The table shown below shows some values for functions f(x) and g(x). What is/are the solution(s) to f(x)=g(x)? Explain your answer(s). (4 points)

x –3 –2 –1 0 1 2

f(x) 0.4 4.5 7 11.3 15 16.2

g(x) 4 8 10 11.3 15 17

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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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]

The missing value in the space provided is given as follows:

75.

A proportional relationship is modeled as follows:

y = kx.

In which k is the constant of proportionality.

The constant for the relationship in this problem is given as follows:

k = 125/5 = 100/4 = 25/1 = 25.

Hence the relationship is given as follows:

y = 25x.

The missing value is the output when x = 3, hence:

y = 25(3)

y = 75.

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Answer: 50

Step-by-step explanation:

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

Step-by-step explanation:

please attached for details

Answer:

1/

Step-by-step explanation:

1/3+1/2=5/6

1-5/6=1/6

1/

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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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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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 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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 The binomial distribution is a discrete probability distribution used in probability theory and statistics to explain the number of successes in a set number of trials, where each trial can only result in success or failure. The probability mass function (PMF) shown below defines the binomial distribution as follows:

P(a) = ⁿСₐ * p^a* (1-p)^(n-a)

Where:

a: the number of successes in n trials

n: the total number of trials

p: the probability of success in one trial

ⁿСₐ : n! / (a! * (n-a)!)

      the binomial coefficient, which shows how many different ways there are to select k successes from n trials.

    A variety of phenomena, including coin tossing, die rolling, and other tests with a set number of trials and only two possible outcomes, can be usefully modelled using the binomial distribution.

In a blind tasting test, if participants are unable to distinguish between bottled and tap water, we can assume that their guesses are random. The probability of accurately predicting the type of water in this situation is 50%.

The likelihood that 8 out of 9 people will properly predict their water type is

(1/2)^8 * (1/2)^1 = (1/2)^9 = 1/512

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The angle of elevation to the balloon of the runner the greatest distance from the balloon is 83.13 degrees.

The concept used in this problem is Trigonometry. Specifically, the problem uses the tangent function, which is one of the three main trigonometric ratios (sine, cosine, and tangent) used to relate the angles and sides of a right triangle.

To solve this problem, we can use the tangent function of trigonometry, which relates the opposite side (the distance from the runner to the balloon) to the adjacent side (the distance from the runner to the point on the highway) and the hypotenuse (the distance from the point on the highway to the balloon).

Let's call the angle of elevation of the runner closest to the balloon as angle A and the angle of elevation of the runner farthest from the balloon as angle B.

tan(A) = opposite / adjacent = (1500 - 421.2) / 421.2 = 878.8 / 421.2

tan(B) = opposite / adjacent = (1500 + 421.2) / 421.2 = 1921.2 / 421.2

We can use the inverse tangent function (arctan) to find the angle of elevation of the runner the greatest distance from the balloon.

B = arctan(1921.2 / 421.2)

The result is in radians, to convert the angle from radians to degrees, we can use the conversion factor of 180/pi.

B = arctan(1921.2 / 421.2) = arctan(4.5536) = 83.13 degrees (approx)

so, the angle of elevation to the balloon of the runner the greatest distance from the balloon is 83.13 degrees.

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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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The number of times more intense that the earthquake in Alaska was than the one in Japan was 1, 000 times more intense.

The Richter magnitude is determined by measuring the height of the greatest wave that has ever been seen at a given distance from the seismic source.

Each order of magnitude is 10 times more intense than the previous one since the Richter scale is a base-10 logarithmic scale. To put it another way, a two is ten times as intense as a one, and a three is one hundred times stronger.

This means that the number of times more intense that the earthquake in Alaska was than the one in Japan was:

= 10 x 10 x 10

= 1, 000 times

Note : Alaska and Japan earthquake difference:

= 9  - 6

= 3

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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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Answer:

Step-by-step explanation:

won 140

lost 140-50=90

Ratio wins to losses: 14:9

Let's call the number of days of labor x, and the number of square feet y.

From the information provided, we can set up the following equation:

What does a math equation mean?

A mathematical statement that shows the equality of two mathematical expressions is the definition of an equation in algebra. As an illustration, the two equations 3x + 5 and 14 are joined by the equal sign to get the equation 3x + 5 = 14.

3.89y + 122.42x = 2882.48

We also know that y = x + 189

We can substitute the second equation into the first equation:

3.89(x + 189) + 122.42x = 2882.48

Expanding and simplifying:

3.89x + 730.91 + 122.42x = 2882.48

x = (2882.48 - 730.91) / (3.89 + 122.42) = 22.98 days

So the renovation took 22.98 days.

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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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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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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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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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Because a 30-year mortgage has a longer term, your monthly payments will be lower and your interest rate on the loan will be higher.

A 30-year fixed-rate mortgage is commonly used to refer to conventional loans. Conventional loans are not backed by the government; however, a 30-year fixed FHA, USDA, or VA loan that is insured by the government is available. Rocket Mortgage® does not currently provide USDA loans.

A 30-year fixed-rate mortgage is a house loan with a 30-year repayment period and an interest rate that remains constant during the loan’s duration. When you take for a 30-year fixed-rate home loan, the amount you make each month remains the same until the loan is paid off.

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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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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:

√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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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/

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: