The table below shows the average attendance of school events by the day of the week on which they are held.

Average Attendance at School Events


Thursday
Friday
School Play
300
x
Band Concert
184
250

Which values of x will indicate an association between the two variables in the two-way table? Select the three correct answers.

Using the empirical rule, we know that for a normal distribution, approximately 68% of the data falls within one standard deviation of the mean, 95% falls within two standard deviations of the mean, and 99.7% falls within three standard deviations of the mean.

In this case, the mean is 56 and the standard deviation is 7. To find the number of phone calls between 35 and 77, we need to find how many standard deviations away from the mean these values are.

For 35: (35-56)/7 = -3

For 77: (77-56)/7 = 3

So the range we are interested in is 3 standard deviations below the mean to 3 standard deviations above the mean. Using the empirical rule, we know that approximately 99.7% of the data falls within this range.

Therefore, the approximate percentage of daily phone calls numbering between 35 and 77 is 99.7%.

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Answer:

one plus one equals two

Step-by-step explanation:

The equation of the variable y in terms of x is y = -2x + 16

From the question, we have the following parameters that can be used in our computation:

(2, 12) and (6, 4)

A linear equation is represented as

y = mx + c

Substitute the given points in the above equation, so, we have the following representation

2m + c = 12

6m + c = 4

When the equations are subtracted, we have

-4m = 8

So, we have

m = -2

Next, we have

2(-2) + c = 12

Evaluate

c = 16

Recall that

y = mx + c

So, we have

y = -2x + 16

Hence, the variable y in terms of x is y = -2x + 16

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The dimensions of the fenced-in area is given as

either length is 35 yards and width is 80 yards ,  

or length is 40 yards and width is 70 yards .

In the question ,

given that the total length of the fence (perimeter) = 150 yards

let L be the length of the portion to be fenced

let B be the width of the house

Given that , one side of the portion is fenced using the back side of the house

So, the perimeter of the portion to be fenced is 2L+B

equating both the perimeter ,we get

2L+B=150

B=150-2L       ....(i)

Also , given that the area of the  fenced-in portion = 2800 yards

also the formula for area of fenced-in portion = L×B

hence

L*B=2800

Substituting the values of B from equation(i) , we get

L*(150-2L)=2800

150L - 2L² = 2800

2L² - 150L + 2800 = 0

simplifying further , we get

L² - 75L + 1400 = 0

L² -40L -35L +1400 = 0          .....using splitting the middle term

L(L-40) -35(L-40) = 0

(L-35)(L-40) = 0

So , L = 35 yards or L = 40 yards

Using L = 35 yards , we get B = 150-2(35) = 80 yards

and using L =40 yards , we get B = 150-2(40) = 70 yards .

Therefore , the dimensions of the fenced-in area is given as

either length is 35 yards and width is 80 yards ,  

or length is 40 yards and width is 70 yards .

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Answer:

  130

Step-by-step explanation:

The number of integers meeting the criteria can be found by counting them using a counting formula.

Integers divisible by 7 will have the form (7n), where n is some positive integer. The number of them less than 1000 can be found from ...

  7n ≤ 1000

  n ≤ 142.857

There are 142 integers less than 1000 that are divisible by 7.

Similarly, integers divisible by 7 and 11 will be of the form (77n), for some positive integer n.

  77n ≤ 1000

  n ≤ 12.987

There are 12 integers less than 1000 that are divisible by both 11 and 7.

The number of integers less than 1000 that are divisible by 7, but not 11, will be the difference of these numbers.

  142 -12 = 130 integers divisible by 7, but not 11.

Answer:

\(\sqrt{29\)

Step-by-step explanation:

Pythagorean theorem is a^2 + b^2 = c^2. "a" and "b" represent the side lengths QR and PR, while "c" represents the hypotenuse PQ.

Let's plug in these values:

2^2 + 5^2 = c^2

4 + 25 = c^2

29 = c^2

sqrt 29 = c

Therefore "c" is the square root of 29.

Answer:

My answers is basically 29^2 or \(\sqrt{29}\)

Step-by-step explanation:

Answer:

answer A

Step-by-step explanation:

i got it right on the test

In statistical experiments, each time the experiment is repeated, a different outcome may occur. The correct answer is C.

Statistical experiments involve random processes, such as the random selection of individuals from a population, the random assignment of subjects to groups, or the random measurement of a variable.

The outcome of a statistical experiment is influenced by chance and is inherently uncertain, so it is not possible to guarantee that the same outcome will occur every time the experiment is repeated. Different outcomes may occur, even if the experimental conditions are kept constant, due to the random nature of the processes involved.

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Based on the calculations, the distance between points (-5, -5) and (-9, -2) on a coordinate plane is equal to: A. 5 units.

Mathematically, the distance between two (2) points that are on a coordinate plane can be calculated by using this formula:

Distance = √[(x₂ - x₁)² + (y₂ - y₁)²]

Given the following points:

Substituting the given points into the formula, we have;

Distance = √[(-2 - (-5))² + (-9 - (-5))²]

Distance = √[(-2 + 5)² + (-9 + 5)²]

Distance = √[3² + 4²]

Distance = √[9 + 16]

Distance = √25

Distance = 5 units.

In conclusion, we can logically deduce that the distance between the given points on a coordinate plane is 5 units.

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Complete Question:

What is the distance between (-5, -5) and (-9, -2?

Choose 1 answer:

A. 5

B. 7

C. √12

D. √29

36 motorcycles were repaired during the month.

To solve this problem, we can use the formula for the total number of wheels of a vehicle, which is equal to the number of vehicles multiplied by the number of wheels per vehicle. In this case, the number of wheels per vehicle is 4 since both autos and motorcycles have 4 wheels each. This formula can be expressed as: Wheels = Vehicles × Wheels per Vehicle.

We can substitute the given values of the total number of wheels (336) and the number of wheels per vehicle (4) into the formula, and solve for the number of vehicles (V): Wheels = Vehicles × Wheels per Vehicle → 336 = Vehicles × 4 → Vehicles = 336 ÷ 4 → Vehicles = 84.

Since we know that both autos and motorcycles were repaired, and the total number of vehicles was 84, we can use the information that 120 vehicles were repaired to solve for the number of motorcycles (M) that were repaired.

If the total number of vehicles was 84, and 120 vehicles were repaired, then the number of motorcycles that were repaired must be equal to the difference between the total number of vehicles and the total number of autos, which is 120 - 84 = 36.

Therefore, 36 motorcycles were repaired during the month.

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Answer:

The answer is 1 1/4 or a.

Step-by-step explanation:

Basicallly percents are based of 100% so there is a 100% which would be a whole then there is only 25% and if you take 4 quarters and each quarter is 25 cents and there is 4 quarters in a whole that would be 1/4. You add the 1 whole and the 1/4 to get 1 1/4.

Hope this helps, tried to explain it in the best way I can.

The appropriate conclusion is:

(1) P-value = 0.0099, There is sufficient evidence at the a=0.05 level of significance

What is null hypothesis?

In statistics, the null hypothesis (H0) is a statement that assumes that there is no significant difference between two or more groups, samples, or populations.

The null hypothesis is that the proportion of Reed College students who graduate in two years is equal to 0.07, and the alternative hypothesis is that the proportion is greater than 0.07.

To determine the p-value, we can use a one-tailed z-test for the proportion.

The test statistic is calculated as:

z = (p - P) / √(P(1-P)/n)

where p is the sample proportion, P is the hypothesized proportion, and n is the sample size.

Plugging in the values, we get:

z = (12/90 - 0.07) / √(0.07 * 0.93 / 90) = 2.72

Using a z-table, we can find the area to the right of z = 2.72, which is approximately 0.003.

Since this is a one-tailed test, we multiply the area by 2 to get the p-value:

p-value = 0.006

The p-value is less than the significance level of 0.05, so we reject the null hypothesis.

Therefore, The appropriate conclusion is:

(1) P-value = 0.0099, There is sufficient evidence at the a=0.05 level of significance, to conclude that the proportion of Reed College students that will graduate in two years is greater than 0.07.

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Answer:

000, 001,010,011 (the next one would be 100,101....)

Step-by-step explanation:

That's the binary system

The answers are 1) The next shape will be  red square, 2) The next number will be 243 and 4) The pattern will be red,blue,blue.

A conjecture is a conclusion or a proposition that is proffered on a tentative basis without proof.

1) According to given pattern, the next shape will be a shape a red square.

2) The given numbers are multiplied by 3 in every next term, 3, 3*3 = 9, 9*3 = 27 and 27*3 = 81 so, next number will be 81*3 = 243.

3) The 4th one is a pattern of binary system:

000, 001,010,011

Therefore, the next one would be 100,101.... That means red, blue, blue.

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Answer: 17.5

Step-by-step explanation:

Q6: Approximately 68.3% of the cherry tomatoes sold by Berkeley Bowl fall within the specified diameter limits of 20 mm to 32 mm.

Q7: To achieve half of the Six Sigma Quality, the standard deviation of the process should be approximately 0.22 mm for Berkeley Bowl's cherry tomatoes.

In Q6, we can use the concept of the normal distribution to determine the percentage of tomatoes within the specification limits. Since the average diameter is 26 mm and the standard deviation is 3 mm, we can assume a normal distribution and calculate the percentage of tomatoes within one standard deviation of the mean. This corresponds to approximately 68.3% of the tomatoes falling within the specified limits.

In Q7, achieving Six Sigma Quality means that the process has a very low defect rate. In this case, half of the Six Sigma Quality means reducing the variability in diameter to half the acceptable range.

The acceptable range is 32 mm - 20 mm = 12 mm. To achieve half the range, the standard deviation should be approximately half of 12 mm, which is 6 mm. Since the standard deviation is given as 3 mm, the process would need to be improved to reduce the standard deviation to approximately 0.22 mm for it to meet half of the Six Sigma Quality.

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Answer:

3

Step-by-step explanation:

1/4 to each kid, she has 3/4. That would be 3

To find the area of triangle ABD, we can use the formula for the area of a triangle: A = (1/2)bh, where b is the base of the triangle and h is the height.

First, we need to find the length of BD. We can use the Pythagorean theorem to do this:

BD^2 = AB^2 - AD^2

BD^2 = 12^2 - 12^2

BD^2 = 144 - 144

BD^2 = 0

BD = 0

This means that D is actually the midpoint of AC, and BD is a height of triangle ABD.

So, the base of triangle ABD is AB = 12, and the height is BD = 0. Therefore, the area of triangle ABD is:

A = (1/2)bh

A = (1/2)(12)(0)

A = 0

The area of triangle ABD is 0 because BD, the height of the triangle, is 0.

Answer:

The area is \(32\sqrt{5}\) or 71.5542 units²

Step-by-step explanation:

Segment AD is a 12 units, and so is segment AB. This makes triangle ABD and isosceles triangle (a triangle with 2 equal side lengths)

The equation for area of an isosceles triangle given only the base and a side length s is

\(A = \frac{1}{2} b \sqrt{s^2-\frac{b^2}{4} } \\\)

\(A = \frac{1}{2} * 16 * \sqrt{12^2-\frac{16^2}{4} } \\A = 8 * \sqrt{144-64} \\A = 8\sqrt{80} \\A = 32\sqrt{5}\)

The area of Triangle ABD is \(32\sqrt{5}\) units², or 71.5542 units² in decimal form.

To conduct the study on the curriculum change for 5th graders in math, the statistical test that should be used is the t-test.

This test is appropriate when there are two groups to compare. The null hypothesis of the t-test is that the means of the two groups are equal while the alternative hypothesis is that they are not equal. To conduct the t-test, the mean and standard deviation of each group will be calculated. The t-test compares the means of the two groups to determine whether the difference between them is statistically significant.

Reporting of the findings of the t-test will be done through the use of graphs and charts. The results will be presented in a clear and concise manner, highlighting the key findings and their implications for the curriculum change. Any potential ethical dilemmas should also be addressed in the report. These may include issues such as informed consent, confidentiality, and potential biases in the data. It is important to ensure that all ethical guidelines are followed throughout the study to ensure the validity and reliability of the findings.

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Step-by-step explanation:

correct is (if only one answer is correct) :

he will take longer, if he checks all the books instead of checking a few.

if 2 answers are correct, then

he will not need a list of all the books

is also correct.

the tricky part here is to understand what is meant by "list".

if it means a printed paper list in addition to all the books on shelves, then this is not needed, as he can go and pick books from the shelves without knowing which ones are there or even how many are there in total.

but if the books on the shelves are the "list" itself, then this is needed, of course.

the option

he will have a more representative sample, if he chooses randomly

is not true.

there is nothing more representative than checking every item, one after the other. and picking fully randomly has a big risk of missing whole subgroups with special "behavior".

in the same way also picking only the books he likes has a big risk of missing large subgroups with different behavior.

and this is therefore not true either.

Answer:

Dan and Anja are both correct.

Step-by-step explanation:

Base on the given;

Total: \(1 \frac{5}{8}\)

Dan:

1st Bottle: \(\frac{5}{8}\)

2nd Bottle: \(\frac{1}{8}\)

3rd Bottle: \(\frac{7}{8}\)

Anja:

1st Bottle: \(\frac{6}{8}\)

2nd Bottle: \(\frac{2}{8}\)

3rd Bottle: \(\frac{5}{8}\)

Since we know all the info now. Let's first add up all the bottles.

Dan:

\(\frac{5}{8}+\frac{1}{8}+\frac{7}{8}=[?]\)    ⇒ Only add the numerator.

\(\frac{5}{8}+\frac{1}{8}+\frac{7}{8}=\frac{13}{8}\) ⇒ Simplify

\(\frac{13}{8}=1\frac{5}{8}\)

Anja:

\(\frac{6}{8}+\frac{2}{8}+\frac{5}{8}=[?]\)   ⇒ Only add the numerator.

\(\frac{6}{8}+\frac{2}{8}+\frac{5}{8}=\frac{13}{8}\)⇒ Simplify

\(\frac{13}{8}=1\frac{5}{8}\)

Base on the given;

Total = \(1\frac{5}{8}\)

From what we solve:

Dan and Anja are both correct.

Since the drop-down menus wasn't given. I can not farther given more info. Please have a link to the image if help is needed.

RevyBreeze

Answer:

450

Step-by-step explanation:

you divide 90 by 20 and times in by 100

Step-by-step explanation:

To find the directional derivative of the function h(r, s, t) = ln(3r + 6s + 9t) at the point (2,2,2) in the direction of the vector v = 8i + 24j + 12k, we can use the formula:

Dv(h) = ∇h · v

where ∇h is the gradient vector of the function h.

To find the gradient vector ∇h, we take the partial derivatives of h with respect to each variable r, s, and t:

∂h/∂r = 3/(3r + 6s + 9t)

∂h/∂s = 6/(3r + 6s + 9t)

∂h/∂t = 9/(3r + 6s + 9t)

Thus, the gradient vector ∇h is:

∇h = (3/(3r + 6s + 9t))i + (6/(3r + 6s + 9t))j + (9/(3r + 6s + 9t))k

At the point (2,2,2), the gradient vector ∇h is:

∇h(2,2,2) = (3/24)i + (6/24)j + (9/24)k

= (1/8)i + (1/4)j + (3/8)k

Now, we can find the directional derivative Dv(h) in the direction of the vector v as follows:

Dv(h) = ∇h · v

= ((1/8)i + (1/4)j + (3/8)k) · (8i + 24j + 12k)

= (1/8)(8) + (1/4)(24) + (3/8)(12)

= 3

Therefore, the directional derivative of the function h(r, s, t) = ln(3r + 6s + 9t) at the point (2,2,2) in the direction of the vector v = 8i + 24j + 12k is 3.

The  probability of event A is P(A) = 1/4 or 0.25.

The formula to find P(A) for a series of simple events is:

P(A) = (number of outcomes that satisfy the event A) / (total number of possible outcomes)

For example, if you are tossing a coin and selecting a number at the same time, and event A is defined as getting a head and an even number, then:

- The number of outcomes that satisfy event A is 1 (getting a head and an even number, i.e., H2)
- The total number of possible outcomes is 4 (H1, H2, T1, T2)
- Therefore, the probability of event A is P(A) = 1/4 or 0.25.

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The probability the a five card poker hand contains the ace of hearts, the king of diamond, and the queen of spades is: 9.62%

Combination and permutation are two alternative strategies in mathematics to divide up a collection of components into subsets.

Now,

A five-card poker hand selects 5 out of 52 cards. Therefore, by Permutations and Combinations:

C(52,5) = \(\frac{52!}{5! (52-5)!}\) = 2598960

Now, we select the ace of hearts, for which we can withdraw any 4 out of 51 remaining cards. Therefore, by Permutations and Combinations:

C ( 51, 4) = \(\frac{51!}{4! (51-4)!}\) = 249900

Finally, 249900 out of 2598960 hands contain a two of diamonds and a three of spades.

Thus, the probability = \(\frac{249900}{2598960} = \frac{5}{52}\) (Approximately) ≈ 0.0962 = 9.62%

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For the given functions, f(x)=x²+3x-7, g(x)=3x+5 and h(x)=2x²-4, f(g(x))= 9x² + 30x + 33, h(g(x))= 18x² + 60x + 46, (h-f)(x)= x² - 3x + 3, (f+g)(x)= x² + 6x - 2.

In mathematics, a function is a mathematical object that takes an input (or several inputs) and produces a unique output. It is a relationship between a set of inputs, called the domain, and a set of outputs, called the range.

Formally, a function f is defined by a set of ordered pairs (x, y) where x is an element of the domain, and y is an element of the range, and each element x in the domain is paired with a unique element y in the range. We write this as f(x) = y.

Functions can be represented in various ways, such as algebraic expressions, tables, graphs, or verbal descriptions. They can be linear or nonlinear, continuous or discontinuous, and may have various properties such as symmetry, periodicity, and asymptotic behavior.

To solve these problems, we substitute the function g(x) for x in f(x) and h(x) and simplify the resulting expressions.

f(g(x)):

f(g(x)) = f(3x+5) = (3x+5)² + 3(3x+5) - 7 (using the definition of f(x))

= 9x² + 30x + 33

h(g(x)):

h(g(x)) = h(3x+5) = 2(3x+5)² - 4 (using the definition of h(x))

= 18x² + 60x + 46

(h-f)(x):

(h-f)(x) = h(x) - f(x) = (2x² - 4) - (x² + 3x - 7) (using the definitions of h(x) and f(x))

= x² - 3x + 3

(f+g)(x):

(f+g)(x) = f(x) + g(x) = x² + 3x - 7 + 3x + 5 (using the definitions of f(x) and g(x))

= x² + 6x - 2

When multiplying out a squared term, such as (3x+5)², we can use the FOIL method, which stands for First, Outer, Inner, Last. We multiply the first terms, then the outer terms, then the inner terms, and finally the last terms, and then add up the results. For example:

(3x+5)² = (3x)(3x) + (3x)(5) + (5)(3x) + (5)(5)

= 9x² + 15x + 15x + 25

= 9x² + 30x + 25

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Answer:

Step-by-step explanation:

17x + 9

Answer:

79.38 m^2

Step-by-step explanation:

Answer:

Step-by-step explanation:

TO=√((4²+(8+4)²)=√(16+144)=√160=√(16×10)=4√10

OU=√(2²+(4+2)²)=√(4+36)=√40=√(4×10)=2√10

area of triangle TOUR=lw=4√10×2√10=8×10=80 units²