Answer:
The null hypothesis is [tex]H_0: \mu = 99[/tex]
The alternate hypothesis is [tex]H_a: \mu > 99[/tex]
The test statistic is [tex]z = 0.31[/tex]
The pvalue of the test is 0.3783 > 0.05, which meas that the results are not significant at the 5% level.
Step-by-step explanation:
It is believed that the average amount of money spent per U.S. household per week on food is about $99. We want to test the hypothesis that the mean weekly food budget for all households in this community is higher than the national average.
At the null hypothesis, we test if the mean is the national average of 99, that is:
[tex]H_0: \mu = 99[/tex]
At the alternate hypothesis, we test if the mean is greater than the national average of 99, so:
[tex]H_a: \mu > 99[/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.
99 is tested at the null hypothesis:
This means that [tex]\mu = 99[/tex]
A random sample of 16 households in a certain affluent community yields a mean weekly food budget of $100. Standard deviation of $13.
This means that [tex]n = 16, X = 100, \sigma = 13[/tex]
Value of the test statistic:
[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
[tex]z = \frac{100 - 99}{\frac{13}{\sqrt{16}}}[/tex]
[tex]z = 0.31[/tex]
The test statistic is [tex]z = 0.31[/tex].
Determine if the results significant at the 5% level.
The pvalue of the test is the probability of finding a sample mean above 100, which is 1 subtracted by the pvalue of z = 0.31.
Looking at the ztable, z = 0.31 has a pvalue of 0.6217
1 - 0.6217 = 0.3783
The pvalue of the test is 0.3783 > 0.05, which meas that the results are not significant at the 5% level.
If function gis defined by the equation y-3x = -14, which equation represents the function in function notation?
O A g(x) = 3x - 14
OB. 8(X) = -3x - 14
OC 8(*) = 3x + 14
OD. 8(X) = -3x + 14
Answer: B
Step-by-step explanation:
-20 POINTS- only answer If you know dont guess again.
Using the Pythagoras theorem, the value of y is [tex]6\sqrt{7}[/tex], and the value that goes in the green box is 6.
What is Pythagoras Theorem?
In a right-angled triangle, the square of the hypotenuse side is equal to the sum of the squares of the other two sides, according to Pythagoras's Theorem. These triangle's three sides are known as the Perpendicular, Base, and Hypotenuse. Due to its position opposite the 90° angle, the hypotenuse in this case is the longest side.
Mark the intersections as A, B, C, and D.
It is given that BC=12 and CD=9.
The relationship between the height on the hypotenuse of a right triangle and the two line segments it generates on the hypotenuse is described by the right triangle altitude theorem, also known as the geometric mean theorem. It claims that the altitude is equal to the geometric mean of the two segments.
Apply the geometric mean theorem -
(AC)^2 = BC x CD
(AC)^2 = 12 x 9
(AC)^2 = 108
AC = [tex]\sqrt{108}[/tex]
AC = [tex]6\sqrt{3}[/tex]
Triangle ABC is a right-angled triangle, so apply Pythagoras theorem -
(AB)^2=(BC)^2+(AC)^2
(AB)^2=(12)^2+([tex]6\sqrt{3}[/tex])^2
(AB)^2=144+108
(AB)^2=252
AB=[tex]\sqrt{252}[/tex]
AB=[tex]6\sqrt{7}[/tex]
Therefore, the value of y is obtained as [tex]6\sqrt{7}[/tex].
To learn more about Pythagoras Theorem from the given link
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what type of accociation would you expect in this a persons age and number of pets the have
Answer:
if they have less pets they are probably young and aren't responsible to take care and if they have alot of old they are probably old
What must be the value…. Please I need help ASAP.
Answer:
y+35=2y-47
35+47=2y-y
82=y
I need help pls now ??
FIND THE SLOPE . THE PICTURE ATTACHED IS THE FULL QUESTION ,
Answer:
-12/5
Step-by-step explanation:
slope = change in y / change in x
change in y = 12 (from top to bottom) = 6 - (-6)
change in x = -5 (from top to bottom) = -2 -3
slope = 12/-5 = -12/5
Equations of Exponential Functions
The population, P, of six towns with time t in years are given by the following exponential equations:
(i) P = 1000(1.08)t (ii) P = 600(1.12)t
(iii) p = 2500(0.9)t (iv) P = 1200(1.185)t
(v) P = 800(0.78)t (vi) 2000(0.99)t
Which town decreasing the fastest?
a. ii c.iii
b. v d. vi
Please select the best answer from the choices provided
Answer:
B. v
Step-by-step explanation:
I calculated it logically
will mark brainliest
Answer:
20
Step-by-step explanation:
if you plug in 20, (20) x 3 = 60 + 10 = 70. plus the other angle equaling 20 it'd be 90 degrees which is what the angle is. mark brainliest pls
Help me with this please lol.
Answer:
Flower Bed A is the 3rd on down
C=10pi, A = 25pi
Flower Bed B is the 5th one down
C=12pi, A=36pi
9514 1404 393
Answer:
A) 10π ft; 25π ft²
B) 12π ft; 36π ft²
Step-by-step explanation:
The circumference is given by ...
C = πd = 2πr . . . . . . . . . . for radius r or diameter d
The area is given by ...
A = πr² = (π/4)d²
__
A) For a diameter of 10 ft, the circumference is π(10 ft) = 10π ft.
The area is (π/4)(10 ft)² = 25π ft².
__
B) For a radius of 6 ft, the circumference is 2π(6 ft) = 12π ft.
The area is π(6 ft)² = 36π ft².
Eden has 300 pounds in his savings accounts. his bank offers him a fixed 5 percent simple interest rate per annum, for a period of 3 years?
How much interest will he have earned after 3 years?
Answer:
Interest of £45
Step-by-step explanation:
£300×.05×3=£45
Please help answers do in 30 minutes
Answer:
The angle for x would be 45°
Lacey runs a stable that boards a range of horses.
brown 8
black 9
gray 3
Considering this data, how many of the next 15 horses that come to board should you expect to be brown horses?
Answer:no it would be 4
Step-by-step explanation:
if you roll a standard six-sided die what is the probability that you get a one or a five give your answer as a simplified fraction
Answer:
2/6 - simplified fraction=1/3
Step-by-step explanation:
Which statement is an accurate comparison of Mrs. Liu’s 3rd and 5th period classes?
The box plot below shows Mrs. Liu’s 3rd period class averages (top) and 5th period class averages (bottom). Use the box plots to answer the following question.
Mrs. Liu’s 5th period has a greater interquartile range than her 3rd period.
Mrs. Liu’s 3rd period has a greater center than her 5th period.
Mrs. Liu’s 5th period has a smaller range than her 3rd period.
The upper extremes for both classes are the same.
Answer: the first answer is correct i think :]
4/8 + 1/4
A 5/12
B 3/4
C 6/8
D 2/8
Answer:
3/4
Step-by-step explanation:
4/8 can be simplified by dividing 2 from the numerator and denominator, which equals 2/4.
This turns the equation into 2/4 + 1/4, giving you a common denominator.
Answer:
Both B & C answers are correct
Step-by-step explanation:
To solve these two fractions, 1st you have to make both the numerator and the denominator the same.
For that, you can multiply both the numerator and the denominator of 1/4 by 2.
[tex]\sf\frac{4}{8} +\sf\frac{1}{4} \\\\\sf\frac{4}{8} +\sf\frac{1*2}{4*2}\\\\\sf\frac{4}{8} +\sf\frac{2}{8}\\\\\sf\frac{6}{8}[/tex]
To write the fraction in its simplest form, divide both sides by 2.
[tex]\sf\frac{3}{4}[/tex]
50 POINTS !!
PLEASE HELP !! ILL GIVE BRAINLIEST TO THE RIGHT ANSWERS.
Answer:
c = 15
Step-by-step explanation:
Ross walked 7 miles in 2 hours. What is his unit rate of miles per hour?
Answer:
3.5 miles per hours
Step-by-step explanation:
7/2 =3.5
Write the equation of a line in slope-intercept form that has a slope of -5 and passes through the point (3,- 2)
9514 1404 393
Answer:
y = -5x +13
Step-by-step explanation:
We know from the slope-intercept equation ...
y = mx + b
that the y-intercept b can be found as ...
b = y - mx
Filling in the given values of m and (x, y), we find ...
b = -2 -(-5)(3) = 13
Then the equation is ...
y = -5x +13
A spinner has regions numbered 1 through 18. What is the probability that ___________________
the spinner, spun once, will stop on an even number or a multiple of 3?
Answer:
Probability that the spinner stop on an even number or a multiple of 3 = [tex]\frac{2}{3}[/tex]
Step-by-step explanation:
Given - A spinner has regions numbered 1 through 18.
To find - What is the probability that the spinner, spun once, will stop on an even number or a multiple of 3?
Solution -
Given that,
A spinner has regions numbered 1 through 18.
So,
The sample space, S = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18}
i.e.
n(S) = 18
Now,
Let A be the outcomes that gives even number or a multiple of 3,
Then
A = {2, 3, 4, 6, 8, 9, 10, 12, 14, 15, 16, 18}
i.e.
n(A) = 12
∴ we get
Probability that the spinner stop on an even number or a multiple of 3 = [tex]\frac{n(A)}{n(S)}[/tex]
= [tex]\frac{12}{18}[/tex]
= [tex]\frac{2}{3}[/tex]
i.e.
Probability that the spinner stop on an even number or a multiple of 3 = [tex]\frac{2}{3}[/tex]
The expression a÷4 is equal to?for a =2.6
Answer:
[tex]\frac{a}{4} = \frac{13}{20}[/tex]
Step-by-step explanation:
GIVEN :-
a = 2.6TO FIND :-
Value of [tex]\frac{a}{4}[/tex]SOLUTION :-
To find the value of [tex]\frac{a}{4}[/tex] , just put a = 2.6 there in the expression.
[tex]=> \frac{a}{4} = \frac{2.6}{4} = \frac{\frac{26}{10} }{4} = \frac{26}{40}[/tex]
Reducing the fraction gives - [tex]\frac{13}{20}[/tex]
In decimal form , it is - [tex]0.65[/tex]
the line Plus shows the differences some students jumped during a field day competition what fraction of the students jumped 5 1/2
Answer:
⅛
Step-by-step explanation:
Each mark (x) on the plot presents the distance that each student jumped.
There are 24 marks there, so it means there is a total of 24 students whose distance jumped were recorded.
Number of students that jumped 5½ ft = 3
Fraction of the students that jumped 5½ ft = no of students that jumped 5½ ft / total number of students
= 3/24
Simplify/reduce the fraction
= 1/8
Mrs. Sarto told her son that if he babysat his baby sister, she would pay him $5.80 per hour. If Mrs. Sarto’s son babysits his sister for 5.2 hours, how much money will he be paid?
Ashanti cashed her paycheck at Cash-n-Go. The fee at Cash-n-Go is 7.5% of the amount of the check. Her paycheck was $670. How much was the fee for Ashanti to cash her paycheck?
Answer:
$50.25
Step-by-step explanation:
7.5% as a decimal is 0.075.
So, the fee is [tex](0.075)(670)=\$50.25[/tex].
how many times does 5 go into 103?
Answer and Step-by-step explanation:
We know that 5 can go into 100 twenty times, so lets try 20 and see what happens.
5 times 20 = 100
103
- 100
3
We get a remainder of 3. This means that 5 goes into 103 only Twenty times.
If we were to fully divide 103 by 5, then 5 goes into 103 '20.6' times.
#teamtrees #PAW (Plant And Water)
Help me please!!! 20 points
Answer:
x=4, y =5
Step-by-step explanation:
there's no factorization involved, just elimination and substitution. First subtract equation 1 and 2. The x's cancel out and you get y by itself and can solve for it. Then plug the value of y into equation 2 and solve for x and you get it. (In my picture I put value of y in equation 1 but your question asks for putting it in equation 2 so do that instead)
If a coin flipped twenty five times and lands tails up seventeen times, the blank
Probability that the coin lands up is 17/25
What is -6 - t/4 = -1
Answer: t=-20
Step-by-step explanation:
Alan has 11 nickels and
dimes in his pocket. When
he counted his change he
found he had $0.95. How
many dimes does Alan
have?
Answer:
4
Step-by-step explanation:
Nickels are 5 cents a piece so you will multiple 11 by 5 to find how much Alan has in nickels. Then subtract that from the total of 95 to get your answer.
11 × 5 = 55
95 - 54 = 40
Since dimes are worth 10 cents you divide 40 by 10 and that is how many dimes Alan has.
40/10=4
A construction worker is making concrete by mixing sand, gravel, and cement in water. For each pound of sand, he uses 1 2/3 pounds of gravel. For each pound of gravel, he uses 2/5 pound of cement. He is making enough concrete that he needs to use 3 pounds of sand. How many pounds of cement does he use? PLEASE HELP DUE NOW !! TYYY
A. 1 pound
B. 1 4/15 pounds
C. 2 pounds
D. 2 1/15 pounds
Using mathematical operations, the construction worker requires C. 2 pounds of cement to mix 3 pounds of sand.
What are the mathematical operations?The basic mathematical operations are subtraction, addition, division, and multiplication.
These mathematical operations combine numbers, variables, mathematical operands, and the equation symbol to solve mathematical problems.
In this situation, we can apply the mathematical operation of multiplication to determine the quantity of cement required for 5 pounds of gravel.
The quantity of gravel per pound of sand = 1²/₃ = 1.667 pounds
For 3 pounds of sand, the quantity of gravel required = 5 pounds (1²/₃ x 3)
The quantity of cement per pound of gravel = ²/₅ pounds or 0.4
For 3 pounds of sand and 5 pounds of gravel, the quantity of cement required = 2 (5 x 0.4) or (5 x ²/₅)
Thus, 2 pounds of cement are needed to mix with 3 pounds of sand and 5 pounds of gravel.
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Whose inverses are also functions
Functions whose inverses are also functions.
What is inverse function?Inverse function is represented by [tex]f^{-1}[/tex] with regards to the original function and the domain of the original function becomes the range of inverse function and the range of the given function becomes the domain of the inverse function. The graph of the inverse function is obtained by swapping (x, y) with (y, x) with reference to the line y = x.
If a horizontal line intersects the original function in a single region, the function is a one-to-one function and inverse is also a function.
Every function has an inverse, but not every inverse will be a function. The inverse may fail the vertical line test. If the original function is a one-to-one function, then its inverse will be a function. A one-to-one function not only passes the vertical line test, it also passes a horizontal line test.
Therefore, functions whose inverses are also functions.
Learn more about the inverse function here:
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