The probability that the sample proportion of airborne viruses in differ from the population proportion by greater than 3% is 0.006.
According to the Central limit theorem, if from an unknown population large samples of sizes n > 30, are selected and the sample proportion for each sample is computed then the sampling distribution of sample proportion follows a Normal distribution.
The mean of this sampling distribution of sample proportion is:
μρ=ρ
The standard deviation of this sampling distribution of sample proportion is:
σρ=[tex]\sqrt \frac{p(1-p)}{n}[/tex]
The information provided is:
n = 533
p = 0.09
As the sample size is quite large, i.e. n = 533 > 30, the central limit theorem can be used to approximate the sampling distribution of sample proportion by a Normal distribution.
The mean and standard deviation are:
μρ=ρ=0.09
σρ=[tex]\sqrt \frac{p(1-p)}{n}[/tex]=[tex]\sqrt\frac{0.09(1-0.09)}{533}=0.01239[/tex]
Compute the probability that the sample proportion of airborne viruses in differ from the population proportion by greater than 3% as follows:
[tex]p(p^-p > 0.03)=P(p^ > 0.12) \\=P(z > \frac{0.12-0.9}{0.012}) \\= P(Z > 2.5) \\= 1-P(Z > 2.5) \\ = 1- 0.993 \\ = 0.00621[/tex]
Thus, the probability that the sample proportion of airborne viruses in differ from the population proportion by greater than 3% is 0.006.
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Find the equivalent expression of the following: x3 (x2 + 5x + 7)
1. x5 + 5x3 + 7x2
2. x6 + 5x4 + 7x3
3. x5 + 4x4 + x4 + 8x3 – x3
4. x5 + 3x4 + x4 + 6x3 + x3
The product of the given function is x^5 + 5x^4 + 7x^3
Product of polynomial functionsThe leading degree of a polynomial function is always greater than or equal to 2.
Given the products below;
x^3 (x^2 + 5x + 7)
Expand
(x^3)(x^2) + 5x(x^3) + 7x^3
Simplify
x^5 + 5x^4 + 7x^3
Hence the product of the given function is x^5 + 5x^4 + 7x^3
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The equivalent expression of x³(x² + 5x + 7) is x⁵ + 5x⁴ + 7x³
How to find equivalent expression?The equivalent expression of the expression can be found as follows;
x³(x² + 5x + 7)
let's open the bracket by multiplying.
Therefore,
x³(x² + 5x + 7) = x⁵ + 5x⁴ + 7x³
Hence,
The equivalent expression of x³(x² + 5x + 7) is x⁵ + 5x⁴ + 7x³
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How many ways are there to fill either the pitcher or catcher field position (but not both) from among the 25 players (leaving the other field positions empty)
Using the permutation formula, it is found that there are 600 ways to fill the pitcher and catcher positions.
The order is important, as one player is the pitcher and the other is the catcher, hence the permutation formula is used to solve this question.
What is the permutation formula?The number of possible permutations of x elements from a set of n elements is given by:
[tex]P_{(n,x)} = \frac{n!}{(n-x)!}[/tex]
2 players are taken from a set of 25, hence the number of ways is given by:
[tex]P_{(25,2)} = \frac{25!}{23!} = 600[/tex].
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During the sale, Carly pays $54 for a wheelbarrow. What was the original price?
The original price of the wheelbarrow is £75
How to determine the original price?Let the original price be x.
From the question, the amount paid is:
Amount paid = 54
The reduced price is calculated as:
Reduced = Original price * (1 - discount)
This gives
x * (1- 20%) = 54
Evaluate the difference
x * 0.8 = 54
Divide by 0.8
x = 67.5
Hence, the original price is $67.5
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Complete question
The price of a wheelbarrow is reduced by 20%. During the sale, Carly pays $54 for a wheelbarrow. What was the original price?
Is Figure B a scale copy of Figure A?
Answer:
No.
Step-by-step explanation:
The ratio of the lengths of the vertical sides from A to B is 2/4 which equals 1/2.
The ratio of the lengths of the horizontal sides of A to B is 4/11.
Since 4/11 is not equal to 1/2, figure B is not a scale copy of figure A.
Jevon Noda's home has a market value of $72,000, the rate of assessment is 30%, and the tax rate is 85.
mills. Find the a) assessed value, b) tax rate as a decimal, and c) real estate tax.
The required a) assessed value = $21600,
b) tax rate = 0.0855,
c) real estate tax = $1836.
Cost price is that price for buyer which he pays to seller for an object or product.
a) assessed value = 72000 x 30/100
= $21600
b) tax rate = 85.5/1000
= 0.0855
c) real estate tax = 0.855 x 21600
= $ 1836
Thus, the required values of a) assessed value, b) tax rate as a decimal, and c) real estate tax is $21600, 0.085 and $1836 respectively.
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If f(x) = -3x - 5 and g(x) = 4x - 2, find (f+ g)(x)
Answer:
(f+g)(x)=f(x)+g(x)
=(-3x-5)+(4x-2)
= -3x-5+4x-2. collect like term
= -3x+4x-5-2
= x-7. the final answer
In constructing 98% confidence intervals for means, what do we expect will be true over the long run?
In constructing 98% confidence intervals for means, it is true that the statistic is good enough, and is less uncertain.
What is a confidence interval?A confidence interval expresses the degree of uncertainty surrounding a given statistic. A margin of error is frequently used with confidence intervals. It reveals the degree to which you may be certain that the findings of a poll or survey correspond to what you would anticipate discovering if it were possible to poll the complete population. Levels of confidence are inextricably linked to confidence intervals.
Your level of confidence in your findings is shown by the confidence interval. You can never be certain that your results will hold for future surveys or experiments. In statistics, being 95% or 98.5% certain is typically seen as "good enough."
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I am studying geometry this summer but can’t solve this question what would be the correct answer
A cylinder has a radius of 5x-1. Write a simplified expression for its volume where V= pi r^2 h
The volume of the cylinder whose radius is 5x-1 unit is 25x²πh + πh - 10xπh.
What is the volume of a right circular cylinder?
Suppose that the radius of the considered right circular cylinder is 'r' units.
And let its height be 'h' units.
Then, its volume is given as:
[tex]V = \pi r^2 h \: \rm unit^3[/tex]
The right circular cylinder is the cylinder in which the line joining centre of the top circle of the cylinder to the centre of the base circle of the cylinder is perpendicular to the surface of its base, and to the top.
Given that the radius of the cylinder is (5x-1), while the height of the cylinder is h. Therefore, the volume of the cylinder is,
The volume of the cylinder = π × (5x-1)² × h
= (25x² + 1 - 10x)πh
= 25x²πh + πh - 10xπh
Hence, the volume of the cylinder is 25x²πh + πh - 10xπh.
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find the perimeter and area of a triangle whose sides are of length 2cm, 5cm and 5cm
Answer:
Perimeter:12cm
Area:5cm²
Step-by-step explanation:
Perimeter is the total distance around the figure ie sum of all sides of figure
∴Perimeter of triangle equals 2cm plus 5cm plus 5cm
∴The perimeter equals 12cm
Area of triangle equals 1/2×base×height,where base is 2cm & height is 5cm
(Inserting values)
∴Area of the triangle equals 1/2×2cm×5cm which equals 5cm²
What is the slope of a line that passes through the points ( -1, 9) and (3,6)?
Answer:
-¾
Step-by-step explanation:
Slope=m
(-1,9) (3,6)
m= Y2-Y1 / X2-X1
m=6-9/3-(-1)
m=-3/3+1
m=-3/4
prove it. this question is from trigonometry
Answer:
See below for step-by-step proof.
Step-by-step explanation:
[tex]\textsf{Given expression}:[/tex]
[tex]\cos^6 \theta+\sin^6 \theta[/tex]
[tex]\textsf{Apply exponent rule} \quad a^{bc}=(a^b)^c:[/tex]
[tex]\implies (\cos^2 \theta)^3+(\sin^2 \theta)^3[/tex]
[tex]\textsf{Use the identity}\quad a^3+b^3=(a+b)^3-3ab(a+b):[/tex]
[tex]\implies (\cos^2 \theta+\sin^2 \theta)^3-3 \cos^2 \theta\sin^2 \theta (\cos^2 \theta+\sin^2 \theta)[/tex]
[tex]\textsf{Use the identity}\quad \sin^2 \theta + \cos^2 \theta=1:[/tex]
[tex]\implies (1)^3-3 \cos^2 \theta\sin^2 \theta (1)[/tex]
[tex]\implies 1-3 \cos^2 \theta\sin^2 \theta[/tex]
[tex]\implies 1-3 (\cos \theta\sin \theta)^2[/tex]
[tex]\textsf{Use the identity}\quad \sin 2 \theta=2 \sin \theta \cos \theta \implies \dfrac{1}{2}\sin 2 \theta= \sin \theta \cos \theta:[/tex]
[tex]\implies 1-3 \left( \dfrac{1}{2}\sin 2 \theta\right)^2[/tex]
[tex]\implies 1-\dfrac{3}{4} \sin^2 2 \theta[/tex]
[tex]\textsf{Use the identity}\quad \sin^2 2\theta + \cos^2 2\theta=1 \implies \sin^2 2\theta=1-\cos^2 2\theta[/tex]
[tex]\implies 1-\dfrac{3}{4} \left(1-\cos^2 2 \theta\right)[/tex]
[tex]\implies 1-\dfrac{3}{4} +\dfrac{3}{4}\cos^2 2 \theta[/tex]
[tex]\implies \dfrac{1}{4} +\dfrac{3}{4}\cos^2 2 \theta[/tex]
[tex]\textsf{Factor out }\dfrac{1}{4}:[/tex]
[tex]\implies \dfrac{1}{4}\left(1+3\cos^2 2 \theta\right)[/tex]
[tex]\textsf{Use the identity}\quad \cos (4 \theta)=2 \cos^2 2\theta - 1 \implies \cos^2 2 \theta=\dfrac{1}{2}\cos 4 \theta+\dfrac{1}{2}:[/tex]
[tex]\implies \dfrac{1}{4}\left(1+3\left(\dfrac{1}{2}\cos 4 \theta+\dfrac{1}{2}\right)\right)[/tex]
[tex]\implies \dfrac{1}{4}\left(1+\dfrac{3}{2}\cos 4 \theta+\dfrac{3}{2}\right)[/tex]
[tex]\implies \dfrac{1}{4}\left(\dfrac{5}{2}+\dfrac{3}{2}\cos 4 \theta\right)[/tex]
[tex]\implies \dfrac{1}{4} \cdot \dfrac{1}{2}\left(5+3\cos 4 \theta\right)[/tex]
[tex]\implies \dfrac{1}{8}\left(5+3\cos 4 \theta\right)[/tex]
Which of these tables represents a linear function?
Answer:
a
Step-by-step explanation:
a is the anwer because b/c it has a constant rate of change unlike the others
Ella needed to get her computer fixed. She took it to the repair store. The technician at the store worked on the computer for 3 hours and charged her $61 for parts. The total was $226. Write and solve an equation which can be used to determine x, the cost of the labor per hour
Which is the principal value of \arcsin\left(0.98\right)arcsin(0.98)\arcsin, left parenthesis, 0, point, 98, right parenthesis?
The principal value of arc sin(0.98)=78.5°.
What is principal value?The value of the inverse function at a place that falls within the range of the unit of the principal value is the primary value of the trigonometric function at that point.
Trigonometric function solutions with a value between 0 and 2π are known as principal values of trigonometric functions. The primary values of trigonometric functions are values smaller than 2π, which is the interval at which the trigonometric function's value repeats.
The principal value of the inverse trigonometric function is always the positive value whenever any positive value and the negative value are presented in a way that these two values are equal.
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10. The figure is reflected across line m and then reflected across line n. What type of transformation is the result?
reflection
translation
rotation
Elliott is standing at the top of a store escalator that leads to the ground floor below. The angle of depression from the top of the escalator to the floor is 42.51°, and the escalator is 16 feet long. How far is the top of the escalator from the ground floor? Round your answer to the nearest foot.
41 feet
17 feet
12 feet
11 feet
Answer: 11
Step-by-step explanation:
[tex]\sin 42.51^{\circ}=\frac{x}{16}\\\\x=16 \sin 42.51^{\circ} \approx 11[/tex]
a woman is 40 years old. her daughter is one quarter her age. what years and months is her daughter
Answer:
10 years old or 120 months old
Is it possible to design a pair of nonstandard dice, with positive integers on the faces (not necessarily all distinct), so that the probability of rolling any given total on those two dice is the same as the probability of rolling that total on two standard dice
you can reduce it to factors of degree 2 or less).
The two dice do not need to be identical. If it is possible, do it. If it is not possible, prove that it is not possible.
Some hints I got were to try to construct a pair of nonstandard dice such that the generating function for their sum matches the corresponding g.f. for a pair of standard dice and to note that the g.f. for a pair of standard dice can be factored quite a bit (you can reduce it to factors of degree 2 or less).
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4. The temperature at 6:00 a.m. was 45°F and the temperature at 10:30 a.m. was 12.8°C. What was the change in temperature between 6:00 a.m. and 10:30 a.m.? I will give brainllest
Answer:
10.04°F
Step-by-step explanation:
(12.8°C × 9/5) + 32 = 55.04 - 45 = 10.04
please help with sin question
Answer: A
Step-by-step explanation:
The cosine of an angle is equal to the sine of its complement, and vice versa.
A pattern of rectangles is formed by decreasing the length and increasing the width, each by the same amount. The relationship between x, the amount of increase, and A, the area of the rectangle represented by the increase, is quadratic.
Which graph could represent the area of each rectangle in terms of the change in the length and width?
A graph shows change in dimensions (units) labeled 1 to 10 on the horizontal axis and area (square units) on the vertical axis. A straight line decreases from 0 to 9 units.
A graph shows change in dimensions (units) labeled 1 to 10 on the horizontal axis and area (square units) on the vertical axis. A line decreases from 0 to 3 units, increases from 3 to 6 seconds, and decreases from 6 to 9 seconds.
A graph shows change in dimensions (units) labeled 1 to 10 on the horizontal axis and area (square units) on the vertical axis. A line increases from 0 to 3 seconds then decreases from 3 to 9 seconds.
A graph shows change in dimensions (units) labeled 1 to 10 on the horizontal axis and area (square units) on the vertical axis. A curved line decreases from 0 to 9 units.
The graph that can represent the area of each rectangle in terms of the change in the length and width is C. A graph shows change in dimensions (units) labeled 1 to 10 on the horizontal axis and area (square units) on the vertical axis. A line increases from 0 to 3 seconds then decreases from 3 to 9 seconds.
How to illustrate the information?It should be noted that a graph gives a diagrammatic representation of an information.
Here, the rectangles are formed by decreasing the length and increasing the width, each by the same amount.
Thai can be illustrated by the third graph in the option as the line increases from 0 to 3 seconds then decreases from 3 to 9 seconds.
In conclusion, the correct option is C.
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Answer:
(っ◔◡◔)っ ♥ the answer is C ♥
Step-by-step explanation:
got it right on edge
Which expression is equivalent to 54 · (5-2)3 ?
uuuuubhbjvykuhctkkhygtcykxmhfxg
The surface area of the spherical ball is given as follows:
[tex]635.04\pi[/tex] yd².
What is the surface area of a sphere?The surface area of a sphere of radius r is given as follows:
[tex]S = 4\pi r^2[/tex].
In this problem, the diameter is of 25.2 yd, hence the radius is given by:
r = 0.5 x 25.2 yd = 12.6 yd.
Then the surface area in yd² is:
[tex]S = 4\pi (12.6)^2 = 635.04\pi[/tex].
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Write the numbers in order from least to greatest. -3, 1 ¹/4, -1 3/4, ¹/10
7. Try It #7 Look at the graph in Figure 22 and identify the following for the function j(t):
e. Is j(t) an increasing or decreasing function (or neither)?
Answer:
The function of j(t) is decreasing.
Step-by-step explanation:
In the question two functions are given as h(t)=3t-4 and j(t)=5-t.
It is required to find whether j(t) is an increasing/decreasing or neither function.
To solve this question, first find the slope of the function. If, the slope is positive the function is increasing and if the slope is negative the function is decreasing.
Step 1 of 1
Find the slope of the function j(t) by comparing these to the standard form.
y=mx+b
Then, m=-1
Since the slope is negative.
Therefore, the function is decreasing.
Point A is the point of concurrency of the angle bisectors of ΔDEF.
Point A is the point of concurrency of triangle D E F. Lines are drawn from each point of the triangle to point A. Lines are drawn from point A to the sides of the triangle to form right angles and line segments A X, A Y, and A Z. The length of F A is 6 centimeters, the length of A D is 5 centimeters, the length of A X is 3 centimeters, and the length of Y D is 4 centimeters.
What is the length of ZA?
ZA = 3cm
ZA = 4cm
ZA = 5cm
ZA = 6cm
The correct answer is option A which is ZA = 3 cm
What is the triangle?Triangle is a shape made of three sides in a two-dimensional plane. the sum of the three angles is 180 degrees.
The triangle is shown below.
From the triangle, A is the concurrency point of angle bisectors of all vertices.
Consider ΔAYD,
Using the Pythagorean theorem,
AD² = AY² + YD²
5² = AY² + 4²
25 = AY² + 16
AY² = 25 - 16
AY² = 9
AY = √9 = 3 cm
Consider triangles ADY and ADZ.
∠AYD ≅∠AZD=90
∠ADY≅∠ADZ ( Angle bisector)
AD ≡ AD (common side)
The two triangles are congruent by the AAS postulate.
Therefore, by CPCTE, AY=ZA=3 cm
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What is EB and DY? DY, EY, and FY are bisectors, and the answers can be "can not be determined"
Based on Pythagoras' theorem, EB is equal to 38.7 and DY is 17.7.
What is the length of the sides EB and DY?The length of the sides EB and DY are obtained using Pythagoras theorem.
Since EY is a perpendicular bisector;
EB = √(64.2² - 51.2²)
EB = 38.7
Since, DY is a perpendicular bisector;
DY = √64.2² - 61.7²)
DY = 17.7
Therefore, EB is equal to 38.7 and DY is 17.7.
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1. Your friend really wants to buy the newest cell phone which will cost him $600. He gets a job detailing cars and SUVs and plans to save all the money he earns. If he gets paid $65 to detail a car
and $90 to detail an SUV, what linear inequality can be used to determine how many of each he must detail in order to earn at least $600?
A. 65c+90s > 600
B. 65c + 90s 2 600
C. 65c+90z ≤ 600
D. 65c+90z< 600
Answer:
I'm not sure if B. is incorrectly written but the answer would be
65c + 90s [tex]\geq[/tex]600
Step-by-step explanation:
since he needs AT LEAST 600$ then the sign should look like that. 65 dollars per car, and c represents the amount of cars, and 90 per SUV and s represents how many SUVS
B. 65c + 90s ≥ 600 is the correct option.
Our friend really wants to buy the newest cell phone which will cost him $600. He gets a job detailing cars and SUVs and plans to save all the money he earns.
What is inequality?Inequality can be defined as the relation of the equation contains the symbol of ( ≤, ≥, <, >) instead of the equal sign in an equation.
Here,
If he gets paid $65 to detail a car and $90 to detail an SUV
The inequality form for above condition so he can earn at least $600
= 65c + 90s ≥ 600, where c = cars and s = SUV
Thus, the required inequality is given by 65c + 90s ≥ 600.
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If the point P(-3/5,y) lies on the unit circle and P is in the 2nd quandrant, what does y equal
The value of y by virtue of the circle description above is; 0.8.
What is the value of y in the task?By definition, a unit circle is a circle whose radius is 1 and has its center at the origin (0,0).
On this note, the value of y can be evaluated as;
1² = (-3/5-0)² + (y-0)²
1 -0.36 = y²
0.64 = y²
±0.8 = y.
However, since point P is in the 2nd quadrant where y is positive, the value of y is 0.8.
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