Answer:
A. 9.7%
Step-by-step explanation:
margin of error:
z * [tex]\sqrt{\frac{p(1-p)}{N} }[/tex]
n is sample size
z is the z score (for a 95% confidence interval you would use 1.96)
p is the sample proportion
to solve for 'p', remember that if a decimal value is given, use that. but if it is a whole number, then divide that number by the sample size, and substitute it into the formula.
in this case we are given 43% so 0.43.
in the formula :
1.96 * [tex]\sqrt{\frac{0.43(1-0.43)}{100} }[/tex]
if you calculate this you get around 0.09703 this is 9.7%
Margin of error is 9.7% (A)
ρ = 43% which is equal to 0.430
[tex]1 - P = 1 - 0.430 = 0.570[/tex]
The number of sample n = 100
We have to calculate Z at 95% confidence interval
∝ = [tex]1 - 95%[/tex]%
∝ = [tex]1 - 0.95[/tex]
∝ = [tex]0.05[/tex]
∝/2 = 0.025
Z(∝/2) = Z(0.025) = 1.96
Standard error = [tex]\sqrt{ ((1-P)xP / n)}[/tex]
Standard error = [tex]\sqrt{(1-0.43)x0.43 / 100)[/tex]
Standard error = [tex]\sqrt{(0.002451)}[/tex]
Standard error = 0.04950758
Standard error = 0.0495
Margin of error = Z*SE. z = 1.96 and standard error = 0.0495
Margin of error = [tex]1.96x0.0496[/tex]
Margin of error = [tex]0.097216[/tex]
Margin of error = [tex]9.7216%[/tex]%
In conclusion, the margin of sampling error for a 95% confidence interval is 9.7%.
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Type the missing number in this sequence:
1,
4,
,64, 256,
1,024
Answer:
16
Step-by-step explanation:
The sequence is 1, 4,...,64, 256, 1024
Notice that:
● 1 = 2^0
● 4 = 2^2
● 64 = 2^6
● 256 = 2^8
● 1024 = 2^10
Notice that we add 2 each time to the exponent so the missing number is:
● 2^(2+2) = 2^4 = 16
Which expression is equivalent to x+y+x+y+3(y+5)
Answer:
2x + 5y + 15
Step-by-step explanation:
add like terms
(x+x) + (y+y)+3y+15
2x+2y+3y+15
2x + 5y + 15
i hope this helps!
Nick needs one more class to complete his schedule. There are 5 writing classes, 3 history classes, and 4 mathematics classes that can fit into his schedule. If Nick chooses a class at random, what is the probability that he chooses a history class? Give your answer as a fraction.
Answer:
1/4
Step-by-step explanation:
Probability = 3/(5+3+4)
= 3/12 or 1/4
Match each polynomial on the left with its two factors on the right.
Answer:
Hello
Step-by-step explanation:
[tex]Formula: \\\\\boxed{\Large a^3\pm b^3=(a \pm b)(a^2 \mp ab+b^2)}\\\\8x^3+1=(2x)^3+1^3=(2x+1)(4x^2-2x+1)\\\\8x^3-1=(2x)^3-1^3=(2x-1)(4x^2+2x+1)\\[/tex]
The factors of the expression 8x³ + 1 and 8x³ - 1³ will be (2x + 1) & (4x² – 2x + 1) and (2x – 1) & (4x² + 2x + 1), respectively.
What is a polynomial?A polynomial expression is an algebraic expression with variables and coefficients. Unknown variables are what they're termed. We can use addition, subtraction, and other mathematical operations. However, a variable is not divisible.
The expression is given below.
8x³ + 1 and 8x³ - 1³
(2x)³ + 1³ and (2x)³ - 1³
We know that the formula is given as,
a³ + b³ = (a + b) (a² – ab + b²)
a³ – b³ = (a – b) (a² + ab + b²)
Then the expression is written as,
(2x)³ + 1³ = (2x + 1) [(2x)² – 2x + 1²]
(2x)³ + 1³ = (2x + 1) (4x² – 2x + 1)
(2x)³ – 1³ = (2x – 1) [(2x)² + 2x + 1²]
(2x)³ – 1³ = (2x – 1) (4x² + 2x + 1)
The factors of the expression 8x³ + 1 and 8x³ - 1³ will be (2x + 1) & (4x² – 2x + 1) and (2x – 1) & (4x² + 2x + 1), respectively.
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A spinner has 10 equally sized sections, 5 of which are gray and 5 of which are blue. The spinner is spun twice. What is the probability that the first spin lands on gray and the second spin lands on blue? Write your answer as a fraction in the simplest form.
Answer:
[tex]P(Gray\ and\ Blue) = \frac{1}{4}[/tex]
Step-by-step explanation:
Given
[tex]Sections = 10[/tex]
[tex]n(Gray) = 5[/tex]
[tex]n(Blue) = 5[/tex]
Required
Determine P(Gray and Blue)
Using probability formula;
[tex]P(Gray\ and\ Blue) = P(Gray) * P(Blue)[/tex]
Calculating P(Gray)
[tex]P(Gray) = \frac{n(Gray)}{Sections}[/tex]
[tex]P(Gray) = \frac{5}{10}[/tex]
[tex]P(Gray) = \frac{1}{2}[/tex]
Calculating P(Gray)
[tex]P(Blue) = \frac{n(Blue)}{Sections}[/tex]
[tex]P(Blue) = \frac{5}{10}[/tex]
[tex]P(Blue) = \frac{1}{2}[/tex]
Substitute these values on the given formula
[tex]P(Gray\ and\ Blue) = P(Gray) * P(Blue)[/tex]
[tex]P(Gray\ and\ Blue) = \frac{1}{2} * \frac{1}{2}[/tex]
[tex]P(Gray\ and\ Blue) = \frac{1}{4}[/tex]
A triangle has a base that is increasing at a rate of 18 mm per minute with the height being held constant. What is the rate of change of the area of the triangle if the height is 7 mm
Answer:
63mm/minStep-by-step explanation:
Area of a triangle = 1/2 * base * height
A = 1/2bh
Rate of change of area is expresssed as dA/dt = dA/db * db/bt
db/dt is the rate at which the base is increasing.
Given db/dt = 18mm/min
A = 1/2*7b
A = 7b/2
dA/db = 7/2
The rate at which the area is changing dA/dt = dA/db * db/bt
dA/dt = 7/2 * 18
dA/dt = 7*9
dA/dt = 63mm/min
Hence the rate at which the area of the triangle is changing is 63mm/min
Simplify, write without exponents.
[tex]2*4^{2} *(128\frac{1}{4})[/tex]
[tex]_\sqrt[_]{_}[/tex]
a.) 8
b.) 20
c.) 2
d.) 64
e.) 4
f.) 16
it is helpful to you
A solid is formed by rotating the region bounded by y = x − x^2 and y = 0 about the line x = 2 . Use the shell method to find the volume of the solid.
Answer:
The volume of the resulting solid is π/2 cubic units.
Step-by-step explanation:
Please refer to the diagram below.
The shell method is given by:
[tex]\displaystyle V = 2\pi \int _a ^b r(x) h(x)\, dx[/tex]
Where the representative rectangle is parallel to the axis of revolution, r(x) is the distance from the axis of revolution to the center of the rectangle, and h(x) is the height of the rectangle.
From the diagram, we can see that r(x) = (2 - x) and that h(x) is simply y. The limits of integration are from a = 0 to b = 1. Therefore:
[tex]\displaystyle V = 2\pi \int_0^1\underbrace{\left(2-x\right)}_{r(x)}\underbrace{\left(x - x^2\right)}_{h(x)}\, dx[/tex]
Evaluate:
[tex]\displaystyle \begin{aligned} V&= 2\pi \int_0 ^1 \left(2x-2x^2-x^2+x^3\right) \, dx\\ \\ &= 2\pi\int _0^1 x^3 -3x^2 + 2x \, dx \\ \\ &= 2\pi\left(\frac{x^4}{4} - x^3 + x^2 \Bigg|_0^1\right) \\ \\ &= 2\pi \left(\frac{1}{4} - 1 + 1 \right) \\ \\ &= \frac{\pi}{2}\end{aligned}[/tex]
The volume of the resulting solid is π/2 cubic units.
Answer:
pi/2
Step-by-step explanation:
I always like to draw an illustration for these problems.
For shells method think volume of cylinder=2pi×r×h
Integrate(2pi(2-x)(x-x^2) ,x=0...1)
Multiply
Integrate(2pi(2x-2x^2-x^2+x^3 ,x=0...1)
Combine like terms
Integrate(2pi(2x-3x^2+x^3) ,x=0...1)
Begin to evaluate
2pi(2x^2/2-3x^3/3+x^4/4) ,x=0...1
2pi(x^2-x^3+x^4/4), x=0...1
2pi(1-1+1/4)
2pi/4
pi/2
what is the definition of a sequence
Answer:
the process of combining things in a particular order, or discovering the order in which they are combined: A common sign of dyslexia is that the sequencing of letters when spelling words may be incorrect. biology specialized.
Step-by-step explanation:
What is the volume of a cone below?
A 10-ft ladder, whose base is sitting on level ground, is leaning at an angle against a vertical wall when its base starts to slide away from the vertical wall. When the base of the ladder is 6 ft away from the bottom of the vertical wall, the base is sliding away at a rate of 4 ft/sec. At what rate is the vertical distance from the top of the ladder to the ground changing at this moment?
Answer:
2.5/ft per sec
Step-by-step explanation:
its vertica.
The height of the ladder is decreasing at a rate of 24 ft/sec.
What is the Pythagorean theorem?Pythagorean theorem states that for a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
We can apply this theorem only in a right triangle.
Example:
The hypotenuse side of a triangle with the two sides as 4 cm and 3 cm.
Hypotenuse side = √(4² + 3²) = √(16 + 9) = √25 = 5 cm
We have,
Let's denote the distance between the base of the ladder and the wall by x.
The length of the ladder = L.
Now,
L = 10 ft
dx/dt = 4 ft/sec
x = 6 ft.
The rate of change of the height of the ladder with respect to time.
Using the Pythagorean theorem, we have:
L² = x² + y²
Differentiating both sides with respect to time t, we get:
2L (dL/dt) = 2x(dx/dt) + 2y(dy/dt)
Substituting L = 10 ft, x = 6 ft, and dx/dt = 4 ft/sec.
20(dL/dt) = 12(4) + 2y(dy/dt)
Simplifying and solving for dy/dt.
dy/dt = (20/2y)(dL/dt) - 24
Now,
The height of the ladder.
Using the Pythagorean theorem again, we have:
y² = L² - x²
= 100 - 36
= 64
y = 8
Now,
Substituting y = 8 ft, dL/dt = 0
(since the length of the ladder is constant), and dx/dt = 4 ft/sec.
dy/dt
= (20/2(8))(0) - 24
= -24 ft/sec
Therefore,
The height of the ladder is decreasing at a rate of 24 ft/sec.
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Solve the following equation algebraically:
3x^2=12
a.+3
b. +2
C.+3.5
d. +1.5
Answer:
Step-by-step explanation:
answer is c just took test
Line L has a slope of 1/2 . The line through which of the following pair of points is perpendicular to L?
The line which crosses through L must have an intersect point with L to become perpendicular.
Gien slope is positive 1/2.
What is a straight line graph?The graph follows a straight line equation shows a straight line graph.equation of a straight line is y=mx+cy represents vertical line y-axis.x represents the horizontal line x-axis. m is the slope of the lineslope(m)=tan∅=y axis/x axis.
c represents y-intercepts (it is the point at which the line cuts on the y-axis)Straight line graphs show a linear relationship between the x and y values.
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Define limit and it's types.
In mathematics, a limit is the value that a function (or sequence) approaches as the input (or index) approaches some value.
g(x) , one may look at how big f(x) and g(x) are. For example: If f(x) is close to some positive number and g(x) is close to 0 and positive, then the limit will be ∞. If f(x) is close to some positive number and g(x) is close to 0 and negative, then the limit will be −∞.
name all sets of numbers to which each real number belongs
Answer:
1. Natural Number
2. Integer
3. Rational Number
4. Rational Number
5. Irrational Number
6. Rational Number
7. Rational Number
8. Natural Number
9. Irrational Number
10. Integer
11. Irrational Number
12. Natural Number
The management of a department store is interested in estimating the difference between the mean credit purchases of customers using the store's credit card versus those customers using a national major credit card. You are given the following information.
Store's Card Major Credit Card
Sample size 64 49
Sample mean $140 $125
Population standard deviation $10 $8
A point estimate for the difference between the means is:________
a. 18
b. 265
c. 15
d. 2
find the value of x, circles and angles
Answer:
x = 50
Step-by-step explanation:
When two secants intersect in the interior of a circle, the angles formed are the average of the arc an angle and its vertical intercept. In this case, our angle, 73, should be the average of x and 96. We can translate this to an equation and solve:
[tex]\frac{x+96}{2} = 73[/tex]
x + 96 = 146
x = 50
The weighted average of the possible values that a random variable X can assume, where the weights are the probabilities of occurrence of those values, is referred to as the:\
Answer: Expected value
Step-by-step explanation: The expected value of a random variable refers to a predicted variable which is obtained from the summation of the product of all possible values and the probability of occurrence of each value. The expected values gives the mean or average possible value over the cause of a certain experiment or scenario. It is thus the probability weighted average of all possible values or outcomes of an experiment.
The expected value could be represented mathematically as thus;
E(x) = [Σ(x * p(x)]
Where x = all possible values or outcomes of x;
p(x) = corresponding probability of each x value.
you write a short story, but you want to make sure your work is protected before you post it online. what should you do to help protect your copyright?
Answer:
Hey there!
Here are a few steps:
Make sure your work is properly marked, because then it will be protected under law.
Register your work.
Keep or register supporting evidence.
Let me know if this helps :)
Pls Help ASAP..................
Answer:
1. 8+(30/(2+4)) = 8+(30/6) = 8+5 = 13
2. ((8+30)/2)+4 = (38/2)+4 = 19+4 = 23
Step-by-step explanation:
:)
Answer:
Step-by-step explanation:
23:
(8 + 30) ÷ 2 + 4
13:
8 + 30 ÷ (2 + 4)
please give me the brainliest if u can
Simple geometry please help
Find KL. Round to the nearest hundredth.
Answer:
KL ≈ 1.94
Step-by-step explanation:
Using the cosine ratio in the right triangle
cos48° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{JL}{KL}[/tex] = [tex]\frac{1.3}{KL}[/tex] ( multiply both sides by KL )
KL × cos48° = 1.3 ( divide both sides by cos48° )
KL = [tex]\frac{1.3}{cos48}[/tex] ≈ 1.94 ( to the nearest hundredth )
In determining your group’s estimate, what mathematical model of a tennis ball did you use? What model of the classroom did you use? Did you make other simplification or assumptions?
Answer:
bro ur question is not understandable
What is the domain of the function represented by the graph
Answer:
C
Step-by-step explanation:
Domain of the function is the whole R
Arborist 96% positive tree has a disease, 97% trees do not have disease. Probability of a false positive?
Answer:
Step-by-step explanation:
the probability that the test result is positive (suggesting the person has the disease), given that the person does not have the disease, is only 2 percent; the probability that the test result is negative (suggesting the person does not have the disease), given that the person has the disease, is only 1 percent.
Find f (3) for the following function:
f (x) = 4x+3/x^2
Answer: [tex]12.333[/tex] or [tex]12\frac{1}{3}[/tex] or [tex]\frac{37}{3}[/tex]
Step-by-step explanation:
Replace every x with (3)
[tex]f(x) = 4x+3/x^2\\f(3) = 4(3)+3/3^2\\f(3) = 12+3/9\\f(3) = 12.333 or 12\frac{3}{9}or \frac{111}{9}\\f(3) = 12.333 or 12\frac{1}{3} or \frac{37}{3}[/tex]
A 20-foot ladder is placed against a tree. The bottom is located 5 feet from the base of the tree and the top of the ladder is 5√15 feet up the tree. Use tangent to find the angle created between the ladder and tree. Include a sketch that shows all known information and clearly shows what you need to find. Show all work and give the answer rounded to the nearest tenth of a degree.
Answer:
14.5°
Step-by-step explanation:
The sketch results in an angle of depression problem.
In this case, the opposite side of the triangle formed is 5 ft
The hypotenuse side is 20 ft
The adjacent side is the [tex]5\sqrt{15}[/tex] ft
Using tangent θ = opp/adj
tangent θ = 5/[tex]5\sqrt{15}[/tex] = [tex]\frac{1}{\sqrt{15} }[/tex] = 0.258
θ = [tex]tangent^{-1}[/tex] 0.258 = 14.5°
Jack’s backpack weighs 15 pounds. Fernando’s backpack weighs less than Jack’s. Which graph shows how much Fernando’s backpack can weigh?
Answer:
A
Step-by-step explanation:
c and d out of the question
b has its circle filled in meaning it could be 15lbs, which it's not
A correct answer by default
Answer:b
Step-by-step explanation: it has a filled in diamond which mean it's that...
The number of values of xx in the interval [0,5π][0,5π] satisfying the equation 3sin2x−7sinx+2=03sin2x-7sinx+2=0 is/are
Answer:
6
Step-by-step explanation:
Given, 3sin2x−7sinx+2=03sin2x-7sinx+2=0
⇒(3sinx−1)(sinx−2)=0⇒3sinx-1sinx-2=0
⇒sinx=13 or 2⇒sinx=13 or 2
⇒sinx=13 [∵sinx≠2]⇒sinx=13 [∵sinx≠2]
Let sinα=13,0<α<π2,sinα=13,0<α<π2, then sinx=sinαsinx=sinα
now x=nπ+(−1)nα(n∈I)x=nπ+(−1)nα(n∈I)
⇒x=α,π−α,2π+α,3π−α,4π+α,5π−α⇒x=α,π−α,2π+α,3π−α,4π+α,5π−α Are the solution in [0,5π][0,5π]
Hence, required number of solutions are 6
A sandman earns a commission of 26%. One week he had sales of $24400. Find the commission for the week.
Answer:
6344
Step-by-step explanation:
Find 26% of 24400
24400 * 26%
24400 * .26
6344
Question 1 of 10
What is the measure of ZXYZ shown in the diagram below?
Y
S
(369
7
Х
1140
Plz help
Answer:
B
Step-by-step explanation:
Secant-secant with vertex outside the circle
1/2(larger-smaller arc)
1/2(114-36)
1/2(78)
39