Problems 11 & 12. Determine whether the triangles are similar by AA~, SSS~, SAS~, or not similar. If the triangles are similar, write a valid similarity statement.

The required Jane is approximately 59.28 inches tall.

Height is a measurement of vertical distance, either in terms of vertical extent (how tall an object or person is) or in terms of vertical position (how high a point is). "The height of that building is 50 meters" or "The height of an airplane in flight is approximately 10,000 meters" are two examples.

Sylvia's height can be represented as:

Sylvia’s height =56[tex]\frac{3}{4}[/tex] inches

Bill is [tex]\frac{1}{3}$[/tex] of 8 inches taller than Sylvia, which means that Bill's height is:

[tex]$\begin{align*}\text{Bill's height} &= \text{Sylvia's height} + \frac{1}{3} \times 8\ \text{inches} \&= 56 \frac{3}{4}\ \text{inches} + \frac{8}{3}\ \text{inches} \&= 58 \frac{7}{12}\ \text{inches}\end{align*}[/tex]

Jane is [tex]1 \frac{1}{5}$[/tex] inches taller than Bill, which means that Jane's height is:

[tex]$\begin{align*}\text{Jane's height} &= \text{Bill's height} + 1 \frac{1}{5}\ \text{inches} \&= 58 \frac{7}{12}\ \text{inches} + 1 \frac{1}{5}\ \text{inches} \&= 59 \frac{17}{60}\ \text{inches}\end{align*}[/tex]

Therefore, Jane is approximately 59.28 inches tall.

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Answer:

1/72

Step-by-step explanation:

There are a total of 17 students in the class, and we want to choose one boy from 9 and one girl from 8 without replacement. The total number of ways to choose two students from the class is:

17C2 = (17!)/(2!15!) = (1716)/(21) = 136

To choose a boy and a girl, we can choose the boy in 9 ways and the girl in 8 ways, for a total of 9*8 = 72 ways.

Now, since the brother and sister are both in the class, there is only one way to choose them together. Therefore, the probability of choosing the brother and sister is:

1/72

So the probability is 1/72, written as a fraction in simplest form.

The correct option for the quadratic function g are-

Mathematical expressions with a two as the highest power are called quadratic functions. A function or numerical statement of degree two is a quadratic function. This indicates that two is the function's highest power.

The correct option for the given quadratic function g from the graph are-

Correction for the incorrect statements:

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As per the mentioned informations and values provided, the mean from this sample frequency distribution is calculated to be approximately 160.50.

To find the mean from the given sample frequency distribution, we need to first calculate the midpoint for each class interval, then multiply it by the corresponding frequency, sum all of these products, and finally divide by the total frequency.

Using the formula: mean = (sum of midpoint x frequency) / (sum of frequency)

Midpoint for the first interval = (0 + 70) / 2 = 35

Midpoint for the second interval = (70 + 200) / 2 = 135

Midpoint for the third interval = (200 + 500) / 2 = 350

Now we can calculate the sum of midpoint x frequency:

35 x 73 + 135 x 37 + 350 x 182 + 232 x 500 = 84,166

The total frequency is the sum of all frequencies: 73 + 37 + 182 + 232 = 524

Finally, we can calculate the mean:

mean = (sum of midpoint x frequency) / (sum of frequency) = 84,166 / 524 ≈ 160.50

Therefore, the mean from this sample frequency distribution is approximately 160.50.

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The probability of the spinner landing on blue and rolling an even number on a six-side die is 1/6.

What is probability?

The probability of the spinner landing on blue is 2/6, which simplifies to 1/3.

The probability of rolling an even number on a six-sided die is 3/6, which simplifies to 1/2.

To find the probability of both events occurring together, we multiply the probabilities:

P(blue and even number) = P(blue) x P(even number)

P(blue and even number) = (1/3) x (1/2)

P(blue and even number) = 1/6

Therefore, the probability of the spinner landing on blue and rolling an even number on a six-side die is 1/6.

What is spinner?

A spinner is a device or a toy used to randomly select or generate a value or outcome. It consists of a circular board or disc, often divided into sections of different colors or with different values or symbols, and a pointer or arrow that is spun around the disc to land on a particular section. Spinners are commonly used in games, educational activities, and statistical experiments to create random outcomes or to simulate probability distributions.

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Complete question is: The probability of the spinner landing on blue and rolling an even number on a six-side die is 1/6.

Answer:

Step-by-step explanation:

The probability of the spinner landing on blue is 2/6, which simplifies to 1/3.

The probability of rolling an even number on a six-sided die is 3/6, which simplifies to 1/2.
To find the probability of both events occurring together, we multiply the probabilities:

P(blue and even number) = P(blue) x P(even number).

P(blue and even number) = (1/3) x (1/2).

P(blue and even number) = 1/6.

Therefore, the probability of the spinner landing on blue and rolling an even number on a six-side die is 1/6.

Answer:

[tex]n = \frac{m - 2p}{3} \\ \\ p = \frac{m - 3n}{2} [/tex]

Step-by-step explanation:

[tex]1. \: m - 2p = 3n \\ 2. \: \frac{m - 2p}{3} \\ 3. \: n = m - 2p \\ \\ 1. \: m - 3n = 2p \\ 2. \: \frac{m - 3n}{2} = p \\ 3. \: p = \frac{m - 3n}{2} [/tex]

Answer:

Step-by-step explanation:

i)

(x+1)(7-x) = (x+1)(-x+7) = -x² + 6x + 7

standard form:  y = -x² + 6x + 7

for the vertex form you have to find the coordinates of the vertex (h, k):

a = -1, b = 6, c = 7

h = -b/2a = -6/2(-1) = 3

k = ah² + bh + c = -1(3)² + 6(3) + 7 = 16

vertex form:  y = a(x-h) + k

y = -1(x - 3) + 16

ii)

Dimensions of the largest rectangle that can be made are:

Plug in maximum value of x, x = 3

x + 1 = 3 + 1 = 4

7 - x = 7 - 3 = 4

largest rectangle is 4 x 4 = 16

A bar chart or a histogram are visual representations of data that can be used to explore a single column of data.

A bar chart is used to compare different categories of data, and a histogram is used to measure the frequency of data within a given range. Bar charts allow a user to compare the differences between the categories of data, while histograms provide a better indication of how the data is distributed within the range.

Both bar charts and histograms are useful for identifying patterns, outliers, and trends in the data. By using a bar chart or a histogram, a user can quickly and easily identify where the data is concentrated, as well as identify any outliers or trends in the data.

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[tex]x^4y^2-2x^3y^3\\\\x^2y^2(x^2-2xy)[/tex]

Answer is the second one.

In a parallelogram, The statement "angle A and angle D are supplementary" is not correct.

The same-side interior angles theorem states that if a transversal intersects two parallel lines, then the same-side interior angles are supplementary. However, in this case, we are dealing with a parallelogram, which has two pairs of parallel sides.

When we say that "ab||dc", we are stating that side AB is parallel to side DC. We cannot assume that side AD is a transversal between these two sides, as it could intersect the sides at some other angle. Therefore, we cannot conclude that angle A and angle D are angles.

However, we do know that opposite angles in a parallelogram are congruent. Therefore, we can conclude that angle A is congruent to angle C, and angle B is congruent to angle D.

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Step-by-step explanation:

ans is 2 nd option

first bracket multiply with 7 and second multiply with 2 multiply the sign also carefully.

Answer:

5

Step-by-step explanation:

Cost of bagels = 50 - 1.75 - 33.5 = 14.75

No. of bagels = 14.75/2.95 = 5

Answer:

You bought 5 bagels.

Step-by-step explanation:

Since you buy a coffee every day and it says "after 10 days" you multiply the price of the coffee by 10:     $3.35 * 10 = $33.5  

It also says that the remaining balance on the gift card is $1.75. So you need to subtract that from the original balance, 50:    $50- $1.75 = $48.25  -  this is the amount of money you spent.

Next, you subtract the price of all the coffees you bought from the amount of total money you spent over the course of 10 days.  $48.25 - $33.5 = $14.75

This remaining money is for the bagels that you bought on some days. The last step should be to divide $14.75 by the price of one single bagel:

$14.75 / 2.95 = 5  

You bought 5 bagels.

Hope this helps!!!!

Answer:

217,100

Step-by-step explanation:

in this equation first you would want to add together 3000 + 340 which is 3340 then multiply that by 65. Remember to do addition and subtraction steps in multi-step equations first

It is not possible for a study to have practical significance without statistical significance because statistical significance provides evidence that the observed effect is unlikely to have occurred by chance.

The Practical significance and statistical significance are two different concepts that are often used in hypothesis testing.

The Statistical significance refers to the probability that the observed results of a study occurred by chance, given a particular level of significance or alpha.

The Practical significance refers to whether the observed effect size is large enough to be meaningful in a real-world context.

It is possible for a study to have statistical significance without practical significance. For example, a study may find a statistically significant difference between two groups, but the difference may be so small that it is not meaningful in practice.

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The equation of the line of reflection is y = (−13 / 45)x − (1376 / 45) in point-slope form.

To find the equation of the line of reflection between the points (-9, 12) and (17, -78), we first need to find the midpoint of the line segment joining these two points, which will lie on the line of reflection. The midpoint formula is:

[(x₁ + x₂) / 2, (y₁ + y₂) / 2]

Using the coordinates of the two given points, we get:

[(−9 + 17) / 2, (12 − 78) / 2] = [4, −33]

So, the midpoint is (4, −33).

Next, we need to find the slope of the line of reflection. This is equal to the negative reciprocal of the slope of the line passing through the two given points, since the line of reflection is perpendicular to this line. The slope of the line passing through the two given points is

m = (y₂ − y₁) / (x₂ − x₁) = (−78 − 12) / (17 − (−9)) = −90 / 26 = −45 / 13

So, the slope of the line of reflection is:

m' = −1 / m = −13 / 45

Finally, we can use the point-slope form of the equation of a line, with the midpoint we found as the point and the slope we calculated as the slope which is

y − (−33) = (−13 / 45)(x − 4)

y + 33 = (−13 / 45)x + (52 / 45)

or

y = (−13 / 45)x − (1376 / 45)

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A probability distribution is a listing of all possible outcomes along with their likelihood of occurrence.

It is a way of describing the likelihood of different outcomes in a statistical experiment or random event. It is used to calculate the probability of different events or outcomes in situations where there is uncertainty or variability. There are two types of probability distributions: discrete and continuous.

Discrete probability distributions are used when the possible outcomes of a statistical experiment are discrete or countable, such as the number of heads obtained in flipping a coin. Continuous probability distributions are used when the possible outcomes of a statistical experiment are continuous or uncountable, such as the height of people in a population.

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The median and the range of the given data above would be =5 and 11 respectively.

The range of a data set can be calculated by the subtraction of the largest variable form the smallest variable of a data set.

That is;

Data set = 1,1,1,1,2,2,2,5,6,6,6,8,9,10,12

largest variable = 12

smallest variable = 1

range = 12-1 = 11

The median of the data set is the figure that fall at the middle of the data set after being arranged either in ascending or descending order.

The median of the data = 5

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step-by-step explanation:

Part A. We can see that within only for a 0-2 second interval, the height of the water balloon increases from 60ft to approximately 80ft.

Part B. In two intervals, 2-4 seconds to approximately 80 ft and 10-14 seconds to 0 ft.

Part C. Between 4 and 6 seconds, the water balloon height changes from approximately 80ft to 40ft, whereas between 6-8 seconds and 8-10 seconds, the height only changes by 20ft.

Part D. According to the graph, we can suppose that the water balloon was thrown up, and after beginning to fall, at 10 seconds touched the floor, so in 16 seconds kept staying on the floor, at 0ft.  

Hope it helps.

[tex]\text{-B$\mathfrak{randon}$VN}[/tex]

Answer is attached

hope it helps you ⬆️

Lola has 9/8 cups of rice left to use for the rice pudding.

What is fraction?

A fraction is a mathematical term that represents a part of a whole or a ratio between two quantities.

To find out how much rice Lola uses for the rice pudding, we need to first determine how much rice she used for the sushi rolls.

Lola used 3/4 of the 4 1/2 cups of rice for the sushi rolls. To calculate this, we can multiply:

4 1/2 cups x 3/4 = (9/2) x (3/4) = 27/8 cups

So Lola used 27/8 cups of rice for the sushi rolls.

To find out how much rice Lola has left for the rice pudding, we need to subtract the amount she used for the sushi rolls from the original amount of rice she had:

4 1/2 cups - 27/8 cups = 36/8 cups - 27/8 cups = 9/8 cups

Therefore, Lola has 9/8 cups of rice left to use for the rice pudding.

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Answer:

[tex]6 {x}^{2} + 21x + 18 [/tex]

Step-by-step explanation:

[tex](2x + 3)(3x + 6)[/tex]

[tex]6 {x}^{2} + 12x + 9x + 18[/tex]

[tex]6 {x}^{2} + 21x + 18[/tex]

The solution for x is -21 when rectangle JKLM below, JN = 44.

If MN = -2x + 2,

What is the rectangle?

A rectangle is a geometric shape with four sides and four right angles. It is a quadrilateral in which opposite sides are equal in length and parallel to each other, and adjacent sides are perpendicular to each other.

To solve for x, we can use the given information that JN = 44 and MN = -2x + 2 in the rectangle JKLM.

Since JN is a side of the rectangle and is equal to 44, and MN is also a side of the rectangle and is equal to -2x + 2, we can set up the equation:

JN = MN

44 = -2x + 2

Now we can solve for x:

Add 2x to both sides:

44 + 2x = 2

Subtract 2 from both sides:

44 + 2x - 2 = 0

42 + 2x = 0

Subtract 42 from both sides:

42 + 2x - 42 = 0 - 42

2x = -42

Finally, divide both sides by 2 to isolate x:

2x / 2 = -42 / 2

x = -21

Hence, the solution for x is -21.

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Answer:

the length of the rectangle is 21 feet.

Step-by-step explanation:

Let's use "w" to represent the width of the rectangle. According to the problem, the length is three times the width, so we can use "3w" to represent the length.

The perimeter of a rectangle is given by the formula:

Perimeter = 2(length + width)

Substituting the expressions for length and width, we get:

56 = 2(3w + w)

Simplifying the right side, we get:

56 = 2(4w)

56 = 8w

w = 7

So the width of the rectangle is 7 feet. To find the length, we can use the expression we derived earlier:

length = 3w = 3(7) = 21

Therefore, the length of the rectangle is 21 feet.

Answer: [tex]6x^{2}[/tex] + 24x + 18

Step-by-step explanation: To multiply these two terms you multiply each individual term in the left parenthesis by each individual term in the right parenthesis.

well, the amount off from the original 125 is just 125 - 87.50 = 37.50.

now, if we take 125(origin amount) as the 100%, what's 37.50 off of it as a percentage?

[tex]\begin{array}{ccll} Amount&\%\\ \cline{1-2} 125 & 100\\ 37.50& x \end{array} \implies \cfrac{125}{37.50}~~=~~\cfrac{100}{x} \\\\\\ 125x=3750\implies x=\cfrac{3750}{125}\implies x=30[/tex]

To determine what percent off the sale for something was, we need to use the formula for percent off calculation.

What is percent off? The percent off is used to refer to the reduction in price or value of something. The percent off calculation is used to determine the amount of discount in percentage of the original price or value.

What is the formula for percent off calculation? The formula for percent off calculation is as follows:

percent off = (discount / original price) x 100, where,discount = original price - sale price

original price = $125 sale price = $87.50

Substitute the given values into the formula and simplify.

percent off = (discount / original price) x 100percent off =

(($125 - $87.50) / $125) x 100percent off

(37.50 / 125) x 100percent off

⇒ 0.3 x 100percent off = 30%

Therefore, the percent off the sale was 30%.

The measure of angle x is 90°

In a semicircle, an angle that has its vertex at the center of the circle will always be a right angle, which is 90 degrees.

This is because a semicircle is defined as half of a full circle, and the diameter of a circle forms a right angle with any chord that it intersects.

Therefore, any angle in a semicircle that has its vertex at the center of the circle will be 90 degrees.

Thus, the measure of angle x is 90°.

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The area of the Tri-Tri-Again board game is 3 1/8 square feet.

To calculate the area of a triangle, we need to know the length of its base and its height. In this case, Bridget's Tri-Tri-Again board game is in the shape of a triangle with a base of 1 1/4 feet and a height of 2 1/2 feet. To find the area of the triangle, we can use the formula for the area of a triangle, which is 1/2 x base x height.

We first convert the mixed numbers to improper fractions. The base is 5/4 feet and the height is 5/2 feet. We can then substitute these values into the formula to get:

Area of triangle = 1/2 x 5/4 feet x 5/2 feet

Area of triangle = 25/8 square feet

We can simplify the answer by dividing the numerator and denominator by the greatest common factor of 25 and 8, which is 1. This gives us:

Area of triangle = 25/8 square feet

Area of triangle = 3 1/8 square feet

Therefore, the area of the Tri-Tri-Again board game is 3 1/8 square feet.

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We must first determine the total price of the bell peppers in order to determine the number of pounds Paula purchased. Paula bought a total of   [tex]2.8[/tex] pounds of bell peppers.

To determine the total pounds of bell peppers Paula bought, we first need to find the total cost of the bell peppers.

The cost of the red bell peppers is $2.56 and the cost of the green bell peppers is $ [tex]1.92[/tex] , so the total cost of both types of bell peppers is:

$ [tex]2.56[/tex] + $ [tex]1.92 =[/tex]$ [tex]4.48[/tex]

Since both types of bell peppers cost $[tex]1.60[/tex] per pound, we can use this information to find the total weight of the bell peppers.

Let x be the total weight of the bell peppers. Then we can set up the following equation:

$ [tex]1.60\times =[/tex]$[tex]4.48[/tex]

To solve for x, we divide both sides by $[tex]1.60[/tex]:

[tex]x = $4.48 / $1.60[/tex]

[tex]x = 2.8[/tex]

Therefore, Paula bought a total of   [tex]2.8[/tex] pounds of bell peppers.

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Answer:   2.8 pounds of bell pepper bought by Paula

Step-by-step explanation:

Given that :

At the grocery store, the amount spent by Paula :

The amount spent on red bell pepper =  $2.56

The amount spent on green bell pepper = $1.92

the total amount spent = $2.56+$1.92 = $4.48

If both the bell peppers are at  $1.60 per pound, then the total pounds of bell pepper Paula bought

= $4.48/ $1.60

= 2.8 pounds

Solution:

Therefore the number of pounds of bell pepper bought by Paula is 2.8.