Factor the following expression using the GCF: 10ab + 20.

Answer:

  1.075%

Step-by-step explanation:

You want the monthly periodic rate corresponding to an APR of 12.9%.

There are 12 months in a year, so the monthly rate is 1/12 of the annual rate:

  12.9%/12 = 1.075%

The monthly periodic rate is 1.075%.

__

Additional comment

The APR does not take compounding into account, so the effective annual rate may be higher.

The equation of the tangent line to the curve \(xey yex\)= 3 at the point (0, 3) is y = 3.

To find the equation of the tangent line to the curve at the point (0, 3), we need to determine the slope of the tangent line and use the point-slope form of a line.

First, let's differentiate the equation implicitly with respect to x:

Differentiating both sides of the equation \(xey yex\)= 3 with respect to x:

\(ey yex + xey dy/dx - yex dex/dx = 0ey yex + xey dy/dx - yex (1) = 0ey yex + xey dy/dx - yex = 0\)

Now, substitute the coordinates of the given point (0, 3) into the equation:

ey(0) (0) + (0)ey dy/dx - (3)ex = 0

0 + 0 + 0 = 0

This implies that the value of dy/dx at (0, 3) is 0.

Therefore, the slope of the tangent line is 0.

Now we can write the equation of the tangent line using the point-slope form, y - y1 = m(x - x1), where (x1, y1) is the point (0, 3) and m is the slope (which is 0):

y - 3 = 0(x - 0)

Simplifying further:

y - 3 = 0

Therefore, the equation of the tangent line to the curve \(xey yex\)= 3 at the point (0, 3) is y = 3.

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The required sample size for the probability that the sample mean differs from the population mean by more than 2.0 hours is less than 0.05 is 68.

Given that the number of hours spent studying by students on large campus in the week before final exams follows a normal distribution with a standard deviation of 8.4 hours.

we want to find the size of the sample which is needed to ensure that the probability that the sample mean differs from the population mean by more than 2.0 hours is less than 0.05.

Here, the margin of error is E=2 and the level of significance is α=0.05

The critical value is Zα/2=Z₀.₀₂₅

or the critical value is 1.96

Now, we will find the sample size

n=((Zα/2)×σ/E)²

n=(1.96×8.4/2)²

n=67.76

n≈68

Hence, the size of sample which is needed to ensure that the probability that the sample mean differs from the population mean by more than 2.0 hours is less than 0.05 is 68.

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Option D correctly states that a function can't satisfy all the given conditions simultaneously.

If a function satisfies f(x) > 0, it means the function takes positive values on the interval. If f'(x) > 0, it indicates that the function is increasing on the interval, meaning its slope is positive. Conversely, if f'(x) < 0, it implies that the function is decreasing on the interval, meaning its slope is negative.

For a function to satisfy both f'(x) > 0 and f'(x) < 0 on the same interval, it would require the function to change from increasing to decreasing or vice versa within that interval. However, such a situation is not possible because if the function is increasing, its derivative (slope) cannot suddenly become negative, and if the function is decreasing, its derivative cannot suddenly become positive.

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Answer:

I believe it's false

Step-by-step explanation:

Answer:

false

Step-by-step explanation:

..................

To find the smallest possible value of $n$, we need to find the smallest value that satisfies all three conditions.

From the first condition, we know that $n = 9a + 5$ for some positive integer $a$.
From the second condition, we know that $n = 7b + 3$ for some positive integer $b$.
From the third condition, we know that $n = 5c + 1$ for some positive integer $c$.
We can set these equations equal to each other and solve for $n$:
$9a + 5 = 7b + 3 = 5c + 1$
Starting with the first two expressions:
$9a + 5 = 7b + 3 \Rightarrow 9a + 2 = 7b$
The smallest values of $a$ and $b$ that satisfy this equation are $a=2$ and $b=3$, which gives us $n = 9(2) + 5 = 7(3) + 3 = 23$.
Now we need to check if this value of $n$ satisfies the third condition:
$n = 23 \not= 5c + 1$ for any positive integer $c$.
So we need to try the next possible value of $a$ and $b$:
$9a + 5 = 5c + 1 \Righteous 9a = 5c - 4$
$7b + 3 = 5c + 1 \Righteous 7b = 5c - 2$
If we add 9 times the second equation to 7 times the first equation, we get:
$63b + 27 + 49a + 35 = 63b + 45c - 36 + 35b - 14$
Simplifying:
$49a + 98b = 45c - 23$
$7a + 14b = 5c - 3$
$7(a + 2b) = 5(c - 1)$
So the smallest possible value of $c$ is 2, which gives us $a + 2b = 2$. The smallest values of $a$ and $b$ that satisfy this equation are $a=1$ and $b=1$, which gives us $n = 9(1) + 5 = 7(1) + 3 = 5(2) + 1 = 46$.
Therefore, the smallest possible value of $n$ is $\boxed{46}$.

To find the smallest possible value of $n$ which is a four-digit positive integer such that dividing $n$ by $9$, the remainder is $5$, dividing $n$ by $7$, the remainder is $3$, and dividing $n$ by $5$, the remainder is $1$, follow these steps:
Step 1: Write down the congruences based on the given information.
$n \equiv 5 \pmod{9}$
$n \equiv 3 \pmod{7}$
$n \equiv 1 \pmod{5}$
Step 2: Use the Chinese Remainder Theorem (CRT) to solve the system of congruences. The CRT states that for pairwise coprime moduli, there exists a unique solution modulo their product.
Step 3: Compute the product of the moduli.
$M = 9 \times 7 \times 5 = 315$
Step 4: Compute the partial products.
$M_1 = M/9 = 35$
$M_2 = M/7 = 45$
$M_3 = M/5 = 63$
Step 5: Find the modular inverses.
$M_1^{-1} \equiv 35^{-1} \pmod{9} \equiv 2 \pmod{9}$
$M_2^{-1} \equiv 45^{-1} \pmod{7} \equiv 4 \pmod{7}$
$M_3^{-1} \equiv 63^{-1} \pmod{5} \equiv 3 \pmod{5}$
Step 6: Compute the solution.
$n = (5 \times 35 \times 2) + (3 \times 45 \times 4) + (1 \times 63 \times 3) = 350 + 540 + 189 = 1079$
Step 7: Check that the solution is a four-digit positive integer. Since 1079 is a three-digit number, add the product of the moduli (315) to the solution to obtain the smallest four-digit positive integer that satisfies the conditions.
$n = 1079 + 315 = 1394$
The smallest possible value of $n$ is 1394.

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Answer:

The measure of JHK is 25 degrees

Step-by-step explanation:

If GHI is equilateral, it means each of the angles are equal to 60 degrees

Thus;

7x - 31 = 60

7x = 60 + 31

7x = 91

x = 91/7

x = 13 degrees

The measure of JHK IS x + 12

simply insert the value of x here

Angle JHK = 13 + 12

Angle JHK is 25 degrees

Answer: 25

Step-by-step explanation:

The radius of the cone is 783.84/√h

A cone is the surface traced by a moving straight line (the generatrix) that always passes through a fixed point (the vertex).

Volume is defined as the space occupied within the boundaries of an object in three-dimensional space.

The volume of a cone is expressed as;

V = 1/3πr²h

643072 × 3 = 3.14 × r²h

r²h = 614400

r² = 614400/h

r = 783.84/√h

therefore the radius of the cone is 783.84/√h

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Answer:

x=15, y=7

Step-by-step explanation:

Angles that form a linear pair are supplementary, so:

\(2(5x-5)+3x-5=180 \\ \\ 10x-10+3x-5=180 \\ \\ 13x-15=180 \\ \\ 13x=195 \\ \\ x=15 \\ \\ \\ \\ 5y+5+20y=180 \\ \\ 25y+5=180 \\ \\ 25y=175 \\ \\ y=7\)

Because r must be between -1.00 and +1.00 and the closer to either indicates a stronger relationship, the strongest must be -0.74. It is a strong negative correlation.

Any statistical association, whether causal or not, between two random variables or bivariate data is referred to in statistics as correlation or dependency. A statistical measure known as correlation expresses how closely two variables are related linearly (meaning they change together at a constant rate). It's a typical technique for describing straightforward connections without explicitly stating cause and consequence.

A relationship between two variables is said to have a positive correlation when both variables move in the same direction. Consequently, when one variable rises as the other rises, or when one variable falls while the other falls. The link between height and weight is a good example.

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True, in a probability model, the sum of the probabilities of all outcomes must equal 1.

The statement is true. In a probability model, the probabilities assigned to all possible outcomes must add up to 1. This principle is known as the Law of Total Probability and is a fundamental property of probability theory.

When working with probabilities, we assign a probability value to each possible outcome or event. These probabilities must satisfy certain conditions, one of which is that their sum must be equal to 1. This ensures that the total probability accounts for all possible outcomes and covers the entire sample space.

The sum of probabilities equal to 1 reflects the notion that the entire sample space represents the complete set of possible outcomes, and therefore, the sum of their probabilities must encompass the entire probability space.

If the sum of the probabilities of all outcomes does not equal 1, it would violate the principles of probability theory, leading to inconsistencies and invalid calculations. Therefore, ensuring that the sum of probabilities equals 1 is crucial for a valid and coherent probability model.

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Answer:71

Step-by-step explanation:

ab +c= d

To solve for b;

First subtract c from both-side of the equation

ab + c - c = d-c

ab = d-c

Then divide both-side of the equation by a

The work done in pumping water out over the top edge to empty the tank is approximately 9984 foot-pounds, rounded to one decimal place.

To calculate the work done in pumping water out of the tank, we will use the formula:

Work = weight of water × height to be lifted

First, let's find the volume of the tank:

Next, find the total weight of the water in the tank:

Since the height of the tank is 4 feet, and we need to pump the water over the top edge, we can assume the average height the water needs to be lifted is half the height of the tank, which is 2 feet.

Now, we can calculate the work done:

So, the work done in pumping water out over the top edge to empty the tank is approximately 9984 foot-pounds, rounded to one decimal place. Here is the visualization:

_______

|       |

|       | 4 feet

|       |

|_______|

  5 feet

|\

| \

h  \

|___\____

    5 feet

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Another solution to the given differential equation x²y" + 3xy' - 8y = 0, with y = x as one solution, is y = x³.

We are given a homogeneous, linear, second-order differential equation: x²y" + 3xy' - 8y = 0. One solution is y = x. To find another solution, we will use the method of reduction of order. Assume the second solution is in the form y = vx, where v is a function of x.

1. Compute y' = v'x + v.
2. Compute y" = v''x² + 2v'x.
3. Substitute y, y', and y" into the differential equation: x²(v''x² + 2v'x) + 3x(v'x + v) - 8(vx) = 0.
4. Simplify the equation: x(v''x² + 2v'x) + 3(v'x + v²) - 8v = 0.
5. Factor out x: v''x² + 2v'x + 3v'x + 3v² - 8v = 0.
6. Solve for v: v''x² + 5v'x + 3v² - 8v = 0, v = x².
7. Calculate the second solution: y = vx = x(x²) = x³.

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Answer:

0.33333333333e3

Step-by-step explanation:

e = infinity

The value such that 50% or more of the students studied longer than that value is 13.

To find the value such that 50% or more of the students studied longer than that value, we need to determine the median of the dataset. The median is the middle value when the data is arranged in ascending order.

The given dataset for hours studied in a week is: 5, 8, 13, 17, 20.

To find the median, we arrange the data in ascending order:

5, 8, 13, 17, 20

Since we have an odd number of values, the median is the middle value, which is 13.

Therefore, the value such that 50% or more of the students studied longer than that value is 13.

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Paper Company will make the following entry:

Debit: Notes Receivable - Dame Company $4,700

Credit: Accounts Receivable $4,700

What is an entry?

An "entry" in accounting refers to the recording of a financial transaction or event in the company's books or accounting system. It is the process of documenting the impact of a transaction on the financial statements.

1. Debit: Notes Receivable - Dame Company ($4,700) - This account represents the amount owed to Paper Company by Dame Company and is classified as a noncurrent asset since it will be settled in more than one year.

2. Credit: Accounts Receivable ($4,700) - This account represents the open accounts receivable from Dame Company, which is now being settled through the promissory note.

By making this entry, Paper Company acknowledges the receipt of the promissory note and removes the outstanding accounts receivable from their books, replacing it with a notes receivable asset.

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Answer:

Step-by-step explanation:

The statement "the ratio of female birds to male birds was 85" means that for every 85 female birds at the pet store, there was 1 male bird. The ratio is typically written as "85:1" or "85/1" to show the comparison between the number of female birds and male birds.

The equation that defines the exponential function with base = a, (a > 0) is y = aˣ. The range of this function is (0, ∞), if a≠1. Therefore, option A. is correct.

To write an equation that defines the exponential function with base = a (a > 0), the equation is:
f(x) = aˣ

If a≠1, the range of this function is (0, ∞) because the function is always positive and approaches infinity as x approaches infinity, but never reaches zero.
This is because an exponential function with a base greater than 0 and not equal to 1 will always have positive outputs, and as x increases, the function will approach infinity. Conversely, as x decreases, the function will approach 0 but never actually reach it.

Therefore, the correct option is A. (0, ∞).

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Answer:

1 6/9 or 1 2/3

Step-by-step explanation:

Answer: A lot of fractions

Step-by-step explanation:

Some Examples: 5/3, 10/6, 20/12

Given equation g = x-1/k in terms of x would be x = 1 + gk

for given question,

we have been given an equation g = x-1/k

Dyani began solving the equation g = x-1/k for x by using the addition property of equality.

We solve given equation for x.

⇒ g = x-1/k                      ..........(Given)

⇒ gk = (x - 1/k)k               .........(Multiply both the sides by k)

⇒ gk = x - 1

⇒ gk + 1 = x - 1 + 1           .........(Add 1 to each side)

⇒ gk + 1 = x

⇒ x = 1 + gk

Therefore, given equation g = x-1/k in terms of x would be x = 1 + gk

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The figure consists of a rectangle and 2 right triangles, as shown in the diagram below

The areas of a rectangle and a triangle are given by the following formulas

In our case,

Thus,

The total area is 150mm^2

Answer:

5

Step-by-step explanation:

The statement "P implies Q" is false under the following conditions: a) P is true and Q is false, and d) P is false and Q is true.

The statement "P implies Q" can be expressed as "if P, then Q." It is a conditional statement where P is the antecedent (the condition) and Q is the consequent (the result).

To determine when the statement is false, we need to identify cases where P is true but Q is false, or when P is false but Q is true.

Option a) states that both P and Q are true. In this case, the statement "P implies Q" holds true because if P is true, then Q is true.

Option b) states that both P and Q are false. In this case, the statement "P implies Q" is considered true because the antecedent (P) is false.

Option c) states that P is true and Q is false. Under this condition, the statement "P implies Q" is false because when P is true, but Q is false, the implication does not hold.

Option d) states that P is false and Q is true. In this case, the statement "P implies Q" is true because the antecedent (P) is false.

Therefore, the conditions under which the statement "P implies Q" is false are a) P is true and Q is false, and d) P is false and Q is true.

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A

Step-by-step explanation:

Answer:

2 cans

Step-by-step explanation:

Calculate how many pounds he needs for one day:

3(0.5)=1.5 pounds for each day Alvin is gone ( 3 represents his dogs, .5 is each dog's food)

Convert into ounces:

1.5*16=24 ounces for one day

Question: If dog food is sold in 12 oz cans, how many will he need?

24/12=2 cans

Thus, he will need 2 cans

I would say the answer is May because May has the highest bar out of each of the two graphs.

The mean is 1, variance is 0.9, and standard deviation is 0.948, rounded to three decimal places. Given data: Of all the registered automobiles in Colorado, 10% fail the state emissions test.

Ten automobiles are selected at random to undergo an emissions test.a. Find the probability:

1) That exactly three of them fail the test.

For the number of success (x) and number of trials (n),

the probability mass function (PMF) for binomial distribution is given by: \(P(X = x) = C(n, x) * p^{(x)} * q^{(n-x)},\)

where \(C(n, x) = (n!)/((n-x)! * x!) ,\)

p and q are the probabilities of success and failure, respectively. Here, the probability of success is the probability of an automobile to fail the test, p = 0.10 and the probability of failure is q = 1 - p = 0.90.

Now, X is the number of automobiles that fail the test.

Thus, n = 10, x = 3, p = 0.10, and q = 0.90.

Using the above formula:

\(P(X = 3) = C(10, 3) * (0.10)^{(3)} * (0.90)^{(10-3)}\\= 0.057\)

The required probability is 0.057, rounded to three decimal places.

1) That fewer than three of them fail the test.

The required probability is P(X < 3).P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2) Using the above formula:

\(P(X = 0) = C(10, 0) * (0.10)^{(0)} * (0.90)^{(10)}\)

= 0.3487P(X = 1)

= \(C(10, 1) * (0.10)^{(1) }* (0.90)^{(9)}\)

= 0.3874P(X = 2) = \(C(10, 2) * (0.10)^{(2)} * (0.90)^{(8)}\)

 = 0.1937

Now, P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2)

= 0.3487 + 0.3874 + 0.1937

 = 0.9298

The required probability is 0.9298, rounded to three decimal places.

1) That at least eight of them fail the test.

The required probability is

P(X ≥ 8).P(X ≥ 8) = P(X = 8) + P(X = 9) + P(X = 10) Using the above formula:

\(P (X = 8) = C(10, 8) * (0.10)^{(8)} * (0.90)^{(2) }\)

= 0.0000049

\(P(X = 9) = C(10, 9) * (0.10)^{(9)} * (0.90)^{(1) }\)

= 0.0000001

\(P(X = 10) = C(10, 10) * (0.10)^{(10)} * (0.90)^{(0)}\)

= 0.0000000001

Now,

P(X ≥ 8) = P(X = 8) + P(X = 9) + P(X = 10)

= 0.0000049 + 0.0000001 + 0.0000000001 = 0.000005

The required probability is 0.000005,

rounded to three decimal places.

b. Find the mean, variance, and standard deviation of the number of automobiles fail the test.

The mean (μ) for binomial distribution is given by: μ = n * p,

where n is the number of trials and p is the probability of success.

The variance (\(= 1 \sigma ^ 2 = n * p * q = 10 * 0.10 * 0.90 ^2\)) for binomial distribution is given by: \(\sigma ^2 = n * p * q\)

The standard deviation (σ) for binomial distribution is given by:

σ = √(n * p * q)

Here, n = 10 and p = 0.10.

Thus, q = 0.90.

Using the above formulas:

μ = n * p = 10 * 0.10

\(= 1\sigma ^2 = n * p * q = 10 * 0.10 * 0.90\)

= 0.9σ = √(n * p * q)

= √(10 * 0.10 * 0.90)

= 0.948

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Hence, the probability that X^2 + Y^2 is less than or equal to 10 is 1.

To show that X and Y are independent, we need to demonstrate that their joint probability mass function (PMF) factorizes into the product of their marginal PMFs.

The joint PMF is given by PXY(k, l) = 1/(2^(k+l)) for k, l = 1, 2, 3, ...

To find the marginal PMF of X, we sum the joint PMF over all possible values of Y:

PX(k) = ∑ PXY(k, l) = ∑ (1/(2^(k+l))) for l = 1, 2, 3, ...

Using the formula for the sum of a geometric series, we have:

PX(k) = 1/(2^k) * ∑ (1/2)^l for l = 1, 2, 3, ...

Applying the formula for the sum of an infinite geometric series, we get:

PX(k) = 1/(2^k) * (1/2) / (1 - 1/2) = 1/(2^k) for k = 1, 2, 3, ...

Therefore, the marginal PMF of X is given by PX(k) = 1/(2^k) for k = 1, 2, 3, ...

Similarly, to find the marginal PMF of Y, we sum the joint PMF over all possible values of X:

PY(l) = ∑ PXY(k, l) = ∑ (1/(2^(k+l))) for k = 1, 2, 3, ...

Using the same approach as before, we find:

PY(l) = 1/(2^l) for l = 1, 2, 3, ...

Therefore, the marginal PMF of Y is given by PY(l) = 1/(2^l) for l = 1, 2, 3, ...

Since the joint PMF can be expressed as the product of the marginal PMFs (PXY(k, l) = PX(k) * PY(l)), X and Y are independent.

Now let's find P(X^2 + Y^2 ≤ 10):

Since X and Y are independent, the joint distribution of X^2 and Y^2 is given by the product of their marginal distributions:

P(X^2 + Y^2 ≤ 10) = P(X^2 ≤ 10) * P(Y^2 ≤ 10)

To find each term, we can sum the marginal PMFs over the appropriate range:

P(X^2 ≤ 10) = PX(1) + PX(2) + PX(3) + ...

= 1/2 + 1/4 + 1/8 + ...

= 1

Similarly,

P(Y^2 ≤ 10) = PY(1) + PY(2) + PY(3) + ...

= 1/2 + 1/4 + 1/8 + ...

= 1

Therefore,

P(X^2 + Y^2 ≤ 10) = P(X^2 ≤ 10) * P(Y^2 ≤ 10) = 1 * 1 = 1

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