Quantitative Reasoning :')

1) This narrative is an example of a sample survey.

2) This narrative is an example of an experiment.

3) This narrative is an example of an observational study.

There are some common methods of data collection in statistical studies which are sample survey, observational study, experiments e.t.c

A sample survey is a survey that is done by taking a sample of people or items that represent a larger population.

An observational study is a type of study whereby a researcher utilizes observed information to gain more information about a group of individuals.

An experiment is where a researcher purposely applies different treatments to different groups and then does a comparison of  the groups to determine if there is any difference in a specific variable of interest.

1) This narrative is an example of a sample survey because he studied a sample of 50 people who exercise regularly to determine if their blood pressures are low or average.

2) This narrative is an example of an experiment because we see that he studies 20 people who exercise and another 20 who don't exercise and uses the result to generate a conclusion about both groups.

3) This narrative is an example of an observational study because he is using the information he gets from the question he asks every fifth patient to learn about a group of individuals.

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Using integrals, the volume generated by rotating the given region about the specified line is of 0.8π cubic units.

Rotating a function f(x) around a function g(x), the volume is given by the following integral:

[tex]V = \pi \int_{a}^{b}[f(x) - g(x)]^2 dx[/tex]

In which a and b are the intersection points of the curve.

For this problem, from the graph, we have that:

Hence:

[tex]V = \pi \int_{0}^{1}[2\sqrt[4]{x} - 2x]^2 dx[/tex]

[tex]V = \pi [\int_{0}^{1} 4\sqrt{x} - 8x\sqrt{x} + 4x^2 dx][/tex]

[tex]V = \pi \left[\frac{8}{3}x^{\frac{3}{2}} - \frac{16}{5}x^{\frac{5}{2}} + \frac{4}{3}x^3}\right]_{x=0}^{x=1}[/tex]

[tex]V = \pi \left[\frac{8}{3} - \frac{16}{5} + \frac{4}{3}\right][/tex]

[tex]V = \pi \left[4 - \frac{16}{5}\right][/tex]

[tex]V = \frac{4\pi}{5}[/tex]

V = 0.8π cubic units.

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Answer: x=38

Step-by-step explanation:

SOLVE FOR X

STEPS FOR SOLVING LINEAR EQUATION

0.50x+0.15(30)=23.5

Multiply 0.15 and 30 to get 4.5.

0.5x+4.5=23.5

Subtract 4.5 from both sides.

0.5x=23.5−4.5

Subtract 4.5 from 23.5 to get 19.

0.5x=19

Divide both sides by 0.5.

[tex]x=\frac{19}{0.5}[/tex]

Expand  [tex]\frac{19}{0.5}[/tex]   by multiplying both numerator and the denominator by 10.

[tex]x=\frac{190}{5}[/tex]

Divide 190 by 5 to get 38.

x=38

Answer:

Your answer is x=0

The rotation of the vertices L(2,-2), M(7,-3), and N(5,2) are L'(-2, -2), M'(-7, -3), and N'(5, 2) respectively.

Let the point be having coordinates (x,y).

If the point is in first quadrant:

Subcase: Clockwise rotation:

Then (x,y) → (y, -x)

Subcase: Counterclockwise rotation:

Then (x,y) → (-y, x)

We know that the rotation of a point (x,y) about the origin by 90° is (-y,x).

Given vertices of ΔLMN are  L(2,-2), M(7,-3), and N(5,2).

Let consider the rotations of L, M, and N are L', M', and N' respectively.

The rotation of a point L(2,-2)  about the origin by 90° is L'(-2,-2).

The rotation of a point M(7,-3) about the origin by 90° is M'(-7,-3).

The rotation of a point N(5,2) about the origin by 90° is N'(5,2).

Hence, the points  L'(-2, -2), M'(-7, -3), and N'(5, 2) are the rotation of vertices.

Therefore, L, M, and N of ΔLMN about the origin by 90°.

Hence, The rotation of the vertices L(2,-2), M(7,-3), and N(5,2) are L'(-2, -2), M'(-7, -3), and N'(5, 2) respectively.

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The given equation of the straight line is y +8x+10=0

We are required to find the equation of a straight line passing  through the point (-2, 6) and has a slope of -8.

An equation of a straight line can be easily found if the slope and any of the points is given

The general form of equation is given by

y-y1 = m (x-x1)

where x1,y1 is the coordinate of the known point

m is the slope of the line

It is given that the coordinate of the known point is (-2,6)

the slope is given to be -8

Thus using these values to form the equation,

y-6 = -8 (x--2)

y-6 = -8 (x+2)

y-6 = -8x-16

y+8x-6+16=0

y+8x+`10=0

Hence, The straight line equation is y +8x+10=0

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Answer: 12 different even 2 digit positive numbers can be witten

Step-by-step explanation:

the even numbers are 44, 24, 54, 84, 22, 42, 52, 82, 28, 48, 58, 88

Answer:

Option 4

Step-by-step explanation:

This is the same as a rotation of 180° about the origin, which means we can negate the x and y coordinates of the preimage to get the coordinates of the image.

The days it would take to complete the building is 104 22/25 days.

A fraction is a non-integer that has a numerator and a denominator. The numerator is the number above. While the denominator is the number below. An example of a fraction is 1/4.

A mixed number is a number that has a whole number and a proper fraction. A proper fraction is a non-integer in which the numerator is less than the denominator. An example of a mixed number is 3 1/2.

The first step is to determine the total height of the office bulding = height of each floor x total number of floors

15 x 10 2/5

15 x 52/5 = 780 /5 = 156

The next step is to determine the floors left to complete the office building :

156 - 24 9/10 = 131 1/10 feet

The last step is to divide the feet that can be built each day by the number of floors needed to complete the builfing :

1311/10 ÷ 1 1/4

1311 / 110 ÷ 5/4

1311 / 10 x 4/5 = 104 days 44/50

104 22/25 days

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Answer:

  32 degrees

Step-by-step explanation:

You want the smallest angle of a triangle in which the other two angles are 20 degrees larger than the smallest, and 3 times the smallest.

The sum of angles is 180 degrees. The three angles are x, (x+20), and (3x). Their sum is ...

  x +(x +20) +3x = 180

Collecting terms gives ...

  5x +20 = 180

  5x = 160 . . . . . . subtract 20

  x = 32 . . . . . . divide by 5

The smallest angle is 32 degrees.

-5 and 7 are real and rational numbers also they are integers.

Numbers which can be written in the form of p/q are rational numbers where q must not be zero.

According to the given question we have to determine what kind of numbers are -5 and 7.

In a most simple way we can say that - 5 is an negative integer and 7 is a positive integer.

But -5 can be written as -5/1 which is a rational number also and 7 can also be written as 7/1 so we can also say they are integers al well as rational numbers.Lastly they are real numbers as they don't have any imaginary part 'i' in it.

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Answer:

64.75

Step-by-step explanation:

The total heights of men is m

so m/15 = 69.65 => m = 1044.75

The total heights of all students is s

so s/35 = 66.85 => s = 2339.75

so the total heights of women = 2339.75 - 1044.75 = 1295

The mean height of women = 1295/20 = 64.75

Answer:

3.82×10^7

Step-by-step explanation:

3.82e+7= 3.82×10^7

Answer:

21000

Step-by-step explanation:

21000

Answer:

7.18421051

Step-by-step explanation:

76 ÷ 6 = 12.6666667

91 ÷ 12.6666667 = 7.18421051

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Answer: 2.95 I think

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

It might be the best one!

Modelling the situation, it is found the price of the ticket without the coupon is of $9 when all the six friends spent $ 42 to buy the tickets.

Total money spent by 6 friends on purchasing of the movie tickets = $ 42

So, the money spent for the purchase of 1 ticket will be calculated by dividing the $ 42 by 6.

So, cost of 1 ticket = 4 42 / 6 = $ 7

Coupon is of $2-off.

This means that with the coupon, $2 is subtracted from the ticket price.

So, price of ticket will be = $ 7 + $ 2 = $ 9.

Therefore, the price of the ticket without the coupons will be $ 9.

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Answer:

1. 1, 9/4

2. 4^4

3. -0.0000000008723

4. -5100023*10^2, -6.6*10^(12)

Step-by-step explanation:

[tex]21^0 = 1;\ n^0\ always\ is\ 1.\\(\frac{2}{3})^{-2} = (\frac{3}{2})^2 = \frac{3^2}{2^2} = \frac{9}{4}; n^m\ is\ performed\ by\ doing\ n*n,\ m\ times.\\i.e.,\\ n^2=n*n;\\n^3=n*n*n;\\ n^4=n*n*n*n\\\\\frac{4^6}{4^2};\ original\\\\\frac{(4^2)^3}{4^2};\ (n^{mc}\ can\ be\ rewritten\ as\ (n^m)^c\\\\\frac{4^2}{4^2}*\frac{(4^2)^2}{1};\ split\ the\ fraction\ into\ two\ parts\ because\ of\ multiplication\ rules.\\\\1*4^4;\ \frac{n}{n}\ can\ be\ written\ as\ 1.\ \frac{n}{1}\ can\ be\ written\ as\ n.\\\\4^4[/tex]

Technically, [tex]4^4[/tex] is 256, but the answer is requested as a number with an exponent.

-8.723 * 10^-10 would be -0.0000000008723.

10^-10 = [tex]\frac{1}{10^{10}}[/tex], which would mean you must move your decimal left by the number of places indicated by the exponent.

[tex]-5.1*10^8-2.3*10^3 = x\\-51*10^7-23*10^2 = x\\10^7=10^{5+2}=10^5*10^2\\-5100000*10^2-23*10^2=x\\-5100023*10^2=x;\ combine\ like\ terms.\\-6*10^5 * 1.1*10^7 = x\\-6*1.1*10^5*10^7;\ rewrite\ for\ simplification.\\-6.6*10^{12}=x[/tex]

Answer:

it is x=8 or x=-8

Step-by-step explanation:

|x|-7=1

  +7 +7

x=8 or x=-8

i'm doing absolute value in math rn so this should be right!! have a good day

Answer: 0.48387

Step-by-step explanation:

Solution set = {9,11,13,15,17,19,21,23,25,27,29,31,33,35,37}

Sample Set = {8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38}

out of the 31 numbers, 15 are odd

15/31 = 0.48387 probability.

Answer:

in the heaven or hell hhhvgvcgdgghh

Therefore, on dividing 6216 by 21 we get 126

Given 6216 / 21

21 ) 6216 ( 296

      42

(-)...................     (By subtracting these two numbers we get )

      201            

       189

(-)..................    

          126

          126

.(-)..........................

            0

Therefore 6216 / 21 = 126

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Answer:333R1 or as a mixed fraction 33 1/3. I believe this is right :]

Step-by-step explanation:

Answer:

i'm pretty sure it's the second option

Step-by-step explanation:

The slope-point form is y + 1 = (1/4) (x +2)

The function notation for the point-slope form is f(x) = -1 + (1/4) (x +2)

From the graph, we get two points (x₁, y₁) = (-2, -1) and (x₂, y₂) = (2,0)

Slope, m = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

               = [tex]\frac{0 --1}{2--2}[/tex]

               = 1/4

The slope-point form of a line is (y-y₁) = m(x-x₁), where (x, y) is the general point on the line, (x₁, y₁) is a given point on the line and m, the slope of the line.

So here the slope-point form of the line is,

(y- -1) = 1/4(x- -2)

⇒ y + 1 = (1/4) (x +2)

For the function notation, we put y = f(x) simply and write it as,

f(x) = -1 + (1/4) (x +2)

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the first one is c

the second is B

Step-by-step explanation:

The set of ordered pairs that represents a function is the third option.

{ (4, 1), (-6, 6), (5, -2), (-4, 1)}

For a relation that maps elements x (inputs) into elements y (outputs), we will have ordered pairs of the form (x, y) that define the relation.

Now, a relation is only a function if input are only mapped to only one output.

For example, if you look at the first set of ordered pairs, you can see that the input x = -4 appears twice with two different outputs, then this relation does not represent a function.

For the second set the same thing happens for the input x = -8, and for the last set the same happens for the input x = -8

The only set where each input appears only once is the third one:

{ (4, 1), (-6, 6), (5, -2), (-4, 1)}

This relation represents a function, so this is the correct option.

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Using the together rate, it will take more 3.45 days to complete the work.

Division is one of the four basic operations of arithmetic, the ways that numbers are combined to make new numbers. The other operations are addition, subtraction, and multiplication.

The together rate is given by the sum of each separate rate.

For this problem, the rates are given as follows,

Ann,1/10 = 0.1

Ben,1/12 = 0.0833

Together,1/x

Hence the amount completed in 2 days is:

2 x (0.1 + 0.0833) = 0.3666

The amount it would take them to complete 100% of the project working together is found by the together rate as follows,

x = 60/11

x = 5.45 days.

The time it would take to do the remaining 100 - 36.66 = 63.34% of the project is,

0.6334 x 5.45 = 3.45 days.

It will take more 3.45 days to complete the work.

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The 4 on the right is 10 times larger than the 4 on the left! (=^.^=)

Answer:

64,765

Step-by-step explanation:

multiplicas porque dice que uno cuesta 315 entonces si hay 205 hay 64,765