In a triangle PQR,the sides PQ, QR and PR measure 15 in, 20 in and 25 in respectively.
Prove that PQR is a right triangle.

Answer:

Complementary angles add up to 90 degrees and Supplementary angles add up to 180 degrees.

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The probability that Marshall wins a prize on his second spin =  0.1875

Consider an event X = the number of spins until Marshall wins a prize.

Given that a prize wheel with 4 segments of equal size, one of which is labeled winner.

So, the sample space n = 4

For given event x, the possible outcomes = 1

Using the formula of probability,

p = x/n

p = 1/4

p = 0.25

So, the probability of success p = 0.25

q = 1 - p

q = 1 - 0.25

q = 0.75

To find the probability that Marshall wins a prize on his 2nd spin.

Using formula, \(P(X = k) = (1 - p)^{k-1}p\)

For  k = 2,

\(P(X = 2) = (1 - 0.25)^{2-1}\times 0.25\)

P(X = 2) = 0.75 × 0.25

P(X = 2) = 0.1875

Thus, the required probability is  0.1875

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Answer:

1,008 pairs of earrings

Step-by-step explanation:

14 multiplied by 72 equals 1,008

Answer: 380.1

Step-by-step explanation:

The area of a circle is pi*r^2. So 11 times 11 is 121. Then multiply by pi. When multiplies by pi you get 380.132711084. rounded to the nearest tenth is 380.1.

A customer would  be charged $ 52 for an international phone call that started at 9:35 p.m. and ended at 11:15 p.m. the same day.

Charge for first 5 charged = $ 4.50

Charge for additional time = $ 0.50 per minute

Starting time = 9:35 p.m.

End time = 11:15 p.m.

Total minutes = 100 minutes

Total charge = 4.50 + (95 x 0.50)

                  = 4.50 + 47.50

                  = 52.00

Hence, a customer would  be charged $ 52 for an international phone call that started at 9:35 p.m. and ended at 11:15 p.m. the same day i.e. for 100 minutes.

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The value of the computer after 5 years is $960

Given that the computer was bought at $3000 and it depreciates at the rate of 20% per year

We can calculate the value of the computer using the formula below;P = A(1 - r)^nwhere; P is the final value of the computer, A is the initial amount, r is the depreciation rate and n is the number of years

Hence, substituting the given values into the formula above,P = $3000(1 - 0.20)^5P = $3000(0.80)^5P = $3000(0.32768)P = $983.04

SummaryThe value of the computer after 5 years is $960.

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9 square meters is the area of triangle LMN. Using the concept of Heron's formula.

Heron of Alexandria is credited with creating Heron's formula, which determines a triangle's area by dividing the lengths of its sides. if the side lengths are represented in symbols by a, b, and c.

According to Heron's formula the area = √s (s - a)(s - b)(s - c)

A triangle's semi-perimeter, whose area has to be calculated, is represented by the letter s in Heron's formula. s = (a+b+c)/2 is the formula for the triangle's semi-perimeter, which is the sum of its three sides.

a triangle with three sides, a, b, and c.

given data was LM = 7,MN = 6 and perimeter was given by 16m

As we know perimeter is the sum of all the sides  

so, Perimeter=LM + MN + NL

NL=Perimeter-(LM+MN)

NL=16 - 7 - 6

NL= 3

By Heron's formula,

Area = √[(s(s-a)(s-b)(s-c)].  

where s = perimeter/2

so, s = 16/2 = 8

area = √[(8(8-7)(8-6)(8-3)]

area = 8.94427191 ≈ 9 square meters.

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Answer: 9m

Step-by-step explanation:

The correct answer is option (b): increases, i.e., if the variability (p times q) increases and the sample size remains the same, then the standard error increases.

The standard error measures the variability of sample means around the true population mean. It is calculated as the standard deviation of the sample divided by the square root of the sample size. The formula for standard error is:

SE = s / √n, where s is the standard deviation and n is the sample size.

When the variability (p times q) increases, it means that there is more dispersion or spread of values in the population. This increased variability leads to a larger standard deviation (s) in the sample, assuming the sample size remains the same.

Since the standard error is calculated by dividing the standard deviation by the square root of the sample size, an increase in the standard deviation will result in a larger standard error. Therefore, if the variability increases and the sample size remains constant, the standard error will increase.

In summary, the standard error increases when the variability increases and the sample size remains the same. This is because a larger standard deviation implies more uncertainty in the sample mean estimate, resulting in a larger standard error.

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the base is 20 ft so the triangular base is 69 feet.

The actual dimensions of Abigail's house are 18 ft by 20 ft.

Abigail's house is represented by a scale drawing with dimensions of 9 cm by 10 cm. We are told that 6 cm on the scale drawing equals 12 ft. To find the actual dimensions of Abigail's house, we need to determine the scale factor.

First, we calculate the scale factor by dividing the actual length (12 ft) by the corresponding length on the scale drawing (6 cm). The scale factor is 12 ft / 6 cm = 2 ft/cm.

Next, we can use the scale factor to find the actual dimensions of Abigail's house. We multiply each dimension on the scale drawing by the scale factor.

The actual length of Abigail's house is 9 cm * 2 ft/cm = 18 ft.
The actual width of Abigail's house is 10 cm * 2 ft/cm = 20 ft.

Therefore, the actual dimensions of Abigail's house are 18 ft by 20 ft.

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Answer: Because all individuals in the sample have the same job, so the sample is biased.

Step-by-step explanation:

Ignoring the fact that 30 is a small sample for a large city, we already know that all the people in the sample has the same profession.

Now, we can expect that two dentists win have around the same income, but not all the residents in the city are dentists

A lot of them work in fast food, others may be lawyers, others may be freelancers.

We have a lot of jobs where the income does not coincide with the average income of a dentist, so with the sample of 30 dentists we are not actually representing all the other possible jobs that there are in the city.

If we want a sample that represents the income of all the residents, we should have a random sample (so the sample is not biased, like in this case).

Answer:

x is 38............ .........

Answer:0.2419218956

Step-by-step explanation:

9514 1404 393

Answer:

  a = (s +t)/(m +r)

Step-by-step explanation:

Add t, then divide by the coefficient of 'a'.

  \(a(m+r)-t=s \qquad\text{given}\\\\a(m+r)=s+t \qquad\text{add $t$}\\\\\boxed{a=\dfrac{s+t}{m+r}} \qquad\text{divide by $m+r$}\)

Answer:

irrational

Step-by-step explanation:

Answer:

It's rational because it isn't a decimal with no end. To simplify it even more, it is an integer.

Step-by-step explanation:

When determining the average amount of money that students spend on books, potential sources of error include sampling bias, self-reporting inaccuracies, and outliers. These errors can be avoided by using a representative sample, ensuring confidentiality and anonymity, and properly handling outliers.

To obtain an accurate average amount of money spent on books, it is important to address potential sources of error. Sampling bias can occur if the sample is not representative of the entire student population. To avoid this, the reporter should use random sampling or stratified sampling techniques to ensure that all groups are adequately represented.

Self-reporting inaccuracies can also affect the accuracy of the data. Students may overestimate or underestimate the amount of money they spend on books. To minimize this error, the reporter can provide clear instructions, use anonymous surveys, and assure confidentiality. This can encourage students to provide more accurate and honest responses.

Outliers, which are extreme values that do not represent the majority, can skew the average. It is important to identify and handle outliers appropriately. The reporter can check for data entry errors, verify extreme values, and consider using measures such as the median or trimmed mean to mitigate the impact of outliers on the average.

By addressing these potential sources of error, the reporter can improve the accuracy of the average amount of money spent on books by students, providing more reliable information for the school newspaper.

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The evaluated probability of randomly choosing a  participant dreams in black and white or color is 0.13, under the condition that the given Students are passing from psychology surveyed 200 of their fellow students regarding their dreams.

Probability means the possible chances of an event occurring in a particular time frame. It is a considered a branch of mathematics that deals with the occurrence of a random event.

The value is presented from zero to one. Probability has been induced in math to predict how prone are the events going to occur. The meaning of probability is basically the express  something that is likely to happen.

Black Probability = 4/200=0.02

White Probability = 12/200=0.06

Probability of all other color = 10/200=0.05

So, probability of randomly choosing a participant dreams in black and white or color =0.02+0.06+0.05=0.13

Therefore, the probability of randomly selecting participant dreams in black and white or color = 0.13

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The complete question is

Students majoring in psychology surveyed 200 of their fellow students about their dreams. The results of the survey are shown in the Venn diagram. Let B be the event that the participant dreams in black and white and let C be the event that the participant dreams in color.

What is the probability that a randomly selected participant dreams in black and white or color?

The probability of renting exactly three apartments in a week is approximately 0.2018 or 20.18%.

If the average number of units rented per week is 2.3 and the distribution is Poisson, then the parameter lambda is also equal to 2.3.

The probability of renting exactly three apartments in a week is given by the Poisson probability function:

\(P(X = 3) = (e^(-lambda) * lambda^x) / x!\)

Substituting the values, we get:

\(P(X = 3) = (e^(-2.3) * 2.3^3) / 3!\)

P(X = 3) = (0.09963 * 12.167) / 6

P(X = 3) = 0.2018

Therefore, the probability of renting exactly three apartments in a week is approximately 0.2018 or 20.18%.

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Answer:

8.

Step-by-step explanation:

P/Q = 3.125 = 3 1/8

- looks like the denominator Q could be 8.

It could not be any of the other choices.

25/8 = 3.125.

Value of x for which defined function f(x) = x²e⁻ˣ² gives the relative maximum value is equal to option D. -1 or  1.

Function 'f' is defined by f(x) = x²e⁻ˣ²

To get the relative maximum value of the function f(x) =  x²e⁻ˣ² find the first derivative we have,

f(x) =  x²e⁻ˣ²

Apply product rule of derivative :

d/dx ( u × v ) = v du /dx + u dv /dx

f' ( x ) =  e⁻ˣ² d/dx (x²) + x² d/dx (e⁻ˣ²)

⇒ f' (x) = 2x  e⁻ˣ² - 2x (x² ) ( e⁻ˣ² )

⇒  f' (x) = 2x  e⁻ˣ² - 2x³ e⁻ˣ²

⇒ f' (x) = 2x  e⁻ˣ²( 1 - x² )

To get the value of x for maximum function f' (x ) = 0 we get,

2x  e⁻ˣ²( 1 - x² ) = 0

⇒ 2≠0 or x =0 or  e⁻ˣ² ≠ 0 or 1 - x² = 0

⇒ x = 0 or x = ± 1

When

x = 0 ⇒ f(x) = 0

x = 1 ⇒ f(x) = e⁻¹

x = -1 ⇒ f(x) = e⁻¹

x = -1 or 1 represents the relative maximum value of f(x).

Therefore , value of x which represents the relative maximum value of the function f(x) = x²e⁻ˣ² is equal to option D. -1 or 1.

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Answer:

D. 3x + 5  = 2x -6

In the given scenario, angle DBC is 51 degrees, and line segment BD is a diameter of circle E. Circle E is inscribed within triangle BCD, where BD is also a diameter.

Line segments DC and CB are secants. We need to determine the measure of arc BC.

Since line segment BD is a diameter, angle BDC is a right angle, measuring 90 degrees. We are given that angle DBC is 51 degrees. In a circle, an inscribed angle is equal to half the measure of its intercepted arc.

Therefore, the measure of arc BC can be calculated as follows:

Arc BC = 2 * angle DBC = 2 * 51 degrees = 102 degrees.

Hence, the measure of arc BC is 102 degrees.

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The value of u is not provided, we cannot determine the exact value of y. None of the given options (a, b, c, d) can be chosen as the approximate value of y.

For the first question, you are given the model yhat = 2.1 + 1.0x^2 and you want to find the estimated marginal effect of x on y when x = 1.3. To find the estimated marginal effect, you need to take the derivative of yhat with respect to x. In this case, the derivative would be 2.0x.

Now, substitute x = 1.3 into the derivative:

2.0(1.3) = 2.6.

Therefore, the estimated marginal effect of x on y when x = 1.3 is 2.6.

For the second question, you are given the model \(lny = β₁ + β₂x^2 + u\), with parameter estimates

β₁ = 2 and

β₂ = 1.

To predict the value of y when x = 2, substitute the given values into the model:
\(lny = 2 + 1(2^2) + u\)
lny = 2 + 1(4) + u
lny = 2 + 4 + u
lny = 6 + u

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Answer:

$1,500

Step-by-step explanation:

To find how much money she made before paying taxes, divide 150 by 0.1:

150/0.1

= 1500

So, Kelly made $1,500 before taxes

Answer:

$1,500

Step-by-step explanation:

Turn 10% into a decimal: To turn a percent into a decimal, you move the decimal twice to the left.

10%=.1

Divide: $150 divided by .1=1500

$1,500

Hope this helped!! :)

Stay safe and have a wonderful day/night!!!!!

Good luck!

Brainliest?!?!

Step-by-step explanation:

you multiply both the top and bottom by the root if it was alone.

let's say if we had (1 - sqrt(2)) in the denominator. here we multiply both the numerator and the denominator by the conjugate.

the conjugate is formed by changing the sign between two terms in a binomial. so in this case the conjugate is

(sqrt(2) -1)

make sure to ask if you need any further guidance :)

The answers of a, and b are the probability that the selected student will be female is approximately 0.607, and the probability that the selected student will be male is approximately 0.393.

(a) To find the probability that a randomly selected student will be female, we can use the following formula: P (female) = (number of degrees awarded to women) / (total number of associate degrees awarded).

P(female) = 612,034 / 1,008,329
P(female) ≈ 0.607 (rounded to three decimal places)

So, the probability that the selected student will be female is approximately 0.607.

(b) To find the probability that a randomly selected student will be male, we first need to determine the number of degrees awarded to men: (total number of associate degrees awarded) - (number of degrees awarded to women).

Degrees awarded to men = 1,008,329 - 612,034 = 396,295

Now, we can use the same formula as before: P(male) = (number of degrees awarded to men) / (total number of associate degrees awarded).

P(male) = 396,295 / 1,008,329
P(male) ≈ 0.393 (rounded to three decimal places)
So, the probability that the selected student will be male is approximately 0.393.

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The answers of a, and b are the probability that the selected student will be female is approximately 0.607, and the probability that the selected student will be male is approximately 0.393.

(a) To find the probability that a randomly selected student will be female, we can use the following formula: P (female) = (number of degrees awarded to women) / (total number of associate degrees awarded).

P(female) = 612,034 / 1,008,329
P(female) ≈ 0.607 (rounded to three decimal places)

So, the probability that the selected student will be female is approximately 0.607.

(b) To find the probability that a randomly selected student will be male, we first need to determine the number of degrees awarded to men: (total number of associate degrees awarded) - (number of degrees awarded to women).

Degrees awarded to men = 1,008,329 - 612,034 = 396,295

Now, we can use the same formula as before: P(male) = (number of degrees awarded to men) / (total number of associate degrees awarded).

P(male) = 396,295 / 1,008,329
P(male) ≈ 0.393 (rounded to three decimal places)
So, the probability that the selected student will be male is approximately 0.393.

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Answer:

d= -79

Step-by-step explanation:

Subtract 18 from both sides which isolates d.

You then have your answer! Have a great day!

Answer:23

Step-by-step explanation: