what does the value of the sample correlation coefficient indicate about the relationship between the admit rate () and the -yr grad. rate ()?

The exact value of cos  is cos([tex]\frac{\pi }{12}[/tex])  = ([tex]\sqrt{2}[/tex] + [tex]\sqrt{6}[/tex]) /4

given that

Trigonometry is a field of mathematics that examines correlations between triangle side lengths and angles (from the Ancient Greek words "trigonon" and "metron"). The field was created in the Hellenistic era in the third century BC as a result of the use of geometry in astronomical research. While Indian mathematicians produced the earliest tables of values for trigonometric ratios (also known as trigonometric functions), such as sine, the Greeks concentrated on chord calculation.

Trigonometry has been used historically in fields like geodesy, surveying, celestial mechanics, and navigation.

Trigonometry has a wide variety of identities. In order to simplify an expression, identify a more practical version of an expression, or solve an equation, trigonometric identities are frequently employed to rewrite trigonometrical expressions.

now , we need to find the value of cos

[tex]\pi[/tex]/12 can be written as [tex]\pi[/tex]/3 and [tex]\pi[/tex]/4

using cos(-) we need to find

cos(A - B) = cos(A)cos(B)+sin(A)sin(B)

cos([tex]\frac{\pi }{3}[/tex] - [tex]\frac{\pi }{4}[/tex]) = cos([tex]\frac{\pi }{3}[/tex])cos([tex]\frac{\pi }{4}[/tex]) + sin([tex]\frac{\pi }{3}[/tex])sin([tex]\frac{\pi }{4}[/tex])

cos([tex]\frac{\pi }{12}[/tex]) = (1/2)(1/[tex]\sqrt{2}[/tex]) +([tex]\sqrt{3}[/tex]/2)(1/[tex]\sqrt{2}[/tex])

          = (1/2)([tex]\sqrt{2}[/tex]/2) + ([tex]\sqrt{3}[/tex]/2)([tex]\sqrt{2}[/tex]/2)

          = ([tex]\sqrt{2}[/tex]/4) + ([tex]\sqrt{6}[/tex]/4)

cos([tex]\frac{\pi }{12}[/tex])  = ([tex]\sqrt{2}[/tex] + [tex]\sqrt{6}[/tex]) /4

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Answer:

add up variables and divide by 2

Answer:

8x + 2y = 10  ==>  y = -4x + 5

12x - 3y = -25​  ==>  y = 4x + 25/3

Step-by-step explanation:

8x + 2y = 10  ==> solve for y

2y = 10 - 8x  ==> subtract 8x on both sides

(2y = 10 - 8x) / 2 ==> divide the equation by 2 to make 2y into y

y = 5 - 4x  ==> simplify

y = -4x + 5  ==> put the equation in y=mx+b form

12x - 3y = -25​  ==> solve for y

12x = -25 + 3y  ==> make y positive by adding 3y on both sides

12x + 25 = 3y ==> add 25 on both sides to isolate y

(3y = 12x + 25) / 3  ==> divide the equation by 3 to make 3y into y

y = 4x + 25/3 ==> simplify

i) Joint density distribution function  is given as

f(x,y) =  1/2Πσ1σ2  exp[(-1)/2 {((x-µ1)^2)/(σ1^2)+ ((y-µ2))/(σ2^2)}]

ii) E(aX + bY + c) = aµx + bµy + c iii) E(X^2) = σx^2 + µx^2

We have been given that, X ~ N(µx , σx^2) and Y~ N(µy , σy^2)

and X and Y are independent that is

                                ρ = 0

Note that the joint density function of two normal distribution is known as bivariate normal distribution which is given as

   (X , Y) ~ BVN(µ1 , µ2 , σ1^2 , σ2^2 , ρ)

And whose joint density function is          

f(x,y)  =   1/(2Πσ1σ2√(1-ρ^2))  exp[(-1)/(2(1-ρ^2)) {((x-µ1)^2)/(σ1^2)-2ρ (x-µ1)(y-µ2)/σ1σ2+ ((y-µ2))/(σ2^2)}]

 Where ρ = correlation coefficient of (x,y)

i) Joint density function of given X and Y which follows

(X , Y) ~ BVN(µx , µy , σx^2 , σy^2 , 0) is given as

f(x,y) =  1/2Πσ1σ2  exp[(-1)/2 {((x-µ1)^2)/(σ1^2)+ ((y-µ2))/(σ2^2)}]

ii) E(aX + bY + c) = aE(X) + bE(Y) + c

                       = aµx + bµy + c

iii) E(X^2) = V(X) + [E(X)]^2      {V(X) = E(X^2) - [E(X)]^2}

           = σx^2 + µx^2

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If Sₙ denotes the sum of the reciprocals of the non-zero digits of the integers from 1 to 10ⁿ inclusive , then the smallest positive integer n for which Sₙ is an integer is 63 .

The "Sₙ" be the sum of reciprocals of the non-zero digits of the integers from 1 to 10ⁿ inclusive ;

We Let [tex]K= \sum_{i=1} ^{9} \frac{1}{i}[/tex] ,

On further examination , we get that , [tex]S_{1} =K+1[/tex] ;

Since each digit "n" appears once and the number 1 appears for an extra time.

Now , we write  S₂ .

So ,Each term of K will appear 10 times in the units place and 10 times in the tens place ,

So , we get [tex]S_{2} = (n10^{n-1})K+1[/tex] ; and there are total "n" places ;

The denominator of K is written as [tex]D=2^{3} .3^{2} .5.7[/tex] .

For Sₙ to be an integer, [tex]n10^{n-1}[/tex] must be divisible by D , we must select "n" to be divisible by [tex]3^{2} .7[/tex]   .

And since need to find the smallest integer "n" , So , the n is [tex]3^{2} .7 = 63[/tex] .

Therefore , For Sₙ to be an integer , the smallest positive integer n is 63 .

The given question is incomplete , the complete question is

Let Sₙ be the sum of the reciprocals of the non-zero digits of the integers from 1 to 10ⁿ inclusive. find the smallest positive integer n for which Sₙ is an integer .

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A spool of thread measuring 8 3/4 inches long and 4 inches wide can be cut into 2 1/7 inch pieces.

In light of the conditions stated, come up with: [tex]$\frac{8 \frac{3}{4}}{2 \frac{1}{7}}$[/tex] To improper fractions, change the mixed numbers to: [tex]$\frac{\frac{35}{4}}{\frac{15}{7}}$[/tex] Multiply the reciprocal of a fraction to get its division: [tex]$\frac{35}{4} \times \frac{7}{15}$[/tex]

Mark this common element as a no-go: Multiplying [tex]$\frac{7}{4} \times \frac{7}{3}$[/tex] Mark the common element as absent: Multiplying [tex]$\frac{7 \times 7}{4 \times 3}$[/tex] . Put the following in one fraction : [tex]$\frac{49}{12}$[/tex] . The product or quotient should be

calculated.Find the biggest number that is greater than [tex]$\frac{49}{12}$[/tex] and less than or equal to it . A spool of thread measuring 8 3/4 inches long and 4 inches wide can be cut into 2 1/7 inch pieces.Otherwise, you or a device will need to count 127 turns (the irreducible repeat, independent of thread pitch), after which the half nut must be closed.

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Determine appropriate formula to model scenarios.

Sometimes, different formulas can generate similar results. The key is to choose the formula that is most appropriate for the scenario, and it's also important to consider the complexity of the formula and its interpretability.

Based on the problem or question, the available data, and the literature review, determine the appropriate mathematical model to use. The model should be able to capture the key features of the problem or question and provide an accurate representation of the data.

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Answer:

5:4

Step-by-step explanation:

girls = 4

boys = 5

ratio = boys:girls = 5:4

HOPE THIS HELPED

Answer:

8.25

Step-by-step explanation:

trapezoid area =

(a+b)/2 times h =

if its 1.5

(4+7)/2 times 1.5 =

11/2 times 1.5 =

5.5 times 1.5 =

8.25

if its 15

5.5 times 15 =

82.5

its probably 1.5

wikipedia

Step-by-step explanation:

let addicts be x and Nike be x+6

so ,

x+x+6=12

or,2x=6

or x=-3

now x+6=3+6=9

therefore he had 9 Nike and 3 Adidas

In graph theory, a 2-factor is a subgraph of a given graph that includes every vertex of the original graph and has the property that every vertex has even degree (i.e. degree is a multiple of 2).

The term "2-factor" is used because it is a factor of the original graph that is made up of edges and every vertex has degree 2.

A 2-factor can also be defined as a set of cycles that cover all vertices of the graph. In other words, it is a collection of cycles such that every vertex belongs to exactly one cycle. A 2-factor can also be thought of as a cycle cover of a graph.

A graph that has a 2-factor is called a 2-factorizable graph. Not all graphs are 2-factorizable, for example a graph with an odd number of vertices can't have a 2-factor.

2-factors have many applications in various fields such as scheduling, coding theory, and computer science. They are also used to study the connectivity and robustness of graphs.

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The slope intercept form of the equation is B) y=2x-6.

What is slope intercept form of the equation?

When the slope of the line being studied is known, and the provided point is also the y intercept, the slope intercept formula, y = mx + b, is utilised (0, b).   It provides both a slope and an intercept, which is why the form is known as the slope-intercept form.

Here According to the table using two points [tex](x_1,y_1) =(0,-6)[/tex] and [tex](x_2,y_2)=(3,0)[/tex] .

Now using slope formula m = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

=> m = [tex]\frac{0-(-6)}{3-0}[/tex]

=> m = [tex]\frac{6}{3} = 2[/tex]

Now using equation formula then

=> [tex]y-y_1=m(x-x_1)[/tex]

=> y-(-6)=2(x-0)

=> y+6 = 2x

=> y = 2x-6

Hence the slope intercept form of the equation is B) y=2x-6.

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No, the conditions for inference have not been met. The two samples must be independent, meaning that the individuals in the college sample should not also be in the high school sample. Without independent samples, it is not possible to construct a 95% confidence interval for the true mean difference.

1. Collect data from the two samples of seniors in high school and college.

2. Calculate the mean difference in the number of hours of sleep for the two samples.

3. Calculate the standard deviation of the differences in hours of sleep for the two samples.

4. Calculate the standard error of the mean difference.

5. Calculate the critical value for a 95% confidence interval.

6. Calculate the lower and upper bounds of the confidence interval by

adding and subtracting the critical value from the mean difference.

7. Interpret the confidence interval to determine the true mean difference in the number of hours of sleep for seniors in high school and colleg

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Answer: [tex]303^{\circ}[/tex]

Step-by-step explanation:

The point [tex]P[/tex] lies in the fourth quadrant, so the angle is given by [tex]360^{\circ}-\alpha[/tex], where [tex]\alpha[/tex] is the reference angle.

The reference angle is given by [tex]\arctan \left(\frac{\frac{\sqrt{7}}{4}}{\frac{\sqrt{3}}{4}} \right)=\arctan \left(\sqrt{\frac{7}{3}} \right)[/tex].

This means [tex]\theta=360^{\circ}-\arctan \left(\sqrt{\frac{7}{3}}} \right) \approx 303^{\circ}[/tex].

The solution to the simultaneous equation is x = -1/2 and y = √71 / 2

What is a Linear Expression?

A linear expression is an algebraic statement where each term is either a constant or a variable raised to the first power. In other words, none of the exponents can be greater than 1.

For example, t² is a variable raised to the second power, but t is a variable raised to the first power.

x² + y² = 18 ----- 1

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

From equation 2

x + 2 = - 3x

x + 3x = -2

4x = -2

x = -2/4

x = -1/2

Substitute x in equation 1

(-1/2)² + y² = 18

1/4 + y² = 18

y² = 18 - 1/4

y² = (72 - 1)/4

y² = 71/4

y = √71 / 2

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The result of.tge evaluation of the given expression as required is; 11 / 4.

It follows from the task content that the value of the expression given be determined upon evaluation.

Since the given expression is; 5 - 3/2 to the second power

5 - (3/2)²

= 5 - 3²/2²

= 5 - 9/4

= 20 / 4 - 9 /4

On this note, the resulting expression is; ( 20 - 9 ) / 4 = 11/4.

Ultimately, the result of the expression evaluation as required to be determined is; 11 / 4.

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The ratio in simplest form in the three cases is 5 : 6, 36 : 29 and 1 : 5.

30 treadmills to 36 elliptical machines can be simplified to 5 treadmills to 6 elliptical machines. To simplify, you can divide both numbers by their greatest common factor, which in this case is 6.

30/6 = 5 and 36/6 = 6

So 30 : 36 = 5 : 6

180 red marbles to 145 blue marbles can be simplified to 12 red marbles to 11 blue marbles. To simplify, you can divide both numbers by their greatest common factor, which in this case is 5.

180/5 = 36 and 145/5 = 29

180 : 145 = 36 : 29

In the word "flashlight", the ratio of vowels to total letters is 2:8. The word "flashlight" has 2 vowels (a,i) and 10 total letters. To simplify divide by 2.

2 : 10 = 1 : 5

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The probability that all three Escher prints will be placed consecutively is 3/5 or 0.6

The probability that all three pieces by Escher will be placed consecutively when hanging the 10 pieces of art in a random order is the probability that the 3 Escher prints will be in a row among the other 7 pieces.

There are 10!/(3! × 7!) = 120 ways to order the 10 pieces of art, and 3! = 6 ways to order the 3 Escher prints among themselves.

So the total number of ways to order the art such that the Escher prints are consecutive is 120 × 6 = 720.

Now to find the probability that all three Escher prints will be placed consecutively, we divide the number of ways that this can happen (720) by the total number of ways the art can be arranged (120) to get 720/120 = 6/10 = 3/5.

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A circle chart, often known as a pie chart, is a means to summarize a set of nominal data or a visual depiction of the many values of a particular variable (e.g. percentage distribution).

A circle is created in the plane by each point that is a specific distance from another point (center). Thus, it is a curve made up of points that are separated from one another by a defined distance in the plane. Additionally, it is rotationally symmetric about center at every angle. Every pair of vertices in a circle's closed, two-dimensional plane are evenly spaced apart from the "center." A circular symmetry line is made by drawing a line through the circle. Additionally, it is rotationally symmetric the about center at every angle.

Here,

The pie chart is divided into sectors and segments, and each sector and segment corresponds to a specific amount of the overall (percentage).

The data is a representation of 360°. The pie is always valued at 100% overall.

A pie chart is useful for organising and displaying data by percentage of the total.

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Answer:

148

Step-by-step explanation:

first plug in w(x) into u(x):

u(w(x)) = 5(-5(x)+4)+3

then plug in -5 for x:

u(w(-5)) = 5(-5(-5)+4)+3

solve:

= 148

This is a composite function:

Composite functions are are functions that are written within each other like f(g(x).

To solve this problem, first solve the function within u(x), which would be w(x)

w(-5) = -5(-5) -4

        = 25 - 4

       = 21

Now, plug in that value into u(x) to get your final answer:

u(21) = 5(21) +3

         = 105 +3

       = 108

Answer: u(w(-5) = 108

Answer:

The radius of the circle is 5.1, and the diameter of the circle is 10.2

Step-by-step explanation:

In the shown circle, the point from the center to the edge is 5.1, so that is the radius. Then, the diameter of a circle is twice its radius, so we have:

5.1 * 2 = 10.2

So the diameter of the circle is 10.2.

The radius of the circle is 5.1, and the diameter of the circle is 10.2.

Hope this helped!

Answer:

they always go smallest to largest!

7.65 x 2= 3.21

Step-by-step explanation:

Answer:

53

Step-by-step explanation:

Three minutes equal 180 beats on the double number line. three minutes of 270 beats 2:180=90 , 3:270=90

In music, a beat is a pulse that occurs repeatedly. Simple meters are those in which the beat first breaks into two, and subsequently into four. There are two beat groups in double meters, three beat groups in triple meters, and four beat groups in quadruple meters.

For double, triple, and quadruple meters, there are several conducting patterns. One group of beats equals one measure (duple, triple, or quadruple). Bar lines divide the measures. Simple meters' time signatures specify two things: the beat unit, or note value that represents the beat, and the number of beats in each measure (the top number). Notes are graphically grouped by beat and connected by a beam.

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The value of x in the simplest radical form is 3.

The trigonometric functions in mathematics are real functions that connect the right-angled triangle's angle to the ratios of its two side lengths. They are extensively employed in all fields of geometry-related study, including geodesy, solid mechanics, celestial mechanics, and many others.

Here, we have

Given: Let the triangle be ΔABC

The triangle ABC is a right-angled triangle and the angles inside the triangles are 45°, 45° and 90°

tan θ = x / 3

Now , θ = 45°

So, tan 45° = x / 3

The value of x is 3.

Hence, the value of x is 3.

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Answer:

[tex]\textsf{1)} \quad 10000(1.06)^t[/tex]

2)   €17,908.48

3)  0.5%

4)  120

[tex]\textsf{5)} \quad 10000(1.005)^{120}[/tex]

6)  €18,193.97

7)  More money.

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{7 cm}\underline{Annual Compound Interest Formula}\\\\$ A=P\left(1+r\right)^{t}$\\\\where:\\\\ \phantom{ww}$\bullet$ $A =$ final amount \\ \phantom{ww}$\bullet$ $P =$ principal amount \\ \phantom{ww}$\bullet$ $r =$ interest rate (in decimal form) \\ \phantom{ww}$\bullet$ $t =$ time (in years) \\ \end{minipage}}[/tex]

Given:

Substitute the given values into the compound interest formula to write an expression that describes the given scenario over t years:

[tex]\implies A=10000(1+0.06)^t[/tex]

[tex]\implies A=10000(1.06)^t[/tex]

To calculate how much money will be in the fund after 10 years, substitute t = 10 into the equation from question 1:

[tex]\implies A=10000(1.06)^{10}[/tex]

[tex]\implies A=10000(1.79084769...)[/tex]

[tex]\implies A=17908.4769...[/tex]

Therefore, there will be €17,908.48 in the emergency fund after 10 years.

If the annual rate is 6%, the monthly interest rate is the annual rate divided by 12 (since there are 12 months in a year):

[tex]\implies \dfrac{6\%}{12}=0.5\%[/tex]

Given that are 10 years in the scenario, the exponent will be the number of months in 10 years:

[tex]\implies 10 \times 12 = 120[/tex]

0.5% = 0.005

Therefore, the complete expression that describes the scenario, given an annual interest rate of 6% that compounds monthly over 10 years is:

[tex]\implies 10000(1 + 0.005)^{120}[/tex]

[tex]\implies 10000(1.005)^{120}[/tex]

To calculate how much money will be in the emergency fund after 10 years if the interest compounds monthly, calculate the expression from question 5:

[tex]\implies 10000(1.005)^{120}[/tex]

[tex]\implies 10000(1.81939673...)[/tex]

[tex]\implies 18193.9673...[/tex]

Therefore, there will be €18,193.97 in the emergency fund after 10 years.

Amount in fund when compounded annually = €17,908.48

Amount in fund when compounded monthly = €18,193.97

Therefore, there is more money in the emergency fund when it is compounded monthly as the compounding frequency is greater (interest is earned on both the principal and the interest, so the more frequent the compounding periods are, the more interest is earned).

The general rule about compounding in exponential functions is the higher the number of compounding periods, the greater the amount of compound interest.  

In terms of compounding interest in investment:

Answer:

yes

Step-by-step explanation:

The absolute value is only greater than or equal to zero.

The total number of different collections of pets your roommate can take is 10 + 10 = 20.

In this scenario, your roommate has two options for which pets to take with him: either the dog or the cat. If he takes the dog, he can take any two of the remaining five pets (fish, turtle, rock, pony). There are 5 choose 2 = 10 ways for him to do this. If he takes the cat, he can take any two of the remaining five pets (fish, turtle, rock, pony, dog). There are 5 choose 2 = 10 ways for him to do this.

Therefore, the total number of different collections of pets your roommate can take is 10 + 10 = 20.

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Answer:

2 1/5

Step-by-step explanation:

Answer:

$27,400.

Step-by-step explanation:

We know that the salesman makes $25,000 annually plus 6% commission on his total sales.

We also know that he sold $40,000 worth of trampolines this year.

So we can find out his commission by multiplying the value of sales with 6% commission rate.

Commission = 0.06 * $40,000 = $2400

To find out his total earnings we need to add his annual salary with commission earned.

Total earnings = $25,000 + $2400 = $27,400

So the salesman's total earnings for this year is $27,400.