Answer:
Ramon will run 1/9 of a mile.
Step-by-step explanation:
The relay race is 1/3 of a mile and there are three of them in his relay squad, himself and his two friends.
If three of them finish each sector and each sector is the same, that means that each of the members will run a third of that distance.
[tex]\frac{1/3}{3}\\=\frac{1}{3} (\frac{1}{3} )\\=\frac{1}{3(3)}\\=\frac{1}{9}[/tex]
Aaron tracks the time it takes him to mow lawns by writing coordinate points relating x, the time in hours it takes to mow a lawn, and y, the area of land mowed in acres. Two of his points are (3, 1.5) and (5, 2.5). Which statement describes the slope of the line through these two points?
Answer:
The slope of the line through these two points is 0.5, which means that for each hour moving a lawn, 0.5 more lands of area are mowed.
Step-by-step explanation:
Slope of a line:
Suppose we have two points in a line. The slope is the change in y divided by the change in x. It states how much y changes when x changes by 1.
In this question:
x: Time in hours to move a lawn.
y: Area of land.
Two of his points are (3, 1.5) and (5, 2.5).
Change in y: 2.5 - 1.5 = 1
Change in x: 5 - 3 = 2
Slope: 1/2 = 0.5
The slope of the line through these two points is 0.5, which means that for each hour moving a lawn, 0.5 more lands of area are mowed.
Based on past experience, the daily revenue, X, for a coffee shop in a city is a normally distributed random variable with a mean daily revenue of $900. The first co-owner of the shop feels that the shop is known throughout the city and as such they could reduce the amount of money spent on advertising without causing a decrease in the population mean daily revenue. The second co-owner is concerned that a reduction in advertising would in fact result in a decrease in the population mean daily revenue. To settle the issue, the first co-owner decides to decrease the advertising dollars for a period of time, during which she will select 64 days at random and compute the sample mean daily revenue. She will then perform a hypothesis test to determine if the sample mean daily revenue provides significant evidence to conclude that the population mean daily revenue is less than $900 when the advertising dollars are reduced. The first co-owner observes a sample mean daily revenue of $892.50 with a sample standard deviation of $24 when the advertising dollars have been reduced. What is the p-value for her test
Answer:
The p-value for her test is 0.0075.
Step-by-step explanation:
She will then perform a hypothesis test to determine if the sample mean daily revenue provides significant evidence to conclude that the population mean daily revenue is less than $900 when the advertising dollars are reduced.
At the null hypothesis, we test that the mean is less than 900, that is:
[tex]H_0: \mu = 900[/tex]
At the alternate hypothesis, we test that the mean is less than 900, that is:
[tex]H_a: \mu < 900[/tex]
The test statistic is:
We have the standard deviation for the sample, which means that the t-distribution is used to solve this question.
[tex]t = \frac{X - \mu}{\frac{s}{\sqrt{n}}}[/tex]
In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, s is the standard deviation of the sample and n is the size of the sample.
900 is tested at the null hypothesis:
This means that [tex]\mu = 900[/tex]
Sample of 64 days. The first co-owner observes a sample mean daily revenue of $892.50 with a sample standard deviation of $24 when the advertising dollars have been reduced.
This means that [tex]n = 64, X= 892.50, s = 24[/tex]
Value of the test:
[tex]t = \frac{X - \mu}{\frac{s}{\sqrt{n}}}[/tex]
[tex]t = \frac{892.50 - 900}{\frac{24}{\sqrt{64}}}[/tex]
[tex]t = -2.5[/tex]
What is the p-value for her test?
The pvalue of the test is the probability of a sample mean below 892.5, which is a left-tailed test for t = -2.5 with 64 - 1 = 63 degrees of freedom.
Using a calculator, the p-value for her test is 0.0075.
Find the GCF of the list of terms.
3x^2,6x^6 and -12x^3
Answer:
3x²
Step-by-step explanation:
3x²
They would all reduce to 1, 2x^4, and -4x
Consider the composite function g(f(x)) =x√6.
If f(x) = 3x², what is g(x)?
O g(x)=√2x
Og(x)=√x+3
Og(x)=√6x
O g(x)=√9-x
So on solving the provided question, we can say that the function g(x) is equal to g(x) = [tex]\sqrt{2x}[/tex]
A composite function is what?The mathematical procedure known as "function composition" takes two functions, f and g, and creates a function, h = g f, such that h(x) = g. This process involves applying the function g to the outcome of applying the function f to x. When the result of one function is utilized as the input for another, this is known as a composite function. The function f g (x) fg(x) fg(x) fg(x), also known as "f of g of x" or "f g fg fg of x," is the composition of the two functions if we have a function f and another function g.
f(f(x)) = [tex]\frac{x}{\sqrt{6} }[/tex]
f(x) = 3x^2
g(f(x)) = [tex]\frac{3x^2}{\sqrt{6} }[/tex]
g(x) = [tex]\sqrt{2x}[/tex]
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Write 1 6/7 as an improper fraction.
Answer:
13/7
Step-by-step explanation:
multiply the 7 x 1 then add 6. 13 would be the numerator.
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42. Let f be a function from the set A to the set B. Let S and T be subsets of A. Show that
a) f(S ∪ T)=f(S) ∪ f(T).
b) f(S ∩ T) ⊆ f(S) ∩ f(T).
Start with any random elements of sets and compute LHS and RHS individually.
a) The proof of f(S ∪ T) = f(S) ∪ f(T) is explained below.
b) The proof of f(S ∩ T) ⊆ f(S) ∩ f(T) is expliane dbelow.
What are sets and subsets?A set is a collection of well-defined objects.
A subset contains all the elements or a few elements of the given set.
The improper subset is when it contains all the elements of the given set and the proper subset is when it doesn't contain all the elements of the given set.
Let, The set A = {1, 2, 3, 4, 5} and B = {2, 4, 5}.
Therefore, S = {1, 2, 3} and T = {1, 4, 5}.
Now, f(S ∪ T) = {1, 2, 3, 4, 5} and f(S) ∪ f(T) = {1, 2, 3} ∪ {1, 4, 5}.
Hence, f(S ∪ T)=f(S) ∪ f(T).
Now, f(S ∩ T) = {1} and f(S) ∩ f(T) = {1, 2, 3} ∩ {1, 4, 5} = {1}.
Therefore, f(S ∩ T) ⊆ f(S) ∩ f(T). (⊆ implies improper subset)
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At a certain restaurant, the distribution of wait times between ordering a meal and receiving the meal has mean 11.4 minutes and standard deviation 2.6 minutes. The restaurant manager wants to find the probability that the mean wait time will be greater than 12.0 minutes for a random sample of 84 customers. Assuming the wait times among customers are independent, what describes the sampling distribution of the sample mean wait time for random samples of size 84?
Using the Central Limit Theorem, the sampling distribution of the sample mean wait time for random samples of size 84 has mean of 11.4 minutes and standard deviation of 0.28 minutes.
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
In this problem, the population has:
Mean of 11.4 minutes, thus [tex]\mu = 11.4[/tex].Standard deviation of 2.6 minutes, thus [tex]\sigma = 2.6[/tex]Samples of 84 are taken, thus, by the Central Limit Theorem:
[tex]n = 84, s = \frac{2.6}{\sqrt{84}} = 0.28[/tex]
The sampling distribution of the sample mean wait time for random samples of size 84 has mean of 11.4 minutes and standard deviation of 0.28 minutes.
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Help pls pls help pls pls help
It's 8, it gave Y so pretty easy from there on
y = 4
y = 1/4 x + 2
______________
4 = 1/4 x + 2
4 - 2 = 1/4 x + 2 - 2
2 = 1/4 x
2 × 4 = 4 × ( 1/4 ) × x
x = 8
Thus the correctly answer is option D.
Answer this! I WILL GIVE BRAINLIEST TO PERSON WHO GIVES CORRECT ANSWER!!!!!!!!!
Answer:
An 18-month loan with a 4.75% annual simple interest rate
Step-by-step explanation:
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Find perimeter
Simplify answer completely
Answer:
[tex]perimeter = 14 \frac{3}{4} + 4 \frac{1}{2} + 8 \frac{1}{2} + 10 \frac{2}{5} + 10 \frac{2}{5} + 12 \frac{4}{5} \\ = \frac{59}{4} + \frac{9}{2} + \frac{17}{2} + \frac{52}{5} + \frac{52}{5} + \frac{64}{5} \\ = 61 \frac{7}{20} \: units[/tex]
y=x-4 and y=4x+2 graph solution of the systems
Answer:
(-2,-6)
Step-by-step explanation:
we can solve this system of equations with the substitution method because y is already by itself.
since they are both equal to y, we can set both equations equal to each other.
4x+2=x-4
subtract 2 from both sides
4x=x-6
subtract x from both sides
3x=-6
divide both sides by 3
x = -2
now that we know x, we can plug this value into one of the original equations and solve for y.
y=-2-4
y=-6
so on a graph, these two equations will intersect at the point (-2,-6)
A theater has 20 rows of seats. If there are 4 seats in the 1st row 12 in the 2nd row, 20 in the 3rd row . How many seats are there in total? Show and explain all work.
Answer:
164 seats
Step-by-step explanation:
you make the equation 4+ 8X to deteremine the seats and x equals the rows and you get your answer.
An arithmetic sequence is a sequence where each consecutive term has a common constant difference. The total number of seats that the theatre has is 156 seats.
What is the sum of terms of an arithmetic sequence?An arithmetic sequence is a sequence where each consecutive term has a common constant difference.
An arithmetic sequence, therefore, is defined by two parameters, viz. the starting term and the common difference.
Let the starting term be 'a' and the common difference be 'd', then we get the arithmetic sequence as:
a, a+d, a+2d, .....
The sum of those 'n' terms is:
[tex]\rm a + (a+d) + (a+2d) + \cdots + (a+(n-1)d) = \dfrac{n}{2}[2a + (n-1)d ][/tex]
The condition is a case of an arithmetic progression. Therefore, the common difference in the progression is of 8 and the first term of the sequence is 4. Therefore, the sum of the series for the first 20 terms will be,
aₙ = 4 + (20-1)8
= 4 + (19)8
= 4 + 152
= 156
Hence, the total number of seats that the theatre has is 156 seats.
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Please help will mark Brainly
Answer: 12
Step-by-step explanation: There are about 12 grams of carbohydrates in a 8 fluid ounce (240 mL) glass of whole milk. The amount of carbohydrates in milk can vary slightly depending on the type of milk you are drinking. For example, skim milk has slightly fewer carbohydrates (about 11 grams per 8 fluid ounces) than whole milk because the fat has been removed. On the other hand, milk that is high in fat, such as heavy cream, has even more carbohydrates (about 4 grams per fluid ounce).
Please help me with this
9514 1404 393
Answer:
3025
Step-by-step explanation:
We observe that increasing x by 1 from 0.5 to 1.5 causes the function value to be multiplied by 55 (from 1 to 55).
So, increasing the x-value by 1 again, from 1.5 to 2.5, will again multiply the function value by 55.
f(2.5) = 55·f(1.5) = 55^2
f(2.5) = 3025
To determine the inverse of function f,
change f(x) to y, switch
and y,
and solve for
The resulting function can be written as
f(x) = (x - 3.
Answer:
To determine the inverse of function f, change f(x) to y, switch x and y, and solve for y.
[tex]\frac{1}{8} (x-4)^3[/tex]
Step-by-step explanation:
f(x) = [tex]\sqrt[3]{8x} +4[/tex]
Change f(x) to y: y = [tex]\sqrt[3]{8x} +4[/tex]
Switch x and y: x = [tex]\sqrt[3]{8y} +4[/tex]
Solving for y: x - 4 = [tex]\sqrt[3]{8y}[/tex]
(x-4)^3 = 8y
y = [tex]\frac{1}{8}[/tex][tex](x-4)^3[/tex]
Therefore: inverse of function f = [tex]\frac{1}{8} (x-4)^3[/tex]
The inverse function of f(x) will be f⁻¹(x) = 1/8(x - 4)³.
What is a function?A statement, principle, or policy that creates the link between two variables is known as a function. Functions are found all across mathematics and are required for the creation of complex relationships.
The function f(x) is given below.
f(x) = ∛(8x) + 4
Then the inverse function of f(x) will be
Put x = f⁻¹(x) and f(x) = x. Then we have
x = ∛{8f⁻¹(x)} + 4
∛{8f⁻¹(x)} = x - 4
Cube on both sides, then we have
8f⁻¹(x) = (x - 4)³
f⁻¹(x) = 1/8(x - 4)³
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A real estate developer wishes to study the relationship between the size of home a client will purchase (in square feet) and other variables. Possible independent variables include the family income, family size, whether there is a senior adult parent living with the family (1 for yes, 0 for no), and the total years of education beyond high school for the husband and wife. The sample information is reported below.
Family Square Feet Income (000s) Family Size Senior Parent Education
1 2,240 60.8 2 0 4
2 2,380 68.4 2 1 6
3 3,640 104.5 3 0 7
4 3,360 89.3 4 1 0
5 3,080 72.2 4 0 2
6 2,940 114 3 1 10
7 4,480 125.4 6 0 6
8 2,520 83.6 3 0 8
9 4,200 133 5 0 2
10 2,800 95 3 0 6
Develop an appropriate multiple regression equation. Which independent variables would you include in the final regression equation? Use the stepwise method.
Answer:=Answer1 has the regression analysis with all 4 independent variables. Using the stepwise method, we toss the one with the largest non-significant p-value which is Senior Present. Then do another regression analysis with only 3 independent variables. Answer2 has this. From this analysis we can toss education (has the largest non-significant p-value) and do another analysis which is in Answer3. In this analysis we see that Income is not quite significant (p=.0586) at the 0.05 level so we can toss it and do an analysis with Family Size as the only independent variable. This result is given in Answer4. The final regression equation has Family Size as the only independent variable and it can stay in the regression equation because it is statistically significant (p=.0003). The prediction equation is given at the bottom of Answer4. This should answer your question. If not let me know.
Step-by-step explanation:
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A parallelogram has two
adjacent angles that are
supplementary. One
angle is 55° less than the
other. What is the
measure of the smaller
angle?
Answer:
x + (x + 55) = 180
2x =125
The angle is 62.5 degrees
Double-Check
62.5 + (62.5 + 55) = 180
125 + 55 = 180
62.5 is the smaller angle
Step-by-step explanation:
Answer:
62.5
Step-by-step explanation:
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If a basketball has a diameter of 9.4 inches, which is closest to the volume of the ball in cubic inches?
A. 521.62 in
B. 434.89 in
Answer:
B. 434.89
Step-by-step explanation:
A basketball is a sphere and the volume formula is:
V = 4/3πr³
Given:
d = 9.4
r = 9.4/2
r = 4.7
Work:
V = 4/3πr³
V = 4/3π(4.7)³
V = 4/3π(103.823)
V = 434.89
I need help with this, I need to simplify but I don't know how
Answer: solve the same variables
Step-by-step explanation:
1. 3y + 4.1
2. 4x +
3. 5x + 22½
4. 4y²
5. + 25
6. 0
Get it right I need this bro
which of the following is the solution to the equation 3^X+9=81^X
a) x=-6
b)x=6
c)x=-3
d)x=3
9514 1404 393
Answer:
d) x = 3
Step-by-step explanation:
The given equation resolves to a quartic equation in (3^x). It has a solution near ...
x = 0.541770946714
__
Perhaps you want the solution to ...
3^(x+9) = 81^(x)
Rewriting in powers of 3, this is ...
3^(x+9) = (3^4)^x = 3^(4x)
Taking logarithms base 3 gives ...
x +9 = 4x
9 = 3x . . . . . . subtract x
3 = x . . . . . . . divide by 3 . . . . matches choice D
_____
Additional comment
The Order of Operations requires that exponential terms be evaluated before addition and subtraction. That means (3^x) must be evaluated before the sum (3^x) + 9. If you want the sum of x and 9 to be evaluated first, it must be in parentheses: 3^(x+9).
In typeset equations, the superscript font serves to group parts of the exponent. In plain text, a grouping symbol (parentheses) must be used.
150, 60, 24,...
Find the 9th term.
Each statement describes a transformation of the graph of f(x)=3/x. which statement correctly describes the graph of y= f(x- 7) + 3?
A It is the graph of f translated 3 units up and 7 units to the left.
B. It is the graph of f translated 7 units down and 3 units to the right.
C It is the graph of f translated 7 units up and 3 units to the
right!
D. It is the graph of f translated 3 units up and 7 units to the right.
Answer:
Pretty Sure its D!
Step-by-step explanation:
I think its either B or D but im not sure
Answer:
Calculate the number of whole years it takes for the population to decrease from 2180 to less than 1000Step-by-step explanation:
Answer:
D
Step-by-step explanation:
Write an equation and solve for b using the diagram
below. YOU MUST WRITE THE EQUATION IN
ORDER TO GET CREDIT.
(3b + 18)°
93°
Step-by-step explanation:
hope this is right hehe.....
Chen tosses a number cube 19 fewer times than Jayden. Chen tosses a number cube 38 times. How many times does Jayden toss a number cube?
Every day, Eve runs 12 mile more than the day before. Which equation can be used to discover how many miles Eve runs on x days?
y=x+12y is equal to x plus 1 half
y=12xy is equal to 1 half x
y=5xy is equal to 5 x
y=5+xy is equal to 5 plus x
Answer:
B) y=1/2x
Step-by-step explanation:
y=1/2x
A paint store makes lime green paint by mixing 3 parts yellow paint to 1 part blue paint. A clerk mixès 5 parts yellow paint to 2 parts blue paint. did the clerk use the correct ratio of yellow paint to blue paint? Explain.
Answer:
No
Step-by-step explanation:
The ratio used should have been 6 parts yellow paint to 2 parts blue paint
hope this helps
Simplify the following expression: -16 -8/2 + 25 ÷ 5 + 1
A. -18
B. 6
C. 10
D. -6
You are given 2 parallel lines on the coordinate plane. You are told to translate x + 3,y-2, rotate 180° clockwise about the origin, then reflect over the y-axis. After the transformations you will have what type of lines?
A Intersecting lines
B. The Same Line
C. Parallel Lines
Since matching angles are formed and the equal corners are congruent when a line joins two parallel lines, one of the choices isc=d.
Parallel lines are what?Geometry refers to parallel lines as beams, straight lines that never overlap. Parallel planes are those that never cross each other while occupying the same three-dimensional space. Curves which are equal with each other and keep a predetermined minimum separation from one another must not overlap or intersect. Parallel lines on a plane are those that always have the same distance between them. A parallel line cannot be crossed. Perpendicular lines are those that intersect directly at a 90 degree angle.
Here,
Given : vertical angles, A = d also represents a solution.
B+d=180 as a result of b+c=180 therefore
B+d=180 as a result of b+c=180 therefore Since a=d, c=d, and b+d=180, the answer is B,C,E.
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