Suppose he got dilates the rectangle shown below with the center of dilation at 0,0 and a scale factor of 2, and then translates the figure 1 unit to the left. What will be the coordinates of the vertices of the similar figure that results

Using the area formula for square, we can find that the area of square CDEF is = 289-unit².

In geometry, a square is a two-dimensional plane object with four equal sides and four equal, 90° angles. Although a rectangle only has its opposite sides equal, a rectangle and a square have some properties in common. As a result, a rectangle can only be described as a square if its four sides are equal in length.

As per the question,

In right-angled ΔABC, as per Pythagoras theorem:

AC = √ (AB² + BC²)

= √ (12² + 9²)

= √ 225

= 15.

Similarly, in ΔACD as per Pythagoras theorem:

CD = √ (AC² + AD²)

= √ (15² + 8²)

= √289

= 17

Now, in square CDEF:

Side of square CDEF, CD = 17.

Area = side²

= 17²

= 289-unit².

Therefore, area of square CDEF is = 289-unit².

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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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Move the figure 2 units to the right  and  Move the figure 3 units downwards are the rules to translate any point on the red figure to the corresponding point on the orange figure, and vice versa

To describe the translation rule for the red figure to the orange figure, we need to determine how the red figure was moved to obtain the orange figure.

First, we can see that the orange figure is shifted to the right of the red figure. This means that the x-coordinate of every point on the orange figure is greater than the corresponding point on the red figure.

Second, we can see that the orange figure is shifted downwards from the red figure. This means that the y-coordinate of every point on the orange figure is less than the corresponding point on the red figure.

Therefore, the translation rule for the red figure to the orange figure is:

• Move the figure 2 units to the right (add 2 to the x-coordinate of every point), and

• Move the figure 3 units downwards (subtract 3 from the y-coordinate of every point).

We can use this rule to translate any point on the red figure to the corresponding point on the orange figure, and vice versa. This translation rule can be used in various applications such as computer graphics, engineering, and architecture, where precise translations of objects are necessary.

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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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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 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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Scarcity principle: Resources are limited and choices must be made, b. Rational person: Makes decisions based on logical thinking and self-interest, c. Economic surplus: Net gain to society from producing and consuming a good, d. Marginal benefit: Additional benefit from consuming one more unit of a good or service.

A statement is a declarative sentence that expresses a fact, opinion, or idea. It is a sentence that makes a claim or assertion that can be true or false, and it can be either affirmative (positive) or negative. A statement can be a simple sentence, or it can be a complex sentence that includes multiple clauses

a. The scarcity principle is the economic principle that states that resources are limited and cannot satisfy all human wants and needs. This principle recognizes that we live in a world of limited resources, and therefore, we must make choices about how to allocate those resources to satisfy our wants and needs. For example, a farmer may have limited land and water resources to cultivate crops, and he must choose which crops to grow based on their profitability, water requirements, and market demand.

b. A rational person is an individual who uses logical thinking and makes decisions based on self-interest to achieve the best possible outcome. A rational person weighs the pros and cons of each option and selects the alternative that maximizes their satisfaction or utility. For example, a consumer may compare prices and quality of different brands before purchasing a product to get the best value for their money.

c. Economic surplus is the difference between the total value that consumers place on a good or service and the total cost of producing it. It represents the net gain to society from producing and consuming the good or service. For example, if a firm produces 100 units of a product at a total cost of $500 and sells them for a total of $700, then the economic surplus is $200.

d. Marginal benefit is the additional benefit that a person receives from consuming one more unit of a good or service. It is the change in total benefit divided by the change in the quantity consumed. For example, if a consumer derives 10 units of satisfaction from consuming the first slice of pizza and 8 units of satisfaction from consuming the second slice, then the marginal benefit of the second slice is 8-10=-2 units of satisfaction.

Therefore, a. Scarcity principle: Resources are limited and choices must be made, b. Rational person: Makes decisions based on logical thinking and self-interest, c. Economic surplus: Net gain to society from producing and consuming a good, d. Marginal benefit: Additional benefit from consuming one more unit of a good or service.

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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)

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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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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These dimensions would work for the swimming pool are

9 feet by 70 feet

10 feet by 63 feet

14 feet by 45 feet

15 feet by 42 feet

18 feet by 35 feet

21 feet by 30 feet

How to find dimensions of the swimming pool?

to find the dimensions of the swimming pool that covers an area of 630 square feet, we can use the formula:

Area = Length x Width = 394

Let x and y be the length and width of the

swimming pool, respectively. Then we have:

x * y = 630

We need to find the values of x and y that satisfy this equation. We can do this by finding the factors of 630 and checking which pairs multiply to 630.

1, 2, 3, 5, 6, 7, 9, 10, 14, 15, 18, 21, 30, 35, 42, 45, 63, 70, 90, 105, 126, 210, 315, 630

From this list, we can see that the following dimensions would work for the swimming pool:

9 feet by 70 feet

14 feet by 45 feet

10 feet by 63 feet

21 feet by 30 feet

15 feet by 42 feet

18 feet by 35 feet

So, the dimensions that would work for the swimming pool.

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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:

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

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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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:

Answer:108 degrees

Step-by-step explanation:easy

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%.

The total distance run by each runner is 1/12 mile.

A relay race is a track and field event where athletes compete as part of a team, taking turns running a certain distance and passing a baton to the next runner until all team members have completed their portion of the race.

Here we have

A relay race is 1 /4 space mile

The number of relay runners on the team is 3

Let each runner, runs for x miles  

The total distance run by 3 relays = 3x

From the data,

The relay race is 1/4 miles

=> 3x = 1/4 miles

=> 12x = 1 miles

=> x = 1/12 miles  

Hence,

The total distance run by each runner is 1/12 mile.

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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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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 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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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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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:

When you have a negative base and an odd exponent, you always get a negative answer.  For example, (-9)^3 written out is -9 * -9 *-9.  Although the answer becomes positive for the first two 9s (81) it becomes negative again for the third 9 (-729).  A base with a positive exponent will always yield a positive number.  Positive numbers are greater than 0 and are always greater than negative numbers.

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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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 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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