Answer:
Step-by-step explanation: We can start the problem by using the principle of Proportional Equivalents. We can write two equations based on the given information:
Let's say that the rate of filling the pool with one large pump is x and the rate of filling the pool with one small pump is y.
Then, we can write the following two equations:
2x + 1y = 1/4 (because two large and one small pump can fill the pool in 4 hours)
1x + 3y = 1/4 (because one large and three small pumps can fill the pool in 4 hours)
Now we have two equations with two unknowns, x and y. We can solve for x and y using either substitution or elimination method. Let's use substitution method.
Solving for x:
From equation (1), we have 2x = 1/4 - 1y
Substituting this value of x in equation (2), we get:
1 (1/4 - 1y) + 3y = 1/4
Expanding and simplifying, we get:
1/4 - 1 + 3y = 1/4
3y = 1/2
y = 1/6
So, the rate of filling the pool with one small pump is 1/6.
Now that we have found the value of y, we can find the value of x.
x = 1/4 - 1y = 1/4 - 1 * 1/6 = 1/4 - 1/6 = 1/12
So, the rate of filling the pool with one large pump is 1/12.
Now that we have found the rate of filling the pool with each large and small pump, we can find the time it will take 4 large and 4 small pumps to fill the pool.
Let's call the rate of filling the pool with 4 large and 4 small pumps as R.
Then, R = 4 * 1/12 + 4 * 1/6 = 1/3
So, it will take 1/R = 3 hours to fill the pool with 4 large and 4 small pumps.
On a weekly basis Tino sets aside ½
of his weekly salary for rent, ½ for
credit card payments, ¼ for groceries
and utilities, and the rest,
approximately $15 for entertainment.
Give an approximation of Tino's
weekly salary.
After all the spending costs, Tino's weekly salary is approximately $60.
What is the linear equation?
A linear equation is an algebraic equation of the form y=mx+b. where m is the slope and b is the y-intercept.
Let's call Tino's weekly salary "x".
Each week, Tino sets aside half of his salary for rent, so:
0.5x = rent
He also sets aside half of his salary for credit card payments, so
0.5x = credit card payments
And he sets aside a quarter of his salary for groceries and utilities, so:
0.25x = groceries and utilities
And he has approximately $15 left for entertainment, so:
x - 0.5x - 0.5x - 0.25x = 15
We can simplify this equation by combining the terms on the left side:
x - 1.25x = 15
And then solving for x:
-0.25x = 15
x = 60
Therefore, Tino's weekly salary is approximately $60.
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Unions, intersections, and complements involving 2 sets
Part A:
[tex]B\cap D[/tex] is asking for what the sets B and D have in common:
[tex]B\cap D = \{4\}[/tex]
since B and D only have 4 in common.
Now [tex](B \cap D)'[/tex] is asking for all of the things in the universal set [tex]U[/tex] that are not in [tex]B\cap D[/tex]. That's what the little tick mark on the right side means.
[tex](B \cap D)' = \{2, 3, 6, 7\}[/tex]
Part B:
[tex]B' = \{2, 3, 7\}[/tex] since those are the things not in B.
[tex]D=\{3, 4\}[/tex]
[tex]B'\cup D[/tex] is asking for all the things in either [tex]B'[/tex] or [tex]D[/tex].
[tex]B'\cup D = \{2, 3, 4, 7\}[/tex]
(We don't need to list 3 twice, even though it was in both sets. )
If 4x + 12 = 76, then x =
Answer:
x = 16
Step-by-step explanation:
subtract 12 from both sides to isolate the variable and its coefficient
4x = 64
divide both sides by 4 to get x
x = 16
Answer:
x = 16
Step-by-step explanation:
4x+12=76
Step 1: Subtract 12 from both sides.
4x + 12 - 12 = 76 - 12
4x = 64
Step 2: Divide both sides by 4.
[tex]\frac{4x}{4} = \frac{64}{4}[/tex]
x = 16
help please i don’t know what to do
Answer:
Add 3 and then multiply by 5.
Step-by-step explanation:
The problem looks like this to me:
[tex] \dfrac{m}{5} - 3 = 8 [/tex]
If this is correct, then the operations are:
Add 3 to both sides.
Multiply both sides by 5.
I don't see that answer. The picture is not very clear to me. What is the denominator of the fraction?
PLSSSS HELP ME ASAP I DONT UNDERSTAND THIS
Jon filled up the tank of his semitruck with 240 gallons of fuel and set out to deliver a shipment of vegetables. His truck uses an average of 0.15 gallons of fuel for each mile he drives. You can use a function to approximate the amount of fuel in Jon's tank after he drives x miles.
Write an equation for the function. If it is linear, write it in the form f(x)=mx+b. If it is exponential, write it in the form f(x)=a(b)^x.
Answer:
Step-by-step explanation:
Step 1: Understanding the Problem
The problem involves finding an equation to approximate the amount of fuel in Jon's semitruck after he drives x miles. Jon started with 240 gallons of fuel and his truck uses 0.15 gallons of fuel for each mile he drives.
Step 2: Writing the Equation
We know that the amount of fuel in Jon's tank decreases as he drives. So, we can write the equation as:
f(x) = 240 - 0.15x
This equation says that the amount of fuel in Jon's tank after he drives x miles is equal to 240 gallons (the amount of fuel he started with), minus 0.15 gallons for each mile he drives.
Step 3: Interpreting the Equation
The function f(x) = 240 - 0.15x is a linear equation, which means that it is a straight line on a graph. The value 240 is the y-intercept, which means that when x = 0, the y-value of the function is 240 (the amount of fuel in Jon's tank when he starts driving). The value -0.15 is the slope of the line, which tells us how much the y-value decreases for each unit increase in x (in this case, how much the fuel decreases for each mile Jon drives).
Step 4: Conclusion
So, the equation f(x) = 240 - 0.15x can be used to approximate the amount of fuel in Jon's semitruck after he drives x miles. The equation is linear and can be written in the form f(x) = mx + b, where m = -0.15 (the slope of the line) and b = 240 (the y-intercept).
Can someone help with some algebra 2 questions?
The specified radical expressions in the questions are evaluated and presented in the simplest form as follows;
(2) [tex]\sqrt[3]{x^2\cdot y^2} \cdot \sqrt[4]{x^5\cdot y^3} = \sqrt[12]{x^{23}\cdot y^{17}}[/tex]
(3) f(g(x)) = √(6·x + 1) - 5
(4) x = (15 ± √(33))/2
(5) x = 126
What is a radical expression?A radical is a mathematical expression which contains the radical expression, '√', which represent a fractional indices of the form 1/n.
(2) The specified radical expression is presented as follows;
∛(x²·y²) × [tex]\sqrt[4]{x^5 \cdot y^3}[/tex]
Expressing the above radical expression in index form, we get;
∛(x²·y²) × [tex]\sqrt[4]{x^5 \cdot y^3}[/tex] = [tex]x^{\frac{2}{3} }\times y^{\frac{2}{3} } \times x^{\frac{5}{4} } \times y^{\frac{3}{4}}[/tex]
Adding the index of like variable terms, we get;
[tex]x^{\frac{2}{3} }\times y^{\frac{2}{3} } \times x^{\frac{5}{4} } \times y^{\frac{3}{4}} = x^{\frac{2}{3} + \frac{5}{4} } \times y^{\frac{2}{3} + \frac{3}{4} }[/tex]
(2/3) + (5/4) = (2×4 + 5×3)/12 = 23/12 = 1 11/12
Therefore; [tex]x^{\frac{2}{3} + \frac{5}{4} } = x^{\frac{23}{12} }[/tex]
2/3 + 3/4 = (2 × 4 + 3 × 3)/(12) = 17/12 = 1 5/12
Therefore; [tex]y^{\frac{2}{3} + \frac{3}{4} } = y^{\frac{17}{12} }[/tex]
Which indicates that we get; [tex]x^{\frac{2}{3} + \frac{5}{4} } \times y^{\frac{2}{3} + \frac{3}{4} } = x^{\frac{23}{12} } \times y^{\frac{17}{12} }[/tex]
Therefore; ∛(x²·y²) × [tex]\sqrt[4]{x^5 \cdot y^3}[/tex] = [tex]x^{\frac{23}{12} } \times y^{\frac{17}{12} }[/tex]
In radical form, we get; [tex]x^{\frac{23}{12} } \times y^{\frac{17}{12} } = \sqrt[12]{x^{23} \cdot y^{17}}[/tex](3) The functions, f(x) = √(3·x + 4) - 5, g(x) = (2·x - 1)
The composite function, f(g(x)) can be found as follows;
f(g(x)) = √(3·g(x) + 4) - 5 = √(3·(2·x - 1) + 4) - 5
f(g(x)) = √(3·(2·x - 1) + 4) - 5 = √((6·x - 3) + 4) - 5 = √(6·x + 1) - 5
The composite function, f(g(x)) is therefore; f(g(x)) = √(6·x + 1) - 5(4) (√(x - 1)) = x - 7
Squaring both sides, we get;
(√(x - 1))² = (x - 7)²
(√(x - 1))² = x - 1(x - 7)² = x² - 14·x + 49Therefore;
(√(x - 1))² = x - 1 = (x - 7)² = x² - 14·x + 49
x - 1 = x² - 14·x + 49
x² - 14·x + 49 - (x - 1) = 0
x² - 15·x + 48 = 0
The quadratic formula can be used to solve the above equation to get;
x = (-(-15) ± √((-15)² - 4×1×48))/(2 × 1) = (15 ± √(33))/2
x = (15 ± √(33))/2(5) 2·∛(x - 1) + 6 = 16
2·∛(x - 1) + 6 = 16
Subtracting 6 from both sides, we get;
2·∛(x - 1) + 6 - 6 = 16 - 6 = 10
2·∛(x - 1) = 10
∛(x - 1) = 10/2 = 5
∛(x - 1) = 5
∛(x - 1)^3 = 5^3
∛(x - 1)^3 = x - 1
5^3 = 125
∛(x - 1)^3 = x - 1 = 125
x = 125 + 1 = 126
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The lengths of the three sides of a triangle are x + 15 , 2x + 15 and x + 12 (where x cannot equal zero). What is the perimeter of the triangle? use the drop-down menu to complete the answer.
Answer:
4x + 42
Step-by-step explanation:
[tex]\text{Perimeter}=(x+15)+(2x+15)+(x+12)=4x+42[/tex]
CAN SOMEONE HELP WITH THESE QUESTIONS?✨
The numeric value of the marginal revenue at 33 units will be $336.
How to calculate the marginal revenueThe sum of the units sold times the price per unit is the revenue. Multiply the output level by the pricing function to get the revenue function.
Revenue function is R(q) = - 8q ^ 2 + 600q
Differentiate with respect to q
R^ prime (q) = - 8(2q) + 600(1)
R' (q)=-16q+600 ...(1)
substitute q = 33 in equation
MR(113) = - 8(33) + 600
=-264 + 600
MR (113)= $336 per unit
The marginal revenue is $336.
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88
Stephen is comparing two mortgage options for his $80, 000 mortgage.
Mortgage A: 15 years at 4.5% with monthly payments of $611.99
Mortgage B: 30 years at 4% with monthly payments of $381.93
How much is the total payback for each mortgage option?
Provide your answer below:
Mortgage A =$
Mortgage B=$
The mortgage of A is $110158.2.
The mortgage of B is $137494.8.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
Mortgage A:
15 years at 4.5% with monthly payments of $611.99.
15 years = 15 x 12 = 180 months
Total paycheck.
= 180 x 611.99
= $110158.2
Mortgage B:
30 years at 4% with monthly payments of $381.93
30 years = 360 months
Total paycheck.
= 360 x 381.93
= $137494.8
Thus,
Mortgage A = $110158.2
Mortgage B = $137494.8
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A well of diameter 5 m is dug 24 m deep. The earth taken out of it has been spread evenly all around it in the shape of a circular ring of width 3 m to form an embankment. Find the height of the embankment.
Answer: To find the height of the embankment, we need to first find the volume of the well and then the volume of the embankment.
Volume of the well = πr^2h = π * (d/2)^2 * h = π * (5/2)^2 * 24 = 157.08 cubic meters
Volume of the embankment = π * (R^2 - r^2) * h, where R is the outer radius of the embankment and r is the inner radius.
Outer radius of the embankment = (5 + 3)/2 = 4 m
Inner radius of the embankment = (5 - 3)/2 = 1 m
Volume of the embankment = π * (4^2 - 1^2) * h = π * 15 * h
We know that the volume of the well is equal to the volume of the embankment, so we can write:
157.08 = π * 15 * h
Solving for h, we get:
h = 157.08 / (π * 15) = 157.08 / 47.12 ≈ 3.32 m
So, the height of the embankment is approximately 3.32 meters.
Step-by-step explanation:
Solve by elimination. {4x+2y=−6
{3x−2y=13
A. (−2,−5)
B. (1,−5)
C. infinite number of solutions
D. (0,−3)
Answer:
[B]. (1,-5)
Step-by-step explanation:
Given:
[tex]\begin{bmatrix}4x+2y=-6\\ 3x-2y=13\end{bmatrix}[/tex]
Solve:
[tex]\begin{bmatrix}4x+2y=-6\\ 3x-2y=13\end{bmatrix}[/tex] Since 2y - 2y = 0 we take that away now we have;
[tex]4x=-6\\3x=13[/tex] Add 4x + 3x = 7x
[tex]\frac{7x}{7} =\frac{7}{7}[/tex] Divide both sides by 7.
[tex]x=1[/tex]
Now substitute x to find y.
[tex]4(1)+2y=-6[/tex]
[tex]4 + 2y =-6[/tex] Add 6 to the other side.
[tex]10 = 2y[/tex] Divide both sides by 2.
[tex]\frac{10}{2} =\frac{2y}{2}[/tex]
[tex]y = 5[/tex]
Hence, the answer is [B]. (1,-5)
RevyBreeze
Please help me!! Quiz due 11:59pm - Match each scatterplot shown below with one of the four specified correlations
I want the answer pleaseee
Answer:
8.6 m
Step-by-step explanation:
DE = 2 7/10 m
= 2 + 7/10
= 2 + 0.7
DE = 2.7 m
EF = 5 9/10 m
= 5 + 9/10
= 5 + 0.9
EF = 5.9 m
DF = DE + EF
= 2.7 + 5.9
= 8.6 m
Solve 2y-k=b+5 for y
Answer:
y=b+5+k/2
Step-by-step explanation:
2y-k=b+5
2y=b+5+k
2y/2=b+5+k/2
y=b+5+k/2
Answer:
y = b+ 5 + k/2.
Step-by-step explanation:
2y - k = b + 5
the subject for y
[tex]2y - k = b + 5 \\ 2y = b + 5 + k \\ \frac{2y}{2} = \frac{b + 5 + k}{2} \\ y = \frac{b + 5 + k}{2}. [/tex]
A small kitchen sink is 14in x 16in x 6in = 3584 cubic inches. If your water faucet in the kitchen is leaking 1 drop of water per second (volume of a typical drop is 0.05 ml ≈ 0.003 cubic inches), how long would it take for a clogged sink to fill and start overflowing. Write your answer in days.
A more accurate value would be 13.8271643518519
Round it however you need to.
======================================================
Explanation:
1 day = 24 hours
1 hour = 60 minutes
1 minute = 60 seconds
Let's see how many seconds there are in a day.
[tex]1 \text{ day} = (1 \text{ day})*\frac{24 \text{ hrs}}{1 \text{ day}}*\frac{60 \text{ min}}{1 \text{ hr}}*\frac{60 \text{ sec}}{1 \text{ min}}\\\\=\frac{24*60*60}{1*1*1}\text{ sec}\\\\=86,400\text{ sec}\\[/tex]
I set up those fractions so that the units "day", "hours", "minutes" cancel out. The only unit left over is "seconds".
There are exactly 86,400 seconds in 1 day.
This leads to the fact the sink fills up at a rate of 86,400 drops per day, since the leak rate is 1 drop per second.
----------
1 drop = 0.003 cubic inches approximately
x of those drops give a volume of 0.003x cubic inches, where x is some positive whole number. Set this equal to the volume of the sink and solve for x.
0.003x = 3584
x = 3584/0.003
x = 1,194,666.66666667 approximately
Round up to the nearest whole number to get 1,194,667
The sink starts to overflow when we have 1,194,667 drops of water in it.
Divide this over 86,400 mentioned earlier.
(1,194,667)/(86,400) = 13.8271643518519 approximately.
Round that however you need to. If for instance you round to 3 decimal places, then it would be 13.827
1 out of 3 adults has worked in the restaurant industry at some point during his or her life. In an office of 81 workers, how many of these people would you expect to have worked in the restaurant industry at some point?
Answer:
Step-by-step explanation:
(1/3) x 81=27 people
a. Draw a tree diagram for the results from tossing a fair two-sided coin (H, T) four times
b. How many stages are there in the tree diagram?
c. List all the possible outcomes (the sample space).
d. How many outcomes are there in the sample space?
▪ You must show ALL of your work in order to receive full credit.
Answer:
Step-by-step explanation:
a) The tree diagram for the results of tossing a fair two-sided coin four times would look like this:
(1)
/ \
(H) (T)
/ \ / \
(2-H) (2-T) (2-H) (2-T)
/ \ / \ /
(3-HH) (3-HT) (3-TH) (3-TT)
b) There are four stages in the tree diagram.
c) The possible outcomes (the sample space) would be all the paths from the root of the tree to the leaves, which represent the results of tossing the coin four times. The possible outcomes are:
HHHHH
HHHTT
HHTHT
HHTTH
HTTHH
HTHHT
HTHTH
THHHH
THHTT
THTHT
TTHHT
TTHTH
TTTTT
d) There are 2^4 = 16 outcomes in the sample space.
ALSO:
a) Draw the Tree Diagram
Start with a root node labeled with the first toss (toss 1)
From the root node, draw two branches, one labeled with "Heads" (H) and the other with "Tails" (T) to represent the possible outcomes of the first toss.
Repeat this process for each of the next tosses (toss 2, 3, and 4)
Continue until all the possible outcomes of the four tosses have been represented.
Here is an example of the tree diagram:
(1)
/
(H) (T)
/ \ /
(2-H) (2-T) (2-H) (2-T)
/ \ / \ /
(3-HH) (3-HT) (3-TH) (3-TT)
/ \ / \ /
(4-HHH) (4-HHT) (4-THH) (4-TTT)
b) Number of Stages in the Tree Diagram
There are four stages in the tree diagram, one for each toss of the coin.
c) Possible Outcomes (Sample Space)
The possible outcomes (sample space) are all the paths from the root of the tree to the leaves, which represent the results of tossing the coin four times.
There are 16 possible outcomes in the sample space, as shown below:
HHHHH
HHHTT
HHTHT
HHTTH
HTTHH
HTHHT
HTHTH
THHHH
THHTT
THTHT
TTHHT
TTHTH
TTTHH
TTTTH
TTTTT
d) Number of Outcomes in the Sample Space
There are 2^4 = 16 outcomes in the sample space.
This is because for each toss, there are two possible outcomes (Heads or Tails), and since there are four tosses, there are 2 * 2 * 2 * 2 = 16 possible combinations.
ALSO:
a) Draw the Tree Diagram
Start with a root node labeled with the first toss (toss 1).
From the root node, draw two branches, one labeled with "Heads" (H) and the other with "Tails" (T) to represent the possible outcomes of the first toss.
Repeat this process for each of the next tosses (toss 2, 3, and 4).
Continue until all the possible outcomes of the four tosses have been represented.
Here is an example of the tree diagram:
(1)
/
(H) (T)
/ \ /
(2-H) (2-T) (2-H) (2-T)
/ \ / \ /
(3-HH) (3-HT) (3-TH) (3-TT)
/ \ / \ /
(4-HHH) (4-HHT) (4-THH) (4-TTT)
b) Number of Stages in the Tree Diagram
There are four stages in the tree diagram, one for each toss of the coin.
c) Possible Outcomes (Sample Space)
The possible outcomes (sample space) are all the paths from the root of the tree to the leaves, which represent the results of tossing the coin four times.
There are 16 possible outcomes in the sample space, as shown below:
HHHHH
HHHTT
HHTHT
HHTTH
HTTHH
HTHHT
HTHTH
THHHH
THHTT
THTHT
TTHHT
TTHTH
TTTHH
TTTTH
TTTTT
d) Number of Outcomes in the Sample Space
There are 2^4 = 16 outcomes in the sample space.
This is because for each toss, there are two possible outcomes (Heads or Tails), and since there are four tosses, there are 2 * 2 * 2 * 2 = 16 possible combinations.
I hope this step-by-step explanation with the diagram helps! Let me know if you need further clarification.
Part D
What do the factors in the factored form represent?
BIUX² X₂ 15px
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Space used (includes formatting): 0/ 15000
AV
The factors in the factored form represents the value of the function when x = 0.
What are Quadratic Functions?Quadratic functions are defined as the polynomial functions consisting of variables and exponents with the degree of the variable being 2.
The general form of a quadratic function is f(x) = ax² + b x + c.
Given is a quadratic function,
y = x² + 2x - 15
This can be factorized as (x + p)(x + q) such that p × q = -15 and p + q = 2.
Two such numbers are -3 and 5.
-3 × 5 = -15 and -3 + 5 = 2
y = x² + 2x - 15
y = (x - 3) (x + 5)
Factors are x - 3 and x + 5
Here, the numbers 3 and -5 represents the input values of the function when the output value or the value of the function equals 0 or they are the x intercepts of the function.
Hence the factors in the factored form are the x intercepts of the function.
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The complete question is as follows :
What do the factors in the factored form represent?
y = x² + 2x - 15
Jenny can jog twice as fast as she can walk. She was able to jog the first 9.5 miles to
her grandmother's house, but then she tired and walked the remaining 2.5 miles. If the
total trip took 1.45 hours, then what was her average jogging speed?
Jenny's average jogging speed in the distance covered is; 10 miles/hr
How to solve Algebra Word problems?
Let x miles/hr be the speed that Jenny walks at
Then, 2x miles/hr is the speed that Jenny runs at
She jogs for 9.5 miles
2x miles = 1 hours
9.5 miles = a hours
a = 9.5/2x hours
She walks for 2.5 miles
x miles = 1 hour
2.5 miles = b
b = 2.5/x hours
Thus;
(9.5/2x) + (2.5)/x = 1.45
Multiply through by 2x to get;
9.5 + 5 = 2.9x
14.5/2.9 = x
x = 5 miles/hr
Jogging speed = 2 * 5 = 10 miles/hr
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What is the solution to the equation?
√x + 2 = 1
O A. 1
OB. 4
O C. 1 and 4
OD. no solution
Answer:
The solution of the equation is B. 4
Step-by-step explanation:
√x + 2 = x
√x = x - 2
(√x)² = (x-2)²
x = (x-2) (x-2)
x = x² - 4x + 4
x moves to the right
0 = x² - 4x - x + 4
0 = x² - 5x + 4
0 = (x-1) and (x-4)
x-1 = 0 x-4 = 0
x = 1 (not) x = 4
So, the solution to the equation is B. 4
13) A theater has 38 rows of seats. The first row has 25 seats, the second
row has 29 seats, the third row has 33 seats, and so on.
What is the total number of seats in the theater?
O3,762
O3,838
O 7,524
O 7,676
Answer:
Step-by-step explanation:
To find the total number of seats in the theater, we can use the formula for the sum of an arithmetic series, which is given by:
S = n/2 * (a_1 + a_n)
where n is the number of terms in the series, a_1 is the first term, and a_n is the last term.
In this case, the first term is 25 seats and the last term is 25 + (38-1) * 4 seats (since the number of seats in each row increases by 4 each time). So, we have:
n = 38 (the number of rows)
a_1 = 25
a_n = 25 + (38-1) * 4 = 25 + 37 * 4 = 25 + 148 = 173
Now, we can substitute these values into the formula:
S = n/2 * (a_1 + a_n) = 38/2 * (25 + 173) = 19 * 198 = 3,762
So, the total number of seats in the theater is 3,762, which corresponds to option O3,762.
Sariah conducted a study on the effect that listening to music has on memory recall.
As part of her study, she compiled the following data:
Hours Spent
Listening to Music
0-2.5
2.5-5
5-7.5
7.5 -10
10- 12.5
Number of
Students
22
15
3
3
1
Find the mean number of hours the students she surveyed spent listening to music.
Enter your answer as a whole number or as a decimal rounded to the nearest tenth.
The mean number of hours the students spent listening to music is 31.25 hours.
What do you mean by Mean?In statistics, the mean is a measure of central tendency of a set of data. It is also referred to as the arithmetic mean and is calculated by adding up all the values in the data set and dividing by the total number of values.
Mean = (sum of all values) / (number of values)
For example, suppose we have the following set of data: 5, 7, 9, 11, 13. To find the mean, we add up all the values and divide by the total number of values, which is 5 in this case:
Mean = 9
Therefore, the mean of this data set is 9.
The mean is a commonly used measure of central tendency because it takes into account all the values in the data set and is sensitive to changes in the data. However, it can be affected by outliers or extreme values in the data set, which can skew the results.
We can find the mean number of hours spent listening to music using the formula:
mean = (sum of (midpoint of each class) * (frequency of each class)) / (sum of frequencies)
The midpoint of each class can be found by taking the average of the upper and lower class limits.
Using this formula, we get:
mean = ((1.25 + 3.75 + 6.25 + 8.75 + 11.25) * (22 + 15 + 3 + 3 + 1)) / (22 + 15 + 3 + 3 + 1)
mean = (31.25 * 44) / 44
mean = 31.25
Therefore, the mean number of hours the students spent listening to music is 31.25 hours.
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triangle ABC has side lengths 42, 21, and 35 units. The shortest side of a triangle similar to
triangle ABC is 9 units long. Find the other lengths of the triangle.
Answer:
Step-by-step explanation:
Using the ratio of corresponding side lengths, we have:
x/42 = 9/35
y/21 = 9/35
z/35 = 9/35
Solving for x, y, and z:
x = (9/35) * 42 = 14
y = (9/35) * 21 = 7
z = 9
So the other two sides of the smaller triangle are 14 and 7 units.
Please help fast!! What is the domain of the relation?
A: (-5,0,3,4)
B: (-4,-1,0,1,3)
C: (-5,-2,0,1,4)
D: (-5,-4,-2,-1,0,1,3,4)
Look at the picture below
The correct option is A {-5, 0, 3, 4}.
What do you mean by Domain?In mathematics, the domain of a function is the set of all possible input values (independent variable) for which the function is defined. In other words, the domain is the set of values that we can substitute for the independent variable in a function to produce a meaningful output.
For example, consider the function f(x) = 2x. Here, we can substitute any real number for x and get a meaningful output. Therefore, the domain of this function is all real numbers, or (-∞, ∞). However, if we consider the function g(x) = 1/x, we can see that we cannot substitute 0 for x because division by 0 is undefined. Therefore, the domain of this function is all real numbers except 0, or (-∞, 0) U (0, ∞).
The domain of a relation is the set of all possible values for the independent variable (x) for which there exists a corresponding value of the dependent variable (y). In this case, the given coordinates are (1,3), (4,1), and (-5,-4).
The domain of the relation would be the set of x-values that correspond to the given coordinates. So, the domain of this relation is {-5, 1, 4}.
Therefore, the correct answer is A: {-5, 0, 3, 4}.
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the division or the multiplication property of equality to solve 1,145 = y
-——
224
Answer:
26.it is all about thinking
The height of two buildings is 34 m and 29 m respectively. If the distance between the two buildings is 12 m, find the distance between their tops.
Answer: To find the distance between the tops of two buildings, we first need to find the horizontal distance between the two buildings. This distance can be found using the Pythagorean theorem.
Let's call the horizontal distance between the two buildings "d".
d^2 = 12^2 + (34 - 29)^2
d^2 = 144 + 25
d^2 = 169
d = 13
So, the horizontal distance between the two buildings is 13 meters.
To find the distance between their tops, we simply add the height of each building:
distance = 34 + 29 = 63 meters
So, the distance between the tops of the two buildings is 63 meters.
Step-by-step explanation:
A population mean is normally distributed with a mean of 56 and a standard deviation of 12.
The mean of the sampling distribution (p) and The standard error of the mean (o) are 56 and 2 respectively.
What is normal distribution?A probability distribution that is symmetric about the mean is the normal distribution, sometimes referred to as the Gaussian distribution. It demonstrates that data that are close to the mean occur more frequently than data that are far from the mean.
According to question:(a) The mean of the sampling distribution (p) is equal to the population mean, which is 56.
(b) The standard error of the mean (o) is calculated as the standard deviation of the population divided by the square root of the sample size. So for a sample of 36 participants:
o = 12 / √36 = 2
(c) The distribution of the sample means (p) will be approximately normal with a mean of 56 and a standard deviation of 2. To sketch this distribution with M ± 3 SEM, we would plot a normal distribution with mean 56 and standard deviation 2, and shade the region that is 3 standard errors away from the mean on either side.
This region would capture approximately 99.7% of the data if the samples were selected randomly and independently from the population.
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Which of the following sequences are geometric?
Check all that apply.
Answer:
A and C are the correct answers
Step-by-step explanation:
Answer:
And C is the answer to the question
Ten times the sum of a number and eight is -10. What is the number?
Answer:
Step-by-step explanation:
Answer:
The number is -10.4
Explanation:
Assume that the number we are looking for is x.
Now, we want to get 10 times te sum of half the number and 6 and equate this expression to 8. Then we can solve for x
Let's take this step by step:
half the number is 0.5x
the sum of half the number and 6 is 0.5x + 6
10 times the sum of half the number and 6 is 10(0.5x +6)
10 times the sum of half the number and 6 equals 8 is 10(0.5x+6) = 8
Now we can solve for x as follows:
10(0.5x + 6) = 8
5x + 60 = 8
5x = 8 - 60
5x = -52
x = -52/5
x = -10.4
Hope this helps :)
verify the identity by converting the left side into sines and cosines:
cotx-tanx = secx(cscx - 2sinx)
Answer: To verify the identity, we need to convert both sides into sines and cosines and see if they are equal.
Starting with the left side:
cotx = 1/tanx
So,
cotx - tanx = 1/tanx - tanx
Using the identity tan^2x = sec^2x - 1, we get
cotx - tanx = (sec^2x - 1) / tanx
Expanding the right side using the definition of cscx and sinx, we get:
cotx - tanx = secx(1/sinx - 2sinx)
So,
cotx - tanx = secx(cscx - 2sinx)
Since both sides are equal, we can conclude that the identity is verified.
Step-by-step explanation:
