Was it possible for any of the kids in dr. vickers' sample (or anyone at all) to have the average number of feet?

The height of the wall where the ladder reaches will be 6.33 feet.

It communicates that the area of the square whose side is the hypotenuse is identical to how much the locale of the squares on the other various sides.

The Pythagoras theorem formula is given as

H² = P² + B²

A 12-foot ladder is set against a vertical mass of construction, with the lower portion of the ladder staying on level ground 10 feet from the underpinning of the design.

The height of the wall where the ladder reaches will be calculated as,

12² = P² + 10²

144 = P² + 100

P² = 44

P =6.33 feet

The level of the wall where the stepping stool arrives freely will be 6.33 feet.

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The radius of convergence of the given series is 5. The interval of convergence is -5 ≤ x < 5, which means the series converges for all values of x between -5 and 5, excluding the endpoint x = 5.

To find the radius of convergence, we can use the ratio test

\(\lim_{n \to \infty}\)  |(-1)ⁿ xⁿ⁺¹ 5ⁿ⁺¹ / (-1)ⁿ xⁿ 5ⁿ|

= \(\lim_{n \to \infty}\) lim |x|/5

The series converges if the ratio is less than 1, which occurs when |x| < 5. Therefore, the radius of convergence is R = 5.

To find the interval of convergence, we can test the endpoints x = -5 and x = 5.

When x = -5, the series becomes

∑ (from ∞ to n=1)  (-1)ⁿ (-5)ⁿ / 5ⁿ

∑(from ∞ to n=1)  (-1/5)ⁿ

which is an alternating geometric series with first term -1/5 and ratio -1/5. By the alternating series test, this series converges.

When x = 5, the series becomes

∑(from ∞ to n=1) (-1)ⁿ (5)ⁿ / 5ⁿ

∑(from ∞ to n=1)  (-1)ⁿ

which is an alternating series that does not converge, since the terms do not approach 0 as n approaches infinity.

Therefore, the interval of convergence is -5 ≤ x < 5, or in interval notation, I = [-5, 5).

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Answer: A C and D

Step-by-step explanation:

Answer: A B

Step-by-step explanation: because I sadly had to figure it out, anyways hope this helps y'all

The expression that represents the number of kids in the fair is 20 + a

From the question, the given parameters are:

Adults = a

Kids = 20 more kids than adults

The above can be represented as

Kids = 20 + Adults

Substitute Adults = a in the equation Kids = 20 + Adults

So, we have the following equation

Kids = 20 + a

Remove the variable "kids"

So, we have the following expression

20 + a

Hence, the expression is 20 + a

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Answer:

127 : 300

Step-by-step explanation:

127 freshman, 63 sophomores, 55 juniors & 55 seniors what is the ratio of freshman to the total number of band members

Total number of members =

127 freshman + 63 sophomores + 55 juniors + 55 seniors = 300

Hence:the ratio of freshman to the total number of band members

Freshman : Total number of band members

127 : 300

Answer: 4w - 5 is in simplified form.

Step-by-step explanation:

The other expressions have like terms that can be combined.

we need 31/2 pounds mirepoix to make 31/2 gallons of soup.

let we need x% (percent) of mirepoix to make 1 gallon of soup

given we have 1 pound of mirpoix which yeilds 1 gallon soup of soup

so total amount of mirepoix that required in the solution is = \(\frac{x}{100} *1 pound\)

so x/100 = 1 gallon / pound

we will use this equation for further calculation

let we need y pounds of mirepoix to make 31/2 gallon of soup  ans we know that x% of mirepoix is required for this solution.

so \(\frac{x}{100} * y = 31/2\)

ans in the above equation x/100 =1 gallon / pound

so  1 * y= 31 /2

and hence y = 31/2 pounds

so we need 31/2 pounds of mirepoix to form requied amount of soup.

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Answer:

0 ≤ x ≤ 18

Step-by-step explanation:

Let 'x' be the number of youth tickets purchased at the zoo and 'y' be the number of adult tickets purchased at the zoo.

At a zoo, youth tickets cost $5 and adult tickets cost $9. A group spent a total of $90 on tickets. We can write as

5x + 9y = 90

to find x we divide both side by 5

x = (90-9y)/5 =>  90/5 - 9y/5

x = 18 - 9y/5

The domain of the relationship is the possible set of values of x and y that satisfies the equation. The domain of this relationship is

0 ≤ x ≤ 18

At x = 0, it means only adult tickets were purchased.

At x = 18, it means only youth tickets were purchased.

Answer:

0 ≤ x ≤ 18

Step-by-step explanation:

got it correct on pluto

The Cartesian equation for the particle's path is y = (1/3)(x - 1)^2, representing a parabolic curve. The particle moves in the positive x-direction as t increases.

To find the Cartesian equation, we eliminate the parameter t by isolating t in one of the equations and substituting it into the other equation:

From x = 3t + 1, we can solve for t as t = (x - 1)/3.

Substituting this value of t into y = 9t^2, we get y = 9[(x - 1)/3]^2.

Simplifying the equation, we have y = (3/9)(x - 1)^2, which simplifies further to y = (1/3)(x - 1)^2.

The Cartesian equation for the particle's path is y = (1/3)(x - 1)^2. This equation represents a parabolic curve.

To graph the Cartesian equation, plot the points on the graph where x and y satisfy the equation. The graph will show a parabolic curve. Since the parameter t ranges from negative infinity to positive infinity, the particle's path extends infinitely in both directions.

The direction of motion can be determined by analyzing the coefficient of t in the parametric equation for x. In this case, the coefficient is 3, indicating that as t increases, the particle moves in the positive x-direction.

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The sum of the series is ∑n=1^∞ an = S∞ = 7.

(a) We have the formula for the partial sums:

Sn = ∑n=1[infinity]an

And we know that:

SN = 7 - (9 / N^2)

So we can find the value of a1 by taking N to infinity:

S∞ = lim(N→∞) SN = lim(N→∞) (7 - (9 / N^2)) = 7

a1 = S1 - S0 = S1 = 7 - S∞ = 0

Now we can use the formula for partial sums to find the other two sums:

∑n=1^{10}an = S10 - S0 = (7 - (9 / 10^2)) - 0 = 6.91

∑n=4^{16}an = S16 - S3 = (7 - (9 / 16^2)) - (7 - (9 / 3^2)) = 6.977

Therefore, ∑n=1^{10}an = 6.91 and ∑n=4^{16}an = 6.977.

(b) We can find a3 using the formula for partial sums:

S3 = a1 + a2 + a3

We know that a1 = 0 and we can find S3 from the formula for partial sums:

S3 = 7 - (9 / 3^2) = 6

So we have:

a3 = S3 - a1 - a2 = 6 - 0 - a2 = 6 - a2

We don't have enough information to determine a2, so we cannot determine the exact value of a3.

(c) We can find a general formula for an by looking at the difference between consecutive partial sums:

Sn - Sn-1 = an

So we have:

a1 = S1 - S0 = 7 - S∞ = 0

a2 = S2 - S1 = (7 - (9 / 2^2)) - 7 = -1/4

a3 = S3 - S2 = (7 - (9 / 3^2)) - (7 - (9 / 2^2)) = 1/9 - 1/4 = -7/36

We can see that the denominators of the fractions are perfect squares, so we can make a guess that the general formula for an involves a square in the denominator. We can then use the difference between consecutive terms to determine the numerator. We get:

an = -9 / (n^2 (n+1)^2)

(d) To find the sum of the series, we can take the limit of the partial sums as n goes to infinity:

S∞ = lim(n→∞) Sn

We can use the formula for the partial sums to simplify this expression:

Sn = 7 - (9 / n^2)

So we have:

S∞ = lim(n→∞) (7 - (9 / n^2)) = 7 - lim(n→∞) (9 / n^2) = 7

Therefore, the sum of the series is ∑n=1^∞ an = S∞ = 7.

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The number of bacteria after 5 hours with initial numbers 3500 increased double in each hour is equal to 112,000.

Initially number of bacteria in a culture =  3500

Total hours the number of bacteria double = Each hour

Then the growth rate is equal to  2

As the number of bacteria after each hour is twice the previous numbers.

Formula used for the number of bacteria after t hours ,

N = N₀ x 2^t

where N₀ is the initial number of bacteria.

Time in hours = t hours

And N is the number of bacteria after t hours.

After 5 hours, the number of bacteria present is equal to,

⇒N = 3500 x 2^5

⇒N = 3500 x 32

⇒N = 112,000

Therefore, number of bacteria present after 5 hours is equal to 112,000.

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We find that the proportion of her laps that fall between 127 and 130 seconds is about 0.139. Any lap time under 135.25 seconds would be considered one of the fastest 2% of her laps. The middle 70% of her laps are between 119 and 131 seconds.

To answer your questions, we first need to have some context on what we're dealing with. You mentioned "her laps," so I assume we're talking about a person who is running or swimming laps. We also need to know the distribution of her lap times (i.e., are they normally distributed, skewed, etc.) in order to answer these questions accurately. For now, let's assume that her lap times are normally distributed.
To find the proportion of her laps that are completed between 127 and 130 seconds, we need to calculate the area under the normal distribution curve between those two values. We can do this using a calculator or a statistical software program, but we need to know the mean and standard deviation of her lap times first.

Let's say the mean is 125 seconds and the standard deviation is 5 seconds. Using a standard normal distribution table or calculator, we find that the proportion of her laps that fall between 127 and 130 seconds is about 0.139.
To find the fastest 2% of laps, we need to look at the upper tail of the distribution. Again, we need to know the mean and standard deviation of her lap times to do this accurately. Let's say the mean is still 125 seconds and the standard deviation is 5 seconds. Using a standard normal distribution table or calculator, we find that the z-score corresponding to the 98th percentile (i.e., the fastest 2% of laps) is about 2.05. We can then use the formula z = (x - mu) / sigma to find that x = z * sigma + mu, where x is the lap time we're looking for. Plugging in the numbers, we get x = 2.05 * 5 + 125 = 135.25 seconds.

Therefore, any lap time under 135.25 seconds would be considered one of the fastest 2% of her laps.
Finally, to find the middle 70% of her laps, we need to look at the area under the normal distribution curve between two values, just like in part However, we need to find the values that correspond to the 15th and 85th percentiles, since those are the cutoffs for the middle 70%. Using the same mean and standard deviation as before, we can use a standard normal distribution table or calculator to find that the z-scores corresponding to the 15th and 85th percentiles are -1.04 and 1.04, respectively.

We can find that the lap times corresponding to those z-scores are 119 seconds and 131 seconds, respectively. Therefore, the middle 70% of her laps are between 119 and 131 seconds.

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The measure of the angle in degrees is approximately 713 degrees. Note that this result is greater than 360 degrees because the angle is not a standard angle in a plane but a measure in three-dimensional space.

Since 1/360th of the circumference of the circle is 0.5 cm long, the circumference of the circle is 360 times longer, or 180 cm long.

The arc subtended by the angle is 79 cm long, which is a fraction of the entire circumference. To find the angle in degrees, we need to convert the arc length to an angle measure using the formula:

angle measure = (arc length / circumference) x 360 degrees

Substituting the values we know, we get:

angle measure = (79 cm / 180 cm) x 360 degrees

Simplifying the fraction, we get:

angle measure = 1.9833 x 360 degrees

Rounding to the nearest degree, we get:

angle measure ≈ 713 degrees

Therefore, the measure of the angle in degrees is approximately 713 degrees. Note that this result is greater than 360 degrees because the angle is not a standard angle in a plane but a measure in three-dimensional space.

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Answer:

a

Step-by-step explanation:

because there is 12 people

Answer:

A

Step-by-step explanation:

There are 12! Since 90 degree rotations of the seats are technically equivalent, so just divide by 4, which yields 12!

I assume that you meant circumference instead of circumstance as circumstance is not a math term.

Given that the circumference is 24,901, determine the diameter.

So, when we find the circumference of a circle. We multiply the diameter by pi (3.14).

However, if we want to find the diameter, we can reverse it by dividing by pi to get the diameter.

So, it would become:

D = C/pi

D = 24901/3.14

D = 7930.25

Thus, the diameter is 7,930.25 (insert units here).

Answer:

C= 2PiR

24901=2 x 22÷7 × R

44R÷7

24901 x 7=44R

174307=44R

R=174307÷44

R= Approx. 3962

D= 3962 x 2

D= 7924

Answer:

1 1/4

Step-by-step explanation:

For 12 dozen cookies, 5/6 cups of better are needed.

We have a oatmeal cookie recipe that calls for 1/2 cup of butter to make 5 dozen cookies. Wyatt needs to make 12 dozen cookies for the bake sale.

1/2 cup butter is needed for 5 dozen cookies.

For 1 dozen cookies, (1/2)/5 = (1/10) cups of better are needed.

For 12 dozen cookies, 10/12 cups or 5/6 cups of better are needed.

Therefore, for 12 dozen cookies, 5/6 cups of better are needed.

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Answer:

5M

Step-by-step explanation:

Answer:

domain: {-9,8,10,11}

range: {-4,-3,0,6}

Step-by-step explanation:

did the test already

iStar Financial (STAR) has a lower PE ratio than Bank Rate (RATE), which suggests that it may be financially stronger

To determine which company is financially stronger using their PE ratios, we need to calculate the PE ratio for each company. PE ratio, or price-to-earnings ratio, is a financial metric used to measure the valuation of a company's stock. It is calculated by dividing the market price per share by the earnings per share.

For Bank Rate (RATE), the PE ratio can be calculated as:

PE ratio = market price per share / earnings per share

PE ratio = $13.95 / $2.71

PE ratio = 5.14

For iStar Financial (STAR), the PE ratio can be calculated as:

PE ratio = market price per share / earnings per share

PE ratio = $12.18 / $3.62

PE ratio = 3.37

A lower PE ratio indicates that a company's stock is relatively undervalued compared to its earnings. In this case, iStar Financial (STAR) has a lower PE ratio than Bank Rate (RATE), which suggests that it may be financially stronger.

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The set of points that represents a function is given by:

A {(2, 1), (7, 9), (3, 12), (4, 10)}.

A set, or a relation, represents a function when each value of x is mapped to only one value of y.

In this problem, we have that option A represents a function, as:

Hence the set of points that represents a function is given by:

A {(2, 1), (7, 9), (3, 12), (4, 10)}.

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Answer: 194

Step-by-step explanation:

From the volumes, we deduce that the side lengths of the cubes are 1 cm, 2 cm, 3 cm, and 5 cm. We position the cubes as follows:

[asy]

unitsize(0.5 cm);

draw((0,0)--(5*dir(-30))--(5*dir(-30) + 5*dir(30))--(10*dir(-30))--(5*dir(-30) + 5*dir(-90))--(5*dir(-90))--(0,0));

draw((5*dir(-30))--(5*dir(-30) + 5*dir(-90)));

draw((0,0)--(0,2)--((0,2) + 2*dir(-30))--(2*dir(-30)));

draw((0,2)--((0,2) + 2*dir(30))--((0,2) + 2*dir(30) + 2*dir(-30))--(2*dir(30)));

draw((2*dir(-30))--(2*dir(-30) + dir(30))--(2*dir(-30) + dir(30) + (0,1))--(2*dir(-30) + 2*dir(30) + (0,1))--(2*dir(-30) + 2*dir(30) + (0,2)));

draw((2*dir(-30) + dir(30))--(3*dir(-30) + dir(30))--(3*dir(-30) + dir(30) + (0,1))--(2*dir(-30) + dir(30) + (0,1)));

draw((3*dir(-30) + dir(30) + (0,1))--(3*dir(-30) + 2*dir(30) + (0,1))--(2*dir(-30) + 2*dir(30) + (0,1)));

draw((2*dir(30) + (0,2))--(2*dir(30) + (0,3))--(2*dir(30) + 3*dir(-30) + (0,3))--(2*dir(30) + 3*dir(-30))--(dir(30) + 3*dir(-30)));

draw((2*dir(30) + (0,3))--(5*dir(30) + (0,3))--(5*dir(30) + 3*dir(-30) + (0,3))--(5*dir(30) + 3*dir(-30))--(5*dir(30) + 5*dir(-30)));

draw((3*dir(-30) + 2*dir(30))--(3*dir(-30) + 5*dir(30)));

draw((3*dir(-30) + 2*dir(30) + (0,3))--(3*dir(-30) + 5*dir(30) + (0,3)));

[/asy]

The surface area of a cube with side length $s$ is $6s^2$, so the total surface area of the cubes is $6 \cdot 1^2 + 6 \cdot 2^2 + 6 \cdot 3^2 + 6 \cdot 5^2 = 234$.

Note that every pair of cubes touches, and furthermore, they have maximum contact. (This is why this solid has the smallest possible area.) The area of contact of the 1-cube and the 2-cube is 1 square centimeter, so we must subtract this twice from 234 (because this portion of the area from both the 1-cube and 2-cube is not seen anymore).

Doing this for every pair of cubes, we find that the surface area of this solid is $234 - 2 \cdot 1^2 - 2 \cdot 1^2 - 2 \cdot 1^2 - 2 \cdot 2^2 - 2 \cdot 2^2 - 2 \cdot 3^2 = \boxed{194}$.

\(x = 30r - 7\)

Let x be that number that is equal to the sentence provided

Answer: try searching it on Google maybe?

Step-by-step explanation:

Answer:

Step-by-step explanation:

-55/11

55/-11

(a) When performing an ANOVA with the data the alternative hypothesis is at least two of the restaurants have different mean delivery times.

(b)75.8

Analysis of variance. or ANOVA, is a statistical method that separate observed variance data into different components to use for additional tests. A one way ANOVA is used for three or more groups of data, to gain information about the relationship between the dependent and independent variables.

The ANOVA table shows how the sum of squares are distributed according to source of variation, and hence the mean sum of squares.

It is given that a pizza lover wants to compare the average delivery times.

Therefore the null hypothesis and alternate hypothesis implies that,

H₀ =  all restaurants have equal mean delivery time

Hₐ = at least two restaurants have different two deliveries

Hence the alternate hypothesis for performing an ANOVA with the data is at least two of the restaurants have different mean delivery times.

The alternate hypothesis (Hₐ) defines that there is a statistically important relationship between two variables. Whereas null hypothesis states that is no statistical relationship between the two variables.

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Answer:

Step-by-step explanation:

The route Landon took starting at time t = 0 is

Home ⇒ Store ⇒ Bank ⇒ Home

Let's compute cumulative distances(in terms of blocks) and cumulative time using  Landon's speed and stay at various places in order to plot a graph. (Note: cumulative means total  so far; we add current value to previous total)

The graph will have cumulative time t (in minutes) on the X-axis and cumulative distance d (in terms of blocks) on the Y-axis. We will indicate Landon's position at any time with the coordinates (t, d)

Answer:

Alternate exterior angles

Step-by-step explanation:

x and y are alternate exterior angles.

They are on opposite sides of the transversal and outside the parallel lines.

Alternate exterior angles are congruent, thus x = y

Answer:

Altitude = Height = AD = ?

Base = 8 cm

Area = 40 cm²

Area = 1/2 (Base * Height)

40 = 1/2 ( 8 * Height)

40 = 4 * Height

Dividing both sides by 4

40 / 4 = Height

Step-by-step explanation:

Hope this helps:)

Paired data refers to observations that are matched or connected in some way. In this case, if we were comparing the rates of return for the two stocks on the same set of 50 days, then it would be considered paired data.

The data comparing the rates of return for the technology company Intel and the U.S. airline Southwest Airlines would not be considered paired data because the samples are not taken on the same days. Paired data refers to observations that are matched or connected in some way. In this case, if we were comparing the rates of return for the two stocks on the same set of 50 days, then it would be considered paired data.

However, in this scenario, two separate random samples of 50 days of stock returns are taken for each company. The days on which the stock returns are recorded are not necessarily the same for both Intel and Southwest Airlines. Therefore, there is no direct pairing or connection between the observations of the two stocks.

To illustrate this further, let's say we take a random sample of 50 days for Intel's stock returns, and another random sample of 50 days for Southwest's stock returns. The first day in the Intel sample may not correspond to the first day in the Southwest sample, and so on. Each sample represents independent observations for each stock, making the data unpaired.

It is important to recognize whether data is paired or unpaired as it can affect the statistical methods used for analysis. In this case, since the data is not paired, we would use different approaches to compare the rates of return for Intel and Southwest Airlines.

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Answer:

778.5

Step-by-step explanation:

Area of any regular polygon = ( apothem * side length * number of sides ) divided by 2

Given information:

Apothem = 15

Side length = 17.3

Polygon Type = Hexagon ( its important to note that a hexagon has 6 sides )

* Plug in the given values into the formula *

Area = \(\frac{15*17.3*6}{2}\)

15 * 17 = 259.5

259.5*6=1557

\(\frac{1557}{2} =778.5\)

Hence, area = 778.5 square units

Answer:

778.5

Step-by-step explanation: