A large school district held a district-wide track meet for all high school students.
for the 2-mile run, the population of female students participating had a mean running time of 8.8 minutes with standard deviation of 3.3 minutes, and the population of male students participating had a mean running time 7.3 minutes with standard deviation of 2.9 minutes.
suppose 8 female students and 8 male students who participated in the 2-mile run are selected at random from each population.
let x-barm represent the sample mean running time for the male students, and let x- barf represent the sample mean running time for the female students. what are the mean and standard deviation of the sampling distribution of the difference in sample means x-barm-x-barf?
a. 0.4 & 4.042.
b. 1.5 & 1.553.
c. 0 -1.5 & 2.413.
d. 1.5 & 2.413.
e. -1.5 & 1.553.

The value of the SW is 12 units.

What is a chord in a circle?

The chord of a circle can be defined as the line segment joining any two points on the circumference of the circle. It should be noted that the diameter is the longest chord of a circle that passes through the center of the circle.

Since we want to find SW to get SV, we can change SW to x.

We already know the other lengths:

ST = 3

SU = 18

SW=x

SV=x-3

So, 3(18)=x(x-3).

From here, we see that when expanded, this becomes 54 = x² - 3x.

Solving the quadratic, we see that SW is 12, therefore SV is 9.

Hence, the value of the SW is 12 units.

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complete question: Let TU and VW be chords of a circle, which intersect at S, as shown. If ST = 3, TU = 15, and VW = 3, then find SW.

$39.99+238.8+1.75x and  $4.99=1.99x+$40 are the algebraic expressions of given data.

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

Given that $39.99 /month, unlimited texting , 120MB data (Overages $1.99 /MB talk is $1.75 /minutes

$39.99+120(1.99)+1.75x

$39.99+238.8+1.75x

$4.99 /month, unlimited texting ,$40 for 80MB data talk is $1.99 /minutes

$4.99+1.99x+$40

Hence, $39.99+238.8+1.75x and  $4.99+1.99x+$40 are the algebaic expressions of given data.

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Since 4x2+1 cannot equal 0, the solution to the above expressions issue indicates that (4x20+1) has no real factors.

It is necessary to substitute a number for each variable and conduct arithmetic operations in order to verify an algebraic equation. The response variable in the example above is comparable to 6, as 6 plus 6 = 12. Knowing the values of the variables will enable us to replace the original values with those known, allowing us to evaluate the expression.

Here,

It is significant to remember that the current ratio of a term's coefficient

Words 8x3 and 2x have a coefficient ratio of 8:2 (4:1), whereas phrases 12x2 and 3 have a coefficient ratio of 12:3 (4:1) This implies that the original sentence should be divided into the following categories: This indicates that the original phrase, which is written as, should be combined as follows:

=> (8x³+2x)(12x²+3)=2x(4x²+1))3(4x²+1),

before figuring out that (4x2+1)=(2x3)(4x2+1) is the common component.

Since 4x2+1 cannot equal 0 due to the fact that 4x20 for x R, (4x20+1) has no real factors. Since 4x2+1 cannot equal 0, the solution to the above expression issue indicates that (4x20+1) has no real factors.

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Answer:

[tex]df = \sqrt{ {29}^{2} - {20}^{2} } = 21 \\ \sin(d) = \frac{20}{29} \\ \cos(d) = \frac{21}{29} \\ \tan(d) = \frac{20}{21} \\ \sin(e) = \frac{21}{29} \\ \cos(e) = \frac{20}{29} \\ \tan(e) = \frac{21}{20} [/tex]

Answer:

Step-by-step explanation:

First, use the pythagorean theorem to complete the vales of each sides of the triangle. Then, use the respective trigonometric formulas and inverse the answer to compute the degree of every corners.

Answer:

To prove that the measure of angle RST is greater than the measure of angle R, we can use the following steps:

By the definition of a triangle, angle RST is supplementary to angles R, S and T.

Since RT > ST, we can conclude that angle R is less than angle S.

Since angle RST is supplementary to angles R and S, the measure of angle RST is greater than the measure of angle R.

This can be written as measure of angle RST = measure of angle R + measure of angle S > measure of angle R

So, we've proven that if RT > ST in triangle RST, then measure of angle RST > measure of angle R.

Proof by contradiction could also be used to prove that if RT > ST in triangle RST, then measure of angle RST > measure of angle R.

Assume that the measure of angle RST <= measure of angle R. By the triangle inequality theorem, we know that RT + ST > R. But we are given that RT > ST, so RT + ST > RT > R which is a contradiction. Therefore, measure of angle RST must be greater than measure of angle R.

The population next year is 240792

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

Initial population = 237,000

Rate = 1.6% per year

The population next year can be calculated as

Population = Initial * (1 + Rate)

Substitute the known values in the above equation, so, we have the following representation

Population = 237000 * (1 + 1.6%)

Evaluate

Population = 240792

Hence, the new population is 240792

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In graph theory, a 2-factor is a subgraph of a given graph that includes every vertex of the original graph and has the property that every vertex has even degree (i.e. degree is a multiple of 2).

The term "2-factor" is used because it is a factor of the original graph that is made up of edges and every vertex has degree 2.

A 2-factor can also be defined as a set of cycles that cover all vertices of the graph. In other words, it is a collection of cycles such that every vertex belongs to exactly one cycle. A 2-factor can also be thought of as a cycle cover of a graph.

A graph that has a 2-factor is called a 2-factorizable graph. Not all graphs are 2-factorizable, for example a graph with an odd number of vertices can't have a 2-factor.

2-factors have many applications in various fields such as scheduling, coding theory, and computer science. They are also used to study the connectivity and robustness of graphs.

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We need to set the function equal to zero.

x² - 3x - 10 = 0

x = 5

x = -2

The answer is -2, 5

Answer:

4 and 7

Step-by-step explanation:

7-4=3

4x7=28

So, on solving the provided question we can say that in the function we have m = 500, after 500 miles of driving, the expenses of the 2 plans are equal.

The subject of mathematics includes quantities and their variations, equations and related structures, shapes and their locations, and places where they can be found. The term "function" refers to the relationship between a set of inputs, each of which has an associated output. A connection between inputs and outputs in which each input leads to a single, distinct result is known as a function. Each function is given a domain and a codomain, or scope. Usually, f is used to denote functions (x). input is an x. There are four main types of functions accessible. based on the following factors: on functions, one-to-one functions, many-to-one functions, inside functions, and on functions.

f(m) = .2m + 75

f(m) = .35m

.2m + 75 = ,35m

.15m = 75

m = 500

After 500 miles of driving, the expenses of the 2 plans are equal.

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P( X < 9.85 or X > 10.15 ) ≈ 0.3171 up to four decimal places.

P( X < 9.85 or X > 10.15 ) ≈ 0.0027 up to four decimal places.

The simple definition of probability is the likelihood that something will occur. We can discuss the probabilities of different outcomes, or how likely they are if we are unclear about how an event will turn out. Statistics refers to the study of occurrences subject to probability.

According to the question

a) Assuming that X is the random variable that takes the place of the number of defectives and has a normal distribution with a mean of 10 ounces and a standard deviation (σ) of 0.15.

The random variable's values deviate from the mean by 1, causing them to either exceed or fall short of (10 + 0.15) and (10-0.15)

= 10.15 or 9.85.

The following formula may be used to determine the likelihood that there will be either more or lesser defects than the range of 10.15 to 9.85:

P( X < 9.85 or X > 10.15 ) = 1 - P [tex](\frac{9.85-10}{0.15} < \frac{X-10}{0.15} < \frac{10.15-10}{0.15} )[/tex]

P( X < 9.85 or X > 10.15 ) = 1 - φ(1) - φ(-1)

Now we calculate the value of z for z = 1 and z = -1; we have: 0.841345 and 0.158655 respectively

P( X < 9.85 or X > 10.15 ) = 1 - (0.841345 - 0.158655)

P( X < 9.85 or X > 10.15 ) = 0.31713

P( X < 9.85 or X > 10.15 ) ≈ 0.3171 up to four decimal places.

b) It is possible to lower the process standard deviation to 0.05 by making modifications to the process design.

The following formula may be used to determine the likelihood that the number of defectives is either larger than 10.15 or lesser than 9.85:

P( X < 9.85 or X > 10.15 ) = 1 - P  [tex](\frac{9.85-10}{0.15} < \frac{X-10}{0.15} < \frac{10.15-10}{0.15} )[/tex]

P( X < 9.85 or X > 10.15 ) = 1 - φ(3) - φ(-3)

Now we calculate the value of z for z = 3 and z = -3; we have: 0.99865 and 0.00135 respectively

P( X < 9.85 or X > 10.15 ) = 1 - (0.99865 - 0.00135)

P( X < 9.85 or X > 10.15 ) = 0.00271

P( X < 9.85 or X > 10.15 ) ≈ 0.0027 up to four decimal places.

(c) What is the benefit of increasing the number of standard deviations from the mean for process control limits by minimizing process variation?

As we can see from the reduction from a to b above, the key benefit of minimizing process variance is that it will decrease the likelihood of receiving a defective item.

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On solving the provide question, we can say that the correct number of significant figures, the area should be expressed as 5 cm and 10 dm and 2500 mm and 750 cm

The number of significant digits in a value—often a measurement—contributes to the accuracy of the value. From the first non-zero digit, begin counting the important digits. To the right of the last non-zero decimal place, all zeros are acceptable. For instance, the number 0.0079800 has five significant digits. When they come from the measurement, any zeros to the right of the final non-zero digit are important. equivalently rounds an integer to 3 significant digits and 3 decimal places. Start counting at the first non-zero digit and go up to three. After that, remove the final digit. Add zeros to the last two numbers to the right of the decimal point.

he sides of a rectangular piece of plywood as =  3.7 cm and 4.85 cm

the correct number of significant figures, the area should be expressed as

1. 5 cm

2. 10 dm

3. 2500 mm

4. 750 cm

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List pairs of corresponding parts of congruent triangles by determining congruent sides, angles, and vertices from the triangle congruence statement.

What is congruent triangles ?

Congruent triangles are triangles that have the same size and shape. They can be matched up exactly, side-by-side, with no gaps or overlaps.

To list the six pairs of corresponding parts of congruent triangles using the triangle congruence statement, we can use the following steps ,

Begin by stating that the two triangles are congruent, using the triangle congruence statement such as "Triangles ABC and DEF are congruent by ASA, SAS, or SSS."

From the statement, we can determine the pairs of corresponding sides by noting which sides are congruent. For example, if the statement is "Triangles ABC and DEF are congruent by ASA," we know that angle A in triangle ABC is congruent to angle D in triangle DEF, angle B in triangle ABC is congruent to angle E in triangle DEF and side AC in triangle ABC is congruent to side DE in triangle DEF

Next, we can determine the pairs of corresponding angles by noting which angles are congruent. For example, if the statement is "Triangles ABC and DEF are congruent by SAS," we know that side AB in triangle ABC is congruent to side DE in triangle DEF, side BC in triangle ABC is congruent to side EF in triangle DEF, and angle A in triangle ABC is congruent to angle D in triangle DEF.

List pairs of corresponding parts of congruent triangles by determining congruent sides, angles, and vertices from the triangle congruence statement.

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The values of x and y are 1.8 units and 1.2 units respectively.

A perpendicular bisector is a line that bisects a line segment in two equal parts and makes an angle of 90° at the point of intersection. In other words, we can say that a perpendicular bisector divides a line segment at its midpoint making an angle of 90°.

Given that, RT = 15x + 5y, RS = 20x - 5y, WT = 40 and ST=21.

Here, RS=RT+ST

20x-5y=15x+5y+21

5x-10y=21 -------(I)

RT=ST

15x+5y=21 -------(II)

Multiply equation (II) by 2, we get

30x+10y=42 -------(III)

Add equation (I) and (III), we get

5x-10y+30x+10y=21+42

35x=63

x=63/35

x=9/5

x=1.8 units

Substitute x=1.8 in equation (I), we get

5(1.8)-10y=21

y=1.2 units

Therefore, the values of x and y are 1.8 units and 1.2 units respectively.

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The range of the function is given by set A = { -11 , -9 , -7 , -5 , -3 }

The domain of a function is the set of values that we are allowed to plug into our function. This set is the x values in a function such as f(x). The range of a function is the set of values that the function assumes. This set is the values that the function shoots out after we plug an x value in.

The range is the set of outputs of a relation or function. In other words, it's the set of possible y values. Recall that ordered pairs are of the form (x,y) so the y coordinate is listed after the x. The output is listed after the input.

Given data ,

Let the range of the function be represented as set A

Now , the function is given by

f ( x ) = 2x - 7   be equation (1)

Let the domain of the function be represented as set B = { -2 , -1 , 0 , 1 , 2 }

Substitute the value for x in the given equation , we get

when x = -2

f ( x ) = 2x - 7

f ( -2 ) = 2 ( -2 ) - 7

f ( -2 ) = -4 - 7 = -11

when x = -1

f ( x ) = 2x - 7

f ( -1 ) = 2 ( -1 ) - 7

f ( -1 ) = -2 - 7 = -9

when x = 0

f ( x ) = 2x - 7

f ( 0 ) = 2 ( 0 ) - 7

f ( 0 ) = 0 - 7 = -7

when x = 1

f ( x ) = 2x - 7

f ( 1 ) = 2 ( 1 ) - 7

f ( 1 ) = 2 - 7 = -5

when x = -2

f ( x ) = 2x - 7

f ( 2 ) = 2 ( 2 ) - 7

f ( 2 ) = 4 - 7 = -3

Therefore , the value of set A is { -11 , -9 , -7 , -5 , -3 }

Hence , the range of the function is { -11 , -9 , -7 , -5 , -3 }

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Measure wall height from floor to ceiling. Exclude baseboards and moldings. Measure length of each wall including doors and windows.

Walls. Use the basic formula of Length x Width = Area to determine the area of a wall. Then, using the same approach, calculate the individual area of windows and doors. After you’ve taken all of these measurements, deduct the area of the windows and doors from the overall wall area. Methods of longwall and shortwall Long walls are those that run the length of the room, whereas short walls are those that run perpendicular to the length of the room.

Next, consider which unit of measurement is most appropriate for measuring a wall. Very tiny units such as inches, centimeters, and millimeters can be ruled out. We can also eliminate.

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Answer:

Step-by-step explanation:

Quadratic: binomial

Cubic: trinomial

Quartic: four terms

Quintic: five terms

8th degree: six terms

Answer:

a) To find out how much money is added to the account each year, we use the simple interest formula: I = Prt, where I is the interest, P is the principal (initial deposit), r is the annual interest rate (expressed as a decimal), and t is the number of years.

In this case, P = 1800, r = 0.03, and t = 1 (because we are finding the interest added for 1 year)

So the formula becomes:

I = 1800 * 0.03 * 1 = 54

Therefore, £54 is added to the account each year.

b) To find out how much money will be in the account after two years, we add the original deposit to the total interest earned over two years.

We know that the interest added each year is £54, and since we are trying to find the balance after 2 years, we will multiply it by 2 to find the total interest earned over 2 years:

Interest = 54 * 2 = £108

Now we add the original deposit and the total interest to find the total amount in the account after 2 years:

Total = 1800 + 108 = £1908

So the amount of money in the account after two years will be £1908.

The account will have £1909.62 after two years.

Simple interest is the amount of interest charged on a specific principal amount at a specific interest rate. Compound interest, on the other hand, is the interest that is computed using both the principal and the interest that has accumulated over the preceding period.

a) The amount of money added to the account each year is determined by multiplying the principal amount (initial amount) by the interest rate. So, the amount added to the account each year is:

Interest = Principal x Rate

Interest = £1800 x 0.03

Interest = £54

Therefore, £54 will be added to the account each year.

b) To find the amount of money in the account after two years, we need to add the interest earned in each year to the principal amount. After one year, the account will have:

Amount after 1 year = £1800 + £54 = £1854

After the second year, the account will have earned another 3% interest on the new balance of £1854. So, the interest earned in the second year is:

Interest = £1854 x 0.03

Interest = £55.62

Therefore, the total amount of money in the account after two years is:

Amount after 2 years = £1854 + £55.62 = £1909.62

So, the account will have £1909.62 after two years.

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Answer:

x = 4

Step-by-step explanation:

For this question we can use the theorem which states that "if the chords of a circle is equal, it is equidistant from the center."

Therefore, FC = CE

or 3x + 8 = 8x - 12

5x = 20

x = 4

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The setup cost for printing the math workbooks, given the printed cost of the books, is $ 1, 800

The setup cost for printing the math workbooks is a fixed cost which means that it will not change regardless of the number of books that are printed.

Since we know that 1, 000 books are printed to be $ 14, 300 and that 5, 000 books cost $ 64, 300, we can find the cost of the books without the setup cost to be :

= Difference in cost of books / ( Difference in number of books )

= ( 64, 300 - 14, 300 ) / ( 5, 000 - 1, 000 )

= 50, 000 / 4, 000

= $ 12. 50

The setup cost is therefore :

= Cost of printing -  (Number of books x cost per book )

= 14, 300 - ( 1, 000 x 12 .5)

= $ 1, 800

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The formula of lateral area of a cone can be equivalent to the formulas:

LA = r√(r^2 + h^2) and

LA = πrl

The formula for the lateral area of a right cone is LA = rs, where r is the radius of the base and s is the slant height of the cone.

The slant height (s) of a cone is the distance from the apex of the cone to the center of the base along a line that is perpendicular to the base and passes through the apex. The slant height of a cone can be found using the Pythagorean theorem using the radius (r) and the height (h) of the cone:

s = √(r^2 + h^2)

So, the formula for lateral area of a cone can be equivalent to the formula:

LA = r√(r^2 + h^2)

Another equation that is equivalent to the lateral area formula is

LA = (1/2)(2πr)(l)

LA = πrl

where l is the slant height of the cone.

This is because the lateral area of a cone is equal to (1/2) of the circumference of the base multiplied by the slant height, and we know that the circumference of a circle is equal to 2πr.

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Step-by-step explanation:

the area of a parallelogram is

base × height

the graphic shows us that the base (AB) is 3 units long.

and the height (BF) is also 3 units long.

so the area of ABJF is

3 × 3 = 9 units²

A race car driver is 3.79 km away from where she started.

Assume that a race car driver turns southwest, at an angle of  45 degrees.

Also she turns East making another 45 degree angle.

So, we get a right triangle.

Let ABC be right triangle with A = 90°, B = 45° and C = 45°

For right triangle ABC, a = 2.75km, b = y km and c = x km (the distance she has traveled east before crossing her northern path)

Consider the sine of angle B

sin(B) = Opposite side of angle B / Hypotenuse

sin(45) = x / 2.75

x = 1.94

sin(C) = Opposite side of angle C / Hypotenuse

sin(45) = y/2.75

y = 1.94

So, the distance to north before paths crossed would be,

N = 4.69 - y

N = 3.31

And the distance after she passed her northern path.

E = 3.89 - x

E = 1.85

Let m be the distance from Starting Point to End Point.

Using Pythagoras theorem,

m² = N² + E²

m² = (3.31)² + (1.85)²

m = 3.79 km

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Answer:

Your three angle measurements are 45, 45, and 90

Step-by-step explanation:

Since we know that all the measures of a triangle add up to 180, we have:

45 + b + c = 180

Then, since it is a right triangle, we know one of the sides is 90 degrees, giving us:

45 + 90 + c = 180

Then subtract 135 from both sides:

c = 45

So, your three angle measurements are 45, 45, and 90.

Hope this helped!

P( X < 9.85 or X > 10.15 ) ≈ 0.3171 up to four decimal places.

P( X < 9.85 or X > 10.15 ) ≈ 0.0027 up to four decimal places.

The simple definition of probability is the likelihood that something will occur. We can discuss the probabilities of different outcomes, or how likely they are if we are unclear about how an event will turn out. Statistics refers to the study of occurrences subject to probability.

According to the question

a) Assuming that X is the random variable that takes the place of the number of defectives and has a normal distribution with a mean of 10 ounces and a standard deviation (σ) of 0.15.

The random variable's values deviate from the mean by 1, causing them to either exceed or fall short of (10 + 0.15) and (10-0.15)

= 10.15 or 9.85.

The following formula may be used to determine the likelihood that there will be either more or lesser defects than the range of 10.15 to 9.85:

P( X < 9.85 or X > 10.15 ) = 1 - P[tex](\frac{9.85-10}{0.15} < \frac{X - 10}{0.15} < \frac{10.15-10}{0.15} )[/tex]

P( X < 9.85 or X > 10.15 ) = 1 - φ(1) - φ(-1)

Now we calculate the value of z for z = 1 and z = -1; we have: 0.841345 and 0.158655 respectively

P( X < 9.85 or X > 10.15 ) = 1 - (0.841345 - 0.158655)

P( X < 9.85 or X > 10.15 ) = 0.31713

P( X < 9.85 or X > 10.15 ) ≈ 0.3171 up to four decimal places.

b) It is possible to lower the process standard deviation to 0.05 by making modifications to the process design.

The following formula may be used to determine the likelihood that the number of defectives is either larger than 10.15 or lesser than 9.85:

P( X < 9.85 or X > 10.15 ) = 1 - P[tex](\frac{9.85-10}{0.15} < \frac{X - 10}{0.15} < \frac{10.15-10}{0.15} )[/tex]

P( X < 9.85 or X > 10.15 ) = 1 - φ(3) - φ(-3)

Now we calculate the value of z for z = 3 and z = -3; we have: 0.99865 and 0.00135 respectively

P( X < 9.85 or X > 10.15 ) = 1 - (0.99865 - 0.00135)

P( X < 9.85 or X > 10.15 ) = 0.00271

P( X < 9.85 or X > 10.15 ) ≈ 0.0027 up to four decimal places.

(c) What is the benefit of increasing the number of standard deviations from the mean for process control limits by minimizing process variation?

As we can see from the reduction from a to b above, the key benefit of minimizing process variance is that it will decrease the likelihood of receiving a defective item.

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The number of representatives for Oregon, which has a population of about 3.3 million is 6 Representatives (Option B).

The regression equation y = 1.73x + 0.39 is the equation of the line of best fit. To use this equation to predict the number of representatives for Oregon, which has a population of about 3.3 million, we need to substitute the population of Oregon (x = 3.3 million) into the equation and solve for y.

y = 1.73x + 0.39

y = 1.73(3.3) + 0.39

y = 5.659 + 0.39

y = 6.049

So the number of representatives for Oregon is approximately 6.049. The closest answer to that is

B. 6 representatives

Therefore, The number of representatives for Oregon, which has a population of about 3.3 million is 6 Representatives (Option B).

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The area of the sector is 113.14 square cm.

Step1:

Given, central angle, θ = 120°

Radius of circle, r = 21 cm

We have to find the area of a sector of the circle.

Area of sector = πr²θ/360°

= π(21)²(120°)/360°

= π(21)²(1/3)

= (22/7)(21)(21)(1/3)

= (22/7)(21)(7)

= (22)(21)

= 462 square cm.

Step2:

Therefore, the area of the sector is 462 square cm.

the area of a sector of circle of radius 12 cm and central angle 90°.

central angle, θ = 90°

Radius of circle, r = 12 cm

We have to find the area of a sector of the circle.

Area of sector = πr²θ/360°

= π(12)²(90°/360°)

= (22/7)(12)(12)(1/4)

= (11/7)(6)(12)

= 113.14 square cm

Therefore, the area of the sector is 113.14 square cm.

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On solving the provided question, we can say that Due to the size and revenue of this startup company, resources are somewhat limited.

In mathematics, "Size is an abstraction from the comparison and measurement of long and short items." Comparing or measuring objects allows us to determine their sizes. The amount's size will be decided by this. B. Mass or length with relation to measurement units. The total area of space occupied by a person or object; the size of someone or something. [Count] Box is 5 inches tall, 6 inches broad, and 12 inches long. The mistake was roughly the size of a dime. The size of twins is the same.

People make mistakes, but there is a potential that she can unintentionally destroy a personal file if she is removing something.

Due to the size and revenue of this startup company, resources are somewhat limited.

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Answer:

[tex]\frac{1}{4}[/tex]

Step-by-step explanation:

When you roll a di, there is a  [tex]\frac{1}{2}[/tex] chance you will either get an even or an odd number. Since this needs to happen twice, we will square this fraction, giving us:

[tex](\frac{1}{2}) ^{2} = \frac{1}{4}[/tex]

So, the probability to roll an even number and then roll an odd number is [tex]\frac{1}{4}[/tex].

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