Answer:
158,760$
Step-by-step explanation:
120,000$ + 40%=168,000$-5.5%=158,760$
If a one-person household spends an average of $52 per week on groceries, find the maximum and minimum amounts spent per week for the middle 50% of one-person households. Assume the standard deviation is $14 and the variable is normally distributed. Round your answers to the nearest hundredth.Minimum: $Maximum: $
Solution
For this case we have the following random variable:
X= amount spend on average for groceries by one person
And we have the following properties:
mean= 52
sd= 14
The distribution of the variable is normal
We can find the middle 50% using a graph like this one:
We can find two quantiles from the normal distribution that accumulates 25% of the area on each tail of the distribution and we have:
Z= -0.674 and 0.674
Now we can use the z score formula given by:
[tex]z=\frac{x-\mu}{\sigma},x=\mu\pm z\cdot\sigma[/tex]So then we have:
Minimum= 52 - 0.674*14 = 42.56
Minimum= 52 + 0.674*14 = 61.44
Evaluate the expression 14-16+8+12\3
Let's evaluate the given expression:
[tex]\text{ 14 - 16 + 8 + }\frac{\text{ 12}}{\text{ 3}}[/tex][tex]=\text{ 14 - 16 + 8 + 4}[/tex][tex]\text{ = -2 + 8 + 4}[/tex][tex]\text{ = -2 + 12}[/tex][tex]\text{ = 1}0[/tex]Therefore, the answer is 10.
A storage tank has a height of 10 feet and a diameter of 6 feet. The tank is half filled with oil. 6 ft Approximately how much oil, in cubic feet, is currently in the cylindrical tank? A 90 ft B 360r ft3 C 455 Ft D 180rt ft3
ok
Volume of a cilinder = pi*r^2*h
Substitution
Volume of a cilinder = 3.14*3^2* 6
Simplification
Volume of a cylinder = 170 ft^3
Approximately, there are 180 ft^3 of oil
Y varies inversely with the square of x. When x=4, then y=3. Find y when x=2
Answer:
y = 6
Step-by-step explanation:
y= [tex]\frac{1}{x}[/tex]
3 = [tex]\frac{1}{4}[/tex]k Solve for k by multiplying both sides by 4
12 = k
y = [tex]\frac{1}{2}[/tex](12)
y = [tex]\frac{12}{2}[/tex]
y= 6
Prove that 3x + y = 7 + y and 3(x + y) = 2 + 3x are perpendicular
Answer:
Since one line is vertical, and one line is horizontal, the lines are perpendicular.
Step-by-step explanation:
The product of the slopes of perpendicular lines is -1.
We find the slopes of the 2 lines and multiply them together.
If the product equals -1, then the lines are perpendicular.
To find the slopes of the lines, we write each equation in the y = mx + b form, where m is the slope. In other words, we solve each equation for y.
3x + y = 7 + y
Subtract y from both sides.
3x = 7
x = 7/3
This is not the y = mx + b form since there is no y in the equation. A line with equation x = k, where k is a number, is a vertical line that passes through the point (k, 0), and the x-coordinate of all points on the line is k.
3(x + y) = 2 + 3x
3x + 3y = 2 + 3x
Subtract 3x from both sides.
3y = 2
y = 2/3
y = 0x + 2/3
Slope = m = 0
A line with 0 slope is a horizontal line.
Since one line is vertical, and one line is horizontal, the lines are perpendicular.
Find the area of the circle pictured above. Round your answer to the nearest tenth in^2
Area of the circle is 28.3 in^2
Here, we want to find the area of the circle
Mathematically, the area is;
[tex]\begin{gathered} \text{Area of circle = }\pi\text{ }\times r^2 \\ But\text{ r = }\frac{d}{2} \\ \\ Area\text{ of circle = }\frac{\pi\text{ }\times d^2}{4} \\ \\ from\text{ the question, d = 6 inches} \\ \pi\text{ = }\frac{22}{7} \\ \\ \\ \text{Area of circle = }\frac{\frac{22}{7\text{ }}\text{ }\times6^2}{4} \\ \\ \text{Area of circle = }\frac{22\text{ }\times\text{ 36}}{28} \\ \\ \text{Area of circle = 28.2857} \\ \\ \text{Area of circle = 28.3 in\textasciicircum{}2} \end{gathered}[/tex]A mother need 6 pieces of ribbon, with lengths of 25 cm each, for her daughter's hair. If the ribbon is only sold per full meter, how many meters does she need to buy?
Given:
The length of each ribbon is 25 cm.
The number of ribbon need by mother is 6.
Explanation:
Determine the length of ribbon for daughter's hair.
[tex]\begin{gathered} 25\cdot6=150\text{ cm} \\ =1.5\text{ m} \end{gathered}[/tex]Since length is in decimal so we need to find multiple of 25 such that it is more than 150 and multiple of 100.
The multiples of 25 are 25,50, 75, 100, 125, 150, 175, 200, ...
Since 200 is more than 150 and multiple of 100 also.
Determine the length of 200 cm in terms of meters.
[tex]200\text{ cm}\cdot\frac{1\text{ m}}{100\text{ cm}}=2\text{ m}[/tex]So mother needs to buy 2 meters of ribbon.
Answer: 2 meters
Find the probability.When a single card is drawn from an ordinary 52-card deck, find the probability of getting a heart.A) 1/13B) 1/4C) 1/26D) 1/52
The probability of getting a red 7 would be; 1/26
What is the probability?Probability refers to a possibility that deals with the occurrence of random events.
The probability of all the events occurring need to be 1.
Given that the total number of cards is 52.
WE are asked to find the he probability of getting a red 7
Since there are 2 red 7 cards in the deck of cards.
So, the number of favourable outcomes would be 2.
n (E) = 2
The probability
P(E) = n (E) /n (S)
Therefore, the probability of getting a red 7 will be;
P(E) = n (E) /n (S)
P(E) = 2/52
P(E) = 1/26
Hence, The probability of getting a red 7 would be; 1/26
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A number when rounded to 3 decimal places, is equal to
0.029
Find the upper and lower bound of
The number
The ratio of boys to girls in Janice's classroom is 3:5, and there are a total of 32 students in the class. Using completesentences, explain how you could draw a tape diagram to represent this situation. In your answer, draw a diagramand make sure to include what quantity each bar represents.
Teh ratio of boys to girls in JAnice's classroom is 3:5
Total number of students 32
Let the ratio constant is K
So,
The equation will be
3K + 5K=32
8K=32
K=32/8
K=4
So,
the boys will be
4 + 4 + 4 =3K =12
The number of girls will be :
4 + 4 + 4 + 4 + 4 = 5K =20
Which of the following ordered pairs represent a direct variation. Find the missing value. 1. (32, 80) and (x, 100) x = _____ 2. (-28,-7) and (20, y) y = _____
When having an ordered pair, we say they are in direct variation if the quotient:
[tex]\frac{y}{x}[/tex]is constant. For case 1 we have:
[tex]\frac{80}{32}=\frac{100}{x}[/tex]we can solve for "x" by multiplying by "x" on both sides:
[tex]\frac{x80}{32}=100[/tex]Now we multiply by 32/80 on both sides:
[tex]x=\frac{100\times32}{80}[/tex]Solving the operations we get:
[tex]x=40[/tex]For case 2 we have:
[tex]-\frac{7}{-28}=\frac{y}{20}[/tex]Now we solve for "y" by multiplying by 20 on both sides:
[tex]\frac{-7\times20}{-28}=y[/tex]Solving the operations:
[tex]y=5[/tex]Latoya opened a savings account and made an intial deposit. After the intial deposit, she added money into the account each week she added the same amount each week with out any withdrawals after the forth week she had $450 by the ninth week she had $825 what was latoya's intial deposit?
She made an initial deposit that we will call "D", as it is one of the unknowns.
We know that she made a weekly deposit (lets call this amount "w").
After 4 weeks she had $450 in the account balance and this is the sum of the initial deposit and 4 weekly deposits, so we can write:
[tex]D+4w=450[/tex]At the ninth week she had $825, that correspond to the initial deposit and 9 weekly deposits. This can be written as:
[tex]D+9w=825[/tex]We have a system of linear equations that we will solve by elimination: we will substract the first equation from the second and then find w.
[tex]\begin{gathered} (D+9w)-(D+4w)=825-450 \\ 5w=375 \\ w=\frac{375}{5} \\ w=75 \end{gathered}[/tex]Now that we know "w", we can calculate D with any of the two equations:
[tex]\begin{gathered} D+4w=450 \\ D+4\cdot75=450 \\ D+300=450 \\ D=450-300 \\ D=150 \end{gathered}[/tex]Answer: the initial deposit was $150.
The Wilsons want to tile their kitchen floor. The floor is 12 feet by 15 feet. The tiles are nine-inch squares.
12 feet = _____ inches
15 feet = _____ inches
Total square inches of the floor = ______ square inches
One tile = _____ square inches
Total number of tiles needed =______ tiles
The number of tiles required to cover the floor is 2880 tiles.
What is the number of Tiles Needed?To solve this problem, we can find the number of tiles by calculating the area of a rectangle:
We have to convert the dimensions from feet to inches will be
1 feet = 12 inches
12 feet = 12 * 12 = 144in
15 feet = 12 * 15 = 180in
The area of the rectangle can be calculated as:
A = l * w
A = 180 * 144
A = 25920in²
The tiles are 9 squared inches, we can divide the area by 9 to find the number of tiles needed:
25920/9= 2880
Hence, The number of tiles needed will be 2880 tiles
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solve for g: g - 0.6 < 3.172. ,part c: in one paragraph explain ur work in parts a and b
Explanation
[tex]g-0.6\leq3.172[/tex]
Step 1
To solve the inequality means to find a range, or ranges, of values that an unknown g can take and still satisfy the inequality.
so
[tex]\begin{gathered} g-0.6\leq3.172 \\ \text{add 0.6 in both sides} \\ g-0.6+0.6\leq3.172+0.6 \\ g\leq3.772 \end{gathered}[/tex]it means the solution is the set of values equal or smaller than 3.772,so
Part A:
[tex]g\leq3.772[/tex]Step 2
Part B:the graph of the inequality looks like a marked line in the number line, from3.772 to negative infinite, as the symbol is smaller or equal, the number3.772 is part of the set , so we use a filled circle
Step 3
in step 1 we used the addition property of inequality to isolate x, then in step 2 we draw the set solution .
I hope this helps you
hwlp
The length of a rectangle is 6 feet more than twice the width. If the perimeter is 132 feet, find the dimensions.
f(t)= 2t/3 For what value of t is f(x)=64?
We are given the following function
[tex]f(t)=\frac{2t}{3}[/tex]We are asked to find out the value of t which results in f(t) = 64
Let us substitute f(t) = 64 into the above function and solve for t
[tex]\begin{gathered} f(t)=\frac{2t}{3} \\ 64=\frac{2t}{3} \\ 3\cdot64=2t \\ 192=2t \\ \frac{192}{2}=t \\ 96=t \\ t=96 \end{gathered}[/tex]Therefore, the value of t is 96
how to solve for x and round it up to tenth
Answer:
4.6
Explanation:
The diagram shown is a right triangle having the following sides;
Opposite = 17
Adjacent = x
Angle of elevation = 75 degrees
Using SOH CAH TOA identity
Tan theta = opposite/adjacent
Tan 75 = 17/x
x = 17/tan 75
x = 17/3.73205
x = 4.6
Hence the value of x to the nearest tenth is 4.6
Museum entrance tickets cost $25. Then each special exhibit a person wishes to visit costs an additional $4. Write an expression that represents the cost to enter the museum and visit any number of special exhibits. Then find the cost for a person to enter and visit three exhibits.
ANSWER
T = 4x + 25;
T = $37
EXPLANATION
Let the number of special exhibits to be visited be x.
The cost of the musuem entrance ticket is $25 and each special exhibit costs an additional $4.
This means that the cost of cisiting x additional exhibits is:
4 * x = $4x
Therefore, the total cost to enter the musuem and visit any number of special exhibits is:
T = 4x + 25
That is the expression that represents the total cost.
If a person wants to visit three exhibits, it means that:
x = 3
Therefore, the total cost, T, is:
T = 4(3) + 25
T = 12 + 25
T = $37
That is the total cost to enter and visit three exhibits.
There are 9 athletes at a track meet. How many different ways can they finish first'orsecond?
For the first place, we have 9 different options from the athletes, then for the second place, we would only have 8 different options, therefore, there are 9x8=72 ways they can finish first or second
help meeeeeee pleaseee !!!!
So, we are writing a function. c(x) is the manufacturing costs, and x is the amount of bikes manufactured. The y-intercept is 1908 because when no bikes are manufactured it still costs 1908 to run the factory. The slope is 75 because it costs $75 to create a bike. So, y = mx + b, where m is the slope and b is the y-intercept is:
c(x) = 75x + 1908
if you have 1/4 cup how many eighths do you have
MATHEMATICALLY WE SAY
BE AWARE THAT EIGHTHS IS
[tex] \frac{1}{8} [/tex]
THEY ARE ASKING HOW MANY
[tex] \frac{1}{8} [/tex]
ARE THERE IN
[tex] \frac{1}{4} [/tex]
[tex] = \frac{1}{4} \div \frac{1}{8} \\ = \frac{1}{4} \times \frac{8}{1} \\ = \frac{8}{4} \\ = 2[/tex]
YOU HAVE 2 .Select all of the expressions equivalent to (m + m)(-4.2m).
Answer choices
2m(-4.2m)
-4.2m³
-2.2m²
4.2m²+4.2m²
-4.2m²+(-4.2m²)
-8.4m²
Answer:
2m(-4.2m)
-4.2[tex]m^{2}[/tex] + - (4.2[tex]m^{2}[/tex])
-8.4[tex]m^{2}[/tex]
Step-by-step explanation:
2m(-4.2m) = -8.4 [tex]m^{2}[/tex]
-4.2 [tex]m^{2}[/tex] + (-4.2 [tex]m^{2}[/tex]) = 8.4[tex]m^{2}[/tex]
What is the decay percentage rate of t h(x) = 20(175)” ?A75%oB.75%Oс25%0D.25%
Given the function :
[tex]h(x)=20(0.75)^x[/tex]So, the decay percentage rate :
[tex]\frac{\triangle h}{\triangle x}=0.75[/tex]convert the decimal to percentage: 0.75 = 75%
So, the answer is option A) 75%
Use the graph to answer the following questions.how much does the cost of cheese and crease for each ounce Milan buys? What is the slope of the line?
The graph given is a linear graph,
so that means that the cost of cheese is linearly related to the weight of cheese bought.
The increase in the cost of cheese increase for each ounce Milan buys is, therefore, the slope of the graph;
to find the slope of the graph, we use any two points on the line; i'll be using (4,96) and (2,48)
[tex]\text{slope}=\frac{96-48}{4-2}=\frac{48}{2}=24[/tex]This means that the cost of cheese increases by 24 cents for each ounce Milan buys.
1-9.b.C.GROWING, GROWING, GROWING, PART ONECopy the tile pattern shown below onto graph paper.Figure 2Figure 3Figure 4Draw the 1st, 5th, and 6th figures on your paper.How is the pattern changing?What would the 100th figure look like? How many tiles would it have?How can you justify your prediction?
Answer:
Explanation:
a) To draw the 1st , 5th and 6th figures, we need to know the count of squares
For the first figure, we would have 3 squares
The fifth figure would have 35 squares
The sixth figure will have 48 squares
The way to get this is to add 2 to the odd number difference between the last two terms
b) Here, we want to know how the pattern is changing
From the information provided, the first pattern has 8 squares, the second has
15 squares while the last has 24 squares
We can have a formula as follows:
[tex][/tex]PLEASE HURRY
What is an equivalent expression for −12(8a − 7b) + 8(4x + 3y)?
Answer:
-96a + 84b + 32x + 24y
Step-by-step explanation:
if you simplify an answer then it is equivilent to the beggining equation
hope this helped:)
The circumference of a circle is 67 inches. What is the area in
terms of π ?
A rectangle has a length that is 3 more than twice the width. Its perimeter is 96 inches. Which equation models this? A. 2w + 3 = 96 B. w + 2m + 3 = 96 C. 2(w) + 2(w + 3) = 96 D. 2(w) + 2(2w + 3) = 96
ANSWER
EXPLANATION
Let the length of the rectangle be L.
Let the width of the rectangle be w.
The length of the rectangle is 3 more than twice the width.
This means that:
L = 3 + (2 * w)
L = 2w + 3
The perimeter of a rectangle is given as:
P = 2w + 2L
The perimeter of the rectangle is 96 inches. This means that:
96 = 2L + 2w
Recall that: L = 2w + 3
=> 96 = 2(w) + 2(2w + 3)
=> 2(w) + 2(2w + 3) = 96
Help me! i need this answer now i am so dead. if i get it worng please help help please
Answer:
70.4
Step-by-step explanation:
c = 2[tex]\pi[/tex]r
c = 2(3.142)(11.2)
c = 70.3808 Rounded to 1 decimal place
c = 70.4
Suppose that the relationship between the tax rate t on imported shoes and the total sales S (in millions of dollars) is given by the function below. Find the tax rate t that maximizes revenue for the government. (Round your answer to three decimal places.)
The given function for the sales of [tex]S(t) = 7 - 6 \cdot \sqrt[3]{t} [/tex], gives the tax rate that maximizes government revenue as t = 343/512
What is a government tax rate?The tax rate is the percentage of an amount that is paid to the government as tax.
The given function is presented as follows;
[tex]S(t) = 7 - 6 \cdot \sqrt[3]{t} [/tex]
Where;
t = The tax rate on imported shoes
S = The total sales
Taking the total sales as contributing to the government revenue, R(t), we have;
Revenue = R(t)
Which gives;
[tex]R(t) = t \times (7 - 6 \cdot {t}^{ \frac{1}{3} }) [/tex]
At the maximum total sales, we have;
[tex] \frac{dR(t)}{dt} = \frac{d t \times\left(7 - 6 \cdot {t}^{ \frac{1}{3} } \right) }{dt} = 0 [/tex]
[tex]\frac{d t \times\left(7 - 6 \cdot {t}^{ \frac{1}{3} } \right) }{dt} = 7- 8 \cdot \sqrt[3]{t} = 0[/tex]
Which gives;
At maximum revenue, t = (7/8)³
t ≈ 0.669921875
The tax rate that maximizes the government revenue is t = 343/512Learn more about government tax rate here:
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