There are 1,295 students attending a small university. There are 714 women enrolled. What percentage of student are women?

Answer:

  x = (π/2 +2nπ) ± π/3

Step-by-step explanation:

You want the solutions to the radical equation involving sin(x).

  [tex]\sqrt{\sin^2{x}-4\sin{x}+4}+\sqrt{\sin^2{x}+4\sin{x}+4}=\sqrt{\sin^2{x}+7\sin{x}+12.25}\\\\\sqrt{(\sin{x}-2)^2}+\sqrt{(\sin{x}+2)^2}=\sqrt{(\sin{x}+3.5)^2}\\\\|\sin{x}-2|+|\sin{x}+2|=|\sin{x}+3.5|\\\\(2-\sin{x})+(\sin{x}+2)=\sin{x}+3.5\\\\0.5=\sin{x}[/tex]

The values of x that make this true are ...

  x = {π/6, 5π/6} +2πn . . . . . for any integer n

__

Additional comments

  √(x²) = |x|

  sin(x) -2 is always less than zero, so its absolute value is 2-sin(x).

The attachment shows the equation written so the x-intercepts give the desired solutions.

The real number solution set for the trigonometric equation is x = 2πn + π/6 or 2πn + 5π/6 where n = is an integer

A trigonometric equation is an equation that contains the trigonometric ratios.

Given the trigonometric equation

√(sin²x - 4sinx + 4) + √(sin²x + 4sinx + 4) = √(sin²x + 7sinx + 12.25)

We know that sin²x - 4sinx + 4 = (sinx - 2)².

Also, sin²x + 4sinx + 4 = (sinx + 2)².

Also, sin²x + 7sinx + 12.25 = (sinx + 3.5)².

So, substituting these into the equation, we have that

√(sin²x - 4sinx + 4) + √(sin²x + 4sinx + 4) = √(sin²x + 7sinx + 12.25)

√(sinx - 2)² + √(sinx + 2)² = √(sinx + 3.5)²

|sinx - 2| + |sinx + 2| = |sinx + 3.5|

(2 - sinx) + (sinx + 2) = (sinx + 3.5)

2 - sinx + sinx + 2 = sinx + 3.5

Colecting like terms, we have that

-sinx + sinx + 2 + 2 = sinx + 3.5

0 + 4 = sinx + 3.5

4 = sinx + 3.5

Subtracting 3.5 from both sides, we have that

sinx = 4 - 3.5

sinx = 0.5

Taking inverse sin, we have that

x = sin⁻¹(0.5)

x = π/6 or 5π/6

So, the real number solution set is x = 2πn + π/6 or 2πn + 5π/6 where n = is an integer

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The simplified form of the given expression as required in the task content is; 8.

It follows from the task content that the simplified form of the given expression; -4 ( 2 - (³√8 × 6) ) / 5 is to be determined.

Therefore, By solving the innermost parentheses; we have;

-4 ( 2 - (2 × 6) ) / 5

= -4 ( 2 - 12 ) / 5

= -4 ( -10 ) / 5

= 40 / 5

= 8.

Therefore, the simplified form of the expression is; 8.

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Mr. Powel, who is our geometry teacher, told us we have a geometry test next week.

A nonrestrictive element is an element of a sentence that is not necessary for understanding the basic meaning of the sentence, but instead provides additional information. Nonrestrictive elements are usually set off with commas, while restrictive elements are not. For example, “My brother, who is an engineer, works in Chicago” is a sentence with a nonrestrictive element. The nonrestrictive element (“who is an engineer”) provides additional information about the brother, but does not provide any information about which brother is being referred to. The restrictive element “My brother who works in Chicago” does provide information about which brother is being referred to.

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Answer:

I am not exactly sure what they want you to put in the boxes, but hopefully the explanation below will shed some light on what is going on with this problem.

Step-by-step explanation:

The equation would be

y = 3x  

It looks like your question wants you to write the equation in the form

r(x) = 3x

y would be the student's score on the test.

x would be the number of questions that the student got right.

The x is the independent variable.  It tells us how many questions the student got right.

The y is the dependent variable.  It is the student's score.  The student's score depends on how many questions the student got right.

R(25) is saying what would be the score if the student got 25 answer correct?

3(25) = 75.  The student would get a score of 75

According to Polynomial System, the correct answer is that the roots of f(x) are (x+1).

A polynomial system (sometimes just a polynomial system) is a set of simultaneous equations f₁ = 0,..., fₙ = 0. where fi is a polynomial in multiple variables such as x₁,..., xₙ over the fields. k.

This is due to the zero product property that when two binomials are multiplied by 0, one of their factors must be 0.

A simple example of a system of polynomial equations is

x²+y²- 5 = 0

      xy-2 = 0.

Its solutions are the four pairs (x, y) = (1, 2), (2, 1), (-1, -2), (-2, -1). These solutions are easily verified by substitution, but proving that there are no other solutions requires more work.

Based on above description, we can say that:

(x+1) must be 0.

(x+1)=0

x=-1

Thus, If (x-1)=0 then x is 1 instead of -1 in question.

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The baker's total sales is a function of the number of boxes of cookies she sells will be y = 5x.

A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.

The linear equation is given as,

y = mx + c

Where m is the slope of the line and c is the y-intercept of the line.

A pastry specialist sells boxes of treats for $5 each. She has a sum of 20 boxes of treats to sell, and each crate contains 12 treats.

Let 'x' be the number of boxes of cookies and 'y' be the total cost. Then the equation is given as,

y = 5x

The baker's total sales is a function of the number of boxes of cookies she sells will be y = 5x.

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The area of the triangle is 48 square units.

To calculate the length of each side of the triangle ACB, the radii of the circles should be added respectively.

Length of side BC = 9+3 = 12 units

Length of side CA = 3+5 = 8 units

Length of side BA = 9+5 = 14 units

Area of triangle = (1/2 × Base × Height) square units

Area of triangle ACB = 1/2 × CA× BC sq units

                          Area = 1/2 × 8 × 12 = 48 sq units

Hence, the area of triangle ACB is 48 square units.

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Answer:

47.91 units²

Step-by-step explanation:

The radius of each circle is:

Therefore, the side lengths of the triangle are:

Heron's Formula allows us to find the area of a triangle in terms of its side lengths.

[tex]\boxed{\begin{minipage}{8 cm}\underline{Heron's Formula}\\\\$A=\sqrt{s(s-a)(s-b)(s-c)}$\\\\where:\\ \phantom{ww}$\bullet$ $A$ is the area of the triangle. \\ \phantom{ww}$\bullet$ $a, b$ and $c$ are the side lengths of the triangle. \\ \phantom{ww}$\bullet$ $s$ is half the perimeter.\\\end{minipage}}[/tex]

The perimeter of a two-dimensional shape is the distance all the way around the outside. Therefore, half the perimeter of the triangle is:

[tex]\implies s=\dfrac{14+12+8}{2}=17[/tex]

To calculate the area of the triangle, substitute the sides lengths and the value of s into Heron's formula and solve for A:

[tex]\implies A=\sqrt{17(17-14)(17-12)(17-8)}[/tex]

[tex]\implies A=\sqrt{17(3)(5)(9)}[/tex]

[tex]\implies A=\sqrt{2295}[/tex]

[tex]\implies A=47.906158268...[/tex]

[tex]\implies A=47.91\; \sf units^2\;\;(nearest\;hundredth)[/tex]

The probability that a corn crop has either an ear worm infestation, a corn borer infestation, or both is 0.27.

What is probability?

The area of mathematics known as probability deals with numerical descriptions of how likely it is for an event to happen or for a proposition to be true. A number between 0 and 1 is the probability of an event, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes its certainty.

We have to find the probability that a corn crop has either an ear worm infestation, a corn borer infestation, or both.

Since,

P(E or B) = P(E) + P(B) - P(E and B)

Given,

P(E) = 0.24

P(B) = 0.16

P(E and B) = 0.13

Hence,

P(E or B) = 0.24 + 0.16 - 013

P(E or B) = 0.27

Option D is correct.

Hence, the probability that a corn crop has either an ear worm infestation, a corn borer infestation, or both is 0.27.

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Probability in that a survey of 250 people ,at most 155 people support such cuts is 0.62.

What is probability?

The area of mathematics known as probability deals with numerical descriptions of how likely it is for an event to happen or for a proposition to be true. A number between 0 and 1 is the probability of an event, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes its certainty.

Given:

If 60% of the population supports massive federal budget cuts.

We have to find the probability in that a survey of 250 people, at most 155 people support such cuts.

So, the probability is, 155 / 250 = 0.62

Hence, probability in that a survey of 250 people ,at most 155 people support such cuts is 0.62.

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69 Passengers (20 plus additional 49) will result in maximum revenue for the owner of the yacht. Maximum Revenue will be $38,088.

current: 20 passengers at $944 each

let the number of additional passengers be x

cost per passenger = 944 - 8x

revenue (R) = (20+x)(944-8x)

= 18880 - 160x + 944x -8 x^2

dR/dx = -160 + 944 - 16x = 0 for a max of R

16x = 784

x = 49

There should be an additional 49 or a total of 69 passengers

The cost per passenger would be 944-8(49) or $552 per day

Maximum revenue for the yacht:

revenue (R) = (20+x)(944-8x)

revenue (R) = (20+49)(944-8(49))

revenue (R) = (69)(944-392)

revenue (R) = $38,088

Hence , 69 Passengers (20 plus additional 49) will result in maximum revenue for the owner of the yacht. Maximum Revenue will be $38,088.

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Answer:

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

Average rate of change for this case is:

The value of x in the diagram is 80°

What is an isosceles triangle?

Isosceles triangles are those triangles that have at least two sides of equal measure. We know that triangles are three-sided enclosed polygons and they are classified as equilateral, isosceles, and scalene, based on the length of their sides. In this article, we will learn about the definition of an isosceles triangle and its properties.

The body of the calculation is attached in a document.

In conclusion the value of x is 80°

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P-value >= 0.05 and adequate evidence supporting the organization's opinion at the a=0.05 significance level prevent the null hypothesis from being rejected.

A common statistical theory called the null hypothesis asserts that there is no statistical relationship or significance between two sets of observed data and measured events for a given single observed variable.

The alternative and null hypotheses are listed below. μ = 61

61 Alternative Hypothesis

Rejection Area

For = 0.05, this test has two tails.

Z has a critical value between -1.96 and 1.96.

Reject H0 thus if z -1.96 or z > 1.96

The test statistic is z = (xbar - mu)/(sigma/sqrt(n)) z = (61.5 - 61)/(2.5/sqrt(95)) z = 1.95.

P-value P-value for the method is 0.0512.

Failure to reject the null hypothesis because P-value >= 0.05.

Approach to the Rejection Zone

Failure to reject the null hypothesis because the test statistic z is within the crucial value range.

P-value >= 0.05 and adequate evidence supporting the organization's opinion at the a=0.05 significance level prevent the null hypothesis from being rejected.

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2.5% of values will lie above 29.

What is normal distribution?

A continuous probability distribution for a real-valued random variable in statistics is known as a normal distribution or Gaussian distribution.

The 68-95-99.7 rule is an illustration of how those many percentage of values lie in between  mean +/- 1, 2, and 3 standard deviations respectively.

For values to lie above 29, their z value comes out to be

(29-19) / 5 = 10/5 = 2

(Note: z value means how many standard deviations above the mean)

Thus for a z value = 2 (which 29 is in this problem) the percentage of values that lie between mean +/- 2*(standard deviation) is 95 (as stated by the 68-95-99.7 rule).

Thus only 5% values wont lie between mean +/-2 standard deviations.

So 5% values wont lie between 29 (z value=2) and 9 (z value=-2).

Since normal curve is symmetric, half of the values of the 5% will lie above 29 and the rest half will lie below 9.

So 50% of 5 % which is 2.5% of values will lie above 29.

Hence, 2.5% of values will lie above 29.

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The value of x is 15. The measurement of m∠M = 20°

What is an equilateral triangle?

An equilateral triangle in geometry is a triangle with equal-length sides on all three sides. In the well-known Euclidean geometry, an equilateral triangle is also equiangular, meaning that each of its three internal angles is 60° and congruent with the others.

The length each side of △ABC is 9 units.

Thus it is an equilateral triangle. The measurement of each angle is 60°.

Given that,  ∠ABC = 4x°.

Therefore, 4x° = 60°

Divide both sides by 4:

x = 15

43)

Given that, △LMN and △QRS are congruent triangle.

∠MNL = ∠QRS = 90°.

∠MLN = ∠QSR = 70°

and ∠NML = ∠RQS = x° (say)

The sum of all three angles of a triangle is 180°.

∠MNL + ∠MLN + ∠NML = 180°

90° + 70° + x° = 180°

Add like terms:

160° + x° =180°

Subtract 160° from both sides:

x° = 20°

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Answer: 19 new bears

Step-by-step explanation: To find the percentage of something, let's recall the formula:

Whole number x part % / 100

So, let's plug in the numbers to the formula:

95 x 20 / 100

95 x 20 = 1900

So, 1900 / 100 = 19; our answer

I hope this helped!

The number of tickets that will be sold is 5,560.

What is division?
A division is one of the fundamental mathematical operations that divides a larger number into smaller groups with the same number of components. How many total groups will be established, for instance, if 20 students need to be separated into groups of five for a sporting event? The division operation makes it simple to tackle such issues. Divide 20 by 5 in this case. 20 x 5 = 4 will be the outcome. There will therefore be 4 groups with 5 students each. By multiplying 4 by 5 and receiving the result 20, you may confirm this value.

Ticket sales for Six Flags White Water totaled $94,520 this summer.

Tickets for the water park cost $17 each.

The number of tickets that will be sold is =  $94,520/17 = 5,560.

Hence the number of tickets that will be sold is 5,560.

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On solving the provided question, we got to know that - recursive function to model the geometric sequence is 0.25

In order to create a sequence of terms, a recursive function either repeats itself or uses a previous term to compute a new term. An arithmetic-geometric series with terms that differ from each other frequently is used to explain this function.

Given, geometric sequence

24, 6, 1.5

First term of this sequence = 6

a1 = 6

Recursive formula geometric sequence

[tex]a_{n} = a_{(n-1)}r[/tex]

[tex]Here r = common. ratio .of .successive. and previous term\\From .the given .sequence\\[/tex]

r = a2/a1

r = 6/24

r = 0.25

[tex]Recursive formula of the given sequence will be,[/tex]

[tex]a_{n} = a_{(n-1)}(0.25)[/tex]

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By Angle-Angle-Side (AAS) triangle congruence theorem we know that two triangles are congruent if they have two sets of congruent angles and a set of non-included congruent sides.

Since no figure is given in the question we employ the reflexive characteristic to demonstrate that the overlapping sections are congruent in order to demonstrate that overlapping triangles are congruent.

If two triangles are precisely the same size and shape—that is, if they have the same side lengths and angle measurements—they are said to be congruent. If we are aware that two triangles have all the same sides and angles, we can conclude that the triangles are congruent.

To demonstrate that two triangles are congruent, however, we don't necessarily need to know that all of their sides and angles are congruent.

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The value of h is 70/17 if they are similar triangles and two sides are given in the figure.

Three edges and three vertices make up a triangle, which is a polygon.

In Euclidean geometry, any three points that are not collinear identify a distinct triangle and a distinct plane at the same time (i.e. a two-dimensional Euclidean space). In other words, every triangle is contained in a plane, and that triangle is contained in just one plane. All triangles are enclosed in a single plane if all of geometry is the Euclidean plane, however in higher-dimensional Euclidean spaces, this is no longer the case. Except as specifically stated, this article is about triangles in the Euclidean plane and general Euclidean geometry.

Given,

The figure has two similar triangles.

Here in the question the two sides are given,

We have the condition,

1/AB  +1/PC=1/MN

From the figure,

(1/7)+(1/10)=(1/h)

17/70=1/h

h=70/17

Therefore, the value of h is 70/17 if they are similar triangles and two sides are given in the figure.

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Answer:

1 milk and 2 oats

Step-by-step explanation:

milk to oats show that milk is first followed by oats and since 1 is first it is 1 milk and 2 oats

Answer:

94%

Step-by-step explanation:

Two examples of geometric sequence are {2, 6, 18, 54, 162, 486, 1458, ...} and {1, 2, 4, 8, 16, 32, 64, 128, 256, …}.

In mathematics, a geometric sequence or geometric progression refers to a sequence of non-zero numbers where the ratio between consecutive terms is constant. In such a sequence, each term (after the initial term) is determined by multiplying the previous one by a fixed, non-zero number called the common ratio. An example of geometric sequence is {2, 6, 18, 54, 162, 486, 1458,  ..} where each term is 3 times the previous term i.e., the common ratio is 3. Another example is {1, 2, 4, 8, 16, 32, 64, 128, 256, .. } where each term is 2 times the previous term i.e., the common ratio is 2.

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The potential energy of an rock of 40 kg and at a height of 10m is 4000 kgm^2s^2

What is potential energy and its formula?

An object possesses potential energy as a result of its position in relation to other objects. Potential energy is so named because it has the ability to transform into other types of energy, such kinetic energy. the formula for potential energy is mgh where m is the mass, g is the acceleration due to gravity and h is the height of the object.

We are given a rock of mass 40 kg which is at a height of 10m

We substitute the values in the formula to find the potential energy of the rock

Potential energy = m*g*h

Potential energy = [tex]40*10*10[/tex]

Potential energy = 4000 kgm^2s^2

Hence the potential energy of the rock is 4000 kgm^2s^2

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The laplace inverse transformation L−1{F(s)G(s)} =  5 [tex]\frac{2s}{s^{2} + 1^{2} }[/tex]  

If L{f(t)} = F(s), then the inverse Laplace transform of F(s) is

L−1{F(s)} = f(t). (1)

The inverse transform L−1is a linear operator:

L−1{F(s) + G(s)} = L−1{F(s)} + L−1{G(s)}, (2)

andL−1{cF(s)} = cL−1{F(s)}, (3)

for any constant c

given functions are

f(t) =5t ,g(t) = sin(t)

L(f(t)) = F(s)

L{F(s)*G(s)} = L^-1{5tsin(t)}

   =5L^-1{tsin(t)}

   =5L^-1{[tex]\frac{d}{ds}[/tex] tsin(t)}

    = 5 [tex]\frac{2s}{s^{2} + 1^{2} }[/tex]  

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At 85% confidence interval, the margin of error is 1.44 when the distribution of this population is approximately normal and has a standard deviation of $9,166.

The margin of error is a statistic that describes how much random sampling error there is in survey results. One should have less faith that a poll's findings would accurately reflect those of a population census the higher the margin of error. In a random survey sample, a margin of error is a statistical measurement that takes into account the discrepancy between actual and anticipated findings.

Given,

Starting salaries of 150 college graduates who have taken a statistics course have a mean of $42,991. Suppose the distribution of this population is approximately normal and has a standard deviation of $9,166.

Margin of error:

At 85% confidence level

α = 1 - 85%  

α = 1 - 0.85 = 0.15

Zα/2 = 0.075

α/2 = Z0.075

Zα/2 = 1.44

At 85% confidence interval, the margin of error is 1.44 when the distribution of this population is approximately normal and has a standard deviation of $9,166.

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The length of the side BC is 21 units.

Option (C) is correct.

What is an equilateral triangle?

In geometry, an equilateral triangle is a triangle whose all three sides are of equal length. The sides of an equilateral triangle are congruent, which means that all sides are of equal length. All the interior angles are equal(60 degrees) too.

The property of an equilateral triangle says that "All sides are equal in lengths".

So by using the above property, we can make the equation as

    3x - 6 = 2x + 3

This simplifies to:

3x = 2x + 9

Then, you can subtract 2x from both sides to get rid of the 2x on the left-hand side:

3x - 2x = 2x + 9 - 2x

This simplifies to:

x = 9

Now find BC as

BC = 2x + 3

    = 2(9) + 3

     = 21

Hence, the length of the side BC is 21 units.

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Therefore ,Based on this sample, of 90% confidence interval that Hot'n Now doughnuts will remain fresher for an additional 1.1 to 2.4 days than Sugar Yum doughnuts.

An estimation range for an unknowable parameter is referred to as a confidence interval in frequentist statistics. The most popular confidence level is 95%, but other levels, such 90% or 99%, are occasionally used for computing confidence intervals.

Here,

Given: random sample of 100 boxes of each brand

The difference of the means,μhn−μsy had a 90% confidence interval that was calculated as follows: (1.1,2.4).

Therefore,

Based on this sample, we are 90% confidence interval that Hot'n Now doughnuts will remain fresher for an additional 1.1 to 2.4 days than Sugar Yum doughnuts.

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Answer:

$226

Step-by-step explanation:

1. define the variable x

x = # of days to rent the carpet cleaner

2. substitute x for 7 days

c(7) = 30(7) + 16

3. solve

c(7) = 210 + 16

c(7) = 226

For 7 days, Rhonda will have to rent the carpet cleaner for $226.

If other factors are held constant, sets of data that would produce the largest value for an independent-measures t statistic is the two samples both have n =30, with sample variances of 20 and 25

In a T test, the T statistic is used to help you decide whether to accept or reject the null hypothesis.

You utilize it in a manner that is quite similar to using a Z-score. When you don't know the population standard deviation or have a limited sample size, you use the t statistic.

You employ the T statistic with a p value while performing a hypothesis test. Your results' likelihood of being the result of chance is indicated by the p-value. Typically, in statistics, you use a T Test with a T Statistic rather than a Z score because you don't know much about the population.

To have larger t value , Combined standard deviation should be less

Therefore, n should be large and standard deviation should be less

Hence , The two samples both have n=30, with sample variances of 20 and 25 will provide us larger t-statistics

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