear equation passes through the points (x₁, y₁) and (x₂, y₂), then the slope of the line is:

a = (y₂ - y₁)/(x₂ - x₁)

From the given data, where we have:

We can use the first two points:

(2, 8.50)

(5, 15.25)

Replacing that in the slope equation we get:

a = (15.25 - 8.50)/(5 - 2) = 2.25

Then the slope of the linear equation is 2.25, which means that the third option is the correct one.

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Answer is 35cm hope it will help you .

EXPLAINATION: π.r² = 3850 cm²  

⇒ r² = 3850/π = 3850/3,14 ≈ 1225.5

⇒ r = √ 1225.5 ≈ 35 cm

P/s: π ≈ 3.14

ANSWER: r = 35 cm

Ok done. Thank to me :>