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
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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Find the number of positive numbers less than 2020, which can be written as the sum of five consecutive positive numbers.
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.
How many triangles exist with the given angle measures?
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:
What is the equation of a horizontal line passing through the point (-3, 8)?
Ox=-3
Oy=8
Ox= 5
Oy=-11
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.
Which of the following describe a simple event?
Answer: B
Step-by-step explanation:
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
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:
What if the diameter of the inner sphere is 1.8 meters. What is the volume of the inflated space?
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
What is the volume of the composite figure? Express the answer in terms of pie.
1443 mm3
1687 mm3
3127 mm3
456 mm3
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 volume of the composite space figure to the nearest whole number.
Answer:
180cm^3
Step-by-step explanation:
Write a formula for quadratic function if its graph has the vertex at point (0,6) and passes through the point (−1,−2).
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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Please respond with the format showed on the picture so use . after the letter and display the answer.
Answer:
c
Step-by-step explanation:
(24 - 15) x 4 - 3 x 2
9 x 4 - 3 x 2
36 - 6
30
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...
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 graph represents -x+ 8y > - 24
Kind of need a picture to help answer the question.
What is the surface area of the square pyramid represented by the net below?
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:
Which fraction is greater than 3/5
4/6
6/12
3/8
4/10
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. :)
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)
20 × (10 + 6) = (20 × 10) + (20 × 6)
(12 × 3) × 8 = 12 (3 × 8)
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?
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
Find the area of a circle whose circumference is 87 m.
A. 4 m 2
B. 8 m2
C. 16 m2
D. 64 m2
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.
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.
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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.
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
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
Answer:
Yes
Step-by-step explanation:
1/2 fruit cocktail—>57
broiled sirloin—>240
baked potato—>145
442 is the total so yes
What is the volume in cubic centimeters if the
pyramid has a height of 27 centimeters?
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
Can someone explain and answer
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
(5×7) + 3 = 5 ×(2×7) true or false
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
Determine whether each statement is true or false.
(FINALEXAM)
Answer:
1. False
2. True
Step-by-step explanation:
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?
Answer:
Dependent Event
Step-by-step explanation:
Sorry if this was late!
The grid you see below is in the shape of a rectangle. What is the area, in square
units, of the shaded part?
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].
if the relationship is proportional, what is the missing value from the table?
A 8
B 9
C 12
D 14
Answer:
C 12
Step-by-step explanation:
16 × 6 ÷ 8 = 12
check answer: 24 × 12 ÷ 16 = 18
find the length of the unknown side round your answer to the nearest 10th
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.
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.
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!
help me plz ill mark u brailiest
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:
