David works as a firefighter, receiving an annual salary of $47,730.00. He also owns stocks that pay a dividend. Last year, David earned
$72,175.00 in total income. What was the amount of David's unearned income?

Answer:

x

−

3

x

−

2

Step-by-step explanation:

Answer:

80

Step-by-step explanation:

The variable "n" is not defined, but rather "k" is used in the summation. Assuming that "n" was meant to be "k", the expression should be:

s4 = ∑ k=1 to 4 of 2(3^(k-1))

To evaluate this expression, we need to substitute each value of k from 1 to 4 into the expression 2(3^(k-1)), and then sum up the results.

Starting with k = 1:

2(3^(1-1)) = 2(3^0) = 2(1) = 2

Moving on to k = 2:

2(3^(2-1)) = 2(3^1) = 2(3) = 6

Next, k = 3:

2(3^(3-1)) = 2(3^2) = 2(9) = 18

Finally, k = 4:

2(3^(4-1)) = 2(3^3) = 2(27) = 54

Now we add up these four results:

s4 = 2 + 6 + 18 + 54 = 80

Therefore, the value of s4 is 80.

Using simple interest, the amounts she invested are given as follows:

Simple interest is used when there is a single compounding per time period, usually measured in years.

The amount of money after t periods in is modeled by:

A(t) = P(1 + rt)

The interest accrued after t periods is modeled by:

I(t) = Prt

In which:

She had two investments, investing a total of $4500, hence:

\(P_1 + P_2 = 4500\)

The return for the 9% investment exceeds that from the 6% investment by $180, hence:

Then:

\(I_2 = 0.06(4500 - P_1)\)

\(I_1 - 180 = 0.06(4500 - P_1)\)

\(0.09P_1 - 180 = 0.06(4500 - P_1)\)

\(0.15P_1 = 450\)

\(P_1 = \frac{450}{0.15}\)

\(P_1 = 3000\)

Which is the amount invested at 9%, hence the amount invested at 6%, considering that a total of $4,500 was invested, is given by:

4500 - 3000 = $1,500.

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For the expression \(x^64 + ax^b + 25\) to be a perfect square for all integer values of x, b must be 64, and a must be a perfect square, written as a = \(y^2.\)

To determine the values of a and b such that the expression\(x^64 + ax^b\) + 25 is a perfect square for all integer values of x, we need to analyze the properties of perfect squares.

A perfect square is an expression that can be written as the square of another expression. In this case, we want the given expression to be in the form of\((x^n)^2,\) where n is an even integer.

Let's examine the given expression: \(x^64 + ax^b\) + 25

For it to be a perfect square, the quadratic term \(ax^b\)must have the same exponent as the leading term\(x^6^4.\) This means b must be equal to 64.

So we have:\(x^64 + ax^64 + 25\)

Now, we can rewrite this as:\((x^32)^2 + 2(x^32) (\sqrt{a}) + (\sqrt{25})^2\)

By comparing this with the standard form of a perfect square, (\(x^n +\sqrt{k} )^2\), we can deduce that √a must be equal to x^32 and \(\sqrt{25}\) must be equal to \(\sqrt{k.}\)

Therefore, we have: \(\sqrt{a} = x^3^2\)and\(\sqrt{25} = \sqrt{k}\)

From the second equation, we know that k = 25.

Now, substituting the value of k back into the first equation, we have: \(\sqrt{a} = x^3^2\)

To satisfy this equation for all integer values of x, a must be a perfect square. Therefore, we can express a as a =\(y^2\), where y is an integer.

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By adding 3 to both sides of the equation (6+3)-3=9-3, this demonstrates the addition property of equality. This results in the equation being simplified to 6+3=9.

The properties of equality describe the relationship between two sides of an equation and state that the two sides remain equal even after the same arithmetic operation is performed on each side. a = a, according to the reflexive property of equality. For example, 5 = 5, because the number's value is equal to itself.

As per the addition property of equality, when we add the same number to both sides of an equation then the two sides remain equal. This can be written as, if a = b, then a + c = b + c.

Translated question "Draw a line from each equation to the property of equality it illustrates. (6+3)−3=9−3 Addition Property of Equality"

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Answer:

5x-2y=3

-3x+4y=1

5x-2y=-3x+4y+2

+2y

5x=-3x+6y+2

+3x

8x=6y+2

divide by 2

4x=3y+1

-3y+4x=1

wait so that means that -3x+4y=-3y+4x so that means that both x and y are equal so lets just say their the same

-3x+4x=1

x=1

y=1

Hope This Helps!!!

An image of the resulting geometric shape based on a scale factor of 2 using O as the center of enlargement is shown below.

In Geometry, dilation is a type of transformation which typically changes the size of a geometric shape, but not its shape. This ultimately implies that, the size of the geometric shape would be increased (enlarged) or decreased (reduced) based on the scale factor applied.

In Mathematics, the following rules are applied to interpret and understand the dilation of a geometric shape:

In this context, we can logically deduce that the size of this geometric shape would be doubled because the scale factor is greater than 1.

The average rate of change of the function over the interval is -6

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

The graph

The interval is given as

From x = 2 to x = 4

The function is a quadratic function

This means that it does not have a constant average rate of change

So, we have

f(2) = -3

f(4) = -15

Next, we have

Rate = (-15 + 3)/(4 - 2)

Evaluate

Rate = -6

Hence, the rate is -6

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(f/g)(-5) is equal to 1/4, and the value -1 is not in the domain of f/g.

To find (f/g)(-5), we need to substitute -5 into the functions f(x) and g(x) and then divide f(-5) by g(-5).

Given:

f(x) = (4+x)(6+x)

g(x) = 1+x

Substituting -5 into the functions:

f(-5) = (4+(-5))(6+(-5)) = (-1)(1) = -1

g(-5) = 1+(-5) = -4

Now, we can calculate (f/g)(-5):

(f/g)(-5) = f(-5) / g(-5) = -1 / -4 = 1/4

Therefore, (f/g)(-5) equals 1/4.

Now let's determine the values that are not in the domain of f/g. The values that are not in the domain of f/g are the values that make the denominator g(x) equal to zero. In this case, the denominator is g(x) = 1+x.

To find the values that make the denominator zero, we solve the equation:

1 + x = 0

Subtracting 1 from both sides, we get:

x = -1

So, the value x = -1 is not in the domain of f/g because it would make the denominator equal to zero.

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Answer:

84

Step-by-step explanation:

The equation that models this situation is 1110 = 15x + 150 where x = cameras sold (note that this doesn't include the first 20 cameras, we'll add those on at the end). Let's solve for x!

1110 = 15x + 150

960 = 15x

x = 64 so the answer is 64 + 20 = 84 cameras.

Using translation concepts, it is found that the point (0, 0) on the graph of f(x) corresponds to point (4,-7) on g(x).

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.

Considering the translations, the equivalent point is found as follows:

Hence the point (0, 0) on the graph of f(x) corresponds to point (4,-7) on g(x).

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Answer:

You cant make him brainiest unless more than one person answers so I'm just "answering" so you can give him brainiest

Step-by-step explanation:

Answer:

No: n=3; 90

No: n=4; 480

Yes: n=5; 540

Yes: n=6; 720

Step-by-step explanation:

(n-2)180

if the sum of the interior angles is not equal to the above equation when substituting the variable for however many sides there are in the polygon, then it is not the correct sum

Answer:

The answer is A.

Step-by-step explanation:

For this graph, you are using the linear equation formula: y = mx + b

Answer:

(-7, -2)

Step-by-step explanation:

If you look on a graph and travel 7 units to the left of the y axis, you are traveling in the x direction (along the x axis). Since you are 7 units to the left, you are at -7 in the x direction.

If you look on a graph and travel 2 units down below the x axis, you are traveling in the y direction (along the y axis). Since you are 2 units down, you are at -2 in the y direction.

Coordinates are listed in (x,y) format, so it would be (-7, -2)

The depth of the aquarium is approximately 4 feet when rounded to the nearest whole number (since 3.64 is closer to 4 than it is to 3 when rounded to the nearest whole number).

To calculate the depth of the aquarium, we need to use the formula for volume of a rectangular prism,

which is V = lwh where V is the volume, l is the length, w is the width, and h is the height (or depth, in this case).

Given that the aquarium holds 11.35 cubic feet of water, the volume of the aquarium can be represented by V = 11.35 cubic feet.We are also given that the length of the aquarium is 2.6 feet and the width is 1.1 feet.

Substituting these values into the formula for volume,

we get:11.35 = 2.6 × 1.1 × h

Simplifying this expression:

11.35 = 2.86h

Dividing both sides by 2.6 × 1.1,

we get:h ≈ 3.64 feet (rounded to two decimal places)

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Answer:

dfgdfg

Step-by-step explanation:

3q4t5eratged/ 435675 //d ge5y C

Based on the given histogram, the data is skewed with a maximum range of 49.

This is because the frequency bars are not evenly distributed across the x-axis intervals, indicating that the data is not symmetric. The lack of a shaded bar for the 40 to 49 interval also suggests that there were fewer donations in that range compared to the other intervals.

One possible explanation for this skewness could be that the charity had suggested donation levels, with a minimum of $10, resulting in a large number of donations in the 10 to 19 interval. Additionally, the shaded bar stopping at 1 for the 30 to 39 and 50 to 59 intervals suggests that there were fewer donations in those ranges. This could be due to a variety of reasons, such as donors being more likely to give in the suggested $10 increments, or the charity's fundraising efforts being more effective at attracting donors in certain age or income brackets.

Overall, the histogram does not suggest a bimodal distribution, as there is not a clear separation between two distinct modes. The maximum range of 49 also indicates that there were no extreme outliers or large donations that would skew the data towards a higher range. Therefore, it is likely that the data represents a typical distribution of donations to a charity, with most donors giving smaller amounts and fewer donors giving larger amounts.

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Answer:

8

Step-by-step explanation:

2(5x2-4+2)=2(10-4+2)=2x4=8

Geometric Sequences

I was given two choices:

* Take a 50,000 gold coins prize, or

* Take a 1 magic coin prize that doubles every day for 28 days.

Which prize do I choose? Clearly, the second choice. But that is because I already know the numbers behind geometric sequences.

Now I explain why by answering these questions:

1. The number of coins on the third day will be 2×2×2. It can be also expressed by using exponents as follows:

The exponent of the base 2 is the number of days that have passed.

For the 28th day, the magic coin will give:

But we need to know how many coins have accumulated since the first day. This will be the result of the sum:

Given 1 equals 2 to the power of 0, we can write the sum as:

This is the sum of a geometric sequence with a1 = 1 and a common ratio of r = 2.

The formula to compute the sum of n terms of a geometric sequence is:

Since our sequence starts at n=0, there are n = 29 terms to sum:

T

Answer:

No.  The data in this study were not based on a random method.  This is a key requirement for an inference to be made from the two-sample t-test.

Step-by-step explanation:

1. Hayden can use the two-sample t-test (also known as the independent samples t-test)to find out if there was a difference in the time spent in the checkout time between two grocery stores and to conclude whether the difference in the average checkout time between the two stores is really significant or if the difference is due to a random chance.  There are three conditions to be met when using the two-sample t-test.

2. The first condition is that the sampling method must be random.  This requirement was not met in this study.  Each customer from each store should have an equal chance of being selected for the study.  This was not achieved.

3. The distributions of the sample data are approximately normal.  This is achieved with a large sample size of 30 customers selected for each study.

4. The last but not the least condition is the independence of the sample data.  Sample data here is independent for both samples.

The graph of a proportional relationship can be described as a graph that always starts at point zero and is always a straight line graph.

A straight line graph is defined as the type of graph that is also called a linear graph which shows a relationship between two or more quantities that uses a graphical form of representation.

There are some characteristics that shows that a graph is of proportional relationship which include the following:

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The volume of the solid is approximately 0.558 cubic units.

To find the volume of the solid, we need to integrate the area of the semi-circles along the a-axis.

We know that the diameter of each semi-circle is the distance between the functions f(x) and g(x), which is:

d(a) = f(a) - g(a) = ln(a) + 1 - (a-1) = ln(a) - a + 2

The radius of each semi-circle is half of the diameter, which is:

r(a) = (ln(a) - a + 2) / 2

The area of each semi-circle is π times the square of its radius, which is:

\(A(a) = πr(a)^2 = π/4 (ln(a) - a + 2)^2\)

To find the volume of the solid, we integrate the area of each semi-circle along the a-axis, from a = e to a = 2:

V = ∫[e,2] A(a) da

V = ∫[e,2] π/4 \((ln(a) - a + 2)^2 da\)

V ≈ 0.558 (rounded to the nearest thousandth)

Therefore, the volume of the solid is approximately 0.558 cubic units.

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Answer:

-(1 + √21)/5

Explanation:

The given expression is

To simplify we need to multiply and divide by the conjugate of the denominator, so we need to multiply and divide by (√7 + √12).

Then, the expression is equal to:

Therefore, the answer is:

-(1 + √21)/5

Answer:

c. 5056

Step-by-step explanation:

The revenue is maximized when the units sold are increased if the selling price is constant. The basket ID 5056 has more units then the other two baskets and its invoice total is greater than the other baskets. The basket 5056 has largest total revenue to the company.

Answer:

the answer is 0.34 (look down to see a trick to find a fast answer0

Step-by-step explanation:

Remember, when people say 34%, it means 34% of 1. So, 34% is equivalent to .34. We multiply 50 by .34 to get 34% of 50. So, 34% of 50 is 17

Percentages are communative. 34% of 50 is the same as 50% of 34.

Answer: P= 30° & R= 60°

Step-by-step explanation:

First, you should find angle "R" as it helps find angle "P"

therefore:

R= 180°- 120°(angles on a straight line add up to 180°)

 = 60°

P= 180°- ( 90°+ 60°) (Angles of a triangle add up to 180°)

 = 180°- 150°

 = 30°

Answer:

D. $544.45

Step-by-step explanation:

step 1:

6 x 45.25 = 271.5.

step 2:

271.5 + 272.95 = 544.45

Answer:

i need a picture

Step-by-step explanation:

Answer: 7 radios

Step-by-step explanation:

The following can be deduced from the question:

Number of radios tested = 125 radios

Percentage acceptable = 60%

Numbers acceptable:

= 60% × 125

= 0.6 × 125

= 75 radios

Numbers rejected = 125 - 75 = 50 radio

We are further told that the inspector tested 25 more radios, this will be:

Number of radios tested

= 125 + 25 = 150 radios

Percentage acceptable = 62%

Numbers acceptable

= 62% × 150

= 0.62 × 150

= 93 radios

Numbers rejected= 150 - 93 = 57 radios

The number of these 25 radios that were rejected will be:

= 57 - 50

= 7 radios