how many years will it.take 10,000 to grow 17,800 if it is invested at 2.50% compounded continuously

The solution of the inequality is -1 ≤ x ≤ 3.

To solve the inequality |2x(x-1)+12| ≤ 18, we can break it down into two separate inequalities:

2x(x-1) + 12 ≤ 18

-(2x(x-1) + 12) ≤ 18

Solving the first inequality:

2x(x-1) + 12 ≤ 18

2x² - 2x + 12 ≤ 18

2x² - 2x - 6 ≤ 0

Solving the second inequality:

-(2x(x-1) + 12) ≤ 18

-2x(x-1) - 12 ≤ 18

-2x² + 2x - 12 ≤ 18

2x² - 2x + 30 ≤ 0

Now, let's solve each inequality separately.

For the first inequality, 2x² - 2x - 6 ≤ 0:

We can factor this quadratic equation:

(2x + 2)(x - 3) ≤ 0

To determine the sign of the inequality, we need to consider the intervals where the expression is positive or negative. We set each factor equal to zero to find the critical values:

2x + 2 = 0 => x = -1

x - 3 = 0 => x = 3

Plotting these critical values on a number line and testing intervals, we find that the solution is -1 ≤ x ≤ 3.

For the second inequality, 2x² - 2x + 30 ≤ 0:

This quadratic equation does not have real solutions, so there are no solutions to this inequality.

Combining the solutions from both inequalities, we have -1 ≤ x ≤ 3.

To graph the solution, we plot the interval -1 ≤ x ≤ 3 on the number line. The shaded region on the number line represents the solution set.

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The surface area and the volume of the cone is 150.8 in², 116. 1in³. option A

The formula for calculating the surface area of a cone is expressed as;

SA = πr² + πrl

Such that the parameters are;

Substitute the values, we have;

Surface area= 3.14 × 16 = 3.14 × 4 × 8

Multiply the values

Surface area = 50.24 + 100.48

Add the values

Surface area = 150.8 in²

Volume of the cone is;

Volume = 3.14 × 4² × 6.9/3

Volume = 3.14 × 16 × 6.9/3

Volume =116. 1in³

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The numerical value of side length x in the right triangle is 8.

The figures in the image are two similar right triagles.

Since the two right triangles are similar, we equate the ratio of the sides of the two triangles.

x/6 = (x + 4)/9

Cross multiply and solve for x:

6( x + 4 ) = x × 9

Apply distributive property:

6 × x + 6 × 4 = x × 9

Simplifying, we get:

6x + 24 = 9x

Subtract 6x from both sides:

6x - 6x + 24 = 9x - 6x

24 = 9x - 6x

24 = 3x

3x = 24

Divide both sides by 3:

x = 24/3

x = 8

Therefore, the value of 8.

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The probability that the mean of the sample will be between 94.7 inches and 95.3 inches is approximately 0.436.

Using the Central Limit Theorem.

The Central Limit Theorem states that for a large enough sample size, the distribution of sample means will be approximately normally distributed, regardless of the shape of the population distribution. In this case, we have a sample size of 30, which is considered large enough for the Central Limit Theorem to apply.

Calculate the standard error of the mean (SEM):

SEM = σ / √n

SEM = 0.52 / √30

SEM ≈ 0.095

Calculate the z-scores for the lower and upper limits:

z1 = (94.7 - μ) / SEM

z2 = (95.3 - μ) / SEM

z1 = (94.7 - 95) / 0.095 ≈ -0.526

z2 = (95.3 - 95) / 0.095 ≈ 0.316

Find the area under the normal distribution curve between the z-scores using a standard normal distribution table or a calculator. The area represents the probability.

Using a standard normal distribution table or a calculator, the area between -0.526 and 0.316 is approximately 0.436.

Therefore, the probability that the mean of the sample will be between 94.7 inches and 95.3 inches is approximately 0.436.

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Maria have to spend $ 45.95 less than what she spends now in order to save $ 70 per month.

Hence the correct option is (A).

From the given Maria's Income Statement we can see that,

Her total income from Fast food Restaurant = Gross Pay + Allowance = $ 580 + $ 50 = $ 630.

Total deductions by taxation = Federal Income Tax + State Income Tax + Social Security Tax = $ 58 + $ 16 + $ 24.36 = $ 98.36

So here net income = $ (630 - 98.36) = $ 531.64.

Here total expenses = Auto + Clothing + Food + Entertainment + Other = $ 290.02 + $ 92.29 + $90.28 + $ 32 + $ 3 = $ 507.59

So Her Savings = Net Income - Total Expenses = $ 531.64 - $ 507.59 = $ 24.05.

Now in order to save $ 70 per month Maria has to spend = $ 70 - $ 24.05 = $45.95 less than she spend now.

Hence the correct option will be (A).

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None of the given expressions (1), (2), (3), or (4) correctly calculates the area of the isosceles triangle. The correct expression is (1/2) * 14 * (7 * tan(44°)).

To calculate the area of an isosceles triangle, we need the base length and the height of the triangle. In this case, the base length is given as 14 inches, but the height is not provided.

However, we can use trigonometry to find the height of the triangle by using one of the base angles. Since the triangle is isosceles and the base angles are each 68°, we know that the remaining angle (at the top of the triangle) is 180° - 68° - 68° = 44°.

We can then use the trigonometric function tangent (tan) to find the height. The formula is: tan(angle) = opposite/adjacent.

tan(44°) = height/7, where 7 represents half of the base length.

Rearranging the equation, we have: height = 7 * tan(44°).

Now, we can calculate the area of the triangle using the formula: area = (1/2) * base * height.

Substituting the given values, we get:area = (1/2) * 14 * (7 * tan(44°)).

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Answer:1/1875

Step-by-step explanation:

the probability of getting any one question correct is 1/5, and the probability of getting any one question incorrect is 4/5.

The probability of getting the first three questions correct and the fourth question incorrect can be calculated as follows:

(1/5) * (1/5) * (1/5) * (4/5) = 4/3125

Since there are six possible positions for the incorrect answer to occur (first, second, third, fourth, fifth, or sixth), the probability of getting the first and only incorrect answer on the fourth question is 4/3125 * 1/6 = 1/1875.

We can see here that it is true that the inverse of the function shown is also a function. This is true because the graph of the inverse of the function shown by reflecting the red graph about the line y = x.  

A function in mathematics is a unique connection between a group of inputs and their results. A function is a rule that specifically assigns one element from another set to each element in a set.

The set of inputs is referred to as the function's domain, while the set of outputs is referred to as the function's codomain.

From the given graph, we can deduce that the resulting graph is true for all x values and for all y values; it passes the vertical line test.

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Answer:

6 divide by 60 into 100

Step-by-step explanation:

is 10

Answer: 9 fish

Step-by-step explanation:

To find the answer all you have to do is multiply the amount of fish per gallon (0.12) to the total amount to gallons (75).

75 x 0.12 = 9

A 75-gallon aquarium will hold about 8 fish.

Stocking guidelines are 1 inch of adult fish per gallon of tank water. When applying this rule of thumb, we have to keep in mind that a 75 gallons water tank only holds about 70 gallons of water.

Then the number of fish in the tank would be:

Number of fish = density of fish * volume of water in the tank

Number of fish = 0.12 * 70

Number of fish = 8.4

So there are about 8 fish in the tank.

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Answer: $383.33 per month for the next 4 years

Step-by-step explanation:

The correct answer is save $383.33 per month for the next 4 years. Tuition for one year at a state university is about $12,500, and Greg would like to attend this university. His parents will give him $4,600 for his first year of tuition, so he must save the remaining $7,900. To have enough money to pay for his first year of tuition, Greg must save $383.33 per month for the next 4 years. This is the minimum amount of money he must save, as the other plans require him to save more money than necessary.

Sorry if this is wrong btw fr fr.

Answer:164.58 (D)

Step-by-step explanation:

12,500-4600= 7900

12 months x 4 years makes 48 months, so 7900/48 = 164.58 per month

If this week there are 144 members at the meeting, which is 90% of the total group, the total number of members on the green team is 160.

If 144 members represent 90% of the total group, we can set up the equation:

144 = 0.9x

where x is the total number of members on the green team.

To solve for x, we can divide both sides of the equation by 0.9:

144 ÷ 0.9 = x

This simplifies to:

160 = x

To check our answer, we can verify that 144 is indeed 90% of 160:

144 ÷ 160 = 0.9

which confirms that our answer is correct.

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The probability of getting Blue then Green while spinning the wheel is

3 / 32

Probability is a branch of mathematics that helps us to understand the likelihood of an event occurring. It is represented by a number between 0 and 1, where 0 means the event is impossible and 1 means the event is certain. Probability can be used to make predictions and informed decisions in real-world situations.

From the given figure we can find out the following information

The probability of getting Blue While spinning the wheel = 3/8

The probability of getting Green While spinning the Wheel = 2 / 8

The probability of getting Blue then Green while spinning the wheel

= 3/8 * 2/8

= 6/64

= 3/32

Therefore, probability of getting Blue then Green while spinning the wheel is 3 / 32

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Answer:

40

Step-by-step explanation:

All questions are worth the same, 1 point each.

80% of 50 = 0.8 × 50 = 40

Answer: 40

Answer:

40

Step-by-step explanation:

80/100*50 = 40

Answer:

55.0ml is answer = 22.05

Step-by-step explanation:

Answer:

Exponential Growth

Step-by-step explanation:

The base of 1.88 is greater than 1, so there will be exponential growth

Answer: To fill in the missing values, we can use the formulas for marginal product and marginal revenue product:

Marginal Product = Change in Total Product / Change in Labor

Marginal Revenue Product = Price x Marginal Product

Using the given information, we can fill in the missing values as follows:

Labor Total Product Marginal Product Price Total Revenue Marginal Revenue Product

0 0 - $12 $0 -

2 48 24 $12 $288 $288

4 66 9 $12 $792 $108

6 82 7 $12 $984 $84

8 96 5 $12 $1,152 $60

10 114 9 $12 $1,368 $108

12 132 9 $12 $1,584 $108

14 150 9 $12 $1,800 $108

So the missing values are:

Total Product for labor = 0 and 14: 0 and 150, respectively.

Marginal Product for labor = 0, 8, and 14: -, 5, and 9, respectively.

Total Revenue for labor = 4, 6, and 8: $792, $984, and $1,152, respectively.

Marginal Revenue Product for labor = 0, 4, and 6: -, $84, and $60, respectively.

Step-by-step explanation: :)

Answer:

82.8°

Step-by-step explanation:

We can solve for θ by first isolating cosθ:

8 cosθ - 1 = 0

8 cosθ = 1

cosθ = 1/8

We can find the inverse cosine of 1/8:

θ = cos⁻¹(1/8) = 82.8191°

Rounding to the nearest 0.1°, we get:

θ ≈ 82.8°

All the first five terms of sequence are,

A) -11, - 11/2 - 11/4 - 11/8 - 11/16

We have to given that;

Rule for sequence is,

⇒ a (n) = - 11 × (1/2)ⁿ⁻¹

Now, WE can find first five terms of sequence as;

⇒ a (n) = - 11 × (1/2)ⁿ⁻¹

Put n = 1;

⇒ a (1) = - 11 × (1/2)¹⁻¹

⇒ a (1) = - 11

Put n = 2;

⇒ a (n) = - 11 × (1/2)ⁿ⁻¹

⇒ a (2) = - 11 × (1/2)²⁻¹

⇒ a (2) = - 11 × (1/2)¹

⇒ a (2) = - 11 / 2

Put n = 3;

⇒ a (n) = - 11 × (1/2)ⁿ⁻¹

⇒ a (3) = - 11 × (1/2)³⁻¹

⇒ a (3) = - 11 × (1/4)

⇒ a (3) = - 11 / 4

Put n = 4;

⇒ a (n) = - 11 × (1/2)ⁿ⁻¹

⇒ a (4) = - 11 × (1/2)⁴⁻¹

⇒ a (4) = - 11 × (1/2)³

⇒ a (4) = - 11 / 8

Put n = 5;

⇒ a (n) = - 11 × (1/2)ⁿ⁻¹

⇒ a (5) = - 11 × (1/2)⁵⁻¹

⇒ a (5) = - 11 × (1/2)⁴

⇒ a (5) = - 11 / 16

Thus, All the first five terms of sequence are,

A) -11, - 11/2 - 11/4 - 11/8 - 11/16

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The result of the transformation of the parent function y = x² are;

13. y =  (x - 2)²

14. y = x² + 5

15. y = (x + 3)² - 4

16. y = (x - 7)² + 4

17. y = -(x²) - 3

18. y = -(x - 5)² - 2

19. y = (1/2)x²

20.  y = (3x²) + 8

The transformations on the parent function y = x² can be described as;

13. Translated 2 units right:

The equation will be y = (x - 2)²

14. Translated 5 units up:

The equation will be y = x² + 5

15. Translated 3 units left and 4 units down:

The equation will be y = (x + 3)² - 4

16. Translated 7 units right and 4 units up:

The equation will be y = (x - 7)² + 4

17. Reflected over the x-axis, then translated 3 units down:

The equation will be y = -(x²) - 3

18. Reflected over the x-axis, then translated 5 units right and 2 units down:

The equation will be y = -(x - 5)² - 2

19. Vertically compressed by a factor of 2:

The equation will be y = (1/2)x²

20. Vertically stretched by a factor of 1/3, then translated 8 units up:

The equation will be y = (3x²) + 8

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The solution is: the value of the angles a, b and c are : a = 60, b = 90, c = 100.

Here,

We have that in line CHF, it has two given and one unknown angle.

The total angle of one straight line is 180.

Given that:

a = 180 - 50 -70 = 60

The angle intersecting the CHFD line can be computed by the the total angle inside the triangle.

Angle on EFH would give 180-40-60 = 80 and on EFD the angle would be 100 from 180-80.

Since angle C is congruent to the angle EFD.

c = 100

Take note that in a 4 sided polygon (GEFH), the total exterior angle is 360 degrees.

The different angle would be

angle GHF = 50 + a = 50+60 = 110

angle EFH = 80

angle FEG = 180- c = 180-100 = 80

ANGLE EGH = 360 - GHF -EFH -FEG = 360 - 110-80-80 = 90

since angle AG is congruent to EGH, we can calculate for the angle b which is congruent to its opposite. This would give us formula of

360 = (90+90) + (b) +(b)

360 = 180 +2b

b = 90

Hence, The solution is: the value of the angles a, b and c are : a = 60, b = 90, c = 100.

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The measure of the angle B of the triangle is 78.15 degrees

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

A = 25 degrees

a = 9.5 units

b = 22 units

Using the law of sines, the angle B is calculated as

sin(A)/a = sin(B)/b

So, we have

sin(25)/9.5= sin(b)/22

This gives

sin(b) = 22 * sin(25)/9.5

Evaluate

sin(b) = 0.9787

Take the arc sin of both sides

b = 78.15

Hence, the measure of the angle is 78.15 degrees

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Answer:

i think 25.019mm2 is the correct answerrrrrrrr.

Answer:

175.130 mm^2

Step-by-step explanation:

Took the test.

The required, the students use eighths as their scale, they will be able to plot all of the data points above the label. Option B is correct.

To make a line plot, the students will mark a number line with a scale that includes all the data points. Since the given data includes fractions with denominators of 2, 4, and 8, it would be best to choose a fraction that is a factor of all of these denominators. The only option that satisfies this condition is B. eighths.

To see why, note that 1/8 is a factor of 1/2 (4/8), 1/4 (2/8), and 1/8 (1/8). Therefore, if the students use eighths as their scale, they will be able to plot all of the data points above the label. Using any other fraction would require rounding some of the data points, which could lead to a loss of information.

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The sum of the number 199 + 61 by vertical table will be 260.

Since, Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

Use the table to add 199 + 61 vertically. Then we have

                                Hundreds          Tens          Ones

Regrouping                    1                       1            

First addend                  1                      9               9

Second addend            0                      6               1

Sum                              2                      6               0

Thus, The sum of the number 199 + 61 by the vertical table will be 260.

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The table to add 199+61 vertically is shown below.

To add 199 and 61 vertically, we'll set up the addition table as follows:

 1  9  9

+   6  1

_________

Let's start by adding the digits in the rightmost column, which is the ones place:

9 + 1 = 10

We write down 0 in the bottom row and carry over the 1 to the top row:    1  9  9

+   6  1

_________

   0

Now, let's add the digits in the next column (the tens place), including the carry-over:

1 + 9 + 1 = 11

We write down 1 in the bottom row and carry over the 1 to the top row:

   1  9  9

+   6  1

_________

  1  1

Finally, let's add the digits in the leftmost column (the hundreds place), including the carry-over:

1 + 1 = 2

We write down 2 in the bottom row:

   1  9  9

+   6  1

_________

  2  1

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The total population of alligators will be 375.

The amount of soy milk that the grocery store should plan to donate is: 158.

To calculate the total population of alligators in the area, we will assign the following variables:

30 Tagged alligators = m

12 Counted alligators = k

150 alligators seen = n

The total population size (N bar) of alligators is calculated with the formula:

N bar = mn/k

= 30 * 150/12

= 4500/12

375

For the amount of soy milk, we can say that if 25 out of 150 students preferred soy milk, then the number that would prefer soy milk out of 950 will be: 950 * 25/150 = 158.

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The value of inequality :  x≤-9

Given,

Inequality 4(x-3) + 4 ≤ 10+ 6x

Firstly,

The distributive property: 4x-12 + 4 ≤ 10+ 6x

Then,

Combine like terms: 4x -8 ≤ 10+ 6x

Then,

The addition property of inequality: 4x ≤ 18 + 6x

Then,

The subtraction property of inequality: -2x ≤ 18

Then,

The division property of inequality:

Divide both sides of inequality by 2,

So,

x≤-9

Hence after last step the value of x is less than or equal to -9 .

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