Write the prime factorization of 12. Use exponents when appropriate and order the factors from least to greatest (for example, 2235).

Answer: A line has one dimension because it is made up of a figure with no thiknes that extends infinitely in both directions.

Step-by-step explanation:

A line is a one-dimensional figure, it has no thickness.

For reference,  point is zero dimesional, a plane is twodimensional.

Then the correct answer would be:

A line has one dimension because it is made up of a figure with no thiknes that extends infinitely in both directions.

-1 us a answer for your questions or support

Answer:

there's a lot:

Step-by-step explanation:

4/6,3/9,4/12,5/15,10/30,20/60,60/180.

this is the most i can do until i cant multiply anymore.

The coordinate of the triangle after the dilation is R'(4, 8), S (4,4). T(4, 8)

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

R(1, 2), S (1,1). T(1, 2)

Scale factor = 4

The coordinate of the triangle after the dilation is calculated as

Image' = triangle * Scale factor

Substitute the known values in the above equation, so, we have the following representation

R(1, 2), S (1,1). T(1, 2) * 4

Evaluate

R'(4, 8), S (4,4). T(4, 8)

Hence, the image is R'(4, 8), S (4,4). T(4, 8)

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(a) The range of c₁ (the objective coefficient of x₁) for which this BFS remains optimal is c₁ ≤ 2.

(b) The range of b₂ (the right-hand side of the second constraint) for which this BFS remains optimal is 3 ≤ b₂ < 4.

(c) The dual price of the second constraint is 0.

(a) The optimality condition for a linear programming problem requires that the objective coefficient of a non-basic variable (here, x₁) should not increase beyond the dual price of the corresponding constraint. In this case, the dual price of the second constraint is 0, indicating that increasing the coefficient of x₁ will not affect the optimality of the basic feasible solution. Therefore, the range of c₁ for which the BFS remains optimal is c₁ ≤ 2.

(b) The range of b₂ for which the BFS remains optimal is determined by the allowable range of the corresponding dual variable. In this case, the dual price of the second constraint is 0, implying that the dual variable associated with that constraint can vary within any range. As long as 3 ≤ b₂ < 4, the dual variable remains within its allowable range, and thus, the BFS remains optimal.

(c) The dual price of a constraint represents the rate of change in the objective function value per unit change in the right-hand side of the constraint, while keeping all other variables fixed. In this case, the dual price of the second constraint is 0, indicating that the objective function value does not change with variations in the right-hand side of that constraint.

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Answer:

D

Step-by-step explanation:

perpendicular to 2 =x is -1/2x, and (0,-3) just happens to be on the y intercept so its -1/2x - 3

Answer:

There are 35 chickens

Step-by-step explanation:

goats : chickens: total

3               7           3+7 = 10

There are 50 animals

50/10 = 5

Multiply each number by 5

goats : chickens: total

3*5          7 *5         10*5

15              35             50

There are 35 chickens

Answer:

15 goats and 35 chickens

Step-by-step explanation:

goats to chickens - 3:7

3:7

3+7=10

50/10=5

3*5:7*5

15:35

Answer:

5! (5 factorial) or 120 ways

Step-by-step explanation:

You can arrange P different ways. R can be arranged only 4 different ways because Pwill be in one of the spots. Next, you can arrange "I" 3 different ways because P and R are already arranged in 2 spots, meaning you cant put "I" there. Next, S can be arranged in 2 different ways for the same reason. And lastly, M can only be arranged in 1 different way because the other spots are taken.

You can put it in any order. For example, M could be arranged 5 ways and P could be arranged in 1 way. You will still get 120 ways

Hopefully this helped. The explanation might be a bit confusing but I tried my best. I'm not good with explaining my solutions but I always try

Answer:

120

Step-by-step explanation:

took the test and i got it right

Answer:

48: 24

Step-by-step explanation:

divide.

Laura should invest approximately $4,210.82 now to reach her goal.

To calculate the amount Laura should invest, we use the compound interest formula \(A = P(1 + r/n)^(nt)\) , where A is the desired future amount, P is the principal (the amount to be invested), r is the interest rate (as a decimal), n is the number of compounding periods per year, and t is the number of years. Substituting the given values, we have

$\($6,500 = P(1 + 0.08/4)^(4*8)\). By solving this equation, we find that P is approximately $4,210.82. Therefore, Laura should invest around $4,210.82 now at an 8% interest rate, compounded quarterly, to reach her goal of $6,500 in 8 years.

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Using the compound interest formula, it was calculated that Laura should invest approximately $3,944.06 initially to have $6,500 in 8 years with an 8% annual interest rate compounded quarterly.

Laura's goal is to accumulate $6,500 in 8 years with an interest rate of 8% compounded quarterly. Hence, we need to work out how much she should invest initially. This is an example of a time value of money problem which can be solved using the compound interest formula.

The compound interest formula is: P = F / (1 + r/n)^(nt).

Where:
P is the principal (initial amount to invest),
F is the future value ($6,500),
r is the annual interest rate in decimal form (0.08),
n is the number of compounding periods in one year (4 since it's quarterly), and
t is the time in years (8 years).

Substituting the values into the formula, Laura should invest approximately: $3,944.06 immediately.

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Step-by-step explanation:

the x value comes from the slope when graphing. for example, the slope on this problem is just x which means its only one. so you move up one and to the right one. for the second equation, its negative so you move back one or down one. the x value coms from when they are both intercepted when graphed.

Answer:

A. 1

Step-by-step explanation:

2(3x − 7) + 18 = 10

(6X - 14 ) + 18 = 10

6X + 4 = 10

6X = 10 - 4

6X = 6

6X ÷ 6 = 6 ÷ 6

X = 1

Answer:

a. 1

Step-by-step explanation:

\(2(3x - 7) + 18 = 10\)

➡️ \(6x - 14 + 18 = 10\)

➡️ \(6x + 4 = 10\)

➡️ \(6x = 10 - 4\)

➡️ \(6x = 6\)

➡️ \(x = 1\) ✅

The first term of the geometric series is  4 and the nth term of the geometric series is an = a1 * r^(n-1) while 21th term of the geometric series is  4,194,304.

STEP 1:

To find the first term of a geometric sequence, we can use the explicit formula:

an = a1 * r^(n-1)

where an is the nth term, a1 is the first term, r is the common ratio, and n is the term number.

We are given that the sixth term is 128 and the common ratio is 2, so we can plug these values into the formula to get:

128 = a1 * 2^(6-1)

Simplifying this equation, we get:

128 = 32a1

Dividing both sides by 32, we get:

a1 = 4

So the first term of the sequence is 4.

STEP 2:

Using the same explicit formula, we can find the nth term of the sequence:

an = a1 * r^(n-1)

We know that the first term is 4 and the common ratio is 2, so we can plug these values into the formula to get:

a21 = 4 * 2^(21-1)

Simplifying this equation, we get:

a21 = 4 * 2^20

a21 = 4 * 1,048,576

a21 = 4,194,304

Therefore, the 21st term of the sequence is 4,194,304.

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Answer:

angke D = 105°

Step-by-step explanation:

All triangles add up to 180°. 30+45=75 180-75=105

In triangle DEF, the measure of angle D is 105°.

A triangle is a geometric figure with three edges, three angles and three vertices. It is a basic figure in geometry.

The sum of the angles of a triangle is always 180°

Given that,

In triangle DEF,

Value of ∠ E = 30°, ∠ F = 45°.

Let the value of ∠ D  is x°.

Since, the sum of the angles of a triangle is 180°.

Apply this property in triangle DEF,

30 + 45 + x = 180

75 + x = 180

x = 180 - 75

x = 105

The value of ∠ D is 105°.

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To find the derivative of the function f(x) = 2e^x + 5x - ln(x), we can apply the rules of differentiation.  here, f'(x) =\(2e^x + 5 - 1/x.\)

The derivative of each term can be calculated separately using the following rules:

d/dx(e^x) = e^x (derivative of e^x is e^x itself)

d/dx(5x) = 5 (derivative of 5x with respect to x is 5)

d/dx(ln(x)) = 1/x (derivative of ln(x) with respect to x is 1/x)

Therefore, the derivative of f(x) is:

f'(x) = \(d/dx(2e^x) + d/dx(5x) - d/dx(ln(x))\)

     =\(2e^x + 5 - 1/x\)

So, f'(x) =\(2e^x + 5 - 1/x.\).

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A

the length of each pipe

Answer:

1.06 m²

Step-by-step explanation:

To find the area of the two ends, you need to find the area of the inner circle, then subtract that from the area of the large circle.

As we know, A = πr²

The diameter of the larger circle is 1.8, so the radius is 0.9.

π(0.9)² = 2.54

The diameter of the smaller circle is 1.6, so the radius is 0.8

π(0.8)² = 2.01

2.54 - 2.01 = 0.53 m² (this is for one end)

0.53 x 2 = 1.06 m²

Answer:

B

Step-by-step explanation:

On a coordinate plane, parallel lines have the same slope as geometric figures are true. Thus option B is correct.

Marks, splines, spheres, and curved are used to build enclosed geometric shapes. We can see these shapes all around us. Illustrations of geometric shapes include circles, rectangles, triangles, and others. Any configuration of points, columns, or angles is a geometry figure.

A point is the most fundamental algebraic concept because it has no boundaries. Simply put, a point upon that plane is a location. A dot is used to symbolize it. A plane can be identified by three non-straight-line points.

As two or much more vectors seldom cross each other and are located on the same dimension, these are said to be parallel. The slope of these lines is constant. Coplanar lines that seem to be parallel are the ones that don't cross. Therefore, option B is the correct option.

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a. The standard error of the mean can be determined using the formula:

Standard error of the mean = population standard deviation / square root of sample size

Plugging in the given values, we get:

Standard error of the mean = 25 / square root of 250
Standard error of the mean = 25 / 15.8114
Standard error of the mean = 1.579 (rounded to 3 decimal places)


The standard error of the mean measures the amount of variability or error that is expected in the sample mean when compared to the true population mean. It is calculated by dividing the population

by the square root of the sample size. In this case, the standard error of the mean is 1.579, indicating that the sample mean of 20 is expected to be off by around 1.579 units from the true population mean.

c. To determine the 95% confidence interval for the population mean, we can use the formula:

Confidence interval = sample mean +/- (critical value) x (standard error of the mean)

The critical value can be obtained from a t-distribution table with n-1 degrees of freedom, where n is the sample size. For a 95% confidence interval and 249 degrees of freedom, the critical value is 1.96.

Plugging in the given values, we get:

Confidence interval = 20 +/- (1.96) x (1.579)
Confidence interval = 20 +/- 3.095
Confidence interval = (16.905, 23.095) (rounded to 3 decimal places)


The confidence interval is a range of values that is expected to contain the true population mean with a certain degree of confidence. In this case, we are 95% confident that the true population mean falls within the range of 16.905 to 23.095. This means that if we were to repeat this sampling process many times, 95% of the resulting confidence intervals would contain the true population mean.

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The probability that at least one 6 will occur on two dice is 30.5%.

To determine probability, divide the total number of possible outcomes by the number of possible ways an event could occur. There are differences between probability and odds. Odds are calculated by dividing a situation's likelihood of occurring by its likelihood of not occurring.

1, 2, and 3 are the six factors. Four of the results of a single die's six possible outcomes are multiples of 6. It follows that 4/6 is the probability.

11.5%, or slightly less than 33.3% (2/6), out of 36 occasions. The probability that at least one 6 will occur on two dice is 30.5%. Without using the picture, one can also calculate this number mathematically.

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Using the concept of likelihood and probability ,The probability that at least one 6 will occur on two dice is 30.5%.

Probability is a measure of the likelihood that a particular event will occur. It is expressed as a number between 0 and 1, with 0 indicating that an event will not occur and 1 indicating that an event will certainly occur. For example, the probability of flipping a fair coin and it landing on heads is 0.5, or 50%. Probability is used in many fields, including mathematics, statistics, finance, and science. In statistics, probability is used to make inferences about a population based on a sample, while in finance, probability is used to evaluate the potential outcomes of investments.

Conditional probability is the probability of an event occurring given that another event has already occurred. It is written as P(A|B), which is read as "the probability of A given B." For example, the probability of rolling a 6 on a fair die given that the roll is an even number would be P(6|even) = 1/3, because there is only one way to roll a 6 out of the 3 possible even numbers (2, 4, 6).

1, 2, and 3 are the six factors. Four of the results of a single die's six possible outcomes are multiples of 6. It follows that 4/6 is the probability.

11.5%, or slightly less than 33.3% (2/6), out of 36 occasions. The probability that at least one 6 will occur on two dice is 30.5%. Without using the picture, one can also calculate this number mathematically.

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∠g and ∠h are complementary angles and ∠g and ∠h are acute angles are true statements from the given information

Two angles are given.

∠g = (2x-90)°

∠h = (180-2x)°

We have to find the statement which is true about the angles g and h.

If both angles are greater than zero.

Complementary angles add up to 90 degrees

i.e., ∠g and ∠h are complementary if ∠g + ∠h = 90°.

Substituting the given values:

∠g + ∠h

= (2x-90)° + (180-2x)° = 90°

Thus, ∠g and ∠h are complementary angles.

and both the angles are less than 90 degrees so we can tell that angles ∠g and ∠h  are acute.

So the statement ∠g and ∠h are acute angles is also true

Hence, ∠g and ∠h are complementary angles and ∠g and ∠h are acute angles are true statements

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Answer: there were 12 chocolates in each box. (Originally, before any got eaten)

Step-by-step explanation: let x represent the total amount of chocolates in each box.

8x - 3(8) = 72

8x - 24 = 72 add 24 to both sides

8x = 96 divide both sides by 8

X = 12

Answer:

That means you had 48 chocolates in each box

Step-by-step explanation:

Since you eat 3 chocolates from all 8 boxes, you do this:

8 x 3 which = 24

Now since you have 72 chocolates left you do this:

72 - 24 which = 48

So, therefore, there were originally 48 chocolates in each box

(Don't eat so much chocolate lol you could get sick)

The minimum wage set by the government at $7.50 per hour does not result in a pay cut for unskilled workers, as it is below the equilibrium wage of $8.00 per hour.

The wage rate remains unchanged, and the labor market remains in balance.

The statement is false.

False.

The equilibrium wage in the market for unskilled labor is $8.00 per hour, which means that the market naturally sets the wage rate at this level, based on the forces of supply and demand.

The government then sets a minimum wage at $7.50 per hour.

Since the minimum wage is below the equilibrium wage, it does not directly impact the wage rate for unskilled workers.
The equilibrium wage represents the point at which the supply of labor (the number of workers willing to work at a given wage) equals the demand for labor (the number of workers that employers are willing to hire at a given wage).

In this case, both workers and employers are satisfied with the $8.00 per hour wage, and the labor market is balanced.
The government sets a minimum wage below the equilibrium wage, it essentially sets a wage floor that is not binding. Employers are still willing to pay the equilibrium wage of $8.00 per hour, and workers are still willing to accept this wage.

The wage for unskilled workers remains at $8.00 per hour, and there is no pay cut of 50 cents per hour.

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cba

Step-by-step explanation:

first first one to see second one is b last one is a

If Kara lines up all the 3/4-inch buttons for her craft project, the total length would be 7.5 inches.

To find the total length of the 3/4-inch buttons that Kara lines up for her craft project, we need to multiply the length of each button by the number of buttons. Let's assume she has 10 of these buttons. Each button has a length of 3/4 inch.

The total length of all the 3/4-inch buttons that Kara lines up for her craft project can be calculated by multiplying the number of buttons by their length.

Let's assume Kara has 10 3/4-inch buttons.

To find the total length, we need to multiply the length of each button by the number of buttons.

The length of each button is 3/4 inch, and the number of buttons is 10.

So, the total length would be (3/4 inch) * 10 = 7.5 inches.

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\(~~~~~~ \textit{Simple Interest Earned Amount} \\\\ A=P(1+rt)\qquad \begin{cases} A=\textit{accumulated amount}\dotfill & \$ 30000\\ P=\textit{original amount deposited}\dotfill & \$20000\\ r=rate\to 9\%\to \frac{9}{100}\dotfill &0.09\\ t=years \end{cases} \\\\\\ 30000 = 20000[1+(0.09)(t)] \implies \cfrac{30000}{20000}=1+0.09t\implies \cfrac{3}{2}=1+0.09t \\\\\\ \cfrac{3}{2}-1=0.09t\implies \cfrac{1}{2}=0.09t\implies \cfrac{1}{2(0.09)}=t\implies 5.6\approx t\)

The solution to the given initial value problem, obtained using Laplace transforms, is y(x) = 0. This means that the function y(x) is identically zero for all values of x.

To find the solution of the initial value problem using Laplace transforms for the equation d²y/dx² + 9y = 9sin(t)u(t - 3), where y(0) = y'(0) = 0, we can follow these steps:

Take the Laplace transform of the given differential equation.

Applying the Laplace transform to the equation d²y/dx² + 9y = 9sin(t)u(t - 3), we get:

s²Y(s) - sy(0) - y'(0) + 9Y(s) = 9 * (1/s² + 1/(s² + 1))

Since y(0) = 0 and y'(0) = 0, the Laplace transform simplifies to:

s²Y(s) + 9Y(s) = 9 * (1/s² + 1/(s² + 1))

Solve for Y(s).

Combining like terms, we have:

Y(s) * (s² + 9) = 9 * (1/s² + 1/(s² + 1))

Multiply through by (s² + 1)(s² + 9) to get rid of the denominators:

Y(s) * (s⁴ + 10s² + 9) = 9 * (s² + 1)

Simplifying further, we have:

Y(s) * (s⁴ + 10s² + 9) = 9s² + 9

Divide both sides by (s⁴ + 10s² + 9) to solve for Y(s):

Y(s) = (9s² + 9)/(s⁴ + 10s² + 9)

Partial fraction decomposition.

To proceed, we need to decompose the right side of the equation using partial fraction decomposition:

Y(s) = (9s² + 9)/(s⁴ + 10s² + 9) = A/(s² + 1) + B/(s² + 9)

Multiplying through by (s⁴ + 10s² + 9), we have:

9s² + 9 = A(s² + 9) + B(s² + 1)

Equating the coefficients of like powers of s, we get:

9 = 9A + B

0 = A + B

Solving these equations, we find:

A = 0

B = 0

Therefore, the decomposition becomes:

Y(s) = 0/(s² + 1) + 0/(s² + 9)

Inverse Laplace transform.

Taking the inverse Laplace transform of the decomposed terms, we find:

L^(-1){Y(s)} = L^(-1){0/(s² + 1)} + L^(-1){0/(s² + 9)}

The inverse Laplace transform of 0/(s² + 1) is 0.

The inverse Laplace transform of 0/(s² + 9) is 0.

Combining these terms, we have:

Y(x) = 0 + 0

Therefore, the solution to the initial value problem is:

y(x) = 0

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Answer:

option 2

Step-by-step explanation:

\(t_{n}=2081.25 + (n - 1) *231.25\)

2081.25 ;   2312.50   ; 2543.75  ; 2775  ; 3006.25

This is and arithmetic series.

First term =a = 2081.25

Common difference = d = 2312.50 - 2081.25 = 231.25

\(t_{n}=a + (n-1)*d\\\\ t{n}=2081.25 + (n-1)*231.25\)