What is the value of the y-intercept of the graph of h(x)=12.3(4.9)^x ?

Record your answer in the boxes below.

The equivalent value of the expression is A = four thousand two hundred and A = 4,200

Given data ,

Let the expression be represented as A

Now , the value of A is

A = four thousand two hundred

On simplifying the equation , we get

A = 4,200

And , when we write "four thousand two hundred," it is written in word form

Hence , the equation is A = 4,200

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Answer:

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The function y = x² - 5 is the translation of the parent function y = x² down by 5 units.

Since the parent function is y = x², it is a parabola that has its vertex at the origin and opens up as its coefficient is positive.

Looking at the answer choices, we see option A is the correct one.

Other options are incorrect:

The probability that the first person will be seated at a plastic table is 0.8

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

Plastic tables = 12

Composite tables = 3

Using the above as a guide, we have the following:

Total tables = 12 + 3

Evaluate the sum

Total tables = 15

So, we have the probability to be

P = Plastic tables/Total tables

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

P = 12/15

Evaluate

P = 0.8

Hence, the probability that the first person will be seated at a plastic table is 0.8

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Answer:

Step-by-step explanation:

You want the amounts invested at 9% and 6% if they total $11,335 and the interest from the 9% investment exceeds the interest from the 6% investment by $865.35.

If we let x represent the amount invested at 9%, the amount invested at 6% is (11335-x). The relation between the values of interest earned is ...

  (x)·9% -(11335-x)·6% = 865.35

  0.15x -680.10 = 865.35 . . . . . simplify

  0.15x = 1545.45 . . . . . . . . add 680.10

  x = 10303 . . . . . . . . . . . divide by 0.15

  11335 -x = 1032

$10,303 was invested at 9%; $1,032 at 6%.

__

Additional comment

It is convenient to use a single variable, and to let it represent the amount invested at the higher rate. If you use a system of 2 equations, you can effectively do this by substituting for the variable representing the amount invested at the lower rate. Using this approach keeps all of the numbers positive, tending to reduce errors.

Answer:

Amount invested at 9% = $6832.15; Amount invested at 6% = $4502.85

Step-by-step explanation:

We'll need a system of equations to find the amounts invested at both 9% and 6% and we'll need to convert the percentages to decimals (i.e., 0.09 and 0.06):

First equation in system:  

We know that the interest earned from the 9% investment is $865.35 greater than the interest earned from the 6% investment.

Thus, one equation we can use is x = y + 865.35

Second equation in system:

We also know that the amount invested at 9% plus the amount invested at 6% equals $11335.00

Thus, our second equation is 0.09x + 0.06y = 11335

Step 1:  We can use substitution to solve.  We must plug in x from the first equation for x in the second equation to solve for y:

0.09(y + 865.35) + 0.06y = 11335

0.09y + 77.8815 + 0.06y = 11335

0.15y + 77.88 = 11335

0.15y = 11257.12

y = 75047.46667

y = 75047.47

Step 2:  Now we can plug in 75047.47 for y into any of the two equations in our system to solve for y.  Because the first equation is simpler, let's use this one:

x = 75047.47 + 865.35

x = 75912.82

Step 3:  We can now find the amount invested by multiplying x by 0.09 and y by 0.06:

0.09x = 0.09(75912.82) = 6832.1538 = $6832.15

0.06y = 0.06(75047.47) = 4502.8482 = $4502.85

Optional Step 4:  We can check that our numbers are correct by substituting 75912.82 for x and 75047.47 for y in the two equations in our system:

Checking solutions for first equation:

75912.82 = 75047.47 + 865.35

75912.82 = 75912.82

Checking solutions for second equation:

0.09(75912.82) + 0.06(75047.47) = 11335

6832.1538 + 4502.8482 = 11335

6832.15 + 4502.85 = 11335

11335 = 11335

The classification , symmetry , maximum r-values and the zeroes of the function are solved

Given data ,

a)

Let the function be represented as A

Now , the value of A is

r² = 25 sin( 2θ )

The equation represents a cardioid

It is symmetric about the polar axis.

The maximum values of r occur at θ = (π/4) + kπ/2, and the maximum value of r is 5.

The equation has zeroes at θ = kπ/2, and the corresponding values of r are given by r = 0

b)

The equation represents a limaçon.

It is symmetric about the polar axis.

The maximum value of r is 7.

The equation has zeroes at θ = arccos(1/3) + 2kπ or θ = -arccos(1/3) + 2kπ, and the corresponding values of r can be found by substituting into the equation r = 4 - 3cos(θ).

c)

The equation represents an Archimedean spiral.

It does not possess any symmetry.

There is no maximum r value.

The equation has a zero at θ = 1/2.

Hence , the zeroes of the function are solved

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Answer:

588π

Step-by-step explanation:

Volume of cylinder = π r ² h

=  π (7)² (12)

= 588π

The total number of atoms represented by Cd(CH₂CICO₂)₂ is 15.

In addition, items are combined and counted as a single large group. The process of adding two or more numbers together is known as addition in mathematics. The terms "addends" and "sum" refer to the numbers that are added and the result of the operation, respectively.

To find the total number of atoms represented by Cd(CH₂CICO₂)₂, we need to count the number of atoms of each element in the molecule and add them up.

Cd(CH₂CICO₂)₂ contains:

1 cadmium (Cd) atom

2 carbon (C) atoms

6 hydrogen (H) atoms

4 oxygen (O) atoms

2 chlorine (Cl) atoms

Adding these up, we get:

1 + 2 + 6 + 4 + 2 = 15

Therefore, the total number of atoms represented by Cd(CH₂CICO₂)₂ is 15.

The answer is (D) 15.

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The required scale factor for the dilation of segment AB to create segment A'B' is 2.

If the length of the original segment AB is 5 units and the length of the dilated segment A'B' is 10 units, the scale factor can be calculated as follows:

Scale factor = Length of A'B' / Length of AB

Scale factor = 10 / 5

Scale factor = 2

Therefore, the correct scale factor for the dilation of segment AB to create segment A'B' is 2.

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Answer:

To have a D/E ratio of 1.6, Oceanic Luxury Vessels, Inc. would need to sell debt securities.

First, we need to calculate the market value of the company's equity.

Market value of equity = Number of shares outstanding × Market price per share

Market value of equity = 5,000,000 × $38

Market value of equity = $190,000,000

Next, we can calculate the current debt-to-equity (D/E) ratio of the company:

Current D/E ratio = Total debt / Total equity

Total debt = Number of bonds outstanding × Bond price per bond × Par value

Total debt = 75,000 × 1.02 × $1,000

Total debt = $76,500,000

Current D/E ratio = $76,500,000 / $190,000,000

Current D/E ratio = 0.403

To achieve a D/E ratio of 1.6, the company would need to increase its total debt by a factor of 1.6/0.403 = 3.97.

New total debt = 3.97 × $76,500,000

New total debt = $304,305,000

To calculate the amount of debt securities the company would need to sell, we can subtract the current total debt from the new total debt:

Amount of debt to be sold = $304,305,000 - $76,500,000

Amount of debt to be sold = $227,805,000

Therefore, the company would need to sell debt securities worth $227.8 million to achieve a D/E ratio of 1.6.

The correct answer is C. Debt; $248.5 million.

The length of side x to the nearest tenth is equal to 2.4 units.

In Mathematics and Geometry, an isosceles triangle simply refers to a type of triangle with two (2) sides that are equal in length (side lengths) and two (2) equal angles.

This ultimately implies that, an isosceles triangle comprises two (2) side lengths that are equal and two (2) angles with the same magnitude.

Therefore, we would apply Pythagorean theorem in order to find the length of side x as follows;

x² + x² = (√11)²

2x² = 11

x² = 11/2

x² = 5.5

x = 2.4 units.

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

Answer:

{0,2,3,4,8}

Step-by-step explanation:

The amount of money Gillians owes for student loans is $12,250

How to determine this

When Gillians net worth = $90,500

House(Current value) = $87,900

Checking account = $950

Credit- card = -$2,650

Automobile(current value) = $10,300

Student loans = ?

Investment = $5,000

Personal loans = 1,200

Savings account = $2,450

To calculate the money Gillians Owen owes student loans

Let x represent the student loans

$90,500 = $87,900 + $950 - $2,650 + $10,300 + x + $5,000 - $1,200 + $2,450

$90,500 = $102,750 + x

Collect like terms

x = $90,500 - $102,750

x = 12,250

Therefore, the money Gillians owes student loans is $12,250

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Considering the dot plot, the tallest conifer is 3.25 inches taller than the shortest conifer.

This shows, with dots, the number of times that each of the measures appears in a data set.

For finding the dot plot, we have that:

The shortest conifer measures 6 and 1/4

= 6.25 inches.

The tallest conifer measures 9.5 inches.

The difference is:

9.5 - 6.25 = 3.25 inches.

Therefore the tallest conifer is 3.25 inches taller than the shortest conifer.

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There are three dots in the greatest height recorded.

We have,

From the table,

We see that,

The greatest height is 75 inches.

The lowest height is 62 inches.

Now,

If we make a line plot with dots above the height as:

*                                      *

*          *        *        *        *

*          *        *        *        *

62     66     68     72     75

Thus,

There are three dots in the greatest height recorded.

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Answer:

The length of the belt needed to go around the drive wheel and the vat is approximately 79.6 feet. This is calculated by using the circumference formula C = 2πr where r is the radius of the wheel (5 feet) and the radius of the vat (9 feet). The total circumference is then 2 x 3.14 x (5 + 9) = 79.6 feet.

Answer:

79.6 feet.

Step-by-step exp

2 x 3.14 x (5 + 9) = 79.6 feet.

The two numbers that multiply to the number 24 and add up to the number -25 as required to be determined are; -24 and -1.

It follows from the task content that the two numbers which multiply to give 24 and add up to give -25 are to be determined.

By observation, the two numbers in discuss are; -24 and -1. This follows from the fact that: -24 × -1 = 24 and also, -24 + -1 = -25.

Consequently the two numbers as required to be determined are; -24 and -1.

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The end behavior of a polynomial with positive leading coefficient is either "up-up" or "down-down" depending on the degree of the polynomial the end behavior of a polynomial with negative leading coefficient is either "up-down" or "down-up" depending on the degree of the polynomial.

Actually, the end behavior of a polynomial refers to the behavior of the function as the input variable (usually x) approaches positive or negative infinity.

The end behavior of a polynomial is determined by the degree and leading coefficient of the polynomial.

If the degree of the polynomial is even and the leading coefficient is positive, then the end behavior is as follows:

As x approaches negative infinity, the graph of the polynomial approaches the x-axis from above (the arrows point in opposite directions).

As x approaches positive infinity, the graph of the polynomial approaches the x-axis from below (the arrows point in opposite directions).

If the degree of the polynomial is even and the leading coefficient is negative, then the end behavior is as follows:

As x approaches negative infinity, the graph of the polynomial approaches the x-axis from below (the arrows point in opposite directions).

As x approaches positive infinity, the graph of the polynomial approaches the x-axis from above (the arrows point in opposite directions).

If the degree of the polynomial is odd and the leading coefficient is positive, then the end behavior is as follows:

As x approaches negative infinity, the graph of the polynomial goes down to negative infinity (the arrows point in the same direction).

As x approaches positive infinity, the graph of the polynomial goes up to positive infinity (the arrows point in the same direction).

If the degree of the polynomial is odd and the leading coefficient is negative, then the end behavior is as follows:

As x approaches negative infinity, the graph of the polynomial goes up to positive infinity (the arrows point in the same direction).

As x approaches positive infinity, the graph of the polynomial goes down to negative infinity (the arrows point in the same direction).

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Answer:

16x^(7/2)

Step-by-step explanation:

When rewriting radicals as fractions, the numerator is the power the term is to and the denominator is how many times the term is “rooted”:

2^4 sqrt(x^7) —> 16x^(7/2)

Sean's statement is correct. Christine's statement is incorrect when a is negative.

The value of a to the -3rd power is always less than 1 if a is positive.

For example, if a = 2, then a to the -3rd power is 1/8, which is less than 1. Therefore, Sean's statement is correct.

The value of a to the -3rd power is always less than 1 if a is positive, but it is always greater than 1 if a is negative.

For example, if a = 2, then a to the -3rd power is 1/8, which is less than 1. But if a = -2, then a to the -3rd power is -1/8, which is greater than 1.

Therefore, Christine's statement is incorrect when a is negative.

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The solution for w is given by the natural logarithm of 88 divided by 3x, all raised to the power of 1/5.

Exponential functions are always increasing or decreasing, depending on the sign of the base "a".

The graph of an exponential function has a characteristic shape that depends on the base "a". When "a" is greater than 1, the graph is an increasing curve that becomes steeper as x increases; when "a" is between 0 and 1, the graph is a decreasing curve that approaches the x-axis as x increases.

Starting with the equation:

[tex]-3xe^{(5w)} = -88[/tex]

We can first isolate the exponential term by dividing both sides by -3x:

[tex]e^{(5w)} = \dfrac{88 }{ (3x)}[/tex]

Then, taking the natural logarithm of both sides, we get:

[tex]5w = ln(\dfrac{88} { 3x})[/tex]

Finally, dividing both sides by 5, we obtain the solution for w:

[tex]w = (\dfrac{1}{5}) ln(\dfrac{88} { 3x})[/tex]

Therefore, the solution for w is given by the natural logarithm of 88 divided by 3x, all raised to the power of 1/5.

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The equivalent fractions of 7/11 are 14/22, 21/33, 28/44 and 35/55

There are infinitely many numbers equivalent to 7/11

since 7/11 is a fraction that can be simplified in different ways.

We can multiply the numerator and denominator with the same number to get the equivalent fractions

7/11×2/2 = 14/22

7/11×3/3= 21/33

7/11×4/4 =28/44

7/11×5/5 =35/55

Hence, the equivalent fractions of 7/11 are 14/22, 21/33, 28/44 and 35/55

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Answer:

y = [tex]\frac{25x+22}{6}[/tex]

Step-by-step explanation:

express the ratios in fractional form

[tex]\frac{5x+2}{y-2}[/tex] = [tex]\frac{6}{5}[/tex] ( cross- multiply )

6(y - 2) = 5(5x + 2) ← distribute parenthesis on both sides

6y - 12 = 25x + 10 ( add 12 to both sides )

6y = 25x + 22 ( divide both sides by 6 )

y = [tex]\frac{25x+22}{6}[/tex]

Answer:

1761 ft²

Step-by-step explanation:

The shape of the attic is a triangular prism.

It has 5 faces: The bases are 2 faces that are congruent triangles. The other 3 faces are rectangles, 2 of which are congruent.

surface area = area of the bases + area of 3 rectangles

surface area = 2 × area of triangle + 2 × area of rectangle + area of other rectangle

surface area = 2 × (1/2)bh + 2 × length × width + LENGTH × WIDTH

surface area = 2 × (1/2)(15 ft)(15 ft) + 2(15 ft)(30 ft) + (21.2 ft)(30 ft)

surface area = 225 ft² + 900 ft² + 636 ft²

surface area = 1761 ft²

Answer:

C. 3/20 of a meter

Step-by-step explanation:

Step 1: To find out how much ribbon Carl has left, we need to subtract the length of ribbon used from the total length of the ribbon.

Step 2:  To add the lengths of the ribbon used, we need to find a common denominator for the fractions used. The least common multiple of 5 and 4 is 20, so we can convert both fractions to twentieths.

Step 3: 2/5 of a meter is equivalent to 8/20 of a meter, and 1/4 of a meter is equivalent to 5/20 of a meter.

Step 4:  To add the lengths of ribbon used, we add the two fractions: 8/20 + 5/20 = 13/20.

Step 5:  To find the length of ribbon Carl has left, we subtract the fraction of the ribbon used from the total length of the ribbon: 4/5 - 13/20 = 16/20 - 13/20 = 3/20.

Step 6: Therefore, Carl has 3/20 of a meter of ribbon left.

The probability of not rolling a 1 when rolling a six-sided die is approximately 83%. This means that if you roll the die many times, you would expect to get a 1 about 1/6 of the time and not get a 1 about 5/6 of the time.

When you roll a six-sided die, there are six possible outcomes, each with equal probability. These outcomes are rolling a 1, 2, 3, 4, 5, or 6. If you want to find the probability of not rolling a 1, you can count the number of outcomes that are not 1 and divide by the total number of outcomes.

Since there are five outcomes that are not 1 (2, 3, 4, 5, and 6) and six total outcomes, the probability of not rolling a 1 is 5/6.

To write this as a percentage rounded to the nearest whole number, we can multiply by 100 and round to the nearest whole number:

5/6 × 100 ≈ 83%.

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The variance and standard deviation of the frequency distribution data are;

The variance, s² = 14

The standard deviation, s ≈ 3.742

A frequency distribution displays the number of data within a specified interval.

The steps to find the variance and the standard deviation of the grouped data are as follows;

The midpoints of the class intervals are found as follows;

Class interval [tex]{}[/tex]       Midpoint

1 - 3                  [tex]{}[/tex]        2

4 - 6                  [tex]{}[/tex]       5

7 - 9                  [tex]{}[/tex]       8

10 - 12                      11

13 - 15                  [tex]{}[/tex]    14

19 - 21                  [tex]{}[/tex]    20

The mean is then found as follows;

(2×1 + 5×9 + 8×25 + 11×35 + 14×17 + 17×10 + 20×3)/(1+9+25+35+17+10+3)

The variance can then be found as follows;

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The solutions are x = 0, 0, -2 and 5.

Given is a polynomial we need to solve it,

3x⁴-9x³-30x².

We know that a polynomial will have the number of solutions equal to its highest degree,

Here the highest degree of the polynomial is 4 so there will be 4 solutions.

3x⁴-9x³-30x²

[tex]= 3x^2\left(x^2-3x-10\right)[/tex]

[tex]= x^2-3x-10 =\quad \left(x+2\right)\left(x-5\right)[/tex]

[tex]= 3x^2\left(x+2\right)\left(x-5\right)[/tex]

Therefore, the solutions are x = 0, 0, -2 and 5.

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Answer:

6,435

Step-by-step explanation:

The number of different committees that can be chosen can be calculated using the combination formula, also known as "n choose k," which calculates the number of ways to choose k items from a set of n items without regard to the order.

In this case, the principal wants to assemble a committee of 7 students from a student council of 15 members. Therefore, the number of different committees that can be chosen is given by the formula:

C(15, 7) = 15! / (7! * (15-7)!)

Calculating this expression gives:

C(15, 7) = 15! / (7! * 8!)

Simplifying further:

C(15, 7) = (15 * 14 * 13 * 12 * 11 * 10 * 9) / (7 * 6 * 5 * 4 * 3 * 2 * 1)

C(15, 7) = 6435

Therefore, there are 6,435 different committees that can be chosen from the 15-member student council.