6. Middle school class representatives conducted a poll during lunch to see which activity students wanted for their year-end party. The results are shown in this relative frequency table:




a) For the entire school, which was more popular, water slides or roller skating? (1 point)


b) 34% of the 6th graders and 50% of the 7th graders want to go to the water slides. What percentage of the 8th graders want to go to the water slides? (1 point)



c) Does there seem to an association between grade level and field trip choice? (2 points)





d) If this trend continued, would you expect 9th graders to prefer the water slides or roller skating? Explain your answer. (2 points)

Answer:

49%

Step-by-step explanation:

to get the percentage you put the number of occupied seats over total number of seats and multiply it by 100 over 1

Answer: The last one

Step-by-step explanation:

The integral defined from 0 to 1 is given by 1/3i.

The integral of the vector-valued function F(t) = (t^2 i + t cos(π) 2 j + sin(π) t k) is to be evaluated over the interval [0,1].

This means we need to integrate each component of the vector-valued function.

We have:

∫F(t) dt = ∫(t^2 i + t cos(π) 2 j + sin(π) t k) dt

= ∫t^2 i dt + ∫t cos(π) 2 j dt + ∫sin(π) t k dt= (1/3) t^3 i + 0 j - (1/π) cos(π) sin(π) t k

= (1/3) t^3 i + 0 j

The answer is (1/3) i

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Answer:

10.4

Step-by-step explanation:

cosine rule=\(a^{2}=b^{2} +c^{2} -2bc*cosa\)

                \((2\sqrt{3}) ^{2}=(x+2)^{2} +x^{2} -2(x+2)x*cos60\\12=x^{2} +4x+4+x^{2} -2x^{2} -4x*\frac{1}{2}\\2x-8=0\\x=4\\Area=\frac{1}{2}absinc\\ = \frac{1}{2}*6*4*sin60\\\\ =6\sqrt{3}\\=10.4(3 sig.fig)\)

Answer:

153.9

Step-by-step explanation:

Diametre = 14, Radius = diametre/2 = 14/2 = 7

Area of circle = π*r^2,   π=3.14

= 3.14*7^2

=3.14*49

=153.9

Answer:

348900

Step-by-step explanation:

3489*100=348900

Answer:

\(\boxed{\textbf{348900}}\)

Step-by-step explanation:

Given that the number is 3,489.

We are looking for a new number which is 100 times greater than 3489.

Next, the number which is one hundred times greater than 3,489​ is as follows:

\(3,489 ~x~100=348900\)

Thus, the required number is 348900.

Answer:

Radius -  4

Apothem -  2

Area - \(12\sqrt{3}\) or 20.8

Step-by-step explanation:

Try to draw out my explanation so you know what this looks like.

~~~~

This is an equilateral triangle, so all sides are the same length. The perimeter can be divided by 3 to get each side length...

\(12\sqrt{3} \div3 = 4\sqrt{3}\)

Now that we know the side lengths, we can get this started!

~~~~

Now, an equilateral triangle has angles that all equal 60 degrees. We can bisect this into TWO special case triangles of measures 90-60-30.

4 times the square root of 3 will be the hypotenuse, and the smallest leg is always half of that. The larger leg is represented as the small leg times the square root of 3.

\(Small=2\sqrt{3} \\Hypotenuse = 4\sqrt{3} \\Long =6\)

By the way, the formula for the area can be either of the two:

\(A= \frac{1}{2} bh\\or\\A = \frac{1}{2} NAS\)

we can easily find the area using the first formula.

\(A= \frac{1}{2} (4\sqrt{3} )(6)\\A=12\sqrt{3}\)

The radius is the distance from the center to the corners & the apothem is the distance from the center to a side...

So we can divide the big triangle into a mini triangle at the bottom left/right

The height (small leg) of that triangle would be the apothem

The hypotenuse of that triangle would be the radius.

I did the math really quick because this is getting long. Anyhow, the small leg is 2 so is the apothem, and the hypotenus is 4, so is the radius

Happy April Fool's btw, lol.

Answer:

Se necesita 36 bolsas con 2 cuadernos, 5 marcadores y 4 lapiceras por unidad.

Step-by-step explanation:

Los cuadernos corresponden a los artículos con menor inventario. Las razones de marcadores y lapiceras por cuaderno son, respectivamente:

Marcadores

\(x = \frac{180\,marcadores}{72\,cuadernos}\)

\(x = \frac{5\,marcadores}{2\,cuadernos}\)

Cada bolsa debe contener 5 marcadores por cada 2 cuadernos.

Lapiceras

\(y = \frac{144\,lapiceras}{72\,cuadernos}\)

\(y = \frac{2\,lapiceras}{1\,cuaderno}\)

Cada bolsa debe contener 2 lapiceras por cada cuaderno.

El número máximo de bolsas es:

\(z = \frac{72\,cuadernos}{2\,\frac{cuadernos}{bolsa} }\)

\(z = 36\,bolsas\)

Se necesita 36 bolsas con 2 cuadernos, 5 marcadores y 4 lapiceras por unidad.

The highest score obtained in this group of 12 scores is 19

What is the distribution in statistics?

In statistics, a distribution refers to the way in which a variable is spread out or distributed across different values. A distribution describes the probability of different outcomes for a variable, and can be visualized using graphs such as histograms, box plots, and probability density functions.

The distribution in Table 2-3 shows frequency (f) for different score ranges (x). Without knowing the exact scoring system, we can't say for certain what the highest score obtained in this group of 12 scores is. However, we can determine the upper limit of the highest score range by multiplying the upper limit of the range by its frequency:

Upper limit of 20-24 range = 24

Frequency of 20-24 range = 2

Upper limit of 15-19 range = 19

Frequency of 15-19 range = 5

Upper limit of 10-14 range = 14

Frequency of 10-14 range = 4

Upper limit of 5-9 range = 9

Frequency of 5-9 range = 1

To find the highest score, we need to determine the upper limit of the score range that has the highest frequency. In this case, the highest frequency is 5, which corresponds to the range 15-19.

Hence, the highest score range is 15-19, and the highest score within that range is the upper limit of that range, which is 19. So, the highest score obtained in this group of 12 scores is 19 (assuming the scoring system is such that higher scores correspond to higher ranges).

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Answer:

To me it looks like B

Step-by-step explanation:

RIP King Von

The 21st term in the following arithmetic sequence: -1, -3, -5, -7, ... is -41

What is Arithmetic Series?

The total of an arithmetic sequence's terms is an arithmetic series. The total of a geometric sequence's terms is a geometric series. Other series exist, but you won't likely use them much until you're a calculus student. You'll most likely be working with these two for the time being. This article provides instructions and examples for using arithmetic series. The total of a sequence of terms, a k, where k=1, 2,..., is an arithmetic series. Each term is calculated from the preceding one by adding (or removing) a constant d. Because of this, when k>1, a k=a (k-1)+d=a (k-2)+2d=...=a 1+d (k-1).

Here, In the given question, we have:

-1, -3, -5, -7, ......

Here,

the first term (a) = -1;

the common difference(d) = -3-(-1) = -3+1 = -2;

So, we can use the formula for the nth term of an arithmetic series aa:

\(a_{n} = a+(n-1)d\)

\(a_{21} = a +(21-1)d\)

\(a_{21} = -1 +(21-1)(-2)\)

\(a_{21} = -1+20(-2)\)

\(a_{21} = -1-40\)

\(a_{21} = -41\)

Hence, the 21st term in the following arithmetic sequence :-1, -3, -5, -7, ... is -41.

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The probability that exactly two out of the next twelve passengers buying a ticket with this airline will prefer a window seat is approximately 0.283, or 28.3%.

To calculate the probability that exactly two out of the next twelve passengers buying a ticket with this airline will prefer a window seat, we can use the binomial probability formula.

The formula for calculating the binomial probability is:

P(X = k) = (nCk) * p^k * (1-p)^(n-k)

Where:

P(X = k) is the probability of exactly k successes,

n is the total number of trials,

k is the number of successful outcomes,

p is the probability of success in a single trial, and

(1-p) is the probability of failure in a single trial.

In this case, we have:

n = 12 (total number of trials)

k = 2 (number of successful outcomes)

p = 0.40 (probability of success, which is 40%)

Substituting these values into the formula, we get:

P(X = 2) = (12C2) * (0.40^2) * (1-0.40)^(12-2)

Calculating this expression, we find:

P(X = 2) ≈ 0.283

So, the probability that exactly two out of the next twelve passengers buying a ticket with this airline will prefer a window seat is approximately 0.283, or 28.3%.

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Answer:

p ≥ 53

Step-by-step explanation:

5 more than a number is greater or equal to 27

The "number" can be represented as x.

\(\boxed{x+5\geq 27}\)

Answer:

h = 3V/πr^2

Step-by-step explanation:

\(IF ;\\V = \frac{1}{3} \pi r^2 h\\Make ; h , subject-of-the-formula\\3V = \pi r^2 h\\Divide-both-sides-of-the-equation -by \pi r^2\\\frac{3V}{ \pi r^2} = \frac{ \pi r^2 h}{ \pi r^2 } \\\frac{3V}{ \pi r^2} = h\)

Answer:

Step-by-step explanation:

the answer is

The standard form for the linear equation is y=6a+38.

An equation can be represented by a linear function. The standard form for the linear equation is: y= ax+b , for example, y=5x+3. Where:

a= the slope.

b= the constant term that represents the y-intercept.

For the given example: a=5 and b=3.

The question gives:

- the value of the slope (a) = 6

- the coordinates of a point = (-3,20)

Thus, you can write from the question information :

y=ax+b

20=6*(-3)+b

20=-18+b

b=20+18=38

Therefore, the standard form for the linear equation is:

y=6a+38

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Answer:

Left box:  1/2n

Right box = 2n - 22

Step-by-step explanation:

Since we want one-half the number and n represents the unknown number, we have 1/2n on the left-hand side of the equation.

Thus, you want to put 1/2n in box on the left.

Twice the number and 22 less than this is given by:  y: 2n - 22 less than this means we subtract.  Thus, we have 2n - 22 as the numerator on the right hand side of the equation.

Thus, you want to put 2n - 22 in the box on the right.

Answer:

Cream = 32 cups

Milk = 48 cups

Step-by-step explanation:

Here, we want to share the ratio

The ratio here is 2:3

cream: milk

For cream;

2/5 * 80 = 32 cups

For milk;

3/5 * 80 = 48 cups

Answer: 5sqrt(35)

Step-by-step explanation:

If the ratio of the side lengths is 1:4, since the ratio of the areas is the square of the ratio of the side lengths, the ratio of the areas is 1:16.

This means the area of square ABCD is 14000/16 = 875.

Therefore, AB=sqrt(875)=5sqrt(35).

The solutions to the respective integrals are a)∫(x-3)/(\(x^{3}\)+9x) dx = ln|x| - (1/3) ln|\(x^{2}\)+9| + C b) ∫\(tan^{4}\)(x) \(sec^{6}\)(x) dx: = (1/5)\(sec^{5}\)(x) + (1/7)\(tan^{7}\)(x) + C        c)∫1/\((9-4x)^{\frac{3}{2} }\) dx = (1/4)\((9-4x)^{\frac{-1}{2} }\)+ C

(a) ∫(x-3)/(\(x^{3}\)+9x) dx:

To solve this integral, we can start by factoring the denominator:

\(x^{3}\) + 9x = x(\(x^{2}\) + 9)

Now we can use partial fraction decomposition to express the integrand as a sum of simpler fractions. Let's assume that:

(x-3)/(\(x^{3}\)+9x) = A/x + (Bx + C)/(\(x^{2}\) + 9)

Multiplying both sides by (x^3+9x) to clear the denominators, we have:

(x-3) = A(\(x^{2}\) + 9) + (Bx + C)x

Expanding and grouping like terms:

x - 3 = (A + B)\(x^{2}\) + Cx + 9A

Comparing the coefficients of corresponding powers of x, we get the following equations:

A + B = 0 (for the \(x^{3}\) terms)

C = 1 (for the x terms)

9A - 3 = 0 (for the constant terms)

From equation 1, we have B = -A. Substituting this into equation 3, we find:

9A - 3 = 0

9A = 3

A = 1/3

Therefore, B = -A = -1/3.

Now we can rewrite the integral as:

∫(x-3)/(\(x^{3}\)+9x) dx = ∫(1/x) dx + ∫(-1/3)(x/(\(x^{3}\)+9)) dx

The first term integrates to ln|x| + C1, and for the second term, we can use a substitution u = \(x^{2}\) + 9, du = 2x dx:

∫(-1/3)(x/(\(x^{2}\)+9)) dx = (-1/3) ∫(1/u) du = (-1/3) ln|u| + C2

= (-1/3) ln|\(x^{2}\)+9| + C2

Therefore, the solution to the integral is:

∫(x-3)/(\(x^{3}\)+9x) dx = ln|x| - (1/3) ln|\(x^{2}\)+9| + C

(b) ∫\(tan^{4}\)(x) \(sec^{6}\)(x) dx:

To solve this integral, we can use the trigonometric identity:

\(sec^{2}\)(x) = 1 + \(tan^{2}\)(x)

Multiplying both sides by \(sec ^{4}\)(x), we have:

\(sec^{6}\)(x) = \(sec^{4}\)(x) +\(sec^{2}\)(x) \(tan^{2}\)(x)

Now we can rewrite the integral as:

∫\(tan^{4}\)(x) \(sec^{6}\)(x) dx = ∫\(tan^{4}\)(x) (\(sec^{4}\)(x) +\(sec^{2}\)(x) \(tan^{2}\)(x)) dx

Expanding and simplifying:

∫\(tan^{4}\)(x) \(sec^{6}\)(x) dx =  ∫\(tan^{4}\)(x) \(sec^{4}\)(x) dx + ∫\(tan^{6}\)(x) \(sec^{2}\)(x) dx

For the first integral, we can use the substitution u = sec(x), du = sec(x)tan(x) dx:

∫\(tan^{4}\)(x) \(sec^{4}\)(x) dx = ∫\(tan^{4}\)(x) \(sec^{2}\)(x)(\(sec^{2}\)(x)tan(x)) dx

= ∫\(tan^{4}\)(x) \(sec^{2}\)(x) dx(du)

Now the integral becomes:

∫\(u^{4}\)du = (1/5)\(u^{5}\) + C1

= (1/5)\(sec^{5}\)(x) + C1

For the second integral, we can use the substitution u = tan(x), du =

\(sec^{2}\)(x) dx:

∫\(tan^{6}\)(x) \(sec^{2}\)(x) dx = ∫\(u^{6}\) du

= (1/7)\(u^{7}\) + C2

= (1/7)\(tan^{7}\)(x) + C2

Therefore, the solution to the integral is:

∫\(tan^{4}\)(x) \(sec^{6}\)(x) dx: = (1/5)\(sec^{5}\)(x) + (1/7)\(tan^{7}\)(x) + C

(c) ∫1/\((9-4x)^{\frac{3}{2} }\) dx:

To solve this integral, we can use a substitution u = 9-4x, du = -4 dx:

∫1/\((9-4x)^{\frac{3}{2} }\) dx = ∫-1/\(-4u^{\frac{3}{2} }\) du

= ∫-1/(8\(u^{\frac{3}{2} }\)) du

= (-1/8) ∫\(u^{\frac{-3}{2} }\) du

= (-1/8) * (-2/1) \(u^{\frac{-1}{2} }\)+ C

= (1/4)\(u^{\frac{-1}{2} }\) + C

Substituting back u = 9-4x:

= (1/4)\((9-4x)^{\frac{-1}{2} }\)+ C

Therefore, the solution to the integral is:

∫1/\((9-4x)^{\frac{3}{2} }\) dx = (1/4)\((9-4x)^{\frac{-1}{2} }\)+ C

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The correct question is given in the attachment.

Answer:

constant term is -3, the leading term is 3x^3, the coefficient is 3.

Step-by-step explanation:

Answer:

They are parallel

Step-by-step explanation:

Same slope but different y-intercept

Answer: It is parallel.

Step-by-step explanation: Both equations have the same slope but different y-intercepts, the -3 and -6 in the picture.

Performing a change of scale we will see that the actual distance is 4 miles.

We know that the scale is:

3/4 inch = 2 miles.

And the distance that Nicole found on the map is (1 + 1/2) inches.

We can rewrrite the scale as:

1 inch = (4/3)*2 miles

1 inch = (8/3) miles.

Then the actual distance will be:

distance = (1 + 1/2) inches = (1 + 1/2)*(8/3) miles = 4 miles.

The correct option is A.

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Answer:

B. 97.5

Step-by-step explanation:

l x w x h

12 x 6.5 x 1.5

The three-month moving average is calculated by adding up the demand for the past three months and dividing the sum by three.

To calculate the forecast for month four, we need to find the average of the demand over the past three months: 700, 750, and 900.

Step 1: Add up the demand for the past three months:
700 + 750 + 900 = 2350

Step 2: Divide the sum by three:
2350 / 3 = 783.33 (rounded to two decimal places)

Therefore, the forecast for month four, based on the three-month moving average, is approximately 783.33.

Keep in mind that the three-month moving average is a method used to smooth out fluctuations in data and provide a trend. It is important to note that this forecast may not accurately capture sudden changes or seasonal variations in demand.

To prove that 6 is a factor of n³-n for all integers n, we can use the identity n³-n=n(n-1)(n+1).

1. Substitute n with n-1:
  (n-1)³ - (n-1) = (n-1)((n-1)-1)((n-1)+1)
                  = (n-1)(n-2)(n)
                  = (n³-3n²+3n-1) - (n-1)
                  = n³-3n²+3n-n+1
                  = n³-3n²+2n+1

2. Substitute n with n+1:
  (n+1)³ - (n+1) = (n+1)((n+1)-1)((n+1)+1)
                  = (n+1)(n)(n+2)
                  = (n³+3n²+3n+1) - (n+1)
                  = n³+3n²+3n+n+1
                  = n³+3n²+4n+1

3. Add the two results:
  (n³-3n²+2n+1) + (n³+3n²+4n+1) = 2n³ + 6n

Since 2n³ + 6n is divisible by 6, it means that 6 is a factor of n³-n for all integers n.

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Answer:

Using a standard normal distribution table, we can find that the percentage of homes that have a monthly utility bill of more than $83 is approximately 13.6%.

Step-by-step explanation:

If the distribution of the monthly utility bill for gas or electric energy can be considered mound-shaped and symmetric, we can use the standard normal distribution table to find the percentage of homes that have a monthly utility bill of more than $83.

To use the standard normal distribution table, we need to standardize the variable by subtracting the mean and dividing by the standard deviation:

(83 - 91) / 8 = -0.875

This means that a monthly utility bill of $83 is 0.875 standard deviations below the mean.

Using a standard normal distribution table, we can find that the percentage of homes that have a monthly utility bill of more than $83 is approximately 13.6%.