Hester sells televisions. She earns a fixed amount for each television and an additional $25 if the buyer gets an extended warranty. If Hester sells 15 televisions with extended​ warranties, she earns $1,350. How much is the fixed amount Hester earns for each​ television?

The tick marks on the two sides mean those two lengths are the same, which also means the angles opposite them are the same measure.  (AKA It's an isosceles triangle.)

Since the two missing angles are equal, we can solve:

    28 + x + x = 180

to find that x = 76.

The two angles are 76 degrees.

And since LM = LN, we know LN = 18 in.

The missing values a, b, c, d and e are included in the given two-way table. The correct values from the options are: a =15, b=18,e=31

Suppose two dimensions are there, viz X and Y. Some values of X are there as \(X_1, X_2, ... , X_n\) and some values of Y are there as \(Y_1, Y_2, ... , Y_n\)

List them in title of the rows and left to the columns. There will be \(n \times k\) table of values will be formed(excluding titles and totals), such that:

Value(ith row, jth column) = Frequency for intersection of \(X_i\) and \(Y_j\) (assuming X values are going in rows, and Y values are listed in columns).

Then totals for rows, columns, and whole table are written on bottom and right margin of the final table.

For n = 2, and k = 2, the table would look like:

\(\begin{array}{cccc}&Y_1&Y_2&\rm Total\\X_1&n(X_1 \cap Y_1)&n(X_1\cap Y_2)&n(X_1)\\X_2&n(X_2 \cap Y_1)&n(X_2 \cap Y_2)&n(X_2)\\\rm Total & n(Y_1) & n(Y_2) & S \end{array}\)

where S denotes total of totals, also called total frequency.

n is showing the frequency of the bracketed quantity, and intersection sign in between is showing occurrence of both the categories together.

For this case, the table given is:

\(\begin{array}{cccc}\rm &\rm \text{Likes swimming}&\rm \text{Doesn't like swimming}&\rm Senior\\\rm \text{Likes baseball}&a&b&33\\\rm \text{Doesn't likes baseball}&c&13&d\\\rm Total & 39& e& 70 \end{array}\)

From this table, we can make 5 equations as:

\(a+b = 33\\a+c=39\\b+39=e\\33+d = 70\\39+e=70\)

From the last two equations, we get the values of d and e as:

\(d = 70-33 = 37\\e = 70-39 = 31\)

Putting this value of 'e' in last third equation, we get:

\(b + 13 = 31\\b = 31-13= 18\)

From this, and first equation, we get:

\(a +18 = 33\\a=33-18=15\)

And from this value of a, and second equation, we get:15+c = 39

\(c = 39-15 = 24\)

Thus, the correct values are: \(a =15, b=18,e=31\)

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Answer:

a,b,e

Step-by-step explanation:

The expression for the number of bacteria after t hours is N(t) = 50e\(^(0.4427t)\) , rounded to four decimal places.

Let N(t) be the number of bacteria after t hours.

Since the culture grows at a rate proportional to its size, we can write:

dN/dt = kN

where k is the proportionality constant.

This is a separable differential equation, which we can solve by separating the variables and integrating:

dN/N = k dt

ln(N) = kt + C

where C is the constant of integration.

To find the value of C, we use the initial condition that the culture initially contains 50 cells:

ln(50) = k(0) + C

C = ln(50)

Substituting C into the previous equation, we get:

ln(N) = kt + ln(50)

Taking the exponential of both sides, we obtain:

N = e\(^(kt + ln(50)) = 50e^(kt)\)

Now we need to find the value of k. We know that after 1.5 hours, the population has increased to 825:

N(1.5) = 825

Substituting this into the previous equation, we get:

825 = 50\(e^(1.5k)\)

Taking the natural logarithm of both sides, we obtain:

ln(825/50) = 1.5k

k = ln(825/50) / 1.5

k ≈ 0.4427

Finally, substituting this value of k into the expression we obtained for N(t), we get:

N(t) = 50e\(^(0.4427t)\)

Therefore, the expression for the number of bacteria after t hours is N(t) = \(50e^(0.4427t)\), rounded to four decimal places.

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The population proportion who participated in voting (63%) is higher than the sample proportion from this survey (58.91%).

To determine whether the population proportion who participated in voting or the sample proportion from the survey is higher, we need to compare the percentages.

The population proportion who participated in voting is given as 63% of all registered voters.

This means that out of every 100 registered voters, 63 participated in voting.

In the survey of retired voters, 162 out of 275 participants voted. To calculate the sample proportion, we divide the number of retired voters who participated (162) by the total number of retired voters in the sample (275) and multiply by 100 to get a percentage.

Sample proportion = (162 / 275) \(\times\) 100 ≈ 58.91%, .

Comparing the population proportion (63%) with the sample proportion (58.91%), we can see that the population proportion who participated in voting (63%) is higher than the sample proportion from this survey (58.91%).

Therefore, based on the given data, the population proportion who participated in voting is higher than the sample proportion from this survey.

It's important to note that the sample proportion is an estimate based on the surveyed retired voters and may not perfectly represent the entire population of registered voters.

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Answer:

50

Step-by-step explanation:

Answer:

50

Step-by-step explanation:

Hope this helps :)

According to reserch about 18 percent people worldwide having sprinter gene.

In the given question, we have to find how many people have the sprinter gene.

As we know that;

The ACTN3 gene is the recently identified "sprinters gene."

A gene, as we already stated, codes for a protein. Alpha-actinin-3 is designated by ACTN3. This protein, which can only be found in fast twitch muscle fibres, gives muscles their explosive ability.

In order to summarise the genetic component, an individual has the ACTN3 gene if alpha-actinin-3 is present in muscle cells. They are therefore better suited for quick movements.

According to reserch about 18 percent people worldwide having sprinter gene.

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This is a table of values of three functions at selected values of x.

It is asking for h(f(-2))

Its saying, take f(-2), and take whatever you get from that and put it into h(x)

So, find f(-2).

Find x = -2, then see what f is there.

f(-2) = -1

So, find h(-1)

h(-1) = 0

Hope this helps :)

If you need any more explanation, feel free to ask.  If this really helps, consider marking brainliest.

- Jeron

The value of each share of common stock, rounded to the nearest penny, is approximately $66.61 according to the given information and values in the question.

step by step:

To calculate the value of each share of common stock using the Discounted Cash Flow (DCF) valuation model, we need to discount the expected future cash flows to their present value and subtract the market value of the outstanding debt. The formula for calculating the value of each share of common stock is:

Value per Share = (Present Value of Future Cash Flows - Debt) / Number of Common Shares

To calculate the present value of future cash flows, we discount each cash flow using the cost of capital.

Let's calculate the present value of future cash flows and the value per share of common stock:

Year 1: FCF = $250,000

Year 2: FCF = $300,000

Year 3: FCF = $350,000

Year 4: FCF = $400,000

Year 5: FCF = $450,000

\(Year 6 onwards: FCF = $450,000 * 1.022^(Year - 5)\)

Cost of Capital = 6.65%

Outstanding Debt = $3,833,340

Number of Common Shares = 60,797

First, let's calculate the present value of future cash flows:

\(PV = FCF / (1 + r)^n\)

where:

PV = Present Value

FCF = Future Cash Flow

r = Cost of Capital

n = Number of years

\(Year 1:PV1 = $250,000 / (1 + 0.0665)^1 ≈ $234,837.45Year 2:PV2 = $300,000 / (1 + 0.0665)^2 ≈ $268,084.17Year 3:PV3 = $350,000 / (1 + 0.0665)^3 ≈ $301,706.42Year 4:PV4 = $400,000 / (1 + 0.0665)^4 ≈ $335,693.63Year 5:PV5 = $450,000 / (1 + 0.0665)^5 ≈ $369,035.06Year 6 onwards:PV6 = $450,000 * 1.022^(Year - 5) / (1 + 0.0665)^Year\)

Now, let's calculate the total present value of future cash flows:

\(Total PV = PV1 + PV2 + PV3 + PV4 + PV5 + ∑(PV6)\)

∑(PV6) represents the sum of present values for Year 6 onwards, up to infinity. Since we have a constant growth rate of 2.2%, we can use the perpetuity formula to calculate this sum:

\(∑(PV6) = PV6 / (r - g)\)

where:

r = Cost of Capital

g = Growth rate

\(∑(PV6) = PV6 / (0.0665 - 0.022) = PV6 / 0.0445Now, let's calculate PV6 and ∑(PV6):PV6 = $450,000 * 1.022^1 / (1 + 0.0665)^6 ≈ $303,212.65∑(PV6) = $303,212.65 / 0.0445 ≈ $6,820,510.11\)

Next, let's calculate the total present value:

\(Total PV = PV1 + PV2 + PV3 + PV4 + PV5 + ∑(PV6)Total PV = $234,837.45 + $268,084.17 + $301,706.42 + $335,693.63 + $369,035.06 + $6,820,510.11Total PV ≈ $8,329,866.84\)

Finally, let's calculate the value per share of common stock:

Value per Share = (Total PV - Debt) / Number of Common Shares

Value per Share = ($8,329,866.84 - $3,833,340) / 60,797

Value per Share ≈ $66.61

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Answer:

M (8, −2) → M ′(3, −1) → M ″(−3, −1)

Step-by-step explanation:

Answer:

They would need 500 liters of soda water and this would make 100 batches of the sparkling orange juice.

Step-by-step explanation:

hope this helps. . . <3

good luck!    uωu

Answer:

500 soda water, 100 batches, just a guess so sorry if im wrong

Step-by-step explanation:

The ratio of the number of squares to the number of triangles is 5 : 2

The number of triangles that should be added to make the ratio is 6

Ratio expresses the relationship between two or more numbers. It is the number of times that one value is contained in another number.

Ratio of the number of squares to the number of triangles = number of squares : number of triangles

10 : 4

5 : 2

The number of triangles that should be added to make the ratio 1 : 1 - 10 - 4 = 6

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Answer:

4/10 and 40%

Step-by-step explanation:

He had 4 Strikes out of a total 10 Tries. 4 of his 10 tries were strikes.

So its 4/10.

The measure of arc BC is 720 times the measure of angle BAC.

Given that AC is the diameter of the circle and AB is a chord with a length of 16 units, we need to find BC (the length of the other chord) and mBC (the measure of angle BAC).

To find BC, we can use the property of chords in a circle. If two chords intersect within a circle, the products of their segments are equal. In this case, since AB = BC = 16 units, the product of their segments will be:

AB * BC = AC * CE

16 * BC = 2 * r * CE (AC is the diameter, so its length is twice the radius)

Since the area of the circle is given as 289 square units, we can find the radius (r) using the formula for the area of a circle:

Area = π * r^2

289 = π * r^2

r^2 = 289 / π

r = √(289 / π)

Now, we can substitute the known values into the equation for the product of the segments:

16 * BC = 2 * √(289 / π) * CEBC = (√(289 / π) * CE) / 8

To find mBC, we can use the properties of angles in a circle. The angle subtended by an arc at the center of a circle is double the angle subtended by the same arc at any point on the circumference. Since AC is a diameter, angle BAC is a right angle. Therefore, mBC will be half the measure of the arc BC.

mBC = 0.5 * m(arc BC)

To find the measure of the arc BC, we need to find its length. The length of an arc is determined by the ratio of the arc angle to the total angle of the circle (360 degrees). Since mBC is half the arc angle, we can write:

arc BC = (mBC / 0.5) * 360

arc BC = 720 * mBC

Therefore, the length of the arc BC equals 720 times the length of the angle BAC.

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The correct answer is c. − 16x^3 / ((x^2 + 16)^(3/2)) + C. To evaluate the integral, we substitute x = 4tan(t) as explained earlier.

The integral simplifies to:

∫ x^4 / ((x^2 + 16)^(3/2)) dx = ∫ (16tan^4(t)) / (16sec^3(t)) sec^2(t) dt

= ∫ tan^4(t) / sec(t) dt.

Using the trigonometric identity tan^2(t) = sec^2(t) - 1, we have:

∫ tan^4(t) / sec(t) dt = ∫ (sec^2(t) - 1)^2 / sec(t) dt

= ∫ (sec^4(t) - 2sec^2(t) + 1) / sec(t) dt

= ∫ sec^3(t) - sec(t) dt.

Integrating each term separately, we obtain:

∫ sec^3(t) dt = (1/2)sec(t)tan(t) + (1/2)ln|sec(t) + tan(t)| + C.

Finally, substituting back x = 4tan(t), we get:

∫ x^4 / ((x^2 + 16)^(3/2)) dx = (1/2)sec(t)tan(t) + C.

Using the relationship sec(t) = sqrt(x^2 + 16) / 4 and tan(t) = x / 4, we can rewrite the answer as c. − 16x^3 / ((x^2 + 16)^(3/2)) + C.

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Answer:

answer is -0.6

Step-by-step explanation:

Answer:

0.6

Step-by-step explanation:

1.4 - -0.6 = 2

In the situation of two parallel lines are crossed by a transversal the value of x is calculated to be 12

The value of x is calculated using the knowledge of alternate internal angels and linear pair.

This can also be determined using corresponding angles and linear pair theorem

Using corresponding angles:

angel 115 is equal to the corresponding position at line b. This makes angel 115 and 5x + 5 to form linear pair

The linear pair theorem says that the two angles 5x + 5 and 115 are supplementary

5x + 5 + 115 = 180

5x + 120 = 180

5x = 180 - 120

5x = 60

x = 12

the value of x is solved to be 12

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Answer:

C, 3 inches

Step-by-step explanation:

The sum of first 20 multiples of 7 will be 1470.

Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.

Given are first 20 multiples of 7.

The sequence of first 20 multiples of 7 will be -

7, 14, 21, 28, ..... , 140

Sum = (20/2)[2 x 7 + (19) x 7]

Sum = 10[14 + 133]

Sum = 10 x 147

Sum = 1470

Therefore, the sum of first 20 multiples of 7 will be 1470.

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[Question translation in english -

find the sum of the first 20 multiples of 7 with procedure.]

The products are not equal

Using the distributive property and multiply each term in the first expression by each term in the second expression:

(5x-3) * (4x^2-x+3) = 5x * (4x^2-x+3) - 3 * (4x^2-x+3)

= 20x^3 - 5x^2 + 15x - 12x^2 + 3x - 9

= 20x^3 - 17x^2 + 18x - 9

Therefore, the product of (5x-3) and (4x^2-x+3) is 20x^3 - 17x^2 + 18x - 9 in standard form.

Performing the same multiplication for the second product:

(3x-5) * (4x^2-x+3) = 3x * (4x^2-x+3) - 5 * (4x^2-x+3)

= 12x^3 - 3x^2 + 9x - 20x^2 + 5x - 15

= 12x^3 - 23x^2 + 14x - 15

The products are not equal because their coefficients for the x^2 term and the constant term differ.

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The product of (5x-3) and (4x²-x 3) is  20x³ - 17x² + 18x - 9, respectively. The products are not equal.

To find the product of (5x-3) and (4x²-x+3), we can use the distributive property:

(5x-3) * (4x²-x+3) = 20x³ - 5x² + 15x - 12x² + 3x - 9

Combining like terms, we get:

20x³ - 17x² + 18x - 9

So the product in standard form is 20x³ - 17x² + 18x - 9.

To determine if the product of (5x-3) and (4x²-x+3) is equal to the product of (3x-5) and (4x²-x+3), we can multiply them both out and see if the results are the same:

(5x-3) * (4x²-x+3) = 20x³ - 17x² + 18x - 9

(3x-5) * (4x²-x+3) = 12x³ - 3x² + 9x - 20x² + 5x - 15

Combining like terms, we get:

20x³ - 17x² + 18x - 9 ≠ 12x³ - 23x² + 14x - 15

So the products are not equal.

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The budgets of Hong Kong, the United States of America, and Korea differ in contents, formats, advantages, and disadvantages. While each budget has its strengths and weaknesses, they all aim to provide a clear and transparent financial plan for their respective countries.

A budget is a financial plan that estimates expected income and expenditure for a specific period. It may include income, expenses, debts, and savings. Budgets may vary from country to country and can be analyzed by comparing their contents, formats, advantages, and disadvantages. Here are the budgets of Hong Kong, the United States of America, and Korea:

United States Budget:

Korean Budget:

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The smallest possible inside length of the cubical steel tank that can hold 275 liters of water is approximately 0.640 meters.

The side length of the cube is found by converting the volume of water from liters to cubic meters, as the unit of measurement for the side length is meters.

Given that the volume of water is 275 liters, we convert it to cubic meters by dividing it by 1000 (1 cubic meter = 1000 liters):

275 liters / 1000 = 0.275 cubic meters

Since a cube has equal side lengths, we find the side length by taking the cube root of the volume. In this case, we find the cube root of 0.275 cubic meters:

∛(0.275) ≈ 0.640

Rounded to the nearest 0.001 meters, the smallest possible inside length of the tank is approximately 0.640 meters.

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Answer:

\(\frac{3}{16}\) f - \(\frac{3}{2}\) g

Step-by-step explanation:

\(\frac{3}{8}\) ( \(\frac{1}{2}\) f - 4g )

multiplying each of the terms inside the parenthesis by \(\frac{3}{8}\)

\(\frac{3}{8}\) × \(\frac{1}{2}\) f

= \(\frac{3(1)}{8(2)}\) f

= \(\frac{3}{16}\) f

and

\(\frac{3}{8}\) × - 4g ( cancel 4 and 8 by 4 )

= \(\frac{3}{2}\) × - g

= - \(\frac{3}{2}\) g

combining the 2 products, gives

\(\frac{3}{16}\) f - \(\frac{3}{2}\) g

Answer:

\(\textsf{Orange partial product}=\dfrac{3}{16}\;f\)

\(\textsf{Pink partial product}=-\dfrac{3}{2} \;g\)

\(\textsf{Product}=\dfrac{3}{16}\;f-\dfrac{3}{2} \;g\)

Step-by-step explanation:

Given expression:

\(\dfrac{3}{8}\left(\dfrac{1}{2}f-4g\right)\)

Calculate the partial products then add these together to find the product of the given expression.

Orange partial product

\(\implies \dfrac{3}{8} \times \dfrac{1}{2}f\)

\(\implies \dfrac{3 \times 1}{8\times 2}\;f\)

\(\implies \dfrac{3}{16}\;f\)

Pink partial product

\(\implies \dfrac{3}{8} \times (-4g)\)

\(\implies \dfrac{3 \times -4}{8} \;g\)

\(\implies \dfrac{-12}{8} \;g\)

\(\implies -\dfrac{\diagup\!\!\!\!4 \times 3}{\diagup\!\!\!\!4 \times 2} \;g\)

\(\implies -\dfrac{3}{2} \;g\)

Product:

\(\implies \dfrac{3}{8}\left(\dfrac{1}{2}f-4g\right)=\dfrac{3}{16}\;f-\dfrac{3}{2} \;g\)

Answer:

Y-intercept = 0 ( aka. (0,0) )

Step-by-step explanation:

The y-intercept of a function is found when x=0:

f(x) = -7x - 2x³

f(0) = -7(0) - 2(0)³

f(0) = 0 - 0

f(0) = 0

Therefore, the y-intercept of the polynomial is 0. You can also say that it is 0 because a cubic function is symmetrical about the origin.

Answer:

Step-by-step explanation:

Kamille is wrong, because:

or

She needs about 8 inches ribbon not 60 inches

The area of each triangle is: 7554.04 m² and 311.26 km².

Here, we have,

from the given figure,

we get,

triangle 1:

a = 104m

b = 226 m

angle Ф= 40 degrees

so, we have,

area = a×b×sinФ/2

        = 104×226×sin40/2

        = 7554.04 m²

triangle 2:

a = 34 km

b = 39 km

angle Ф= 28 degrees

so, we have,

area = a×b×sinФ/2

        = 34×39×sin28/2

        = 311.26 km²

Hence, the area of each triangle is: 7554.04 m² and 311.26 km².

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Answer: 9

Step-by-step explanation:

Answer:To find the average rate of change for the interval from x = 5 to x = 6, we need to calculate the change in the function values over that interval and divide it by the change in x.

Given the points (5, 0) and (6, 4), we can calculate the change in the function values:

Change in y = 4 - 0 = 4

Change in x = 6 - 5 = 1

Average rate of change = Change in y / Change in x = 4 / 1 = 4

Therefore, the correct answer is 4. None of the given options (A, B, C, or D) match the correct answer.

Step-by-step explanation:

Answer: x=-3

Step-by-step explanation:

Answer:

I believe x=3

Step-by-step explanation:

0.7x- 1.4 = -3.5

+1.4. +1.4

0.7x = 2.1

divide both sides by 0.7 x= 3

The choose (C) 60

The measure of the angles of a triangle is 180, and this triangle is equilateral, so 180/3=60, each angle is 60°

Answer:  A

Step-by-step explanation:

When multiplying: Numbers multiply with numbers and for the x's, add the exponents

If there is no exponent, you can assume an imaginary 1 is the exponent

2x⁴ (3x³ − x² + 4x)

= 6x⁷ -2x⁶ + 8x⁵

Answer:

A. \(6x^{7} - 2x^{6} + 8x^{5}\)

Label the parts of the expression:

Outside the parentheses = \(2x^{4}\)

Inside parentheses = \(3x^{3} -x^{2} + 4x\)

You must distribute what is outside the parentheses with all the values inside the parentheses. Distribution means that you multiply what is outside the parentheses with each value inside the parentheses

\(2x^{4}\) × \(3x^{3}\)

\(2x^{4}\) × \(-x^{2}\)

\(2x^{4}\) × \(4x\)

First, multiply the whole numbers of each value before the variables

2 x 3 = 6

2 x -1 = -2

2 x 4 = 8

Now you have:

6\(x^{4}x^{3}\)

-2\(x^{4}x^{2}\)

8\(x^{4} x\)

When you multiply exponents together, you multiply the bases as normal and add the exponents together

\(6x^{4+3}\) = \(6x^{7}\)

\(-2x^{4+2}\) = \(-2x^{6}\)

\(8x^{4+1}\) = \(8x^{5}\)

Put the numbers given above into an expression:

\(6x^{7} -2x^{6} +8x^{5}\)

distribution

variable

like exponents