To save for retirement, Karla Harby put $300 each month into an ordinary annuity for 20 years. Interest was compounded monthly. At the end of the 20 years, the annuity was worth $147,126. What annual interest rate did she receive?

The Linear function for the line represented by the point-slope equation y - 5 = 3(x - 2) is y = 3x - 1.

The point-slope equation for a line is of the form y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope of the line. Given the point-slope equation y - 5 = 3(x - 2),

we can see that the slope of the line is 3 and it passes through the point (2, 5).

To find the linear function for the line, we need to write the equation in slope-intercept form, which is y = mx + b, where m is the slope of the line and b is the y-intercept (the point at which the line intersects the y-axis).

To get the equation in slope-intercept form, we need to isolate y on one side of the equation.

We can do this by distributing the 3 to the x term:y - 5 = 3(x - 2)  y - 5 = 3x - 6  y = 3x - 6 + 5  y = 3x - 1

Therefore, the linear function for the line represented by the point-slope equation y - 5 = 3(x - 2) is y = 3x - 1.

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Answer:

Undefined

Step-by-step explanation:

Gradient/slope = \(\frac{8-3}{2-2} = \frac{5}{0}\) (change in y / change in x) = Undefine

It will take approximately 8.5 years to triple the population and approximately 10 years to quadruple the population.

Given that the population of a community is known to increase at a rate proportional to the number of people present at time t, and an initial population p0 has doubled in 5 years.

To calculate:

How long will it take to triple?

How long will it take to quadruple?

Let p be the population of a community at any time t. According to the given information, the population p is proportional to the number of people present at time t. Therefore, we have p ∝ p_0 …… (1)

where p_0 is the initial population of the community. It is given that the initial population p_0 has doubled in 5 years.

So, we have 2p_0 = p_0e^(rt) 2 = e^(5r)

Taking natural logarithm on both sides, ln 2 = ln e^(5r) = 5rln 2/5 = r …… (2)

Using equation (1) and (2), we can write population p asp = p_0e^(rt) = p_0e^(ln2/5 t) = p_0 2^(t/5)

Now, we have to find for how many years (t) we need to wait until the population of the community triples, i.e.

3p_0 = p_0 2^(t/5) 3 = 2^(t/5)

Taking logarithm (with base 2) on both sides,

log_2 3 = log_2 2^(t/5)log_2 3 = (t/5)log_2 2t = 5 log_2 3t ≈ 8.5 (Rounded to one decimal place)

Therefore, it will take approximately 8.5 years to triple the population.

Now, we need to find for how many years (t) we need to wait until the population of the community quadruples, i.e. 4p_0 = p_0 2^(t/5) 4 = 2^(t/5)

Taking logarithm (with base 2) on both sides,

log_2 4 = log_2 2^(t/5)

log_2 4 = (t/5)log_2 2t = 5 log_2 4t ≈ 10 (Rounded to one decimal place)Therefore, it will take approximately 10 years to quadruple the population.

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Answer:

y = 105x

Step-by-step explanation:

He loses $105 per month

In each scenario, the choice between mean and median as a representative measure of central tendency depends on the nature of the data and the specific context..

1. Scenario: Income distribution of a population

- If the income distribution is skewed or contains extreme values (outliers), the median would be a better representation of the central tendency. This is because the median is not influenced by outliers and provides a more robust estimate of the "typical" income level. However, if the income distribution is approximately symmetric without outliers, the mean can also be an appropriate measure.

2. Scenario: Exam scores in a class

- If the exam scores are normally distributed without significant outliers, the mean would be a suitable measure as it takes into account the value of each score. However, if there are extreme scores that deviate from the majority of the data, the median may be a better representation. This is especially true if the outliers are indicative of errors or exceptional circumstances.

3. Scenario: Housing prices in a city

- In this case, the median would be a more appropriate measure to represent the central tendency of housing prices. This is because the housing market often exhibits a skewed distribution with a few high-priced properties (outliers). The median, being the middle value when the data is sorted, is not influenced by these extreme values and provides a better understanding of the typical housing price in the city.

Ultimately, the choice between mean and median depends on the specific characteristics of the data and the objective of the analysis. It is important to consider the distribution, presence of outliers, and the context in which the data is being interpreted.

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A 9-pound bag of sugar can fill 18 containers that hold 0.5 pounds of sugar each.

To determine how many containers of sugar a 9-pound bag can fill, we need to divide the total weight of the bag by the weight of each container. In this case, the weight of each container is given as 0.5 pounds. So, we can use the following formula:

Number of containers = Total weight of the bag / Weight of each container

Substituting the values given in the problem, we get:

Number of containers = 9 / 0.5 = 18

Therefore, a 9-pound bag of sugar can fill 18 containers that hold 0.5 pounds of sugar each. None of the options provided in the problem matches the correct answer. We can round the answer to the nearest whole number, which would be 18.

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Answer:

-32 = 3x - 4y

Step-by-step explanation:

Let's first eliminate the fraactional coefficient by multiplying both sides by 4:

4y - 8 = 3x + 24

Next, combine the constants:  4y = 3x + 32

Finally, write this result in the form Ax + By = C:

-32 = 3x - 4y

Answer: height = 1.91 m

Step-by-step explanation: Using the formula

V=πr2h

Solving for h

h=V

πr2=37.5

π·2.52≈1.90986m

5) Notice that angles 4 and 2 are corresponding angles, since FG is parallel to HJ then:

If m<2=45º, then by the transitive property we get:

7) Notice that angles 3 and 6 are aternating exterior angles, since FG is parallel to HJ then:

If m<6=135º then by the transitive property we get:

Answer:

(5)

(7)

Saved:-

\(\\ \sf\Rrightarrow 2\dfrac{1}{4}-\dfrac{3}{8}\)

\(\\ \sf\Rrightarrow \dfrac{9}{4}-\dfrac{3}{8}\)

\(\\ \sf\Rrightarrow \dfrac{18-3}{8}\)

\(\\ \sf\Rrightarrow \dfrac{15}{8}\)

\(\\ \sf\Rrightarrow 1\dfrac{7}{8}\)

Answer:

\(\textsf{D)} \quad 1 \dfrac{7}{8}\)

Step-by-step explanation:

Subtract the used volume of punch from the starting volume of punch.

Convert the mixed number to an improper fraction:

\(\begin{aligned} \implies 2\frac{1}{4}-\frac{3}{8} & = \dfrac{2 \times 4+1}{4}-\dfrac{3}{8}\\\\ & = \dfrac{9}{4}-\dfrac{3}{8}\end{aligned}\)

Make the denominators of both fractions the same by multiplying the numerator and the denominator of 9/4 by 2:

\(\implies \dfrac{9 \times 2}{4 \times 2}-\dfrac{3}{8} = \dfrac{18}{8}-\dfrac{3}{8}\)

\(\textsf{Apply the fraction rule} \quad \dfrac{a}{c}-\dfrac{b}{c}=\dfrac{a-b}{c}:\)

\(\begin{aligned} \implies \dfrac{18}{8}-\dfrac{3}{8} & = \dfrac{18-3}{8}\\\\ & = \dfrac{15}{8}\end{aligned}\)

Convert back into a mixed number:

\(\begin{aligned}\implies \dfrac{15}{8} & = \dfrac{8+7}{8}\\\\ & = \dfrac{8}{8}+\dfrac{7}{8}\\\\ & = 1\dfrac{7}{8}\end{aligned}\)

For a pure resistive circuit, the RMS value of the current is used to determine the power dissipated by the resistor. P = I2R, where P is the power, I is the RMS value of the current, and R is the resistance of the circuit.

The given function is I(t) = 10 sin t, where I represent the time-dependent current in amperes. Mean and RMS values of the current over time 0 to π and 0 to 2π can be calculated as follows:

Mean value:

The mean value of the current waveform is given as Zero mean value implies the current waveform has equal positive and negative areas over the period.

RMS value:

The RMS (root mean square) value of a periodic waveform is defined as the square root of the mean value of the squares of the instantaneous values over one period.

Mathematically,

RMS current overtime period 0 to π is I

RMS = I 1

= 10/√2

=7.07A

RMS current overtime period 0 to 2π is I RMS = 7.07A

The RMS value of the current gives a better indication of the heating effect of the current in the circuit. The larger the RMS value of the current, the greater the amount of heat produced in the circuit.

For a pure resistive circuit, the RMS value of the current is used to determine the power dissipated by the resistor. P = I2R, where P is the power, I is the RMS value of the current, and R is the resistance of the circuit.

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To form a polynomial with given zeros and degree, we need to use the fact that if a polynomial has a zero of x = a, then it can be factored as (x - a) times some other polynomial.

This means that if we know the zeros of a polynomial, we can write it in factored form, and then multiply out the factors to get the polynomial in standard form.

The degree of the polynomial tells us how many factors are necessary. For example, if the degree is 3, we know that the polynomial can be factored into three linear factors, one for each zero.

To illustrate this process, let's say we want to form a polynomial of degree 4 with zeros of x = 2, x = -1, and x = 3. We would start by writing the polynomial in factored form as:

f(x) = (x - 2)(x + 1)(x - 3)(ax + b)

Since the degree is 4, we need to include one more factor. We can use the coefficients a and b to determine this factor. To do so, we can either use the value of the leading coefficient (which is a in this case) or a point on the polynomial (i.e., a value of x and f(x)).

Once we have determined the value of a, we can solve for b by setting a point on the polynomial equal to a known value.

Finally, we can multiply out the factors to get the polynomial in standard form:

f(x) = (x - 2)(x + 1)(x - 3)(2x - 4)

f(x) = 2x^4 - 8x^3 - 13x^2 + 22x - 12

In conclusion, to form a polynomial with given zeros and degree, we need to use the fact that a polynomial can be factored as (x - a) times some other polynomial if it has a zero of x = a.

We can write the polynomial in factored form, determine the missing factor(s) using the degree and coefficients, and then multiply out the factors to get the polynomial in standard form.

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Using the triangle inequality theorem, the largest possible whole-number length for the third side is 4.

The third side of a triangle must be shorter than the sum of the other two sides and longer than the difference between the other two sides.

So, for a triangle with sides of length 1, 4, and x (where x is the length of the third side), we have:

1 + 4 > x

4 + x > 1

1 + x > 4

Simplifying these inequalities, we get:

5 > x

x > 3

x > -3 (this inequality is always true)

The largest possible whole-number length for the third side is 4, since it is the largest integer that satisfies the above inequalities.

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Here, Statement a) B is more stable than A  is correct, while statements b), c), and d) are incorrect.

Lindane, also known as gamma-hexachlorocyclohexane, exists as a mixture of two stereoisomers. These stereoisomers have different chair conformations, often referred to as conformer A and conformer B. I will describe these conformations to help you analyze the statements provided.

Conformer A: In conformer A, one of the chlorine atoms is positioned in an axial (up) position, while the other five chlorine atoms are in equatorial (outward) positions. This arrangement is less stable due to steric hindrance caused by the axial chlorine atom, which experiences stronger interactions with neighboring groups.

Conformer B: In conformer B, the axial and equatorial positions of the chlorine atoms are interchanged compared to conformer A. The chlorine atom that was previously axial is now equatorial, and vice versa. This arrangement reduces the steric hindrance, leading to a more stable conformation.Now, let's analyze the provided statements:

a) B is more stable than A:

This statement is correct. Conformer B is indeed more stable than conformer A because it minimizes steric hindrance by placing the chlorine atoms in more favorable positions.b) A is more stable than B:

This statement is incorrect. As explained above, conformer B is more stable than conformer A.

c) A is not the correct representation of Lindane:

This statement is incorrect. Both conformers A and B are valid representations of Lindane, and the compound exists as a mixture of these conformations.

d) The two chair conformations of Lindane are degenerate:

This statement is incorrect. Degenerate conformations have the same energy level. In the case of Lindane, conformer B is more stable than conformer A, indicating that they have different energy levels and are not degenerate.

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Answer:

A. 540 cubic inches

Step-by-step explanation:

so 100% full would be 600cubic inches. ( I get this by finding volume Length times width times height)

Find 90% if 600 and get 540 cubic inches.

to find 90% do 0.9 times 600

Answer:

m || n only when the corresponding angles will be equal.

Step-by-step explanation:

Here its only given that vertical angles are equal. But it doesn't prove m || n . If the corresponding angles wouls have been equal , then only we can prove that m || n.

Answer:

8 31/50

Step-by-step explanation:

HOPE THIS HELPS

Answer:

831 / 50

Step-by-step explanation:

Welcome !!!!!

Answer:

\(\huge\boxed{\sf \$ 2.2}\)

Step-by-step explanation:

5 pounds of flour = $11

5/5 pound of flour = $11 / 5

\(\rule[225]{225}{2}\)

Answer:

0

Step-by-step explanation:

To find the number of integer solutions there are to the inequality, we need to  separate \(x\) so it is on its own.

\(17<5x-8 < 22\) (given inequality)

\(25 < 5x < 30\) (add \(8\) )

\(5 < x < 6\) (divide by \(5\) )

Since there are no integers between \(5\) and \(6\), it means there are 0 integer solutions for the inequality \(17 < 5x - 8 < 22\).

Hope this helps :)

Based on the facts behind the scores of Tom, Mary, Hector, and Sue, the players' scores are:

Tom's score is said to be the opposite of Mary's score. The only scores that are the opposites of each other are 2 and -2.

This means that Tom's score is either 2 or -2. However, Tom's score is said to be only larger than Sue's. 2 is greater than -4 and -2 so violates this. Tom's score can therefore only be -2.

Mary's score is then 2. Sue will have the lowest score of -4 and Hector will have the highest score of 3.

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Answer: The answer is valid, because you survey 100 people and 80 of them support building a new stadium.

Step-by-step explanation:

80% agree. 80/100 = 80%

Answer:

the first truck

Step-by-step explanation:

the cost difference between the first truck and the second truck = $160,000-$145,000 = $15,000

the difference of gas cost between the first truck and the second truck = $0.31 - $0.26= $0.05 per mile.

so,

I think, this is a very significant number of truck cost compared with gas cost

for the best deal, the first truck is the best choice.

Answer:

Answer is 6.40 units

Step-by-step explanation:

Pythagorean theorem

a^2+b^2=c^2

fill in the sides for a and b

4^2 + 5^2 = c^2

simplify

16+25 = c^2

41 = c^2

Sqrt both sides

c = 6.4

Answer:

6.40 units

Step-by-step explanation:

You can use the equation a^2+b^2=c^2 for this. C is the unknown and the hypotenuse.

In this case, 4^2+5^2=c^2.

16+25=c^2

41=c^2

sqrt{41}= c

Approximately 6.40312

Answer:

Logan was supposed to add -6x and 5x, obtaining -x.

(2x + 5)(x - 3) = 2x² - 6x + 5x - 15

= 2x² - x - 15

1. The actual area of the rectangle is 2x² -x -15

2. The dimensions of the rectangle is (3x-2)( x-5)

A Rectangle is a four sided-polygon, having all the internal angles equal to 90 degrees.

The area of a rectangle is expressed as;

A = l × w

1. l = x -3

w = 2x +5

area = x-3)( 2x+5)

= x( 2x +5) -3( 2x+5)

= 2x² + 5x - 6x -15

= 2x² -x -15

The mistake Logan made was he multiplied -6x and 5x instead of adding them

2. For a area of 3x² -13x -10, to find the dimensions, we need to factorize

= 3x² - 15x +2x -10

= (3x²-15x)( 2x-10)

= 3x( x-5) 2( x-5)

= (3x-2)( x-5)

Therefore the dimensions are (3x-2) and ( x-5)

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Answer:

14 cups of m&m's to make 84 cookies

Step-by-step explanation:

If it takes 2 cups of m&m's to make 12 cookies. then you need to see how many times the original recipe will go into 84. Seeing that 84/12=7 you would need to multiply the original recipe by 7.  

For example:

84/12=7 This is how many times the recipe is multiplied if you make 84 cookies.

2x7 is the amount of m&m's you would need to make the larger batch of cookies.

Answer:

4

Step-by-step explanation:

Answer:

≈11.7 [ft].

Step-by-step explanation:

1) the ladder and the wall form the right triangle, where the length of the ladder (12 ft) is hypotenuse and the distance between the base of the latter and the base of the wall is the shortest side.

2) the longest side can be calculated according the Pythagoras theorem:

\(L=\sqrt{12^2-2.8^2}=\sqrt{136.16}=11.7[ft].\)

y = -1/3x + 1

y = -2x - 3

We can compare the equations to the graphs and see which graph represents the intersection point of the two equations.

The first equation, y = -1/3x + 1, has a negative slope (-1/3) and a y-intercept of 1.

The second equation, y = -2x - 3, also has a negative slope (-2) and a y-intercept of -3.

Based on the slopes and y-intercepts, we can identify the correct graph by finding the point where the two lines intersect.

Unfortunately, since the graphs are not provided, I am unable to determine which specific graph shows the solution to the system of linear equations. I recommend referring to the graph representation of the equations and identifying the intersection point to determine the correct graph.

Answer:

26 1/4

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

You add up both fractions, sorry for the lazy explanation

Answer:

42.78cm2

Step-by-step explanation:

Area =100°/360 * 22/7 * 7^2

=42.78cm2