Answer:
The p-value of the test is 0 < 0.05(standard significance level), which means that this is enough evidence to state that more than 24.5% of all adults in the U.S. are obese
Step-by-step explanation:
Researchers believe that 24.5% of the adults in the United States are obese. Test if there is enough evidence to state that more than 24.5% of all adults in the U.S. are obese.
At the null hypothesis, we test if the proportion is of 24.5% or less, that is:
[tex]H_0: p \leq 0.245[/tex]
At the alternative hypothesis, we test if this proportion is greater than 24.5%, that is:
[tex]H_1: p > 0.245[/tex]
The test statistic is:
[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, [tex]\sigma[/tex] is the standard deviation and n is the size of the sample.
0.245 is tested at the null hypothesis:
This means that [tex]\mu = 0.245, \sigma = \sqrt{0.245*0.755}[/tex]
Survey 86,664 randomly sampled U.S. adults. Of the adults surveyed, 23,053 said that they were obese.
This means that [tex]n = 86664, X = \frac{23053}{86664} = 0.266[/tex]
Value of the test statistic:
[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
[tex]z = \frac{0.266 - 0.245}{\frac{\sqrt{0.245*0.755}}{\sqrt{86664}}}[/tex]
[tex]z = 14.37[/tex]
P-value of the test and decision:
The p-value of the test is the probability of finding a sample proportion of 0.266 or higher, which is 1 subtracted by the p-value of z = 14.37.
The p-value of z = 14.37 is 1.
1 - 1 = 0
The p-value of the test is 0 < 0.05(standard significance level), which means that this is enough evidence to state that more than 24.5% of all adults in the U.S. are obese
1. Rita is hiking along a trail that is 113.7 miles long. On the first day she hiked of 1 10 the distance of the trail. On the second day she hiked the same distance as the first day. How much of the trail does she have left to hike?
Answer:
She has 90.96 miles of the trail to hike.
Step-by-step explanation:
Length of the trail:
The length of the trail is of 113.7 miles.
On the first day she hiked of 1/10 the distance of the trail.
Thus:
[tex]\frac{1}{10(113.7) = 11.37[/tex]
On the first day she hiked 11.37 miles.
On the second day she hiked the same distance as the first day.
Also 11.37 miles on the second day, and thus, 2*11.37 = 22.74 miles on the first two days.
How much of the trail does she have left to hike?
113.7 - 22.74 = 90.96
She has 90.96 miles of the trail to hike.
If line r is parallel to —- ?
Answer:
the correct answer is 10
What’s the answer to this question?
Answer:
f(x) = x/8
Step-by-step explanation:
f(x) = y
y = 8x
switch the x and y
x = 8y
solve for y
Pleaseeee help is for today
Answer: a + ( 2a - 7 ) = 41
Explanation:
Let be "a" the Nicci's age and "s" the Nicci's sister.
You know that the sum of Nicci's age and her sister's age is 41. This can be represented with the following equation:
a + 8 = 41
And knowing that Nicci's sister is 7 years less than twice Nicci's age, you can write another equation to represent this:
8 = 2a - 7
Now, substitute the second equation into the first equation in order to find the equation that represents this relationship.
Then, this is:
a + ( 2a - 7 ) = 41
Hope it helps...
Larissa drives into a pool that is 8 feet deep she touches the bottom of the pool with her hands 6 feet horizontally from the point at which entered the water. What is the approximate angle of elevation from the point on the bottom of the pool where she touched her entry point
Answer:
53 degrees
Step-by-step explanation:
tan(theta)=8/6,
theta= [tex]tan^{-1} (\frac{8}{6} )=53.13 degree[/tex]
Which point represents the value of -(-2) on the number line?
Answer:
2
Step-by-step explanation:
-(-2)
negative x negative always give positive .
=>2
You can easily represent 2 on number line
Researchers conducted a study to determine whether magnets are effective in treating back pain. Pain was measured using the visual analog scale, and the results given below are among the results obtained in the study. Higher scores correspond to greater pain levels. Is this study an experiment or an observational study?
The study conducted in the scenario above is an experimental study because the subjects were given treatment.
Observational study involves monitoring the relationship between variables through observation without giving any treatment during the course of the study.
Experimental study on the other hand involves the introduction of a treatment or intervention in other to study the cause and effect or relationship between the variables.
In the scenario above, the research intends to demonstrate the effectiveness of a treatment(magnets) for back pain. The presence of a treatment in this research study makes it an experimental study.
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A payday loan company charges a $90 fee for a $500 payday loan that will be repaid in 16 days.
Treating the fee as interest paid, what is the equivalent annual interest rate?
Answer:
Kindly check explanation
Step-by-step explanation:
Given :
Interest amount paid on loan = $90
Principal value, amount borrowed = $500
Period, t = 16 days
The equivalent annual interest :
Using the simple interest formula :
simple interest = principal * rate * time
Using, days of year = 365
Plugging in the values into the formula :
90 = 500 * rate * (16/365)
90 = 500 * rate * 0.0438356
90 = 21.917808 * rate
Rate = 90 / 21.917808
Rate = 4.10 = 4.10 * 100% = 410%
If days of year = 360 is used :
90 = 500 * rate * (16/360)
Rate = 90 / 22.222
Rate = 4.05 = 4.105 * 100% = 405%
Compute the product AB by the definition of the product ofmatrices, where Ab1 and Ab2 are computed separately, and by therow-column rule for computing AB.
Matrix A= [2 -2]
[3 4]
[4 -3]
Matrix B =
[4 -1]
[-1 2]
Answer:
[tex]A * B = \left[\begin{array}{ccc}10&-6\\8&5\\19&-10\end{array}\right][/tex]
Step-by-step explanation:
Given
[tex]A =\left[\begin{array}{cc}2&-2\\3&4\\4&-3\end{array}\right][/tex]
[tex]B = \left[\begin{array}{cc}4&-1\\-1&2\end{array}\right][/tex]
Required
[tex]AB[/tex]
To do this, we simply multiply the rows of A by the column of B;
So, we have:
[tex]A * B = \left[\begin{array}{ccc}2*4 + -2*-1&2*-1+-2*2\\3*4+4*-1&3*-1+4*2\\4*4-3*-1&4*-1-3*2\end{array}\right][/tex]
[tex]A * B = \left[\begin{array}{ccc}10&-6\\8&5\\19&-10\end{array}\right][/tex]
What are the x-coordinates for the maximum points in the function f(x) = 4 cos(2x − π) from x = 0 to x = 2π? (1 point) Select one: a. x = 3 pi over 2 , x = π b. x = pi over 2 , x = 3 pi over 2 c. x = 0, x = 2π d. x = 0, x = π
9514 1404 393
Answer:
b. x = π/2, x = 3π/2
Step-by-step explanation:
The maximum is found where the argument of the cosine function is a multiple of 2π.
2x -π = 2nπ
2x = (2n+1)π . . . . . . . add π
x = (2n+1) · π/2 . . . . . divide by 2
x = {π/2, 3π/2}
what percentage of 7 1/2 is 2 1/2
Answer:
7+½ = (7*2+(1))/2=15/2
Step-by-step explanation:
2+½ =5/2 and. (15/2)/(5/2)=3. this means %33.3333
Ms. Harlow had 56 tickets. She gave 2 tickets to each of her 21 students.
Which set of equations shows how many tickets Mrs. Harlow had left?
21 x 2 = 42
OA)
56 - 42 = 14
56 - 21 = 35
ОВ)
35 - 2 = 33
21 x 2 = 42
OC)
56 + 42 = 98
56 - 21 = 35
OD)
35 + 2 = 37
Answer: 56 - 42
Step-by-step explanation: She gave 2 to EACH of her 21 students. So 2 * 21 = 42. 56 - 42
Which row of the table reveals the y-intercept of function f?
Answer:
No solution is possible from the informatin provided.
Step-by-step explanation:
You didn't include the table,
Answer:
y intercept is found from the pair that has a 0 for the x variable.
Step-by-step explanation:
if a choice was (0,2) this would be the point where the line intercepts the y axis.
x=0 is the position of the vertical line, and 2 is how high up the graph the line passes through the y-axis
expression 6 times 50
Answer:
6x50=300
Step-by-step explanation:
because math
Answer:
6*50
HOPE THIS HELPS
- Todo ❤️
Step-by-step explanation:
6*5=30*10=300
The shortest route from London to Edinburgh is 400 miles.
A lorry is expected to take 10 hours to travel this route.
The lorry actually travels by a different route which increases the distance by 15%, but it still arrives in 10 hours.
By how many more mph than the expected speed does the lorry travel?
Answer:
if it takes the lorry ten hours we divide 400 by 10
40 mph
if it takes 15% longer that means it will take
10*1.15=11.5
if we divide 400 by 11.5
we get 34.7826086957
or 34.8
so the lorry travels 5.2 mph faster then the expected speed
Hope This Helps!!!
At the end of the week the mileage is 2834
Fayez knows he used 75.2 litres of petrol during this week.
The handbook states that the limousine uses 1 gallon of petrol for every 20 miles.
Fayez wants to know if his limousine used 1 gallon of petrol for every 20 miles that week.
1 gallon = 4.54 litres
Did his limousine use 1 gallon of petrol for every 20 miles that week?
Mileage = 2529
Answer: Yes
Step-by-step explanation:
The National Highway Traffic Safety Administration reported the percentage of traffic accidents occurring each day of the week. Assume that a sample of accidents provided the following data. Sunday= 64, Monday=53, Tuesday=55, Wednesday=49, Thursday=55, Friday=68, Saturday=76. Conduct a hypothesis test to determine if the proportion of traffic accidents is the same for each day of the week. What is the -value? Compute the value of the test statistic (to 3 decimals).
Answer:
Hence,
a)
Test statistic [tex]X^{2}[/tex] = 9.269.
p value = 0.148
b)
Sunday= 15.23%, Monday= 12.62%, Tuesday= 13.10%, Wednesday=11.67%,
Thursday= 13.10%, Friday= 16.19%, Saturday= 18.09%.
Step-by-step explanation:
a)
relative observed Expected Chi square
Category frequency(p) [tex]O_{i}[/tex] Ei=total*p [tex](O-E)^{2}[/tex] [tex]R^{2}_{i} =(O_{i} -E_{i} )^{2} /E_{i}[/tex]
1 0.142857143 64.0 60.00 16.00 0.267
2 0.142857143 53.0 60.00 49.00 0.817
3 0.142857143 55.0 60.00 25.00 0.417
4 0.142857143 49.0 60.00 121.00 2.017
5 0.142857143 55.0 60.00 25.00 0.417
6 0.142857143 68.0 60.00 64.00 1.067
7 0.142857143 76.0 60.00 256.00 4.267
Total 1.000 420 420 556 9.269
Test statistic [tex]X^{2}[/tex] = 9.269.
p value = 0.148 from excel: chidist(9.269,6)
b)
Percentage %= Frequency of traffic occur on category x 100 / Total number of frequency given.
Category Percentage%
Sunday 15.23%
Monday 12.62%
Tuesday 13.10%
Wednesday 11.67%
Thursday 13.10%
Friday 16.19%
Saturday 18.09%
Please help! What is the domain of the function shown in the graph?
Answer:
nnmb cgchmfxmgfmv vb , mnio qrstuvwxyz
abcdefghijklmnoprstuvxxyz
Step-by-step explanation:
now i know my abcs next time wont you sing with me
Write a linear equation in standard form for the line that goes through
(-14,-5) and (4,5).
O A. y- 5 = (x-4)
B. -5x+9y= 25
C. -5x +9y= 1
D. 5x-9y= 25
The linear equation of line passing through the (-14,-5) and (4,5) is given by -5x + 9y = 25
What is an Equation of a line?The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept
And y - y₁ = m ( x - x₁ )
y = y-coordinate of second point
y₁ = y-coordinate of point one
m = slope
x = x-coordinate of second point
x₁ = x-coordinate of point one
The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Given data ,
Let the equation of line be represented as A
Now , the value of A is
Let the first point be P ( -14 , -5 )
Let the second point be Q ( 4 , 5 )
Now , the slope of the line is m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Substituting the values in the equation , we get
Slope m = ( -5 - 5 ) / ( -14 - 4 )
Slope m = -10 / -18
Slope m = 5/9
Now , the equation of line is y - y₁ = m ( x - x₁ )
y - 5 = ( 5/9 ) ( x - 4 )
Multiply by 9 on both sides , we get
9y - 45 = 5x - 20
Adding 45 on both sides , we get
9y = 5x + 25
Subtracting 5x on both sides , we get
-5x + 9y = 25
Hence , the equation of line is -5x + 9y = 25
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Inflation is running 1.1% per year when you deposit $5,000 in an account earning 4.4% compounded continuously. In constant dollars, how much money will you have 6 years from now?
a. $6439.80
b. $6097.01
c. $1169.51
d. $6510.64
The value of the money including inflation after 6 years will be $6510.64.
What is inflation?The rate at which prices grow over a specific time period is known as inflation. Inflation is often measured in broad terms, such as the general rise in prices or the rise in a nation's cost of living. But it may also be computed more precisely for some products, like food, or for services, like a haircut, for instance. In any situation, inflation refers to how much more costly the pertinent collection of products and/or services has grown over a predetermined time frame, most frequently a year.
Given that, Inflation is running at 1.1% per year when you deposit $5,000 in an account earning 4.4% compounded continuously.
deposit amount (P) = $ 5000
Rate (r) = 4.4 %
Time (t) = 6 years
Compound continuously
Amount (A)= 5000 e⁰°⁰⁴⁴ˣ ⁶
A = $ 6,510.64098
A = $ 6510.64
Total accumulated money after 6 years = $ 6,510.64
value of money decreases due to inflation
The real value of money after n years with the rate of inflation i = 1.1%
yₙ = A( 1 / (1+i) )ⁿ
y₆ = 6510.64 (1 / ( 1 + 0.011))⁶
y₆ = 6,097.008
Real value of money = $ 6,097.01
Therefore, after 6 years real value of the money including inflation will be $ 6,097.01.
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Amber rode her bike around the park 4 times. It took her 9 minutes each time.
How many minutes did she ride in all?
Answer:
Amber rode for 36 minutes in total.
Step-by-step explanation:
Lets create a ratio table:
Time elpased (minutes) : Laps around park
9 : 1
36 : 4
Amber rode for 36 minutes in total.
đã đi 36 phút.
từng bước
9: 1
36: 4
Amber đã đi tổng cộng 36 phút.
Solve for A
a=22/7•13/4^2
Answer:
A= ~2.55
Step-by-step explanation:
Using Pemdos, or gemdos, you can find you do the exponent first
4^2 = 16
then to everything else in left to right order since they're all multiplication or division
22/7 = ~3.14 * 13 = ~40.86/16 = ~2.55
(I'm using "~" to mean about/rounded to)
The square root of -2 rounded to nearest 100th?
Answer:
√-2 ≈ 1.41i
Step-by-step explanation:
√-2 = i√2 = i × 1.414.. ≈ 1.41i
Can someone help PLSSS
Answer:
Step-by-step explanation:
Area stage = 1/2 h (ab +cd)
Area = 5(14+22)
meeting center Area = 180
room = 25*32 = 800
800-180 = 620 tile
620*$4.90 = $3038
So no not enough money....
Note: even if it was $2999 it still would not be enough because
you have to cut tiles to fit in corners and edges... Just having fun with that comment, the math problems sometimes don't take reality into account (ha ha ha)
In what time will #250 gain #120 at 2%
Answer: 24 years
Step-by-step explanation:
Based on the information given, we've been given,
Principal = #250
Interest = #120
Interest rate = 2%
Time = Unknown
Interest = PRT/100
120 = (250 × 2 × Time)
Cross multiply
120 × 100 = (250 × 2 × T)
12000 = 500T
Time = 12000/500
Time = 24
It will take 24 years.
Una persona ha sido mordida por un insecto venenoso. Se comenzó a sentir mal pasados 30 minutos, 2 horas después acudió a un centro de urgencias donde fue atendido pasados 90 minutos. Si se estima que el porcentaje de sangre contaminada t horas después de ocurrida la mordedura es P =18t – t2 + 6
¿Qué porcentaje de sangre contaminada tiene este paciente al momento de ser atendido?
A final statistics exam had a mean of 70 and a variance of 25. If Bruce earned an 80 on his exam, what is his score?
Answer:
2
Step-by-step explanation:
Value = 80
Mean = 70
Variance = 25
Standard deviation=root(Variance)=root(25)=5
z score = (value - mean)/standard deviation
= (80-70)/5
= 10/5
= 2
z-score using mean 70 and variance 25 is 2
Given :
A final statistics exam had a mean of 70 and a variance of 25
First we find out standard deviation using variance
standard deviation =[tex]\sqrt{variance} =\sqrt{25} =5[/tex]
Now we find out z-score
[tex]z-score =\frac{value - mean}{standard \; deviation }[/tex]
value =80
mean=70 and standard deviation =5
substitute all the values
[tex]z-score = \frac{80-70}{5} =2[/tex]
So, his z-score using mean and variance is 2
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Matt had 60 questions correct on a Percent’s Chapter Test that had 150 one-mark questions. What was his mark written as a percentage?
Answer:
His mark, as a percentage, was of 40%.
Step-by-step explanation:
Mark as a percentage:
His mark as a percentage is the number of questions correct multiplied by 100% and divided by the number of questions.
In this problem:
60 questions correct out of 150. So
60*100%/150 = 40%
His mark, as a percentage, was of 40%.
Which of the following question is not considered a statistical question?
Answer:
B. How many total customers were at the story today?
Step-by-step explanation:
Option 'B' is not a statistical question because there is not more than one answer.
There is only one answer to this question.
Option 'A,' 'C,' and 'D' are statistical questions because there is more than one answer.
What amounts did each person at the store spend on their purchase?
This question has more than one answer.
How long did each customer spend shopping at the store?
What are the heights of each customer who entered the store?
These questions have more than one answer as well.
Statistical questions are questions that have more than one answer. This means you can collect data.
I, therefore, believe that option 'B' is not a statistical question.
DJ Kenisha is making a playlist for a radio show; she is trying to decide what 6 songs to play and in what order they should be played. If she has her choices narrowed down to 5 reggae, 15 hip-hop, and 13 blues songs, and she wants to play an equal number of reggae, hip-hop, and blues songs, how many different playlists are possible? Express your answer in scientific notation rounding to the hundredths place.
Answer:
[tex]8.19 \times 10^{4}[/tex] different playlists are possible
Step-by-step explanation:
The order in which the songs are played is not important, which means that the combinations formula is used to solve this question.
Combinations formula:
[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
In this question:
6 songs, so 2 reggae(from a set of 5), 2 hip hop(from a set of 15) and 2 blues(from a set of 13). So
[tex]T = C_{5,2}C_{15,2}C_{13,2} = \frac{5!}{2!3!} \times \frac{15!}{2!13!} \times \frac{13!}{2!11!} = 10*105*78 = 81900[/tex]
In scientific notations:
4 digits after the first, which is 8, so:
[tex]8.19 \times 10^{4}[/tex] different playlists are possible