Answer:
The 95% confidence interval for the true percentage of all adults over 30 who shop at that mall who admit to having lost their car at the mall is (25.37%, 43.93%).
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the z-score that has a p-value of [tex]1 - \frac{\alpha}{2}[/tex].
Of 101 randomly selected adults over 30 who frequent a very large mall, 35 admitted to having lost their car at the mall.
This means that [tex]n = 101, \pi = \frac{35}{101} = 0.3465[/tex]
95% confidence level
So [tex]\alpha = 0.05[/tex], z is the value of Z that has a p-value of [tex]1 - \frac{0.05}{2} = 0.975[/tex], so [tex]Z = 1.96[/tex].
The lower limit of this interval is:
[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.3465 - 1.96\sqrt{\frac{0.3465*0.6535}{101}} = 0.2537[/tex]
The upper limit of this interval is:
[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.3465 + 1.96\sqrt{\frac{0.3465*0.6535}{101}} = 0.4393[/tex]
As percentages:
0.2537*100% = 25.37%
0.4393*100% = 43.93%
The 95% confidence interval for the true percentage of all adults over 30 who shop at that mall who admit to having lost their car at the mall is (25.37%, 43.93%).
Let f(x)= x^2+1. Find and simplify the following:
(a) f(x-4)=
(b) f(x-4)-f(-4)
Answer:
f(x-4) = x²-8x + 17
f(x-4)-f(-4) = x²-8x
Step-by-step explanation:
Given the function:
f(x) = x^2+1
f(x-4) = (x-4)^2+1
f(x-4 ) = x² - 8x + 16 + 1
f(x-4) = x²-8x + 17
For f(x-4)-f(-4)
f(-4) = (-4)²+1
f(-4) = 16+1
f(-4) = 17
f(x-4)-f(-4) = x²-8x + 17 - 17
f(x-4)-f(-4) = x²-8x
Find the length of side x in simplest radical form with a rational denominator.
[tex]\huge{ \mathfrak{ \underline{ Answer }\: \: ✓ }}[/tex]
The given triangle is a right angled triangle,
therefore, by using trigonometry :
[tex] \boxed{ \cos(45) = \frac{6}{x} }[/tex]
[tex] \frac{1}{ \sqrt{2} } = \frac{6}{x} [/tex][tex]x = 6 \sqrt{2} [/tex][tex]x = 8.485 \: \: units[/tex]_____________________________
[tex]\mathrm{ ☠ \: TeeNForeveR \:☠ }[/tex]
Game Pitches Seen
1 25
2 20
3 20
4 17
5 15
6 14
The table lists the number of pitches seen by a player in 6 games. What is the mean of the data set?
Answer:
Mean- 18.5
25+20+20+17+15+14=111
111/6=18.5
Susan gets a home loan of $300,000 at a rate of 6.8% compounded monthly for 30 years. What is her monthly payment?
Answer:
$1,955.86
Step-by-step explanation:
We have to use the MS Excel to solve this question
PV = -300000
FV = 0
I = 6.8%/12 = 0.5667%
N = 30*12 = 360
Monthly payment = PMT(-PV, FV, I, N)
Monthly payment = PMT(-300,000, 0, 0.5667%, 360)
Monthly payment = $1955.8555499
Monthly payment = $1,955.86
So, her monthly payment is $1,955.86.
Complete the assignment on a separate sheet of paper
Please attach pictures of your work.
Answer:
TO FIND :-
Length of all missing sides.FORMULAES TO KNOW BEFORE SOLVING :-
[tex]\sin \theta = \frac{Side \: opposite \: to \: \theta}{Hypotenuse}[/tex][tex]\cos \theta = \frac{Side \: adjacent \: to \: \theta}{Hypotenuse}[/tex][tex]\tan \theta = \frac{Side \: opposite \: to \: \theta}{Side \: adjacent \: to \: \theta}[/tex]SOLUTION :-
1) θ = 16°
Length of side opposite to θ = 7
Hypotenuse = x
[tex]=> \sin 16 = \frac{7}{x}[/tex]
[tex]=> \frac{7}{x} = 0.27563......[/tex]
[tex]=> x = \frac{7}{0.27563....} = 25.39568.....[/tex] ≈ 25.3
2) θ = 29°
Length of side opposite to θ = 6
Hypotenuse = x
[tex]=> \sin 29 = \frac{6}{x}[/tex]
[tex]=> \frac{6}{x} = 0.48480......[/tex]
[tex]=> x = \frac{6}{0.48480....} = 12.37599.....[/tex] ≈ 12.3
3) θ = 30°
Length of side opposite to θ = x
Hypotenuse = 11
[tex]=> \sin 30 = \frac{x}{11}[/tex]
[tex]=> \frac{x}{11} = 0.5[/tex]
[tex]=> x = 0.5 \times 11 = 5.5[/tex]
4) θ = 43°
Length of side adjacent to θ = x
Hypotenuse = 12
[tex]=> \cos 43 = \frac{x}{12}[/tex]
[tex]=> \frac{x}{12} = 0.73135......[/tex]
[tex]=> x = 12 \times 0.73135.... = 8.77624....[/tex] ≈ 8.8
5) θ = 55°
Length of side adjacent to θ = x
Hypotenuse = 6
[tex]=> \cos 55 = \frac{x}{6}[/tex]
[tex]=> \frac{x}{6} = 0.57357......[/tex]
[tex]=> x = 6 \times 0.57357.... = 3.44145....[/tex] ≈ 3.4
6) θ = 73°
Length of side adjacent to θ = 8
Hypotenuse = x
[tex]=> \cos 73 = \frac{8}{x}[/tex]
[tex]=> \frac{8}{x} = 0.29237......[/tex]
[tex]=> x = \frac{8}{0.29237.....} = 27.36242.....[/tex] ≈ 27.3
7) θ = 69°
Length of side opposite to θ = 12
Length of side adjacent to θ = x
[tex]=> \tan 69 = \frac{12}{x}[/tex]
[tex]=> \frac{12}{x} = 2.60508......[/tex]
[tex]=> x = \frac{12}{2.60508....} = 4.60636....[/tex] ≈ 4.6
8) θ = 20°
Length of side opposite to θ = 11
Length of side adjacent to θ = x
[tex]=> \tan 20 = \frac{11}{x}[/tex]
[tex]=> \frac{11}{x} = 0.36397......[/tex]
[tex]=> x = \frac{11}{0.36397....} =30.22225....[/tex] ≈ 30.2
Which expression matches the graph
Answer:
a
Step-by-step explanation:
Anybody know how to do this
It’s a yes or no ?
Answer:
what's the full question
beti ate 1/8 of the cake.nati had 2 smaller pieces.she ate 2/16 of the cake.who ate more cake? what fraction of the cake left?
Answer:
Both ate the same amount of cake, there will be 6/8 or 3/4ths of the cake left.
Step-by-step explanation:
2/16 is equivalent to 1/8. Therefore they ate the same amount of cake.
Answer:
they ate the same amount 1/8 and 2/16 are the same thing.3/4
Step-by-step explanation:
they both ate 1/8 so 8/8-2/8=6/8=3/4 of the cake left
if 124 is subtracted from the square of a number the result is 200 what is the number
Answer:
x=18
Step-by-step explanation:
let the number =x
then
x²-124=200
x²=200+124
x²=324
x=18
Answer:
x=18
Step-by-step explanation:
number = x
x^2 - 124 = 200
x^2 = 200 +124
x^2 = 324
(square root both sides)
x = 18
Nandini uses a code to open a security door.
The code is a letter followed by a 2-digit number.
The letter is Por Q.
The number is a prime number between 30 and 40
Write down all the possibilities for Nandini's code.
Can someone plz help me
Answer:
35 is a prime number between 30 and 40
Giving Brainliest!
Explain the difference between low and high-frequency waves
Answer:
Frequency refers to the number of waves that pass a given point in a given time period and is often expressed in terms of hertz (Hz), or cycles per second. Longer wavelengths will have lower frequencies, and shorter wavelengths will have higher frequencies
calculate: 3^10 * 30^18 / 9^13 * 8^6 * 0.04^-9
Answer:
9e+36
Step-by-step explanation:
ㄒɦĄŊĸ ĦØφĒ ĮŤ ɧėŁP ♡✧♡
What is the slope of the line?
Answer:
The slope of a line characterizes the direction of a line.
Step-by-step explanation:
To find the slope, you divide the difference of the y-coordinates of 2 points on a line by the difference of the x-coordinates of those same 2 points.
Answer:
-2
Step-by-step explanation:
Solve for x: 2(x + 4) + 6 = 12x - 8
Answer:
x = 2.2
Step-by-step explanation:
2(x+4)+6 = 12x-8
Use distribution property
2x+8+6 = 12x-8
Combine like terms
2x+14 = 12x-8
Subtract 14 from both sides
2x = 12x-22
Subtract 12x from both sides
-10x = -22
Divide both sides by negative 10
x = 2.2 or x = 11/5 in fractions.
Hope this helps
Identify the graph of exponential graph
answer this please and thanksss
Answer:
x^2+4x-21
Step-by-step explanation:
hope it helps
Answer:
Option D, x² + 4x - 21
Step-by-step explanation:
Using FOIL;
x * x = x²
x * (-3) = -3x
7 * x = 7x
7 * (-3) = -21
Therefore; x² + (-3x) + 7x - 21
=> If simplified:
=> x² + 4x - 21
Hope this helps!
A farmer has 100 acres of available land that he wishes to plant with a mixture of potatoes, corn, and cabbage. It costs him $400 to produce an acre of potatoes, $160 to produce an acre of corn, and $280 to produce an acre of cabbage. He has a maximum of $20,000 to spend. He makes a profit of $120 per acre of potatoes, $40 per acre of corn, and $60 per acre of cabbage. How many acres of each crop should he plant to maximize his profit?
a. Create a chart to organize this information.
b. Write the objective function
c. Write all the constraints to the problem.
Objective (Profit) Function : 120 Po + 40 Co + 60 Ca
Constraint Functions : Po + Co + Ca = 100 (Land Constraint) ; Budget Constraint : 400 Po + 160 Co + 280 Ca = 20000
LET : Acres of land for Potato, Corn, Cabbage = Po, Co, Ca respectively.
Objective Function is the function to be minimised or maximised. Here, 'PROFIT' is to be maximised.
So, profit function is the objective function. Profit per acre potatoes, corn, cabbage = 120, 40 , 60 respectively.Constraint functions denote the other conditions to be maintained, while maximising & minimising objective profit function.
Here, Land constraint & budget constraints need to be satisfied. Total acres of land for potato, corn, cabbage = 100. Cost per acre potatoes, corn, cabbage = 400, 160, 280 respectively & total budget is 20000.To learn more, refer https://brainly.com/question/2500020?referrer=searchResults
What is 840 increased by 20%
Answer:
1,008
Step-by-step explanation:
have a nice day
Answer:
1008
Step-by-step explanation:
1. [tex]840.\frac{20}{100}[/tex]
2. 168
3. 840 + 168 -> 1008
Evan has 8 dollars. The price of farro is 3 dollars per pound.
Move values to the boxes to create an equation that can be used to solve for f, the number of pounds of farro Evan can buy.
3
5
8
11
24
Answer:
24
Step-by-step explanation:
8x3=24
hey guys what is the factors of 8 (i need all of them)
Answer:
1,2,4,8
Step-by-step explanation:
Cara's muffin recipe calls for 1 1/4 cups of flour for the muffins and 3/4 cups of flour for the topping. If she makes 1/2 of the original recipe, how much flour will she use?
Answer:
3/2 X 1/4 +1/2
Step-by-step explanation:
Try using that to work out the answer.
!!!!!MAJOR HELP!!!!!
!!!!!I will give Brainy!!!!!
The function Y equals 5X is graft in coordinate plane. Which point will not be on the line?
A.(0,5)
B.(3,15)
C.(4,4,22)
D,(5,25)
If no idea then look at image
Answer: its b or c try one then the other
Step-by-step explanation:
PLEASE HELP(Mainly 15 & 16) I can give BRAINLIEST!!!
Answer: sorry I don't get it but the answer for 16 is B sorry
Step-by-step explanation:
What do they teach you they are weird t doesn't make any sense
Help pleaseeeeeeeeeeee
What is the area of the shaded region? Use 3.14 for it and round your answer to the nearest tenth opinions:12.6 cm2 6 cm 50.2 cm 78.5 cm 10 cm 201.0 cm
Someone please answer I need help on this one to
PLS HELP ASAP I WIL MARK BRAINLIEST
Answer:
[tex]x=80^{\circ},\\y=80^{\circ}[/tex]
Step-by-step explanation:
The measure of an angle formed by a secant and a tangent outside of a circle is half of the absolute difference between the two arcs it forms. Therefore, we have the following equation:
[tex]m\angle A=\frac{\widehat{BC}-\widehat{BD}}{2}[/tex]
Substituting given values, we get:
[tex]20=\frac{120-x}{2},\\40=120-x,\\x=\boxed{80^{\circ}}[/tex]
Since there are 360 degrees in a circle, we can write the following equation, using [tex]x[/tex], to solve for [tex]\widehat{DC}[/tex]:
[tex]x+\widehat{DC}+120=360,\\80+\widehat{DC}+120=360,\\\widehat{DC}=\boxed{160^{\circ}}[/tex]
The value of the angle formed by a chord and a tangent is half the measure of the arc it forms. Therefore,
[tex]y=\frac{\widehat{DC}}{2}=\frac{160}{2}=\boxed{80^{\circ}}[/tex]
Please helo me with the following question.
What is the sum of 150,000 times 130,000?
150,000
x 130,000
__________
?????????????
Answer:
19500000000
Step-by-step explanation:
A piece of machinery depreciates $7000 the first year, $6800 the second year, and $6600 the third year. If the rate of depreciation is constant, what is the amount of depreciation of the piece of machinery in the sixth year?
Answer:
$6000
Step-by-step explanation:
hope it helps correct me if i am wrong
3 √ 7 + √ 7 can someone elaborate this for me
Answer:
9.3
Step-by-step explanation:
Answer:
The answer is 4 \sqrt{7}.
Step-by-step explanation:
The formula is a\sqrt{x} + b\sqrt{x} = (a+b)\sqrt{x}, but if you don't understand it, here's an easier way to think about it.
You can think of \sqrt{7} as x (or any other variable). Now, the equation is 3x + x. If you've ever done algebra, (you probably have if square roots popped up on your homework) you know that this equals to 4x. Now, replace the x with \sqrt{7}, because we already decided that those two were equal. Therefore, the answer is
4 \sqrt{7}.
Solve the following: You purchase a set of Bluetooth earbuds for $45 and use a $5 off manufacturer's coupon. If sales tax is 8.25%, how much do you pay for the earbuds? Include the dollar sign in your answer and round to two decimal places.
Answer:
43.3
Step-by-step explanation:
45-5=40,
0.0825*40=3.3
40+3.3=43.3