A random sample of 145 students is chosen from a population of 4,250 students. The mean IQ in the sample is 130, with a standard deviation of 7. Using a margin of error of 0.95%, what is the 90% confidence interval for the students' mean IQ score?

Answer:

The standard deviation of the given data is 11.34.

Step-by-step explanation:

We have to find the standard deviation for the given data;

Grade on     No. of students          

 test (X)        with that score (f)        [tex]X \times f[/tex]       [tex]( X - \bar X)^{2}[/tex]        [tex]f \times ( X - \bar X)^{2}[/tex]

     50                  1                       50      1073.218      1073.2176

     57                 2                       114      663.578      1327.1552

     60                 4                       240       518.018     2072.0704

     65                 3                       195       315.418      946.2528

     72                 3                       216        115.778       347.3328

     75                12                       900        60.218       722.6112

     77                10                       770        33.178       331.776

     81                 6                       486        3.098       18.5856

     83                 6                       498        0.058        0.3456

     88                9                       792        27.458      247.1184

     90                12                      1080        52.418      629.0112

     92                12                       1104        85.378     1024.5312

     95                 2                        190        149.818      299.6352

     99                 4                        396        263.738     1054.9504

    100                 5                      500         297.218     1486.088    

   Total                  91                          7531                              11580.68    

Firstly, the mean of the above data is given by;

            Mean, [tex]\bar X[/tex]  =  [tex]\frac{\sum X \times f}{\sum f}[/tex]

                             =  [tex]\frac{7531}{91}[/tex]  =  82.76

Now, the standard deviation of the data is given by;

          Standard deviation, S.D.  =  [tex]\sqrt{\frac{\sum f(X-\bar X)^{2} }{\sum f-1}}[/tex]

                                                     =  [tex]\sqrt{\frac{11580.68}{91-1}}[/tex]

                                                     =  11.34

Hence, the standard deviation of the given data is 11.34.

Answer:

Since the Crayola box contains more markers that should be the right choice.

Step-by-step explanation:

In order to calculate the number of markers each box contains, we need to divide the width of the box by the width of the markers for each box and compare their numbers. Since the lengths are given in mixed fractions, we will first convert them to pure fractions.

For Crayola:

[tex]\text{box width} = 2 + \frac{3}{4} = \frac{8}{4} + \frac{3}{4} = \frac{11}{4} \text{ inches}[/tex]

[tex]n = \frac{\frac{11}{4}}{\frac{1}{4}} = 11[/tex]

For the Sharpie:

[tex]\text{box width} = 3 + \frac{3}{5} = \frac{15}{5} + \frac{3}{5} = \frac{18}{5} \text{ inches}[/tex]

[tex]n = \frac{\frac{18}{5}}{\frac{4}{10}} = \frac{18*10}{5*4} = \frac{180}{20} = 9[/tex]

Since the Crayola box contains more markers that should be the right choice.

Answer:

≈ 4614 mL

Step-by-step explanation:

I'm guessing you want to add them. So, let's convert them all to mL first and then add them!

3/4 gallons (U.S. I'm assuming) ≈ 2839 mL OJ

3 pints (U.S. I'm assuming) ≈ 1420 mL GA

1.5 cups (U.S. I'm assuming) ≈ 355 mL PJ

Add them up and you get around 4614 mL of a disgusting mixture of juice. I hope this is what you were looking for!

Answer:

Step-by-step explanation:

1) Let the number be x

Quotient of a number & 3 : x/3

Ten less than the quotient of a number : (x/3) -10

[tex]\frac{x}{3}-10=6[/tex]

Add 10 to both sides

[tex]\frac{x}{3}-10+10=6+10\\\\\frac{x}{3}=16[/tex]

Multiply both sides by 3

[tex]\frac{x}{3}*3=16*3\\\\x=48[/tex]

2)  Let the number be x

Quotient of a number & 5 : x/5

Seven plus  the quotient of a number : (x/5)+7

[tex]\frac{x}{5}+7=-12\\[/tex]

Subtract 7 form both sides

[tex]\frac{x}{5}+7-7=-12-7\\\\ \frac{x}{5}=-19\\[/tex]

Multiply both sides by 5

x = -19*5

x = -95

3) Let the  number be x

Difference of a number and 3 : x - 3

Eight time the difference of a  number & 3: 8*(x-3)

8*(x - 3 ) = 40

Divide both sides by 8

[tex]\frac{8*(x-3)}{8}=\frac{40}{8}[/tex]

x - 3 = 5

Add 3 to both sides

x - 3 +3 = 5 +3

x = 8

4) Let x be the number

Twice a number : 2x

The difference of twice a number and 7: 2x - 7

2x - 7 = 9

Add 7 to both sides

2x - 7 + 7 = 9 + 7

2x = 16

Divide both sides by 2

2x/2 = 16/2

x = 8

Answer:

43.6 amp

Step-by-step explanation:

Given

A 40 amp fuse carries a temporary 9 % current overload.

9% current overload means that whatever will be the normal current carrying capacity of fuse, during overload it carries 9% more than that.

Current carrying capacity of fuse is 40 amp.

during overload it carries 9% more

over load current = 9% of 40 amp  = 9/100 *40 = 3.6 amp

total current flowing through fuse during overload = 40 amp + 3.6 amp

                                           = 43.6 amp (answer)

Answer:

-2

Step-by-step explanation:

hello

output means that you have to check in the f(x) column

the answer is -2

hope this helps

Answer:

Karim

Step-by-step explanation:

1. Turn 2/5 into a percentage by multiplying the numerator and denominators of 2/5 with 20 so the new fraction's denominator can be 100.

2. Your new fraction should be 40/100 also known as 40%.

3. Compare who's probability is more likely.

4. The answer will be (40%) Karim's.

Answer:

Karim

Step-by-step explanation:

35% is equivalent to 0.35, whereas 2/5 is equivalent to 0.40.  Karim is correct; 0.40 represents a greater probability than does 0.35.

Answer:

24 units.

Step-by-step explanation:

we can use  concept of Thales intercept theorem in this problem

according to this theorem, if  there are n lines parallel to each then and two transverse line drawn such that they intersect the three parallel line given the problem, then the parallel line divides the transverse line equal proportion.

For this problem

For the line having length 45, one of the length is 25 units,

then other length will be 45-25 = 20 unit

Now using Thales intercept theorem

30/? = 25/20

30/? = 5/4

? = 30*4/5 = 24

Thus, missing side length will be 24 units.

Answer:

Hey there!

That wouldn't be possible.

130% of something is more than the total amount.

For example, if she had 100 stamps, and gave away 130%, she would have -30 stamps, which is unreasonable.

Hope this helps :)

Answer:

The point will be on the line.

Step-by-step explanation:

Answer:

No, see below.

Step-by-step explanation:

10% of 150 is .1 times 150= 15

15+75=90

So, Jordan is incorrect.

Answer:

The students points will decrease 10 points in 4 days

Step-by-step explanation:

In 2 days he loses 5 points. So for 4 days all you have to do is double the amount of points because the amount of days have doubled

Answer:

p > -3

Step-by-step explanation:

the open circle means that its either more than or less than

the closed circle means less than or equal to or more than or equal to

the point also landed on -3

hope this helps

Answer:

Its c. p > -3

Step-by-step explanation:

becuase the open circle mean less then or greater then and the way the arrow is facing means p is bigger !!

Answer:

No

Step-by-step explanation:

The question is:

Are 3/5 and 6/25 equivalent fractions?

Multiply the first fraction by 5/5:

3/5 * 5/5 = 15/25

3/5 is equivalent to 15/25

15/25 is not equal to 6/25.

Answer: No

Answer:

The area of polygon MNOPQR = Area of a rectangle that is 15 square units + Area of a rectangle that is 2 square units.

Step-by-step explanation:

We are given that a polygon MNOPQR is shown. The top vertex on the left is labeled M, and the rest of the vertices are labeled clockwise starting from the top-left vertex labeled, M. The side MN is parallel to side QR. The side MR is parallel to side PQ.

The side MN is labeled as 5 units. The side QR is labeled as 7 units. The side MR is labeled as 3 units, and the side NO is labeled as 2 units.

Firstly, we will draw a perpendicular line from point O which meets the line RQ at point T. Now, the polygon MNOPQR is divided into two rectangles MNTR and OPQT.

As we know that the area of the rectangle = [tex]\text{Length of rectangle} \times \text{Breadth of rectangle}[/tex]

In the rectangle MNTR, the length (MN) = 5 units and the breadth (MR) = 3 units.

So, the area of the rectangle MNTR = [tex]\text{Length (MN)} \times \text{Breadth (MR)}[/tex]

                                                            = [tex]5 \times 3[/tex]  = 15 square units

Now, as we know that in rectangle MNTR, the side NT = 3 units and the side NO is labeled as 2 units. This means that the side OT = NT - NO = 3 units - 2 units = 1 unit

Similarly, the side QR is labeled as 7 units and the side RT is labeled as 5 units. This means that the side TQ = QR - RT = 7 - 5 = 2 units

Now, in the rectangle OPQT, the length (TQ) = 2 unit and the breadth (OT) = 2 units.

So, the area of the rectangle OPTQ = [tex]\text{Length (TQ)} \times \text{Breadth (OT)}[/tex]

                                                            = [tex]2 \times 1[/tex]  = 2 square units

Hence, the area of polygon MNOPQR = Area of a rectangle that is 15 square units + Area of a rectangle that is _2_ square units.

Answer:

7

Step-by-step explanation:

Answer:

tatol price= $335.16

Step-by-step explanation:

regular price for one item= $168

sale=1/2 %

168 × 0.5/100 = 0.84 (discount)

price of discounted chair= 168-0.86

                                         = 167.16

168+167.16 = $335.16

Work Shown:

x - xy = z

x*1 - x*y = z

x*(1 - y) = z .... distributive rule in reverse

x = z/(1-y) ..... divide both sides by (1-y)

The distributive rule is a*(b+c) = a*b+a*c. You can also say a*(b-c) = a*b-a*c. In this case, we factored out the common factor x.

Answer:

(1,1) (2,1) (2,3) (1,3) They form a rectangle because there are two pairs of parallel sides.

:)

Answer:

A

Step-by-step explanation:

x= 1 2/3, y=4 2/3

y=4(1 2/3)-2.    y=4 2/3

y=1 2/3+3        y=4 2/3

and that make the answer going to be A. Also other answer didn't work so yet. Then, A should be the right answer!

Hope this help!

A. x = [tex]\frac{5}{3}[/tex] or [tex]1\frac{2}{3}[/tex]  and y = [tex]\frac{14}{3}[/tex] or [tex]4\frac{2}{3}[/tex]

y = 4x - 2  ; y = x + 3

1. UNDERSTAND what you are given.

2. SUBSTITUTION METHOD means you replace one of the variables in terms of the other to start solving.

4x - 2 = x + 3 (write eq.)

3x - 2 = 3 (combine like terms: part 1)

3x = 5 (combine like terms: part 2)

x = [tex]\frac{5}{3}[/tex] or [tex]1\frac{2}{3}[/tex] (inverse operations: division)

3. PLUG IN VALUE FOR X to solve for y. Pick the simpler equation.

y = x + 3 (pick an original equation, either will work)

y  = [tex]\frac{5}{3}[/tex] + 3

y = [tex]\frac{5}{3}[/tex] + [tex]\frac{9}{3}[/tex]

y = [tex]\frac{14}{3}[/tex] or [tex]4\frac{2}{3}[/tex]

More explanations...

Answer:

The number of distinct triangles that can be drawn using the dots = 6

Step-by-step explanation:

The parameters given are;

Two rows of three evenly spaced dots

To form a triangle, two dots will be selected from 1 row while the third dot will be selected from the other row

The number of ways of selecting the dots are therefore;

₃C₂ × ₃C₁ = 3 × 3 = 9 triangles

The same procedure can be done from the top row to give another 9 triangles

Which gives the total number of triangles = 18 triangles

The number of distinct triangles are found as follows;

Given that triangles obtained from the top row are similar to those of the bottom row, we reduce the range from which the distinct triangles can be found to 19 - 9 = 9 triangles

Of the 9 triangles formed by one dot on top and two dots on the bottom, the two adjacent dots of the three dots which are on the left and on the right of the lower row of dots, form the same three triangles with the three dots on the top row

Therefore, since there are 3 sets of two dots forming 9 triangles, each pair of dots can form 3 triangles, and as mentioned, 2 pairs of dots of the 3 pairs form the same triangles making the distinct triangle = 9 - 3 = 6.

Answer:

We can prove that ΔTVU ≅ ΔTXW because of SAS (TU = TV = TW = TX because they are all radii and all radii of the same circle are congruent, ∠UTV = ∠WTX, that is given). Because of this, UV = XW due to CPCTC so we can write:

2y - 3 = y + 4

y = 7

Answer:

C,110°

Step-by-step explanation:

when the angle on circumference=50°

then the angle at center=2×50=100°

other angles of this triangle are equal and each=1/2(180-100)=1/2×80=40

so angle of quadrilateral=30+40=70°

as opposite angles of a cyclic quadrilateral are supplementary.

so y+70=180

y=180-70=110°

Answer:

40 + 8pi

Step-by-step explanation:

1/2 circle = 1/2 pi r-squared = 1/2x4x4x pi = 8pi

triangle = 1/2bh = 1/2x8x10 = 40

total area = 40 + 8pi

Answer:

Option (A)

Step-by-step explanation:

Parent function of the function graphed is,

G(x) = x²

Graph shows the vertex of the given parabola is at (3, 3).

Vertex form of a parabola is,

F(x) = a(x - h)² + k

where (h, k) is the vertex.

By substituting the coordinates of the vertex in the equation,

F(x) = a(x - 3)² + 3

Since the given parabola is opening upwards, value of 'a' will be positive.

So the equation will be,

F(x) = 2(x - 3)² + 3

Therefore, from the given options, equation given in Option (A) matches the answer.

Answer:

A is the correct answer.

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

1 ,2 , 0.5

Step-by-step explanation:

edgy2021

Answer:

Step-by-step explanation:

Let's solve (4y - 3)^2 = 72 for y.  To do this, take the square root of both sides.  This yields:

4y - 3 = ±√72 = ±√(36·2) = ±6√2

Then 4y = 3 ±6√2, or

       3 ± 6√2

y = ----------------

             4

The required solution of quadratic equation is y = (3±6√2)/4. Option A is correct.

Solution of the quadratic equation (4y - 3)2 = 72 to be determine.

Quadratic equation are the equation having maximum power 2.

Here,
(4y - 3)² = 72
4y-3 = ±√72
4y = ±√72 +3
y = (3 ± 6√2)/4

Thus, The required solution of quadratic equation is y = (3±6√2)/4.

Learn more about quadratic equation here:
https://brainly.com/question/2263981

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Answer:

[tex]C. \[/tex]   [tex]\frac{1}{2}x^3 + 3.4y = 21[/tex]

Step-by-step explanation:

Given

[tex]x = 2[/tex]

[tex]y = 5[/tex]

Required

[tex]\frac{1}{2}x^3 + 3.4y[/tex]

Substitute 2 for x and 5 for y;

The expression becomes

[tex]=\ \frac{1}{2} * 2^3 + 3.4 * 5[/tex]

Multiply 3.4 by 5

[tex]=\ \frac{1}{2} * 2^3 + 17[/tex]

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

[tex]2^3 = 2 * 2 * 2 = 8[/tex]

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

[tex]=\ \frac{1}{2} * 8 + 17[/tex]

[tex]=\ \frac{8}{2} + 17[/tex]

[tex]=\ 4 + 17[/tex]

[tex]=\ 21[/tex]

Hence;

[tex]\frac{1}{2}x^3 + 3.4y = 21[/tex]