Identify the general shape and direction of this graph of this function on the interval (1, infinity)

The marginal frequency of students who chose dancing is 37.

The correct answer to the given question is option 3.

The marginal frequency of students who chose dancing can be calculated by adding up the number of students who chose dancing in each row or column. In this case, we need to add up the number of art students who chose dancing (22) and the number of music students who chose dancing (15), which gives us a total of 37. This is the marginal frequency of students who chose dancing.

Based on the survey results, it appears that a slightly higher percentage of art students prefer dancing (41.5%) compared to music students (31.9%). However, both groups of students seem to be fairly evenly split between dancing and playing sports, with a slight preference for playing sports overall.

It's worth noting that cardiovascular activity is important for overall health and well-being, and both dancing and playing sports can provide great opportunities for exercise and physical activity. Additionally, both activities can also be enjoyable and provide a sense of community and social connection, which is important for middle school students who are still developing their social skills and relationships. Ultimately, the choice between dancing and playing sports will depend on individual interests, preferences, and abilities.

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Given that 16 families went on a trip and the cost of the trip was Rs. 2,16,352.The amount paid by each family is to be determined by unitary method Hence each family paid Rs.13522

Now, let's solve this by using the method of unitary method. To find the cost of 1 family trip, we will divide the total cost of the trip by the number of families.2,16,352 / 16 = 13,522 So, the cost of the trip per family is Rs. 13,522.Hence, each family paid Rs. 13,522 for the trip.

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Answer:

Step-by-step explanation

1. The total cost of the trip for all 16 families is Rs 2,16,352.
2. To find out how much each family paid, we need to divide the total cost by the number of families: Rs 2,16,352 ÷ 16.
3. When we do the division, we get the result: Rs 13,522.

Now let's check if this result is correct:

1. If each family paid Rs 13,522 for the trip, then the total cost for all 16 families would be: 16 × Rs 13,522 = Rs 2,16,352.
2. This is exactly the same as the total cost given in the problem statement.

So we have shown that each family paid **Rs 13,522** for the trip

1. The domain of \(V (h(r))\) is restricted to values of r greater than 0.

2. \(V(h(r)) = 3.5\pi r^3\)

3. The volume depends on the radius of the cylinder

Answer:

see below

Step-by-step explanation:  5 23  8 03

the lenght of the longer leg of a right triangle is 9 ft longer than the lenght of the shorter leg x. The hypotenuse is 9 ft shorter than twice the lenght of the shorter leg.

shorter leg    = x

longer leg     = x + 9

hypotenuse  =  2x - 9

Pythagorean theorem  =    a² + b²  = c²

             shorter-leg² + longer-leg² = hypotenuse²

                         x²  +  (x+9)²  = (2x - 9)²                  solve for x

                  x² +  (x+9) (x+9)  =  (2x - 9)(2x - 9)

                 x² +  (x²+18x+81)  =  (4x² - 36x + 81)

                       (2x²+18x+81)  =  (4x² - 36x + 81)

                                          0 =   2x² -54x

                                          0 =  x(2x - 54)  

                           0 = x      and         0 = 2x -54  

                                                       54 = 2x

                                                      27 =  x

shorter leg    = 27        

longer leg     = 36

hypotenuse  =  45

divided all the values by 9 and you get a 3, 4, 5  right triangle, so the answer checks correct  

Answer:

Step-by-step explanation:

Let's call the total number of plants in the field "x".

7/15 of the plants have wilted, which means that 7/15 * x plants have wilted.

And we know that 105 plants have wilted, so we can set up an equation to solve for x:

7/15 * x = 105

x = 105 / 7 / 15

x = 105 × 15 / 7

x = 1575 / 7

x = 225 plants.

x  =  3  − log  565/  log  2  =  −  6.142107057

Step-by-step explanation:

2^3-x =565

Log 2^3-x =  log  565

(3-x) times log 2 = log 565

3 −  x  =  log  565 / log  2

3  −  log  565 / log  2  =  x

x  =  3  − log  565/  log  2  =  −  6.142107057

Answer:

x = -557

Step-by-step explanation:

2^3 is 2x2x2 which equals 8. 8 - x = 565. Move the constant to the right-hand side and change its sign. -x = 565 - 8. This is 557. Now change the negative sign on the x to a positive and the positive sign on the 557 to a negative. x= -557.

Answer:

If you really meant that the number of dogs is 12 greater than 3 times the number of cats then:

3 cats

Step-by-step explanation:

21= number of dogs

c = number of cats

21 = 12 + (3c)

3c = 9

c = 3

The quadratic equation for an equation with double roots 9 is : \(x^{2}\)-18x+81 = 0.

what is a Quadratic equation?

A quadratic equation is an Algebraic equation with the highest power of its variable as 2.

It can be solved by several methods : Factorization, completing the square and graphical methods.

Analysis

if 9 is the double root of the equation, it means x = 9 or  x = 9

So (x-9)(x-9) are factors

Therefore,

(x-9)(x-9) = 0

\(x^{2}\) - 9x-9x + 81 = 0

\(x^{2}\) -18x+81 = 0

in conclusion, the quadratic equation of the double root 9  is:  \(x^{2}\) -18x+81 = 0

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Answer:

The "middle" term is 11x.

Step-by-step explanation:

(3x + 5)(4x - 3)

Solve this by using FOIL: first – outer – inner – last

F: 3x • 4x = 12x²

O: 3x • -3 = -9x

I: 5 • 4x = 20x

L: 5 • -3 = -15

Combine the terms.

12x² - 9x + 20x - 15

Combine like terms.

12x² + 11x - 15

The "middle" term is 11x.

Hope this helps!

Answer:

Just some background:

Congruent means that a triangle has the same angle measures and side lengths of another triangle.

SAS congruence theorem: If two sides and the angle between these two sides are congruent to the corresponding sides and angle of another triangle, then the two triangles are congruent. Congruent triangles: When two triangles have the same shape and size, they are congruent.

Let's look at A first.

The triangle on left, we know 40 and 30 degree angles. So 3 all angles together = 180, so the 3rd angle = 180-30-40 = 110.

Now look at the triangle on the right. The angle shown is 110! This angle is between the sides marked with || and ||| marks, indicating that those two sides are the same length between both triangles.

Therefore both triangles are the same by Side-Angle-Side or SAS.

Now look at B.

It's a right triangle. We are missing 1 side of each triangle.

Let's solve for the missing "leg" of the triangle on the right. The pythagorean theorem says that a^2 + b^2 = c^2 where a and b are the 'legs' or sides of the triangle and c is the hypotenuse (always the longest length opposite the right angle).

so 2^2 + b^2 = 4^2

4 + b^2 = 16

b^2 = 16-4

b^2 = 12

That missing side is the \(\sqrt{12}\).

This does NOT match the triangle on the left.

Theses two triangles are NOT congruent.

The types of insurance is the minimum required by law is Bodily Injury Liability

What is Insurance?

Insurance is a tool for risk management. You purchase protection against unforeseen financial losses when you purchase insurance. If something unpleasant happens to you, the insurance company pays you or someone else of your choosing.

What is Bodily Injury Liability?

Bodily injury liability coverage pays for the victims' medical expenses if you are at fault for an automobile accident (not including yourself). In the event that you are sued for damages, this coverage also aids in covering the cost of your defence.

For most drivers, 100/300/100, or $100,000 per person, $300,000 per accident in bodily injury liability, and $100,000 per accident in property damage liability, is the optimum liability coverage.

The types of insurance is the minimum required by law is Bodily Injury Liability

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Answer:

a. The equation is separable, as we can write it as (1 - y²) dy = x² dx. Integrating both sides, we have (1/2)*ln|1 - y²| = (1/3)*x³ + C, where C is the constant of integration. Solving for y, we get an equation for the integral curves: y = ±sqrt(1 - exp(2/3*x³ + 2C)).

b. Rearranging the equation, we get (2/(y - 1)) dy/dx = (3x² + 4x + 2). This is separable, so integrating both sides, we have 2 ln|y - 1| = x³ + 2x² + 2x + C, where C is the constant of integration. Solving for y, we get y = 1 + Ce^(x³+2x²+2x)/2. Using y(0) = -1, we have -1 = 1 + C, so C = -2. Thus, the solution to the initial value problem is y = 1 - 2e^(x³+2x²+2x)/2. The solution exists for all values of x.

Answer:

2x + 10 + 2y

Step-by-step explanation:

6x + 3 – 4x + 2y + 7

(6x - 4x) = 2x

2x + 3 +2y + 7

(3 + 7) = 10

Answer: 2x + 10 + 2y

Answer:

x = - 1

Step-by-step explanation:

P = \(\frac{x-2}{x+1}\)

the denominator of the rational function cannot be zero as this would make it undefined. Equating the denominator to zero and solving gives the value that x cannot be.

x + 1 = 0 ( subtract 1 from both sides )

x = - 1

P is undefined when x = - 1

Answer:

-5

Step-by-step explanation:

-15/-3

-5

If im wrong sorry :(

Step-by-step explanation:

the answer is -63 lol for some reason it said i need 20 letters to answer your question but there you go -63

The result suggests that the mean wake time might have really reduced since the values barely fall above 100 min as in before treatment with a high degree of confidence. thus , the drug is effective.

Confidence interval is written in the form as;

(Sample mean - margin of error, sample mean + margin of error)

The sample mean represent x , it is the point estimate for the population mean.

Margin of error = z × s/√n

Where s = sample standard deviation = 21.8

n = number of samples = 17

Now the population standard deviation is unknown and the sample size is small, hence, we would use the t distribution to find the z score

then the degree of freedom, df for the sample.

df = n - 1 = 17 - 1 = 16

Since confidence level = 99% = 0.99, α = 1 - CL = 1 – 0.99 = 0.01

α/2 = 0.01/2 = 0.005

Therefore the area to the right of z0.005 is 0.005 and the area to the left of z0.005 is 1 - 0.005 = 0.995

the t distribution table, z = 2.921

Margin of error = 2.921 × 21.8/√17

= 15.44

The confidence interval for the mean wake time for a population with drug treatments will be; 90.3 ± 15.44

The upper limit is 90.3 + 15.44 = 105.74 mins

The lower limit is 90.3 - 15.44 = 74.86 mins

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Answer:

13 and 44

Step-by-step explanation:

let x and y be the 2 numbers with y < x , then

x - y = 31 ( add y to both sides )

x = y + 31 ( subtract 31 from both sides )

x - 31 = y → (1)

4y = x + 8 → (2)

substitute y = x - 31 into (2)

4(x - 31) = x + 8

4x - 124 = x + 8 ( subtract x from both sides )

3x - 124 = 8 ( add 124 to both sides )

3x = 132 ( divide both sides by 3 )

x = 44

substitute x = 44 into (1)

44 - 31  = y , then

y = 13

the 2 numbers are 13 and 44

Answer:

Step-by-step explanation:

In the question, it is given that a right cone has a diameter of 12 units and volume of 168π units³ and we have to find the height of the cone.

\( \: \)

To Find the height of the cone, we must know this formula :

\(\\{\longrightarrow{ \qquad{\underline{\boxed {\pmb{\frak { \dfrac{1}{3} \: \pi r^2h ={ Volume_{(cone) }}}}}}}}} \\ \\\)

Where,

Now, we will substitute the values in the formula :

\(\\ {\longrightarrow{ \qquad{{ {\pmb{\sf { \dfrac{1}{3} \times \pi \times (6)^2 \times h = 168 \pi}}}}}}} \\ \\\)

Cancelling π from both sides we get :

\(\\ {\longrightarrow{ \qquad{{ {\pmb{\sf { \dfrac{1}{3} \times \cancel\pi \times 36 \times h = 168 \cancel\pi}}}}}}} \\ \\\)

\(\\ {\longrightarrow{ \qquad{{ {\pmb{\sf { \dfrac{1}{3} \ \times 36 \times h = 168 }}}}}}} \\ \\\)

\(\\ {\longrightarrow{ \qquad{{ {\pmb{\sf { \dfrac{36}{3} \times h = 168 }}}}}}} \\ \\\)

\(\\ {\longrightarrow{ \qquad{{ {\pmb{\sf { 12 \times h = 168 }}}}}}} \\ \\\)

\(\\ {\longrightarrow{ \qquad{{ {\pmb{\sf { h = \frac{168}{12} }}}}}}} \\ \\\)

\(\\{\longrightarrow{ \qquad{\underline{\boxed {\pmb{\frak { h ={14 }}}}}}}} \\ \\\)

Therefore,

The simplified form of √([2m5z6]/[xy]) is (√2m√5z√6) / (√x√y).

To simplify the expression √([2m5z6]/[xy]), we can break it down step by step:

Simplify the numerator:

√(2m5z6) = √(2) * √(m) * √(5) * √(z) * √(6)

= √2m√5z√6

Simplify the denominator:

√(xy) = √(x) * √(y)

Combine the numerator and denominator:

√([2m5z6]/[xy]) = (√2m√5z√6) / (√x√y)

Thus, the simplified form of √([2m5z6]/[xy]) is (√2m√5z√6) / (√x√y).

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The value of x is figure calculate from the to be 20

In geometry, a kite is a quadrilateral shape that has two pairs of congruent sides and two pairs of congruent angles. This means that the opposite sides of a kite are equal in length and the opposite angles are equal in measure.

A kite has two diagonals, one of which bisects the other, and these diagonals are perpendicular to each other. The diagonals of a kite are also equal in length.

Considering the quadrilateral in the image, the value of x is calculate noting that:

DA = DB

AE and EB intersect at right angle, forming a right triangle

Using Pythagoras theorem given by the  the formula

hypotenuse² = opposite² + adjacent²

plugging the values as in the problem

let x be the required distance

x² = 29² - 21²

x² = 841 - 441

x = √400

x = 20

x = 20

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Complete Question

Suppose that the random variable X represents the length of a punched part in

centimeters. Let Y be the length of the part in millimeters. If E(X) = 5 and V(X) = 0.25,

what are the mean and variance of Y?

Answer:

The mean

\(E(Y) =50 mm\)

The variance

\(V(Y) = 25 mm\)

Step-by-step explanation:

From the question we are told that  

   Length in cm is  X

   Length in mm is Y

  Generally  10 mm  =  1 cm

So

    \(Y = 10 X\)

Hence the expected mean of Y is  

  \(E(Y) = E (10 X)\)

=>    \(E(Y) = 10 E(X)\)

From the question \(E(X) = 5\)

So

      \(E(Y) = 10 * 5\)

=> \(E(Y) =50 mm\)

Gnerally the variance of  X is  

      \(V(X) = E [X^2] -E[X]^2\)

From the question we are told that \(V(X) = 0.25\)

=> \(0.25 = E [X^2] -E[X]^2\)

Gnerally the variance of Y

    \(V(Y) = E [Y^2] -E[Y]^2\)

=> \(V(Y) = E [10X^2] -E[X]^2\)

=> \(V(Y) = 10^2[ E [X^2] -E[X]^2]\)

=> \(V(Y) = 10^2* V(X)\)

=> \(V(Y) = 10^2* 0.25\)

=> \(V(Y) = 25 mm\)

307.3 feet is the perimeter of fencing that is required to fence a four sided residential lot that measures 112.7 ft, 85.3 ft, 110.8 ft, and 98.5 ft.

The distance around a shape or space is measured by its perimeter. The length of a shape's outline is what it is, simply put.

Children may have an easier time understanding this new term if they are given an analogy like walking completely around a shape or erecting a fence around a field.

When determining the size of a space, such as a garden or a room in your home, the perimeter is frequently used. The distance around your living room or garden, for instance, would be necessary if you wanted a new carpet or garden fence.

We need to simply find the perimeter of the polygon lot to find measure of fencing required.

Perimeter = sum of sides

                = 12.7 + 85.3 + 110.8 + 98.5

                = 307.3 ft

Thus, 307.3 feet of fencing are required to fence  a  four sided residential lot that measures 112.7 ft, 85.3 ft, 110.8 ft, and 98.5 ft.

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Answer:4 3/8

Step-by-step explanation:

Answer:

B) 92.03 < μ < 97.97

99% confidence interval for the mean score of all students.

92.03 < μ < 97.97

Step-by-step explanation:

Step(i):-

Given sample mean (x⁻) = 95

standard deviation of the sample (s) = 6.6

Random sample size 'n' = 30

99% confidence interval for the mean score of all students.

\(((x^{-} - Z_{0.01} \frac{S}{\sqrt{n} } , (x^{-} + Z_{0.01} \frac{S}{\sqrt{n} })\)

step(ii):-

Degrees of freedom

ν =   n-1 = 30-1 =29

\(t_{0.01} = 2.462\)

99% confidence interval for the mean score of all students.

\(((95 - 2.462 \frac{6.6}{\sqrt{30} } , 95 + 2.462\frac{6.6}{\sqrt{30} } )\)

( 95 - 2.966 , 95 + 2.966)

(92.03 , 97.97)

Final answer:-

99% confidence interval for the mean score of all students.

92.03 < μ < 97.97

Answer:

\(\frac{7}{9} = 0.777777 ..\)

\(\frac{1}{3} = 0.33333..\)

Step-by-step explanation:

Explanation:-

Non -terminating decimals are the one that does have an end term. it has infinite number of terms

Example :-

\(\frac{7}{9} = 0.777777 ..\)

\(\frac{1}{3} = 0.33333..\)

The total number of workers that were studied can be found to be 139,340,000.

The percent of workers unemployed would be 5. 4 %.

Percentage of unemployed men is 5. 6 % and unemployed women is 5. 1%.

Number of employed workers :

= 74,624,000 + 64, 716, 000

= 139,340,000

Percentage unemployed :

= ( 4, 209,000 + 3,314,000 ) / 139,340,000

= 5. 4 %

Percentage of unemployed men :

= 4,209,000 / 74,624,000

= 5.6 %

Percentage of unemployed women:

= 3,314,000 / 64, 716, 000

= 5. 1 %

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The full question is:

a. How many workers were studied?

b. What percent of the workers were unemployed?

c. Compare the percent unemployed for the men and the women.

Answer:

x < -3

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Equality Properties

Step-by-step explanation:

Step 1: Define Inequality

15 < -5x

Step 2: Solve for x

Here we see that any number x that is smaller than -3 would work as a solution to the inequality.

Answer: The answer is x<-3 Hope this help :)

Step-by-step explanation:

15<-5x

15/-5  -5x/-5

x=-3= X<-3

In order to find the solution of this inequality, first let's find its roots:

The roots are 1 and -6.

Since the concavity of this function is upwards (because a > 0), we have that the function is negative for value of x between the roots and positive for the other values (x < -6 or x > 1).

Since the inequality has the symbol "greater than or equal", we want the positive values, including zero, therefore the answer is x ≤ -6 or x ≥ 1 (option B).

Answer:

\(x < - 6 \ \text{and} \ x > 1\)

Step-by-step explanation:

We are given an inequality:

\(7x^2 + 35x > 42\)

We are asked to find the solution to this inequality.

First, treat this as a quadratic equation. Get the inequality to quadratic form:

\(ax^2+bx+c > 0\\\\7x^2+35x > 42\\\\7x^2+35x-42 > 42-42\\\\7x^2+35x-42 > 0\)

Then, divide both sides by 7:

\(\displaystyle 7x^2+35x-42 > 0\\\\\frac{7x^2+35x-42}{7} > \frac{0}{7}\\\\x^2+5x-6 > 0\)

Then, separate 5x to create a factorable expression. Ask yourself: what two numbers will add up to -6 and multiply to create -6?

\(x^2+5x-6 > 0\\\\x^2+6x-x-6 > 0\)

Then, group the terms together:

\(x^2+6x-x-6 > 0\\\\(x^2+6x)(-x-6) > 0\)

Then, factor out x from the inequality:

\((x^2+6x)(-x-6) > 0\\\\x(x+6)(-x-6) > 0\)

Then, factor out the negative sign from the second part of the expression:

\(x(x+6)(-x-6) > 0\\\\x(x+6)-(x+6) > 0\)

Then, factor out x + 6 from the inequality:

\(x(x+6)-(x+6) > 0\\\\(x+6)(x-1) > 0\)

Then, separate the factors and create two separate inequality sets:

\((x+6)(x-1) > 0\\\\\displaystyle \left \{ {{x+6 > 0} \atop {x-1 > 0}} \right. \\\\\left \{ {{x+6 < 0} \atop {x-1 < 0}} \right.\)

Then, solve the inequalities for x:

\(x+6 > 0\\\\x+6-6 > 0-6\\\\x > -6\\---------------\\x-1 > 0\\\\x-1+1 > 0+1\\\\x > 1\\---------------\\x+6 < 0\\\\x+6-6 < 0-6\\\\x < -6\\---------------\\x-1 < 0\\\\x-1+1 < 0+1\\\\x < 1\)

Then, test each value in the inequality:

\(7x^2+35x > 42\\\\7(-5)^2+35(-5) > 42\\\\7(25)-175 > 42\\\\175-175 > 42\\\\0 \ngtr 42\\\\\text{x} > \text{-6 is not a solution.}\\---------------\\7x^2+35x > 42\\\\7(2)^2+35(2) > 42\\\\7(4)+70 > 42\\\\28+70 > 42\\\\98 > 42\\\\\text{x} > \text{1 is a solution.}\\---------------\)

\(\\7x^2+35x > 42\\\\7(-7)^2+35(-7) > 42\\\\7(49)-245 > 42\\\\343-245 > 42\\\\98 > 42\\\\\text{x} < \text{-6 is a solution.}\\---------------\\7x^2+35x > 42\\\\7(-1)^2+35(-1) > 42\\\\7(1)-35 > 42\\\\7-35 > 42\\\\-28\ngtr42\\\\\text{x} < \text{1 is not a solution.}\)

Therefore, the solutions are x > 1 and x < -6. This means that answer choice A is correct.