The linear function that can be used to model this relationship is:
y = -0.27x + 23
A linear function is in the form:
y = mx + b
where y, x are variables, m is the rate of change and b is the initial value of y.
Let P(x) represent the percentage of total spending x years after 1950.
Since In 1950, the group spent 23% of their budget on food, hence b = 23.
Also, this has been decreasing at 0.27% per year. Hence m = -0.27.
The linear function that can be used to model this relationship is:
y = -0.27x + 23
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In 2013, the Public Religion Research Institute conducted a survey of 1,033 adults, 18 years of age or older, in the continental United States. One of the questions on their survey was as follows:
On any given Sunday, are you more likely to only be in church, more likely to only be watching football, doing both, or doing neither?
(a) To only be in church [269 respondents selected this answer]
(b) To only be watching football [175 respondents selected this answer]
(c) Doing both [217 respondents selected this answer]
(d) Doing neither [372 respondents selected this answer]
Create a 95% confidence interval to estimate the actual percentage of adults in the U.S., aged 18 and older, that are "likely" to ONLY be in church on any given Sunday.
Using the z-distribution, it is found that the 95% confidence interval to estimate the actual percentage of adults in the U.S., aged 18 and older, that are "likely" to ONLY be in church on any given Sunday is (23.36%, 28.72%).
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]\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]\frac{1+\alpha}{2}[/tex].
269 out of 1033 respondents said they were likely to only be in church, hence:
[tex]n = 1033, \pi = \frac{269}{1033} = 0.2604[/tex]
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 [tex]z = 1.96[/tex].
The lower limit of this interval is:
[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.2604 - 1.96\sqrt{\frac{0.2604(0.7396)}{1033}} = 0.2336[/tex]
The upper limit of this interval is:
[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.2604 + 1.96\sqrt{\frac{0.2604(0.7396)}{1033}} = 0.2872[/tex]
As a percentage:
0.2336 x 100% = 23.36%
0.2872 x 100% = 28.72%
The 95% confidence interval to estimate the actual percentage of adults in the U.S., aged 18 and older, that are "likely" to ONLY be in church on any given Sunday is (23.36%, 28.72%).
A similar problem is given at https://brainly.com/question/25743435
can some one help me solve this
Answer:
time = 0.4, height = 24.8mStep-by-step explanation:
We need to find the coordinates of the vertex of the parabola.
[tex]f(x)=ax^2+bx+c\\\\v(p,\ q)-\text{vertex}\\\\p=\dfrac{-b}{2a};\ q=f(p)[/tex]
We have
[tex]h(t)=24+4t-5t^2=-5t^2+4t+24\\\\a=-5,\ b=4;\ c=24\\\\p=\dfrac{-4}{2(-5)}=\dfrac{-2}{-5}=\dfrac{2}{5}=0.4\\\\q=h(0.4)=-5(0.4)^2+4(0.4)+24=-5(0.16)+1.6+24\\\\=-0.8+25.6=24.8[/tex]
Look at picture for question.
Answer:
A) - 3/7
B) -1/5
C) - 0.4
Step-by-step explanation:
HOPE IT CAN HELP YOU LOVELOTS
Is the following a reflection,
rotation or translation?
In a recent tennis tournament, women playing singles matches used challenges on 133 calls made by the line judges. Among those challenges, 31 were found to be successful with the call overturned. a. Construct a 90% confidence interval for the percentage of successful challenges. b. Compare the results from part (a) to this 90% confidence interval for the percentage of successful challenges made by the men playing singles matches: 20.9%
Using the z-distribution, it is found that the 90% confidence interval for the percentage of successful challenges is (17.28, 29.34).
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]\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]\frac{1+\alpha}{2}[/tex].
31 out of 133 challenges were successful, hence:
[tex]n = 133, \pi = \frac{31}{133} = 0.2331[/tex]
90% confidence level, hence [tex]\alpha = 0.9[/tex], z is the value of Z that has a p-value of [tex]\frac{1+0.9}{2} = 0.95[/tex], so [tex]z = 1.645[/tex].
The lower limit of this interval is:
[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.2331 - 1.645\sqrt{\frac{0.2331(0.7669)}{133}} = 0.1728[/tex]
The upper limit of this interval is:
[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.2331 + 1.645\sqrt{\frac{0.2331(0.7669)}{133}} = 0.2934[/tex]
As percentages:
0.1728 x 100% = 17.28%
0.2934 x 100% = 29.34%
The 90% confidence interval for the percentage of successful challenges is (17.28, 29.34).
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4) A teacher has an annual income of $51,750. The income tax the teacher has to pay is 7%. What is the amount of income tax in dollar and cents the teacher has to pay?
A) $3,448.25
B) $3,622.50
C) $3,891.10
D) $3,933.01
9514 1404 393
Answer:
B) $3,622.50
Step-by-step explanation:
To find the tax, multiply the income by the tax rate:
$51,750 × 0.07 = $3,622.50
What is 3/4+1 2/3+1/2=
Answer:
Exact Form:
35/12
Decimal Form:
2.916- (6 goes on)
Mixed Number Form:
2 11/12
If a shirt cost $60 is on sale for 50% off and you have another offer that gives you an additional 20% off the sale price does that mean you get a total of 70% off show your work to justify your answer
Answer:
No
Step-by-step explanation:
50 % off $60 =$30
20% off $30 =$6
But 70% =42
Therefore it's not the same as 70%
logx=(logx)^2
find the value of x without using calculator
Answer:
x = 1
Step-by-step explanation:
log(1) = 0
log(1) = [tex]log(1)^{2}[/tex]
0 = [tex]0^{2}[/tex]
0 = 0
Travel agents collected data from recent travelers about their modes of transportation for their vacations, They found that 37% traveled by airplane, 8% traveled by train, and 7% traveled by airplane and train. Let A be the event that the mode of travel was airplane and let T be the event that the mode of travel was train.
Using Venn probabilities, it is found that the probability is [tex]P(A \cap T^{c}) = 0.3[/tex]
In this problem, the events are:
Event A: Traveled by airplane.Event T: Traveled by train.Event [tex]T^{c}[/tex]: Did not travel by train.The desired probability is:
[tex]P(A \cap T^{c}) = P(A) + P(T^{c}) - P(A \cup T^{c})[/tex]
The probabilities are:
37% traveled by airplane, hence [tex]P(A) = 0.37[/tex]8% traveled by train, hence [tex]P(T^c) = 1 - 0.08 = 0.92[/tex]37% traveled by airplane, 62%(100 - [37 + 8 - 7]) did not travel, hence [tex]P(A \cup T^c) = 0.37 + 0.62 = 0.99[/tex]Then:
[tex]P(A \cap T^{c}) = P(A) + P(T^{c}) - P(A \cup T^{c})[/tex]
[tex]P(A \cap T^{c}) = 0.37 + 0.92 - 0.99[/tex]
[tex]P(A \cap T^{c}) = 0.3[/tex]
A similar problem is given at https://brainly.com/question/24707032
Answer:
B: .30
Step-by-step explanation:
edg 2021
Can someone help me on theses?
Help please on part b
Answer:
-0.045
Step-by-step explanation:
you first take the derivate of A(t)
A'(t)=1.4e^-0.05t X (-0.05)
A'(t)=-0.07e^-0.05t
so when t=0
amount remaining is -0.07e^-0.05(0) ---- e^0 = 1
so its -0.07
when t=9
do the same thing,
-0.07e^-0.05(9) ---use calculator
-0.045
Anne bought an aquarium priced at $44.96. Shipping and handling cost an additional 25%of the price. What was the total cost of the aquarium, including shipping and handling?
Dylan had 300 5p coins in a box last month. He now has 360 5p coins. Find the percentage increase.
Therefore the percentage increase is 72
72Hello, can you help me?, thank you
Answer:105216
Step-by-step explanation:17,536*6=105216
Answer:
105,216
Step-by-step explanation:
17,536*6
The speed of an object is the ratio of its distance traveled to time. If the speed of a bicycle is 4.5 meters per second, what is the distance traveled in 9 seconds?
Answer:
40.5 meters
Step-by-step explanation:
4.5m/s • 9s = 40.5m
A hummingbird lives in a nest that is 12 meters high in a tree. The hummingbird flies 15
meters to get from its nest to a flower on the ground. How far is the flower from the base of
the tree?
Answer:
The flower is 9 meters from the base of the tree.
Step-by-step explanation:
Use the Pythagorean theorem to solve. We are given the length of one leg and the length of the hypotenuse of a right triangle.
[tex]a^{2} +b^{2} =c^{2}[/tex]
where a and b are the legs, and c is the hypotenuse.
Plug in the given values and solve:
[tex]x^{2} +12^{2} =15^{2} \\x^{2} +144=255\\x^{2} =81\\x=9[/tex]
The flower is 9 meters from the base of the tree.
$1689 invested for 4 years at 3% compounded annually ?
The amount gotten after $1689 invested for 4 years at 3% compounded annually is $1901
The amount of money gained after an investment is compounded is given by:
[tex]A=P(1+\frac{r}{n} )^{nt}[/tex]
Where P is principal, A is the final amount, r is the rate, n is the number of times compounded per period and t is the time
Given that P = $1689, t = 4, r = 3% = 0.03, n = 1, hence:
[tex]A=P(1+\frac{r}{n} )^{nt}\\\\A=1689(1+\frac{0.03}{1} )^{4*1}\\\\A=\$1901[/tex]
The amount gotten after $1689 invested for 4 years at 3% compounded annually is $1901
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I drove to the beach at a rate of 40 miles per hour. If I had driven at a rate of 30 miles per hour instead, then I would have arrived 25 minutes later. How many miles did I drive?
Step-by-step explanation:
x = number of hours driven
25 minutes = 5/12 hour
remember,
1 hour = 60 Minuten
5 minutes = 60/12 minutes = 1/12 hour
25 minutes = 5×5 minutes = 5/12 hour
x hours × 40 miles/hour = (x + 5/12) hours × 30 miles/hour
the dimensions "hour" eliminate each other from the top and the bottom of the fractions leaving only miles. and the miles must be the same either way.
40x = (x + 5/12)×30 = 30x + 150/12
10x = 150/12
x = 15/12 = 5/4 hours
40 miles/hour × 5/4 hours = 40×5/4 miles = 10×5 = 50 miles.
I drove 50 miles.
I need to know how to subtract fractions 4 2/3 - 3/4
Answer: The answer would be 3.91666666667
[tex]\huge\textsf{Hey there!}[/tex]
[tex]\mathsf{4 \dfrac{2}{3} - \dfrac{3}{4}}[/tex]
[tex]\mathsf{= \dfrac{4\times3+2}{3} - \dfrac{3}{4}}[/tex]
[tex]\mathsf{= \dfrac{12 + 2}{3} - \dfrac{3}{4}}[/tex]
[tex]\mathsf{= \dfrac{14}{3} - \dfrac{3}{4}}[/tex]
[tex]\mathsf{= \dfrac{56}{11} - \dfrac{9}{12}}[/tex]
[tex]\mathsf{= \dfrac{14\times4}{12 - 0}}[/tex]
[tex]\mathsf{= \dfrac{56 - 9}{12}}[/tex]
[tex]\mathsf{= \dfrac{47}{12}}[/tex]
[tex]\mathsf{= 3 \dfrac{11}{12}}[/tex]
[tex]\huge\textsf{Therefore, your answer should be: }\huge\boxed{\\\mathsf{\dfrac{47}{12} \ or\ 3 \dfrac{11}{12}}}\huge\checkmark[/tex]
[tex]\huge\textsf{Good luck on your assignment \& enjoy your day!}[/tex]
The mean number of accidents per month at a certain intersection is 1. a) What is the probability that in any given year at least 3 accidents (including 3 accidents) will occur at this intersection? [10 points] b) What’s the mean and variance for the number of accident for a given year? [10 points]
Answer:
(Hope this helps can I pls have brainlist (crown)☺️)
Step-by-step explanation:
(1) mean value = 6
use excel function POISSON(x,mean,cumulative)
set x = 4, mean =6 and cumulative = TRUE
P(X>4) =1 -POISSON(4,6,TRUE) = 0.7149
(2) mean value = 6
use excel function POISSON(x,mean,cumulative)
set x = 1, mean =6 and cumulative = TRUE
P(X \le 1) =POISSON(1,6,TRUE) = 0.0174
Sara left a bin outside in her garden to collect rainwater. She notices that one over eight gallon of water fills two over three of the bin. Write and solve an equation to find the amount of water that will fill the entire bin. Show your work. Explain your answer in words.
Answer:
3/16
Step-by-step explanation:
In order to get the amount of water to fill a bin, we just divide the amount of water by the fraction of the bin it fills. This makes the unit of the resulting answer as gallons/bin or gallons per bin.
tal) In a survey of 185 college students, they were asked whether they have dogs, cats,
or birds as pets:
90 have dogs,
68 have cats,
8 have birds only,
15 have both cats and dogs only,
20 have both birds and dogs,
12 have both cats and birds, and
7 students have all three animals as pets
a). Draw a Venn diagram to represent the given information.
b). How many students have cats only?
c). What proportion of the students have exactly one type of animal as pets?
9514 1404 393
Answer:
a) see attached
b) 41
c) 56.2%
Step-by-step explanation:
a) We have drawn three circles, labeled D, C, B representing students who have dogs, cats, and birds, respectively. Based on the given information we can fill numbers in for all three animals (7), cats and dogs only (15), and birds only (8).
Then we can fill in cats and birds only by subtracting the number with all three. That will be 12 -7 = 5. Birds and dogs only is similarly filled by subtracting all three to get 20 -7 = 13 birds and dogs only.
Dogs only is found by subtracting the numbers in multiple categories from the total number of dogs: 90 -13 -7 -15 = 55. Cats only is found the same way: 68 -5 -7 -15 = 41.
The completed diagram is shown in the attachment. (We haven't figured the quantity for "none.")
__
b) 41 students have cats only
__
c) The total number with dogs only, cats only, or birds only is ...
55 +41 +8 = 104
Of the 185 total students, that is 104/185 ≈ 56.2%.
56.2% of students have exactly one type of animal as a pet.
$200 is shared between Bill and Ann. Ann’s share is $50 more than Bill’s share. Calculate the size of each of their shares.
First subtract the difference between the two:
200 - 50 = 150
Now divide that by 2:
150/2 = 75
Bills share is $75
Now add the $50 to 75 to get Ann's share:
75 + 50 = $125
Ann's share is $125
Bill's share is $75
What is the slope of the line that passes through the points (6, -10) and (3, -13)?
Write your answer in simplest form.
[tex](x_1, y_1) = (6,-10),~~ (x_2, y_2) = (3,-13)\\\\\\\text{Slope,}~ m = \dfrac{y_2 - y_1}{x_2 - x_1} = \dfrac{-13 +10}{3 -6} =\dfrac{-3}{-3} =1[/tex]
A circular garden has a diameter of 10 feet approximately how much edging trim is needed to surround the garden by placing the trim all along the gardens circumference
Answer: 31.4 feet
Step-by-step explanation:
For this, you basically need to calculate the perimeter of the circle. You do this using this formula:
diameter of the circle times Pie = the circumference of the circle
Since The number of Pie is infinite use the rounded version of pie to 2 decimal points which is 3.14(This is why the question asks for an approximate)
(Diameter = 10 Pie = 3.14 therefore circumference = 31.4)
10 times 3.14 = 31.4 feet
The amount of edging trim needed to surround the garden by placing the trim all along the gardens circumference is 31.4 ft.
The garden is circular in shape. Thereforem the trim that is needed to surround the garden is the circumfernce of the graden.
Circumference of a circleThe circumference of a circle is the perimeter of the circle. Therefore,
circumference = 2πr
where
r = radiusTherefore, the amount of edging trim needed to surround the garden by placing the trim all along the gardens circumference is as follows:
circumference = 2 × 3.14 × 5
circumference = 10 × 3.14
circumference = 31.4 ft
learn more on circumference here: https://brainly.com/question/25730499
Where is the point (0, -2) located on the coordinate plane?
A. On the y-axis
B. On the x-axis
O C. In quadrant III
D. In quadrant IV
Answer:
A
Step-by-step explanation:
The x- coordinate of any point on the y- axis is zero, that is (0, c ) , then
(0, - 2 ) is located on the y- axis
Find the length of a diagonal of a 6 inch square.
Answer:
Step-by-step explanation:
If square is split into two from diagonal then it forms two right angled triangles which are congruent.
Therefore we can use Pythagoras theorem as we know side
d^2=6^2+6^2
d=√72
d=6√2
d=8.485 inches
Method 2:
Using formula
d=s√2
d=6√2
d=8.485 inches
You can find length of diagonal of any square if you know the length of side using formula.
d=s√2
Where s is length of side
Please help! Will give 50 points!!
Answer:
- 5 | - 1 | 3 | 7Step-by-step explanation:
Given function:
y = 2x + 3Complete table by finding y values:
x = - 4 ⇒ y = 2*(-4) + 3 = - 8 + 3 = - 5x = - 2 ⇒ y = 2*(-2) + 3 = - 4 + 3 = - 1x = 0 ⇒ y = 2*0 + 3 = 0 + 3 = 3x = 2 ⇒ y = 2*2 + 3 = 4 + 3 = 7need help asap PLS HURRY