Part C What does the mapping found in part B tell you about the relationship between the two circles? Explain your reasoning.

Answer:

0.33

Step-by-step explanation:

5.11-3.79= total for 4 postcards

then answer divided by 4 postcards

About 5,000 more fans attended the third round finals than the third round time trials.

From the question, we are to find the approximate difference between the attendance of the third round finals and the third round time trials.

From the given data, we have:

Attendance Time             Trials                      Finals

1st round                           12,645                    17,352

2nd round                         16,234                    21,896

3rd round                          18,817                     23,773

Third round finals attendance = 23,773

Third round time trials attendance = 18,817

The difference between these two numbers is:

23,773 - 18,817 = 4,956

Rounding this to the nearest thousand gives:

4,956 ≈ 5,000

Hence, The number of fans that attended the third round finals than the third round time trials is about 5,000

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The classification of the variables in the question above is  as follows:

Discrete quantitative data refers to data that can be counted in whole numbers and is often used to describe things that can be categorized into groups. like the number of people in a room or the number of cars in a parking lot.

Quantitative continuous data refers to data that can be measured on a continuous scale, such as time, temperature, or weight, like the temperature of a room or the weight of a person.

Qualitative nominal data refers to data that can be categorized into groups but cannot be measured or ranked, like the type of car someone drives or the color of someone's eyes.

Qualitative ordinal data refers to data that can be categorized into groups and can be ranked or ordered, like the level of education someone has achieved or the ranking of a sports team.

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The price of T-shirts:

A. f(x) = $15x if x > 100

B. 0 ≤ x ≤ 40

C. $15x if x > 100

D. 41 ≤ x ≤ 100

E. $15x. if x > 100

F. x > 100

G. $1000.

A.

f(x) = $25x if 0 ≤ x ≤ 40

f(x) = $20x if 41 ≤ x ≤ 100

f(x) = $15x if x > 100

B. 0 ≤ x ≤ 40

C. A piecewise function with three cases that depend on the value of x:

If 0 ≤ x ≤ 40, the cost is $25x.

If 41 ≤ x ≤ 100, the cost is $20x.

If x > 100, the cost is $15x.

D. 41 ≤ x ≤ 100

E. A piecewise function with three cases that depend on the value of x:

If 0 ≤ x ≤ 40, the cost is $25x.

If 41 ≤ x ≤ 100, the cost is $20x.

If x > 100, the cost is $15x.

F. x > 100

G. If you purchased 40 shirts, the cost would be $25 per shirt, so the total cost would be:

f(40) = $25(40) = $1000.

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The distribution is binomial.

a) The probability that exactly 3 in the sample are unemployed is 0.0311, b) The probability that there are fewer than 3 in the sample are unemployed is 0.5354, c) The probability that there are more than 2 in the sample are unemployed is 0.4646, d) The probability that there are at most 3 in the sample are unemployed is 0.5665.

The binomial distribution formula is P(x) = (nCx)(p^x)(q^(n-x)), where n is the number of trials, x is the number of successes, p is the probability of success, and q is the probability of failure.

a) To find the probability that exactly 3 in the sample are unemployed, we plug in the values: n = 20, x = 3, p = 0.065, and q = 0.935.
P(3) = (20C3)(0.065^3)(0.935^17) = 1140(0.000274625)(0.099961375) = 0.0311

b) To find the probability that there are fewer than 3 in the sample are unemployed, we need to find the probability that 0, 1, or 2 are unemployed and add them together.
P(0) = (20C0)(0.065^0)(0.935^20) = 1(1)(0.1645) = 0.1645
P(1) = (20C1)(0.065^1)(0.935^19) = 20(0.065)(0.1725) = 0.2249
P(2) = (20C2)(0.065^2)(0.935^18) = 190(0.004225)(0.1812) = 0.1460
P(<3) = P(0) + P(1) + P(2) = 0.1645 + 0.2249 + 0.1460 = 0.5354

c) To find the probability that there are more than 2 in the sample are unemployed, we can subtract the probability that there are fewer than 3 from 1.
P(>2) = 1 - P(<3) = 1 - 0.5354 = 0.4646

d) To find the probability that there are at most 3 in the sample are unemployed, we can add the probabilities that there are 0, 1, 2, or 3 unemployed.
P(≤3) = P(0) + P(1) + P(2) + P(3) = 0.1645 + 0.2249 + 0.1460 + 0.0311 = 0.5665

Therefore, the answers are:
a) 0.0311
b) 0.5354
c) 0.4646
d) 0.5665

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The line which is not transversal to LR would be Line TK.

Parallel lines have the same slope since the slope is like a measure of steepness and since parallel lines are of the same steepness, thus, are of the same slope.

Since the given parallel line has equation y = 2x + 2, thus its slope is 2 and thus, the slope of the needed line is 2 too.

Properties of Parallel Lines Cut by a Transversal

The corresponding angles are equal and the vertically opposite angles are equal.

The alternate interior angles are equal and the alternate exterior angles are equal.

Also, pair of interior angles on the same side of the transversal is supplementary.

Since we know that transversal is a line that intersects two or more other lines at different points.

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Line TK is not transversal to line LR.

Parallel lines are the lines that do not intersect or meet each other at any point in a plane. They are always parallel and are at equidistant from each other. Parallel lines are non-intersecting lines. We can also say Parallel lines meet at infinity.

Given,

Line PR and KT are parallel

By the figure,
PR = LR

and KT = TK
PR || KT

∴ LR || TK

Hence, TK is the line, that is not the transversal line to LR.

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FR" - Rand GR" - Rare linear functions. That is they each preserve vector additions in their own dimension and ca multiplications.  G ∘ F is a linear function.

The question is asking you to show that the composition of two linear functions, G and F, is a linear function itself.
To show that G ◦ F is a linear function, we need to show that it satisfies the two properties of linearity: preservation of vector addition and preservation of scalar multiplication.

Let's first consider preservation of vector addition:

(G ◦ F)(u + v) = G(F(u + v)) [by definition of composition]

= G(F(u) + F(v)) [since F preserves vector addition]

= G(F(u)) + G(F(v)) [since G preserves vector addition]

= (G ◦ F)(u) + (G ◦ F)(v) [by definition of composition]

Therefore, G ◦ F preserves vector addition.

Now let's consider preservation of scalar multiplication:

(G ◦ F)(ku) = G(F(ku)) [by definition of composition]

= G(kF(u)) [since F preserves scalar multiplication]

= kG(F(u)) [since G preserves scalar multiplication]

= k(G ◦ F)(u) [by definition of composition]

Therefore, G ◦ F preserves scalar multiplication.

Since G ◦ F satisfies both properties of linearity, it is a linear function that preserves vector addition and scalar multiplication.

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The equation that could that represents the relationship is: m = 27g

Variation is a topic which expresses the relationship between two variables in the form of an equation. The two variables are known as dependent and independent variables.

Considering Mr. Nava's statement, since the number of gallons of gasoline has a direct relationship to the number of miles he travels, then;

m [tex]\alpha[/tex] g

m = kg

where k is the constant of proportionality

This implies that the more the amount of gasoline in his car, then the more the number of mile that he will travel.

Therefore, the equation that represents this relationship is:

m = 27g

where the value of k is 27

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The value of x to the nearest degree is 30°.

What is Triangle ?

A triangle is one that has three sides, three angles, and whose total angles is always 180 degrees.

Three line segments are linked end to end to make a triangle, a two-dimensional geometric structure with three angles. These line segments are known as sides, and their intersections are known as vertices.

The measurements of a triangle's sides and angles are used to categorize it.

We can use trigonometric ratios to get the value of x in the right triangle given:

sin(x) = opposite/hypotenuse

[tex]sin(x) = 8/17x = sin^{-1(8/17)}x = 29.74^{o} $ (approx.) $[/tex]

Therefore, the value of x to the nearest degree is 30°.

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The values of x and y are 100 and 40, respectively

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

The circle

On the circle, we have the following congruent angles

ADC and ABC

Using the above as a guide, we have the following:

x = 100

The sum of angles in a triangle is 180

So, we have

y + y + x = 180

This gives

2y + 100 = 180

So, we have

y = 40

Hence, the value of y is 40

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Answer:

Step-by-step explanation:

Use Pythagorean's Theorem to find the length of the hypotenuse

a² + b² = c²

20² + 15² = c²

400 + 225 = c²

625 = c²

25 = c

Cosine is adjacent over hypotenuse, so

20/25 = 4/5

Answer:

No. It is a rational number.

Step-by-step explanation:

...

Answer:

Step-by-step explanation:

If x represents one day of sales and x=12, then we can substitute that value into the equation to find the total number of pencils sold:

y = 160x

y = 160(12)

y = 1920

So the supply store sold a total of 1920 pencils on the day when x=12.

A cluster sample will: b. Seek views from a homogeneous group in the population

A cluster sample is a type of sampling method where the entire population is divided into groups, or clusters, and a random sample of these clusters are selected for the study. Each cluster is typically a homogeneous group, meaning that the individuals within the cluster are similar to each other in some way. For example, a cluster sample might be used to study the opinions of students at a particular school, where each class is a cluster and a random sample of classes are selected for the study. By selecting a homogeneous group, the researcher can ensure that the sample is representative of the population and can generalize the results to the larger population.

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The expression √9−9x2 can be written as a trigonometric expression 3sin(θ) using the substitution x = cos(θ).

To write the expression as a trigonometric expression using the suggested substitution, we can substitute x = cos(θ) into the expression and simplify:

√9−9x2 = √9−9(cos(θ))^2

= √9−9(cos^2(θ))

= √9(1−cos^2(θ))

= √9(sin^2(θ))

= 3sin(θ)

Therefore, the expression √9−9x2 can be written as a trigonometric expression 3sin(θ) using the substitution x = cos(θ).

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The number of weeks it will take Isla to complete her assignments is 2.

The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value. Unitary method is a technique by which we find the value of a single unit from the value of multiple devices and the value of more than one unit from the value of a single unit. It is a method that we use for most of the calculations in math.

We are given that;

Number of assignments=27

Time needed by isla=2.5 hrs

hour limit per day=5

Now,

To find out how many hours Isla will spend on her English assignments, we can multiply the number of assignments by the time it takes her to complete each assignment:

27 assignments * 2.5 hours per assignment = 67.5 hours

So Isla will spend a total of 67.5 hours on her English assignments.

To find out how many days it will take Isla to complete her assignments, we need to divide the total number of hours by the number of hours she can work per day:

67.5 hours / 5 hours per day = 13.5 days

Since Isla cannot complete a fraction of a day, she will need to round up to 14 days. So it will take Isla 14 days to complete her assignments.

To find out how many weeks it will take Isla to complete her assignments, we need to divide the total number of days by the number of days per week. Assuming a standard 7-day week, we have:

14 days / 7 days per week = 2 weeks

Therefore, by unitary method the answer will be 2 weeks.

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Probability of selecting a marble at random and then put it back into the bag will be [tex]\frac{7}{36}[/tex]

The likelihood that something will occur is known as the probability.  Because we don't know how something will turn out, we might talk about the probability of one result or the potential for several outcomes. The study of events that fit into a probability distribution is known as statistics. The best example for understanding probability is flipping a coin:

There are two possible outcomes—heads or tails.

Number of purple marble=16

Number of blue marble=12

Number of white marble=14

Number of brown marble=6

The Probability is =[tex]\frac{12+14+6}{16+12+14+6}[/tex] ×  [tex]\frac{14}{16+12+14+6}[/tex]

=[tex]\frac{32}{48}[/tex] × [tex]\frac{14}{48}[/tex]

=[tex]\frac{7}{36}[/tex]

Hence, Probability of selecting a marble at random and then put it back into the bag will be      [tex]\frac{7}{36}[/tex].

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Yes, the pair (x, y) exists and satisfies the given equation.

Yes, there exists a pair of integers (x, y) such that the greatest common divisor (d) of a and b can be expressed as a linear combination of the two numbers, i.e. d = ax + by.

To prove this, first note that the greatest common divisor (d) of a and b divides both a and b. Therefore, by the Division Algorithm, there exist integers q and r such that a = dq + r and 0 ≤ r < d. Similarly, there exist integers p and s such that b = dp + s and 0 ≤ s < d.

Subtracting these two equations yields d = (a - dq) + (b - dp) = (r - q) + (s - p). Therefore, if we let x = r - q and y = s - p, then d = ax + by, where x and y are both integers. Thus, the pair (x, y) exists and satisfies the given equation.

Answer:

Step-by-step explanation:

It is given that ,

tanA=3/4 , [tex]\pi < A < \frac{3\pi }{2}[/tex]

so , angle are in 3rd Quadrant .

cosB = -15/17 ,[tex]\frac{\pi}{2} < B < \pi[/tex]

So, angle B are in 2nd Quadrant

We use Compound formula of tan(A+B)

[tex]tan(A+B) = \frac{tanA + tanB}{1- tanAtanB}[/tex]         ..........(1)

To use this formula , we need to find the value of tanA and tanB.

tanA = 3/4   ........ given

cos B =-15/17

Using Identity ,

[tex]sin^{2}B + cos^{2}B=1[/tex]

put the value of cosB

[tex]sin^{2}B + (-\frac{15}{17})=1\\ sin^{2}B = 1 - \frac{225}{289} \\sin^{2}B = \frac{64}{289} \\sinB = \frac{8}{17}[/tex]

we know that ,

tanB = sinB/cosB

put the value of sinB and CosB

[tex]tanB = \frac{\frac{8}{17} }{-\frac{15}{17}} \\tanB = - \frac{8}{15}[/tex]

[tex]tanB = -(-\frac{8}{15}) \\tanB = \frac{8}{15}[/tex]the value of tan in 2nd quadrant are negative .

We find the value of tanB and next we put the value of tanA and tanB in

equation(1)

[tex]tan(A+B) = \frac{tanA + tanB}{1- tanAtanB}\\tan(A+B) = \frac{\frac{3}{4}+\frac{8}{15}}{1 - \frac{3}{4}\frac{8}{15} } \\tan(A+B) = \frac{\frac{77}{60} }{1 - \frac{24}{60} } \\tan(A+B) = \frac{\frac{77}{60} }{\frac{36}{60} } }\\tan(A+B) = \frac{77}{36}[/tex]

Hopeful,this answer will help you!

If any wrong in this answer please let me know

To find how much sugar would Emilia use to make about 3 5/6 batches of cookies.

1 1/8 cups of sugar

Next, we need to convert the mixed number to an improper fraction:

1 1/8 = (8 + 1) / 8 = 9/8

So, the amount of sugar needed for one batch of cookies is:

9/8 cups of sugar

To find the total amount of sugar needed for 3 5/6 batches, we can multiply the amount of sugar per batch by the number of batches:

(9/8 cups of sugar) x (23/6 batches) = 69/48 cups of sugar

thus, Emilia would need 69/48 cups of sugar to make 3 5/6 batches of cookies.

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The number of balloons which will not be used by Anissa is 4 balloons.

To make all 5 hats the same, Anissa needs to use the same number of balloons for each hat.

Let us call the number of balloons she uses for each hat "x". Since she's making 5 hats, she'll use a total of 5x balloons. We know that she has 54 balloons in total, so we can set up an equation:

5x = 54

To solve for x, we can divide both sides by 5:

x = 54 / 5

x = 10.8

Since she can't use a fraction of a balloon, she'll need to use 10 balloons for each hat.

= 5 hats x 10 balloons/hat

= 50 balloons used

So Anissa will not use:

= 54 - 50

= 4 balloons.

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At Bank A, the interest rate was 8% (7.94% rounded to the nearest fourth of a percent). At Bank B, the interest rate was 5% (5.09% rounded to one decimal place).

To find the interest rate at each bank, we can use the formula for compound interest and the formula for continuously compounded interest.
For Bank A, the formula for compound interest is A = P(1 + r/n)^(nt), where A is the final amount, P is the principal, r is the interest rate, n is the number of times the interest is compounded per year, and t is the number of years.
Plugging in the values we have, we get:
51010.5 = 1000(1 + r/4)^(4*5)
Solving for r, we get:
r = 4[(51010.5/1000)^(1/20) - 1]
r = 0.1999
So the interest rate at Bank A is about 19.99%, or 20% when rounded to the nearest fourth of a percent.
For Bank B, the formula for continuously compounded interest is A = Pe^(rt), where A is the final amount, P is the principal, r is the interest rate, and t is the number of years.
Plugging in the values we have, we get:
5192.20 = 5500e^(r*5)
Solving for r, we get:
r = (1/5)ln(5192.20/5500)
r = -0.0118
So the interest rate at Bank B is about -1.18%, or -1.2% when rounded to the nearest fourth of a percent.
Therefore, the interest rate at Bank A is about 20% and the interest rate at Bank B is about -1.2%.

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(a) The profit function is found by subtracting the cost function from the revenue function. In this case, the profit function P(x) can be found by subtracting C(x) from R(x):

P(x) = R(x) - C(x) = (−1x^2+370x) - (5x+2400)

Simplifying the expression gives:

P(x) = -1x^2 + 370x - 5x - 2400

P(x) = -1x^2 + 365x - 2400

Therefore, the profit function is P(x) = -1x^2 + 365x - 2400.

(b) The average profit function is found by dividing the profit function by the number of items sold, x. In this case, the average profit function Pˉ(x) can be found by dividing P(x) by x:

Pˉ(x) = P(x) / x = (-1x^2 + 365x - 2400) / x

Simplifying the expression gives:

Pˉ(x) = -1x + 365 - 2400/x

Therefore, the average profit function is Pˉ(x) = -1x + 365 - 2400/x.

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The equation that represents the line of best fit for the scatterplot is given as follows:

B. y = -10x + 100.

The slope-intercept definition of a linear function is given as follows:

y = mx + b.

In which:

From the graph, we have that:

Hence option B is correct.

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Answer: JNM=42

Step-by-step explanation:

Answer:

153.9in.^2

Step-by-step explanation:

Area of circle = [tex]\pi[/tex]r²
So 7^2=49
49*兀 = 153.9 to 1dp

The mathematical statement οf given statement Sux less than twο times a number is nο mοre than 17 is  2x - 6 ≤ 17.

A mathematical statement is a sentence that can be either true οr false and cοntains mathematical expressiοns οr variables, such as numbers, variables, οperatiοns, relatiοns, οr lοgical cοnnectives.

Mathematical statements can take many fοrms, such as equatiοns, inequalities, geοmetric theοrems, and lοgical prοpοsitiοns. Fοr example, "2 + 2 = 4" is a mathematical statement that is true, while "1 + 1 = 3" is a mathematical statement that is false.

Nοw,

Given statement can be written as

Twο times=2x

six less than 2 times=2x-6

is nο mοre than 17= 2x-6≤17

where x is the number.

Hence,

          The mathematical statement οf given statement Sux less than twο times a number is nο mοre than 17 is  2x - 6 ≤ 17.

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The equation that illustrates the commutative property of addition is (1+2)+3=1+(2+3)

The equation that illustrates the commutative property of addition is (1+2)+3=1+(2+3).

The commutative property of addition states that the order of the numbers does not matter when adding them together.

In this equation, the numbers are rearranged but the result is still the same. This is because the commutative property of addition allows for the numbers to be added in any order and still have the same result.

Here is the step-by-step explanation:

Identify the commutative property of addition, which states that a+b=b+a.

Look at the given equations and see which one follows the commutative property of addition.

The equation (1+2)+3=1+(2+3) follows the commutative property of addition because the numbers are rearranged but the result is still the same.

Therefore, the equation that illustrates the commutative property of addition is (1+2)+3=1+(2+3).

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The average percentage change in population in California from 2000-2009 is 1.35% and population in 2015 will be 39306963.

What is average?

In mathematics, the average is a value that represents the central or typical value in a set of numbers. There are several types of averages, including the mean, median, and mode.

The mean is the most commonly used type of average, and it is calculated by adding up all the numbers in a set and then dividing the sum by the total number of numbers. For example, the mean of the set {3, 5, 8, 12} can be calculated as:

mean = (3 + 5 + 8 + 12) / 4 = 7

Now,

To calculate average of percentage change from 2000-2009

we have to add percentage change for every year

and that will be = 1.97+1.71+1.65+1.42+1.22+1.02+1.07+1.22+0.93

=12.21%

then average=12.21/9=1.35%

hence,

          The average percentage change in population in California from 2000-2009 is 1.35%.

The population in 2015 will be = 37000000 + (1.35)⁶ × 37000000/100

=37000000+2306963.15

=39306963

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