Given data:
Population Mean = 346
Standard Deviation = 72
Expected Value of e(x) = population mean = 346
Sample Size = 216
In this case, if many random samples of 216 are taken, then the mean of the sample mean numbers per week is 346. (Option C)
To solve for the variance of x or var(x), we follow the formula below:
[tex]var(x)=\frac{\sigma^2}{n}=\frac{(s\tan darddeviation)^2}{\text{sample size}}[/tex]In this case, the given standard deviation is 72 and the sample size is 216. Therefore, we have:
[tex]var(x)=\frac{72^2}{216}=\frac{5184}{216}=24[/tex]One of the properties of the Sampling Distribution of the Mean is that the sampling distribution of the mean is approximately normally distributed so long as the sample size is 30 or higher. Our sample mean here is 346 with a sample standard deviation of √24 or 4.899.
How likely is it to observe a sample mean number of sags per week that exceeds 390?
For this one, we have this formula to use:
[tex]z=\frac{\bar{x}-\mu}{\frac{\sigma}{\sqrt[]{n}}}[/tex]Our bar "x" is 390. The "myu" symbol is our population mean which is 346. This σ symbol is the population standard deviation 72 and n is our sample size = 216.
[tex]z=\frac{390-346}{\frac{72}{\sqrt[]{216}}}=\frac{44}{2\sqrt[]{6}}=8.98[/tex]Under a normal curve, the areas defined are between z = -3.5 to z = +3.5. Since our z should exceed > 8.98 and thus far greater than +3.5, then we can say that the probability of having a sample mean that exceeds 390 is zero.
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
The circumference of a circle is 67 inches. What is the area in
terms of π ?
In the figure below, circle 1 is a unit circle. Circle 2 has a diameter that is one and half times longer than that of circle 1, and circle 3 has a diameter that is twice as long as that of circle 1. If angle Z is equal to 2 radians, what is the length of the arc between points I and J?
The length of an arc is given by:
[tex]s=r\timesθ[/tex]where r is the radius and θ is the measure of the angle in radians.
To find the radius:
radius in circle 1 = 1 (unit circle)
radius in circle 3 = 2 x 1 = 2.
Hence:
[tex]s=2\times2=4[/tex]ANSWER
the length of the arc between points I and J is 4
351,528.094 in word form
Three hundred fifty-one thousand five hundred twenty-seven and ninety-four thousandths
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 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 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
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
If a number is added to the number of 5/6 and twice as much is added to the denominator, the result is 3/5, find the number
Answer:
[tex]x=7[/tex]Step-by-step explanation:
We have the number:
[tex]\frac{5}{6}[/tex]If a number is added to the numerator and twice as much is added to the denominator and the result is 3/5, we can create the following equation:
[tex]\frac{5+x}{6+2x}=\frac{3}{5}[/tex]Solve for x, using cross multiplication:
[tex]\begin{gathered} 5(5+x)=3(6+2x) \\ 25+5x=18+6x \\ -x=-7 \\ x=7 \end{gathered}[/tex]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 .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
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.
if tommy has 34 has apples and she puts them in 3 baskets whats the anwser and with the reminder if it has one
What is the rest of the pattern.
3, 6, 10, 15, _, _, _.
Answer:
3, 6, 10, 15, 21, 28, 36.
Step-by-step explanation:
3 (+3),
6 (+4),
10 (+5),
15 (+6),
21 (+7),
28 (+8),
36
Answer:
If my theory is right the next 3 numbers are 21,28,36
Step-by-step explanation:
Looking at the beginning you see that 3 goes to 6 which is a hop of 3
Then next is 6 to 10 which is a hop of 4
Then next is 10 to 15 which is a hop of 5
So I think it’s going in a chronological number order
So I say the next hops will be 6,7,8
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]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
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
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.
hwlp
The length of a rectangle is 6 feet more than twice the width. If the perimeter is 132 feet, find the dimensions.
Write the equation for f(x) and g(x). Then identify the reflection that transforms the graph of f(x) to the graph of g(x).
Given the figure of the functions f(x) and g(x)
The graph of the function is the shown lines
The equation of f(x):
As shown the line of f(x) passes through the points: (-2, 0) and (0, -1)
The slope of the line will be:
[tex]slope=\frac{rise}{run}=\frac{y_2-y_1}{x_2-x_1}=\frac{-1-0}{0-(-2)}=\frac{-1}{2}[/tex]The y-intercept = -1
so, the equation of f(x) =
[tex]f(x)=-\frac{1}{2}x-1[/tex]The equation of g(x):
As shown the line of g(x) passes through the points: (-2, 0) and (0, 1)
The slope of the line will be:
[tex]slope=\frac{rise}{run}=\frac{y_2-y_1}{x_2-x_1}=\frac{1-0}{0-(-2)}=\frac{1}{2}[/tex]The y-intercept = 1
So, the equation of g(x) will be:
[tex]g(x)=\frac{1}{2}x+1[/tex]Identify the reflection that transforms the graph of f(x) to the graph of g(x).
As shown, the functions are symmetric around the x-axis
And as we can see for the same value of x: g(x) = -f(x)
So, the type of transformation is: Reflection over the x-axis
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:)
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 number when rounded to 3 decimal places, is equal to
0.029
Find the upper and lower bound of
The number
Metric area unit conversion with decimal valuesA rectangular field is 0.35 kilometers long and 0.2 kilometerswide. What is the area of the field in square meters? Do notround your answer.mX 5 ?Conversion facts for length1000 millimeters (mm) = 1 meter (m)100 centimeters (cm) = 1 meter (m)10 decimeters (dm) = 1 meter (m)1 decameter (dam) = 10 meters (m)1 hectometer (hm) = 100 meters (m)1 kilometer (km) = 1000 meters (m) I need help with this math problem.
Given that
The length of the rectangular field is 0.35 km and the width is 0.2 km. And we have to find the area of this field.
Explanation -
The formula for the area of the rectangle is
[tex]Area=length\times breadth[/tex]On substituting the values we have
[tex]\begin{gathered} Area=0.35\times0.2\text{ km}^2 \\ Area=0.07\text{ km}^2 \end{gathered}[/tex]Since the conversions are given as
[tex]\begin{gathered} 1\text{ km = 1000 m}^{\text{ }}=10^3\text{ m} \\ 1\text{ km}^2=10^6\text{ m} \end{gathered}[/tex]So the required answer in sq meters will be
[tex]\begin{gathered} Area=0.07\times10^6\text{ m}^2 \\ Area=7\times10^4\text{ m}^2=70000\text{ m}^2 \end{gathered}[/tex]So the final answer is 70000 sq meters.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.
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
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
Which is the equation of a circle that is centered at the origin?O (– 1)2 + (y – 1)2 = 4O2? + (y - 1)2 = 2O 2 + y2 = 7Ox+y=8
Standard equation of circle:
[tex](x-h)^2+(y-k)^2=r^2[/tex][tex]\begin{gathered} \text{If centered at the origin:} \\ (h,\text{ k) = (0, 0)} \\ h\text{ = 0, k = 0} \end{gathered}[/tex][tex]\begin{gathered} \text{The equation of circle becomes:} \\ (x-0)^2+(y-0)^2=r^2 \\ x^2+y^2=r^2 \end{gathered}[/tex]comparing the above equation with the options given:
[tex]\begin{gathered} x^2+y^2=7\text{ has the form} \\ x^2+y^2=r^2,wherer^2\text{= }7 \end{gathered}[/tex][tex]x^2+y^2\text{ = 7 (option C)}[/tex]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]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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