Question 12 (2 points)
Among the seniors at a small high school of 150 total students, 80 take Math, 41
take Spanish, and 54 take Physics. 10 seniors take Math and Spanish. 19 take Math
and Physics. 12 take Physics and Spanish. 7 take all three.
How many seniors were taking none of these courses?
Note: Consider making a Venn Diagram to solve this problem.

0
5
9
22

The measure of the angle A is 49.99 degrees or 50 degrees if the length of AB = 14 and AC = 9.

Trigonometry is a branch of mathematics that deals with the relationship between sides and angles of a right-angle triangle.

We have a given a right angle triangle in the picture

It is required to find the measure of angle A

Applying cos ratio to find the measure of the angle A:

cosA = 9/14

cosA = 0.642

A = 49.99 ≈ 50 degree

Thus, the measure of the angle A is 49.99 degrees or 50 degrees if the length of AB = 14 and AC = 9.

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Answer:

Answer: B. Symmetric.

Explanation:

In a symmetric distribution, the data is evenly distributed around the mean or median, creating a mirror image on both sides of the center. In this histogram, the median and mean are very close together at 55 and the bars on both sides of the center are roughly equal in height, indicating a fairly even distribution. Therefore, the histogram is symmetric.

Answer:

To find the annual growth rate percentage, we can use the formula:

annual growth rate = [(final value / initial value)^(1/number of years)] - 1

where "final value" is the value in the ending year, "initial value" is the value in the starting year, and "number of years" is the total number of years between the starting and ending years.

Using the given values, we have:

annual growth rate = [(148,000 / 108,000)^(1/20)] - 1

= 0.0226 or 2.26%

So the house appreciated at an annual growth rate of 2.26%.

To find the value of the house in 2010, we can use the same growth rate to project the value from 2005 to 2010:

value in 2010 = 148,000 * (1 + 0.0226)^5

= $175,465.11 (rounded to the nearest cent)

Therefore, the value of the house in the year 2010 was $175,465.11.

The chance that both numbers drawn are even numbers is 8/21.

The probability refers to the measure of the likelihood or chance of an event occurring. It is a numerical value between 0 and 1, where 0 indicates that the event is impossible, and 1 indicates that the event is certain.

There are 4 even numbers and 3 odd numbers in the first box, and 2 even numbers and 1 odd number in the second box.

The probability of drawing an even number from the first box is 4/7, and the probability of drawing an even number from the second box is 2/3.

By the multiplication rule of probability, the probability of drawing an even number from both boxes is

(4/7) × (2/3) = 8/21

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Answer:

Step-by-step explanation:

We can use the formula for the future value of an annuity to determine how much Marcia needs to invest today to meet her retirement goal of $90,000. The formula for the future value of an annuity is:

FV = PMT x [(1 + r/n)^(n*t) - 1] / (r/n)

where:

FV = future value of the annuity

PMT = payment (or deposit) made at the end of each compounding period

r = annual interest rate

n = number of compounding periods per year

t = number of years

In this case, we want to solve for the PMT (the amount Marcia needs to invest today). We know that:

Marcia wants to retire in 15 years (when she is 65), so t = 15

The interest rate is 10% per year, compounded semiannually, so r = 0.10/2 = 0.05 and n = 2

Marcia wants to have $90,000 in her retirement account

Substituting these values into the formula, we get:

$90,000 = PMT x [(1 + 0.05/2)^(2*15) - 1] / (0.05/2)

Simplifying the formula, we get:

PMT = $90,000 / [(1.025)^30 - 1] / 0.025

PMT = $90,000 / 19.7588

PMT = $4,553.39 (rounded to the nearest cent)

Therefore, Marcia needs to invest $4,553.39 today in order to meet her retirement goal of $90,000, assuming an interest rate of 10% per year, compounded semiannually.

Answer:

the answer would be 100 I guess

In response to the stated question, we may state that Hence, the 95% CI function for u is (16.72, 19.48), rounded to two decimal places in increasing order.

In mathematics, a function is a connection between two sets of numbers in which each member of the first set (known as the domain) corresponds to a single element in the second set (called the range). In other words, a function takes inputs from one set and produces outputs from another. Inputs are commonly represented by the variable x, whereas outputs are represented by the variable y. A function can be described using an equation or a graph. The equation y = 2x + 1 represents a linear function in which each value of x yields a distinct value of y.v

We use the following formula to create a confidence interval around the population mean u:

CI = x ± z*(s/√n)

where x represents the sample mean, s represents the sample standard deviation, n represents the sample size, z represents the z-score associated with the desired degree of confidence, and CI represents the confidence interval.

Because the degree of confidence is 95%, we must calculate the z-score that corresponds to the standard normal distribution's middle 95%. This is roughly 1.96 and may be determined with a z-table or calculator.

CI = 18.1 ± 1.96*(4.1/√34)

CI = 18.1 ± 1.96*(0.704)

CI = 18.1 ± 1.38

Hence, the 95% CI for u is (16.72, 19.48), rounded to two decimal places in increasing order.

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Step-by-step explanation:

A + B = 188

A = 188 - B - (1)

Now,

A - B = 34

188 - B - B = 34 (Substituting eqn 1 in A)

188 - 34 = 2B

154 = 2B

• B = 77 tons

Now

A = 188 - B

A = 188 - 77

A = 111 tons

The answer of the given question based on finding the missing length of a triangle the answer is , None of the answer choices match this value exactly, but the closest one is D) 15. Therefore, the answer is D) 15.

In geometry,  triangle is  two-dimensional polygon with three straight sides and three angles. It is one of  basic shapes in geometry and can be defined as  closed figure with three line segments as its sides, where each side is connected to two endpoints called vertices. The sum of  interior angles of  triangle are 180° degrees.

Triangles are classified based on length of their sides and  measure of their angles. A triangle can be equilateral, isosceles, or scalene based on whether all sides are equal, two sides are equal, or all sides are different, respectively.

To find the missing length indicated, we can use the Pythagorean theorem, which states that in a right triangle, the sum of the squares of the lengths of the two legs (the sides adjacent to the right angle) is equal to the square of the length of the hypotenuse (the side opposite the right angle).

In this triangle, we can see that the two legs have lengths of 9 and 16, and the hypotenuse has length X. So we can write:

9²+ 16² = X²

Simplifying the left-hand side:

81 + 256 = X²

337 = X²

Taking the square root of both sides (and remembering that X must be positive, since it is a length):

X = sqrt(337)

X ≈ 18.3575

So the missing length indicated is approximately 18.3575. None of the answer choices match this value exactly, but the closest one is D) 15. Therefore, the answer is D) 15.

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Method to list all non-isomorphic trees on n vertices is to add edges to a single vertex tree. Using A, B, C, D, E, we list 5 non-isomorphic trees on 6 vertices.

A by-hand method to give a list of all non-isomorphic trees on exactly n vertices is to start with a tree on n vertices and then generate all possible trees by adding edges between vertices that are not already connected.

For example, to find all non-isomorphic trees on 4 vertices, we can start with a single vertex and then add edges to form a tree with 2 vertices, then add edges to form a tree with 3 vertices, and finally add edges to form a tree with 4 vertices. We can then check each tree for isomorphism by comparing their adjacency matrices.

Using the method from (a), we can find all non-isomorphic trees on exactly six vertices by starting with a single vertex and adding edges until we have a tree on six vertices.

To ensure that we generate all possible trees, we can use the following five vertices: A, B, C, D, E. We can then generate all trees by adding edges between vertices that are not already connected, making sure to avoid creating cycles. After generating all trees, we can check for isomorphism by comparing their adjacency matrices.

The resulting list of non-isomorphic trees on six vertices, in alphabetical order, is shown. The tree 1 and tree 2 are the same. Also, trees 3, 4, and 5 are not isomorphic to each other or to trees 1 and 2.

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The measure of the arc intercepted by the angle and the vertical angles make up the angle subtended at the center. As a result, XYZ has a value of 35°.

Two lines intersect at a location, creating an angle.

An "angle" is the term used to describe the width of the "opening" between these two rays. The character is used to represent it.

Angles are frequently expressed in degrees and radians, a unit of circularity or rotation.

In geometry, an angle is created by joining two rays at their ends. These rays are referred to as the angle's sides or arms.

An angle has two primary components: the arms and the vertex. T

he two rays' shared vertex serves as their common terminal.

Hence, The measure of the arc intercepted by the angle and the vertical angles make up the angle subtended at the center. As a result, XYZ has a value of 35°.

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On the fifth day there were 4 tοmatοes left tο be sοld. Jοann had 71 tοmatοes tο begin with.

Prοbability is a measure οf the likelihοοd οr chance οf an event οccurring. It is a number between 0 and 1, where 0 indicates that the event is impοssible, and 1 indicates that the event is certain tο οccur.

Let's wοrk backwards frοm the last day and figure οut hοw many tοmatοes Jοann had οn the fοurth day.

On the fifth day, there were 4 tοmatοes left tο be sοld, which means she sοld half οf what was left οn the fοurth day. Sο she must have started with 8 tοmatοes οn the fοurth day (since half οf 8 is 4).

On the fοurth day, she sοld half οf what was left, which means she had 16 tοmatοes befοre she sοld any.

On the third day, she sοld 12 tοmatοes, which means she had 28 tοmatοes befοre she sοld any.

On the secοnd day, she sοld half οf what was left, which means she had 56 tοmatοes befοre she sοld any.

Finally, οn the first day, she sοld 15 tοmatοes.

Therefοre, Jοann had 71 tοmatοes tο begin with.

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Answer:

[tex]v = \frac{7}{2}[/tex]

Step-by-step explanation:

√9+25 = 28

π-4 = -0.8571

³√-27 = -3

2 / 3 = 0.6667

18÷2 = 9

√-27​ = 5.196

In mathematics, a surd is a term used to describe an irrational number that is expressed as the root of an integer. Specifically, a surd is a number that cannot be expressed exactly as a fraction of two integers, and is usually written in the form of a radical (e.g. √2, √3, √5, etc.).

We have √9+25 = 28

find the square root of 9 = 3

3 + 25 = 28

π-4 = 3.14 - 4

= -0.8571

³√-27 = ³√3³

= 3

2÷3 = 0.6667

18÷2 = 9

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question:

given :√9+25 : π-4 : ³√-27 : 2÷3 : 18÷2 : √-27​

find the value of the terms

Roberto needs 4 square yards of fabric to make his costume.

A fraction that has the numerator higher than or equal to the denominator is said to be inappropriate. For instance, the fraction 7/3 is incorrect since 7 is bigger than 3. Mixed numbers, which combine a whole number and a correct fraction, can be created from improper fractions.

Given that, piece of fabric that is 2 2/3 yards long and 1 1/2 yard wide.

Convert the length from a mixed number to an improper fraction:

2 2/3 = (2 x 3 + 2)/3 = 8/3

1 1/2 = 3/2

The area of the rectangle is:

Area = Length x Width

Substituting the values we have:

Area = (8/3) x (3/2) = 4

Hence, Roberto needs 4 square yards of fabric to make his costume.

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Answer: The total cost of buying 5 balls individually is $2.00 x 5 = $10.00.

The box costs $8.50, which means it is $10.00 - $8.50 = $1.50 cheaper to buy the box.

To calculate the percentage difference, we can use the formula:

% difference = (difference ÷ original value) x 100%

In this case, the difference is $1.50, and the original value is $10.00.

% difference = ($1.50 ÷ $10.00) x 100%

% difference = 0.15 x 100%

% difference = 15%

Therefore, it is 15% cheaper to buy the box than to buy 5 individual balls.

Step-by-step explanation:

Toward the end of a game of Scrabble, you hold the letters D, O, G, and Q. You can choose 3 of these 4 letters and arrange them in order in 24 different ways.

To solve this problem, we need to use the concept of permutations. A permutation is an arrangement of objects in a specific order. In this case, we need to find the number of permutations that can be made from the letters D, O, G, and Q when we choose 3 of these 4 letters.

The formula for finding the number of permutations is:

n! / (n-r)!

where n is the total number of objects and r is the number of objects we choose.

Using this formula, we can calculate the number of permutations as follows:

4! / (4-3)!

= 4! / 1!

= 4 x 3 x 2 x 1 / 1

= 24

Therefore, we can arrange the chosen 3 letters in 24 different ways.

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The unique solution to the initial value problem of differential equation is y(t) = -t^2 + 2t + 3sin(3t) - 1 with e(t) = -t^2 + 2t + 3sin(3t) - 9, a = 2, and B = -21.

To find the solution to the initial value problem, we first need to solve the differential equation.

Taking the derivative of y(t), we get:

y'(t) = -2t + a

Taking the derivative again, we get:

y''(t) = -2

Substituting y''(t) into the differential equation, we get:

y''(t) + 2y'(t) + 10y(t) = 20sin(3t)

Substituting y'(t) and y(t) into the equation, we get:

-2 + 2a + 10(-2t + a) = 20sin(3t)

Simplifying, we get:

8a - 20t = 20sin(3t) + 2

Using the initial condition y(0) = 2, we get:

y(0) = -2(0) + a = 2

Solving for a, we get:

a = 2

Using the other initial condition y'(0) = 21, we get:

y'(0) = -2(0) + 2(21) + B = 21

Solving for B, we get:

B = -21

Therefore, the solution to the initial value problem is:

y(t) = -t^2 + 2t + 3sin(3t) - 1

Thus, we have e(t) = y(t) - 8, so

e(t) = -t^2 + 2t + 3sin(3t) - 9

and a = 2, B = -21.

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

Consider the initial value problem >= [22. 2.1]+20). 361) = [2] Suppose we know that (t) = -2t + a 21? + is the unique solution to this initial value problem. Find e(t) and the constants and B. a = B= 8(t) =

Answer

6255 pounds

8.34×750=6255lbs

Answer:

30, rational

Step-by-step explanation:

[tex]3\sqrt{20}\cdot\sqrt{5}=3\sqrt{4}\sqrt{5}\cdot\sqrt{5}=(3\cdot2)\cdot5=6\cdot5=30[/tex]

The result is rational because it can be written as a fraction of integers.

Answer:

57

57

123

123

57

57

123

that's all.

Answer:

m<1 = 57°

m<2 = m<1 = 57°

m<3 = x = 123°

m<4 = x = 123°

m<5 = m<1 = 57°

m<6 = m<5 = 57°

m<7 = m<4 = 123°

Step-by-step explanation:

[tex]{ \tt{m \angle 1 + x = 180 \degree}} \\ { \colorbox{silver}{corresponding \: angles}} \\ { \tt{m \angle 1 = 180 - 123}} \\ { \tt{ \underline{ \: m \angle 1 = 57 \degree \: }}}[/tex]

Answer: Let's denote the length, width, and height of Sam's pool as l, w, and h, respectively. Then, we have:

lwh = 600

For the neighbor's pool, we know that it has the same length and height as Sam's pool, but the width is three times larger. Let's denote the width of the neighbor's pool as 3w. Then, the volume of the neighbor's pool is:

l(3w)h = 3lwh = 3(600) = 1800 cubic feet

Therefore, the volume of the neighbor's pool is 1800 cubic feet.

Step-by-step explanation:

The square root of 138 lies between 11 and 12, as 11²=121 and 12²=144.

Number is a mathematical object used to count, measure, and label. Numbers are used in almost every field of mathematics and science, including algebra, calculus, geometry, physics, and computer science. Numbers can also be used to represent data, such as population, income, temperature, or time. In addition, numbers are used to represent abstract concepts, such as love, truth, beauty, and justice.

This is because the square root of a number is the number that, when multiplied by itself, produces the original number. Therefore, to find the square root of 138, we need to identify two consecutive integers such that one of them squared is smaller than 138 and the other squared is larger than 138.

To do this, we can work our way up from the integer closer to 0, in this case 11. 11 squared is 121, which is smaller than 138, so we know that the square root of 138 must be between 11 and a larger integer. Then, if we square 12, we get 144, which is larger than 138. Therefore, we can definitively say that the square root of 138 lies between 11 and 12.

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The square root of 138 lies between 11 and 12, as 11² is 121 and 12² is 144.

Number is a mathematical object used to count, measure, and label. Numbers are used in almost every field of mathematics and science, including algebra, calculus, geometry, physics, and computer science. Numbers can also be used to represent data, such as population, income, temperature, or time. In addition, numbers are used to represent abstract concepts, such as love, truth, beauty, and justice.

To calculate this, we can divide 138 by 11 and 12, and see which integer is closer to the answer.

138 divided by 11 is 12.545454545454545454545454545455.
138 divided by 12 is 11.5.

Since 11.5 is closer to the answer, the square root of 138 lies between 11 and 12.

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Cold fronts generally move faster than warm fronts because cold air is denser and thus, moves more quickly. Precipitation with a cold front typically covers a broader area, especially during the winter.

On the other hand, warm fronts move more slowly as they are characterized by the gradual lifting of warm air over colder air. Cold fronts also typically have steeper slopes than warm fronts. This is because the leading edge of a cold front is more abrupt.

With a steep rise in the cold air mass. In contrast, the leading edge of a warm front has a gentler slope as the warm air gradually rises over the colder air.

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To calculate the actual distance in km, we need to use the scale factor of 1:100 000. This means that 1 cm on the map is equivalent to 100 000 cm in real life.

Therefore, 12.3 cm on the map is equivalent to 12.3 x 100 000 cm in real life.

Now, 1 km is equivalent to 100 000 cm.

Therefore, 12.3 x 100 000 cm is equivalent to 1.23 km.

Hence, the actual distance in km is 1.23 km.

The appropriate 0.5 adjusted formula for normal approximation is option (d) p(x > 8.5)

The appropriate 0.5 adjusted formula for normal approximation to approximate binomial probabilities when n is large is

P(Z > (x + 0.5 - np) / sqrt(np(1-p)))

where Z is the standard normal variable, x is the number of successes, n is the number of trials, and p is the probability of success in each trial.

To approximate binomial probability p(x > 8) when n is large, we need to use the continuity correction and find the appropriate 0.5 adjusted formula for normal approximation. Here, x = 8, n is large, and p is unknown. We first need to find the value of p.

Assuming a binomial distribution, the mean is np and the variance is np(1-p). Since n is large, we can use the following approximation

np = mean = 8, and

np(1-p) = variance = npq

8q = npq

q = 0.875

p = 1 - q = 0.125

Now, using the continuity correction, we adjust the inequality to p(x > 8) = p(x > 8.5 - 0.5)

P(Z > (8.5 - 0.5 - 8∙0.125) / sqrt(8∙0.125∙0.875))

= P(Z > 0.5 / 0.666)

= P(Z > 0.75)

Therefore, the correct option is (d) p(x > 8.5)

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The given question is incomplete, the complete question is:

To approximate binomial probability p(x > 8) when n is large, identify the appropriate 0.5 adjusted formula for normal approximation. a) p(x > 7.5) b)  p(x >= 9) c) p(x > 9) d) p(x > 8.5)

The missing side is 30.

Three line segments that cross at three non-collinear locations to form a triangle constitute a triangle in geometry. The triangle's three line segments are referred to as its sides, and its three points of intersection as its vertices.

A triangle is a three-sided polygon formed by three line segments intersecting at three non-collinear points, and it can be classified based on the length of its sides and the measure of its angles.

Given figure, there are two lines ate parallel, that's why two triangles are similar triangle.

Assume that the missing side is x.

So that side ratio in similar triangle are equal;

14/20 = 21/x

So, x = 30.

Therefore, the missing side x is 30

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Triangle Three line segments that cross at three non-collinear locations to form a triangle constitute a triangle in geometry. According to the question the missing side is 30.

Three line segments that cross at three non-collinear locations to form a triangle constitute a triangle in geometry. The triangle's three line segments are referred to as its sides, and its three points of intersection as its vertices. A triangle is a three-sided polygon formed by three line segments intersecting at three non-collinear points, and it can be classified based on the length of its sides and the measure of its angles.

Given figure, there are two lines ate parallel, that's why two triangles are similar triangle.
Assume that the missing side is x.
So that side ratio in similar triangle are equal;
14/20 = 21/x

So, x = 30.
Therefore, the missing side x is 30

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