f(x) = x − 2, g(x) = 4x + 5
(a)
(f ∘ g)(x) =

(b)
(g ∘ f)(x) =

(c)
(f ∘ g)(5) =

(d)
(g ∘ f)(5) =

For rectangle ABCD, the new coordinate of A' is (5,1) and the correct rule is (x, y) → (-x, y).

What exactly is a rectangle?

A rectangle is a four-sided flat shape (quadrilateral) where all four angles are right angles (90 degrees) and opposite sides are parallel and congruent (equal in length). In other words, a rectangle is a parallelogram with all right angles.

Now,

The rule that shows the input and output of reflecting a point over the y-axis is (x, y) → (-x, y). This means that the x-coordinate of the point is negated, while the y-coordinate stays the same.

To find the new coordinate of A', we need to reflect the original point A(-5,1) over the y-axis. Using the rule above, we get:

A' = (-(-5), 1) = (5, 1)

Therefore, the new coordinate of A' is (5,1) and the correct rule is (x, y) → (-x, y).

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Answer:

x= 14

Step-by-step explanation:

103 +47=150

180- 150= 30

30=3x-12

30 + 12 = 42

42=3x

42/3= 14

X = 14

Answer:

The probability of getting a 2, 4, or 6 when a dice is rolled is 1/2, or 50%. This is because there are six possible outcomes when a dice is rolled, and three of them are favorable outcomes (2, 4, or 6). Therefore, the probability of getting a 2, 4, or 6 is 3/6, which simplifies to 1/2 or 50%.

Step-by-step explanation:

See image.....as these are definitions, it is self-explanatory:

Margin of error is the maximum difference between the point estimate of an unknown population parameter and the true value of that parameter.

Point estimate: A single number estimate of an unknown population parameter. This is the value that is calculated based on the data collected from a sample of the population.

Confidence level: The proportion of times a confidence interval will capture the true value of an unknown parameter assuming the estimation process is repeated many times.

Confidence interval: The plausible range of values for an unknown population parameter based on an observed sample and a confidence level. This is calculated based on the point estimate and the margin of error.

Critical value: A value that separates statistics that are likely to occur from those that are unlikely to occur. This value is determined by the level of significance and the degrees of freedom for the statistical test.

Margin of error: The maximum difference between the point estimate of an unknown population parameter and the true value of that parameter. This is calculated based on the level of confidence and the variability in the sample data.

To summarize:

Point estimate is a single number estimate of an unknown population parameter.

Confidence level is the proportion of times a confidence interval will capture the true value of an unknown parameter assuming the estimation process is repeated many times.

Confidence interval is the plausible range of values for an unknown population parameter based on an observed sample and a confidence level.

Critical value is a value that separates statistics that are likely to occur from those that are unlikely to occur.

Margin of error is the maximum difference between the point estimate of an unknown population parameter and the true value of that parameter.

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The area of the figure is approximately 163.8 square units, rounded to the nearest tenths place.

To find the area of this figure, we need to find the area of the parallelogram and the area of the semicircle, and then add them together.

The area of the parallelogram is given by the formula:

A = base x height

In this case, the base is 12 and the height is 9, so:

A_parallelogram = 12 x 9 = 108

The area of a semicircle is given by the formula:

[tex]A = (πr^2)/2[/tex]

where r is the radius of the semicircle.

The diameter of the semicircle is equal to the base of the parallelogram, which is 12. So, the radius of the semicircle is half of the diameter, or 6.

Substituting the values, we get:

A_semicircle = [tex](π x 6^2)/2 = 18π[/tex]

Adding the areas of the parallelogram and the semicircle, we get:

A = A_parallelogram + A_semicircle = 108 + 18π

Using a calculator to approximate π to the nearest tenths place, we get:

A ≈ 108 + 18 x 3.1 = 163.8

Therefore, the area of the figure is approximately 163.8 square units, rounded to the nearest tenths place.

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Answer:

the volume of the cylinder is approximately 100.48 yards.

[tex] \: \: [/tex]

Volume of a cylinder is:

V = πr²h

where r is the radius of the base, h is the height, and π is approximately 3.14.

Substituting the given values, we get:

V = π(2 yards)²(8 yards)

V = π(4 yards²)(8 yards)

V = 32π yards³

Using the approximation π ≈ 3.14, we get:

V ≈ 100.53 yards³

Therefore, the volume of the cylinder is approximately 100.53 cubic yards rounded to the nearest hundredth.

Answer:

Step-by-step explanation:

This looks like a quadratic function is it?

The transformations are:

The general sine function is:

y = sin(x)

The first thing we can see, is that the amplitude is not 1 like in the parent sine function, in this case the amplitude goes from the top value to the midline, so it is:

A = 5 - 3 = 2

Then we can write:

y = 2*sin(x)

So this is a vertical dilation of scale factor 2

We also can see the midline is at y = 3 instead of at y  = 0, so we have a vertical shift of 3 units up to get.

y = 2sin(x) + 3

Finally, we can see that the function starts decreasing after x = 0, so we have a shift of 1  (the horizontal axis is in units of pi)

y = 2*sin(x + 1) + 3

That is the graphed function.

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Answer:

16.7 degrees

Step-by-step explanation:

We can use the tangent ratio of a right triangle to solve this problem.

The tangent of an angle is the ratio of the opposite side to the adjacent side. In this case, the opposite side is the height of the ramp (3m) and the adjacent side is the length of the ramp (10m).

So we have:

tan(theta) = opposite / adjacent

tan(theta) = 3 / 10

To find the angle, we need to take the inverse tangent (or arctangent) of both sides:

theta = arctan(3 / 10)

Using a calculator, we get:

theta ≈ 16.7 degrees

Therefore, the angle formed by the ramp and ground is approximately 16.7 degrees.

Answer:

4.6 inches

Step-by-step explanation:

i believe. IM SORRY IF IM WRONG!!

If this portion leads to two segments that come to a point, and from that point, there is a height of 3 meters labeled.  The total area is 45 square meters.

Area is the measure of a region's size on a surface. The area of a plane region or plane area refers to the area of a shape or planar lamina, while surface area refers to the area of an open surface or the boundary of a three-dimensional object.

Here, we have,

Since the rectangle has a length of 4 meters and a width of 9 meters we need to find the area of rectangle

Area of rectangle  = length × width

Area of rectangle = 4 m × 9 m

Area of rectangle = 36 m^2

Since the  triangle has a base of 6 meters (9 meters - 3 meters o) and a height of 3 meters we need to find the Area of triangle

Area of triangle  = (1/2) × base × height

Area of triangle  = (1/2) × 6 m × 3 m

Area of triangle  = 9 m^2

Now let find the total area of the composite figure

Total area = Area  of rectangle + Area of triangle

Total area = 36 m^2 + 9 m^2

Total area = 45 m^2

Therefore the total area of the figure is 45 square meters.

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the length of AC is 5. we can get the answer with the help of  Pythagorean theorem in triangle ABC.

what is Pythagorean theorem ?

The Pythagorean theorem is a fundamental concept in geometry that relates to the relationship between the sides of a right triangle. It states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides (the legs).

In the given question,

In triangle ABC, we have:

angle ABC = 90 degrees (given)

AB = 4 (given)

AD = 3 (given)

Let's call the length of AC "x". We want to find the value of x.

From the given information, we know that BD is the altitude of triangle ABC from vertex B to the side AC. Therefore, the length of BD is equal to the length of AD, which is 3.

Using the Pythagorean theorem in triangle ABD, we can find the length of the hypotenuse AB:

AB² = AD² + BD²

AB² = 3² + 4²

AB² = 9 + 16

AB² = 25

AB = 5

Now, we can use the Pythagorean theorem in triangle ABC to find the length of AC:

AC² = AB² + BC²

AC² = 5² + BC²

But we don't know the length of BC. However, we can use the fact that triangle ABD and triangle ABC are similar. This is because angle ABD is a right angle (from the definition of altitude BD), and angle ABC is a right angle (given), so angle ABD and angle ABC are both right angles. Therefore, the two triangles share angle A and are similar by the AA (angle-angle) similarity criterion.

Since triangles ABD and ABC are similar, we have:

AB/AD = AC/BD

Substituting the known values, we get:

5/3 = x/3

Solving for x, we get:

x = 5

Therefore, the length of AC is 5.

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By answering the presented question, we may conclude that Therefore, the future value of the ordinary annuity is $16,178.55 when interest is compounded annually.

In mathematics, interest is the amount of money gained or payable on an original investment or loan. You can use either simple or compound interest. Simple interest is calculated as a percentage of the initial amount, whereas compound interest is calculated on the principal amount plus any previously earned interest. If you invest $100 at a 5% annual simple interest rate, you will get $5 in interest per year for three years, for a total of $15.

the future value of an ordinary annuit

[tex]FV = R x [(1 + i)^n - 1]/i\\FV = $1,000 x [(1 + 0.04)^14 - 1]/0.04\\FV = $1,000 x (1.647142 - 1)/0.04\\FV = $1,000 x 16.17855\\FV = $16,178.55\\[/tex]

Therefore, the future value of the ordinary annuity is $16,178.55 when interest is compounded annually.

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The value of arc angle FH is 102⁰.

The value of arc angle FH is calculated by first; determining the value of the bigger arc HGF by applying the intersecting chords theorem.

The intercepting chord theorem, also known as the tangent chord theorem, states that when a tangent line intersects a chord of a circle at a point on the chord, then the measure of the angle formed by the tangent line and the chord is equal to half the measure of the intercepted arc (the arc that lies between the endpoints of the chord).

arc HGF = 2 x 129⁰

arc HGF = 258⁰

The value of arc FH is calculated as;

arc FH = 360⁰ - 258⁰ ( sum of angles in a circle)

arc FH = 102⁰

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1.  The triangles formed from the bisection of the perpendicular lines are equal, then, ΔACE ≅ΔBDE

2. The diagonals bisects the kite perpendicularly to form equal triangles.

ΔCBA ≅ CDA

3. The diagonals bisects the parallelogram into equal sides,

ΔABD≅ ECD

First, it is important to note the properties of a parallelogram. These properties are;

From the diagram shown, we can see that the diagonals are lines CD and BD.

Hence, the triangles formed from the bisection of the perpendicular lines are equal.

2. Also, following the properties of a kite,

The diagonals bisects the kite perpendicularly to form equal triangles.

Triangle CBA is equal to CDA

3. Since the diagonals bisects the parallelogram into equal sides,

Triangle ABD is equal to triangle ECD

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Answer: 10.95

Step-by-step explanation:

To identify the pattern, we need to look at the differences between the given numbers.

The difference between 10.21 and 9.47 is 0.74.

The difference between 10.57 and 10.21 is 0.36.

The difference between 12.15 and 10.57 is 1.58.

We can see that the differences between the numbers are not constant. However, the differences themselves follow a pattern: they are increasing by 0.38 each time.

So, to find the missing number, we can add 0.38 to 10.57:

10.57 + 0.38 = 10.95

Therefore, the missing number is 10.95.

The total no. of seats available in an baseball game is 450000.

How to find the percentage?

As the total is 100%, grandstand and bleacher's total percentage of seats are 42+18 = 60%.

Remaining 40% are of box and club seats which is equal to 12600 + 5400 = 18000.

So, let's say x is the total no. of seats

[tex]40\%\ of\ x = 18000\\\\x = \frac{18000 \times 100}{40}\\\\x = 450000\ seats[/tex]

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the total number of seats available for the baseball game is 45,000.

To find the total number of seats available, we need to know the percentage of seats that are in the bleacher and grandstand sections.

According to the graph, the bleacher seats account for 18% of the total seats, while the grandstand seats account for 42% of the total seats. Based on the information provided, we are aware that there are 12,600 box seats and 5,400 club seats available.

To calculate the total number of seats, we can add up the number of seats in each section and then divide by the percentage of total seats that each section represents:

Total seats = (12,600 + 5,400) / (100% - 18% - 42%)

Total seats = 18,000 / 40%

Total seats = 45,000

Therefore, the total number of seats available for the baseball game is 45,000.

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Answer:

x = [tex]\frac{19}{6}[/tex]   or   x = [tex]3\frac{1}{6}[/tex]

Hope this helps!

Step-by-step explanation:

x + [tex]\frac{1}{2}[/tex] = [tex]3\frac{2}{3}[/tex], subtract both sides by [tex]\frac{1}{2}[/tex]

x = [tex]\frac{11}{3}[/tex] -  [tex]\frac{1}{2}[/tex]   :   x = [tex]\frac{22}{6}[/tex] -  [tex]\frac{3}{6}[/tex]    :    x = [tex]\frac{19}{6}[/tex]   :   x = [tex]3\frac{1}{6}[/tex]

Answer:

Step-by-step explanation:

To draw in units, take one box as one unit, so a width of 7 will be 7 boxes from left to right, and a width of 4 will be 3 boxes down.

Answer:

To draw in units, take one box as one unit, so a width of 7 will be 7 boxes from left to right, and a width of 4 will be 3 boxes down.

Step-by-step explanation:

The 99% confidence interval for the mean weight is 12.61 < μ < 14.15 where μ is the sample mean.

A confidence interval is used to represent a range of values that are likely to contain the true population parameter.

In this case, the population parameter we are interested in is the mean weight of boxes of cereal labeled as containing 14 ounces.

The 99% confidence interval for the mean weight can be calculated by first determining the sample mean and standard deviation. The sample mean is 13.38 ounces and the sample standard deviation is 0.33 ounces.

To calculate the 99% confidence interval, we use the t-distribution to find the t-critical value for a sample size of 12 and a confidence level of 99%. The t-critical value for a 99% confidence level is 2.76. The formula for the confidence interval is given by:

μ ± t*√(s/√n)

Where μ is the sample mean, t is the t-critical value, s is the sample standard deviation and n is the sample size.

Therefore, the 99% confidence interval for the mean weight is

13.38 ± 2.76*√(0.33/√12) = 13.38 ± 0.82.

Therefore, the 99% confidence interval for the mean weight is 12.61 < μ < 14.15.

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The probability of getting an 8 or 4 on the spinner is 1÷4 or 25%.

What is Probability ?

Probability is a branch of mathematics that deals with the study of random events or outcomes. It is a measure of the likelihood or chance of an event occurring, expressed as a number between 0 and 1, where 0 represents an impossible event and 1 represents a certain event.

the probability of getting an 8 or 4 by assuming that the spinner has equally likely outcomes for each number from 1 to 8.

There are two possible outcomes that satisfy the condition of getting an 8 or 4: either the spinner lands on 8 or it lands on 4.

Since there are 8 equally likely outcomes on the spinner, the probability of getting an 8 or 4 is:

P(8 or 4) = number of favorable outcomes ÷ total number of outcomes

= 2 ÷ 8

= 1÷4

Therefore, the probability of getting an 8 or 4 on the spinner is 1÷4 or 25%.

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The image vertices of P' if the preimage is rotated 90° counter clockwise is P'(-5,1)

An image vertex refers to a point in the plane that results from applying a transformation to a given vertex. A transformation is a mathematical operation that changes the position, size, or shape of a figure.

The image vertices of P' when the preimage polygon PSRT is rotated 90° counter clockwise can be found by applying a transformation to each vertex of the polygon. This transformation involves switching the x- and y-coordinates of each vertex and negating the new y-coordinate.

(x, y) -> (-y, x)

For the vertex P(1, 5), we can apply this transformation to get the image vertex P':

P' = (-5, 1)

Similarly, we can apply the transformation to the other vertices of the polygon:

S(1, 0) -> S'(0, 1)

R(−2, −3) -> R'(3, -2)

T(−4, 2) -> T'(2, 4)

Therefore, the image vertices of P' are P'(-5, 1), S'(0, 1), R'(3, -2), and T'(2, 4).

This means that the rotated polygon has the vertices P', S', R', and T', which form a new polygon that is 90° counter clockwise rotated from the original polygon PSRT.

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The value of the surds are;

11. 12√3 - 16

13. -15√5 + 30

Surds are defined as the values in square root that can no longer be further simplified into whole numbers or integers.

From the information given, we have that;

(-2√3 + 2)(√3 - 5)

expand the bracket, we have;

-2√3×√3 + 10√3 + 2√3 -10

-2(3) + 10√3 + 2√3 - 10

expand the bracket

-6 +  10√3 + 2√3 - 10

collect like terms

12√3 - 16

(-2- 3√5)(5 - √5)

expand the bracket

-2(5) + 25 - 15√5 + 3(5)

expand further

-10 + 25 - 15√5 + 15

collect the like terms

-15√5 + 30

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the distance from the first plant to the last plant, ignoring the width of each plant stem, is 10.5 feet.

Why is it?

To find the distance from the first plant to the last plant, we need to add up the distances between each adjacent pair of plants. Since there are 8 plants, there are 7 pairs of adjacent plants, and each pair is separated by 1.5 feet.

So, the total distance from the first plant to the last plant is:

7 ×1.5 = 10.5 feet

Therefore, the distance from the first plant to the last plant, ignoring the width of each plant stem, is 10.5 feet.

Distance refers to the measurement of the physical space between two points or objects. It is a scalar quantity that only considers the magnitude of the separation between two points and does not take into account the direction of the separation.

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Answer:

the final factored form of the function is:

f(x) = 6(x+1)^2(x-3)(x-1)

Step-by-step explanation:

To write the function in factored form, we need to use the zeros and their multiplicities.

From the given zeros, we can write:

x = -1 (multiplicity 2) means (x+1)(x+1) = (x+1)^2 = 0

x = 3 (multiplicity 1) means (x-3) = 0

x = 1 (multiplicity 1) means (x-1) = 0

So the factored form of the function is:

f(x) = a(x+1)^2(x-3)(x-1)

To find the value of "a" and satisfy the condition that the function goes through the point (2,-18), we can substitute the given point into the function:

-18 = a(2+1)^2(2-3)(2-1)

-18 = a(-3)

Solving for "a", we get:

a = 6

So the final factored form of the function is:

f(x) = 6(x+1)^2(x-3)(x-1)

The probability that a number greater than 4 comes up exactly 2 of the 5 times is about 32.9%.

When rolling a standard number cube, the probability of getting a number greater than 4 is 2/6 = 1/3.

Using the binomial probability formula, the probability of getting a number greater than 4 exactly 2 times out of 5 rolls is:

P(X = 2) = (5 choose 2) * (1/3)^2 * (2/3)^3

P(X = 2) = 10 * 1/9 * 8/27

P(X = 2) = 80/243

To the nearest tenth of a percent, this probability is approximately:

P(X = 2) ≈ 32.9%

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To solve this problem, we can use the geometric distribution, which models the number of trials needed to obtain the first success in a sequence of independent trials.

Let X be the random variable representing the number of people a designer needs to ask until they find someone who agrees to be their model. Then X follows a geometric distribution with probability of success p = 0.38.

The probability that a designer needs to ask at most 3 people is the sum of the probabilities that they need to ask 1, 2, or 3 people:

P(X ≤ 3) = P(X = 1) + P(X = 2) + P(X = 3)

We can calculate these probabilities as follows:

P(X = 1) = p = 0.38

P(X = 2) = (1-p) × p = 0.62 × 0.38 = 0.2356

P(X = 3) = [tex](1-p)^{2}[/tex] × p = [tex](0.62)^{2}[/tex] × 0.38 = 0.1448

Therefore, the probability that a designer would have to ask at most 3 people to find someone that would agree to be their model is:

P(X ≤ 3) = P(X = 1) + P(X = 2) + P(X = 3) = 0.38 + 0.2356 + 0.1448 = 0.7604

Rounding this to four decimal places, we get 0.7604, which is closest to the answer option (D) 0.6156. However, none of the given answer options matches the calculated probability exactly.

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Answer:

1, the mid point

The midpoint of a line segment with endpoints (x1, y1) and (x2, y2) can be found using the midpoint formula:

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

Substituting the given endpoints (4, -4) and (0, 9), we get:

midpoint = ((4 + 0) / 2, (-4 + 9) / 2) = (2, 2.5)

Therefore, the midpoint of the line segment with endpoints (4, -4) and (0, 9) is (2, 2.5).

2,  the slope

The slope of the line passing through the points (4, -4) and (0, 9) can be found using the formula:

slope = (y2 - y1) / (x2 - x1)

where (x1, y1) and (x2, y2) are the coordinates of the two points.

Substituting the given coordinates, we get:

slope = (9 - (-4)) / (0 - 4) = 13 / (-4) = -3.25

Therefore, the slope of the line is -3.25.

3, the length

The length of the line passing through the points (4, -4) and (0, 9) can be found using the distance formula:

distance = sqrt((x2 - x1)^2 + (y2 - y1)^2)

Substituting the given coordinates, we get:

distance = sqrt((0 - 4)^2 + (9 - (-4))^2) = sqrt(16 + 169) = sqrt(185)

Therefore, the length of the line is sqrt(185).

4,  the equation

The equation of the line passing through the points (4, -4) and (0, 9) can be found using the point-slope form of the equation of a line:

y - y1 = m(x - x1)

where m is the slope and (x1, y1) is one of the points.

Substituting the given slope and one of the points, we get:

y - (-4) = -3.25(x - 4)

Simplifying, we get:

y + 4 = -3.25x + 13

y = -3.25x + 9

Therefore, the equation of the line passing through the points (4, -4) and (0, 9) is y = -3.25x + 9.

Answer: 8c3 = 56

the rest of the equation;
P(3) = 56 * (0.45)^3 * (0.55)^5

P(3) = 56 * 0.091125 * 0.05031737

P(3) = 0.257

To express this probability as a percentage, we multiply by 100:

P(3) = 25.7%

25.7% is the final answer (not 8c3)

We can use the formula for the monthly payment of a loan to calculate the amount we need to pay each month:

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

Where:

M = the monthly payment

P = the principal (the amount borrowed)

r = the monthly interest rate (which is the annual interest rate divided by 12)

n = the total number of months in the loan term (which is the number of years multiplied by 12)

Plugging in the given values, we get:

P = $3825

r = 15% / 12 = 0.0125

n = 4 years * 12 = 48 months

M = ($3825 * 0.0125 * (1+0.0125)^48) / ((1+0.0125)^48 - 1)

M ≈ $94.87

Therefore, the monthly payment will be approximately $94.87.