the intelligence quotient (iq) test scores for adults are normally distributed with a population mean of 100 and a population standard deviation of 15.

Answer:

Step-by-step explanation:

sin(x+y) = sin(x)cos(y) + sin(y)cos(x)

sin(x-y) = sin(x)cos(y) - sin(y)cos(x)

Sin(x+y)sin(x-y) = (sin(x)cos(y) + sin(y)cos(x))(sin(x)cos(y) - sin(y)cos(x))

= sin^2(x)cos^2(y) - sin^2(y)cos^2(x)

= sin^2(x)(1-sin^2(y)) - sin^2(y)(1-sin^2(x))

= sin^2(x) - sin^2(x)sin^2(y) - sin^2(y) + sin^2(x)sin^2(y)

= sin^2(x) - sin^2(y)

So L.H.S=R.H.S

Hence proved

Answer:

h = 41.25 foot

Step-by-step explanation:

Given that,

Height of a street light = 7.5 feet

It casts a 3-foot-long shadow.

A nearby flagpole casts a 16.5 foot long shadow. We need to find the height of the flag pole. Let the height be h. It can be calculated as :

\(\dfrac{\text{height of street light}}{\text{height of shadow of street light}}=\dfrac{\text{height of flagpole}}{\text{height of shadow of the flag pole}}\\\\\dfrac{7.5}{3}=\dfrac{h}{16.5}\\\\h=\dfrac{7.5\times 16.5}{3}\\\\h=41.25\ foot\)

So, the height of the flag pole is equal to 41.25 foot.

The height of the flag pole is 41.25 feet tall.

Word problems in mathematics are methods used to solve real-life cases. They usually follow a logical approach with the use of arithmetic operations when solving them.

From the parameters given:

Let the height of the flag pole be = x

∴

To determine the height of the flag pole, we have:

\(\mathbf{x = \dfrac{7.5 feet \ tall \times 16.5 \ foot \ long} {3 \ foot \ long} }\)

x = 41.25 feet tall

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When calculating S² pooled, each sample's estimate of population variance is weighted by its respective contribution to the total degrees of freedom. Therefore, the correct option is (c).

When conducting a hypothesis test for the difference between two population means, it is often necessary to estimate the common population variance. In this case, the pooled variance or S² pooled is used, which is a weighted average of the sample variances from each of the two samples. To calculate S² pooled, each sample's estimate of population variance is weighted by its respective contribution to the total degrees of freedom. The total degrees of freedom is equal to the sum of the degrees of freedom of each sample, which is n1 - 1 + n2 - 1 = n1 + n2 - 2. The weights are proportional to the degrees of freedom of each sample, so the weight for the first sample is (n1 - 1)/(n1 + n2 - 2) and the weight for the second sample is (n2 - 1)/(n1 + n2 - 2).

Therefore, S² pooled = [(n1 - 1)S1² + (n2 - 1)S2²]/(n1 + n2 - 2), where S1² and S2² are the sample variances of the two samples. The pooled standard deviation is then the square root of S² pooled.

In summary, S² pooled is the weighted average of the sample variances, where the weights are proportional to the degrees of freedom of each sample. The total degrees of freedom is equal to the sum of the degrees of freedom of each sample.

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Answer:

12/7

Step-by-step explanation:

4/5 ÷ 7/15

Keep Change Flip

4/5 × 15/7

Simplify

4/1 × 3/7

Multiply

12/7

I hope this helped and please mark me as brainliest!

Answer: 24 games

Step-by-step explanation: 60-60%=24

The Wilcoxon signed-rank test is employed to see if there is a substantial difference between two related samples. Here the new cognitive therapy group and placebo group are related samples as they both belong to the same sample of cognitive therapy's study. The Wilcoxon signed-rank test is performed on the rank-based data as the data is not normally distributed. Following is the calculation for Wilcoxon’s signed rank test:The null hypothesis for the Wilcoxon signed-rank test is that there is no difference between the new cognitive therapy and placebo treatments. While the alternative hypothesis is that there is a difference between the two treatments.

The Wilcoxon signed-rank test is performed as follows:
Rank all the data, with the lowest value being ranked 1 and the highest value being ranked 12.
Calculate the difference between the new cognitive therapy and placebo group scores.
Take the absolute values of the differences.
Rank the differences in ascending order and ignore the signs.
Calculate the sum of the ranks of the new cognitive therapy group.
Calculate the test statistic T.
For this dataset, the calculations of the Wilcoxon signed-rank test are as follows:
Data Ranked (New therapy) Difference Absolute Difference Ranked Differences + Rank Therapy Differences - Rank Placebo 5 1 4 3 4 4 6 2 4 4 2 2 4 4 8 7 1 1 1 12 10 2 2 3 5 1 6 13 12 1 8 7 7 4 4 1 5 5 5 1 14 13 1 2 1 15 7 8 7 7 5 9 10 3 5 8 56 12 44 12 12 11 7 Total 49
Calculating T:

\($$T =\) \(\frac{Total\ of\ positive\ ranks - \frac{n(n+1)}{4}}{\sqrt{\frac{n(n+1)(2n+1)}{24}}}$$\)

Here, n is the number of pairs, which is 12.
T = 3.52
Using the Wilcoxon signed-rank test table, the critical value at the 0.05 level for n = 12 is 18.
Since T (3.52) is less than the critical value (18), the null hypothesis cannot be rejected.
There is no evidence to suggest that there is a difference between the new cognitive therapy and placebo treatments.

The probability of having the first two children as color-blind boys and the last two children as girls with normal vision is 1/16 or approximately 0.0625, assuming equal probabilities of gender and independent events.

To calculate the probability of having the described sequence of children, we need to consider the probability of each individual event occurring and then multiply them together.

Assuming the probability of having a color-blind boy is p(CB) and the probability of having a girl with normal vision is p(GNV), the desired probability can be calculated as follows:

Probability of the first child being a color-blind boy: p(CB) = 1/2 (assuming an equal probability of a child being a boy or a girl, and the probability of color blindness is independent of gender).

Probability of the second child being a color-blind boy: p(CB) = 1/2 (assuming independent events).

Probability of the third child being a girl with normal vision: p(GNV) = 1/2 (assuming an equal probability of a child being a boy or a girl).

Probability of the fourth child being a girl with normal vision: p(GNV) = 1/2 (assuming independent events).

To calculate the combined probability, we multiply the individual probabilities together:

\(p(2CB-2GNV) = p(CB) \timesw p(CB) \times p(GNV) \times p(GNV) = (1/2) \times (1/2) \times (1/2) \times (1/2) = 1/16.\)

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Answer:

6. 2(2a-3b) 7. 3(3a-b)

Step-by-step explanation:

6. 4a-6b , 2^2 .a-(2.3)b = 2(2a-3b)

7. 9a-3b , 3^2. a-3b =3(3a-b)

There are irrational values of x and y for which their sum, x + y, is a rational number.

Assume \($\sqrt{2}$\) is irrational.

Therefore,\($\sqrt{2}+\sqrt{2} = 2\sqrt{2}$\) is irrational

Since \($\sqrt{2}$\) is irrational, and the product of a non-zero rational number and an irrational number is irrational.

Let \($x= \sqrt{2}$\) and \($y = -\sqrt{2}$\).

Since x and y are irrational,

\($x+y = \sqrt{2}-\sqrt{2} = 0$\) is rational.

Consequently, we have proved that there exist irrational numbers x and y such that x + y is rational.

Note: Any two irrational numbers are not necessarily a good choice for this question.

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Answer:

2\(n\) = \(\alpha n\) and \(n + n\) = \(\alpha n\)

Step-by-step explanation:

Answer: y ≥ \(\frac{3}{2}\)x + 3

Step-by-step explanation:

       Since the shaded area is above the line, we will use either > or ≥ for our inequality.

       Next, since this is a solid line we will use the ≥ symbol for our inequality. This means the answer is the first option.

The value of CDF at U = max {S₁,..., Sn} is \((1 - (1-p)^u+1)^n\).

We are given that;

The number of failures is between = (k-1)th and the kth success.

Now,

(a) The random variables S₁, S₂, ..., Sn are geometrically distributed with parameter p. The joint probability mass function of S₁,..., Sn is given by:

\(P(S_1 = k_1, S_2= k_2, ..., Sn = kn) = (1-p)^(k_1 + k_2+ ... + kn) * p^n\)

(b) The random variables S₁,..., Sn are independent. This can be shown by considering the definition of independence. Two random variables X and Y are independent if and only if P(X = x, Y = y) = P(X = x)P(Y = y) for all x and y. In our case, we have:

\(P(S_1 = k_1, S_2 = k_2, ..., Sn = kn) = (1-p)^(k_1 + k_2 + ... + kn) * p^n= (1-p)^k_1 * p * (1-p)^k_2 * p * ... * (1-p)^kn * p= P(S_1 = k_1)P(S_2 = k_2)...P(Sn = kn)\)

Therefore, the random variables S₁,..., Sn are independent.

(c) The cdf of U = max {S₁,..., Sn} is given by:

P(U ≤ u) = P(S₁ ≤ u, S₂ ≤ u, ..., Sn ≤ u)= P(S₁ ≤ u)P(S₂ ≤ u)...P(Sn ≤ u)

=  \((1 - (1-p)^u+1)^n\).

Therefore, by the sequence the answer will be  \((1 - (1-p)^u+1)^n\).

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The "switch" statement is useful when you need to test a single variable against a series of exact integer, character, or string values.

The switch statement is a control structure found in many programming languages, including C++, Java, and JavaScript. It allows you to evaluate a variable or expression and compare it against multiple cases.

Each case represents a specific value that the variable or expression is tested against. When a match is found, the corresponding block of code associated with that case is executed.

The switch statement is particularly useful when you have a variable that can take on different values and you want to perform different actions based on those values. Instead of writing multiple if-else statements, the switch statement provides a more concise and efficient way to handle such scenarios.

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Answer:

X=18

Y=52

Step-by-step explanation:

Let X represent the first type of ticket sold at the concert

Let Y represent the second type of ticket sold at the concert-----equation 1

X + Y= 70 (Total number of tickets sold) ------equation 2

(X×10) + ( Y×12)=$804. ( Total money generated in the concert

Since,

X+Y= 70

X= 70-Y

Substitute (70-Y) for X in equation 2

(70-Y)×10 + Y×12=804

700-10Y+12Y= 804

Collect the like terms

700+2Y=804

2Y=804-700

2Y= 104

Divide both sides by the coefficient of Y which is 2

2Y/2= 104/2

Y=52

Substitute 52 for Y in equation 1

X+Y=70

X+ 52=70

collect the like terms

X= 70-52

X=18

Hence the first type of ticket sold is 18 tickets and the second type of ticket sold is 52 tickets.

Answer:

its either between D or C  but i would pick D because the line looks like it dosen't pass through orgin (0,0).

Step-by-step explanation:

To determine whether x and y have a proportional relationship, see if the line through these points passes through the origin (0, 0). The points are on a line that passes through the origin. So, x and y have a proportional relationship.

Answer:

1,350

Step-by-step explanation:

15% of 9,000 is 1,350, you can multiply 9000 by .15.

Answer:

A, determine if they have slopes with opposite values.

Step-by-step explanation:

If two non-vertical lines in the same plane intersect at a right angle then they are said to be perpendicular. Horizontal and vertical lines are perpendicular to each other i.e. the axes of the coordinate plane.

Answer: $57.25

Step-by-step explanation:

Answer:

675

Step-by-step explanation:

4 +3+653=675

Answer:

6: (0,9)

7: ( -10, -3)

8: (-12,9)

9: (2,0)

Step-by-step explanation:

The ratio of students who bike to school to the number of students who do not bike to school is 1:6, indicating that for every one student who bikes to school, there are six students who do not bike.

The ratio of students who bike to school to the number of students who do not bike to school can be calculated by dividing the number of students who bike to school by the number of students who do not bike to school. In this case, Rowan found that four out of 28 students bike to school.

To find the ratio of students who bike to school to the number of students who do not bike to school, we divide the number of students who bike by the number of students who do not bike. In this case, Rowan found that four out of 28 students bike to school. Therefore, the ratio of students who bike to school to the number of students who do not bike to school is 4:24 or 1:6.
To defend this solution, we can look at the definition of a ratio. A ratio is a comparison of two quantities or numbers expressed as a fraction. In this case, the ratio represents the number of students who bike to school (4) compared to the number of students who do not bike to school (24). This ratio can be simplified to 1:6 by dividing both numbers by the greatest common divisor, which in this case is 4.
Therefore, the ratio of students who bike to school to the number of students who do not bike to school is 1:6, indicating that for every one student who bikes to school, there are six students who do not bike.

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sin θ = -4/5

To find the value of sin θ, we can use the Pythagorean identity, which states that sin²θ + cos²θ = 1. Since we know that cos θ is positive, we can determine the value of cos θ by using the identity cos²θ = 1 - sin²θ.

Given that tan θ = -3/5, we can determine the value of cos θ. Recall that tan θ is equal to sin θ divided by cos θ. Therefore, we can write:

tan θ = sin θ / cos θ

-3/5 = sin θ / cos θ

From this, we can solve for sin θ by multiplying both sides of the equation by cos θ:

(-3/5)cos θ = sin θ

Next, we can substitute cos²θ = 1 - sin²θ into the equation:

(-3/5)√(1 - sin²θ) = sin θ

Simplifying further, we have:

-3√(1 - sin²θ) = 5sin θ

Squaring both sides of the equation to eliminate the square root:

9(1 - sin²θ) = 25sin²θ

Expanding and rearranging the equation:

9 - 9sin²θ = 25sin²θ

34sin²θ = 9

Dividing both sides by 34:

sin²θ = 9/34

Taking the square root of both sides, we get:

sin θ = ±√(9/34)

Since sin θ is negative when cos θ is positive, we take the negative value:

sin θ = -√(9/34) = -3/√34 = -3√34/34 = -3√34/34

Therefore, the exact value of sin θ is -4/5.

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Answer:

your anwser is 7.74596669241

Answer:

\(\sqrt{60} = 7.74596669241\)

Step-by-step explanation:

On solving the provided question, we can say that - the percentage decrease in the number of students​ is -10%.

A percentage in mathematics is a figure or ratio that is stated as a fraction of 100. The abbreviations "pct.," "pct," and "pc" are also occasionally used. It is frequently denoted using the percent symbol "%," though. The amount of percentages has no dimensions. It has no measuring systems. With a denominator of 100, percentages are basically fractions. To show that a number is a percentage, place a percent symbol (%) next to it. Your score is 75%, for instance, if you correctly answer 75 out of 100 questions on a test (75/100).

Given that,

The school has 1,200 students last year.

And, this year it is 1,080.

Based on the above information, the calculation is as follows:

1080-1200/1200

= -10%

Therefore we can conclude that the percentage decrease in the number of students​ is -10%.

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Given statement solution is :- If I were to assume the flipping process is entirely random and the coin is unbiased, the chances of correctly guessing the outcome of each flip would be 1 out of 2, or a 50% probability.

If I were to assume the flipping process is entirely random and the coin is unbiased, the chances of correctly guessing the outcome of each flip would be 1 out of 2, or a 50% probability. However, the psychic claims to have the ability to sense the outcome of each flip, which would suggest that he believes he can accurately predict the results.

To put the psychic to the test, you can proceed with flipping the coin six times and ask the psychic to guess the outcome of each flip. After the coin has been flipped, compare the psychic's guesses with the actual outcomes to evaluate the accuracy of their predictions.

Keep in mind that even if the psychic does make correct predictions, it does not necessarily prove their psychic abilities. Random chance can occasionally lead to a streak of correct guesses, even if there is no true psychic ability involved. To draw any meaningful conclusions, a larger sample size or repeated testing would be required.

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Answer:

\(M=\frac{280}{140} =2\)

\(C=2+5=7\)

(2 Movies and 7 Commercials)

Step-by-step explanation:

Let's represent every time Carson's songs are played in a commercial as C and in movies as M.

Set up the following equations:

\(20C+120M=380\)  (1)

\(C=M+5\)   (2)

Substitute equation 2 for equation 1:

\(20(M+5)+120M=380\)

Distribute:

\(20M+100+120M=380\)

Simplify:

\(140M=280\)

Divide both sides by 140:

\(M=\frac{280}{140} =2\)

Substitute 2 as M back into either original equation, I will use (2):

\(C=2+5=7\)

Answer:

Step-by-step explanation:

Answer:

Law of Cosines, all sides are known

Step-by-step explanation:

q² = p² + r² − 2pr cos(Q) or

\(\frac{-q^{2}+p^{2}+r^{2} }{2pr}\) = cos (Q)

Q = \(cos^{-1}\) \((\frac{-q^{2}+p^{2}+r^{2} }{2pr})\)

The cos law should use in the provided situation, option (A) Law of Cosines, all sides are known is correct.

In terms of geometry, the triangle is a three-sided polygon with three edges and three vertices. The triangle's interior angles add up to 180°.

We have given a triangle in which sides r, p, and q are given.

As per the cos law,

If we have three sides of a triangle known then we can find the unknown angle.

q² = r² + p² - 2rpcosQ

Q is the angle opposite to the side.

The angle can be defined as when two lines or rays converge at the same point, the measurement between them is called an "Angle."

Thus, the cos law should use in the provided situation, option (A) Law of Cosines, all sides are known is correct.

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Answer:

c and d

Step-by-step explanation:

Answer:

C AND D

Step-by-step explanation:

HOPE I HELPED

PLS MARK BRAINLIEST  

DESPERATELY TRYING TO LEVEL UP

✌ -ZYLYNN JADE ARDENNE

JUST A RANDOM GIRL WANTING TO HELP PEOPLE!

                     PEACE!