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To use the change of base formula, we first identify the base of the original logarithm and the desired base of the new logarithm.

The change of base formula is a useful tool in logarithmic functions that allows us to rewrite a logarithm with one base as an equivalent logarithm with a different base. The formula is as follows:

logᵦ a = logᵦ(x) / logₐ(x)

where a is the value being logged, β is the base of the original logarithm, and x is any positive number other than 1.

We then apply the formula by taking the logarithm of the value being logged with the desired base, and dividing it by the logarithm of the same value with the original base.

For example, let's say we want to rewrite the logarithm log₂ 8 in base 10. Using the change of base formula, we have:

log₂ 8 = log₁₀ 8 / log₁₀ 2

The value of log₁₀ 8 is simply 0.9031, and the value of log₁₀ 2 is 0.3010, so we have:

log₂ 8 = 0.9031 / 0.3010 ≈ 3

Therefore, log₂ 8 is equivalent to log₁₀ 8 ≈ 3. By using the change of base formula, we can simplify logarithmic expressions and evaluate them using common logarithms or natural logarithms.

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The function that has the greatest rate of change is y = x

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

y = -x ,

y = 3/4x +1,

y = 1/2x +2,

y = x

A linear function is represented as

y = mx + c

Where

rate of change = m

So, we have

y = -x , rate = -1

y = 3/4x +1, rate = 3/4

y = 1/2x +2, rate = 1/2

y = x, rate = 1

This means that the function with the highest rate is y = x

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The volume of the fully - inflated balloon is 4186.67 cubic inches. The solution has been obtained by using the formula for sphere.

What is a sphere?

The geometric equivalent of a circle in two dimensions in three dimensions is a sphere. A collection of three-dimensional points with the same r separation between them are referred to as a sphere.

We are given diameter as 20 inches.

So, the radius is half of the diameter which comes out to be 10 inches.

From this, we get the volume as

⇒ Volume = [tex]\frac{4}{3}[/tex] π [tex]r^{3}[/tex]

⇒ Volume = [tex]\frac{4}{3}[/tex] π [tex]10^{3}[/tex]

⇒ Volume = [tex]\frac{4000}{3}[/tex] π

⇒ Volume = 4186.67 cubic inches

Hence, the volume of the fully - inflated balloon is 4186.67 cubic inches.

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It should be noted that 3/10 kg to grams will be 300 grams.

To convert 3/10 kg to grams (g), we can use the following conversion factor:

1 kg = 1000 g

Therefore:

3/10 kg = (3/10) x 1000 g = 300 g

Hence, 3/10 kg is equal to 300 grams (g).

In conclusion, it should be noted that 3/10 kg to grams will be 300 grams.

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Answer:

1213124

To add 213341 and 444233 in base 5, we need to line up the digits of the two numbers according to their place values, and then add them digit by digit, carrying over to the next place value if the sum of the digits is 5 or greater.

Here's how to do it:

 2   1   3   3   4   1

+ 4   4   4   2   3   3

-----------------------

 1   2   1   3   1   2   4

Therefore, the sum of 213341 and 444233 in base 5 is 1213124.

The interest that Tamika will be charged in interest after 24 months of borrowing $5,000 at 8% simple interest per year is $800.

Simple interest is the interest system that computes interest only on the principal for each period.

Unlike the compound interest system, simple interest does not charge interest on accumulated interest and the principal.

The principal loan amount borrowed by Tamika = $5,000

The interest rate per year = 8%

The loan period = 24 months = 2 years (24/12)

Simple Interest = Principal x Rate x Period

= $800 ($5,000 x 8% x 2)

Thus, for borrowing $5,000 for 24 months of 2 years, Tamika would pay a simple interest of $800.

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Tamika is seeking a loan with a simple interest rate of 8% per year. If she wants to borrow $5,000, then how much will she be charged in interest after 24 months?

Answer:

The p-value is the probability of observing a test statistic as extreme or more extreme than the observed one, assuming the null hypothesis is true. In this case, since it is a right-tailed test, the p-value is the area to the right of the observed test statistic Z=1.74 under the standard normal distribution curve.

The accounting terms when matched with their relevant actions would be;

A company's free cash flow is an indicator of its ability to cover expenses and invest in future growth opportunities. A high level of free cash flow suggests that the business is doing well financially, while a low amount indicates that the opposite is true.

In order to generate income or save money over time, companies will make capital expenditures. However, if investors deem a company to be underperforming or unlikely to provide returns on investment, they may choose to sell their shares as a preventative measure against further financial losses.

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Answer: 2.303

Explanation: In image

Answer:

True proportion of homeowners in the population lies between 0.333 and 0.847

Step-by-step explanation:

If 9 out of 22 randomly picked people said they rented their homes, then the remaining 13 must own their homes. Therefore, the point estimate of the proportion of homeowners is:

Point estimate = Number of homeowners / Total number of people surveyed

Point estimate = 13 / 22

Point estimate = 0.59 (rounded to two decimal places)

To calculate the 95% confidence interval for the true proportion of homeowners, we can use the following formula:

Confidence interval = Point estimate ± (Z-value x Standard error)

where the Z-value corresponds to the desired level of confidence and the standard error is given by:

Standard error = sqrt [ (Point estimate x (1 - Point estimate)) / Sample size]

For a 95% confidence interval, the Z-value is 1.96 (from the standard normal distribution). Using the point estimate obtained earlier, the sample size is 22, and we can calculate the standard error as:

Standard error = sqrt [ (0.59 x 0.41) / 22 ]

Standard error = 0.131 (rounded to three decimal places)

Substituting these values into the formula, we get:

Confidence interval = 0.59 ± (1.96 x 0.131)

Confidence interval = 0.59 ± 0.257

Confidence interval = (0.333, 0.847)

Therefore, with 95% confidence, we can say that the true proportion of homeowners in the population lies between 0.333 and 0.847.

Answer:

The answer to the question provided is option 2.

The vocabulary for a is called the apothem

The area of the regular polygon is [tex]2419.68 cm^2.[/tex]

a = 7√3 cm

s = 14 cm

The perimeter of the polygon is:

P = ns

where n is the number of sides of the polygon. We can find n using the formula:

[tex]n = 360 / (180 - (360 / 2n))[/tex]

where n is the number of sides. Substituting the given value for s, we get:

[tex]n = 360 / (180 - (360 / 2*7)) = 14[/tex]

Therefore, the polygon has 14 sides.

a = [tex]\sqrt{31.820 cm)^2 - (14 cm/2)^2}[/tex])

= 24.615 cm

A = (1/2) * apothem * perimeter

[tex](\frac{1}{2} ) * 24.615 cm * 196 cm \\=\\ 2419.68 cm^2[/tex]

Therefore, the area of the regular polygon is [tex]2419.68 cm^2.[/tex][tex]2419.68 cm^2.[/tex]

In summary,

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The values of angles x in the parallelogram maze are calculated below

The question is solved by taking the shapes from left to right on each row

So, we have

x + 65 = 180 --- adjacent angles

x = 115

x + 103 = 180 --- adjacent angles

x = 77

9x = 90 --- angles in a rectangle

x = 10

x + 85 = 180 --- adjacent angles

x = 95

x + 60 = 180 --- adjacent angles

x = 120

2x = 90 --- angles in a rectangle

x = 45

x = 98 -- opposite angles in a parallelogram

3x = 81 -- opposite angles in a parallelogram

x = 27

4x + 76 = 180 --- adjacent angles

x = 26

3x = 78 -- opposite angles in a parallelogram

x = 26

8x + 68 = 180 --- adjacent angles

x = 14

4x = 72 -- opposite angles in a parallelogram

x = 18

x + 126 = 180 --- adjacent angles

x = 54

x = 90 -- opposite angles in a parallelogram

6x = 90 -- opposite angles in a parallelogram

x = 15

2x + 62 = 180 --- adjacent angles

x = 59

6x = 106 --- opposite angles in a parallelogram

x = 17.6

5x = 90 --- angles in a rectangle

x = 18

5x + 80 = 180 --- adjacent angles

x = 20

10x = 90 --- angles in a rectangle

x = 9

2x = 100 --- opposite angles in a parallelogram

x = 50

6x = 96 --- opposite angles in a parallelogram

x = 16

x + 105 = 180 --- adjacent angles

x = 75

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Therefore, the volume of the composite solid is approximately 1357.28 cubic feet, rounded to the nearest hundredth.

Volume is a measure of the amount of space occupied by an object or a substance. In other words, it is the three-dimensional space that an object or substance occupies. The SI unit for volume is cubic meters (m³), although other units such as cubic centimeters (cm³) and liters (L) are also commonly used.

Here,

The composite solid is made up of a hemisphere and a cone with the same base radius and height. The volume of the hemisphere is given by (2/3)πr³, and the volume of the cone is given by (1/3)πr²h, where r is the radius and h is the height. Given that the radius is 6 feet and the height is 12 feet, we can find the volumes of the hemisphere and the cone as follows:

Volume of hemisphere = (2/3)π(6³)

= 288π cubic feet

Volume of cone = (1/3)π(6²)(12)

= 144π cubic feet

The total volume of the composite solid is the sum of the volumes of the hemisphere and the cone, which is:

Total volume = Volume of hemisphere + Volume of cone

= 288π + 144π

= 432π

To find the numerical value of this volume, we can use the approximation π ≈ 3.14 and round the result to the nearest hundredth:

Total volume ≈ 432(3.14)

= 1357.28 cubic feet

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Answer:

the function f(x) is f(x) = 5x + 4.

Step-by-step explanation:

To find f(x), we need to use the formula:

(gof)(x) = g(f(x)) = 3f(x) - 2

We are given that (gof)(x) = 15x + 10, so we can substitute this expression into the formula to get:

3f(x) - 2 = 15x + 10

Simplifying this equation, we get:

3f(x) = 15x + 12

Dividing both sides by 3, we get:

f(x) = 5x + 4

Therefore, the function f(x) is f(x) = 5x + 4.

Answer:

It can't be factor

Step-by-step explanation:

n^4 − 4n^3 − 17n^2 − 36n + 108

The GCF of this is 1, so the equation can't be factor.

Answer:

x=6.4

Step-by-step explanation:

2/3.2 = 4/x

2x=4(3.2)

2x=12.8

x=6.4

The distance of the point from the line is d =

Given data ,

Let the point be P ( 1 , 1 )

Let the equation of line be represented as e

where A ( -5 , 0 ) and B ( 1 , -2 ) lies on the line

So , slope m = ( 0 + 2 ) / ( -5 - 1 )

m = 2/-6

m = -1/3

So , the equation of line is

y - 0 = ( -1/3 ) ( x + 5 )

y = ( -1/3 ) ( x + 5 )

( 1/3 )x + y + 5/3 = 0

Now , the Distance of a point to line D = | Ax₀ + By₀ + C | / √ ( A² + B² )

On simplifying , we get

D = | ( 1/3 )( 1 ) + ( 1 ) ( 1 ) + ( 5/3 ) | / √[ ( 1/3 )² + ( 1 )² ]

D = | ( 6/3 ) + 1 | / √ [ ( 1/9 ) + 1 ]

D = 3 / ( 10 ) / 9

D = 27/10

D = 2.7 units

Hence , the distance is 2.7 units

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The difference in what you have as a balance in your check register versus your online statment by 11/18 is $34.78.

The combined total of the 2 transactions they have in common is $206.99.

Use the amount in 11/1 as your balance, then compute by deducting the checks (chk) and debit purchases and adding the deposits. Then get the difference.

Check Register:

Total = 397.45 - 50.32 - 16.32 + 190.67

Total = 521.48

Online Statement:

Total = 486.44 - 84.80 - 19.73 - 16.32 + 190.67

Total = 556.26

Difference = online - check register

Difference = 34.78

On 11/10 and 11/18, check and online have the same transactions (same date, same amount) which are 16.32 and 190.67. Add them together to get 206.99

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The image of point R by rotation is equal to R'(x, y) = (- 4, 7).

The statement of the problem asks us to find the image of point by a kind of rigid transformation known as rotation, whose formula is:

(x, y) → (x · cos θ - y · sin θ, x · sin θ + y · cos θ)

Where:

If we know that x = 4, y = 7 and θ = - 180°, then the coordinates of the image of point R are:

R'(x, y) = (4 · cos 180° - 7 · sin 180°, 4 · sin 180° + 7 · cos 180°)

R'(x, y) = (- 4, 7)

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The limit [tex]\lim _{x\to \infty \:}\frac{1}{3^x}+3^{\frac{1}{x}}[/tex] without using L'Hopital's Rules has a value of 1

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

[tex]\lim _{x\to \infty \:}\frac{1}{3^x}+3^{\frac{1}{x}}[/tex]

By substitution, we have

[tex]\lim _{x\to \infty \:}\frac{1}{3^x}+3^{\frac{1}{x}} = \frac{1}{3^{}\infty}+3^{\frac{1}{\infty}}[/tex]

So, we have

[tex]\lim _{x\to \infty \:}\frac{1}{3^x}+3^{\frac{1}{x}} = 0+3^0[/tex]

Evaluate the exponents

[tex]\lim _{x\to \infty \:}\frac{1}{3^x}+3^{\frac{1}{x}} = 0+1[/tex]

Evaluate the sum

[tex]\lim _{x\to \infty \:}\frac{1}{3^x}+3^{\frac{1}{x}} = 1[/tex]

Hence, the solution is 1

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The calculated value of the maximum possible value of the objective function is 46

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

Objective function, F = 5x + 6y

The coordinates of the feasible region are

(0, 6), (1, 6.5) and (2, 6)

Substitute (0, 6), (1, 6.5) and (2, 6) in the above equation, so, we have the following representation

F(0, 6) = 5(0) + 6(6) = 36

F(1, 6.5) = 5(1) + 6(6.5) = 44

F(2, 6) = 5(2) + 6(6) = 46

The maximum value above is 46 at (2, 6)

Hence, the maximum possible value of the objective function is 46

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Answer:380.1 square inches

Step-by-step explanation:Area of a circle in terms of diameter: Area = π· (d2) 2 = 3.14· (222) 2 = 3.14· (11) 2 = 380.1 square inches (*)

Jim's rate of savings (slope): 3

Cassie's rate of savings (slope): 3

Jim's y intercept: 3

Cassie's y intercept: 12

Jim's Savings Equation: y = 3x + 3

Cassie's Savings Equation: y = 3x + 12

Number of weeks it will take to Cassie to save $27: 5

Number of weeks it will take to Jim to save $27: 8

Yes, Jim and Cassie's rates parallel.

Cassie will be able to buy the hat first.

We know that the slope intercept form of a straight line is,

y = mx + c, where m is the slope of the line and c is the y intercept.

For the straight line for Cassie:

The line passing through the points (0, 12) and (1, 15).

So the slope = (15 - 12)/(1 - 0) = 3

The y intercept is = 12.

Equation of the straight line is: y = 3x + 12 ....... (i), where y represents earning in dollars and x represents the time in weeks.

For the straight line for Jim:

The line passing through the points (0, 3) and (1, 6).

So the slope = (6 - 3)/(1 - 0) = 3

The y intercept is = 3

Equation of the straight line is: y = 3x + 3 .......... (ii), where y represents earning in dollars and x represents the time in weeks.

Since the slope of both are equal so the rates of both are parallel.

Substituting the value y = 27 in equation (i) and (ii) we get,

equation (i): 3x + 12 =27

3x = 27 - 12

3x = 15

x = 15/3

x = 5

So Cassie needs 5 weeks to save $27.

Equation (ii): 3x + 3 = 27

3x = 27 - 3

3x = 24

x = 24/3

x = 8

So Jim needs 8 weeks to save $27.

Hence Cassie will be able to buy the hat first.

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The question is incomplete. The complete question will be -

Answer: We can use Bayes' theorem to find the probability that a randomly chosen applicant has a graduate degree, given that they are male. Bayes' theorem states:

P(A|B) = P(B|A) * P(A) / P(B)

where A and B are events, P(A|B) is the conditional probability of event A given that event B has occurred, P(B|A) is the conditional probability of event B given that event A has occurred, P(A) is the prior probability of event A, and P(B) is the prior probability of event B.

In this case, we want to find P(grad degree | male), which is the probability that an applicant has a graduate degree given that they are male. Using Bayes' theorem, we have:

P(grad degree | male) = P(male | grad degree) * P(grad degree) / P(male)

We are given that 134 applicants are male, and 40 of those males have a graduate degree. Therefore:

P(male | grad degree) = 40 / total number of applicants with a graduate degree

We are not given the total number of applicants with a graduate degree, but we can find it using the fact that 40 applicants are male and have a graduate degree, and that there are 134 male applicants in total. Therefore:

total number of applicants with a graduate degree = 40 / (40/134) = 118.33 (rounded to the nearest whole number)

Next, we need to find the prior probability of having a graduate degree, P(grad degree). We can use the total number of applicants and the number of applicants with a graduate degree to calculate this probability:

P(grad degree) = number of applicants with a graduate degree / total number of applicants = 118 / 300 = 0.3933 (rounded to four decimal places)

Finally, we need to find the prior probability of being male, P(male). This probability can be calculated similarly:

P(male) = number of male applicants / total number of applicants = 134 / 300 = 0.4467 (rounded to four decimal places)

Now, we can substitute these values into Bayes' theorem to find the probability that a randomly chosen applicant has a graduate degree, given that they are male:

P(grad degree | male) = (40 / 118) * 0.3933 / 0.4467 = 0.332 (rounded to three decimal places)

Therefore, the probability that a randomly chosen applicant has a graduate degree, given that they are male, is approximately 0.332 or 33.2%.

Step-by-step explanation: