Use the information given in the figure to find the length R U.
If applicable, round your answer to the nearest whole number.

The lengths on the figure are not drawn accurately.

Answer:

B

Step-by-step explanation:

calculate the slope m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (20, 30 ) and (x₂, y₂ ) = (40, 14 )

m = [tex]\frac{14-30}{40-20}[/tex] = [tex]\frac{-16}{20}[/tex] = - [tex]\frac{4}{5}[/tex]

Step-by-step explanation:

a) The complement of the set of pupils who do not jog or swim or cycle would be the set of pupils who do at least one of these activities.

b) We can use a Venn diagram to help us visualize the information given and answer the questions:

```

_____________

/ \

/ \

jog / A \ swim

/ \

/ \

________/_________ _______\_________

/ \ / \

/ \ / \

cycle B \ / C \ none

/ \ /

/ \____________/

/

/

/

/

/

```

- i) To find the percentage of pupils who do both jog and cycle, we look at the intersection of sets A and B, which is 8%. Therefore, 8% of pupils do both jog and cycle.

- ii) To find the percentage of pupils who swim or cycle, we add the percentages of sets B, C, and D (the parts of the circles that include swimming or cycling), which gives 8% + 15% + 18% = 41%. Therefore, 41% of pupils swim or cycle.

- iii) To find the percentage of pupils who do not swim, we add the percentages of sets A, B, and D (the parts of the circles that do not include swimming), which gives 15% + 8% + 18% = 41%. Therefore, 41% of pupils do not swim.

- iv) To find the percentage of pupils who do not jog, swim, or cycle, we look at the complement of the set of pupils who do at least one of these activities. This is given as 15%, so the percentage of pupils who do not jog, swim, or cycle is 15%.

15% of pupils do not jog, swim or cycle. Of the remaining pupils, 19% both jog and cycle, 61% either swim or cycle, and 39% do not swim. The numbers are based on a full 100% participation rate in regards to these three activities only.

The cardinality of a complement of a set refers to the elements that are not in the original set. In context of this question, the complement of the set would be the 15% of pupils who do not partake in jogging, swimming or cycling.

To answer the other parts of the question:

Please note that this solution is assuming that all pupils participate in at least one of these activities or none at all and that there are no other activities available.

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Answer: (0,10)

Step-by-step explanation:

To find the y-intercept, substitute in 0 for x and solve for y.

Answer:

The y-intercept is 10. Also can be thought of as the point (0, 10).

Step-by-step explanation:

This equation is in Slope-Intercept form. The y is all by itself on the left side of the equal sign. On the right, there is an x term. The number next to the x (the co-efficient of x) is the slope. The constant, the number all by itself is the y-intercept.

In the equation,

y = 3x + 10 the slope is 3 and the y-intercept is 10.

This is where the graph crosses the y-axis, the point (0,10)

For any equation you can find the y-intercept by letting x = 0.

y = 3(0) + 10

y = 0 + 10

y = 10

Answer:

(a) $ 315000

(b) $ 3103448.28

Step-by-step explanation:

(a)

tax = 45% of buying price

Buying price = $700000

tax = 45% × 700000

= $ 315000

(b)

Final price = $4500000

145% = 4500000

buying price = 100%

= 4500000/145 × 100

= 3103448.28

The missing dimension of the rectangle is 8 inches.

To determine the missing dimension of an area of 112 in.², we need to know at least one of the dimensions. Let's assume we know the length of the rectangle is 14 inches.

We can then use the formula for the area of a rectangle, which is length multiplied by width, to solve for the missing dimension.

We can rearrange the formula to solve for the width by dividing both sides by the length: width = area/length. Plugging in the values we know, we get: width = 112 in.² / 14 in. = 8 inches.

It's important to note that if we had started with the width instead of the length, we would have used the same formula but rearranged it to solve for the length instead. The formula for the area of a rectangle is very useful for solving these types of problems.

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it will be 26 cm as diagonals bisect each other

This means that the value of x should not exceed 2.5, as Leanna needs no more than 2.5 hours to complete her homework.

The inequality that represents the number of hours, x, Leanna needs to finish her homework is: x ≤ 2.5.

The inequality x ≤ 2.5 means that the value of x should not exceed 2.5. Since Leanna needs no more than 2.5 hours to finish her homework, we can use this inequality to represent the possible values of x. If x is greater than 2.5, then Leanna would take more than 2.5 hours to finish her homework, which contradicts the given condition. Therefore, the inequality x ≤ 2.5 is the correct representation of the number of hours Leanna needs to finish her homework.

In conclusion, the inequality x ≤ 2.5 represents the number of hours, x, Leanna needs to finish her homework. This means that the value of x should not exceed 2.5, as Leanna needs no more than 2.5 hours to complete her homework.

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The area of the region is (27π/4) square units.

We have,

To find the area of the region inside the circle (x + 3)² + y² = 9 and outside the circle x² + y² = 9, we can use a double integral in polar coordinates.

The region is an annulus (a region between two concentric circles) with the smaller circle centered at (-3,0) and radius 3, and the larger circle centered at the origin and radius 3.

We can rewrite the equations of the circles in polar coordinates as:

(x + 3)² + y² = 9

And,

r² + 2r cos(theta) + 9 = 9

r² + 2r cos(theta) = 0
r = -2 cos(theta)

And,

x² + y² = 9

r² = 9

The region can be described as 0 ≤ r ≤ 3 and -π/2 ≤ θ ≤ π/2 since we are only interested in the part of the region above the x-axis.

The area of the region can be calculated using the following double integral:

A = ∫∫R r dr dθ

where R is the region in polar coordinates.

We can integrate with respect to r first:

A = ∫(-π/2)^(π/2) ∫0³ r dr dθ

= ∫(-π/2)^(π/2) [(1/2) r²]_0³ dθ

= ∫(-π/2)^(π/2) (9/2) dθ

= (9/2) [θ]_(-π/2)^(π/2)

= (9/2) [π - (-π/2)]

= (9/2) (3π/2)

= (27π/4)

Thus,

The area of the region is (27π/4) square units.

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To eliminate one of the variables by adding a multiple of one equation to the other, you should multiply the equation containing the variable you want to eliminate by a suitable multiplier.

Let's assume you want to eliminate the variable y. In this case, you should multiply the equation containing y by a multiplier that will make the coefficient of y in one equation equal to the negative coefficient of y in the other equation. This will ensure that when you add the two equations, the y terms will cancel out.

For example, if the equation you want to eliminate y from is 2x + 3y = 7, and the other equation is 4x + 5y = 9, you would multiply the first equation by -5 and the second equation by 3 to obtain:

-5(2x + 3y) = -5(7) (equation 1 multiplied by -5)

3(4x + 5y) = 3(9) (equation 2 multiplied by 3)

This will result in:

-10x - 15y = -35 (equation 1 after multiplication)

12x + 15y = 27 (equation 2 after multiplication)

Now, when you add the two equations, the y terms will cancel out, and you can solve for the remaining variable x.

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The measure of <1 is 147 degree.

Given:

m∠2 = 12x - 15

m∠7 = 3x + 21

Since angles 2 and 7 are alternate Exterior angles, they are congruent.

So, 12x - 15 = 3x + 21

12x - 3x = 21 + 15

9x = 36

x = 4

So, <2 = 12x - 15= 48 - 15 = 33

Now, <1 + <2 = 180 (Linear Pair)

<1 + 33 = 180

<1 = 147 degree

Thus, the measure of <1 is 147 degree.

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Answer:

36 π and 12 π respectively.

Step-by-step explanation:

To find the area of a circle, we do πr^2. For circumference, we do 2πr, where r is the radius. Since we know the diameter of this circle is 12, and we know the radius is half the diameter, then:

12/2 = 6 = r

knowing r, we can find out the area and the circumference. The area is:

πr^2 = π 6^2, so it is 36π for the area. The circumference is:
2πr = 2 π 6 = 12π.

Therefore, the probability that a student likes papa john's given they do not like chipotle is approximately 0.275 or 27.5%.

Bayes' theorem allows us to calculate conditional probabilities, which is the probability of an event occurring given that another event has already occurred. In this case, we want to find the probability that a student likes Papa John's pizza given that they do not like Chipotle.

We start by using the given probabilities to calculate the probability that a student does not like Chipotle, which is the complement of the probability that they do like Chipotle. Then, we calculate the probability that a student likes both Papa John's and Chipotle, and use this to find the probability that a student likes Papa John's given that they do not like Chipotle.

Bayes' theorem is a powerful tool that is used in a wide range of fields, including statistics, probability theory, and machine learning. It provides a systematic way to update probabilities based on new information or evidence, which is a crucial aspect of many real-world applications.

P(B) = 1 - 0.8 = 0.2 (the probability that a student does not like chipotle)

P(A|B) = P(A and B) / P(B) = (0.65 - 0.69*0.8) / 0.2 ≈ 0.275

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The rate of change of item I is greater than the rate of change of item II

The rate of change of  item I is 0.6

Let us find the rate of change of item II

Rate of change = 1.2-0.6/4-2

=0.6/2

=0.3

So rate of change of item II is 0.3 which is lesser than rate of change of I

the rate of change of item I is greater than the rate of change of item II

Hence, the rate of change of item I is greater than the rate of change of item II

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Answer:

6/12

Step-by-step explanation:

this is because if you do the math it is 6/12

Answer: How many distinct license plates can be formed if the first number cannot be zero and the three letters cannot form "DOG"?

Step-by-step explanation:

Since the first digit cannot be 0, there are 9 choices for the first digit.

For the three letters, there are 26 choices for the first letter, 26 choices for the second letter, and 25 choices for the third letter (since we cannot use "D", "O", or "G").

For the last three digits, there are 10 choices for each digit.

Therefore, the total number of distinct license plates can be formed is:

9 x 26 x 26 x 25 x 10 x 10 x 10 = 16,290,000

So there are 16,290,000 distinct license plates that can be formed if the first number cannot be zero and the three letters cannot form "DOG".

{I Hope This Helps! :)}

Answer:

x = 11.0

Step-by-step explanation:

Since this is a right triangle, we can find the measure of x using one of the trigonometric ratios.  

sin (27) = BC / AB

sin (27) =  5 / x

x * sin (27) = 5

x = 5 / sin (27)

x = 11.01344632

x = 11.0

Answer:

------------------------

Set one variable to 0 and solve for the other.

For the x-intercept, set y = 0 and solve for x:

For the y-intercept, set x = 0 and solve for y:

The x-intercept is (32, 0) and the y-intercept is (0, -16).

The true statement about trend lines include the following: B. The distance from the points to the line should be as small as possible.

In Mathematics and Statistics, a trend line is sometimes referred to as a line of best fit and it can be defined as a statistical tool which is commonly used in conjunction with a scatter plot, in order to determine whether or not there's any form of correlation (either positive or negative) between a given data.

Generally speaking, the line of best fit or trend line should be very close to the data points as much as possible. This ultimately implies that, a characteristics of a trend line is that the distance from each of the data points to the line must be as small as possible i.e closer to the line.

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Answer:To verify whether triangle DEF is a right triangle, we can use the slope formula and the perpendicularity criterion.

a) Verification of DEF as a right triangle:

Calculate the slopes of the two sides:

Slope of DE = (y2 - y1) / (x2 - x1) = (4 - 2) / (1 - (-2)) = 2 / 3

Slope of EF = (y2 - y1) / (x2 - x1) = (1 - 2) / (3 - (-2)) = -1 / 5

Check if the product of the slopes is -1 (perpendicular lines):

(Slope of DE) * (Slope of EF) = (2 / 3) * (-1 / 5) = -2 / 15

Since the product of the slopes is not -1, the sides DE and EF are not perpendicular. Therefore, triangle DEF is not a right triangle.

b) Another method to determine if triangle DEF is a right triangle:

Another method to answer part a) is by calculating the lengths of the three sides DE, EF, and DF. Then, we can check if the Pythagorean theorem holds true.

Calculate the lengths of the sides:

Length of DE = sqrt((x2 - x1)^2 + (y2 - y1)^2) = sqrt((1 - (-2))^2 + (4 - 2)^2) = sqrt(9 + 4) = sqrt(13)

Length of EF = sqrt((x2 - x1)^2 + (y2 - y1)^2) = sqrt((3 - 1)^2 + (1 - 4)^2) = sqrt(4 + 9) = sqrt(13)

Length of DF = sqrt((x2 - x1)^2 + (y2 - y1)^2) = sqrt((3 - (-2))^2 + (1 - 2)^2) = sqrt(25 + 1) = sqrt(26)

Apply the Pythagorean theorem:

If DF^2 = DE^2 + EF^2, then triangle DEF is a right triangle.

DF^2 = (sqrt(26))^2 = 26

DE^2 + EF^2 = (sqrt(13))^2 + (sqrt(13))^2 = 13 + 13 = 26

Since DF^2 equals DE^2 + EF^2, the Pythagorean theorem holds true, indicating that triangle DEF is a right triangle.

Therefore, the two methods of verification provide conflicting results. One method (using the perpendicularity criterion) suggests that DEF is not a right triangle, while the other method (using the Pythagorean theorem) suggests that it is a right triangle. In such cases, it is important to double-check the calculations and verify the accuracy of the given points to resolve the discrepancy.

Step-by-step explanation:

The adjacent angle is  BFD.

We are given to find the adjacent angle to angle DFE in the figure.

The two angles that have a common vertex and a common side are called adjacent angles.

We can see that angles DFE and AFB have a common vertex F but they do not have a common side. So, the angles are not adjacent.

We can see that angles DFE and AFC have a common vertex F but they do not have a common side. So, the angles are not adjacent.

We can see that angles DFE and BFD have a common vertex F and a common side FD. So, the angles are adjacent.

Hence,

∠BFD adjacent angle.

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The double integral ∫∫R 2x/(1+xy) dA over R = [0,2] x [0,1] is equal to -4ln(3) + 4.

We have:

∫∫R 2x/(1+xy) dA = ∫[0,2]∫[0,1] 2x/(1+xy) dy dx

Using u-substitution with u = 1 + xy, we have du/dy = x. Solving for x, we get x = du/dy / y. Substituting this into the integral, we get:

∫∫R 2x/(1+xy) dA = ∫[0,2]∫[0,1] 2u/(u) * (1/u) du dx

Simplifying and evaluating the inner integral, we get:

∫∫R 2x/(1+xy) dA = ∫[0,2] (-2ln|1+xy|)[y=0]^{y=1} dx

= ∫[0,2] -2ln(1+x) dx

= [-2(xln(1+x)-x)]_{x=0}^{x=2}

= -4ln(3) + 4

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Answer:

√((-10 - (-7))^2 + (-9 - 4)^2)

= √((-3)^2 + (-13)^2)

= √(169 + 9) = √178 = 13.342

If the cost of one paperback book is less than $1, he would receive even more change.

To solve this problem, we need to know the cost of one paperback book. Unfortunately, that information is missing from the question. Without it, we cannot determine the total cost of the 5 paperback books and therefore cannot calculate Prakash's change.

However, we can make an educated guess based on the fact that the question mentions both paperback and hardcover books. Typically, hardcover books are more expensive than paperbacks, so we can assume that the cost of one paperback book is less than the cost of one hardcover book.

Assuming that each hardcover book costs $10, the total cost of 3 hardcover books would be $30. If Prakash gives the clerk $20 bills, he would pay $60 in total. If we subtract the cost of the 3 hardcover books ($30) from the total amount paid ($60), we are left with $30.

This is the maximum amount of change Prakash could receive if each paperback book costs $1.

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when X = 3, Ŷ equals 4,601. The correct answer is (c) 4,601.

If the least squares regression equation is Ŷ = 1,202 + 1,133X, we can find the value of Ŷ when X = 3 by substituting X = 3 into the equation and solving for Ŷ:

Ŷ = 1,202 + 1,133(3)

Ŷ = 1,202 + 3,399

Ŷ = 4,601

what is equation?

An equation is a mathematical statement that shows that two expressions are equal. It typically consists of two sides separated by an equals sign (=). The expressions on either side of the equals sign can be numbers, variables, or combinations of both, connected by arithmetic operations such as addition, subtraction, multiplication, and division, as well as more advanced operations such as exponents, logarithms, and trigonometric functions.

An equation can be either true or false, depending on the values of the variables and constants involved. Equations are used in a wide variety of mathematical contexts, from basic arithmetic to advanced calculus, physics, and engineering.

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The maximum number of elements in $s$ is $\boxed{7}$, which we can achieve by choosing one element from each of the residue classes modulo $7$.

To find the maximum number of elements in $s$, we need to consider the elements of $\{1,2,3,...,50\}$ that are congruent to each residue class modulo $7$. There are seven residue classes modulo $7$, namely $\{0,1,2,3,4,5,6\}$. Since the sum of two elements from the same residue class modulo $7$ will also be in the same residue class modulo $7$, we cannot include more than one element from each residue class in $s$.
We can include one element from the residue class $0$, which gives us one element. For the other six residue classes, we can choose at most one element from each of them without violating the condition that no pair of distinct elements in $s$ has a sum divisible by $7$. This gives us a total of $1+6=7$ elements in $s$.
Therefore, the maximum number of elements in $s$ is $\boxed{7}$, which we can achieve by choosing one element from each of the residue classes modulo $7$.
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Answer:

Step-by-step explanation:

the anser is 16

The Value of cos B is,

⇒ cos B = 0.64

We have to given that;

Two angles, ∠A and ∠B, are complementary.

And, sin A = 4/7

Now, We can simplify as;

sin A = 4/7

A = sin⁻¹ 4/7

A = 39.8°

Since, Two angles, ∠A and ∠B, are complementary.

Hence, We get;

∠A + ∠B = 90°

39.8° + ∠B = 90°

∠B = 90 - 39.8°

∠B = 50.2°

Thus, Value of cos B is,

⇒ cos B = cos 50.2° = 0.64

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A graph that uses images to symbolize the data that appears on the graph is known as a pictograph.

A pictograph is a type of chart that represents data using images or symbols. Each symbol on the pictograph represents a specific quantity, and the quantity is determined by the number of times the symbol appears on the chart. Pictographs are used to present data in a visually appealing and easy-to-understand manner, especially when the data is complex or there are multiple variables involved. Pictographs can be useful for a wide range of applications, from presenting sales figures to illustrating demographic information. They are often used in advertising, marketing, and educational materials to make data more engaging and memorable.

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