Figure LMNO is a reflection of HIJK. Which angle is congruent to ZH?

Answer:

8 pounds

Step-by-step explanation:

Simply add the fractions. Think of mixed fractions as whole numbers + fractions.

[tex]4\frac{1}{4} =\\4+\frac{1}{4} \\\\\\3\frac{3}{4} =\\3+\frac{3}{4}[/tex]

Now, add all the terms together:

[tex]4+\frac{1}{4}+3+\frac{3}{4} =\\\\ 7+\frac{4}{4}[/tex]

4/4 can be rewritten as 1, so we have:

[tex]7+\frac{4}{4} =\\\\ 7+1= \\\\8[/tex]

Thus, Sarah and Nathan picked 8 pounds of strawberries altogether.

The Gabrielsons ran a total of 30 kilometers in the family relay race.

What is the equivalent expression?

Equivalent expressions are expressions that perform the same function despite their appearance. If two algebraic expressions are equivalent, they have the same value when we use the same variable value.

It seems that there are five family members who participated in the relay race, and the distance run by each of them in kilometers is listed as follows:

11, 4, 8, 2, 5

To find the total distance run by the family, we simply add up the distances:

11 + 4 + 8 + 2 + 5 = 30

Therefore, the Gabrielsons ran a total of 30 kilometers in the family relay race.

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2. The appropriate measure of center for the given data is the median, and it equals 19.

5.  We can predict that there were about 169 principals in attendance at the conference.

6. The best graphical representation for the teacher's data would be a bar graph.

7.  A histogram is used to display continuous data, while a bar graph is used to display categorical data.

8. The correct circle graph to represent the data is titled "New York City Visitor's Transportation"

9. We can predict that the college will need about 1440 scoops of ice cream.

Answer 2:

The appropriate measure of center for the given data is the median, and it equals 19. We can determine this from the box plot since the line inside the box represents the median of the data, and the box itself represents the middle 50% of the data. Since the box extends from 17 to 21, we know that half of the data falls below 19 and half above, making it the median. The mean is not a good measure of center for this data because it can be influenced by outliers, which are present in this dataset.

Answer 5:

Since we know that 15 out of 80 people in the exhibit room were principals, we can assume that about 15/80 (or about 0.1875) of the attendees were principals. To estimate the number of principals in attendance, we can multiply this fraction by the total number of attendees:

0.1875 x 900 ≈ 169

Therefore, we can predict that there were about 169 principals in attendance at the conference.

Answer 6:

The best graphical representation for the teacher's data would be a bar graph. A bar graph is a useful way to display categorical data, such as the subject preferences of the students. Each subject can be represented by a bar, with the height of the bar representing the frequency or percentage of students who prefer that subject.

Answer 7:

The correct graph to display the data is a bar graph with the title "Favorite Sport" and the x-axis labeled "Sport" and the y-axis labeled "Number of Students". The bars should be labeled "Basketball" with a value of 17, "Baseball" with a value of 12, "Soccer" with a value of 27, and "Tennis" with a value of 44. A histogram is used to display continuous data, while a bar graph is used to display categorical data.

Answer 8:

The correct circle graph to represent the data is titled "New York City Visitor's Transportation" and has five sections labeled "Walk" at 30%, "Bicycle" at 6%, "Car Service" at 11.25%, "Bus" at 7.5%, and "Subway" at 20.25%. To calculate the percentages, we can divide the number of visitors for each mode of transportation by the total number of visitors (i.e., 300), then multiply by 100% to get the percentage.

Answer 9:

To estimate the number of students who prefer ice cream, we can add up the number of students who chose ice cream, which is 81. Then, we can set up a proportion:

81/225 = x/4000

where x represents the number of students who prefer ice cream out of the total population of 4000. Solving for x, we get:

x = 81 x 4000 / 225 = 1440

Therefore, we can predict that the college will need about 1440 scoops of ice cream.

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Answer:

59.5[tex]cm^{2}[/tex]

Step-by-step explanation:

You have two shape: a square and a triangle

Square:

The area of a square is the sides squared

a = [tex]s^{2}[/tex]  The side length is 7 (7 x 7 = 49)

a = [tex]7^{2}[/tex]

a = 49

Triangle:

a [tex]\frac{bh}{2}[/tex]  The base times the height divided by 2

The base is 7 and the height is 3.

a = [tex]\frac{7x3}{2}[/tex] = [tex]\frac{21}{2}[/tex] = 10.5

Add the two areas together: 49 + 10.5 = 59.5

Helping in the name of Jesus.

Answer:

5 units is the distance

Step-by-step explanation:

7,2 is point c

7,7 is point d

7 - 7 = 0

7 - 2 = 5

5 is the answer

Answer:

BC=4

AC=[tex]4\sqrt{2}[/tex]

The process of bisecting an angle with a straightedge and compass is an important process in geometry. It is used to prove theorems, construct regular polygons, and much more. With enough practice, anyone can perfect this process and use it to their advantage.

Angle is a mathematical concept that describes the relationship between two lines (or edges) that share a common point (or vertex). It is measured in degrees, with a full circle being equal to 360 degrees. Angles can be either acute (less than 90 degrees), right (equal to 90 degrees), obtuse (greater than 90 but less than 180 degrees), or straight (equal to 180 degrees). Angles can also be classified as complementary (two angles whose sum equals 90 degrees) or supplementary (two angles whose sum equals 180 degrees).

1. Draw two rays from the vertex of the angle, and label them A and B.

2. Place the compass at A and draw an arc that intersects both rays.

3. Place the compass at B and draw an arc that intersects both rays.

4. The two arcs intersect at the bisector of the angle.

Bisecting an angle with a straightedge and compass is a simple process, but requires some practice to perfect. The process of bisecting an angle can be used to prove theorems in geometry, such as the Angle Bisector Theorem, which states that the bisector of an angle divides it into two congruent angles. This theorem can be used to prove the equality of two angles, or to construct an angle with a given measure.

Bisecting an angle can also be used to construct regular polygons, such as a hexagon. To construct a regular hexagon, one can use the process of bisecting an angle to construct six congruent angles. These angles can then be connected to form the sides of the hexagon.

The process of bisecting an angle with a straightedge and compass is an important process in geometry. It is used to prove theorems, construct regular polygons, and much more. With enough practice, anyone can perfect this process and use it to their advantage.

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So the radius and diameter for each plate are:

Plate 1: radius ≈ 7 in., diameter ≈ 14 in.

Plate 2: radius ≈ 4.5 in., diameter ≈ 9 in.

Plate 3: radius ≈ 3.5 in., diameter ≈ 7 in.

Circumference is the distance around the edge of a circle. It is the total length of the boundary of a circle. It is also referred to as the perimeter of a circle. The circumference of a circle can be calculated using the formula: C = 2πr where C is the circumference, r is the radius of the circle, and π is a mathematical constant with an approximate value of 3.14. The circumference of a circle is directly proportional to its radius; that is, as the radius of a circle increases, the circumference also increases.

Here,

Part A:

To find the radius and diameter of each plate, we can use the formula for the circumference of a circle:

C = 2πr

where C is the circumference and r is the radius. We can rearrange this formula to solve for the radius:

r = C / 2π

Using the given circumferences and the value of π as 3.14, we can find the radius for each plate:

Plate 1:

C = 43.96 in.

r = 43.96 / (2 x 3.14) ≈ 7 in.

d = 2r ≈ 14 in.

Plate 2:

C = 28.26 in.

r = 28.26 / (2 x 3.14) ≈ 4.5 in.

d = 2r ≈ 9 in.

Plate 3:

C = 21.98 in.

r = 21.98 / (2 x 3.14) ≈ 3.5 in.

d = 2r ≈ 7 in.

So the radius and diameter for each plate are:

Plate 1: radius ≈ 7 in., diameter ≈ 14 in.

Plate 2: radius ≈ 4.5 in., diameter ≈ 9 in.

Plate 3: radius ≈ 3.5 in., diameter ≈ 7 in.

Part B:

To find the radius and diameter of each plate, we used the formula for the circumference of a circle and rearranged it to solve for the radius. We then used the formula for the diameter of a circle, which is simply twice the radius, to find the diameter. We also used the value of π as 3.14 in our calculations.

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$2,560 needs to be invested at time 3 in order to have $3,200 at time 8.

Since the money grows according to the simple interest accumulation function a(t) = 1.05t, the amount of money A at time t, given an initial amount P, can be calculated using the formula:

A = P + Pr(t)

where r is the interest rate (in this case, 5% or 0.05) and t is the time period (measured in years).

To determine how much money needs to be invested at time 3 to have $3,200 at time 8, we can use the above formula and solve for P:

3200 = P + Pr(8-3)

3200 = P + 5P(0.05)

3200 = P + 0.25P

3200 = 1.25P

P = 3200 / 1.25

P = 2560

Therefore, an initial investment of $2,560 at time 3 would be needed to have $3,200 at time 8, assuming a simple interest accumulation function with an interest rate of 5%.

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If total sales were $624 and customers bought 7 times as many pens as flashlights, then the number of pens sold is 84.

Let's start by assigning variables to represent the unknown quantities.

Let x be the number of flashlights sold.

Then, since "customers bought 7 times as many pens as flashlights," the number of pens sold would be 7x.

The total sales can be expressed as the sum of the sales of each item:

10x (sales from flashlights) + 6(7x) (sales from pens) = 624

Simplifying this equation

10x + 42x = 624

52x = 624

x = 12

So, the number of flashlights sold is 12.

And the number of pens sold would be 7x = 7(12) = 84.

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The value of the expression 8w - 4j² when w = 0.25 and j = 0.5 is 1.

The expression 8w - 4j² is a combination of variables, w and j, and a constant, 8 and 4. In order to evaluate the expression when w = 0.25 and j = 0.5, we substitute these values for w and j in the expression and perform the necessary calculations.

First, we substitute w = 0.25 and j = 0.5 in the expression:

8(0.25) - 4(0.5)²

Next, we simplify the expression by performing the calculations in the parentheses first. Since 0.5² = 0.25, we can simplify 4(0.5)² to 4(0.25) = 1. We can then simplify 8(0.25) - 4(0.5)² to:

= 2 - 1

= 1

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The given question is incomplete, the complete question is:

What is the value of the expression 8w−4j² when w=0. 25 and j=0. 5?

Answer:

63.3%

Step-by-step explanation:

30 divided by 100 and then multiplied by 19 gives u the answer

The approximation of √300 to the nearest integer is 17

An integer is a whole number that can be positive or negative or zero. Examples of integers are 0, -5, 10, 15, 1000. e.t.c. Decimal numbers are not integers.

Since the value of √300 can not give a whole number because 300 is not a perfect square. This means that the answer given will not be an integer. Therefore saying that we should approximate to integer means approximation to whole number.

√ 300 = 17.32. Therefore the approximation of the value of √300 to the nearest integer = 17.

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The correct answer is option b. Burger Quick, because it has a larger mean.

Statistics is a branch of mathematics that deals with the collection, analysis, interpretation, presentation, and organization of data. It involves using mathematical and computational methods to gather, analyze, and interpret data from various fields, including business, economics, medicine, engineering, psychology, and social sciences. Statistics allows researchers and analysts to draw conclusions and make predictions based on data, and is used in a wide range of applications, from designing experiments and conducting surveys to testing hypotheses and making decisions based on data-driven insights.

Burger Quick typically has more wait time, because it has a larger interquartile range (IQR) and a larger upper whisker on the box plot, indicating that there is more variability in the wait times and some customers have experienced longer wait times. Although the median wait time for Burger Quick is also larger, it is the IQR and upper whisker that provide more evidence for the longer wait times. The mean is not shown on the box plot and therefore cannot be used to determine which drive-thru typically has more wait time.

Therefore, the correct answer is option b. Burger Quick, because it has a larger mean.

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There are 19 people who own a cat or a dog.

A number is a mathematical object used to represent quantity, measurement, or a count of something. It can be an integer (whole number), a rational number (fraction), an irrational number (such as pi), or a real number (which includes all rational and irrational numbers).

To find the number of people who own a cat or a dog, we need to add the number of people who own only cats to the number of people who own only dogs, and then add the number of people who own both cats and dogs.

Let's start by finding the number of people who own only cats. We know that 16 people own cats, and 5 people own both cats and dogs. Therefore, the number of people who own only cats is:

16 - 5 = 11

Next, let's find the number of people who own only dogs. We know that 8 people own dogs, and 5 people own both cats and dogs. Therefore, the number of people who own only dogs is:

8 - 5 = 3

Finally, we can add the number of people who own only cats to the number of people who own only dogs, and then add the number of people who own both cats and dogs:

11 + 3 + 5 = 19

So, there are 19 people who own a cat or a dog.

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There are 302,702,400 possible baseball teams of nine that can be formed with three designated pitchers and 12 multitalented players who can play any of the remaining positions.

Since three players are designated as pitchers, we need to choose three players out of the total 15 players on the team. This can be done in C(15, 3) ways, where C(n, r) represents the number of combinations of r objects selected from a set of n objects.

For the remaining six positions, any of the 12 multitalented players can be assigned to any of the positions, which means that there are 12 choices for the first position, 11 choices for the second position, and so on, down to 7 choices for the sixth position.

Therefore, the total number of baseball teams of nine that can be formed is:

C(15, 3) x 12 x 11 x 10 x 9 x 8 x 7

which simplifies to:

(15 x 14 x 13 / 3 x 2 x 1) x (12 x 11 x 10 x 9 x 8 x 7)

= 455 x 665,280

= 302,702,400

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The ratio of their surface areas is x^2

Let's assume that the lengths of the edges of the first cube are a, and the lengths of the edges of the second cube are bx, where b is a constant.

The surface area of a cube is given by the formula A = 6a^2, where a is the length of an edge.

Therefore, the surface area of the first cube is 6a^2 and the surface area of the second cube is 6(bx)^2 = 6b^2x^2.

The ratio of their surface areas is:

(6b^2x^2) / (6a^2) = b^2x^2 / a^2

Since the ratio of the lengths of the edges of the two cubes is x, we have:

a / bx = 1 / x

Solving for a, we get:

a = bx^2

Substituting this value into the ratio of their surface areas, we get:

(b^2x^2) / (bx^2)^2 = (b^2x^2) / b^2x^4 = x^2

Therefore, the ratio of the surface areas of the two cubes is x^2.

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Answer:

The missing side of the right triangle is 8, and it is one of the legs.

Step-by-step explanation:

Step 1: Write down the Pythagorean theorem.

The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides. In equation form, it looks like this:

a^2 + b^2 = c^2

where a and b are the lengths of the legs (the shorter sides) and c is the length of the hypotenuse.

Step 2: Identify which sides are the legs and which is the hypotenuse.

In our triangle, we are given the lengths of two sides, 10 and 6. We don't know which one is the hypotenuse and which one is a leg. However, we can use the fact that the hypotenuse is always the longest side to figure it out. Since 10 is longer than 6, we know that 10 is the hypotenuse.

Step 3: Apply the Pythagorean theorem to find x.

Now that we know which side is the hypotenuse, we can use the Pythagorean theorem to find x. We substitute the values we know into the formula and solve for x:

a^2 + b^2 = c^2

6^2 + x^2 = 10^2

36 + x^2 = 100

x^2 = 100 - 36

x^2 = 64

x = √64

x = ±8

Step 4: Choose the positive value of x.

Since x represents a length of a side of a triangle, it must be a positive value. Therefore, x = 8.

Step 5: Verify that the answer is correct.

We can check that our answer is correct by substituting x = 8 into the Pythagorean theorem and seeing if it holds true:

6^2 + 8^2 = 10^2

36 + 64 = 100

100 = 100

The volume of the sphere with a radius of 7 feet is therefore 1436.8 cubic feet when expressed in terms of pi and rounded to the closest tenth (or about 1436.76 cubic feet).

The volume of such a three-dimensional object is the amount of space it takes up in algebra and geometry. It is a description of an object's capacity and, depending on the situation, may be stated in terms of cubic metres, cubic centimetres, litres, or gallons. A cube's volume, for instance, can be determined by adding up its length, width, and height. An equation for calculating a cube's volume is: V = l × w × h where V indicates for volume, l for length, w for width, and h for height.

given

The following equation determines a sphere's volume:

[tex]V = (4/3)\pi r^3[/tex]

where r denotes the sphere's radius.

If we substitute r = 7 feet, we obtain:

[tex]V = (4/3)\pi (7 feet)^3[/tex]

Using V, 1436.76 cubic feet (3.14159)

To the nearest tenth, we round and obtain:

1436.8 cubic feet equals V.

The volume of the sphere with a radius of 7 feet is therefore 1436.8 cubic feet when expressed in terms of pi and rounded to the closest tenth (or about 1436.76 cubic feet).

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Answer:

The radius of the circle is 3 units.

The center of the circle lies on the y-axis.

Step-by-step explanation:

The circle equation is :

x² + (y-1)² = 3²

center: (0, 1)  The center of the circle lies on the y-axis.

Radius:  3     The radius of the circle is 3 units.

Answer:

Table 4 represents a function because each x-value corresponds to exactly one y-value.

Answer:

Step-by-step explanation:

yeah she is... i think.. this is twisting my mind rn

1. The characters in "The Town Mouse and the Country Mouse" are two mice who are cousins. The town mouse is described as elegant, refined, and sophisticated, while the country mouse is simple and unsophisticated.

2. The main idea of the story is that one should be content with their simple life rather than crave for a luxurious life full of dangers and uncertainties.

"The Town Mouse and the Country Mouse" is a fable, a short story that teaches a moral or lesson. It tells the story of two cousins, a town mouse and a country mouse, who visit each other's homes and experience each other's way of life. The town mouse lives in luxury and eats rich food, but is always in danger from the cat, while the country mouse lives a simple life but is safe and content.

3. The sequence of events in the story is as follows:

4. Important details in the story include the description of the town and country mice, the differences in their lifestyles, and their reactions to each other's homes. These details are important because they emphasize the theme of the story, which is that it's better to be content with one's simple life than to crave for a luxurious but dangerous life.

5. I think "The Town Mouse and the Country Mouse" is a great story because it teaches an important lesson in a fun and engaging way. The characters are well-developed, and the plot is entertaining, making it easy for readers to understand the message.

6. One question I have about the writing is whether the author intended the story to be a commentary on social class and wealth.

7. A fable is a short story that teaches a moral or lesson. Fables usually feature animals or other non-human characters that can talk and behave like humans.

8. The moral of "The Town Mouse and the Country Mouse" is that it's better to be content with a simple life than to crave for luxury and danger. The story shows that the country mouse is happier and safer in his simple life than the town mouse, who is always in danger despite his luxurious lifestyle. This lesson teaches readers to be satisfied with what they have rather than always craving for more.

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town mouse and country mouse are cousins, the town mouse is working hard, (keep up the good work bud,) and the city mouse is relaxing, one day, town mouse was invited to city mouse’s city, they were relaxing, and then, a dog almost killed the mouses.

the distance between point A and point B is approximately 777.9 feet.

what is  distance ?

Distance is a numerical measurement of how far apart two objects or points are from each other. It is a fundamental concept in mathematics and physics, and it can be defined in different ways depending on the context.

In the given question,

Let's denote the distance between Jeriel and point A as x, and the distance between Jeriel and point B as y. We want to find the distance between point A and point B, which we can call d.

From the first measurement, we can draw a right triangle with one leg of length x, another leg of length 113, and an acute angle of 8 degrees. The angle opposite the leg of length 113 is 90 degrees minus 8 degrees, or 82 degrees. We can use tangent to find x:

tan(8) = 113/x

x = 113/tan(8)

x =802.5

From the second measurement, we can draw another right triangle with one leg of length y, another leg of length 113, and an acute angle of 52 degrees. The angle opposite the leg of length 113 is 90 degrees minus 52 degrees, or 38 degrees. We can use tangent to find y:

tan(52) = 113/y

y = 113/tan(52)

y =72.4

Now we can use the Law of Cosines to find d:

d² = x² + y² - 2xy cos(130)

where 130 degrees is the angle between the sides of length x and y. We can simplify this equation and substitute the values we found for x and y:

d² = (802.5)² + (72.4)² - 2(802.5)(72.4) cos(130)

d =777.9

Therefore, the distance between point A and point B is approximately 777.9 feet.

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The ratio of 2:3:30 in 385​ can be expressed with the values 22:33:330 repectively.

To find the actual values represented by the ratio 2:3:30 in 385, we need to first add up the parts of the ratio: 2 + 3 + 30 = 35.

Next, we can find the value of each "part" of the ratio by dividing the total value (385) by the total number of parts (35):

385 ÷ 35 = 11

Now we can multiply each part of the ratio by this value to find the actual values:

2 x 11 = 22

3 x 11 = 33

30 x 11 = 330

So the ratio 2:3:30 in 385 represents the values 22:33:330.

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The value of the test statistic is approximately 2.84. Its significance can't be determined.

To determine whether or not there is a significant difference between the hourly wages of two companies, we need to conduct a hypothesis test.

The null hypothesis states that there is no significant difference between the hourly wages of the two companies, while the alternative hypothesis states that there is a significant difference.

The test statistic for this hypothesis test is calculated using the formula:

[tex]t = (x1 - x2) / (s1^2/n1 + s2^2/n2)^(1/2)[/tex]

where x1, x2 are the sample means for companies A and B, s1 and s2 are the sample standard deviations for companies A and B, and n1 and n2 are the sample sizes for companies A and B.

Plugging in given values, we get:

[tex]t = (6.75 - 6.25) / [(1^2/80) + (0.95^2/60)]^(1/2)[/tex]

t = 0.5 / 0.1759

t = 2.8437

Without knowing the significance level or the degrees of freedom, we cannot determine whether or not the test statistic is statistically significant.

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The value of the test statistic is 2.75.

To determine the test statistic for comparing the hourly wages of two companies, the researcher would need to conduct a two-sample t-test with equal variances.

The formula for the test statistic is:

[tex]t = (\bar x1 - \barx2) / [s_p \times \sqrt(1/n1 + 1/n2)][/tex]

where:

[tex]\bar x1[/tex] and[tex]\bar x2[/tex] are the sample means for Company A and Company B, respectively

[tex]s_p[/tex] is the pooled standard deviation of the two samples, calculated as:

[tex]s_p = sqrt [((n1 - 1) \times s1^2 + (n2 - 1) \times s2^2) / (n1 + n2 - 2)][/tex]

n1 and n2 are the sample sizes for Company A and Company B, respectively

s1 and s2 are the sample standard deviations for Company A and Company B, respectively.

Plugging in the given values, we get:

[tex]t = (6.75 - 6.25) / [\sqrt(((80-1)\times 1^2 + (60-1)\times 0.95^2)/(80+60-2)) \times \sqrt(1/80 + 1/60)][/tex]

[tex]t = 2.75[/tex]

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The measure of angle A and angle B are 30° and 60° respectively.

The figure in the image is a right-triangle.

To find the measure of angle A and angle B, we use the trigonometric ratio.

Solving for the measure of angle A:

sinθ = opposite / hypotenuse

opposite of angle A = 8

hypotenuse = 16

Plug in the values

sinθ = 8/16

sinθ = 1/2

θ = sin⁻¹( 1/2 )

θ = 30°

Solving for angle B

cosB = adjacent / Hypotenuse

adjeacent of angle B = 8

Hypotenuse = 16

Plug in the given values

cosB = 8/16

cosB = 1/2

B = cos⁻¹( 1/2 )

B = 60°

Therefore angle A is 30 degrees and angle B is 60 degree.

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The value of the expression as a single rational number is -8.

Kent was likely referring to the idea that subtracting a negative number is the same as adding a positive number. Specifically, to subtract a negative number, we can add the opposite of that number (i.e., the positive version of that number). In this case, we can rewrite the expression as:

= -9.5 - (-8) - 6.5

= -9.5 + 8 - 6.5      (replacing -(-8) with its positive equivalent 8)

= (-9.5 - 6.5) + 8    (grouping like terms)

= -16 + 8                (simplifying)

= -8

Therefore, the value of the expression is -8, which is a single rational number.

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Answer:

X = 65°

Y = 75°

Z = 65°

Step-by-step explanation:

Hello!

Angle Y and the angle measuring 75 degrees are corresponding angles, and corresponding angles are congruent to each other in degree measure.

There is also another set of corresponding angles, and those are Angle Z and Angle X.

Since Angle Y and 75° are corresponding, we can state that Angle Y is also 75°. We can now find Angle Z by subtracting 40° and 75° from 180°. This is because the sum of angles in a triangle is 180°.

The measure of Angle Z is 65°. We know that Z and X are corresponding, so X is also 65°.

Therefore, the probability of exactly 5 cars arriving over a 5-minute interval during rush hour is approximately 0.017 or 1.7%.

To solve this problem, we first need to determine the rate of cars arriving per minute. We can do this by dividing 25 cars by 11 minutes, which gives us a rate of approximately 2.27 cars per minute.

Next, we need to use the Poisson distribution formula to calculate the probability of exactly 5 cars arriving over a 5-minute interval. The Poisson distribution is used to model the probability of a certain number of events occurring within a given time frame when those events occur randomly and independently of each other.

The formula for the Poisson distribution is:

[tex]P(X = k) = (e^-lambda * lambda^k) / k![/tex]

Where:
- P(X = k) is the probability of k events occurring within the specified time frame
- e is Euler's number (approximately equal to 2.718)
- λ is the average rate of events occurring per unit of time (in our case, 2.27 cars per minute)
- k is the number of events we want to calculate the probability for
- k! is the factorial of k (i.e., k! = k * (k-1) * (k-2) * ... * 2 * 1)

Plugging in the values we have, we get:

[tex]P(X = 5) = (e^-2.27 * 2.27^5) / 5![/tex]
P(X = 5) = (0.040 * 51.84) / 120
P(X = 5) = 0.017

Therefore, the probability of exactly 5 cars arriving over a 5-minute interval during rush hour is approximately 0.017 or 1.7%.

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The probability that exactly five cars will arrive over a 5-minute interval during rush hour is approximately 0.0126 or 1.26%.

To solve this problem, we will use the Poisson distribution formula.

Calculate the average arrival rate (λ) for a 5-minute interval.
Since 25 cars arrive in 11 minutes, we can find the rate per minute as follows:
(25 cars) / (11 minutes) ≈ 2.27 cars per minute
For a 5-minute interval, multiply the rate per minute by 5:
(2.27 cars per minute) × (5 minutes) ≈ 11.36 cars.

Use the Poisson distribution formula to find the probability.
The Poisson distribution formula is:
[tex]P(x) = (e^{-\lambda} *  (\lambda^x)) / x![/tex]
In this problem, x = 5 (exactly five cars) and λ ≈ 11.36.
Calculate the probability.
P(5) = (e^(-11.36) × (11.36^5)) / 5!
P(5) ≈ 0.0126.

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