13. FURNITURE Sai is rearranging his furniture. He wants his couch to sit along the 20-foot wall,
labeled AC on the diagram. He wants the left side of his couch to sit at a point B so that the
ratio of AB to BC is 1:2. What distance from the left side of the wall should Randall place the left side of his couch?

[tex]2~~,~~\stackrel{2\cdot \frac{5}{2}}{5}~~\stackrel{5\cdot \frac{5}{2}}{\cfrac{25}{2}}~~,~~...\hspace{5em}\stackrel{\textit{common ratio}}{r=\cfrac{5}{2}} \\\\[-0.35em] ~\dotfill\\\\ n^{th}\textit{ term of a geometric sequence} \\\\ a_n=a_1\cdot r^{n-1}\qquad \begin{cases} a_n=n^{th}\ term\\ n=\textit{term position}\\ a_1=\textit{first term}\\ r=\textit{common ratio}\\[-0.5em] \hrulefill\\ a_1=2\\ n=9\\ r=\frac{5}{2} \end{cases}[/tex]

[tex]a_9=2\left( \frac{5}{2} \right)^{9-1}\implies a_9=2\left( \frac{5}{2} \right)^8\implies a_9=2\left( \cfrac{390625}{256} \right) \\\\\\ a_9=\cfrac{390625}{128}\implies {\Large \begin{array}{llll} a_9=3051\frac{97}{128} \end{array}}[/tex]

Answer:

√18.75 ≈ 4.33

Step-by-step explanation:

The median joins a vertex and the opposite side's midpoint.

side = 5

half side = 2.5

a² + b² = c²

2.5² + b² = 5²

b² = 18.75

b = √18.75

b = 4.33

The length of every median in an equilateral triangle whose side length is 5 is 4.330127018922193.

An equilateral triangle is one in which the angles and all three sides are equal. An equilateral triangle is also known as an equiangular triangle since each of its angles has a value of 60 degrees. Due to its equal sides and angles, the equilateral triangle is regarded as a regular polygon or triangle.

In an equilateral triangle, all three medians have the same length.

The length of a median in an equilateral triangle can be found using the formula:

median length = (side length * sqrt(3))/2.

Therefore, in an equilateral triangle with a side length of 5, the length of each median would be,

[tex]=5*\sqrt{3}/2 \\=2.5*\sqrt{3}\\= 4.330127018922193[/tex].

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The ratio of female birds is 3/7.

One way to express something as a percentage of another is to use a ratio, which is a mathematical concept.

By typically dividing two figures, ratios contrast them. If you were comparing one data point (A) to another data point, your formula would be A/B. (B). You are multiplying information A by information B, as indicated by this. For instance, if A is 5 and B is 10, your ratio will be 5/10.

The pet store has 12 male birds for every 9 female birds.

total birds = 12 + 9 = 21 birds.

So, the ratio of female birds =  female birds / total birds

                                              = 9/21

                                              = 3/7

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The angular speed of the wheels is approximately 1480 / π radians per minute.

We can start by converting the velocity of the truck from miles per hour to feet per minute, since the diameter of the wheels is given in feet.

50 miles/hour = 50 x 5280 feet/hour = 264,000 feet/hour

264,000 feet/hour / 60 minutes/hour = 4,400 feet/minute

Next, we can find the circumference of the wheel and then divide it by the velocity of the truck to find the angular velocity in radians per minute:

Circumference = 2 * π * r = 2 * π * (diameter/2) = 2 * π * (3 feet / 2) = 3π feet

Angular velocity (ω) = velocity / circumference = 4,400 feet/minute / (3π feet) = 1480 / π radians/minute

So the angular speed of the wheels is approximately 1480 / π radians per minute.

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let's firstly convert the mixed fraction to an improper fraction.

[tex]\stackrel{mixed}{1\frac{1}{3}}\implies \cfrac{1\cdot 3+1}{3}\implies \stackrel{improper}{\cfrac{4}{3}} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{trail mix}}{\cfrac{4}{3}}\div \stackrel{bags}{4}\implies \cfrac{4}{3}\div \cfrac{4}{1}\implies \cfrac{4}{3}\cdot \cfrac{1}{4}\implies \cfrac{4}{4}\cdot \cfrac{1}{3}\implies \stackrel{per~bag}{\cfrac{1}{3}}[/tex]

Answer:

Step-by-step explanation:

the new one will tell you be

Joint and 2/3 survivor means that if the insured passes away, two of the beneficiaries will receive two-thirds of the insurance benefits, and the remaining third will be divided among all three beneficiaries.

Joint and 2/3 survivor is a settlement option for life insurance policies which means that when the insured passes away, two of the beneficiaries will receive two-thirds of the death benefits, while the remaining third will be divided equally among all three beneficiaries. This is beneficial because it ensures that two of the beneficiaries will receive the majority of the death benefits, while the remaining third will be split equally among all three. This provides a more secure financial future for the two beneficiaries receiving the most money as well as allowing the remaining third to be split equally, providing more financial security for all beneficiaries.

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Over a period of 5 years, the amount that you would have to pay monthly is given as  $3,201.37

To calculate the monthly mortgage payment for a house that costs $621,900 with an interest rate of 5.4% over 5 years, you can use the following formula:

P = (r(1 + r)^n) / (((1 + r)^n) - 1) * L

Where:

P = monthly payment

r = monthly interest rate (5.4%/12 = 0.0045)

n = total number of payments (5 years x 12 = 60)

L = the loan amount ($621,900)

Plugging in the values, we get:

P = (0.0045(1 + 0.0045)^60) / (((1 + 0.0045)^60) - 1) * 621,900

P = $3,201.37

So you have to pay  $3,201.37 monthly over 5 years.

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The size of each angle to draw the pie chart is given as follows:

The size of each angle in this problem is found applying the proportions.

First we obtain the relative frequency of each item, dividing the absolute frequency by 40.

Then we obtain the angle size, multiplying the relative frequency by 360º, which is the angle measure of the entire circumference of the pie chart.

Then the angle measures are obtained as follows:

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Answer:

Step-by-step explanation:

won 140

lost 140-50=90

Ratio wins to losses: 14:9

Answer: (x + 3)^2 + (y + 8)^2 = 14pi^2

(x-h)^2 + (y-k)^2 = r^2

The three inequalities that define the shaded region are given as follows:

The inequality that defines the values below the vertical line y = 2 is given as follows:

y < 2.

(open interval as the line is dashed).

The increasing line has an intercept of 0 and slope of 2, with values to the right being shaded and the line being dashed, hence the inequality is given as follows:

y > 2x.

The decreasing line has an intercept of -2 and a slope of -1, with values to the left being shaded, with a closed interval, as the line is shaded, hence the inequality is given as follows:

y ≤ -x - 2.

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The correct equation for Jeff after every cost will be   y = 750 -100x

Cost of the television = $750

Loan amount paid per month = $100

Amount put in savings = $200

A mathematical equation is a formula that uses the equals sign to represent the equality of two expressions.

Since the amount of $200 is being saved, this means that it is not going away or is being spent. Now, as per the question, the initial remaining balance with Jeff is 750. The balance decreases by the loan amount of 100 per month.

This means that the amount is reduced by = 100x.

Therefore, the equation describing the scenario is -

y = 750 -100x

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The sum of the relative frequencies for all classes will always equal option (C) 1 i.e. when all relative frequencies on a set of values are added it is always equal to one.

A relative frequency tells us the number of times a particular value for a data item has been perceived to occur in relation as compared to the total number of values for that set of data items.

It is calculated by dividing the absolute frequency by the total number of values for the set of data items. It is used to express proportions, ratios, percentages, etc.

Absolute frequency is a mathematical term used in statistics to calculate the number of times a value occurs in a trial set of values. It is used to calculate relative frequency, and display a graph to give a visual representation.

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Answer:

In an equilateral pentagon, all angles have equal degree measures, so to find the degree measure of one angle, we need to find the sum of the degree measures of the interior angles and then divide by the number of angles.

Step 1: Find the sum of the degree measures of the interior angles of the pentagon:

180 * (5 - 2) = 540 degrees

Step 2: Divide the sum by the number of angles:

540 degrees / 5 angles = 108 degrees

The degree measure of angle E is 108 degrees.

The degree measure of angle E is 108°.

We can use interior angels theorm.

The sum of the interior angles of a pentagon can be calculated using the formula:

Interior angle sum = (n - 2) × 180

where n is the number of sides of the polygon.

In this case, n = 5, so the sum of the interior angles of the pentagon is (5 - 2) × 180 = 540°.

Since angle A and angle B are both equal to 108°, we can say that:

angle A + angle B = 2 × 108 = 216°.

So, the sum of the remaining three interior angles (angles C, D, and E) is:

540 - 216 = 324°

Since each of these three angles is equal, the measure of each angle must be 324° divided by 3, or:

324 ÷ 3 = 108°

So, the degree measure of angle E is also 108°.

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Step-by-step explanation:

( x1 + x2 /2 , y1 + y2 / 2 )

= ( -7 + 7 / 2 , 0 + 7 / 2 )

= ( 0, 3.5 )

We must first plot the given linear equation before we can draw the graph for it. Using the equation x = (-b (b2 - 4ac))/2a, the roots are determined. D = b2 – 4ac serves as the discriminant.

link the points that lie on it to form a straight line.

Y = 2x - 1 is the first equation.

Calculate the corresponding values of y by substituting various values of x into the equation.

X      Y = 2x-1   point (x, y)

0           -1         (0, -1)

2            3         (2, 3)

4            7          (4, 7)

-1           -3         (-1, -3)

-3           -7         (-3, -7)

On the graph paper, place these points and draw a straight line connecting them.

Using the equation x = (-b (b2 - 4ac))/2a, the roots are determined. D = b2 – 4ac serves as the discriminant.

In order to determine the critical point, we will set the first derivative of the function to zero and solve for x. We may determine whether this point will be a maximum or minimum by taking the second derivative, or f"(x). It will be a minimal value if the second derivative is positive.

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According to the following graph, the y intercept is 0, the asymptote is ∞ and the range is (-∞, ∞)

In math the term called graph is defined as  a pictorial representation or a diagram that represents data or values in an organized manner and the points on the graph often represent the relationship between two or more things.

Here we know that the function is f(x) = 8x.

When we plot the function then we get the graph like the following.

While we looking into plotted graph, then we have identified that the y-intercept is 0.

And the horizontal asymptote is the limit as x goes to ∞.

And the range is the set of values above the horizontal asymptote (-∞, ∞).

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Answer:

D is the one trust me man I do this all the time and good luck on your exam

The solution to the inequality |2x + 3| < 7 is x < 2 or x > -5.

What is inequality?

An inequality is a statement that compares two expressions and asserts that one is greater or less than the other. It can be represented using mathematical symbols such as <, >, ≤, ≥, ≠.

|2x + 3| < 7 is a type of absolute value inequality. The absolute value of a number is its distance from zero on the number line, and is always positive. So, |2x + 3| is the absolute value of 2x + 3, which is always greater than or equal to zero.

To solve this inequality, we need to consider two cases:

If 2x + 3 is greater than or equal to zero, we can drop the absolute value bars and solve the inequality as is:

2x + 3 < 7

2x < 4

x < 2

If 2x + 3 is less than zero, we need to reverse the inequality sign:

-2x - 3 < 7

-2x < 10

x > -5

Hence, the solution to the inequality |2x + 3| < 7 is x < 2 or x > -5.

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To find the sum of interior angles of a polygon, multiply the number of triangles formed inside the polygon to 180 degrees.

How to find the sum of interior angles ?

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Answer: $4,914

Step-by-step explanation:

To calculate the final balance in Brandon's account, we need to use the formula for compound interest: A = P(1 + r/n)^(nt)

where A is the final balance, P is the initial investment, r is the interest rate, n is the number of times the interest is compounded per year, and t is the time in years.

In this case, we have:

P = $11,000

r = 1% = 0.01

n = 4 (because the interest is compounded quarterly)

t = 20

so, A = $11,000(1 + 0.01/4)^(4*20) = $11,000(1.0025)^80 = $22,817.20

To calculate the final balance in Robert's account, we need to use the same formula, but with different values for r, n, and t.

In this case, we have:

P = $11,000

r = 13/100 = 0.13

n = 12 (because the interest is compounded monthly)

t = 20

so, A = $11,000(1 + 0.13/12)^(12*20) = $11,000(1.01083333)^240 = $27,731.34

To find the difference in the final balances, we subtract the final balance in Brandon's account from the final balance in Robert's account:

$27,731.34 - $22,817.20 = $4,914.14

To the nearest dollar, the difference is $4,914.

Answer:391

Step-by-step explanation:

The values of five remaining trigonometric functions of θ.

sinθ = 1/√5, cosθ = 2/√5, tanθ = 2, secθ = √5/2, cosecθ = √5

We have to determine values of five remaining trigonometric functions of θ. ​Suppose θ is an angle in the standard position whose terminal side is in quadrant IV and cot θ = -9/18.

The ratio of trigonometry is:

sinθ = Perpendicular/Hypotenuse

cosθ = Adjacent Side/Hypotenuse

tanθ = Perpendicular/Adjacent Side

cotθ = Adjacent Side/Perpendicular

sec = Hypotenuse/Adjacent Side

cosec = Hypotenuse/Perpendicular

We know that;

Adjacent Side = 9, Perpendicular = 18

Now finding the value of Hypotenuse using the Pythagorean Theorem

(Hypotenuse)^2 = (Adjacent Side)^2 + (Perpendicular)^2

(Hypotenuse)^2 = (9)^2 + (18)^2

(Hypotenuse)^2 = 81 + 324

(Hypotenuse)^2 = 405

Taking square root on both side, we get

Hypotenuse = 9√5

Now finding the other trigonometry ratio:

sinθ = Perpendicular/Hypotenuse

sinθ = 9/9√5

sinθ = 1/√5

cosθ = Adjacent Side/Hypotenuse

cosθ = 18/9√5

cosθ = 2/√5

tanθ = Perpendicular/Adjacent Side

tanθ = 18/9

tanθ = 2

secθ = Hypotenuse/Adjacent Side

secθ = 9√5/18

secθ = √5/2

cosecθ = Hypotenuse/Perpendicular

cosecθ = 9√5/9

cosecθ = √5

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Answer:A.½ B.-½ C.2⁷/20

Step-by-step explanation:A. 5¾+(-¼) =23/4 - ¼ =22/

=5½

B. -⅔+⅙ = (-4+1)/6=-½

 C. -8/5-¾= (-32-15)/20 =47/20 =2⁷/

The correct expression that will form with one multiplication operation is 8 × (5.95 + 84 + 3.60 + 2.25).

Firstly rewriting the correct expression according to the amount spent by each person on different entities. The expression will be -

Total amount spent by 8 people = number of people × (amount spent on dinner + laser tag + bowling shoes + video games)

Now keeping the values in formula to find the total amount spent by eight people in desired format.

Total amount spent by eight people = 8 × (5.95 + 84 + 3.60 + 2.25)

Performing addition to simplify the expression is -

Total amount spent by eight people = 8 × 95.8

Thus, the correct simplified expression will be 8×95.8.

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In a multicellular organism such as a dog or cat have tens of trillions of cells and 60 to 80 million cells respectively. So we can say that dog have greatest number of cells

Organisms with many cell types and specialized cells that are gathered together to perform specific duties are known as multicellular organisms. An example of a multicellular organism with organization is a tree or a cat, which have tissues, organs, and organ systems.

Although we are unsure of the actual number of cells in a typical dog, we can estimate it roughly. We may apply this number to dogs, which have in the tens of trillions of cells, as some sources give a ballpark estimate of about fifty trillion cells within a human body. 60 to 80 million cells make up a cat.

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Answer: 50

Step-by-step explanation:

i don't know how i got this but yeah its 50

Answer:

In Explanation

Step-by-step explanation:

To solve for x in the equation log₂ 3+ log₂ (x-4)= 4, we can first use the logarithm identity: log₂ a + log₂ b = log₂ (ab)

So, we can rewrite the equation as:

log₂ (3(x-4)) = 4

Then we can use the definition of logarithm to find the value of x:

2^4 = (3(x-4)) = 3x-12

16 = 3x - 12

28 = 3x

x = 9 + 4 = 9

Therefore, x = 9 is the solution of the equation log₂ 3+ log₂ (x-4)= 4

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