A company specializing in building robots that can clean your house has found that the average amount of time kids spend cleaning their houses is about 2 hours per week. If their sample size was 1000 randomly chosen kids and the standard deviation was 0.3 hours, what is the margin of error for a confidence interval of 95%?

Answers

Answer 1

Answer:

0.588

Step-by-step explanation:

Margin of error is:

ME = CV × SE

where CV is the critical value (z score or t score), and SE is the standard error (standard deviation of the sample).

Since n is large, we can approximate as a normal distribution.  At 95% confidence level, z = 1.96.

Therefore, the margin of error is:

ME = 1.96 × 0.3

ME = 0.588

Answer 2

Using the z-distribution, it is found that the margin of error for a 95% confidence interval was of 0.0186.

What is a z-distribution confidence interval?

The interval is:

[tex]\overline{x} \pm z\frac{\sigma}{\sqrt{n}}[/tex]

In which:

[tex]\overline{x}[/tex] is the sample mean.z is the critical value.n is the sample size.[tex]\sigma[/tex] is the standard deviation for the population.

The margin of error is given by:

[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]

In this problem, we have a 95% confidence level, hence[tex]\alpha = 0.95[/tex], z is the value of Z that has a p-value of [tex]\frac{1+0.95}{2} = 0.975[/tex], so the critical value is z = 1.96.

The standard deviation for the population and the sample size are given, respectively, by:

[tex]\sigma = 0.3, n = 1000[/tex]

Hence, the margin of error is given by:

[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]

[tex]M = 1.96\frac{0.3}{\sqrt{1000}}[/tex]

M = 0.0186.

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Related Questions

(5×7) + 3 = 5 ×(2×7) true or false

Answers

Step-by-step explanation:

35 + 3 = 5 x 14

38 = 70

False

Answer:

false

Step-by-step explanation:

(5×7)+3

(35)+3

38

5×(2×7)

5×(14)

70

What is the volume in cubic centimeters if the
pyramid has a height of 27 centimeters?

Answers

Answer:

The volume of the pyramid would be 4500 cm³.

Step-by-step explanation:

Formulas you would be using:

Volume of a pyramid: [tex]V = \frac{bh}{3}[/tex]  b = base, h = height

Area of a trapezoid: [tex]A = \frac{a+b}{2} h[/tex]  a = base₁ , b = base₂ , h = height

First, we're going to find the area of the trapezoid, which is the base of the pyramid.

We are given that a = 20, b = 30, h = 20

Plug it in:

[tex]\frac{20+30}{2} (20)[/tex] = 500 cm²

Now that we have found the base of the pyramid, we can plug it in along with the height of the pyramid.

[tex]V = \frac{(500)(27)}{3}[/tex] = 4500 cm³

Hope this helps :D

Use the table below.



If Sally is trying to keep her dinner under 500 calories, can she have a broiled sirloin, baked potato and salad and ½ cup fruit cocktail?

No
Yes

Answers

Yes. Broiled Sirloin:240 + Baked Potato:145 + salad:33 + fruit cocktail:57= 475

Answer:

Yes

Step-by-step explanation:

1/2 fruit cocktail—>57

broiled sirloin—>240

baked potato—>145

442 is the total so yes

Find the volume of the composite space figure to the nearest whole number.

Answers

Answer:

180cm^3

Step-by-step explanation:

The volume of a rectangular prism is v = Lwh, where v is the volume, L is the length, w is the width, and h is the height. Rewrite this equation with w solved in terms of v, l, and h.

Answers

Answer:

w=v/lh

Step-by-step explanation:

lwh=v

To isolate w, we'd have to divide both sides by (lh)

Therefore, w = v/lh

Hope this helped and have a good rest of your day!

Simpson deposits $1,200 in a savings account that earns simple interest at the rate of 5%
per year. What interest does he earn at the end of 1 year?

Answers

Answer:

$60

Step-by-step explanation:

SI = (PRT)/100

SI = Simple Interest

P = Principal

R = Rate ( in decimal form)

T = Time

SI = (1200 x .5 x 1)/100

SI = 6000 / 100

SI = 60

How many triangles exist with the given angle measures?

Answers

Answer:  An infinite number

We're given angles adding to 180 degrees, so we can generate as many similar triangles with these angles as we like.  They'll all have the same shape but different sizes.

Answer:

1

Step-by-step explanation:

Can someone explain and answer

Answers

The answer is D. y = -2x + 20. This is because it has a negative slope (-2x). When a number in a slope-intercept equation has the variable (x), that determines the positive or negative association. If it is a positive slope, it travels up from left to right. If it is a negative slope, it travels down from left to right.

Answer:

D. y = -2x + 20

Step-by-step explanation:

first, plot these points on a linear graph.

work down from the top:

A. y = 2x + 5

look at the last number first, this means the line will cross over the y axis (vertical line) at + 5. draw a point on + 5

y = 2x + 5

From this point (+5), the 2x means that for every 1 square you move across (to the right), you will go up 2. This will make the second point of the line. connect the dots. (see picture 1 below)

B. y = 2x - 6

the last number means the first point will be on -6 on the y axis.

y = 2x - 6

the 2x means that every 1 square you go across (to the right) from that point, you will move up 2

C. y = 2x

as there is no second number, this line will cross through the center of the graph. the 2 means that for every 1 square you move across from that point, you will move up 2

D. y = -2x + 20

the +20 means this line will cross the y axis and + 20, the -2 means that for every 1 square you move across to the right, you move DOWN 2.

this is the only line that moves down from left to right

What is the volume of the composite figure? Express the answer in terms of pie.
1443 mm3
1687 mm3
3127 mm3
456 mm3

Answers

Answer:

3127

Step-by-step explanation:

YES

The volume of the given composite figure is 312π mm³

Given is a composite figure, having two solids, a cone and a hemisphere,

We need to find the volume of the solid, so for the same, we simply need to add the volumes of the cone and the hemisphere,

= 1/3 π r² h + 2/3 π r³

= 1/3 π r²[h+2r]

= 1/3 π 36[12+14]

= 312 π

Hence, the volume of the given composite figure is 312π mm³

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find the length of the unknown side round your answer to the nearest 10th

Answers

Answer:

4.4 ft

Step-by-step explanation:

The sides of a right triangle are "tied together" mathematically by an equation called the Pythagorean theorem, which says: in any right triangle, the relationship between the two sides that make the right angle (we'll call them a and b) and the side across from it (c) is

[tex]a^2+b^2=c^2[/tex]

Let's sustitute these for the values we have in our problem (measured in feet)

[tex]9^2+a^2=10^2\\81+a^2=100\\a^2=19\\a=\sqrt{19}[/tex]

19 is between the perfect squares [tex]4^2=16[/tex] and [tex]5^2=25[/tex], so [tex]\sqrt{19}[/tex] must be between 4 and 5, a little bit closer to 4. Punching the expression into the calculator confirms this with a value of [tex]\sqrt{19}\approx4.3588[/tex] which we can round to 4.4 ft.

Aiyanna and Rose have 42 cards to sign.Aiyanna signs 1/3 of the cards,while Rose signs 4/7.How many cards are left to be signed

Answers

Answer:  Rose

Step-by-step explanation:

Aiyanna.  1/3 of 42=  14.        1/3 =  7/21

Rose.       4/7 of 42 = 24       4/7 =  12/21    

Answer:

Aiyanna.  1/3 of 42=  14.        1/3 =  7/21

Rose.       4/7 of 42 = 24       4/7 =  12/21  

Step-by-step explanation:

The grid you see below is in the shape of a rectangle. What is the area, in square
units, of the shaded part?​

Answers

Answer:

The area of the shaded region is [tex]18\ \text{units}^2[/tex].

Step-by-step explanation:

On the attached figure, a rectangle is shown. It is required to find the area of the shaded part. The shaded part forms a triangle. The area of a triangle is given by :

[tex]A=\dfrac{1}{2}\times b\times h[/tex]

b is base and h is height

From this figure, each box is a square of side 1 unit say.

Its height will be 4 units and its base is 9 units

So,

[tex]A=\dfrac{1}{2}\times 9\times 4\\\\A=18\ \text{units}^2[/tex]

So, the area of the shaded region is [tex]18\ \text{units}^2[/tex].

What is the surface area of the square pyramid represented by the net below?

Answers

Answer:

64 cm^2

Step-by-step explanation:

Square: 4*4 = 16

Triangles: 4((4*6)/2))

       = 4(24/2)

       = 4(12)

       = 48

Add the square and triangles together

       = 16 + 48

       = 64

The total will be 64 cm^2

Answer: 64 cm2

Step-by-step explanation:

Pythagorean theorem:
Is a triangle with the following side lengths a right triangle? Why?
a = 4
b = 6
c = 8
Example:
This does/does not make a right triangle because...

Answers

Answer/Step-by-step explanation:

This does not make a right triangle because the Pythagorean Theorem shows that 4^2 + 6^2 does not equal 8^2.

16 + 36 = 64

52 doesn't equal 64.

Answer:

This does not make a right triangle because according to the pythagorean theorem, a^2+b^2=c^2. 16+36 does not equal 64, thefore, the triangle with the following sides is not a right triangle.

Which of the following describe a simple event?

Answers

Answer: B

Step-by-step explanation:

Find the number of positive numbers less than 2020, which can be written as the sum of five consecutive positive numbers.

Answers

Integers*?

Let [tex]n[/tex] be the smallest of these five consecutive integers. Then the sum of the five consecutive integers is [tex]\frac{5(2n+4)}{2}=5n+10,[/tex] so we seek the largest positive integer [tex]n[/tex] such that [tex]5n+10<2020.[/tex] Solving this inequality, we find that [tex]n<402,[/tex] so there are [tex]\boxed{401}[/tex] such positive integers.

What if the diameter of the inner sphere is 1.8 meters. What is the volume of the inflated space?

Answers

Answer:

Volume is 3.05m³

Step-by-step explanation:

This problem bothers on the mensuration of solid shapes, sphere

Step one

The formula for the volume of a sphere is expressed as

V=4/3πr³

Step two

Given data

Diameter d = 1.8m

Radius r = d/2= 1.8/2= 0.9m

Step three

Substituting our given data we have

V= 4/3*3.142*0.9³

V= 4/3*3.142*0.729

V= 9.162/3

V=3.05m³

Which graph represents -x+ 8y > - 24

Answers

Kind of need a picture to help answer the question.

help me plz ill mark u brailiest

Answers

Answer:

The product of 21 and 18

Step-by-step explanation:

When you multiply the word is product

The product of 21 and 18

Answer:

the answer is H

Step-by-step explanation:

if the relationship is proportional, what is the missing value from the table?
A 8
B 9
C 12
D 14​

Answers

Answer:

C 12

Step-by-step explanation:

16 × 6 ÷ 8 = 12

check answer: 24 × 12 ÷ 16 = 18

PLEASE ANSWER QUICKLY!!!

You have a regular deck of 52 cards. You are wanting to draw a king, than an ace. You draw the first card, then replace it back into the deck. Have you created an independent or dependent event?

Answers

Answer:

Dependent Event

Step-by-step explanation:

Sorry if this was late!

Which fraction is greater than 3/5

4/6

6/12

3/8

4/10

Answers

Answer:

a.) 4/6

Step-by-step explanation:

3/5 = .6

4/6 = .666666666667

6/12= 0.5

3/8= .375

4/10= .4

Answer: 4/6

Step-by-step explanation:

IT IS THE BIGGEST. :)

Plz Help!
On the coordinate plane shown, each grid unit represents 10 feet. Polygon QRST has vertices Q(20, 10), R(−20, 10), S(−20, −20), and T(20, −20), and represents the floor plan of a room. Find the perimeter and area of the room.

Answers

Answer:

P  140 units

A  1200 units^2

Step-by-step explanation:

The length of the rectangle is 20 to -20 = 20 - -20 = 40 units

The width of the rectangle is 20 to -10 = 20 - -10 = 30 units

The perimeter is given by

P = 2 ( l+w) = 2 (40+30) = 2 (70) = 140 units

The area is given by

A = lw = 40*30 = 1200 units^2

What is the equation of a horizontal line passing through the point (-3, 8)?
Ox=-3
Oy=8
Ox= 5
Oy=-11

Answers

Answer:

Y=8

Step-by-step explanation:

A horizontal line is going to be parallel to the x-axis, so you need to use your y-value to determine the equation of the line. Your y-value in the coordinate (-3,8) is 8, so y=8

Answer: y = 8

Step-by-step explanation: Whenever we are given a line and the problem says that it's horizontal or a flat line, we know that the equation of the line will always be in the form "y = a number".

Since we are given that the y-coordinate is 8, that means that

the equation of this line will be y = 8.

Find the area of a circle whose circumference is 87 m.
A. 4 m 2
B. 8 m2
C. 16 m2
D. 64 m2

Answers

Answer:

None of those are right, the answer is about 602.32 m2

Step-by-step explanation:

Ellen’s dog has a pen that is 32 feet by 33 feet. What is the area of the dog pen? A rectangle with length 3 cubed feet and width of 3 squared feet. Find the area. 1. Multiply powers:    32 · 33 2. Expand each power:  (3 · 3) · (3 · 3 · 3) 3. Simplify:       35   Complete each sentence. The of the original exponent is the exponent in the power of product. The dog pen has an area of square feet.

Answers

Answer:

3^5 = 243 square feet

Step-by-step explanation:

Ellen’s dog has a pen that is 3² feet by 3³ feet. To find its area we follow the next steps:

1. Multiply powers:

A = 3² * 3³

2. Expand each power:

A = (3*3) * (3*3*3)

3. Simplify:

[tex]A = 3^5[/tex]

The addition of the original exponents is the exponent in the power of product. The dog pen has an area of [tex]3^5[/tex] square feet.

The area of Ellen's dog pen is [tex]\bold{3^5}[/tex]square feet.

The complete sentences are actually the way to solve the question and can be completed as mentioned below:

A rectangle with a length of 3 cubed feet and a width of 3 squared feet.

Find the area.

1. Multiply powers: Area = 3² · 3³

2. Expand each power: Area = (3 · 3) · (3 · 3 · 3)

3. Simplify: Area = [tex]\bold{3^5}[/tex]

The addition of the original exponents is the exponent in the power of the product. The dog pen has an area of [tex]\bold{3^5}[/tex] square feet.

Hence, the area of Ellen's dog pen is [tex]\bold{3^5}[/tex]square feet.

Learn more about the Area:

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Please respond with the format showed on the picture so use . after the letter and display the answer.

Answers

Answer:

c

Step-by-step explanation:

(24 - 15) x 4 - 3 x 2

9 x 4 - 3 x 2

36 - 6

30

Determine whether each statement is true or false.

(FINALEXAM)

Answers

Answer:

1. False

2. True

Step-by-step explanation:

Number 1 False
Number 2 true

Which of the following number sentences is an example of the associative property of multiplication?

4 × 5 = 5 × 4
6 × 1 = 6
20 × (10 + 6) = (20 × 10) + (20 × 6)
(12 × 3) × 8 = 12 (3 × 8)

Answers

20 × (10 + 6) = (20 × 10) + (20 × 6)

(12 × 3) × 8 = 12 (3 × 8)

Write a formula for quadratic function if its graph has the vertex at point (0,6) and passes through the point (−1,−2).

Answers

Answer:

y = - 8x² + 6

Step-by-step explanation:

The equation of a parabola in vertex form is

y = a(x - h)² + k

where (h, k) are the coordinates of the vertex and a is a multiplier

Here (h, k) = (0, 6), thus

y = a(x - 0)² + 6, that is

y = ax² + 6

To find a substitute (- 1, - 2) into the equation

- 2 = a(- 1)² + 6, that is

- 2 = a + 6 ( subtract 6 from both sides )

- 8 = a

y = - 8x² + 6

The formula of the quadratic function is [tex]y = -8x^2 + 6[/tex]

A quadratic function is represented as:

[tex]y = a(x - h)^2 + k[/tex]

The vertex of the quadratic function is given as:

[tex](h,k) = (0,6)[/tex]

So, we have:

[tex]y = a(x - 0)^2 + 6[/tex]

This gives:

[tex]y = ax^2 + 6[/tex]

The quadratic function passes through (-1,-2).

So, we have:

[tex]-2 = a(-1)^2 + 6[/tex]

[tex]-2 = a + 6[/tex]

Subtract 6 from both sides

[tex]a = -8[/tex]

Substitute -8 for a in [tex]y = ax^2 + 6[/tex]

[tex]y = -8x^2 + 6[/tex]

Hence, the formula of the quadratic function is [tex]y = -8x^2 + 6[/tex]

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