Find the average value of f(x)=−2sin(x)+5cos(x) over the interval [π,2π] .

The system that has linear inequalities has the point (3, -2) in its solution set is y > -3; y ≥ 2/3x - 4.

We know that

If a ordered pair is a solution of the system of inequalities, then the ordered pair must satisfy both inequalities (makes true both inequalities)

In option B, we have

y > -3 ----> inequality A

y ≥ 2/3x - 4 ----> inequality B

In both inequality, change the values of x and y at the point (3, -2) and then compare the outcomes.

Inequality A

y > -3 ----> is true

Inequality B

y ≥ 2/3x - 4 ----> is true

Therefore

The ordered pair is a solution of the system B

As a result, the point (3, -2) in the solution set of the system with linear inequalities is y > -3; y 2/3x - 4.

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The regression equation y=0.37x+62.5 predicts statistics performance based on math aptitude scores, with a strong positive correlation and 65.1% of the variation explained.

a. The regression equation that best predicts statistics performance, based on math aptitude scores is y = 0.37x + 62.5, where y is the statistics grade and x is the math aptitude test score.

b. The significance of a is the intercept of the regression line, which is the predicted value of the statistics grade when the math aptitude score is 0. The significance of b is the slope of the regression line, which indicates the amount of change in the statistics grade for a unit change in the math aptitude score.

c. If a student scored an 80 on the aptitude test, the estimated statistics grade would be 79.5.

d. The standard error of the estimate is 6.36. This indicates the average amount of error between the observed values and the predicted values.

e. The coefficient of correlation is 0.807 and the coefficient of determination is 0.651. The coefficient of correlation indicates a strong positive linear relationship between the math aptitude scores and statistics grades. The coefficient of determination indicates that 65.1% of the variation in statistics grades is explained by the math aptitude scores.

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The value of the standard deviation does not change and remains the same.

Given, a retired statistic professor has recorded final exam results for decades. the mean final exam score for the population of a student is 82.4 with a standard deviation of 6.5.

The mean μ = 82.4

The standard deviation σ = √[ ((x - μ)2 + (y - μ)2 + (z - μ)2)/3 ]

we have to find the variance,

We now add a constant k to each data value and calculate the new mean μ'.

μ' = ((x + k) + (y + k) + (z + k)) / 3 = (x + y + z) / 3 + 3k/3 = μ + k

We now calculate the new mean standard deviation σ'.

σ' = √[ ((x + k - μ')2 +(y + k - μ')2+(z + k - μ')2)/3 ]

Note that x + k - μ' = x + k - μ - k = x - μ

also y + k - μ' = y + k - μ - k = y - μ and z + k - μ' = z + k - μ - k = z - μ

Therefore σ' = √[ ((x - μ)2 +(y - μ)2+(z - μ)2)/3 ] = σ

If we add the same constant k to all data values included in a data set, we obtain a new data set whose mean is the mean of the original data set PLUS k. The standard deviation does not change.

Hence, the standard deviation does not change.

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Answer:

it is using the Pythagorean theorem its basically a^2 + b^2 = c^2 watch videos on it, it will explain better

A hypothesis is a tested statement regarding the relationship between two or more variables or a proposed explanation for some observable occurrence.

An complete group is referred to as a population when making inferences about it.

Your chosen group for data collection is referred to as a sample. Always, a sample's size is smaller than the population as a whole.

Using a statistical test, researchers compare the evidence supporting the null and alternative hypotheses, which are two conflicting claims:

There is no population impact, or null hypothesis (H0).

There is a population effect, or alternative hypothesis (Ha or H1).

No effect, no difference, or no association are all examples of null hypotheses. They always have an equivalence when expressed in mathematical terms.

The complement of the null hypothesis is the alternative hypothesis. The extensive nature of null and alternative hypotheses ensures that they account for all potential outcomes.

The question is incomplete so, I've answered in general

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According to the manufacturer's claim, we build an hypothesis test, find the test statistic and the p-value relative to this test statistic.

The value of the test statistic is z = 1.65.

The p-value of the test is of 0.0495 > 0.02, which means that there is not sufficient evidence to say that his batting average has improved at the 0.02 level of significance.

Average of 0.48 in 25 at bats,

Test if there was improvement:

At the null hypothesis :

[tex]H_0 : P_1 - P_2 = 0[/tex]

At the alternative hypothesis:

[tex]H_1 : P_1 - P_2 > 0[/tex]

The p-value of the test is the probability of finding a difference of at least 0.19, which is 1 subtracted by the p-value of z = 1.65.

Looking at the z-table, z = 1.65 has a p-value of 0.9505.

1 - 0.9505 = 0.0495.

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The ratio a : b represented in the table of values is (c) 3 : 5

From the question, we have the following table of values that can be used in our computation:

a b

1.5 2.5

51 85

99 165

Remove the last two entries in the table

So, we have the following representation

a b

1.5 2.5

Express the remaining entries as a ratio

So, we have the following representation

Ratio = a : b

Substitute the known values in the above equation, so, we have the following representation

Ratio = 1.5 : 2.5

Divide the ratio by 0.5

So, we have the following representation

Ratio = 1.5/0.5 : 2.5/0,5

Evaluate the quotients

So, we have the following representation

Ratio = 3 : 5

Hence, the ratio is (c) 3 : 5

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POLYGON

A polygon is a plane figure that is described by a finite number of straight line segments connected to form a closed polygonal chain or polygonal circuit.

TYPES OF POLYGON

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Answer:

Step-by-step explanation:

You want the amount spent on ads in each medium given the total and relations between amounts spent for newspaper, television, and radio ads.

Let n, t, r represent the amounts spent on ads in newspapers, television, and radio, respectively. The given relations tell you ....

  n +t +r = 87.5

  -n +t +r = 2.9

  n -t = 5.4

The augmented coefficient matrix can be reduced to row-echelon form using a suitable calculator or spreadsheet. This tells you the amounts spent in each medium. The attachment shows this.

__

Additional comment

The value of n can be found by subtracting the second equation from the first. That can be used in the third equation to find t, and both of those values can be used in either of the first two equations to find r.

Answer:

70.73%

29/41 = 0.7073...

Move the decimal over 2 places and get: 70.73

The team a finishes with more points than team b with a probability of 319/512

seven teams play a soccer tournament in which each team plays every other team exactly once

in the first game of the tournament, team a beats team b

We need to find  the probability that team a finishes with more points than team b

Both teams, a and b play 6 matches each

In the first match, a wins. Now they can play 5 matches each

Of the remaining 5 games

a win 0 and b win zero

P(a > b) = 5C1/2^5 x 5C1 / 2^5 = 1/1024

a win 1 and b win 1 or zero

P(a > b) = 5C1/2^5 x(5C0 + 5C1) / 2^5 = 30/1024

a win 2  and b win 2 or 1 or zero

P(a > b) = 5C2/2^5 x(5C0 + 5C1 + 5C2) / 2^5 = 160/1024

a win 3 and b win 3 or 2 or 1 or zero

P(a > b) = 5C3/2^5 x(5C0 + 5C1 + 5C2 + 5C3) / 2^5 = 260/1024

a win 4 and b win 4 or less

P(a > b) = 5C4/2^5 x(5C0 + 5C1 + 5C2 + 5C 3 + 5C4) / 2^5 = 155/1024

a win 5 and b win 5 or less

P(a > b) = 5C1/2^5 x(5C0 + 5C1+ 5C2 + 5C3 + 5C4 + 5C5) / 2^5 = 32/1024

P(a> b) = (1 + 30 + 160 + 260 + 155 + 32)/1024 = 638/1025 = 319/512

Therefore, the  the probability that team a finishes with more points than team is 319/512

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The value of g(t) is 18 when x is 2.

Proportionality is defined as, the fact or quality of being in proper balance or relation as to size or quantity, degree, severity, etc

Given that, g(t) varies inversely with t and g(t)=9 when t=4.

According to question,

g(t) ∝ 1/t

Let k be constant of proportionality, then,

g(t) = k/t

Solving for k, we get,

9 = k/4

k = 36

When, t = 2, then

g(t) = 36/2

g(t) = 18

Hence, The value of g(t) is 18 when x is 2.

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1164 [tex]inch^{3}[/tex] is the surface area of a pyramid with a side of 4 inches and a slant height of 6 inches.

The quantity of space enclosing a three-dimensional shape's exterior is its surface area. The sum of the exterior surfaces of a three-dimensional object, or the item's faces, is what determines an object's surface area. The units used for measurement are square.

n order to calculate a pyramid's surface area, we use the formula SA=B+12ps, where B denotes the base's size, p its perimeter, and s its slant height. Since the base is a triangle, we will use the triangle's area formula to determine B.

so area of triangle = 1/2 * base* height = 1/2* 4 *6

area of triangle= 12 [tex]inch^{2}[/tex]

and perimeter of pyramid = 4a = 16 [tex]inch^{2}[/tex]

and surface  area of pyramid = base + 12 * perimeter * slant height

= 12 + 12*16*6

= 1164 [tex]inch^{3}[/tex]  is the area of a pyramid with a side of 4 inches and a slant height of 6 inches.

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Answer:64

Step-by-step explanation:

The ASA (angle-side-angle) congruence rule states that two triangles are congruent if two angles and the side between them are equal in both triangles.

The ASA congruence rule is a fundamental rule of geometry that states that two triangles are congruent when two angles and the side between them are equal in both triangles. This rule is especially important when solving geometry problems, as it can help determine the size and shape of a triangle.

The ASA congruence rule is applicable to all triangles, regardless of their size or shape, and can be used to find the missing angles or sides of a triangle. By applying the ASA congruence rule, students can gain a better understanding of the properties of triangles and other geometric shapes.

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Answer: 18 with a remainder of 17

Step-by-step explanation:

The amount of cabbage 12.82 pounds will be to buy for $5.00.

What is Division method?

Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications. For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.

Given that;

The cabbage costs $0.39 per pound.

Now,

Since, The cabbage costs $0.39 per pound.

Hence, The amount of cabbage to buy for $5.00 = 1/0.39 × 5

                                                                            = 12.82 pounds

Thus, The amount of cabbage 12.82 pounds will be to buy for $5.00.

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Check the picture below.

The probability of getting a queen if a card is drawn out from a pack of 52 cards is 1/13

Probability is the chance of an event to occur with respect to the given conditions.

Probability of an event P(E) = number of favorable outcomes (n)/total number of outcomes(N)

P(E) = n/N

Total cards in a pack (N) = 52

Number of queens (n) = 4

P(getting a queen from pack of cards) = Number of queens/Total cards in a pack

P(E) = n/N

P(E) = 4/52

P(E) = 1/13

Hence, the probability of the given event is 1/13.

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The shorter piece is 56 inches and the longer piece is 180 inches when cut into two halves is a 224-inch pipe.

Given that,

Cut into two halves is a 224-inch pipe. The length of one component is three times that of the other.

We have to determine the shorter piece's length.

We know that,

Let's use the variable L to represent the longer pipe and the variable S to represent the shorter pipe.

Since the pipe will be the sum of L and S, we can create the following equation:

L+S=224

The longer piece is three times the shorter piece, which is another thing we know.

L=3S

Substituting the second equation for the first equation

L+S=224

3S+S=224

4S=224

S=224/4

S=56

The shorter piece is 56 inches.

The lengthier component should be used to replace the following:

L=3S

L=3(56)

L=168

The longer piece is 180 inches.

Therefore, The shorter piece is 56 inches and the longer piece is 180 inches when cut into two halves is a 224-inch pipe.

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The solution is 194, rounded to the closest whole number. Thus, x2≈194. In light of this, the weight ranges for raisin bags that require new packaging are less than 157 grams and also more than 194 grams.

A statistic called the standard deviation describes how much variation or dispersion there is in a set of statistics .In contrast to a high standard deviation, which shows that the values are spread out, a low standard deviation suggests that the values tend to be close to the mean of the collection. out over a wider range.

Here,

In this instance, the standard deviation is 11 and the mean is 175. Assume that x1 is the heaviest weight at which the bags fall into the lower 5% and x2 is the lightest weight at which they fall into the upper 4.5%. 5% of the time, and 4.5% of the time, the likelihood is below x1 and above x2. The raisin bags should fall below x1 and above x2 if they need to be repackaged. The points x1 and x2 are illustrated in the image below.

1 x 0.045 x 0.05 = 0.905 is the probability between x1 and x2. Below is a picture of the normal distribution curve for raisins bag weights.

To calculate x1 and x2, locate x1 first. To the left of x1, there is a 0.05 probability. To find x1, use Excel. 1. Start Excel. Toggle a cell that is empty. Press ENTER after typing =NORM.INV(0.05,175,11).

The answer is 157, rounded to the nearest whole number. Thus, x1≈157. To compute x2, use the formula 0.05+0.905=0.955 for the probability to the left of x2. To determine x2, use Excel. Start Excel. Toggle a cell that is empty. Enter the command =NORM.INV(0.955,175,11).

The solution is 194, rounded to the closest whole number. Thus, x2≈194. In light of this, the weight ranges for raisin bags that require new packaging are less than 157 grams and also more than 194 grams.

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The likelihood of this question will be determined as P( E | ~H)=1 - P(E|H).

For independent events the probability P( E | H ) is calculated as:

P( E | H ) = P( E ) * P( E and H)

P( E and H) = P(E) * P(H).

Since the event E has already happened and is obvious, if P(E | H)>P(E | H) then the event E is dependent on the mind of maya, but if P(E | H)>P(E | H) then the event E is not dependent on the mind of maya.

In our situation, P(E | H), which means that the plane crushing is independent of Maya's thoughts, is the probability that will suit this argument.

Since it is illogical to claim that Maya can perceive far-off objects with her mind, the likelihood of this question will be determined as P( E | ~H ) = 1 - P( E | H ).

For independent events the probability P( E | H ) is calculated as

P( E | H ) = P( E ) * P( E and H)

P( E and H) = P(E) * P(H).

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The time required for the total amount in Harrison's account to reach $410 is 4.49 years.

The simple interest formula is expressed as;

A = P( 1 + rt )

Where A is accrued amount, P is principal, r is interest rate and t is time.

Given the data in the question;

Plug the given values into the above formula and solve for time t.

A = P( 1 + rt )

A/P = 1 + rt

A/P - 1 =  rt

t = ( A/P - 1 ) / r

t = ( $410/$345 - 1 ) / 0.042

t = ( 13/69 ) / 0.042

t = 4.49 years

Therefore, the time needed to reach accrued amount is 4.49 years.

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Answer:-2.3, -1/3, square root of 3, square root of 7, 5.1

Answer: x = 56

Step-by-step explanation:

The angle horizontally adjacent from 73 is also equal to 73 due to the triangle being isosceles (the legs are given as equal). Therefore the other angle in that triangle has to be 180 - (73*2) = 34. This angle is a part of the 90 degree angle that is noted in the figure. The other part of that angle must be 90 - 34 = 56. Since this angle is in another isosceles triangle, the angle horizontally adjacent to it must also be 56. x is equal to this angle by definition of vertical angles, so x = 56.

The value of the expression; 6 × 10 + 4³ as given in the task content is; 124.

It follows from the task content that the value of the expression given in the task content; 6 × 10 + 4³ is to be determined.

Hence, the value of the expression can be evaluated using PEMDAS guidelines as follows;

Since the given expression is;

6 × 10 + 4³

Since the exponent, so that we have;

6 × 10 + 64

Next, solve the multiplication, so that we have;

60 + 64

= 124.

On this note, the value of the expression is; 124.

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6/11 is the probability that a randomly selected student speaks French, given that the student is male

It is a branch of mathematics that deals with the occurrence of a random event.

There are 11 members who speak french and 5 are females in 11 members

5/11

p(a given b) = p(a and b) / p(b).

6 of the people in the group are men that speak french, then the probability of (a and b) becomes 6/40

probability that a person speaks french is 11/40

p(a given b)=6/40/11/40

=6/40×40/11=6/11

Hence, 6/11 is the probability that a randomly selected student speaks French, given that the student is male.

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Slope is: 2/5.

The y-intercept of this equation is located at point (0, 1/5).

[tex]5y - 2x = 1[/tex]

[tex]5y=1+2x\\ \\\frac{5y}{5}=\frac{1+2x}{5} \\ \\y=\frac{1}{5}+\frac{2x}{5} \\ \\y=\frac{2}{5} x+\frac{1}{5}[/tex]

The slope of a linear equation will always be the coefficient of the variable "x" when the equation is solved for "y". Therefore, the slope of this linear equation is [tex]\frac{2}{5}[/tex] .

The Y incercept is the value of "y" where the line of the equation touches the y axis. In other words, the y-intercept is the value when x= 0. Hence, we may substitute x by 0 in the equation and calculate a value for y:

[tex]y=\frac{2}{5} (0)+\frac{1}{5}\\ \\y= \frac{1}{5}[/tex]

The y-intercept of this equation is located at point (0, 1/5).

Answer:

In step 2 you would multiply both sides by 2 not divide by 2

Step-by-step explanation:

1/2w=30

 *2      *2

w=60

Answer:

The mistake is between Step 1 and Step 2.

Step-by-step explanation:

Leon is isolating the variable, w. In this case, he should have multiplied 2 to both sides of the equation to isolate the variable, w.

[tex]2 * (\frac{1}{2})w = 3 * 2\\ w = 3 * 2\\w = 6[/tex]

For the whole question

1) Add 12 to both sides of the equation:

[tex]\frac{1}{2} w - 12 = 18\\\frac{1}{2} w - 12 (+12) = 18 (+12)\\\frac{1}{2} w = 18 + 12\\\frac{1}{2} w = 30[/tex]

2) Multiply 2 to both sides of the equation:

[tex](2 *) (\frac{1}{2}w) = 30 (* 2)\\w = 30 * 2\\w = 60[/tex]

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The value of x will be equal to -1 so that ab and cd are parallel to each other.

It is possible to determine a line's direction and steepness by looking at its slope. Finding the slope between lines inside a coordinate plane can aid in anticipating if the lines are perpendicular, parallel, or none at all without physically using a compass.

As per the given information provided by the question,

(a)

Let's determine their slopes based on these line segments.

The first one is AB.

[tex]m=\frac{2-(-12)}{-2-(-9)}[/tex]

m = 14/7

m = 2

(b)

The slope of two parallel lines is the same, thus let's set this slope formula to provide the value of m=2. In consideration of CD :

[tex]2=\frac{-2-6}{-5-x}[/tex]

2(-5 -x) = -8

-10 -2x = -8

-2x = -8 + 10

x = -2/2

x = -1

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