Use a Venn Diagram or Union Rule; and the given information to determine the number of elements in the indicated region.

If n(U) = 103, n(A)= 32, n(B) = 52, n(A ∩ B)=11, n(A ∩ C)=14, n(A ∩ B ∩ C)= 6, n(A' ∩ B ∩ C')=35, n(A' ∩ B' ∩ C')=24

Find n(C)

Answer:

Both the slopes and y-intercepts are the same

Step-by-step explanation:

both slopes are -2 and both y-intercepts are at (0,3)

Answer:

195.4

Step-by-step explanation:

Volume of a right cylinder is:

V = π r² h

where r is radius and h is height.

V = π (2.6 cm)² (9.2 cm)

V = 195.4 cm³

Answer:

Let's denote:

- The number of orders Diane served as `D`

- The number of orders Sam served as `S`

- The number of orders Boris served as `B`

From the problem, we know:

1. `D + S + B = 54` (the total number of orders they served)

2. `D = S - 6` (Diane served 6 fewer orders than Sam)

3. `B = 2S` (Boris served 2 times as many orders as Sam)

We can substitute equations 2 and 3 into equation 1 to solve for the variables:

Substitute `D` and `B` in equation 1:

`(S - 6) + S + 2S = 54`

Combine like terms:

`4S - 6 = 54`

Add 6 to both sides:

`4S = 60`

Divide by 4:

`S = 15`

Now that we know `S = 15`, we can find `D` and `B` by substituting `S` into equations 2 and 3:

`D = S - 6 = 15 - 6 = 9`

`B = 2S = 2 * 15 = 30`

So, Diane served 9 orders, Sam served 15 orders, and Boris served 30 orders.

The distance from the north most ship to the observation is 2.9 miles and the distance from the south most ship to the observation is 9.9 miles.

The bearing is defined as the angle measured clockwise from the north direction. A ship is anchored off a long straight shoreline that runs north and south.

From two observation points miles apart on shore, the bearings of the ship are 52 degrees and 134 degrees respectively. To find the distance from the ship to each of the observation points, we can use trigonometry.

Let's call the distance from the north observation point to the ship x, and the distance from the south observation point to the ship y. The bearings from the north and south observation points can be drawn as follows:

[asy]

unitsize(1cm);

pair O = (0,0), N = (-2,0), S = (2,0), A = (-2,1), B = (2,-1);

draw(O--N--A,Arrow);

draw(O--S--B,Arrow);

\(label("$52^\circ$", N + 0.3*dir(52), NE);\)

\(label("$134^\circ$", S + 0.3*dir(134), SE);\)

draw(O--A--B--cycle,dashed);

\(label("$x$", (N+A)/2, W);\)

\(label("$y$", (S+B)/2, E);\)

[/asy]

We can use the tangent function to find x and y, since we have the angle and opposite side.

From the north observation point, we have:

\($$\tan(52^\circ) = \frac{x}{2}$$$$x = 2\tan(52^\circ) \approx 2.95$$\)

From the south observation point, we have:

\($$\tan(134^\circ) = \frac{y}{2}$$$$y = 2\tan(134^\circ) \approx 9.88$$\)

Therefore, the distance from the north most ship to the observation is 2.9 miles and the distance from the south most ship to the observation is 9.9 miles.

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The values of x and y would be   \(x=\frac{20 \sqrt{3}}{3}\) and \(y=\frac{40\sqrt{3}}{3}\).

What are trigonometric ratios?

Trigonometric ratios are mathematical functions that describe the relationship between the angles and sides of a right triangle. The three main trigonometric ratios are the sine, cosine, and tangent.

In the given figure, by using trigonometric ratios, we can find x

tan60° = 20/x

√3 = 20/x

x = 20/√3

=> \(x=\frac{20 \sqrt{3}}{3}\)

Now by using the ratio sin60°

sin60° = 20/y

√3/2  = 20/y

y = 40/√3

\(y=\frac{40\sqrt{3}}{3}\)

Hence, the values of x and y would be   \(x=\frac{20 \sqrt{3}}{3}\) and \(y=\frac{40\sqrt{3}}{3}\).

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Answer: 212.5 square feet

Step-by-step explanation:

If we were to complete the square, the total area of the square would be \(15^2=225\) square feet.

The area of the triangle added to 'complete the square' is \(\frac{1}{2}(15-10)(15-10)=12.5\) square feet.

So, the area of the floor is \(225-12.5=212.5\) square feet.

Answer:

212.5 ft^2

Step-by-step explanation:

A=s^2

A=15^2=225 ft^2

15-10=5

5*5=25

25/2=12.5

225-12.5=212.5

Answer:

x

=

3

2

−

y

2

Step-by-step explanation: just write them in order sorry for how i rote it

The number of pounds of strawberries sold and the number of pounds of grapes sold is 32 and 20 respectively.

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side. It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Given that the selling price of strawberries each pound = $2.50,

The selling price of grapes each pound = $2

The total earning = $160

Let x is the no of a pound of strawberries and y is the no of a pound of grapes sold, then equation will be,

x = y + 12 and 2.50x + 2y= 160

Solve the equation by substitution method;

x = 32 and  y = 20

Therefore, the number of pounds of strawberries sold is 32

the number of pounds of grapes sold is 20.

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Answer:

17.68 feat long

Step-by-step explanation:

Answer:

17.68 feet

Step-by-step explanation:

Answer:

(4x + 3) • (x + 2) • (3x - 2)

Thats finding the root polynomials hope it helps a bit

Answer:

Given - A triangle UTS

angle U = 43°

angle T = 103°

As we know that the side opposite to the largest angle is longest. angle T is longer so side opposite to it Us is longer

US , UT , TS

The graph of g(x) = 4x, is the translation of f(x) by subtracting 3.5 units, 2 of 3.

A graph can be defined as a pictorial representation or a diagram that represents data or values.

The cost can be modeled by the function f(x)=4x+3.5, where x represents the number of games bowled.

As per the given question, the required solution would be as:

g(x) = 4x , is the translation of f(x) by subtracting 3.5 units, 2 of 3.

The graph of g(x) would be identical to the graph of f(x), but shifted 3.5 units downward, 3 of 3.

This is because the flat fee for the rental of bowling shoes is not present in the function g(x), so the y-intercept of the graph would be at (0,-3.5) instead of (0,0) in f(x) function.

The slope and the shape of the function will remain the same.

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Answer:

0.09

Step-by-step explanation:

First off, we can write 0.9 as a fraction. Reading this, we would say "nine tenths"; this means the number in fraction form is 9/10.

The word "of" in mathematics means we multiply. Thus when we take 1/10 "of" 9/10, we multiply the two:

1/10(9/10)

To multiply fractions, multiply the numerators and multiply the denominators:

1/10(9/10) = (1*9)/(10*10) = 9/100

Converting this back to a decimal, we read 9/100 as "nine one-hundredths"; this means decimal form is 0.09.

Answer:Can u explain more ?

Step-by-step explanation:

Answer:

8=12-4

x/2

46k

12= n+6

5*9=45

Step-by-step explanation:

I am not too sure(didn't pay attention)

The number 100 would land in column 2

Given that we have the array of numbers

The length of each row in the array is 7

Dividing 100 by 7, we have

100/7 = 14 Remainder 2

This means that

Column = 2

In (a), we have

100/7 = 14 Remainder 2

This means that

Row = 14

Here, we have

The length of each row in the array is 6

Dividing 100 by 6, we have

100/6 = 16 Remainder 3

So, the location of 100 in rows of 6 numbers is row 16 and column 3

Let the length of each row in the array be n

Dividing 100 by n, we have

100/n = q Remainder r

This means that the location of 100 in rows of n numbers is row q and column r

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The measure of angle ∠NSR  is 118 degrees

The central angle of an arc is the central angle subtended by the arc.

The measure of an arc is the measure of its central angle.

We have to find angle ∠NSR

The measure of angle NSR is the half of the sum of the two arc measures

186 degrees and 50 degrees are the measures of the arcs in the given circle.

∠NSR = 1/2(186+50)

= 1/2(236)

When we divide numerator and denominator by 2 we get one hundred eighteen

=118 degrees

Hence, the measure of angle ∠NSR  is 118 degrees

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Using the integers −9 to 9 at most one time each, place a digit in each box (1, 3) and (9, 3) or (-9, 3) to create endpoints for the longest possible line segment both numerically and graphically whose midpoint is (1, 3).

To find the endpoints of the longest possible line segment with midpoint (1, 3), we can use the midpoint formula, which states that the midpoint of a line segment with endpoints (x₁, y₁) and (x₂, y₂) is ((x₁+x₂)/2, (y₁+y₂)/2).

In this case, we know the midpoint is (1, 3), so we can set up two equations using the variables for the endpoints (x and y) and solve for them:

(x₁ + x₂)/2 = 1

(y₁ + y₂)/2 = 3

We also know that the line segment must be as long as possible, so the endpoints should be as far away from each other as possible. To maximize the distance between the endpoints, we can choose one endpoint to be -9 and the other endpoint to be 9. This gives us:

(x₁ + x₂)/2 = 1 => x₁ + x₂ = 2

(y₁ + y₂)/2 = 3 => y₁ + y₂ = 6

Now we can solve for x₁ and y₁, since x₂ and y₂ will be 2-x₁ and 6-y₁ respectively:

x₁ + (2-x₁) = 2 => x₁ = 1

y₁ + (6-y₁) = 6 => y₁ = 3

So the endpoints of the longest possible line segment with midpoint (1, 3) are (1, 3) and (9, 3) or (-9, 3), and its length is 8 units.

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The length of side x is approximately 24.87, rounded to the nearest hundredth.

how can we find side of the triangle?

To find the length of side x, we can use the sine function, which relates the opposite side to an angle to the hypotenuse:

sin(11°) = opposite side/hypotenuse

Rearranging this equation, we get:

opposite side = sin(11°) * hypotenuse

We know that the hypotenuse has a length of 130, so we can substitute that in:

opposite = sin(11°) * 130

Using a calculator, we can evaluate sin(11°) to be approximately 0.1919, so we can substitute that in as well:

opposite = 0.1919 * 130

Simplifying this expression, we get:

opposite ≈ 24.87

Therefore, the length of side x is approximately 24.87, rounded to the nearest hundredth.

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Answer: Katherine should reject the null hypothesis.

Step-by-step explanation:

We reject the null hypothesis when p-value is less than the significance level.

here,  H0:μ=329 versus Ha:μ<329

α=0.05 (significance level)

p-value<0.005

so , we should reject the null hypothesis as p-value is less than the significance level.

Hence, Katherine should reject the null hypothesis.

The probability that the battery life is  20 ± 2 hours (between 18 and 22 hours) for each of the phones is:

Using the normalcdf function on a calculator, the probability that Phone C's battery would last between 18 and 22 hours can be found by inputing the function:

normalcdf (20, IE99, 18, 2)

The result is 0.158655 or 15.9%.

For Phone T, the function is:

normalcdf (20, IE99, 20, 3)

The result is 0.5 or 50%.

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Answer:

5 zeros

Step-by-step explanation:

Answer:

5

Step-by-step explanation:

There are 5 zeroes in the multiple of ten

In light of this, 1,0,8 is the value of the function h(x) = (x+1)2 where h is defined for all real integers.

The subject of mathematics includes quantities and their variations, equations and related structures, forms 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 relationship 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, within functions, and on functions.

given

h(x) = (x+1)²

h(-2) = 1

h(-1) = 0

h(3) = 8

In light of this, 1,0,8 is the value of the function h(x) = (x+1)2 where h is defined for all real integers.

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The probability, if Greg gets dressed in the dark, that he winds up wearing the white shirt and tan pants is 0.125 or 12.5%.

To find the probability that Greg winds up wearing the white shirt and tan pants while getting dressed in the dark, we need to find out all the possible outfit options. According to the question given, first we nned to find out number of outfit combinations possible.

Total number of Outfit Combinations:

There are 4 shirts: a white one, a black one, a red one, and a blue one and also two pairs of pants, one blue and one tan. So, total number of possible outfit combinations would be 4 * 2 = 8.

No of favourable options:

As given in the question, Greg wears white shirt and tan pants. There is only one white shirt and one tan pant. So, number of favourable options would be only 1 .

Probability = Number of favourable outcomes/Total no. of combinations

Probability = 1/8

Probability = 0.125 or 12.5%

Therefore, the probability, if Greg gets dressed in the dark, that he winds up wearing the white shirt and tan pants is 0.125 or 12.5%.

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Answer:

6 percent

Step-by-step explanation:

6/100 is shaded. This is the same thing as 0.06. Once I move the decimal two places to the right, I get 6. (I move the decimal place because percents are out of 100, so two decimal places.) This means 6 percent.

According to the question there are 35 distinct website graphics that can be created by using at least four of seven different bitmap images.

A website is a collection of related web pages, images, videos, and other digital assets that are hosted on a web server and can be accessed by users over the internet. A website is typically identified by a unique domain name and can be accessed by typing the URL into a web browser.

Using the formula for calculating the number of combinations of size k from a set of size n (n choose k), we can calculate the number of distinct website graphics that can be created by using at least four of seven different bitmap images as follows:

n = 7 (7 different bitmap images)
k = 4 (at least 4 of the 7 bitmap images)
Number of distinct website graphics = (7 choose 4) = 35
Therefore, there are 35 distinct website graphics that can be created by using at least four of seven different bitmap images.

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The correct answer is March, as it was the month in which the average number of hours worked by the website designers was closest to 50 hours.

A month is a unit of time typically consisting of 30 or 31 days. It is used for measuring periods of time, for example, when we say something happened "a month ago". Months are used in both the Gregorian calendar and the Julian calendar.

This data was gathered from a survey of website designers, which was conducted to determine the average number of hours each month that these professionals spent working.

In January, the average number of hours worked was 46.5. In February, it was 48.8. However, in March, the average number of hours worked was 49.4, which was the closest to 50 hours. This was followed by April, in which the average was 49.7.

Overall, it can be concluded that March was the month in which the average number of hours worked by website designers was closest to 50 hours. This is important data for website designers, as it allows them to understand the amount of time they should be spending on their work in order to be successful. It also helps employers gauge the workload of their website designers and ensure they are providing an adequate amount of work.

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Answer:

See the image below for answer:)

Step-by-step explanation:

Answer:

B. (1 ± sqrt(33)) / 4

Step-by-step explanation:

the 2 solutions for a quadratic equation

ax² + bx + c = 0

are defined as

x = (-b ± sqrt(b² - 4ac)) / 2a

in our example here we have

a = -2

b = 1

c = 4

=>

x = (-1 ± sqrt(1 + 32)) / -4 = (1 ± sqrt(33)) / 4

as we can easily divide top and bottom by -1 to turn the -1 and -4 into positive numbers, and the second top part, the square root, is a ± factor anyway. just withing the sign dues not change the fact that is is still a ± factor (both signs apply).

and now it is clear, it has to be option B.

the others disqualify because they have either no division by any form of 4, or the "1" and the "4" have different signs. but our equation shows they need to have equal signs (either both negative or both positive).

Answer:

ok x should be 30

Step-by-step explanation:

Step-by-step explanation:

When dealing with transversals, most angles either add to 180 or equal to each other. These angles form a linear pair so they add to 180

\((x + 1) + 4x - 36 = 180\)

\(5x - 35 = 180\)

\(5x = 215\)

\(x = 43\)

So

\(x + 1 = 43+ 1 = 44\)

\(4(43) - 36 = 136\)

Answer:

x + 1 = 44 degrees

4x - 36 = 136 degrees

Step-by-step explanation:

Since the lines are parallel, the angles are same-side-interior angles, which means they are supplementary and add up to 180:

x + 1 + 4x - 36 = 180

5x - 35 = 180

5x = 180 + 35

5x = 215

x = 43

x + 1 = 43 + 1 = 44 degrees

4x - 36 = 4(43) - 36 = 136 degrees