In a survey about a change in public policy, 100 people were asked if they favor the change, oppose the change, or have no opinion about the change. Of the 100 people surveyed, 50 are male and 37 oppose the change in policy. Of the 37 who oppose the change, 25 are female. What is the probability that a randomly selected respondent to the survey is a man or opposes the change in policy? Express your answer as a percent

Answer:

Step-by-step explanation:

d.

The possible solutions to the equation are:

3π/4

π/4

Trigonometric equations involve trigonometric functions such as sine, cosine, tangent, etc. The goal is to solve for the unknown variable in the equation.

csc²x - 2 = 0

csc²x = 2

csc x = √2

sin x = 1/√2    (Remember: csc x  = 1/sinx)

x = sin⁻¹(1/√2 )

x = 90° or 135°  (sine is positive in 1st and 2nd quadrants)

x = π/4 or 3π/4

Thus, the possible solutions to the equation are x = π/4 or 3π/4.

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Answer:

x = 5;

[tex]y = \frac{5 \sqrt{2} }{2} [/tex]

Step-by-step explanation:

Use trigonometry:

[tex]y = \tan(45°) = \frac{ \frac{5 \sqrt{2} }{2} }{y} [/tex]

Use the property of proportion to find y:

[tex]y = \frac{ \frac{5 \sqrt{2} }{2} }{ \tan(45°) } = \frac{ \frac{5 \sqrt{2} }{2} }{1} = \frac{5 \sqrt{2} }{2} [/tex]

Use the Pythagorean theorem to find x:

[tex] {x}^{2} = {y}^{2} + { (\frac{5 \sqrt{2} }{2}) }^{2} [/tex]

[tex] {x}^{2} = {( \frac{5 \sqrt{2} }{2}) }^{2} + { (\frac{5 \sqrt{2} }{2}) }^{2} = \frac{25 \times 2}{4} + \frac{25 \times 2}{4} = \frac{50}{4} + \frac{50}{4} = \frac{100}{4} = 25[/tex]

[tex]x > 0[/tex]

[tex]x = \sqrt{25} = 5[/tex]

Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

Applying absolute value rule the solutions are:

x + 1/2 = 3/2/3       or        x + 1/2 = -3 2/3

Changing to fractions:

x + 1/2 = 11/3   or   x + 1/2 = -11/3

and then changing to a common denominator

x + 3/6 = 22/6    or    x + 3/6  = -22/6

Solve left equation first:

x + 3/6 - 3/6 = 22/6 - 3/6

x = 19/6 or 3 1/6

Solve the right equation:

x + 3/6 - 3/6 = -22/6 - 3/6

x = -25/6 or  -4 1/6

So the two solutions are:

19/6 and -25/6 as improper fractions

And

as mixed numbers:  3 1/6 and -4 1/6

The total rainfall is given as 16

Average rainfall is given as 1.23

The average temperature is given as 22.8

we would add all of the weekly rain values

2.6 + 1.6 + 10.2 + 1.4 + 0.2 = 16

The total rainfall is 16

The average rainfall would be 16 divided by the total number of days that we have here:

16 / 13

= 1.23

The average rainfall is 1.23

total temperature

22.9 + 28.5 + 24.6 + 36.2 + 19 + 20.8 + 19.4 + 22.8 + 22.6 + 21.6 + 19.6 + 19.9 + 18.3

= 296.2

average = 296.2 / 13

= 22.8

average temperature is given as 22.8

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Therefore, the rotated triangle has vertices at (-5, -10), (-3, -1), and (-4, -2), which forms a new triangle.

In mathematics, a vertex refers to a point where two or more lines, edges, or curves meet. In geometry, a vertex is a point where two or more edges of a polygon or polyhedron intersect. For example, in a triangle, each of the three points where the sides meet is a vertex.

A vertex is a fundamental unit of a graph, which is a collection of vertices connected by edges. Each vertex represents an entity or object, and the edges represent the relationships or connections between them. For example, in a social network graph, the vertices could represent individual users, and the edges could represent their friendships or connections with other users.

To perform a 270° counterclockwise rotation of a point about a center point, we can use the following formula:

[tex](x', y') = (x - a) * cos(theta) - (y - b) * sin(theta) + a, (x - a) * sin(theta) + (y - b) * cos(theta) + b[/tex]

where (x, y) is the original point, (x', y') is the rotated point, (a, b) is the center point, and theta is the angle of rotation in radians.

Let's first find the center point C(-5, -4) of the rotation. Then, we'll apply the formula to each vertex of the triangle to find its new location after the rotation.

[tex]Center point C = (-5, -4)[/tex]

Vertex P(-13, -3):

[tex]x' = (-13 - (-5)) * cos(270^{0} ) - (-3 - (-4)) * sin(270^{0} ) + (-5) = -5[/tex]

[tex]y' = (-13 - (-5)) * sin(270) + (-3 - (-4)) * cos(270) + (-4) = -10[/tex]

So, after the rotation, vertex P is at (-5, -10).

Vertex Q(-7, 3):

[tex]x' = (-7 - (-5)) * cos(270) - (3 - (-4)) * sin(270) + (-5) = -3[/tex]

[tex]y' = (-7 - (-5)) * sin(270) + (3 - (-4)) * cos(270) + (-4) = -1[/tex]

So, after the rotation, vertex Q is at (-3, -1).

Vertex R (-6, 2):

[tex]x' = (-6 - (-5)) * cos(270) - (2 - (-4)) * sin(270) + (-5) = -4\\y' = (-6 - (-5)) * sin(270) + (2 - (-4)) * cos(270) + (-4) = -2[/tex]

So, after the rotation, vertex R is at (-4, -2).

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The interest is $9.To find the interest, we can use the simple interest formula:

I = P * r * t

what is interest ?

Interest is the amount of money charged by a lender to a borrower for the use of money, usually expressed as a percentage of the amount borrowed. In other words, it is the cost of borrowing money.

In the given question,

To find the interest, we can use the simple interest formula:

I = P * r * t

where I is the interest, P is the principal, r is the annual interest rate as a decimal, and t is the time in years.

Here, the principal is $200, the annual interest rate is 9%, and the time is 1/2 year.

Converting the annual interest rate to a decimal, we get:

r = 9% = 0.09

And, converting the time to years, we get:

t = 1/2 year

Substituting the values into the formula, we get:

I = $200 * 0.09 * (1/2) = $9

Therefore, the interest is $9.

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Answer:

Step-by-step explanation:

Scatterplots and correlation never prove causation. Causation may only be determined by well-designed experiments.

A scatterplot is a type of graph commonly used to observe and visually represent the relationships between variables. Variable values ​​are represented by dots. The position of the points on the vertical and horizontal axes indicates the value of each data point. Therefore, scatterplots use Cartesian coordinates to display the values ​​of the variables in the dataset. A scatterplot is also called a scatter graphs, scatter charts, or scattergrams.

Correlation means association, and more specifically, it measures how well two variables are related. Correlation analysis have three possible outcomes: Positive correlation, negative correlation, no correlation.

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Step-by-step explanation:

So what this question is asking is the volume of the cube. volume can be found with V=lwh or V=l^3 because it is a cube. So

V=(8)^3
V=512

The cube can fit 512 cubic inches.

Answer:

277.5

Step-by-step explanation:

first you multiply 37 * 90 then you get 3330 then you divide it by 12 and you get 277.5

The fifth multiple of each fraction is shown as follows:

1. 2/6 = 5/3

2. 7/10 = 7/2

3. 3/8 = 15/8

4. 5/12 =25/12

5. 7/6 = 35/6

To get the multiple of a fraction, the best thing to do will be to multiply the fraction by the whole number in question. In this case, the whole number is five.

So, to get the right answers, you can begin by multiplying the functions with the whole number five. The values obtained are the fifth multiples. for the fraction, 2/6, the fifth multiple is 5/3.

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We need a sample size of at least 879 to be 99.5% confident that our estimate of the population mean will be within 1 of the true population mean.

To determine the required sample size, we use mathematical formula:

[tex]n = (z * σ / E) ^ 2[/tex]

Where:

n: sample size

z: z-score corresponding to desired level of confidence (99.5%)

σ: population standard deviation

E: margin of error (1 in this case)

Substitute given values into formula:

[tex]n = (2.807 * 29.6 / 1) ^ 2\\n = 878.3[/tex]

Hence, in order to be 99.5% confident that our estimate of the population mean would be within 1 of the actual population mean, we need a sample size of at least 879.

It's vital to remember that the estimate will be more accurate the larger the sample size. Larger sample numbers might, however, also be more costly and time-consuming to gather. Hence, while choosing the sample size, researchers must carefully weigh the trade-offs between the required level of confidence, the margin of error, and the resources at their disposal.

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The exact value of the trigonometric expression, given the conditions of sin and sec is -85/36.

The exact value of the trigonometric expression with u and v in Quadrant III is 304/425.

We are given sin(u) = -3/5 with 3π/2 < u < 2π and cos(v) = 15/17 with 0 < v < π/2.

cos(v - u) = cos(v)cos(u) + sin(v)sin(u)

We are given cos(v) = 15/17 and sin(u) = -3/5. To find sin(v) and cos(u), we can use the Pythagorean identities:

sin^2(v) + cos^2(v) = 1

sin(v) = sqrt(1 - (15/17)^2) = 8/17

Similarly, for cos(u):

sin^2(u) + cos^2(u) = 1

cos(u) = -sqrt(1 - (-3/5)^2) = -4/5

Now we can find cos(v - u):

cos(v - u) = cos(v)cos(u) + sin(v)sin(u)

cos(v - u) = -36/85

Since sec(v - u) = 1/cos(v - u), we have:

sec(v - u) = 1/(-36/85) = -85/36

Since both u and v are in Quadrant III, sin(u) and cos(u) are both negative, and sin(v) and cos(v) are both negative. We are given sin(u) = -7/25 and cos(v) = -15/17.

To find sin(v) and cos(u), we can use the Pythagorean identities:

sin^2(u) + cos^2(u) = 1

cos(u) = -sqrt(1 - (-7/25)^2) = -24/25 (since u is in Quadrant III)

Similarly, for sin(v):

sin^2(v) + cos^2(v) = 1

sin(v) = -sqrt(1 - (-15/17)^2) = -8/17 (since v is in Quadrant III)

Now we can find cos(u + v):

cos(u + v) = (-24/25)(-15/17) - (-7/25)(-8/17)

cos(u + v) = 304/425

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The total number of college students is 204,700,000.

Percentage, a relative value indicating hundredth parts of any quantity. One percent (symbolized 1%) is a hundredth part; thus, 100 percent represents the entirety and 200 percent specifies twice the given quantity.

Here, Percentage of enrolled student for part time = 23%

         Total enrolled students = 8.9 millions

Number of part time student = 23% x 8.9 million

                                              [tex]= 0.23 \times 8900000[/tex]

                                             [tex]=204,700,000[/tex]

Thus, the total number of college students is 204,700,000.

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The value of X in the given fraction is 1/12

A fraction is a mathematical expression that represents a part of a whole or a quotient of two numbers. It is expressed as one integer or number (called the numerator) divided by another integer or number (called the denominator), separated by a line or a slash.

Here, we are going to find the LCM of both 4 and 6 to determine the value of X.

LCM = 12

X = 1/4 - 1/6

X = (3 - 2)/12

X = 1/12

Therefore, we can conclude that the value of X in the given fraction is 1/12.

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scalar factor= 2, in order to find the scalar factor between two triangle  we need to get the ratio between any of thier side of both the triangle on same side

what is scalar factor?

In mathematics, a scalar factor is a numerical value that scales or stretches a vector or a matrix by a certain factor. In other words, a scalar factor is a constant that is multiplied to a given vector or matrix to change its size or magnitude.

In the given question,

In mathematics, a scalar factor is a numerical value that scales or stretches a vector or a matrix by a certain factor. In other words, a scalar factor is a constant that is multiplied to a given vector or matrix to change its size or magnitude.

For instance, if we have a vector v = (x, y, z), then multiplying it by a scalar factor k will result in a new vector kv = (kx, ky, kz), which is stretched or shrunk according to the value of k. Similarly, if we have a matrix A, multiplying it by a scalar factor k will result in a new matrix kA, where each element of A is multiplied by k.

in order to find the scalar factor between two triangle  we need to get the ratio between any of thier side of both the triangle on same side

scalar factor= opposite side of bigger triangle / opposite side of smaller triangle

scalar factor= 20/10

scalar factor= 2

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The equation of the graph is

The table is completed by substituting the x to the function y = sqrt(x) + 2

When x = 0:

y = sqrt(0) + 2

y = 0 + 2

y = 2

When x = 1:

y = sqrt(1) + 2

y = 1 + 2

y = 3

When x = 4:

y = sqrt(4) + 2

y = 2 + 2

y = 4

When x = 9:

y = sqrt(9) + 2

y = 3 + 2

y = 5

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Therefore , the solution of the given problem of equation comes out to be  line passing through the spot (-4,1) and perpendicular to [tex]y = 1/3x + 5[/tex] is [tex]y = -3x - 11.[/tex]

Variable words are commonly used in complex algorithms to show consistency between two contradictory claims. Academic expressions called equations are used to show the equality of various academic numbers. Instead of a different method that could split 12 to two parts, consider the data supplied by y + 7,.

Here,

[tex]Y = mx + b[/tex], where m is the line's slope and b is its y-intercept, is the given equation in slope-intercept notation.

Provided that the slope of the provided line is 1/3, the slope of a line perpendicular to it will be the reciprocal of the negative of 1/3, or -3.

=> [tex]y - y_{1} = m(x - x_{1} )[/tex]

in which m [tex]= -3, x_{1} = -4,[/tex] and y1 = 1.

By replacing these numbers, we obtain:

=>[tex]y - 1 = -3(x - (-4))[/tex]

By condensing and figuring out x, we arrive at:

=> [tex]y - 1 = -3(x + 4)[/tex]

=>[tex]y - 1 = -3x - 12[/tex]

=> [tex]y = -3x - 11[/tex]

Consequently, the equation of the line passing through the spot (-4,1) and perpendicular to y = 1/3x + 5 is y = -3x - 11.

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The weight of the pumpkins that Gina's class grew was measured.

a) There is a total of 23 pumpkins.

b) 7 pumpkins weigh 10 pounds.

c) The number of pumpkins that weigh 6 pounds is equal to 3 times the number of pumpkins that weigh 9 pounds.

Based on the given information, we can complete the sentences as follows:

a) There is a total of 23 pumpkins.

To get this number, we need to add up the number of dots for each weight:

3 + 5 + 1 + 7 + 4 + 2 + 1 = 23

b) 7 pumpkins weigh 10 pounds.

To find the weight with the most dots, we look for the peak in the line plot, which corresponds to 10 pounds, and count the number of dots on this peak, which is 7.

c) The proportion of pumpkins that weigh 6 pounds to those that weigh 9 pounds is 3 times.

To find the number of pumpkins that weigh 6 pounds, we count the number of dots on the peak corresponding to 6 pounds, which is 3. To find the number of pumpkins that weigh 9 pounds, we count the number of dots on the peak corresponding to 9 pounds, which is 1. Multiplying the number of pumpkins at 9 pounds by 3, we get 3 x 1 = 3, which is the same as the number of pumpkins at 6 pounds. Therefore, the statement is true.

The complete question is:-

Gina's class measured the weights of the pumpkins that they grew.

A line plot named “Pumpkin Weights” shows data from six to fourteen pounds. Six has three dots. Eight has five dots. Nine has one dot. Ten has seven dots. Twelve has four dots. Thirteen has two dots. Fourteen has one dot. Fill in the boxes to complete the sentences below to make each statement true.

a)there is a total of ____ pumpkins.

b) 7 pumpkins weigh _____ pounds.

c) the number of pumpkins that weigh ____ pounds is equal to 3 times the number of pumpkins that weigh 9 pounds.

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The series [tex]a_n=\frac{(-1)^{n+1}}{n}[/tex] is converges.

What is a series?

An n-arithmetic sequence is a sequence in which the difference d of successive terms is constant.

The general term of the arithmetic progression can be written using its first term [tex]a_1[/tex], tolerance [tex]d[/tex], and index [tex]n[/tex] as [tex]a_n=a_1+(n-1)d[/tex].

According to the alternating series test, if a sequence {b_n} satisfies the following three conditions:

[tex]b_n[/tex] is positive for all [tex]n[/tex].

[tex]b_n[/tex] is decreasing (i.e., [tex]b_n > = b_{n+1}[/tex] for all n).

[tex]\lim_{n \to \infty} b_n =0\\[/tex]

Then the alternating series [tex](-1)^n b_n[/tex] converges.

To apply the alternating series test to the sequence {a_n}, we first note that [tex]a_n = (-1)^{n+1}/n[/tex] satisfies condition 3, since [tex]\lim_{n \to \infty} \frac{1}{n} =0[/tex].

Next, we observe that [tex]a_n[/tex] is positive for n = 1, 3, 5, ... and negative for n = 2, 4, 6, ..., so [tex](-1)^n a_n = (-1)^{n+1}/n[/tex] is an alternating sequence.

Finally, we show that a_n is decreasing by considering the difference between successive terms,

[tex]a_{n+1} - a_n = (-1)^n/n - (-1)^{n+1}/(n+1)\\ = (-1)^{n} [(n+1)/(n(n+1))] \\= (-1)^{n}/n(n+1) < 0[/tex]

since n and n+1 are both positive. Therefore, a_n is decreasing.

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Table A is showing the correct relation of equation y=1.5x

An equation is a mathematical statement that asserts that two expressions are equal. It typically consists of two parts: the left-hand side (LHS) and the right-hand side (RHS), separated by an equal sign (=). They are used to model real-world phenomena, to solve problems, and to make predictions. Examples of equations include linear equations, quadratic equations, systems of equations, and differential equations.

Using the relation;

y=1.5x

Putting the value x=9

y=1.5×9

y=13.5

Putting the value x=11

y=1.5×11

y=16.5

On observing the tables, option A is satisfying the relation

Hence, Table A is showing the correct relation of equation y=1.5x.

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The complete question is:

Image is attached below.

Answer:

y = -2x + 5

Step-by-step explanation:

slope = rise/run = 2/-1 = -2

b = y-intercept = 5

y = -2x + 5

Answer:

Step-by-step explanation:

area of trapezoid

[tex]= \frac{sum~of~parallel~sides}{2} \times altitude\\69.6=\frac{sum~of~parallel~sides}{2} \times 8.7\\139.2=sum~of~parallel~sides \times 8.7\\sum~of~parallel~sides=\frac{139.2}{8.7} =16[/tex]

minimum parameter=16+2(8.7)=16+17.4=33.4 in

Answer: Let's denote the length, width, and height of the cuboid as l, w, and h, respectively. We know that the shaded face is a square, which means that two of its dimensions are the same. Without loss of generality, let's assume that the dimensions of the square face are l and w.

Since the volume of the cuboid is 4900 cm³, we have:

lwh = 4900

Substituting l = 25 - w (since the length of the cuboid is 25 cm) and simplifying, we get:

(25 - w)w h = 4900

Now, we use the fact that the shaded face is a square. Since two of its dimensions are the same, we have:

l = w

Substituting this into the equation above, we get:

(25 - l)l h = 4900

Simplifying further, we have:

25l^2 - 4900 = 0

Solving for l using the quadratic formula, we get:

l = 14 or -14/5

Since the length of the cuboid cannot be negative, we have l = 14. Therefore, the length of one side of the square face is 14 cm.

Step-by-step explanation:

Answer:

yes

Step-by-step explanation:

the distance between the points P=(-7, -2) and E=(1,-9) in the coordinate plane is √113

The length of the line segment bridging two points on a plane is known as the distance between the points. d=((x2 - x1)2 + (y2 - y1)2) is a common formula to calculate the distance between two points. This equation can be used to calculate the separation between any two locations on an x-y plane or coordinate plane.

We have two points p=(-7,-2) and E=(1,-9)

then the distance between PE is

d=√(1+7)²+(-9+2)²

d= √(64+49)

d=√113

the distance between the points P=(-7, -2) and E=(1,-9) in the coordinate plane is √113

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This argument is invalid because the premises do not logically lead to the conclusion. The conclusion is simply a repetition of the first premise and does not follow from the second premise. The argument lacks coherence and fails to establish a clear relationship between the premises and the conclusion. Therefore, we cannot accept the conclusion as a logical consequence of the premises.