please bold the answers and show work aswell

Based on the information given, we can use the Pythagorean theorem to determine the distance traveled by the northbound car.

Let's denote the distance traveled by the northbound car as 'x' kilometers.

According to the Pythagorean theorem, in a right triangle, the square of the hypotenuse (the straight-line distance between the two cars) is equal to the sum of the squares of the other two sides (the distances traveled by each car).

In this case, the northbound car's distance is 'x' kilometers and the eastbound car's distance is 5 kilometers.

So we have the equation:

x^2 + 5^2 = 13^2

Simplifying, we get:

x^2 + 25 = 169

Subtracting 25 from both sides, we get:

x^2 = 144

Taking the square root of both sides, we get:

x = 12

So the northbound car has traveled 12 kilometers.

Answer: 12 km

Step-by-step explanation:

As seen in the figure the distance that the northbound car traveled equals to the distance from point N to the parking lot.

pythagorean: [tex]\sqrt{13^{2}-5^{2} }=12km[/tex]

to find the mean you add al the numbers together and divide it by how many numbers there were. so to find the mean it would be (682+612+756+674+714+790+668+652+776)÷9=702.6 which can be rounded up to 703. Also pls mark as brainliest answer

Therefore , the solution of the given problem of percentage comes out to be D) 28% is the right response.

The shorthand "a%" is used in statistics to represent a number or metric that may be expressed as a percentage of 100. Additionally strange spelling include "pct," "pct," as "pc." The approach that is most frequently employed for this is the percentage symbol ("%"). Any hints or set proportions of any part for the total are also unknown. Since numbers commonly add up to 100, they are effectively integers.

Here,

According to the facts provided, 30% of the male population and 60% of the people in Math Town are male.

This suggests that between 30% and 60% of people have brown eyes.

Let's figure out what proportion of the entire population is equal to 30% of 60%:

=> 30% of 60% = (30/100) * (60/100)

=>  0.3 * 0.6

=>  0.18 or 18%

Therefore, brown eyes are present in Math Town's overall population of 18%.

Since the only other gender listed is females and we are aware that 18% of the population as a whole has brown eyes, we can infer that 18% of women also have brown eyes.

Therefore, D) 28% is the right response.

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Answer:

21.8 - 0.1 = 21.7

21.7 is 0.1 less than 21.8

Answer:

The answer is 21.7

Step explanation

21.8 - 0.1 = 21.7

I hope it helped you.

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The three consecutive integers are 18, 19, and 20.

Consecutive integers are integers that follow each other in order, without any gaps, and differ by 1. For example, 3, 4, and 5 are consecutive integers because they follow each other in order and differ by 1.

Let's assume that the three consecutive integers are x, x+1, and x+2. Then, according to the problem statement:

4x + (x+2) = 92

Simplifying this equation, we get:

5x + 2 = 92

Subtracting 2 from both sides, we get:

5x = 90

Dividing both sides by 5, we get:

x = 18

Therefore, the three consecutive integers are 18, 19, and 20. We can check that these integers indeed satisfy the condition given in the problem:

4 times the first integer is 4*18 = 72, and when we add the third integer 20 to it, we get 72 + 20 = 92, as required.

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63% of people Surveyed shop at a local grocery store.

A number can be expressed as a fraction of 100 using a percentage. The word "%" stands for percentage.

For instance, 50% represents 50 out of 100, or 0.5 in decimal form. Frequently, proportions, rates, and changes in quantity are represented as percentages.

In many aspects of daily life, including the calculation of sales tax, loan interest rates, and price discounts, percentages are frequently utilised. They are also employed in many academic disciplines, including math, physics, economics, and statistics.

The equality of two ratios is referred to as a percentage in mathematics. A ratio is a comparison of two amounts or values;

it is frequently stated as a fraction.

For instance, "3/5" can be used to represent the proportion of boys to girls in a classroom.

An assertion of equality between two ratios is a proportion.

For instance, the ratio of males to girls is the same as the ratio of boys to all pupils,

hence the sentence "3/5 = 6/10" is a proportion.

Analysis: -

people surveyed at store = 45

total no. of people = 72

the

Percent of peopla = 45/72  x100

= 0.625 × 100

= 62.5 %

= 63 %

63% of people Surveyed shop at a local grocery store.

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The function has a vertical asymptote at x = 1, x-intercepts are x = 1 and x = 5, hole at x = 5 and horizontal asymptote is y = 0.

A rational function is a function that can be expressed as the ratio of two polynomial functions. In other words, it is a function of the form f(x) = p(x)/q(x), where p(x) and q(x) are polynomial functions and q(x) is not equal to zero for any value of x.

To plot the rational function f(x) = (x² - 6x + 5)/(-x + 1)

Vertical asymptote: The denominator of the function (-x + 1) is equal to zero when x = 1.

Therefore, there is a vertical asymptote at x = 1.

x-intercept: To find the x-intercept, we set the numerator equal to zero and solve for x:

x² - 6x + 5 = 0

This quadratic equation can be factored as:

(x - 5)(x - 1) = 0

Therefore, the x-intercepts are x = 1 and x = 5.

y-intercept: To find the y-intercept, we set x equal to zero:

f(0) = (0² - 6(0) + 5)/(-0 + 1) = 5

Therefore, the y-intercept is (0, 5).

Hole: The function has a hole at x = 5 because both the numerator and the denominator become zero at x = 5.

Horizontal asymptote: To find the horizontal asymptote, we need to compare the degrees of the numerator and the denominator. The degree of the numerator is 2 and the degree of the denominator is 1, so the horizontal asymptote is y = 0.

Now, we can plot the function by choosing some values of x and calculating the corresponding values of y:

x y = f(x)

-1 4

0 5

0.5 3.25

1 undefined

2 -1

Image is attached below.

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a. It will take 7 months to pay off the credit card. b. it will take 4 months to pay off the credit card.

APR stands for Annual Percentage Rate. It is the interest rate charged on a loan or credit card, expressed as a yearly percentage rate. The APR takes into account not only the interest rate, but also any fees or charges associated with the loan or credit card.

a. If you put half of the available money each month toward the credit card, then you are paying $150.00 per month towards the credit card balance. We can use the formula for the present value of an annuity to find how many months it will take to pay off the credit card:

PV = PMT × ((1 - (1 + r)⁻ⁿ) / r)

where:

PV is the present value of the debt

PMT is the payment amount per period

r is the monthly interest rate

n is the number of periods

Substituting the values, we get:

754.43 = 150 × ((1 - (1 + 0.011333)⁻ⁿ) / 0.011333)

Simplifying and solving for n, we get:

n = log(1 + (PV ×r / PMT)) / log(1 + r)

= log(1 + (754.43×0.011333 / 150)) / log(1 + 0.011333)

= 6.18

Therefore, it will take approximately 7 months to pay off the credit card if you put half of the available money each month toward the credit card.

b. If you put all of the available money each month toward the credit card, then you are paying $300.00 per month towards the credit card balance.

754.43 = 300 ×((1 - (1 + 0.011333)⁻ⁿ) / 0.011333)

Simplifying and solving for n, we get:

n = log(1 + (PV × r / PMT)) / log(1 + r)

= log(1 + (754.43× 0.011333 / 300)) / log(1 + 0.011333)

= 3.43

Therefore, it will take approximately 4 months to pay off the credit card if you put all of the available money each month toward the credit card.

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First we turn the 17.2 km into mm. To do that we turn it into 17,200 m then into 1,720,000 cm then into 17,200,000 mm. Then we just divide 17.2 million by 86 so 17,200,000÷86=200,000. so we know that the scale of the map is 1:200,000. Also pls mark as brainliest answer thx.

(a) The total surface area of the triangular prism is 560 in².

(b) The surface area of the cuboid is 944 ft².

(c) The surface area of the cylinder is  678.58 in².

Cuboid;

The surface area of the cuboid is calculated as;

S.A = 2(12 x 16  +  12 x 10  + 16 x 10)

S.A = 944 ft²

Cylinder:

The surface area of the cylinder is calculated as follows;

S.A = 2π x 6 (6 + 12)

S.A = 678.58 in²

The surface area of a triangular prism can be calculated by summing the areas of its individual faces.

A triangular prism has three rectangular faces and two triangular faces.

The formula for the surface area of a triangular prism is:

Surface Area = Area of triangular faces + Area of rectangular faces

To calculate the area of a triangular face, we can use the formula for the area of a triangle:

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

Given that S₁ = 8 in, S₂ = 12 in, S₃ = 8 in, and the length between the two triangular faces is 18 in, we can proceed with the calculations.

The area of the triangular face with dimensions S₁ = 8 in and S₂ = 12 in is:

Area of triangular face 1 = (8 in × 12 in) / 2 = 48 in²

The area of the triangular face with dimensions S₂ = 12 in and S₃ = 8 in is:

Area of triangular face 2 = (12 in × 8 in) / 2 = 48 in²

The area of the triangular face with dimensions S₃ = 8 in and S₁ = 8 in is:

Area of triangular face 3 = (8 in × 8 in) / 2 = 32 in²

Now, let's calculate the area of the rectangular faces.

Area of rectangular face 1 = 18 in × 12 in = 216 in²

Area of rectangular face 2 = 18 in × 12 in = 216 in²

Finally, we can sum up all the areas to get the total surface area of the triangular prism:

Surface Area = Area of triangular faces + Area of rectangular faces

Surface Area = 48 in² + 48 in² + 32 in² + 216 in² + 216 in² = 560 in²

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The mean score is 628.

What is mean?

In statistics, the mean is a measure of central tendency, which represents the average value of a data set. It is also known as the arithmetic mean and is calculated by adding up all the values in the data set and then dividing by the number of observations in the data set. The formula for calculating the mean is:

mean = (sum of all values) / (number of observations)

Now,

To find the mean score, you need to add up the three scores and then divide by 3:

(650 + 600 + 635) / 3 = 628.33

Rounding to the nearest whole point, the mean score is 628.

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Therefore, the correct response From these integral is option D   is.  

``` 10 + ∫₅¹  R(t) dt

An integral is a mathematical construct in mathematics that can be used to represent an area or a generalization of an area. It computes volumes, areas, and their generalizations. Computing an integral is the process of integration.

Integration can be used, for instance, to determine the area under a curve connecting two points on a graph. The integral of the rate function R(t) with respect to time t can be used to describe how much water is present in a tank.

The following equation can be used to determine how much water is in the tank at time t = 5 if there are 10 gallons of water in the tank at time t = 1.

``` 10 + ∫₅¹  R(t) dt

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Answer:

[tex]25.5h = 153[/tex]

[tex]h = 6[/tex]

The height is 6 feet, so A is correct.

The equation of p(x) in vertex form is;

p(x) = 9.67(x + 1.04)² - 10.25

The closest answer choice is:

p(x) = 3(x - 1)²  - 2, which is not correct.

In the context of a quadratic function, the vertex is the highest or lowest point on the graph of the function. It is the point where the parabola changes direction. The vertex is also the point where the axis of symmetry intersects the parabola.

To find the vertex form of the quadratic function p(x), we need to first find the vertex, which is the point where the function reaches its maximum or minimum value.

To find the vertex, we can use the formula:

x = -b/2a, where a is the coefficient of the x²  term, b is the coefficient of the x term, and c is the constant term.

Using the table, we can see that the highest value of p(x) occurs at x = 5, and the value is 46.

We can then use the formula to find the vertex:

x = -b/2a = -5/2a

Using the values from the table, we can set up two equations:

46 = a(5)² + b(5) + c

1 = a(0)²  + b(0) + c

Simplifying the second equation, we get:

1 = c

Substituting c = 1 into the first equation and solving for a and b, we get:

46 = 25a + 5b + 1

-20 = 5a + b

Solving for b, we get:

b = -20 - 5a

Substituting b = -20 - 5a into the first equation and solving for a, we get:

46 = 25a + 5(-20 - 5a) + 1

46 = 15a - 99

145 = 15a

a = 9.67

Substituting a = 9.67 and c = 1 into b = -20 - 5a, we get:

b = -20 - 5(9.67) = -71.35

Therefore, the equation of p(x) in vertex form is:

p(x) = 9.67(x - 5)²  + 1

Simplifying, we get:

p(x) = 9.67(x²  - 10x + 25) + 1

p(x) = 9.67x²  - 96.7x + 250.85 + 1

p(x) = 9.67x²  - 96.7x + 251.85

Rounding to the nearest hundredth, we get:

p(x) = 9.67(x - 5²  + 1 = 9.67(x + 1.04)²  - 10.25

Therefore, the answer is:

p(x) = 9.67(x + 1.04)² - 10.25

The closest answer choice is:

p(x) = 3(x - 1)²  - 2, which is not correct.

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Answer: 76 pages

Step-by-step explanation:

700 photo spaces = 100%

-The total

168 photo spaces = 24%

-The number of empty spaces in the album.

- Find 24% of 700:

70(10%) x 2 = 140

7(1%) x 4 = 28

140 + 28 = 168

532 photo spaces = 76%

- The number of photos in the album

700 - 168 = 532

Finding the number of pages.

-As we know 1 page holds 7 photos, if we had 532 photos we'd have to divide it by 7 to see how many pages all the photos would be held in.

532 ÷ 7 = 76.

Answer: The actual difference between the numbers is:

87.71 - 5.8 = 81.91

Therefore, Yasmine's estimate was 81, and the actual difference between the numbers is 81.91. Brainliest?

Step-by-step explanation:

To round 87.71 to the nearest whole number, we look at the digit in the ones place, which is 1. Since 1 is less than 5, we round down to 87. To round 5.8 to the nearest whole number, we look at the digit in the ones place, which is 8. Since 8 is greater than or equal to 5, we round up to 6.

Using these rounded values, Yasmine estimated the difference between the numbers to be 87 - 6 = 81.

The actual difference between the numbers is:

87.71 - 5.8 = 81.91

Therefore, Yasmine's estimate was 81, and the actual difference between the numbers is 81.91.

Answer:

Yasmine estimated the difference to be 82. The actual difference is 81.91.

Step-by-step explanation:

The rounded whole number of 87.71 is 88 and the rounded whole number of 5.8 is 6.

So, the difference between the numbers 87.71 and 5.8 by rounding each number to the nearest whole numbers will be

(88 - 6) = 82.

The actual difference between the numbers 87.71 and 5.8 is (87.71 - 5.8) = 81.91.

Therefore, Yasmine estimated the difference to be 82. The actual difference is 81.91.

The value or measure of following are :-

x = 17.18°

∠JK = 143.78°

∠MJ = 116.48°

∠LMK = 47.17°

A segment of a circle called an arc is made up of two endpoints on the circle and the curve that connects them.

Since the two lines JL and MK intersect at the center of the circle at point N, the angles formed by them are inscribed angles of the circle. Moreover, the angles formed by an inscribed angle and its corresponding arc are equal. Therefore, we can write:

∠JNK = ½ arc JNK = ½(5x+23)° = 2.5x + 11.5°

∠KNL = ½ arc KNL = ½(17x-41)° = 8.5x - 20.5°

We are also given that arc MNJ and LNK are similar, so their corresponding angles are equal. Similarly, arc MNL and JNK are similar, so their corresponding angles are equal. Let's use these facts to find x:

∠MNJ = ∠LNK

The arc MNJ is equal to the sum of arcs MNL and LNK. Therefore, we have:

½(5x+23)° + ½(17x-41)° = ∠MNJ + ∠LNK

2.5x + 11.5° + 8.5x - 20.5° = 2∠MNJ

11x - 9° = 2∠MNJ

∠MNL = ∠JNK

The arc MNL is equal to the sum of arcs MNJ and JNK. Therefore, we have:

½(5x+23)° + ½(8.5x-20.5°) = ∠MNL + ∠JNK

2.75x + 1.5° = 2∠JNK

1.375x + 0.75° = ∠JNK

Since ∠MNJ = ∠LNK and ∠MNL = ∠JNK, we can write:

2∠MNJ + 2∠JNK = 360°

Substituting the expressions we found for ∠MNJ and ∠JNK, we get:

22x - 18° = 360°

22x = 378°

x = 17.18° (rounded to two decimal places)

Now that we know x, we can find the values of the other angles of arc-

∠JNK = 1.375x + 0.75° = 24.43°

∠KNL = 8.5x - 20.5° = 119.35°

∠MNJ = (11x - 9°)/2 = 92.05°

∠LNK = ∠MNJ = 92.05°

∠MNL = 360° - ∠MNJ - ∠JNK = 243.52°

∠JK = ∠JNK + ∠KNL = 143.78°

∠MJ = ∠MNJ + ∠JNK = 116.48°

∠LMK = 360° - ∠MNJ - ∠JNK - ∠KNL = 47.17°

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The probability that a person who tests positive actually has the disease is ≈0.0158.

        Probability is a way to gauge how likely something is to happen. Many things are difficult to forecast with absolute confidence. Using it, we can only make predictions about the likelihood of an event happening, or how likely it is. Probability can range from 0 to 1, with 0 denoting an impossibility and 1 denoting a certainty. 1 is the probability of every event in a sample space.

    For instance, when we flip a coin, there are just two possible results: Head OR Tail. (H, T). However, if two coins are tossed, there are four possible results: (H, H), (H, T), (T, H), and (T, T).

we solve the given question using BAYE's theorem:

Bayes' Theorem states that the conditional probability of an event, based on the occurrence of another event, is equal to the likelihood of the second event given the first event multiplied by the probability of the first event.

P(disease/positive)= [tex]\frac{P(disease)P(positive/disease)}{P(disease)P(positive/disease)+P(no disease)P(positive/disease)}[/tex]

P(disease/positive)= [tex]\frac{(0.008)(0.04)}{(0.008)(0.04)+(0.992)(0.02)}[/tex]  ≈ 0.0158

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Answer:

Step-by-step explanation:

I think its 42 because 7/20ths of 120 is 42

7/20 x 120 =42

The answers to each question are:

(a)  0.351.

(b)  0.317.

(c)  20.24 years.

(d)  16.

What is the mean and standard deviation?

The standard deviation is a summary measure of the differences of each observation from the mean. If the differences themselves were added up, the positive would exactly balance the negative and so their sum would be zero. Consequently, the squares of the differences are added.

(a) What is the probability that a randomly selected male has growth plates that fuse between the ages of 18 and 20 years?

To answer this question, we need to standardize the values of 18 and 20 using the mean and standard deviation provided. Let X be the age at which growth plates fuse for males. Then,

Z = (X - mean) / standard deviation

Z for X = 18 is (18 - 18.8) / (15.1/12) = -0.53

Z for X = 20 is (20 - 18.8) / (15.1/12) = 0.53

Using a standard normal distribution table or a calculator, we can find the probability of Z being between -0.53 and 0.53, which is approximately 0.351.

Therefore, the probability that a randomly selected male has growth plates that fuse between the ages of 18 and 20 years is 0.351.

(b) What is the probability that a randomly selected male has growth plates that fuse between the ages of 16 and 18 years?

We need to standardize the values of 16 and 18 using the mean and standard deviation provided.

Z for X = 16 is (16 - 18.8) / (15.1/12) = -2.03

Z for X = 18 is (18 - 18.8) / (15.1/12) = -0.53

Using a standard normal distribution table or a calculator, we can find the probability of Z being between -2.03 and -0.53, which is approximately 0.317.

Therefore, the probability that a randomly selected male has growth plates that fuse between the ages of 16 and 18 years is 0.317.

(c) What is the age at which growth plates fuse for the top 5% of males?

We need to find the age X such that the probability of a male having growth plates fuse at an age less than X is 0.95 (since 5% is the complement of 95%).

Using a standard normal distribution table or a calculator, we can find the Z-score corresponding to the 95th percentile, which is approximately 1.645.

Then, we can solve for X using the formula:

Z = (X - mean) / standard deviation

1.645 = (X - 18.8) / (15.1/12)

Simplifying the equation, we get:

X = 18.8 + (1.645)(15.1/12) = 20.24

Therefore, the age at which growth plates fuse for the top 5% of males is approximately 20.24 years.

(d) What percentage of males have growth plates that fuse before the age of 16?

We need to find the probability of a male having growth plates fuse before the age of 16, which is equivalent to finding the probability of Z being less than -2.03 (calculated in part (b)).

Using a standard normal distribution table or a calculator, we can find the probability of Z being less than -2.03, which is approximately 0.0228.

Therefore, approximately 2.28% of males have growth plates that fuse before the age of 16.

hence, the answers to each question are:

(a)  0.351.

(b)  0.317.

(c)  20.24 years.

(d)  16.

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Therefore, the height of the right triangle is 9.6 units.

A triangle is a geometric figure that consists of three line segments that intersect at three endpoints, called vertices. The line segments are called sides, and the vertices where they intersect are called angles. A triangle can be classified based on the length of its sides and the measure of its angles. Triangles are fundamental to many areas of mathematics and physics, and they have a wide range of applications in real-life situations, such as in architecture, engineering, and surveying.

Here,

To find the height of a right triangle, we can use the formula:

h = (a * b) / c

where "a" and "b" are the lengths of the legs of the right triangle, and "c" is the length of the hypotenuse.

In this case, we have a right triangle with legs of lengths 12 units and 16 units, and a hypotenuse of length 20 units. Therefore, we can substitute these values into the formula and solve for the height:

h = (12 * 16) / 20

h = 192 / 20

h = 9.6

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The statements that are always true regarding the given diagram of the triangle are m∠2 + m∠3 = m∠6, m∠3 + m∠4 + m∠5 = 180°, m∠5 + m∠6 = 180°. Therefore, options (4) and (5) are not always true.

An exterior angle of a polygon is an angle that forms a linear pair with an interior angle of the polygon. In other words, it is an angle formed by extending one of the sides of the polygon. For any given vertex of the polygon, the exterior angle is the angle between a line containing the side of the polygon next to the vertex and a line that is an extension of the adjacent side. The measure of an exterior angle is equal to the sum of the measures of its corresponding remote interior angles (interior angles that are not adjacent to the exterior angle). The sum of the exterior angles of any polygon, including a triangle, is always equal to 360 degrees. Exterior angles are used in a variety of geometric proofs and constructions.

We know that the sum of all the interior angles of any triangle is 180 degrees. Therefore, we can use this fact to determine which statements are always true regarding the given diagram.

Now, we can use the following relationships between the interior and exterior angles of a triangle:

Exterior angle = Sum of interior angles adjacent to it

Interior angle = 180  - Exterior angle

Using these relationships, we can determine which statements are always true:

m∠5 + m∠3 = m∠4: This is true because the exterior angle at angle 3 is equal to the sum of angles 3 and 4, and the exterior angle at angle 5 is equal to the sum of angles 5 and 6. Therefore, m∠5 + m∠3 + m∠6 = m∠4 + m∠3, which simplifies to m∠5 + m∠3 = m∠4.

Given m∠3 + m∠4 + m∠5 = 180°: This is true because the sum of all the interior angles of a triangle is 180 degrees.

m∠5 + m∠6 = 180°: This is not always true because sum of all the angles should be 180. It is true in this specific case because angle 1 is a straight angle, which means that m∠5 + m∠6 = 180°. However, in general, this statement is not always true.

m∠2 + m∠3 = m∠6: This is true because the exterior angle at angle 2 is equal to the sum of angles 2 and 6. Therefore, m∠2 + m∠3 = m∠6.

Given m∠2 + m∠3 + m∠5 = 180°: This is may not always true. It is true in this specific case because angle 1 is a straight angle, which means that m∠2 + m∠3 + m∠5 = 180°. However, in general, this statement is not always true.

Therefore, the three statements that are always true from the diagram are:

m∠5 + m∠3 = m∠4

m∠3 + m∠4 + m∠5 = 180°

m∠2 + m∠3 = m∠6

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Answer:

fraction form: 1/20

decimal form:0.05

Experimental and theoretical probabilities do not match; Field Trip B is the most popular with 32% relative frequency.

What is frequency?

Frequency refers to the number of times an event or observation occurs within a given period, sample size, or population. In the context of data analysis, frequency is often used to describe how often a particular value or category appears in a dataset or sample. It can be expressed as an absolute frequency (the actual number of times an event occurred) or a relative frequency (the proportion or percentage of times an event occurred compared to the total number of observations).

The experimental probability of selecting each field trip can be calculated by dividing the number of times each trip was selected by the total number of spins. For example, the experimental probability of selecting Field Trip A is 8/50 = 0.16 or 16%, the experimental probability of selecting Field Trip B is 16/50 = 0.32 or 32%, and so on.

The theoretical probability of selecting each field trip is 1/5 or 0.2 or 20%. This is because the spinner has 5 equal sections, and each section represents a different trip.

The experimental and theoretical probabilities do not match exactly. For example, the experimental  of selecting Field Trip B is 0.32 or 32%, while the theoretical probability is only 0.2 or 20%. This could be due to chance or random variation, as the teacher only spun the spinner 50 times. With a larger sample size, the experimental and theoretical probabilities should converge closer to each other.

The relative frequency of selecting each field trip can be calculated by dividing the number of times each trip was selected by the total number of spins, and then multiplying by 100 to express it as a percentage. For example, the relative frequency of selecting Field Trip A is (8/50) x 100 = 16%, the relative frequency of selecting Field Trip B is (16/50) x 100 = 32%, and so on.

Based on the data, Field Trip B appears to be the most popular, as it was selected the most number of times (16 times out of 50 spins).

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Commplete Question:

A science teacher uses a fair spinner to simulate choosing one of five different field trips for her classes. The spinner has 5 equal sections, each representing a different trip. The teacher spins the spinner 50 times and records the results in the table below:

Field Trip Number of times selected

A                8

B                16

C               9

D                12

E                5

Apply math models to analyze the data and answer the following questions:

What is the experimental probability of selecting each field trip?

What is the theoretical probability of selecting each field trip?

Do the experimental and theoretical probabilities match? If not, what could be the reason for the difference?

What is the relative frequency of selecting each field trip?

Based on the data, which field trip appears to be the most popular?

Answer:

Step-by-step explanation:

You want three equations that can be used to solve for the length (y) of a room that is whose width is 5 feet less than its length and whose area is 750 square feet.

The area of the room is the product of its length and width. We are given that the length is y, so the width is (y-5) and that product is ...

  A = LW

  750 = y(y -5)

This equation can be rearranged into several different forms:

  y² -5y = 750 . . . . . . . multiply it out

  750 -y(y -5) = 0 . . . . . subtract the right side expression

  (y +25)(y -30) = 0 . . . . factor it

Answer: 0.6954

Step-by-step explanation:

To find the area between two z scores, in this case P(-0.82<z<1.29), we can either use a z score calculator or a standard normal distribution table, which I will use for this.  

The probability of P(-0.82<z<1.29) = P(z<1.29)-(z<-0.82).

To find P(z<2.01), we use a positive z score standard normal distribution table and find that P(z<1.29)=0.9015

Using a negative z score standard normal distribution table, we can find that (z<-0.82)=0.2061.

So,  P(-0.82<z<1.29) = P(z<1.29)-(z<-0.82)=0.6954.

The type of the relation are

A linear expression is an algebraic expression in which each term has a degree of 1 (or 0), and the variables are raised only to the first power.

In the given expressions:

Therefore, the linear expressions are "5x", "6x + 1", and "17". The nonlinear expressions are "10xy" and "4x^2".

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Answer: 46 ft by 92 ft

Step-by-step explanation:

The largest area is enclosed when half the fence is used parallel to the wall and the other half is used for the two ends of the fenced area perpendicular to the wall. Half the fence is 184 ft/2 = 92 ft. Half that is used for each end of the enclosure.

Step-by-step explanation:

6^2 / 6^1   x    6^12 / 6^8   =

6^(2-1)      x    6^(12-8)   =

6^1          x    6^4   =

6^(1+4)  =   6^5     or  = 7776