Find 175.7% of 163. Round to the nearest tenth.

Comparing the estimated probabilities with the actual probability, we can see that Keeley had the best estimate for the probability.

a) To find out who had the best estimate for the probability of the spinner landing on 2, we need to compare their estimated probabilities with the actual results. The actual probability of the spinner landing on 2 can be found by dividing the total number of times it landed on 2 by the total number of spins.

Sam's estimated probability = 21/80 = 0.2625
Keeley's estimated probability = 20/50 = 0.4
Cody's estimated probability = 23/70 = 0.3286

The actual probability of the spinner landing on 2 = (21+20+23)/(80+50+70) = 0.315



b) To work out the estimated probability of the spinner landing on 2 by combining all of their results, we need to add up the total number of times the spinner landed on 2 and divide it by the total number of spins.

Total number of times the spinner landed on 2 = 21 + 20 + 23 = 64
Total number of spins = 80 + 50 + 70 = 200

Estimated probability of the spinner landing on 2 = 64/200 = 0.32

c) Using the combined results will give a better estimate than using only one person's results. This is because combining the results gives a larger sample size, which makes the estimate more accurate and reliable.

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Answer/Step-By-Step Explanation:

Part A:

To determine the measure of angle A (m/A), we can use the Law of Cosines, which states that:

c^2 = a^2 + b^2 - 2ab*cos(A)

where c is the length of the side opposite angle C, and a and b are the lengths of the other two sides.

Substituting the given values, we have:

(32)^2 = (16)^2 + (16√5)^2 - 2(16)(16√5)*cos(A)

Simplifying:

1024 = 256 + 1280 - 512√5*cos(A)

512√5*cos(A) = 512

cos(A) = 1/√5

Using a calculator, we find:

A ≈ 63.43 degrees

Therefore, m/A ≈ 63.43 degrees.

Part B:

To use the unit circle to find tan A, we first draw a unit circle with its center at the origin of a coordinate plane. We then draw a ray from the origin through the point (1,0) on the circle, which corresponds to the angle of 0 degrees.

Next, we draw another ray from the origin through the point on the circle that corresponds to angle A. This ray intersects the circle at a point (x,y), where x = cos(A) and y = sin(A).

Since cos(A) = 1/√5, we have:

x = cos(A) = 1/√5

To find y, we use the Pythagorean theorem:

x^2 + y^2 = 1

Substituting x = 1/√5, we get:

(1/√5)^2 + y^2 = 1

y^2 = 4/5

y = ± 2/√5

Since angle A is in the first quadrant, we take y = 2/√5.

Therefore, tan(A) = y/x = (2/√5)/(1/√5) = 2.

Part C:

To calculate the area of triangle AABC, we can use Heron's formula, which states that:

Area = √(s(s-a)(s-b)(s-c))

where s is the semiperimeter of the triangle, given by:

s = (a+b+c)/2

Substituting the given values, we have:

s = (16+16√5+32)/2 = 24+8√5

Using this value of s, we can calculate the area:

Area = √[(24+8√5)(8√5-8)(8√5)(24-8√5)]

Simplifying:

Area = √[4096] = 64

Therefore, the area of triangle AABC is 64 square inches.

In this problem, we use the tangent function to solve for angle A, understand that the unit circle cannot be directly used to find the tangent of A, and finally find the area of the triangle using the formula 1/2*base*height.

Part A: Assuming triangle AABC is a right triangle, we can determine m∠A by using the tangent function (tan ∠A = opposite side / adjacent side). Here, the opposite side is 'b' and the adjacent side is 'a'. So, m∠A = tan⁻¹ (b/a) = tan⁻¹ (16 5/16). To get the correct result, we then use a calculator with the inverse tangent or arctan function.

Part B: The unit circle is a fundamental tool in trigonometry. But in this case, having calculated m∠A in Part A, we cannot directly use the unit circle to find tan A as tan A is not represented on the unit circle.

Part C: The area of a triangle can be calculated using the formula 1/2*base*height. In a right triangle, this can be represented as 1/2*a*b: 1/2*16*16 5 = 130 square inches.

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The probability that the sample mean will fall within $600 of the population of average family income mean is 0.3203 or 32.03%.

Population standard deviation = σ = $4800

Sample size = n = 225

Difference between the sample mean and population mean = d = $600

We need to find the probability that the sample mean will fall within $600 of the population mean.

We can use the z-score formula for sample means to find this probability:

z = (x - μ) / (σ / √n)

where z is the z-score, x is the sample mean, μ is the population mean, σ is the population standard deviation, and n is the sample size.

Substituting the given values, we get:

z = ($600) / ($4800 / √225)

z = 0.75

Using the standard normal distribution table or calculator, we can find the probability that z is between -0.75 and 0.75:

P(-0.75 < z < 0.75) = 0.5469 - 0.2266 = 0.3203

Therefore, the probability that the sample mean will fall within $600 of the population of average family income mean is 0.3203 or 32.03%.

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The vertex of the function g(x) = 3[tex]x^{2}[/tex] - 12x + 7 is at (2, -5).

The vertex of a parabola in the form of y = a[tex]x^{2}[/tex] + bx + c can be found using the formula x = -b/2a for the x-coordinate of the vertex and then substituting this value into the equation to find the y-coordinate.

For the function g(x) = 3[tex]x^{2}[/tex] - 12x + 7, we can see that a = 3 and b = -12. We can use the formula to find the x-coordinate of the vertex:

x = -b/2a = -(-12)/(2*3) = 2

So the x-coordinate of the vertex is 2. To find the y-coordinate, we can substitute x = 2 into the equation:

g(2) = 3 [tex](2)^{2}[/tex]- 12(2) + 7 = -5

Therefore, the vertex of the function g(x) = 3[tex]x^{2}[/tex] - 12x + 7 is at (2, -5).

So the correct answer is (c) (2, −5).

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Answer: 12800 cm³

Step-by-step explanation:

Area of Rectangular Prism = [tex]lwh[/tex]

A = 32 x 25 x 16

A = 12800

A total of 336 tubs of cookie dough were sold in all.

A ratio or figure stated as a fraction of 100 is called a percentage. The sign "%" is frequently used to indicate it as a percentage or a component of a total.

So, the number of tubs sold in each week can be represented by the following sequence:

Week 1: 100

Week 2: 0.8(100) = 80

Week 3: 0.8(80) = 64

Week 4: 0.8(64) = 51.2 ≈51

Week 5: 0.8(51) = 40.8≈41

To find the total number of tubs sold in all 5 weeks, we can add up the number of tubs sold in each week:

Total = 100 + 80 + 64 + 51 + 41

Total = 336

Therefore, a total of 336 tubs of cookie dough were sold in all.

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Mikey needs to save for at least 9 weeks to buy the bike.

What is inequality?

An inequality is a mathematical statement that compares two values, indicating that they are not equal. It uses symbols such as <, >, ≤ (less than or equal to), or ≥ (greater than or equal to) to express the relationship between the two values.

Let's call the number of weeks that Mikey needs to save "w". We can set up an equation using the given information:

$25 x w > $200

Simplifying this inequality, we get:

w > 8

This means that Mikey needs to save for more than 8 weeks to have more than $200. Since the number of weeks has to be a whole number, Mikey needs at least 9 weeks to save enough money to buy the bike.

Therefore, Mikey needs to save for at least 9 weeks to buy the bike.

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The FR of the hydraulic jack is 1.94, the VR is 1.95, and the Efficiency is 90%.

To find the FR, VR, and Efficiency of the hydraulic jack, we can use the following formulas:

FR = (F2 / F1)

VR = (D1 / D2)

Efficiency = (F2 x D2) / (F1 x D1)

where F1 is the input force, D1 is the input distance, F2 is the output force, and D2 is the output distance.

Given:

F1 = 6800N

D1 = 0.76m

F2 = ?

D2 = 0.39m

m = 1162kg

To find F2, we can use the formula for work:

Work input = Work output

F1 x D1 = F2 x D2

(6800N) x (0.76m) = F2 x (0.39m)

F2 = (6800N x 0.76m) / 0.39m

F2 = 13,216.41N

To find VR, we can use the formula:

VR = (D1 / D2) = (0.76m / 0.39m) = 1.95

To find Efficiency, we can use the formula:

Efficiency = (F2 x D2) / (F1 x D1)

Efficiency = (13,216.41N x 0.39m) / (6800N x 0.76m)

Efficiency = 0.90 or 90%

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The metro bus travels 5 miles per gallon of gas.

The formula used to calculate the distance traveled per gallon of gas is number of miles traveled divided by number of gallons used. Therefore, to calculate how far the metro bus travels in one gallon, we use the following formula:

Distance per gallon = Miles Traveled / Gallons Used

Distance per gallon = 275 miles / 55 gallons

Distance per gallon = 5 miles

Therefore, the metro bus travels 5 miles per gallon of gas.

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Answer:

  132 in

Step-by-step explanation:

You want to know the perimeter of a triangle after the dimensions are quadrupled.

"Quadrupled" means "multiplied by 4."

The perimeter is the sum of the lengths of the sides of the triangle:

  P = 8 +10 +15 = 33 . . . . inches

If the sides are quadrupled, it is ...

  P' = 4(8) +4(10) +4(15) = 4(8 +10 +15) = 4(33) = 132 . . . . inches

As you can see, if the sides are quadrupled, the perimeter is quadrupled.

The new perimeter is 132 inches.

Answer:

Step-by-step explanation:

We can use algebra to determine how many years it has been since the cost of a box of pencils was $0.00, and therefore calculate how many years the price has been increasing by $1.10 per year.

Let's say that x is the number of years since the cost of a box of pencils was $0.00.

If the price of a box of pencils is increasing by $1.10 per year, then the cost of a box of pencils x years after it cost $0.00 would be:

$0.00 + ($1.10 * x)

We know that the current cost of a box of pencils is $2.19. Setting this equal to the expression above, we can solve for x:

$0.00 + ($1.10 * x) = $2.19

$1.10 * x = $2.19

x = $2.19 / $1.10

x = 1.99

So, it has been approximately 1.99 years (or just under 2 years) since the cost of a box of pencils was $0.00, and the price of a box of pencils has been steadily increasing by $1.10 per year during that time.

According to the given information the limit of the given equation is 1.25 so the correct answer is option a.

Limit, a closeness-based mathematical notion, is largely used to give values to some functions at locations where none are specified, in a manner that is compatible with neighbouring values.

The value that a function assumes when its input approaches as well as approaches a particular number is really the function's limit. Limits determine continuity, integrals, as well as derivatives. The behaviour of the function at a certain place is always of relevance to the limit of the function.

[tex]\lim_{x \to 3} \frac{x^2-x-6}{x^2 - 2x - 3} \\\\ \lim_{x \to3} \frac{(x-3)(x+2)}{(x-3)(x+1)} \\\\ \lim_{x \to3} \frac{(x+2)}{(x+1)} \\\\$putting the value x=3$\\\\=\frac{3+2}{3+1} \\\\=\frac{5}{4} \\\\=1.25[/tex]

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Triangles ACD and CAB are congruent by SAS, their corresponding sides are equal, so we have:

AB || DC, as required.

What is the congruent angle?

When two parallel lines are cut by a transversal, the angles that are on the same side of the transversal and in matching corners will be congruent.

Corresponding Parts of Congruent Triangles are Equal

AD || BC, AD = CB

Given

1 = 4

From statements 1 and 5, we can conclude that:

ACD is congruent to CAB because they are corresponding angles of parallel lines AD and BC.

If Lines are Parallel, then Alternate Interior Angles are Equal.

ACD = CAB

From statement 4, we know that angles ACD and CAB are equal because AD is parallel to BC. Therefore:

ACD = CAB

Reflexive Property of Equality

AC = AC

From statement 2, we know that segment AC is equal to itself because of the reflexive property of equality. Therefore:

AC = AC

If Alternate Interior Angles are Congruent, then Lines are Parallel.

2 = 3

From statement 3, we know that if alternate interior angles are congruent, then the lines are parallel. Therefore, since ACD = CAB (statement 4) and AC = AC (statement 2), we can apply the SAS (Side-Angle-Side) congruence theorem to triangles ACD and CAB to conclude that they are congruent.

SAS (Side-Angle-Side)

AB || DC

Hence, As a result, since triangles ACD and CAB are congruent by SAS, their corresponding sides are equal, so we have:

AB || DC, as required.

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The probability of having an error when confidence limits are 3 standard deviations far from the mean is approximately 0.27.

Assume that the data is normally distributed. For a normal distribution, approximately 99.7% of the data is within 3 standard deviations of the mean.

As a result, if the lower and upper specification limits are 3 standard deviations away from the mean, they encompass 99.7% of the data.

As a result, there is only a 0.3% chance of an error. Since this is a two-tailed test, the probability of an error on each side is 0.15%

As a result, the probability of an error when the lower and upper specification limits are 3 standard deviations away from the mean is approximately 0.27.

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The mathematical equations of each problem is 24 = 2x - 2, y + 16 = 85, 56 = (1/2)x - 6, x = 1/3 * 12600 and 120 + 50x = 270 and their solution are Sister is 13 years old, Arvin sold 69 cakes yesterday, You have 124 stamps, Chiz earned P4,200 this month and The horse ride lasted for 60 minutes, with 30 minutes being the initial ride and 30 minutes for the additional ride, respectively.

The translation of each problem into a mathematical equation then solution is.

Let x be the age of the sister.

Then, we have the equation:

24 = 2x - 2

Adding 2 to both sides gives:

26 = 2x

Dividing both sides by 2 gives:

x = 13

Therefore, the sister is 13 years old.

Let y be the number of cakes Arvin sold yesterday.

Then, we have the equation:

y + 16 = 85

Subtracting 16 from both sides gives:

y = 69

Therefore, Arvin sold 69 cakes yesterday.

Let x be the number of stamps you have.

Then, we have the equation:

56 = (1/2)x - 6

Adding 6 to both sides gives:

62 = (1/2)x

Multiplying both sides by 2 gives:

x = 124

Therefore, you have 124 stamps.

Let x be the amount Chiz earned this month.

Then, we have the equation:

x = 1/3 * 12600

Simplifying gives:

x = 4200

Therefore, Chiz earned P4,200 this month.

Let x be the number of 10-minute blocks for the additional horse ride time.

Then, we have the equation:

120 + 50x = 270

Subtracting 120 from both sides gives:

50x = 150

Dividing both sides by 50 gives:

x = 3

Therefore, the additional horse ride time was 3 blocks of 10 minutes, or 30 minutes in total. Adding this to the initial 30 minutes gives a total ride time of 60 minutes.

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_____The given question is incomplete, the complete question is given below:

Learning Task 3: Translate each problem into a mathematical equation then

solve:

1. i am 24 years old. My age is 2 less than twice my sister's age.

2. Arvin has a bake shop. He sold 85 cakes today. That is 16 cakes

fewer than yesterday. How many cakes did he sell yesterday?

3. Ann has 56 stamps that is 6 less than one-half of my stamps. How

many stamps do I have

4. This month Chiz eamed only of his earnings last month. If his

eaming last month is P12,600. How much did he earn this month?

5. In Baguio City a horse ride costs P120.00 per person for the first 30

minutes and P50.00 for every additional 10 minutes. If you spent

P270.00 for a horse ride, for how long did you ride?​

Assume that the actual ratio is 0.07. If 310 people are sampled, there is a 0.0716 percent chance that the sample percentage and population proportion will deviate by more than 0.04.

The sample proportion, denoted by p', is an estimate of the population proportion p. The formula for the standard error of p' is:

SE = [tex]\sqrt{[p(1-p)/n]}[/tex]

where n denotes sample size and p denotes population proportion.

In this case, p = 0.07 and n = 310. Therefore, the standard error of p' is:

SE = [tex]\sqrt{[0.07(1-0.07)/310]}[/tex] = 0.019

To find the probability that the sample proportion will differ from the population proportion by more than 0.04, we need to find the probability that |p' - p| > 0.04. We can use the normal distribution to approximate this probability since the sample size is large (n = 310).

The z-score for a difference of 0.04 is:

z = 0.04 / 0.019 = 2.1053 (rounded to four decimal places)

Using a standard normal distribution table, the probability of a z-score being greater than 2.1053 or less than -2.1053 is approximately 0.0358. where n denotes sample size and p denotes population proportion.

P(|p' - p| > 0.04) = 2(0.0358) = 0.0716

Rounding to four decimal places, the probability is 0.0716.

The complete question is;-

A direct mail company wishes to estimate the proportion of people on a large mailing list that will purchase a product. Suppose the true proportion is 0.07. If 310 are sampled, what is the probability that the sample proportion will differ from the population proportion by more than 0.04? Round your answer to four decimal places.

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Step-by-step explanation:

let the number be y

one-third of the number = 1/3 × y = y/3

the total is 3054

therefore,. y/3 = 3054

multiply both sides by 3

y/3 × 3 = 3054 × 3

y = 9162

Thus, the whole number is 9162

3054 is 1/3 of a whole number.

In order to find the whole number, you need to find the other 2/3's. Since we already have the 1/3, we can easily solve this problem.

3054x3 = 9162

3054+3054+3054 = 9162

The whole number is 9162.

Hope this helped!

Answer:

#15 (a)

[tex]{ \sf{a + 2b - c + 4d}} \\ \\ \hookrightarrow \: { \sf{ \binom{4}{6} + 2 \binom{4}{ - 2} - \binom{ - 3}{ - 2} + 4 \binom{5}{1} }} \\ \\ \hookrightarrow \: { \sf{ \binom{4}{6} + \binom{8}{ - 4} + \binom{3}{2} + \binom{20}{4} \: \: \: \: \: \: }} \\ \\ { \sf{ \hookrightarrow \: \binom{4 + 8 + 3 + 20}{6 - 4 + 2 + 4} }} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ { \sf{ \hookrightarrow \: { \boxed{ \binom{45}{8} }}}}[/tex]

#15 (b)

Step-by-step explanation:

15 (a)

if it is a vector

First, we need to multiply each vector component by its corresponding scalar value and then add them together.

a + 2b - c + 4d = (4)(1) + (4)(2) + (-3)(-1) + (5)(4) = 4 + 8 + 3 + 20 = 35

Therefore, the value of a + 2b - c + 4d is 35.

if it is a matrix

we can form a 1x4 matrix for vector a, b, c, and d respectively. We can also form a 4x4 matrix for the scalar values. Then we can perform matrix multiplication as follows:

(4 4 -3 5) (1 0 0 0) (0 2 0 0) (0 0 -1 0) (0 0 0 4)

= (41 + 40 - 30 + 50) (40 + 42 - 30 + 50) (40 + 40 - 3*(-1) + 50) (40 + 40 - 30 + 5*4)

= (4, 8, 3, 20)

Therefore, the value of a + 2b - c + 4d is (4, 8, 3, 20).

15 (b)

To find the product of the two matrices, we need to multiply each element of the first matrix by its corresponding element in the second matrix and add the products. The resulting matrix will be a 2 x 2 matrix.

| 5 -2 | | 2 6 | |(5)(2) + (-2)(5) (5)(6) + (-2)(3)|

| 4 1 | x | 5 3 | = |(4)(2) + (1)(5) (4)(6) + (1)(3)|

Performing the matrix multiplication, we get:

| 5 -2 | | 2 6 | | 10 -12 |

| 4 1 | x | 5 3 | = | 13 27 |

Therefore, the product of the matrices (5 -2, 4 1) and (2 6, 5 3) is the 2 x 2 matrix:

| 10 -12 |

| 13 27 |

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The perimeter of the shape is approximately 314.

The perimeter of a shape made from part of a circle can be found using the formula P = 2πr + 2s, where r is the radius of the circle and s is the length of the straight line segments. For example, if a shape is composed of a semicircle with radius 5 and two straight line segments of length 10, then the perimeter can be calculated as P = 2π(5) + 2(10) = 30π + 20 = 100π. To solve this calculation, we can use the value of π, which is approximately 3.14, to get the approximate perimeter of the shape as 100π ≈ 314.

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Complete question

What is the perimeter of a shape made from part of a circle composed of a semicircle with radius 5 and two straight line segments of length 10?

Answer:

Step-by-step explanation:

x > -12

The probability of reaching into the bag and choosing either a blue or yellow piece of candy is 38/60 or 56%.

What is probability?

The probability of an occurrence is a figure that represents how likely it is that the event will take place. In terms of percentage notation, it is expressed as a number between 0 and 1, or between 0% and 100%. The higher the likelihood, the more likely it is that the event will take place.

Here, we have

Given: a bag has 10 blue,12 green,8 yellow,11 pink, and 10 orange pieces of candy.

The probability of reaching into the bag and choosing a blue piece of candy is 5/10 or 50%.

The probability of reaching into the bag and choosing a yellow piece of candy is 3/5 or 60%.

Hence, the probability of reaching into the bag and choosing either a blue or yellow piece of candy is 38/60 or 56%.

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Multiplying 13 m by itself and multiplying the result by π gives us the area of the sidewalk as A = 530.94 m². We can calculate the area of the sidewalk with A = πr²

The area of the circular sidewalk around the flower bed can be calculated using the formula for the area of a circle: A = πr². To find the radius of the sidewalk, we need to subtract the radius of the flower bed from the diameter of the flower bed and the sidewalk. Therefore, the radius of the circular sidewalk is (19 m - 3 m - 3 m) = 13 m.Using the formula for the area of a circle, we can calculate the area of the sidewalk with A = πr², where r = 13 m. Substituting 13 m for r, we get A = π(13 m)². Multiplying 13 m by itself and multiplying the result by π gives us the area of the sidewalk as A = 530.94 m².

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Answer:An obtuse-angled triangle is a triangle in which one of the interior angles measures more than 90° degrees. In an obtuse triangle, if one angle measures more than 90°, then the sum of the remaining two angles is less than 90°.

Step-by-step explanation:basically its more than 90 degrees

Answer:

An obtuse triangle is a triangle where one of the interior angles measures more than 90°

Here's the tree diagram for the given scenario:

(1) The probability of getting tails and a 3 is the probability of following the path T-3, which is 1/2 x 1/4 = 1/8.

(ii) The probability of getting heads and an even number is the probability of following the path H-2 or H-4, which is 1/2 x 1/2 + 1/2 x 1/2 = 1/2.

(iii) The probability of not getting heads and an even number is the probability of following the paths T-2 or T-4, which is 1/2 x 1/2 + 1/2 x 1/2 = 1/2.

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The given statement "the probability of an earth-impacting asteroid causing a person's death" is empirical probability, which is based on observations and data.

Empirical probability, also known as experimental probability, is based on observations or data. It involves collecting data through repeated trials of an experiment and calculating the probability of an event based on the frequency of its occurrence.

Subjective probability, also known as personal probability, is based on personal judgment or belief. It reflects an individual's degree of belief in the likelihood of an event occurring, based on their own knowledge and experience.

Now, let's classify the statement in the prompt. The statement is "the probability of an earth-impacting asteroid causing a person's death is." We can see that the statement does not specify which type of probability is being used.

In conclusion, probability is a crucial concept in mathematics and science, and there are different types of probability, including classical, empirical, and subjective probability.

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To obtain the remaining funds necessary to purchase the skateboard, Seth must labor for 13 hours at a rate of $7.25 per hour.

To find out how many hours Seth needs to work to earn the remaining money, we need to first calculate how much money he still needs to earn:

Money needed = Cost of skateboard - Money in the bank

Money needed = $167 - $72.75

Money needed = $94.25

Now we can use Seth's hourly rate to figure out how many hours he needs to work to earn the remaining money:

Hours needed to work = Money needed / Hourly rate

Hours needed to work = $94.25 / $7.25 per hour

Hours needed to work = 13 hours (rounded up to the nearest hour)

Therefore, Seth needs to work for 13 hours at $7.25 per hour to earn the remaining money needed to buy the skateboard.

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Answer:

45x261

Step-by-step explanation:

261

x45

---------

11745

The frequency for boys is 16% and the frequency for girls is 19%. Adding these two values together gives us the marginal relative frequency of 16%.

The marginal relative frequency of students who prefer swimming as their preferred type of exercise is 16%. Marginal relative frequency is a measure of the proportion of a certain group in relation to the total population. In this case, the marginal relative frequency of students who prefer swimming as their preferred type of exercise is 16%, which means that out of the total population of students, 16% prefer swimming as their preferred type of exercise.To calculate this, we need to add up the frequency of swimming for boys and girls. The frequency for boys is 16% and the frequency for girls is 19%. Adding these two values together gives us the marginal relative frequency of 16%.

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Answer:

[tex]\left(\begin{array}{cc}0&24\\13&27\end{array}\right)[/tex]

Step-by-step explanation:

I will attempt to explain using the following example. Let us consider the  product (multiplication) of the following matrices:

[tex]\left(\begin{array}{cc}a_{1,1}&a_{1,2}\\a_{2,1}&a_{2,2}\end{array}\right) \cdot \left(\begin{array}{cc}b_{1,1}&b_{1,2}\\b_{2,1}&b_{2,2}\end{array}\right) = \left(\begin{array}{cc}c_{1,1}=c_{1\times 1}&c_{1,2}=c_{1\times2}\\c_{2,1}=c_{2\times1}&c_{1,2}=c_{2\times2}\end{array}\right)[/tex]

Note that the first number in each coefficient refers to the row number, while the second number refers to the column number.

Then [tex]a_{2,1}[/tex] indicates the element in the second row and first column.

To calculate the product of two matrices, we need to multiply each row of the first matrix by each column of the second matrix.

Example:

[tex]c_{1,1}= (a_{1,1} \cdot b_{1,1} + a_{1,2} \cdot b_{2,1})[/tex]

Now, we can apply this to the original exercise:

[tex]\left(\begin{array}{cc}5&-2\\4&1\end{array}\right) \left(\begin{array}{cc}2&6\\5&3\end{array}\right) =\left(\begin{array}{cc}c_{1,1}&c_{1,2}\\c_{2,1}&c_{2,2}\end{array}\right)[/tex]

Next, we will calculate each value of c using the multiplication process we just discussed.

[tex]c_{1,1}= (5(2)+-2(5)) = 10-10 =0\\c_{1,2}= (5(6)+-2(3)) = 30-6 =24\\c_{2,1}= (4(2)+1(5)) = 8+5 =13\\c_{2,2}= (4(6)+1(3)) = 24+3 =27\\[/tex]

Thus, we have obtained the final result of the matrix product:

[tex]\left(\begin{array}{cc}5&-2\\4&1\end{array}\right) \left(\begin{array}{cc}2&6\\5&3\end{array}\right) =\left(\begin{array}{cc}0&24\\13&27\end{array}\right)[/tex]

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