Sam has a deck that is shaped like a triangle with a base of 18 feet and a height of 7 feet. He plans to build a 2:5 scaled version of the deck next to his horse's water trough.

Part A: What are the dimensions of the new deck, in feet? Show every step of your work. (4 points)

Part B: What is the area of the original deck and the new deck, in square feet? Show every step of your work. (4 points)

Part C: Compare the ratio of the areas to the scale factor. Show every step of your work. (4 points)

The following sequences of transformations do not show congruency by mapping shape I onto shape II:

These sequences of transformations do not map shape I onto shape II because they either change the size or shape of the figure. The second sequence of transformations reflects shape I across the x-axis, rotates it 90° clockwise, and then translates it 4 units down.

This results in a figure that is flipped sideways and shifted down. The third sequence of transformations reflects shape I across the x-axis, rotates it 90° counterclockwise, and then translates it 6 units down. This results in a figure that is flipped upside down and shifted to the left.

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The solution for f in terms of g is: f = -6g / 5. Out of the answer options provided, none of them exactly match this solution.

To solve for f in the equation 6f + 9g = 3g + f, we can simplify the equation and isolate the variable f.

Starting with the given equation as follows:

6f + 9g = 3g + f

We can combine like terms by subtracting f from both sides and subtracting 3g from both sides:

6f - f = 3g - 9g

Simplifying further we get:

5f = -6g

To solve for f, we divide both sides of the equation by 5:

f = -6g / 5

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Based on the information given, the null hypothesis states that the newscast reaches 41% of the viewing audience, while the alternate hypothesis states that it does not reach 41% of the audience. So, the correct answer is d. Fail to reject the null hypothesis.

To determine the decision, we need to perform a hypothesis test using the given significance level α = 0.01. This significance level represents the maximum acceptable probability of making a Type I error, which is rejecting the null hypothesis when it is actually true.

In the survey of 100 viewers, 36% indicated that they watch the late evening news on the local CBS station. To test the hypothesis, we can use a one-sample proportion test. We compare this sample proportion to the claimed 41% to see if there is a significant difference.

Using a statistical calculator or software, we calculate the p-value associated with the observed sample proportion. If this p-value is less than α (0.01), we reject the null hypothesis. If the p-value is greater than or equal to α, we fail to reject the null hypothesis.

Based on the decision criteria, if the p-value is less than 0.01, we would reject the null hypothesis and conclude that the newscast does not reach 41% of the audience. However, if the p-value is greater than or equal to 0.01, we would fail to reject the null hypothesis. To summarize, the correct decision, given α = 0.01, would be d. Fail to reject the null hypothesis.

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Answer:

Since all four sides are equal in length, quadrilateral ABCD is a rhombus

Step-by-step explanation:

Therefore, approximately 0.3% of IQ scores are at least 46.

The empirical rule, also known as the 68-95-99.7 rule, states that in a bell-shaped distribution:

   Approximately 68% of the data falls within one standard deviation of the mean.

   Approximately 95% of the data falls within two standard deviations of the mean.

   Approximately 99.7% of the data falls within three standard deviations of the mean.

Given a mean IQ score of 97 and a standard deviation of 17, we can calculate the number of standard deviations below the mean that a score of 46 corresponds to:

Number of standard deviations = (46 - 97) / 17 = -3

Since the empirical rule tells us that approximately 99.7% of the data falls within three standard deviations of the mean, we can conclude that the percentage of IQ scores that are at least 46 is 0.3% (100% - 99.7%).

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Step-by-step explanation:

The inscribed angle MPN intercepts twice as many degrees of arc as its measure

 so  MN = 62 degrees

   the lower NP is 180 degrees

      the remainder of the 360 degree circle is MP

               360 - 180 - 62 = MP = 118 degrees

Answer:

[tex]m\overset\frown{MP} =118^{\circ}[/tex]

Step-by-step explanation:

The diagram shows a circle with an inscribed angle NPM and an intercepted arc NM.

To find the measure of arc MP, we first need to find the measure of the intercepted arc NM.

According to the Inscribed Angle Theorem, the measure of an inscribed angle is half the measure of the intercepted arc. Therefore:

[tex]m \angle NPM = \dfrac{1}{2} \overset\frown{NM}[/tex]

         [tex]31^{\circ} = \dfrac{1}{2} \overset\frown{NM}[/tex]

       [tex]\overset\frown{NM}=62^{\circ}[/tex]

The minor arcs in a semicircle sum to 180°. Therefore:

[tex]\overset\frown{MP} + \overset\frown{NM} = 180^{\circ}[/tex]

Substitute the found measure of arc MN into the equation:

[tex]\overset\frown{MP} +62^{\circ} = 180^{\circ}[/tex]

[tex]\overset\frown{MP} +62^{\circ} -62^{\circ}= 180^{\circ}-62^{\circ}[/tex]

[tex]\overset\frown{MP} =118^{\circ}[/tex]

Therefore, the measure of arc MP is 118°.

[tex]\hrulefill[/tex]

Additional information

You need to multiply by 5 instead of 6 because each pair of opposite faces on a cuboid has the same area, so by considering one face from each pair, you ensure that you don't count any face twice.

When calculating the total surface area of a cuboid, you need to understand the concept of face pairs.

A cuboid has six faces, but each face has a pair that is identical in size and shape.

Let's break down the reasoning behind multiplying by 5 instead of 6 in the given scenario.

To find the surface area of a cuboid, you can add up the areas of all its faces.

However, each pair of opposite faces has the same area, so you avoid double-counting by only considering one face from each pair. In this case, you have five pairs of faces:

(1) top and bottom, (2) front and back, (3) left and right, (4) left and back, and (5) right and front.

By multiplying the average area of a pair of faces by 5, you account for all the distinct face pairs.

Essentially, you are considering one face from each pair and then summing their areas.

Since all the pairs have the same area, multiplying the average area by 5 gives you the total surface area.

When dividing 150 by 4 (to find the average area of a pair of faces), you are essentially finding the area of a single face.

Then, by multiplying this average area by 5, you ensure that you account for all five pairs of faces, providing the total surface area of the cuboid.

Thus, multiplying by 5 is necessary to correctly calculate the total surface area of the cuboid by accounting for the face pairs while avoiding double-counting.

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X = 45 degrees. ------------------

Answer:

The equation QS = 32 is false.

Step-by-step explanation:

In a right triangle, the Pythagorean theorem states that 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.

Given:

QT = 16

RT = 16

QS = 32

We can apply the Pythagorean theorem to the right triangle:

RT^2 + QT^2 = QS^2

Substituting the given values:

16^2 + 16^2 = 32^2

Calculating:

256 + 256 = 1024

However, we find that 512 (the sum of the squares of the other two sides) does not equal 1024 (the square of the hypotenuse). This contradicts the Pythagorean theorem, which means the equation QS = 32 is false.

The time required to get an accrued amount of $6,450.00 with compoundeded interest on a principal of $3,030.00 at an interest rate of 10.2% per year and compounded 4 times per year is 7.5 years.

The formula accrued amount in a compounded interest is expressed as;

[tex]A = P( 1 + \frac{r}{n} )^{(nt)}[/tex]

Where A is accrued amount, P is principal, r is interest rate and t is time.

Given that:

Principal P = $3,030

Accrued amount A = $6,450

Compounded quarterly n = 4

Interest rate r = 10.2%

Time t = ?

First, convert R as a percent to r as a decimal

r = R/100

r = 10.2/100

r = 0.102

Now, plug these values into the above formula and solve for time t.

[tex]A = P( 1 + \frac{r}{n} )^{(nt)}\\\\t = \frac{In(\frac{A}{p}) }{n[In( 1 + \frac{r}{n}) ]} \\\\t = \frac{In(\frac{6450}{3030}) }{n[In( 1 + \frac{0.102}{4}) ]} \\\\t = 7.501 \ years[/tex]

t = 7.5 years.

Therefore, the time taken to get the accrued amount is approximately 7.5 years.

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Using simultaneous method to solve the system of linear equations, 56 $10 tickets, 1310 $20 tickets, and 1902 $30 tickets were sold.

Let's solve the problem step by step.

Let:

x = number of $10 tickets sold

y = number of $20 tickets sold

z = number of $30 tickets sold

From the given information, we can form the following equations:

Equation 1: x + y + z = 3268 (Total number of tickets sold)

Equation 2: y = x + 259 (259 more $20 tickets than $10 tickets were sold)

Equation 3: 10x + 20y + 30z = 63920 (Total sales from ticket sales)

We can use these three equations to solve for the values of x, y, and z.

First, let's substitute Equation 2 into Equation 1:

x + (x + 259) + z = 3268

2x + 259 + z = 3268

2x + z = 3009 (Equation 4)

Now, let's substitute the value of y from Equation 2 into Equation 3:

10x + 20(x + 259) + 30z = 63920

10x + 20x + 5180 + 30z = 63920

30x + 30z = 58740

x + z = 1958 (Equation 5)

We now have a  (Equations 4 and 5) with two variables (x and z). We can solve this system to find the values of x and z.

Multiplying Equation 4 by 30, and Equation 5 by 2, we get:

60x + 30z = 60270 (Equation 6)

2x + 2z = 3916 (Equation 7)

Now, subtract Equation 7 from Equation 6:

(60x + 30z) - (2x + 2z) = 60270 - 3916

58x + 28z = 56354

Simplifying, we have:

29x + 14z = 28177 (Equation 8)

Now, we can solve Equations 5 and 8 simultaneously:

x + z = 1958 (Equation 5)

29x + 14z = 28177 (Equation 8)

Multiplying Equation 5 by 14, and Equation 8 by 1, we get:

14x + 14z = 27332 (Equation 9)

29x + 14z = 28177 (Equation 8)

Now, subtract Equation 9 from Equation 8:

(29x + 14z) - (14x + 14z) = 28177 - 27332

15x = 845

Divide both sides of the equation by 15:

x = 56

Substituting the value of x into Equation 5, we can find z:

56 + z = 1958

z = 1958 - 56

z = 1902

Now that we have the values of x and z, we can substitute them back into Equation 1 to find y:

56 + y + 1902 = 3268

y + 1958 = 3268

y = 3268 - 1958

y = 1310

Therefore, the solution to the problem is:

x = 56 (number of $10 tickets sold)

y = 1310 (number of $20 tickets sold)

z = 1902 (number of $30 tickets sold)

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Out of the possible outcomes HH, HT, TH, and TT when a coin is tossed twice, the missing outcome is TT. Option B.

To determine the missing outcome when a coin is tossed twice, we need to consider all the possible combinations of heads (H) and tails (T) that can result from two coin tosses.

Given that three of the possible outcomes are HH, HT, and TH, we can deduce that the missing outcome must be TT.

Let's analyze each option to confirm:

(A) TH: This outcome is already mentioned, so it is not the missing outcome.

(B) TT: This is the missing outcome as it has not been mentioned among the given options.

(C) HT: This outcome is already mentioned, so it is not the missing outcome.

(D) TH: This outcome is already mentioned, so it is not the missing outcome.

Therefore, the missing outcome is TT. Option B is correct.

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Answer:

The growth model that represents the population of this city is not linear--it is exponential:

[tex]f(t) = 10000( {1.025}^{t} )[/tex]

[tex]t = 0 \: represents \: 2010[/tex]

The correct answer is: Starting with one, every consecutive line has two more marbles than the previous line. This is the result inferred using deductive reasoning.

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The set of reflections and rotations that would carry rectangle ABCD onto itself is (a) Reflect over the y-axis, reflect over the x-axis, rotate 180°

From the question, we have the following parameters that can be used in our computation:

The figure (see attachment)

The figure is located in the second quadrant

So, we have the following series of transformations

This means that the series of transformation is (a)

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The amount of Bruno's yearly pay deducted for FICA is approximately

A. $4,524.15. The closest option provided is A. $4521.15.

To calculate the amount of FICA deducted from Bruno's yearly pay, we need to consider the specific FICA tax rates for Social Security and Medicare.

As of 2021, the Social Security tax rate is 6.2% on income up to a certain threshold, and the Medicare tax rate is 1.45% on all income.

Given that Bruno's gross income per pay period is $4925 and he is paid monthly, we can calculate the yearly gross income as follows:

Yearly gross income = $4925 * 12 = $59,100

To calculate the FICA deduction, we need to find the sum of the Social Security and Medicare taxes. Using the respective tax rates mentioned earlier:

Social Security deduction = $59,100 * 6.2% = $3,667.20

Medicare deduction = $59,100 * 1.45% = $856.95

Adding these two deductions together:

FICA deduction = $3,667.20 + $856.95 = $4,524.15

Therefore, the amount of Bruno's yearly pay deducted for FICA is approximately $4,524.15.

The closest option provided is A. $4521.15.

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The estimate for the percent body fat in 75-year-old men would be 24%.

with aging, body fat increases and muscle mass declines, and this means that that the percent body fat is likely to increase as the age progresses.

Looking at the given vertical components, we see that the values are decreasing as we move from top to bottom and can be inferred as that the percent body fat decreases as the age increases.

The horizontal component for the age are :

15

25

35

45

55

65

75

The age values are evenly spaced. In this case, the difference between each age value is 10.

The decreasing trend of the vertical components and evenly spaced data, we can estimate the percent body fat in 75-year-old men to be closer to the value of 24.

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The 98% confidence interval for the true mean statistics anxiety score μ is approximately (39.023, 39.777).

To calculate the 98% confidence interval for the true mean statistics anxiety score μ, we can use the formula:

[tex]\[\text{CI} = \bar{X} \pm Z \cdot \left(\frac{\sigma}{\sqrt{n}}\right)\][/tex]

where [tex]\bar{X}[/tex] is the sample mean (39.4), Z is the Z-score corresponding to the desired confidence level (in this case, 98% corresponds to a Z-score of 2.33), σ is the population standard deviation (0.9), and n is the sample size (33).

Plugging in the values, we get:

CI = 39.4 ± 2.33 * (0.9/√33).

Calculating this expression, we find:

CI = 39.4 ± 2.33 * (0.162),

CI ≈ 39.4 ± 0.377.

Therefore, the 98% confidence interval for the true mean statistics anxiety score μ is approximately (39.023, 39.777).

This means that we are 98% confident that the true average statistics anxiety score for all undergraduate students in the U.S. falls within this interval.

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The line of best fit and the correlation coefficient are both useful tools for determining the correlation between two variables on a graph.

The line of best fit is a straight line that represents the trend or average relationship between the variables. It is drawn to minimize the overall distance between the line and the data points. By examining the slope of the line, we can determine whether there is a positive or negative correlation. If the line slopes upwards, it indicates a positive correlation, while a downward slope suggests a negative correlation. Additionally, the steepness of the line indicates the strength of the correlation. A steeper line signifies a stronger correlation.

The correlation coefficient, often denoted as r, is a numerical measure of the strength and direction of the correlation. It ranges from -1 to +1. A positive value of r indicates a positive correlation, while a negative value indicates a negative correlation. The magnitude of r represents the strength of the correlation, with values closer to -1 or +1 suggesting a stronger correlation, and values closer to 0 indicating a weaker correlation.

By analyzing both the line of best fit and the correlation coefficient, we can gain insights into the nature and strength of the correlation between the variables on the graph.

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The probability that a point chosen at random lies on the shaded region is given as follows:

4/7.

The parameters that are needed to calculate a probability are listed as follows:

Then the probability is calculated as the division of the number of desired outcomes by the number of total outcomes.

The area of the shaded region in this problem is given as follows:

4² = 16.

The total area of the figure is given as follows:

16 + 2 x 1/2 x 3 x 4 = 28.

Hence the probability is given as follows:

16/28 = 4/7.

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Answer:

If AJKL is similar to ARST, the angles of AJKL must be congruent to the

Step-by-step explanation:

Answer:

C.  5x(-x + 2)

Step-by-step explanation:

To factor the expression -5x² + 10x, we need to look for a common factor that can be factored out.

Finding a common factor involves identifying a term or expression that can be factored out from each term of a given expression.

Both terms have the common factor of 5x, so we can factor out 5x:

5x(-x + 2)

Therefore, the factored form of -5x² + 10x is -5x(x - 2).

[tex]\hrulefill[/tex]

Additional notes:

If we expand the expressions in the given answer options, we get:

  A.  −5x(x + 2) = -5x² - 10x

  B.  5(−x² + 10x) = -5x² + 50x

  C.  5x(−x + 2) = -5x² + 10x

  D.  x(5x + 10) = 5x² + 10x

Hence confirming that the correct answer is option C.

To factor [tex]-5x^2+10x[/tex], we can begin by factoring out the greatest common factor, which is [tex]-5x[/tex]:

We can check our answer by distributing [tex]-5x[/tex] to the expression inside the parentheses:

[tex]\therefore[/tex] The answer is [tex]-5x(x-2)[/tex].

[tex]\blue{\overline{\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad}}[/tex]

The result of the sum in this problem is given as follows:

675

An arithmetic sequence is a sequence of values in which the difference between consecutive terms is constant and is called common difference d.

The sum of the first n terms is given by the equation presented as follows:

[tex]S_n = \frac{n(a_1 + a_n)}{2}[/tex]

The parameters for this problem are given as follows:

Hence the sum is given as follows:

S = 10/2 x (27 + 108)

S = 675.

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By using trigonometric functions, the value of [tex]\sin \text{x}^\circ[/tex] is [tex]\frac{\text{a}}{\text{b}}[/tex].

Trigonometric functions are also known as Circular Functions can be simply defined as the functions of an angle of a triangle. It means that the relationship between the angles and sides of a triangle are given by these trig functions. The basic trigonometric functions are sine, cosine, tangent, cotangent, secant and cosecant.

Given

[tex]\sin \text{x}^\circ= \ ?[/tex]

[tex]\tan \text{x}^\circ=\dfrac{\text{a}}{4}[/tex]

[tex]\cos \text{x}^\circ=\dfrac{4}{\text{b}}[/tex]

Formula to find [tex]\sin \text{x}^\circ[/tex]

[tex]\sin \text{x}^\circ=\dfrac{\text{Opposite}}{\text{Hypotenuse}}[/tex]

[tex]\rightarrow\sin \text{x}^\circ=\bold{\dfrac{a}{b}}[/tex]

Therefore, by using trigonometric functions, the value of [tex]\sin \text{x}^\circ[/tex] is [tex]\frac{\text{a}}{\text{b}}[/tex].

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The equation you provided, 2W - TB = D, is a way to find the difference between wins and losses by doubling the number of wins and subtracting the total number of battles. Let's break it down to understand why it works.

First, let's define the variables:

W = number of wins

L = number of losses

D = difference between wins and losses

TB = total battles

The equation 2W - TB = D can be understood as follows:

Doubling the number of wins (2W) represents a hypothetical scenario where every win is counted twice.

Subtracting the total number of battles (TB) from the doubled wins accounts for the fact that the total number of battles includes both wins and losses.

The resulting value (D) represents the difference between wins and losses.

Let's consider an example using your values:

Total battles (TB) = 50

Wins (W) = 10

Using the equation 2W - TB = D:

2(10) - 50 = D

20 - 50 = D

D = -30

In this example, the difference (D) between wins and losses is -30, indicating that there are 30 more losses than wins.

The same principle applies when using losses instead of wins. For example, the equation 2L - TB = D can be used to find the difference between wins and losses by doubling the number of losses and subtracting the total number of battles.

In summary, by doubling either the wins or losses and subtracting the total battles, you can find the difference between wins and losses. This approach takes into account the total number of battles and provides a measure of the difference between the two.

The answer is:

C. circumference

Work/explanation:

Here's the correct answer:

The distance around a circle is called the circumference.

How to find the circumference :

In 12 years, Maxwell will deposit $290 into the savings account each month.

To calculate how much money Maxwell will deposit into the account each month in 12 years, we need to determine the pattern of increasing deposits over time.

Maxwell deposits $125 into the savings account each month this year, which we can consider as Year 1. Starting from Year 2, he plans on increasing the monthly deposit by $15.

In Year 2, the monthly deposit will be $125 + $15 = $140.

In Year 3, the monthly deposit will be $140 + $15 = $155.

This pattern continues, increasing the deposit by $15 each year.

Therefore, in Year 12, the monthly deposit will be $125 + ($15 * 11) = $125 + $165 = $290.

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