The probability that the proportion of Rolls Royce owners in a sample of 694 Americans would differ from the population proportion by less than 3% is; 0.36%
How to use the central limit theorem?
The Central Limit Theorem states that, for a normally distributed random variable X, with mean μ and standard deviation σ, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean μ and standard deviation s = σ/√n
The standard deviation for proportion is given by the formula;
s = √(p(1 - p)/n)
We are given;
p = 8% = 0.08
n = 694
Thus;
s = √(0.08(1 - 0.08)/694)
s = 0.0103
Proportion above 8% + 3% = 11% or below 8% - 3% = 5%. Due to the fact that the normal distribution is symmetric, the probabilities will be equal, and as a result, we find one of them and multiply by 2.
Probability the proportion is less than 5%:
P-value of Z when X = 0.05.
z = (X - μ)/s
z = (0.05 - 0.08)/0.0103
z = -2.91
From p-value from z-score calculator, we have;
p-value = 0.001807
We multiply it by 2 to get the probability
Probability = 2 * 0.001807 = 0.0036 = 0.36%
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Jake and Llana make and sell wooden birdhouses. Jake spent $150 buying supplies. He sells each birdhouse for $15. The equation P = 12x - 120
represents the profit, P, Liana earns for selling x birdhouses. Jake and Llana each made 50 birdhouses.
Which statements are true? Choose all that apply.
A. Jake spent $30 more on supplies than Liana.
B. Jake's birdhouses cost $3 more than Liana's.
C. Llana will have a greater profit than Jake if they each sell all 50 birdhouses.
D.
Llana and Jake will have the same profit if they each sell exactly 20 birdhouses.
E. Llana and Jake each need to sell a minimum of 11 birdhouses in order to make a profit.
(A) and (E) are the true statement.
Given,
In the question:
Jake and Liana make and sell wooden birdhouses. Jake spent $150 buying supplies. He sells each birdhouse for $15. The equation P = 12x - 120 represents the profit, P, Liana earns for selling x birdhouses. Jake and Llana each made 50 birdhouses.
To find the which statement is true?
Now, According to the question:
Jake's Profit: J = 15x - 150
Liana's Profit : P = 12x - 120
(A) when x = 0, P = -120, J = -150
then, 150 - 120 = $30
So, Jake spent $30 more than Liana
So, A is true, B is wrong.
(C) when x = 50 , J = 15 x 50 - 150 = $600
P = 12 x 50 - 120 =$480
Since, 600> 480
(D) when J = P
then, 15x - 150 = 12x = 120
3x = 30
x = 10
x = 10 not equal to 20
So, D is wrong
(E) when P> -0 , and J > 0
then, 12x -120 > 0 and 15x - 150 > 0
=> x > 10
So, the minimum is 11, E is true .
Hence, Above the solution (A) and (E) are the true statement.
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1. Two spherical solids have masses of 15g and 405kg respectively. If the radius of the smaller sphere is 10cm. Find the radius of the bigger sphere.
2. Triangle PQR is such that the angle P=90° and PQ=37cm. Find RP when angle Q=16° degrees (Use tan 46°=1.04).
The radius of the bigger sphere is 30cm.
Two spherical solids have masses of 15g and 405kg respectively
Mass is directly proportional to volume for same metal (Density)
Let Mass of Solid 1 be M₁ and Volume be V₁
Mass of Solid 2 be M₂ and Volume be V₂
Now M₁/M₂ = V₁/V₂
Volume of sphere is directly proportional to R³
So, M₁/M₂ = V₁/V₂ = R₁³/R₂³
15/405000 = 10³/x³
∛15/∛405000 = 10/x
2.466/73.986 = 10/x
2.466x = 73.986 x 10
x = 739.86/2.466
x = 30
Therefore, the radius of the bigger sphere is 30cm.
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f: x → 15/x - 5 What number must be excluded from the domain of f?
Answer:
x = 5
Step-by-step explanation:
You want to know what number must be excluded from the domain of f(x) = 15/(x -5).
DomainThe domain of a function is the set of numbers for which it is defined. The function f(x) = 15/(x-5) will be undefined when the denominator is zero:
x -5 = 0
That will be the case when x = 5.
The domain of f must exclude x=5.
Solve the inequality for p
4 - 1/6 (p - 3) > 7
Answer:
p < -15
Step-by-step explanation:
[tex]4 - \frac{1}{6} (p - 3) > 7[/tex]
[tex] - \frac{1}{6} (p - 3) > 3[/tex]
[tex]p - 3 < - 18[/tex]
[tex]p < - 15[/tex]
equation for the perpendicular bisector of the line segment whose endpoints
are (-9, 3) and (-3, -1).
Equation for the perpendicular bisector of the line segment is
2y = 3x +20.
A line segment that bisects another line segment at a 90° angle is known as a perpendicular bisector.
What is perpendicular bisector?A line segment that bisects another line segment at a 90° angle is known as a perpendicular bisector. In other terms, a perpendicular bisector separates a line segment into two equal halves by intersecting it at a 90° angle.
Given coordinates of the endpoints of a line segment (-9, 3) and (-3,-1).
In order to find the equation of perpendicular line, we need to find the slope between given coordinates.
Slope between (-9, 3) and (-3, -1). :
slope = [tex]\frac{-1-3}{-3+9} =\frac{-2}{3}[/tex]
Slope of the perpendicular line is reciprocal and opposite in sign.
Therefore, slope of the perpendicular line = 3/2
Now, we need to find the midpoint of the given coordinates.
[tex]Mid points : \\x= \frac{ -9-3}{2} =-6\\ y= \frac{3-1}{2} = 1\\ pint = (-6,1)[/tex]
Let us apply point-slope form of the linear equation:
y-y1 = m(x-x1)
y - 1 = 3/2 (x + 6)
2y = 3x +20
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mathematical shapes
Answer:
A square is an sqaure.
Step-by-step explanation:
circle is a circle. :) happy to help
find the Cartesian coordinate of the point where polar coordinates are [5√2, π/4 ]
The Cartesian coordinate of the point where polar coordinates are [5√2, π/4 ] is ( 5/√2, -5/√2)
The polar cordinates given are (r,θ)=(5,− π/4)
And we need to find the cartesian coordinates
We have,
x=rcosθ, y=rsinθ
x=5cos(− π/4) ,y=5sin(− π/4)
x= 5/√2 ,y=− 5/√2
So, the cartesian form is ( 5/√2, -5/√2)
The Cartesian coordinate of the point where polar coordinates are [5√2, π/4 ] is ( 5/√2, -5/√2)
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How to solve step by step
How many bit strings are there of length eight?
There are 28 which is 256. That means there are 256 different values you can store in a byte, since a byte is eight bits. There are 256 eight-bit ASCII codes, for instance.
1 byte = 8 bits
Number of bits = [tex]2^{8}[/tex]
= 2*2*2*2*2*2*2*2
= 4*2*2*2*2*2*2
= 8*2*2*2*2*2
= 16*2*2*2*2
= 32*2*2*2
= 64*2*2
= 128*2
= 256 bits.
Therefore that means there are 256 different values you can store in a byte, since a byte is eight bits.
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Martha's employee benefits include family health-care coverage. She contributes 18% of the
cost. Martha gets paid biweekly and $108.00 is taken out of each paycheck for family health-care
coverage. How much does her employer contribute annually for the family coverage?
use dollar sign, decimal and comma
The family coverage paid by Martha's employer for health care coverage is $2592.
What is a health care coverage?
Health insurance is a sort of insurance that pays for unexpected medical costs brought on by a disease. These expenditures may be associated with the price of hospitalisation, or the cost of medical visits.
Main body:
Let the total biweekly salary of Martha be x.
Therefore according to question :
18% of x =$108
(18/100)*x =108
x= 600
Martha earns $600 biweekly.
monthly earning of Martha be 600*2 =$1200
Therefore total coverage annually = 108*total salary day
=108*24
=$2592
Hence the answer is $2592.
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9. Every 4th person who walks into the dance gets a free water bottle. Every 9th person who walks in
gets an integrity ticket. Who will be the first person to get both a water bottle and an integrity ticket at
the dance?
The first person to get both integrity ticket and free water bottle is the person who comes 36th. This can be calculated by using L.C.M
What is L.C.M?
The value that's equally divided by 2 provided numbers is that the lowest common multiple of any two. Least common multiple is its full name. Another name for it's the Lowest common divisor (LCD)
Main Body:
According to question,
Every 4th person who walks into the dance gets a free water bottle
Every 9th person who walks in gets an integrity ticket.
so the L.C.M of 4 and 9 should be calculated.
L.C.M of 4 and 9 is 36.
Hence L.C.M is 36
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1.25x10^-3/1.25x10^3
By solving the given fraction equation we get the answer is 1.
What is an exponent?
Exponent is the process of expressing large numbers in terms of powers. In other words, the exponent describes how many times a number has been multiplied by itself.
According to the zero exponent rule, any base with a zero exponent is equal to one. For instance, [tex]x^{0} = 1[/tex].
We have,
[tex]= \frac{1.25\\ * \\ 10^{-3}}{1.25 \\ * \\ 10^{-3}}[/tex]
[tex]= \frac{1.25\\ * \\ 10^{-3}}{1.25 \\} * 10^{3}[/tex]
Using the multiplication rule of fraction [tex]a\cdot \frac{b}{c}=\frac{a\:\cdot \:b}{c}[/tex]
[tex]= \frac{1.25 \ * \ 10^{-3} \ * \ 10^{3}}{1.25 \\}[/tex]
= [tex]= 10^{-3} * 10^{3}[/tex]
By applying the exponent rule [tex]\:a^b\cdot \:a^c=a^{b+c}[/tex] we get,
Add or subtract the numbers = 3 + 3 = 0
[tex]= 10^{0}[/tex]
By applying the rule [tex]a^{0} = 1[/tex], [tex]a \neq e^{0}[/tex]
= 1
Hence, by solving the above fraction equation we get the answer is 1.
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The Monty Corporation has a staff of sales people who are paid a monthly salary of $1,600.00 plus an incremental commission based on the table below. If Sally sells $29,700.00, what is her total gross pay for the month
Answer:
Step-by-step explanation:
-28,100 if you subtract 29,700.00 - 1,600.00 = -28,100
not really sure what to do here??
Answer:
[tex]d=-6[/tex]
[tex]a_9=-49[/tex]
Step-by-step explanation:
If the first term of a sequence is [tex]-1[/tex] and the second term is [tex]-7[/tex], then each successive term in the sequence is [tex]6[/tex] less than the previous term. The common difference is [tex]-6[/tex] ( [tex]d=-6[/tex] ).
The formula representing the arithmetic sequence is:
[tex]a_n=-6n+5[/tex]
Therefore, the ninth term in the sequence is:
[tex]a_9=-6(9)+5[/tex]
[tex]a_9=-54+5[/tex]
[tex]a_9=-49[/tex]
Anthony claims that A KLM is an isosceles triangle. Find the length of KM using the distance formula.
Answer:√53 or 7.28010988928
Step-by-step explanation:
An architect designs a rectangular flower garden such that the width is exactly two-thirds of the length. if 420 feet of antique picket fencing are to be used to enclose the garden, find the dimensions of the garden. what is the length of the garden?
The structure's length is 93 feet long and its width is 62 feet.
What is rectangle?We also refer to a rectangle as an equiangular quadrilateral since all of its angles are equal. A closed 4-sided shape is called a quadrilateral.A rectangle can also be referred to as a right-angled parallelogram because its sides are parallel. A quadrilateral with equal and parallel opposite sides is referred to as a parallelogram. Paralleograms are a specific instance of rectangles.acc to our question -
Let W stand for the rectangle's flower garden's width and L for its length.
A rectangle flower garden with a width that is precisely two thirds of its length is created by an architect.
The following can be written:
W=2/3L
Given that the fence is 310 feet long, the rectangle's perimeter must also be 310 feet.
Perimeter = 2 (L + W)
The perimeter surrounding it)
2w + 2h = 310
2((2/3) * h) + 2h = 310
4h/3 + 2h = 310
10h/3 = 310
10h = 930
h = 93 feet
w = (2/3) * 93
w = 62 feet
Hence, The structure's length is 93 feet long and its width is 62 feet.
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Keiko tracks the change in outside
one afternoon. She records
temperature
a temperature of 85.4°F at noon. The
temperature rises 3.85°F over the
next 4 hours. At 5:00 PM, Keiko records
a temperature of 89.25°F. How does the
temperature change between
4:00 PM
and 5:00 PM?
Answer:
no change
Step-by-step explanation:
Given a temperature rise of 3.85 °F over 4 hours after noon, when the temperature is 85.4 °F, you want to know the change between 4 pm and 5 pm if the temperature at 5 pm is 89.25 °F.
Temperature at 4The temperature at 4 pm is the sum of the noon temperature and the change in the 4 hours after noon:
85.4 °F + 3.85 °F = 89.25 °F
Change after 4The change from 4 pm to 5 pm is the difference between the 5 pm temperature and the 4 pm temperature:
82.25 °F -89.25 °F = 0 °F
There is no change in the temperature between 4 pm and 5 pm.
Jamar has invested $300 in an annuity each month, earning 5.5% interest for 30 years.
Beth has invested $600 in an annuity each month, earning 5.5% interest for 15 years.
Which of the following must be true?
Select the correct answer below:
Answer:
(d) Jamar's ending account balance is higher than Beth's ending balance.
Step-by-step explanation:
You want to know the best description of the relationship between final balances of two ordinary annuities:
300 per month for 30 years at 5.5%600 per month for 15 years at 5.5%Future valueThe attached calculator display shows the ending balance for Jamar's annuity and for Beth's annuity. We assume the final balance is the balance after the final payment. That is, Beth's balance will be known 15 years before Jamar's balance is known.
Jamar's balance: $274,083.57
Beth's balance: $167,247.33
The best description is ...
Jamar's ending account balance is higher than Beth's ending balance.
__
Additional comment
Jamar makes twice as many payments of half the amount each, so his total contribution is the same as Beth's. His early payments are earning interest for twice as long as Beth's, so his account earns more interest.
Find the mean, μ, for the binomial distribution which has
the stated values of n and p. Round answer to the nearest
tenth.
n = 38; p = 0.2
Select one:
Ο Α. μ = 8.3
OB. μ = 7.9
Cu = 7.1
OD. μ = 7.6
The mean value is 7.6. Option (D) is the correct answer.
The number of successes in a sample of size n drawn with replacement from a population of size N is frequently modeled using the binomial distribution.
The mean value of a binomial distribution is,
[tex]\mu =np\\=38*0.2\\=7.6[/tex]
Multiplication:
In mathematics, multiplying two or more numbers yields the product of the numbers. It is one of the basic mathematical operations that we carry out on a regular basis. The most obvious application is using multiplication tables. The multiplication of two numbers in mathematics represents the repeated addition of one number in respect to another. These numbers can be natural numbers, whole numbers, fractions, integers, or other types of numbers. When m is multiplied by n, m is either multiplied by n times or added to itself n times.
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5x-3/x-1 what is the inverse of this
Answer:
[tex]f^{-1}(x)=\dfrac{3-x}{5-x}, \quad \{x|x\neq 5\}[/tex]
Step-by-step explanation:
Given function:
[tex]f(x)=\dfrac{5x-3}{x-1}[/tex]
As the given function is a rational function, the domain and range are restricted.
Domain: (-∞, 1) ∪ (1, ∞).Range: (-∞, 5) ∪ (5, ∞).f⁻¹(x) is the notation for the inverse of the function.
The inverse of a function is a reflection in the line y = x.
To find the inverse of the given function, swap f(x) for y:
[tex]\implies y=\dfrac{5x-3}{x-1}[/tex]
Rearrange the equation to isolate x:
[tex]\implies y(x-1)=5x-3[/tex]
[tex]\implies xy-y=5x-3[/tex]
[tex]\implies 3-y=5x-xy[/tex]
[tex]\implies 3-y=x(5-y)[/tex]
[tex]\implies x=\dfrac{3-y}{5-y}[/tex]
Swap the x for f⁻¹(x) and the y for x:
[tex]\implies f^{-1}(x)=\dfrac{3-x}{5-x}[/tex]
The range of the function is the domain of the inverse function.
Therefore, the domain of the inverse function is restricted:
Domain of f⁻¹(x): (-∞, 5) ∪ (5, ∞).Find the values of x and y.
Answer:
x = 20 degrees ; y = 70 degrees
Step-by-step explanation:
angle supplementary to 40 = 180 - 40 = 140 degrees
in isosceles triangle has the angles of the base with the same measure
140 + (2x) = 180
2x = 180 - 140
2x = 40
2/2 x = 40/2
x = 20 degrees
90 - 20 = 70 degrees
70 + y + 40 = 180
110 + y = 180
y = 180 - 110
y = 70 degrees
Answer:
Step-by-step explanation:
PART B
How can the stage manager use the constant of proportionality to find the
dimensions of any new props the director requires?
a) the constant of proportionality multiplies every actual linear dimension
b) height of a can of fruit juice is 3.85 inches high
What is Proportionality?
The term proportionality describes any relationship that is always in the same ratio.
Explanation for answer:
Since the desire is to have students look twice as tall, we expect the constant of proportionality to be [tex]\frac{1}{2}[/tex].
Instead, we're told that the stage manager is using a height of 44 inches to represent an 80-inch door.
This means their constant of proportionality is [tex]\frac{40}{80} = 0.55[/tex]
a) Any new props can be scaled by this factor (0.55) to find their height on set.
b) A 7-inch can would be scaled to [tex]7\times 0.55 = 3.85\ inches[/tex]
Question: The school's theater club is building sets that will make ordinary students look like giants. The actors need a door, a table, and a stool that will make them look almost twice as tall!
DOOR: actual height is 80 inches and Height on Set is 44 inches
TABLE: actual height is 28 inches
STOOL: actual height is 18 inches
How can the stage manager use the constant of proportionality to find the dimensions of any new props the director requires?
What should the height of a can of fruit juice used as a prop be if its actual height is 7 inches? Show your work.
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How do I factor 250n2 + 20n8?
Step-by-step explanation:
[tex]250n^2+20n^8[/tex]
common factor is [tex]10n^2[/tex]:
[tex]10n^2(25 +2n^6)[/tex]
rearrange:
[tex]10n^2(2n^6+25)[/tex]
At the beginning of a journey, the fuel tank of a car was 34 full. When the car reached its destination, it had consumed 60% of the gasoline in the tank. The full capacity of the fuel tank was w gallons.
a Enter an algebraic expression for the amount of gasoline left in the fuel tank.
gal
b If w = 15.5, how much gasoline was left in the tank at the end of the journey?
gal
a) An algebraic expression for the gasoline left in the fuel tank is L = 0.4w.
b) If w = 15.5, the amount of gasoline left in the tank at the end of the journey was 6.2 gallons.
What is an algebraic expression?An algebraic expression is a mathematical statement that combines constants and variables together with mathematical operands.
The mathematical operands include addition, subtraction, division, multiplication, etc.
Let L = the amount of gasoline left
Let the full capacity of the fuel tank = w gallons
Gasoline consumed on the journey = 60% = 0.6
Equation:L = w - 0.6w
L = 0.4w
Solution:If w = 15.5
L = 0.4(15.5)
= 6.2 gallons
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The drama club sold $1,416 worth of tickets for its fall play. If each ticket cost $8, how many tickets did the club sell?
What is the equivalent equation to the given equation?
x = x² - 20
The equivalent equation to the given equation i.e, x = x² - 20 is x² - x - 20 = 0
What is a Quadratic equation ?
A second-degree equation of the form ax² + bx + c = 0 is known as a quadratic equation in mathematics. Here, x is the variable, c is the constant term, and a and b are the coefficients. Since x is a second-degree variable, this quadratic equation has two roots, or solutions.
The given expression is,
x = x² - 20
We have to make the equation in quadratic form i.e, ax² + bx + c = 0
so, first take x to the right side
0 = x² - 20 - x
Now swap the equation,
x² - 20 - x = 0
put 'x' term in middle and constant term at last like this,
x² - x - 20 = 0
Hence, The equivalent equation to the given equation i.e, x = x² - 20 is x² - x - 20 = 0
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What is the volume of a cylinder, in cubie centimeters, with a height of 2 centimeters
and a base diameter of 20 centimeters? Round to the nearest tenths place?
The volume of the cylinder in cubie centimeter is 628 [tex]cm^{3}[/tex]
How to find the volume of cylinder?
1. Find the radius of the circular base: Since both circles are the same size, either one will work. Move on if you are aware of the radius. If you don't know the radius, you can divide the diameter of the circle by 2.
2. Find the height of the cylinder : Continue if you already know the height. Otherwise, measure it with a ruler. The height is determined by the separation of the two bases' edges.
diameter (d) = 20
radius = [tex]\frac{20}{2}[/tex]
r = 10
height (h) = 2cm
volume v = [tex]\pi r^{2} h[/tex]
v = 3.14(10*10)2
= 628 [tex]cm^{3}[/tex]
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a- 10 units
b-12.0 units
c-11.4 units
d-13.4 units
Using the distance formula, the distance between the point is √130.
In the given question we have to find the distance between given point in the graph.
From the graph the given points are (4,4) and (-3, -5).
The formula for the distance between point is
Distance = √{x(2)-x(1)}^2+{y(2)-y(1)}^2
From the given points; x(1)=4, y(1)=4, x(2)= -3 and y(2)= -5.
Now putting the value:
Distance = √{-3-4}^2+{-5-4}^2
Distance = √{-7}^2+{-9}^2
Distance = √49+81
Distance = √130
The distance between the point is √130.
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Myles has 12 markers and 20
pencils. What is the greatest
number of groups that can be
made with equal number of
markers and pencils?
In linear equation, No of marker is 5 and no of pencil is 3 .
What is a linear equation example?
Ax+By=C is the typical form for linear equations involving two variables. A linear equation in standard form is, for instance, 2x+3y=5. When an equation is given in this format, finding both intercepts is rather simple (x and y). For the purpose of resolving systems involving two linear equations, this form is also highly helpful.Myles has 12 markers and 20 pencils.
take LCM of 12 and 20 = 60
no of 12 markers = 5
no of 20 pencils = 3
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hourly wage is $10.50. If she
regularly works 40 hours per week, what is
her regular weekly pay?
Answer:
$420
Step-by-step explanation:
multiple 10.50 by 40 to get 420
