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Related Questions
He number of years of education of self-employed individuals in the united states has a population mean of 13.6 years and a population standard deviation of 3.0 years. if we survey a random sample of 100 self-employed people to determine the average number of years of education for the sample, what is the standard deviation of the sampling distribution of (the sample mean)
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We can solve this problem by using the formula:
s = σ / sqrt(n)
where,
s = standard deviation of the sample
σ = standard deviation of the population = 3 years
n = number of samples = 100
Substituting:
s = 3 years / sqrt (100)
s = 0.3 years (ANSWER)
A family has two cars. the first car has a fuel efficiency of 15 miles per gallon of gas and the second has a fuel efficiency of 20 miles per gallon of gas. during one particular week, the two cars went a combined total of 675 miles, for a total gas consumption of 40 gallons. how many gallons were consumed by each of the two cars that week?
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car 1 = x
car 2 = y
x+y =40 gallons
x=40-y
15x +20y = 675
15(40-y) +20y = 675
600-15y +20y =675
600+5y = 675
5y=75
y=75/5 = 15 gallons
x=40-15 =25 gallons
Car 1 used 25 gallons
Car 2 used 15 gallons
What of the above terms indicates imaginary parallel lines that circle the earth?
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Between these two, the imaginary lines parallel to the equator of the Earth are the latitudes. Imagine a Cartesian plane that is revolved about either the x or y axis. You would form a sphere with x and y coordinates. The x-coordinates or the horizontal axis with respect to the equator of the Earth are the latitudes. The vertical axis are the longitudes.
The East Bay Deli, makes 6.85 pounds of pasta salad each day. West Bay Deli makes four times that amount each day. How many combined pounds of pasta salad is made per week between the two delis? Find a fourth of their combined weekly production of pasta salad.
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East Bay Deli: 6.85 lb
West Bay Deli: 4*6.85 = 27.4 lb
Total amount made per day is
6.85 + 27.4 = 34.25 lb
Total amount made per week is
34.25*7 = 239.75 lb
Answer: 239.8 lb (nearest tenth)
A fourth of the combined weekly production is
(1/4)*239.75 = 59.9375 lb
Answer: 59.9 lb (nearest tenth)
If y = f(x), and y = a f(x) is a vertical stretch or compression, a > 1 causes the graph to be stretched vertically by a factor of a.
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A vertical stretch in the context of graphing functions occurs when the function is multiplied by a positive constant greater than 1, resulting in the graph being stretched vertically by that factor without affecting the y-intercept.
A vertical stretch occurs when we multiply the function by a positive constant greater than 1. For example, if we have y = a f(x) and a is greater than 1, this results in the graph being stretched vertically by a factor of a. This type of transformation doesn't affect the y-intercept since the behavior of the graph at x=0 remains unchanged. Multiplying the independent variable by a constant such as 1/2 would result in a horizontal stretching or compression, but this is different from the vertical stretching effect we are discussing here.
Additionally, suppose the vertical stretch factor is a natural number. In that case, we can think of the stretched function as being the sum of the original function added to itself repeatedly that number of times. This additive property also extends to the derivative, as the derivative of the vertically stretched function is the original derivative multiplied by the stretch factor. This is known as the vertical stretch property in the context of derivatives and calculus.
If the tire is flat, then I will have to change it. Using the statement above, first state your variables in terms of p and q and which variable represents which statement. Then write this statement in symbolic form.
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Correct Answer:
p: The tire is flat. q: I will have to change it. p -> q
No. Of roots in eq 8sec^x-6secx+1=0
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[tex] 8\sec^2x-6\sec x+1=0\\ 8\sec^2x-2\sec x-4\sec x+1=0\\ 2\sec x(4\sec x-1)-1(4\sec x-1)=0\\ (2\sec x-1)(4\sec x-1)=0\\ 2\sec x-1=0\\ 2\sec x=1\\ \sec x=\dfrac{1}{2}\\ x\in\emptyset\\\\ 4\sec -1=0\\ 4\sec =1\\ \sec x =\dfrac{1}{4}\\ x\in\emptyset [/tex]
So, the number of solutions (real ones) is 0.
What is the length of the hypotenuse in the triangle below ?
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In 45-45-90 triangles hypotenuse = x√2 [x=leg]
If leg = 14cm, then hypotenuse = 14√2 cm.
Decide if the situation involvesâ permutations, combinations, or neither. explain your reasoning.
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Combinations are when the order doesn't matter, like if you had 3 numbers behind your back and you had to guess the 3 not in order
It needs neither when you don't need to find the amount of choices you have (or something similar) for something
Solve for x. A.x=7.5 B.x=16 C.x=17.5 D.x=27.5
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The Pyramid of Giza is one of the largest pyramid structures still standing in Egypt. It is a right pyramid with a square base, a base length of 230 m, and height of 150 m.
The area of the base is __________
The volume is _________
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The square base has a base length of a = 230 m.
The area of the base is
A = a*a = 230*230 = 52,900 m²
The height is h = 150 m.
The volume is
V = (1/3)*A*h
= (1/3)*52900*150
= 2,645,000 m³
Answer:
The area of the base is 52,900 m²
The volume is 2,645,000 m³
Answer:
The area of the base is 52,900 m²
The volume is 2,645,000 m³
Step-by-step explanation:
I need the blue one done! please help!!
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Examples: Night and Day, Black an White, Alive and Dead, Awake and Sleeping
Can i get branielst
A shoe repairman is working with his assistant, who takes twice as long to repair a pair of shoes. Together they can fix 16 pairs of shoes in an eight-hour day. How long does it take the repairman to fix one pair of shoes by himself?
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[tex]\boxed{\boxed{Answer: \tex{ }$45$ minutes}}[/tex]
Hello!
The number of pairs of shoes each man can repair is its speed times the time.
Call x the repair speed of the assistant. Then, the repair speed of the repairman is 2x, and the joint speed is 2x + x = 3x.
Also, the joint speed is 16 pairs in 8 hours = 16 pairs/ 8 hours = 2 pairs/hour.
Thus, we can equate:
[tex]3x = 2 pairs/hour, \text { or } x = (2/3) pairs / hour.$\\[/tex]
That is the speed of the assistant. Then, the speed of the repairman is:
[tex]2x = 2 (2/3) pairs/hour\\2x = (4/3) pairs/hour.[/tex]
That means that the repairman takes the inverse of 4/3 of an hour to repair one pair of shoes. That is 3/4 of an hour (to repair on pair)
3/4 of an hour is 45 minutes and this is the answer.To find out how long it takes the repairman alone to fix a pair of shoes, we solve a joint work rate problem. By setting equations based on their combined and individual work rates, we find out it takes the repairman 0.75 hours or 45 minutes to fix one pair of shoes by himself.
Explanation:To determine how long it takes the repairman to fix one pair of shoes by himself, we start by establishing the rates at which both the repairman and his assistant work.
Let's denote the time it takes the repairman to repair one pair of shoes by x hours.
Since the assistant takes twice as long, their time would be 2x hours for one pair.
Working together, their combined rate allows them to fix 16 pairs in 8 hours, or 2 pairs per hour.
Now, we express their combined work rate as the sum of their individual work rates.
The repairman's rate is 1/x pairs per hour, and the assistant's rate is 1/(2x) pairs per hour.
Together, this should equal their combined rate of 2 pairs per hour:
1/x + 1/(2x) = 2
Solving this equation for x, we first find a common denominator and get:
2/2x + 1/2x = 2
3/2x = 2
3 = 4x
x = 3/4
Therefore, it takes the repairman 0.75 hours, or 45 minutes, to fix one pair of shoes by himself.
What is the r value of the following geometric sequence?
64, 48, 36. 27
2/3
3/4
5/8
3/8
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What does it mean for an equation to have no solution or infinitely many solutions?
PLEASE GIVE ME A DETAILED RESPONSE AS IM TAKING MODULE 7 ALGEBRA DBA TOMORROW AT 7PM
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If an equation has infinitely many solutions, all equations of x will make the equation true. For example, x+1=1+x.
No-Solution implies an inconsistent equation, while infinitely many solutions indicate a condition that holds true for any value of variable.
When an equation has No-Solution, it means that there is no value of variable that satisfies equation. In other words, equation represents an inconsistent condition, and solution set is empty. For example, equation 2x + 5 = 2x + 7 has no solution because the variable x cancels out, leaving an inconsistency (5 ≠ 7),
When an equation has infinitely many solutions, it means that any value of variable will satisfy equation. The equation represents a condition that is always true, regardless of chosen value.
For example, the equation x + 5 = x + 5 has infinitely many solutions because any value of x will make the equation true (such as x = 1, x = 2, x = 3, and so on).
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triangle pqr is a right triangle. If PQ = 8, what is PR?
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The 30-60-90 triangle is known as a special right triangle because its angles have a unique ratio of 1:2:3. The length of the side PR in ΔPQR is 4√3 units.
What is the 30-60-90 right triangle?The 30-60-90 triangle is known as a special right triangle because its angles have a unique ratio of 1:2:3. Furthermore, the hypotenuse is twice the length of the shorter leg, and the larger leg is √3 times the length of the shorter leg.
For the given right-angled triangle, we can use the 30-60-90 rule. The 30-60-90 triangle is known as a special right triangle because its angles have a unique ratio of 1:2:3. Furthermore, the hypotenuse is twice the length of the shorter leg, and the larger leg is √3 times the length of the shorter leg.
Therefore, we can write,
PQ = 2(RQ)
8 = 2(RQ)
RQ = 4
PR = (RQ)√3
PR = 4√3
Hence, the length of the side PR in ΔPQR is 4√3 units.
The complete question is mentioned in the image below.
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What is the common difference of the following arithmetic sequence?
100, 102, 104, 106,…
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The common difference in the arithmetic sequence 100, 102, 104, 106,... is 2.
Arithmetic Sequence: 100, 102, 104, 106,...
Common Difference: The common difference in an arithmetic sequence is the constant value by which each term is increased or decreased. In this sequence, the common difference is 2 because each term increases by 2.
Calculation: 102 - 100 = 2, 104 - 102 = 2, 106 - 104 = 2, so the common difference is 2.
Simplify 1 over quantity x minus 3 plus 4 over x all over 4 over x minus 1 over quantity x minus 3
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(1/(x-3)+4/x)/(x-1)/(x-3), giving us the common denominator of x(x-3). We then take each individual fraction in the complex fraction, making it so that each one has the denominator x(x-3). 1/(x-3) becomes x/x(x-3), 4/x becomes 4(x-3)/x(x-3), and (x-1)/(x-3) becomes x(x-1)/x(x-3).
Now, our fraction is (x/x(x-3)+ 4(x-3)/x(x-3))/x(x-1)/x(x-3), or simply ((x+4(x-3)/x(x-3))/x(x-1)/x(x-3)). If we multiply the numerator and denominator by x(x-3), we get the fraction (x+4(x+3))/(x(x-1)).
Distributing the 4, we get (x+4x+12)/(x(x-1)), or (3x+12)/(x(x-1)). (I don't know if you want the denominator factored or not, but if you want it expanded then it's (3x+12)/(x^2-x).)
I hope this was easy enough to follow! I haven't written anything like this before so I'm sorry if it wasn't very good.
Given expression: [tex]\frac{\frac{1}{x-3}+\frac{4}{x}}{\frac{4}{x}-\frac{1}{x-3}}[/tex].
[tex]\mathrm{Least\:Common\:Multiplier\:of\:}x,\:x-3:\quad x\left(x-3\right)[/tex]
[tex]\mathrm{Adjust\:Fractions\:based\:on\:the\:LCM}[/tex]
[tex]\frac{4}{x}-\frac{1}{x-3}=\frac{4\left(x-3\right)}{x\left(x-3\right)}-\frac{x}{x\left(x-3\right)}[/tex]
[tex]=\frac{4\left(x-3\right)-x}{x\left(x-3\right)}[/tex]
[tex]=\frac{3x-12}{x\left(x-3\right)}[/tex]
[tex]\frac{4}{x}-\frac{1}{x-3}=\frac{x}{x\left(x-3\right)}+\frac{4\left(x-3\right)}{x\left(x-3\right)}[/tex]
[tex]=\frac{x+4\left(x-3\right)}{x\left(x-3\right)}[/tex]
[tex]=\frac{5x-12}{x\left(x-3\right)}[/tex]
[tex]\frac{\frac{1}{x-3}+\frac{4}{x}}{\frac{4}{x}-\frac{1}{x-3}}=\frac{\frac{5x-12}{x\left(x-3\right)}}{\frac{3x-12}{x\left(x-3\right)}}[/tex]
[tex]\mathrm{Divide\:fractions}:\quad \frac{\frac{a}{b}}{\frac{c}{d}}=\frac{a\cdot \:d}{b\cdot \:c}[/tex]
[tex]=\frac{\left(5x-12\right)x\left(x-3\right)}{x\left(x-3\right)\left(3x-12\right)}[/tex]
[tex]\mathrm{Cancel\:the\:common\:factor:}\:x[/tex]
[tex]=\frac{\left(5x-12\right)\left(x-3\right)}{\left(x-3\right)\left(3x-12\right)}[/tex]
[tex]\mathrm{Cancel\:the\:common\:factor:}\:x-3[/tex]
[tex]=\frac{5x-12}{3x-12} \ \ \ : Final Answer.[/tex]
2x – 4y = 12 3x – 6y = 21 solve
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3x - 6y = 21..= x - 2y = 7
these are parallel lines with no solution
Help please.........,
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y-6 = -4(x+1)
y-6 = -4x-4
add 6 to each side
y=-4x+2
A is the correct answer
Philip buys the pizza shown below: A circular pizza is shown. The center is labeled as point A and a point on the circumference is marked B. What does AB represent?
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Help me please!!!!!!
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V1 = volume of the smaller cube (with 1/3 cm sides)
V2 = volume of the box shown
The first volume is
V1 = (1/3)*(1/3)*(1/3)
V1 = 1/27
The second volume is
V2 = (5/3)*(4/3)*(2)
V2 = 40/9
Now divide the two volumes
(V2)/(V1) = (40/9)/(1/27) = (40/9)*(27/1) = 120
Therefore you can fit 120 of the smaller cubes in the larger box shown.
Cloverville has a population of 25,000 people and is increasing at a rate of 0.2%. The population in 3 years will be
Approximately 25,500 people
Approximately 24,8500 people
Approximately 25,150 people
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A=pe^rt
A ?
P 25000
E constant
R 0.002
T 3years
A=25,000×e^(0.002×3)
A=25,150 ...Answer
How many sides does a polygon have with an interior angle of 108?
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360/72 = 5
A ramp leading to the freeway overpass is 200 feet long and rises 37 feet. what is the measure of the angle formed between the ramp and the freeway?
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First, we find the angle made between the ramp and the rise (dashed line). Let's denote this is angle α. We make use trigonometric functions like cosine. Cosine of an angle is equal to the ratio of its adjacent side to the hypotenuse. In equation form:
cos α = 37/200, where α is the angle of inclination of the ramp
cos α = 0.185
α =cos^-1(0.185)
α = 79.34°
Next, let's denote the unknown angle as angle β. When you add the right angle and angle α, the sum would be angle β. Therefore,
β = 90° + 79.34°
β = 169.34°
A ramp leading to the freeway overpass is 200 feet long and rises 37 feet. The measure of the angle formed between the ramp and the freeway is
[tex]\mathbf{ \theta = sin^{-1} \Big ( \dfrac{37}{200} \Big)}[/tex]
From the information given:
The measure of the angle formed θ between the ramp and the freeway overpass can be determined by using the sine angle which is:
[tex]\mathbf{sin \theta = \dfrac{opposite}{hypotenuse}}[/tex]
[tex]\mathbf{sin \theta = \dfrac{37}{200}}[/tex]
[tex]\mathbf{ \theta = \dfrac{1}{sin} \Big( \dfrac{37}{200}\Big)}[/tex]
[tex]\mathbf{ \theta = sin ^{-1} \Big( \dfrac{37}{200}\Big)}[/tex]
Therefore, the measure of the angle formed between the ramp and the freeway is
[tex]\mathbf{ \theta = sin^{-1} \Big ( \dfrac{37}{200} \Big)}[/tex]
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what type of number can be written as a fraction where p and q are intergers and q is not equal to zero
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Irrational numbers are the opposite.
Hope this helps!
The screen aspect of a widescreen tv is 16.9. What are the width and height of a 32 inch tv? Round answer to the nearest tenth of an inch.
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thus
[tex]\bf 32^2=w^2+\left( \cfrac{9w}{16} \right)^2\implies 32^2=w^2+\cfrac{(9w)^2}{16^2}\implies 32^2=w^2+\cfrac{9^2w^2}{16^2} \\\\\\ 32^2=\cfrac{16^2w^2+81w^2}{16^2}\implies 32^2\cdot 16^2=337w^2 \\\\\\ (32\cdot 16)^2=337w^2\implies \sqrt{(32\cdot 16)^2}=\sqrt{337w^2} \\\\\\ 32\cdot 16=w\sqrt{337}\implies \cfrac{32\cdot 16}{\sqrt{337}}=w\implies \boxed{\cfrac{512}{\sqrt{337}}=w}\\\\ -------------------------------\\\\[/tex]
and we can rationalize that to [tex]\bf \cfrac{512}{\sqrt{337}}\cdot \cfrac{\sqrt{337}}{\sqrt{337}}\implies \boxed{\cfrac{512\sqrt{337}}{337}}[/tex]
thus, its height is [tex]\bf h=\cfrac{9w}{16}\implies h=\cfrac{9}{16}\cdot \cfrac{512\sqrt{337}}{337}\implies \boxed{h=\cfrac{4608\sqrt{337}}{5392}}[/tex]
what are the coordinates of a point on the unit circle if the angle formed by the positive x- axis and the radius is 45°??
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sin(angle( = y-coordinate / radius = y-coordinate / 1 = y-coordinate = y
cos(angle) = x-coordinate / radius = x-coordinate / 1 = x
Then:
y = sin(angle) = sin(45°) = √2 / 2
x = cos (angle) = cos (45°) = √2 / 2
=> Answer: (√2 / 2 , √2 / 2), which is the option A)
Which of the following would best represent a cosine function with an amplitude of 3, a period of pi/2 , and a midline at y = –4? (1 point)
f(x) = –4 cos 4x + 3f(x) = 3 cos(x – pi/2 ) – 4
f(x) = 4 cos(x – pi/2 ) + 3
f(x) = 3 cos 4x – 4
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To transform the function [tex]f(x)=cos(x)[/tex] to have the midline [tex]y=-4[/tex] we need to subtract [tex]f(x)[/tex] by 4, so we have [tex]y=f(x)-4[/tex],
To transform the function [tex]f(x)=cos(x)[/tex] to have period of [tex] \frac{ \pi }{2} [/tex], we need to divide the original period [tex]2 \pi [/tex] by 4, so we have [tex]y=f(4x)[/tex]. Note that it is the [tex]4x[/tex] gives the effect of dividing the points on x-axes by 4 and the period is read on x-axes
Hence, the full transformation is given [tex]y=3f(4x)-4[/tex] which is the last option
Answer:
D) f(x) 3 cos 4x-4 (I just took it)
Susie is paying $558.16 every month for her $150,000 mortgage. If this is a 30 year mortgage, how much interest will she pay over the 30 years of payments?
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558.16 x 12 = 6697.92 every year
6697.92 x 30 = 200937.60 total
200937.60-150000 = $50,937.60 total interest paid