Alberto conducted an experiment by rolling a fair six-sided number cube 60 times. He rolled a 2 fifteen times. Which statement about rolling a 2 in Alberto's experiment is correct?

Answer:

\(27\pi\)

Step-by-step explanation:

The area of a circle is given by the formula \(A = \pi r^2\).

We are given the radius of this circle, so we can plug in.

\(A = \pi r^2\\A=6^2\pi \\A=36\pi\)

Seeing that there is \(\frac{3}{4}\) of the circle left, multiply \(36\pi\) by \(\frac{3}{4}\).

\(36\pi(\frac{3}{4})\\ 9\pi (3)\\27\pi\)

Since 2 is not in this range, we can conclude that there is evidence against the hypothesis that Psi (theta) = 2.

Given a 0.95-confidence interval for a characteristic Psi (theta) is given by (1.23, 2.45). We are then asked if there is any evidence against the hypothesis H0: Psi (theta) = 2, the conclusion and reasoning are as follows: Conclusion: There is evidence against the hypothesis H0: Psi (theta) = 2.Justification:We know that the confidence interval is given by (1.23, 2.45), which means that if the true value of Psi (theta) is 2, then we would expect the confidence interval to contain the value 2. However, since the confidence interval does not contain the value 2, we have evidence against the hypothesis that Psi (theta) = 2. This is because the confidence interval represents the range of values that we are reasonably certain the true value of Psi (theta) falls within.

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To determine if there is evidence against the hypothesis \(H_0: \Psi (\theta) = 2\), we need to check if the hypothesized value of 2 falls within the given 0.95-confidence interval (1.23, 2.45).

Since the hypothesized value of 2 lies within the confidence interval, we can conclude that there is no evidence against the hypothesis \(H_0: \Psi (\theta) = 2\). In other words, the data supports the hypothesis that the characteristic \(\Psi\) is equal to 2.

The confidence interval (1.23, 2.45) suggests that we can be 95% confident that the true value of the characteristic \(\Psi\) falls within this interval. Since the hypothesized value of 2 falls within this interval, it is consistent with the data, and we do not have sufficient evidence to reject the hypothesis \(H_0: \Psi (\theta) = 2\).

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The bank's loan is better because it has a lower APR of 9.2% compared to the dealer's loan with an APR of 34.5%.

Given that, Vin Lin wants to buy a used car that costs $9,780. A 10% down payment is required. The used car dealer offered him a four-year add-on interest loan at 7% annual interest. We need to find the monthly payment.

(a) Calculation of monthly payment:

Loan amount = Cost of the car - down payment

= $9,780 - 10% of $9,780

= $9,780 - $978

= $8,802

Interest rate (r) = 7% per annum

Number of years (n) = 4 years

Number of months = 4 × 12 = 48

EMI = [$8,802 + ($8,802 × 7% × 4)] / 48= $206.20 (approx.)

Therefore, the monthly payment is $206.20 (approx).

(b) Calculation of APR of the dealer's loan:

As per the add-on interest loan formula,

A = P × (1 + r × n)

A = Total amount paid

P = Principal amount

r = Rate of interest

n = Time period (in years)

A = [$8,802 + ($8,802 × 7% × 4)] = $11,856.96

APR = [(A / P) − 1] × 100

APR = [(11,856.96 / 8,802) − 1] × 100= 34.5% (approx.)

Therefore, the APR of the dealer's loan is 34.5% (approx).

(c) APR of the bank's loan is less than the dealer's loan. So, the bank's loan is better for him.

(d) APR of the bank's loan is 9.2%.

APR of the dealer's loan is 34.5%.

APR of the bank's loan is less than the dealer's loan.

So, the bank's loan is better for him. Answer: The bank's loan is better.

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Answer:

¡Hola, soy Za'Riah! Con gusto te ayudaré con este problema. (ver explicación)

Step-by-step explanation:

Resolvamos tu problema usando la división larga.

(See image)

Answer:

D & A

Step-by-step explanation:

Any coordinate that is above the y-axis of 0, will have a greater y intercept. I hope this helps :)

a) The number of insects at t=0 days is 63.9

b) The growth rate is 0.071, or 7.1% per day.

c) The population after 10 days is 63.9.

d) The insect population will reach 13,507 insects approximately 26.4 days after the initial time.

e) The insect population will double approximately 19.0 days after the initial time.

In this problem, we are given a function that describes the size of a certain insect population at time t. We will use this information to answer various questions about the population, such as the initial size, growth rate, population after a certain number of days, and the time it takes for the population to reach specific thresholds.

The given function that describes the size of the insect population is

P(t) = 900 * 0.071.

(a) Determine the number of insects at t=0 days:

To find the number of insects at t=0 days, we substitute t=0 into the function P(t):

P(0) = 900 * 0.071 = 63.9

Therefore, the number of insects at t=0 days is 63.9.

(b) What is the growth rate of the insect population:

The growth rate of the insect population can be determined by examining the coefficient multiplying t in the function P(t).

In this case, the coefficient is 0.071. Since this coefficient is positive, it indicates that the population is growing.

The growth rate is 0.071, or 7.1% per day.

(c) What is the population after 10 days:

To find the population after 10 days, we substitute t=10 into the function P(t):

P(10) = 900 * 0.071 = 63.9

Therefore, the population after 10 days is 63.9.

(d) When will the insect population reach 13,507 insects:

To determine when the population reaches 13,507 insects, we need to solve the equation P(t) = 13,507. Let's set up the equation:

900 * 0.071 * t = 13,507

t = 13,507 / (900 * 0.071)

Simplifying the expression, we find:

t ≈ 26.4

Therefore, the insect population will reach 13,507 insects approximately 26.4 days after the initial time.

(e) When will the insect population double:

To determine when the insect population will double, we need to find the time at which P(t) is twice the initial population, P(0). Let's set up the equation:

2 * P(0) = 900 * 0.071 * t

2 * 63.9 = 900 * 0.071 * t

Simplifying the equation, we find:

t ≈ 19.0

Therefore, the insect population will double approximately 19.0 days after the initial time.

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Complete Question:

A The size of a certain insect population at time t (in days) obeys the function P(t) = 900 0.071

(a) Determine the number of insects at t=0 days.

(b) What is the growth rate of the insect population?

(c) What is the population after 10 days?

(d) When will the insect population reach 13507 insects ?

(e) When will the insect population double?

(Do not round until the final answer. Then round to the nearest tenth as needed.)

Answer:

the answer is 264000.....

Answer:

264,000

Step-by-step explanation:

4% of 220000 is 8800

8800 x 5 = 44000

220000 + 44000 = 264000

The correct interpretation of the statement x - 9 ≤ 0.3 is that the cut values should be less than or equal to 0.3 inches away from 9 inches.

If the cut values were greater than or equal to 0.3 inches away from 9 inches, it would violate this constraint and may result in incorrect or uneven cuts.

The statement x - 9 ≤ 0.3 in the context of the board cutting problem means that the cut values from the edge of the board should not exceed 0.3 inches.

In the board cutting problem, a carpenter needs to cut a board into smaller pieces of a certain length. To make accurate cuts, the carpenter needs to measure the distance between the blade of the saw and the edge of the board. The statement x - 9 ≤ 0.3 is a constraint on this distance.

Here, x represents the distance between the blade and the edge of the board. The value 9 represents the length that the carpenter wants to cut. The inequality x - 9 ≤ 0.3 means that the distance between the blade and the edge of the board should be less than or equal to 0.3 inches away from the cut line.

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Answer:

Option D

Step-by-step explanation:

By using geometric mean theorem in the given right triangle ABC,

\(\frac{AD}{BD}= \frac{BD}{DC}\)

BD² = AD × DC

h² = (AC - CD) × DC

h² = (25 - 16) × 16

h² = 9 × 16

h = \(\sqrt{144}\)

h = 12

Therefore, measure of side h = 12 units.

Option D will be the correct option.

Answer:

12 is correct via a p e x

The first quartile of the dataset {1, 2, 3, 4, 5, 6} is 2.

Given data set: {1,2,3,4,5,6}

Median of the given data set =3.5

The data set can be split into 2 parts as, {1,2,3} and {4,5,6}. The first quartile is calculated by simply finding the median of the first part of the data set.

Thus, the first quartile is 2.

The quarter divides the distribution into four groups and calculates the range of values above and below the mean.

A quartile separates the dataset into four categories by dividing the data into three points: the lowest, median, and upper quartiles.

The interquartile range, a measurement of variation around the median, is calculated using quartiles.

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Answer:

6,375 or 595

Step-by-step explanation:

Answer:

Step-by-step explanation:

To find f(g(x)) substitute g(x) into f(x) that's for every x in f (x) replace it by g (x)

We have

We have the final answer as

Hope this helps you

Answer:

\( {7}^{ - 8} \)

Step-by-step explanation:

\( {7}^{ - 1} \times {7}^{ - 7} \\ {7}^{ - 1 + - 7} \\ {7}^{ - 8} \)

Hope this helps you.

Required:

We need to convert from standard form to scientific notation and also scientific notation to standard form.

Explanation:

a) Convert from standard form to scientific notation:

1) Consider the number 4,520,000.

The given number can be written as follows.

The scientific notation of s

2) Consider the number

Multiply and divide by 10.

The scientific notation is

3) Consider the number.

Multiply and divide by 100.

The scientific notation is

b) convert from scientific notation to standard form:

1)

Consider the notation:

The standard form is 0.00006285.

2) Consider the notation.

The standard form is 79,000.

3) Consider the notation.

The standard form is 900,800.

Answer:

function gis defined as g (6) = - f (-4) graph

Answer:5.83

Step-by-step explanation:

Answer:

there are 5

Step-by-step explanation:

"im different"

The sample space of the statement is 2.

"A sample space is a collection or a set of possible outcomes of a random experiment. The sample space is represented using the symbol, “S”. The subset of possible outcomes of an experiment is called events. A sample space may contain a number of outcomes that depends on the experiment. If it contains a finite number of outcomes, then it is known as discrete or finite sample spaces."

"The samples spaces for a random experiment is written within curly braces “ { } “. There is a difference between the sample space and the events."

The given statement is "Answering a false question"

Sample space of the following is S = {True, False}

Hence B is the correct option.

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Answer:

39.24 sec

How long will it take a 1500 W motor to lift a 300 kg piano to a sixth-story window 20 m above? All tutors are evaluated by Course Hero as an expert in their subject area. Answer is t = 39.24 sec

Step-by-step explanation:

It will take the motor 39.2 seconds to lift the piano to the sixth-story window.

Given the following data;

We know that acceleration due to gravity is equal to 9.8 m/s².

To find how long it will take to lift the piano to the sixth-story window;

First of all, we would have to determine the gravitational potential energy required to lift the piano up.

Mathematically, gravitational potential energy is given by the formula;

\(G.P.E = mgh\)

where:

Substituting into the formula, we have;

\(G.P.E = 300*9.8*20\)

G.P.E = 58,800 Joules

Next, we would determine the time using the following formula;

\(Time = \frac{Energy}{Power}\)

Substituting the values into the formula, we have;

\(Time = \frac{58800}{1500}\)

Time = 39.2 seconds.

Therefore, it will take the motor 39.2 seconds to lift the piano to the sixth-story window.

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The integral of 1/ (x √(x²-a²)) is (1/2) ln[(x/ a) + √((x/a)² - 1)] + (1/2) sin⁻¹(x/a) + C, where C is a constant of integration.

To find the integral of 1/ (x √(x²-a²)), we can use a trigonometric substitution.

First, let's rewrite the denominator as:

√(x² - av) = a sin(θ)

where θ is an angle in the right triangle formed by a, x, and √(x² - a²).

Differentiating both sides with respect to x, we get:

(x / √(x² - a²)) dx = a cos(θ) dθ

Solving for dx, we get:

dx = (a cos(θ) / √(x² - a²)) dθ

Substituting this into our integral, we get:

∫ [1 / (x √(x²-a²))] dx = ∫ [1 / (a² sin(θ) cos(θ))] (a cos(θ) / √(x² - a²)) dθ

Simplifying, we get:

∫ [1 / (x √(x²-a²))] dx = ∫ [1 / (a sin(θ) cos(θ))] dθ

We can use the trigonometric identity:

1 / (sin(θ) cos(θ)) = 1 / (2 sin(θ) cos(θ)) + 1 / 2

to rewrite the integral as:

∫ [1 / (x √(x²-a²))] dx = (1/2) ∫ [1 / (sin(θ) cos(θ))] dθ + (1/2) ∫ dθ

Using the substitution u = sin(θ), we get:

∫ [1 / (x √(x²-a²))] dx = (1/2) ∫ [1 / (u(1-u²\()^{0.5}\))] du + (1/2) θ + C

where C is the constant of integration.

We can solve the first integral using a substitution of v = u^2, and then use the natural logarithm to obtain:

∫ [1 / (x √(x²-a²))] dx = (1/2) ln[(u + (1-u²\()^{0.5}\)) / u] + (1/2) θ + C

Substituting back in terms of x, we get:

∫ [1 / (x √(x²-a²))] dx = (1/2) ln[(x/ a) + √((x/a)² - 1)] + (1/2) sin⁻¹(x/a) + C

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Answer:

m = 32

Step-by-step explanation:

-4(2m-7) = 3(52 - 4m)

-8m + 28 = 156 - 12m

-8m + 12m = 156 - 28

4m = 128

m = 32 Ans...

The required solution is m = 32 to the given equation −4(2m − 7) = 3(52 − 4m).

Arithmetic operations can also be specified by subtracting, dividing, and multiplying built-in functions.

The equation is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are equal.

We have been given an equation as

⇒ -4(2m-7) = 3(52 - 4m)

Apply the distributive of multiplication,

⇒ -8m + 28 = 156 - 12m

Rearrange the terms of m in the above equation,

⇒ -8m + 12m = 156 - 28

Apply the subtraction operation,

⇒ 4m = 128

Divided by 4 both sides of the equation, we get

⇒ m = 32

Therefore, the solution is m = 32 to the given equation −4(2m − 7) = 3(52 − 4m).

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Answer:

Time when Jessie starts doing her he: 4:30

Time talked to complete the hw : 40minutes

Time Jessie finishes the hw: 5:10

Answer:

Step-by-step explanation:

For missing hypotenuse: \(\sqrt({a^{2} + b^{2})\)

Plug in the side lengths that are known to find the hypotenuse.

1. No, the angle is less than 18 degrees (closer to 15), so it is not safe

2. The length rounded to the nearest tenth is approximately 15.5 feet.

A line is the shortest distance between two points. The value of x from the given parameters is 3

A line is defined as the shortest distance between two points. Given the following parameters

TU = 1 - x,

UB = 4x + 17,

TB = -3x

According to the addition postulate;

TU + UB = TB

Substitute the given parameters to have:

1 - x + 4x + 17 = -3x

Collect the like terms to have:

1+3x+17 = -3x

3x+3x = -1-17

Simplify

6x = -18

Divide both sides by 6

6x/6 = -18/6

x = -18/6

x = -3

Hence the value of x from the given parameters is 3

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Answer:

y=-9x²+54x+63

Step-by-step explanation:

y=-9(x²-7x+x-7)

y= -9(x²-6x-7)

y=-9x²+54x+63

There are 4 integers between 20 and 30 that have a prime factorization with exactly 3 factors that are not necessarily unique.

To find the integers with a prime factorization having exactly 3 factors, we need to look for numbers that can be expressed as the product of two distinct prime numbers.

Step 1: Identify the prime numbers between 20 and 30. The prime numbers in this range are 23, 29.
Step 2: Determine all possible pairs of distinct prime numbers. In this case, we have only one pair: (23, 29).
Step 3: Calculate the products of these pairs. The products of (23, 29) are 667 and 667.
Step 4: Count the integers between 20 and 30 that match these products. We have two integers that match, which are 21 and 27.
Step 5: Check if these integers have exactly 3 factors. The factors of 21 are 1, 3, 7, and 21 (a total of 4 factors), so it does not meet the criteria. The factors of 27 are 1, 3, 9, and 27 (a total of 4 factors), so it also does not meet the criteria.

Therefore, there are no integers between 20 and 30 with a prime factorization having exactly 3 factors that are not necessarily unique.

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Answer:

-6

Step-by-step explanation:

this is written in point slope form, y=mx+b

we just need to recognize which numbers represent which variables,

(the "b" in the equation is the y-intercept)

Let's line them up to find out our "b"

y=-4x-6

y=mx+b

the -6 is where the "b" is located

Hope this helped and feel free to comment or ask questions!

Answer: 3/5

Step-by-step explanation: if you make a probability fraction and simplify it by dividing by 4, you would get 3/5.

The probability of of a random student having blue eyes and dark hair

 is 35% .

let consider the total students in the school be (U) = 100%

out of them ,

students having blue eyes (A) = 60%

students having  dark hair (B) = 55%

students with neither blue eyes nor dark hair (A∪B)' = 20%

let the students with blue eyes and dark hair be (A∩B) = x %

Then according to the set theorem

U = n(A∪B) + n(A∪B)'

U = n(A) + n(B) - n(A∩B) + n(A∪B)'

100 = 60 + 55 - x +20

∴ x = 60 + 55 +20 - 100

x = 35 %

So the probability of random student having blue eyes and dark hair is 35% .

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Answer:

Q1.  =213 Q.2 2145 Q.3 =23.2$ Q.4 53 Q.5 10.5

Step-by-step explanation: