Part 1: a. A. The sample size needs to be greater than or equal to 30.
Part 2: The probability is approximately 0.0013.
Part 3: There is a 10% chance of being at or below a mean oil-change time of 14.9 minutes.
What is sample size?The number of individuals or items in a population that are selected for study.
A. The sample size needs to be greater than or equal to 30.
This is due to the Central Limit Theorem, which states that the sample size of a normal distribution must be 30 or more to produce reliable results.
If a sample size is less than 30, the results may be skewed and not accurately represent the true population mean and standard deviation.
B. The probability is approximately 0.0013.
This probability can be calculated by using the z-score formula and plugging in the mean, standard deviation, and sample size.
The z-score for a sample mean of 15 minutes =-3.3,
which translates to a probability of 0.0013 using the z-score table.
C. There is a 10% chance of being at or below a mean oil-change time of 14.9 minutes.
This can be calculated by using the z-score formula and plugging in the mean, standard deviation, and sample size.
The z-score for a 10% chance= -1.28,
which translates to a mean oil-change time of 14.9 minutes.
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The diagram below represents how rock is affected when water enters cracks in rock, freezes, and becomes ice.
Which geologic process is represented in the diagram?
Answer: Physical weathering, more specifically, ice wedging
Step-by-step explanation:
:D
The radius of a circle is 11 meters. What is the circle's circumference?
Use 3.14 for л.
r=11 m
Answer:
The formula for the circumference of a circle is C = 2πr, where r is the radius of the circle and π (pi) is a mathematical constant approximately equal to 3.14.
Substituting the given value of r=11 m and using π = 3.14, we get:
C = 2πr
C = 2 x 3.14 x 11 m
C = 69.08 m
Therefore, the circumference of the circle is 69.08 meters
help I don't understand
With the help of proportions in the given similar triangles we know that the value of x is 3.5 units.
What is triangle similarity?Euclidean geometry states that two objects are comparable if they have the same shape or the same shape as each other's mirror image.
One can be created from the other more precisely by evenly scaling, possibly with the inclusion of further translation, rotation, and reflection.
These three theorems—Angle-Angle (AA), Side-Angle-Side (SAS), and Side-Side-Side (SSS)—are reliable techniques for figuring out how similar triangles are to one another.
So, in the given situation:
TR and WY are as follows:
TR/WU
24/2
2/1
Similarly,
TS/WV
2/1
7/x
7/3.5
Therefore, with the help of proportions in the given similar triangles we know that the value of x is 3.5 units.
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Write an equation to determine each unknown length. Then, solve the equation. Round your answer to the nearest tenth, if necessary.
X=___ Round to the nearest tenth (One number after the decimal)
Answer: 40
Step-by-step explanation:
a(2) + b(2) = c(2)
a(2) + 9(2) = 11(2)
121 - 81 = 40
What is the percent change from 310 to 155?
Answer: 50% decrease
Step-by-step explanation:
50% of 310 = 155
310-155=155
50% decrease :)
ANSWER: 50% decrease
SOLUTION:
50% of 310 = 155
310-155=155
So in all the answer is.......
50% decrease :)))))
-XOXOXO:)
help! find the area of the trapezoid using 30-60-90 special right triangles theorem
AFE triangle,
FE= 6cos60
= 3
dc= 3
ae= 6sin60
= 3*squareroot3
Area= 1/2(10+4)*3*squareroot3
= 7*3*squareroot3
= 21*squareroot3
= 21*1.73
= 36.33square units
Determine if it’s linear or non linear
The first and second equations satisfy standard form of the linear equation, hence they are linear. While, third, fourth, and fifth are non linear equations.
What is system of linear equation?A group of two or more simultaneous solutions to linear equations is referred to as a system of linear equations. A collection of values that satisfy every equation in a system of linear equations is the solution. There might not be a unique solution if the number of equations in the system is less than or equal to the number of variables in the system. Systems of linear equations can be solved using various methods, such as substitution, elimination, or matrix algebra.
The standard form of linear equation is given as:
y = mx + b
The first and second equations satisfy, or represent the standard form of the linear equation, hence they are linear.
While, third, fourth, and fifth do not represent the standard form and hence are non linear equations.
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1. linear function 2. non linear function 3. linear function 4. non linear function 5. non linear function.
What is linear function?
In mathematics, a linear function is a type of function that can be represented by a straight line on a graph.
1.The equation m = 5.45p represents a linear function. It has the form y = mx + b, where m is the slope and b is the y-intercept. In this case, m = 5.45, which is a constant rate of change, and there is no other term involving p, so the equation is linear. When p increases or decreases by 1 unit, m increases or decreases by 5.45 units, respectively.
2.The equation 1=56.01+5 is not a function. It is a simple linear equation in one variable, but it has no independent variable to define a function. It is just an equation that states a relationship between two constants, 56.01 and 5, which sum up to 61.01.
3.The function d = (g-28)7/11 is a linear function because it can be written in the form y = mx + b, where m and b are constants and y and x are variables.
In this case, if we let d = y and g = x, we get:
y = (x-28)7/11
This can be simplified as:
y = 7/11 * x - 196/11
So we can see that the function has a constant slope of 7/11, and a constant intercept of -196/11. Therefore, it is a linear function.
4. This is a non-linear function since it includes a variable raised to a power (r³).
5.The function e=124² is a non-linear function as it involves squaring the value of 124, which produces a curved graph instead of a straight line.
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Find the value of x and y. If your answer is not an integer, leave it in simplest radical form. The diagram is not drawn to scale.
Step-by-step explanation:
For x;
[tex]{ \tt{ \tan( \theta) = \frac{opposite}{adjacent} }} \\ \\ { \tt{ \tan( 60 \degree) = \frac{x}{5} }} \\ \\ { \tt{x = 5 \tan(60 \degree) }} \\ \\ { \tt{x = 5 \sqrt{3} }}[/tex]
For y;
[tex] { \tt{\cos( \theta) = \frac{adjacent}{hypotenuse} }} \\ \\ { \tt{cos(60 \degree) = \frac{5}{y} }} \\ \\ { \tt{y = 5 \cos(60 \degree) }} \\ \\ { \tt{y = 2.5}}[/tex]
If Planet I is 31.1 million miles farther from the sun than Planet II, then Planet III is 24.6 million miles farther from the sun than Planet I. When the total of the distances for these three planets from the sun is 197.8
million miles, how far away from the sun is Planet II?
After solving the equations e know that Planet II is 35 million miles away from the sun.
What are equations?The equals sign is a symbol used in mathematical formulas to denote the equality of two expressions.
An equation is a mathematical statement that contains the symbol "equal to" between two expressions with identical values.
As in 3x + 5 = 15, for example.
There are many different types of equations, including linear, quadratic, cubic, and others.
The three primary forms of linear equations are point-slope, standard, and slope-intercept.
So, let x be the separation between planet I and the sun.
Planet II's distance from the sun is x-30.2.
Planet iii's distance from the sun is equal to x+24.8.
x + x-30.2 + x+24.8 = 190.2
Mix related phrases to find x.
3x - 5.4 = 190.2
3x = 195.6
x = 65.2
65.2 million miles separate planet I from the sun.
Planet II is 35 million miles from the sun or 65.2-30.2.
Planet iii is 90 million miles from the sun (65.2 + 24.8 = miles).
Therefore, after solving the equations e know that Planet II is 35 million miles away from the sun.
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2 eggs are needed to make 24 cookies. how many eggs are needed to make 60 cookies
Answer:
5 eggs.
Step-by-step explanation:
Since two eggs are needed for 24 cookies, we know by dividing both numbers by two that the rate is one egg for 12 cookies. 60/12 = 5. Multiply both numbers by 5 to get the answer. So, the answer is 5 eggs.
BONUS SECTION
This section is optional. Each correct answer will receive 2 points (12 points total)
which will be added to your test's raw score. Clearly indicate the necessary steps,
including appropriate formula substitutions, diagrams, graphs, charts, etc. For all
questions in this part, correct numerical answers without work shown or an
explanation will not receive any credit.
1. Shanika has a dilemma. She has five choices for future employment but does not
know which job opportunity to take. Calculate the annual income for each option
and let her know which job would earn her the most money.
Option 1: Keeping her present job at $15,000 per
year plus a 20% year-end bonus.
Option 2: Taking a job that pays $1,250 per month
Answer:
A
Step-by-step explanation:
What is 7% as a decimal ?
Answer: 0.07%
Step-by-step explanation:
Answer:
0.07
Step-by-step explanation:
A merchant mixed 12 lb of a cinnamon tea with 3 lb of spice tea. The 15-pound mixture cost $39. A second mixture included 16 lb of the cinnamon tea and 6 lb of the spice tea. The 22-pound mixture cost $58. Find the
cost per pound of the cinnamon tea and of the spice tea.
cinnamon
spice
Answer:
Step-by-step explanation:
Let x be the cost per pound of the cinnamon tea and y be the cost per pound of the spice tea.
From the first mixture, we have:
12x + 3y = 39
From the second mixture, we have:
16x + 6y = 58
We can solve this system of equations by elimination. Multiplying the first equation by 2 and subtracting it from the second equation gives:
16x + 6y = 58
(24x + 6y = 78)
-8x = -20
Dividing both sides by -8 gives:
x = 2.5
Substituting this value of x into the first equation, we get:
12(2.5) + 3y = 39
Simplifying, we get:
30 + 3y = 39
Subtracting 30 from both sides gives:
3y = 9
Dividing both sides by 3 gives:
y = 3
Therefore, the cost per pound of the cinnamon tea is $2.50 and the cost per pound of the spice tea is $3.
The circumference of the circle is 20 pi inches. What is the arc length of the shaded sector? Express the answer in terms of Pi. A circle. The shaded sector has an angle measure of 45 degrees. Recall that StartFraction Arc length over Circumference EndFraction = StartFraction n degrees over 360 degrees EndFraction. 2.5 pi inches 5 pi inches 7.9 pi inches 10 pi inches
The provided remark indicates that option (A) is accurate for 2.5 inches.
What length of time is an example?The measurement or size of something to end to end is referred to as its length. To put it another way, it is the bigger of the upper two or three dimensions of a geometric form or object. For instance, the length and width of a parallelogram define its measurements.
Using the given equation:
Arc Length / 20π = 45/360
Cross multiply:
Arc length × 360 = 20π x 45
Arc length x 360 = 900π
Divide both sides by 360:
Arc length = 900π / 360
Arc Length = 2.5 π inches.
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Angles M, N, and P are supplementary.
What is the measure of angle P?
60°
34°
45°
36°
Step-by-step explanation:
The measure of angle p is 60°
FACTOR BY GROUPING
SEE ATTACHED IMAGE
SOLVE 4-6 BY STEPS 1-4
Answer:
see explanation
Step-by-step explanation:
(4)
5x³ - 10x² - 3x + 6
factor out 5x² from first 2 terms and - 3 from last 2 terms
= 5x²(x - 2) - 3(x - 2) ← factor out (x - 2) from each term
= (x - 2)(5x² - 3)
----------------------------------------------------
(5)
9a³ - 45a² - 7a + 35
factor out 9a² from first 2 terms and - 7 from last 2 terms
= 9a²(a - 5) - 7(a - 5) ← factor out (a - 5) from each term
= (a - 5)(9a² - 7)
-----------------------------------------------------
(6)
5x²y - 15y - 2x² + 6
factor out 5y from the first 2 terms and - 2 from the last 2 terms
= 5y(x² - 3) - 2(x² - 3) ← factor out (x² - 3) from each term
= (x² - 3)(5y - 2)
in which place is the first digit of the quotient: 3,587 ÷ 18
Answer: The quotient is 199.277777778, the answer is the hundreds place
Step-by-step explanation:
199.277777778, the 1 in 199 is in the hundreds place :)
The perimeter of a rectangle is 34 units. Its width is 6.5 units.
Write an equation to determine the length of the rectangle
Given:
P = 34 [Perimeter]
W = 6.5 {let's use W and L to make it easy to read]
Also known:
P = W + L + W + L = 2(W+L)
Fill in values:
34 = 2(6.5+L) [NOTE: This is an equation to determine the length (L) of the rectangle."]
17 = 6.5 + L [NOTE: This is a simplified form of the above equation.]
10.5 = L [NOTE: This is the solution (the value of L)]
A rectangular sheet of paper 72 cm x 48 cm is rolled along its length and a cylinder is formed. Find the volume of the cylinder.
Answer:
5
Step-by-step explanation:
this is wrong
Let a and b be real numbers, where Which of the following functions could represent the graph on the right? f(x) = x (x – a)(x – b)2 f(x) = (x – a)(x – b)2 f(x) = x(x – a)³(x – b) f(x) = x2(x – a) 2(x – b)2
Answer:
Without a graph provided, it's difficult to determine which of the given functions represents the graph on the right. However, we can analyze each function to see if it has any characteristics that match the shape of the graph.
f(x) = x(x – a)(x – b)2
This function has one x-intercept at x = 0 and a double root at x = b. If b > a, then the function will have a local maximum at x = a and a local minimum at x = b. This function may represent a graph with a single x-intercept, a double root, and a local maximum and minimum.
f(x) = (x – a)(x – b)2
This function has one x-intercept at x = a and a triple root at x = b. If b > a, then the function will have a local minimum at x = a and a local maximum at x = b. This function may represent a graph with a single x-intercept, a triple root, and a local minimum and maximum.
f(x) = x(x – a)³(x – b)
This function has one x-intercept at x = 0 and a triple root at x = a. If a < b, then the function will have a local minimum at x = b. This function may represent a graph with a single x-intercept, a triple root, and a local minimum.
f(x) = x²(x – a)²(x – b)²
This function has two x-intercepts at x = 0 and x = a and a double root at x = b. If b > a, then the function will have a local maximum at x = a and a local minimum at x = b. This function may represent a graph with two x-intercepts, a double root, and a local minimum and maximum.
Based on these analyses, it's unclear which function represents the graph on the right, as all four functions have characteristics that could match the shape of the graph.
Answer:
It's A
Step-by-step explanation:
2023 edge
yw
Explain the difference between a) comparing, b) non-standard units of measurement and c) standardised units of measurement.
Answer:
a) Comparing: Comparing means evaluating the similarity or difference between two or more objects, values, or variables. It is a process of identifying and highlighting the similarities and differences among objects, values, or variables based on specific criteria.
b) Non-standard units of measurement: Non-standard units of measurement are those that are not part of the International System of Units (SI) and are often created for specific purposes or contexts. These units may be used to measure variables such as time, distance, weight, or volume, but they are not universally recognized or standardized.
c) Standardized units of measurement: Standardized units of measurement are those that are part of the International System of Units (SI) and are universally recognized and accepted. These units provide a standard framework for measuring variables such as time, distance, weight, or volume, making it possible to compare and communicate measurements accurately across different contexts and languages. Some examples of standardized units of measurement include seconds, meters, kilograms, and liters.
can someone please solve????!! thanks
Answer:
(a) Figure 3
(b) 66.2 meters per second
Step-by-step explanation:
You want to know the figure that shows the best fit of a curve to the data, and you want to know the value of the curve when x = 8 seconds.
Best fitThe fit is best when the difference between the data points and the curve is minimized. Often the sum of the squared differences is the metric that is minimized when the fit is best.
The gaps between the data points and the curve shown are greatest in Figures 1 and 2, so Figure 3 has the best fit.
Estimated valueThe speed is estimated by the equation of the curve of best fit as ...
y = 0.6x² +2.1x +11
A slight rearrangement can make this easier to evaluate:
y = (0.6x +2.1)x +11
For x=8, the value of y is ...
y = (0.6·8 +2.1)·8 +11 = 6.9·8 +11 = 66.2
The predicted speed at 8 seconds is 66.2 meters per second.
jay eats 2/3 of a pizza but if dan eats 4 times that amount how much did dan eat
Answer:
Dan eat 2 2/3 of a pizza
Step-by-step explanation:
the answer is above
Let
x-----> amount of pizza Jay ate
y-----> amount of pizza Dan ate
we know that
----> equation A
-----> equation B
substitute equation A in the equation B and solve for y
Convert to mixed number
If I get paid $12.50 an hour and I worked a total of 15 hours and 35 minutes how much did I make?
Answer: $194.79
Step-by-step explanation:
It is easiest to approach this question in two parts.
First part is simple - multiply the wage per hour times the number of whole number you have worked. ($12.50)(15) = $187.50
Next you need to find how much you make in 35 minutes at a wage rate of 12.50 an hour. You can set up a ratio to find this out -
($12.50) | (60 min) - (x dollars) | (35 min)
then cross multiply and divide - (12.5 * 35) / 60 = 7.291
This means you make $7.29 for 35 minutes of work.
$187.50 + $7.29 = $194.79 for 15 hours 35 minutes of work.
(this is based on a per minute/hour scale)
Type the correct answer in the box. Use numerals instead of words.
The cone and cylinder below both have a height of 11 feet.
The cone has a radius of 3 feet.
The cylinder has a volume of 310.86 cubic feet.
Complete the statements using 3.14 for pi. Any non-integer answers in this problem should be entered as decimals rounded to the nearest hundredth.
The volume of the cone is [?]
cubic feet.
The radius of the cylinder is [?]
feet.
The ratio of the volume of the cone to the volume of the cylinder is 1:[?]
.
Help with number 4!!!
Answer:forgot the explanation
Step-by-step explanation: give me a equation to solve
Dylan claims that the coordinates of the center of dilation are (4.8, 3.2). He explains that to locate the center of dilation, he first joins P and P ’. Then, he marks a point X on line segment PP’ such that PX : XP’ = 1 : 4, since the scale factor of dilation is 4. Finally, he reads off point X from the coordinate plane, and concludes that point X has coordinates (4.8, 3.2).
Part A:
Explain how you know that Dylan’s claim is wrong in the space below. What is the location of the center of dilation (x,y)?
Part B:
What is the location of the center of dilation (x,y)?
I need help quick this is for a test
The correct coordinates of the center of dilation are (2.8, 3.8).
What is dilation?
In geometry, dilation is a transformation that changes the size of an object. When a figure is dilated, each point of the original figure is moved away from or toward the center of dilation.
Dylan's claim is incorrect because the center of dilation is not necessarily located on the line segment PP'.
To find the center of dilation, we need to locate the image point of a known point after dilation.
Let's consider a point Q on the same line as PP', but on the other side of P', such that PQ = 1 unit. After dilation with a scale factor of 4, the image of Q will be on the line passing through P and P'. Let's denote this image point by Q'.
Since PQ : P'Q' = 1 : 4, the distance from P to Q' is 4 units. Similarly, since PP' : PQ' = 1 : 5, the distance from P to Q' is 5 times the distance from P to P'. Thus, the distance from P to P' is 1 unit and the distance from P to Q' is 5 units.
Therefore, the center of dilation is located on the line passing through P and Q', and is 4 units away from P and 1 unit away from Q'.
Using the midpoint formula, we can find the coordinates of the center of dilation:
[tex]x &= \frac{1}{2}(4.8 + 0.8)[/tex]
[tex]&= 2.8[/tex]
[tex]y &= \frac{1}{2}(3.2 + 4.4)[/tex]
[tex]&= 3.8[/tex]
Thus, the correct coordinates of the center of dilation are (2.8, 3.8).
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What’s the answer to this question? I can’t seem to find the answer.
You could try factoring.
[tex]6x^2-x-1=(2x-1)(3x+1)\\3x^2+25x+8=(x+8)(3x+1)\\x^2+4x-32=(x+8)(x-4)\\2x^2+7x-4=(x+4)(2x-1)[/tex]
So your expression becomes...[tex]\frac{(2x-1)(3x+1)}{(x+8)(3x+1)}*\frac{(x+8)(x-4)}{(x+4)(2x-1)}=\frac{x-4}{x+4}[/tex].
If Marie were to paint her living room alone, it would take 3 hours. Her sister Fran could do the job in 6 hours. How many hours would it take them working together? Express your answer as a fraction reduced to lowest terms, if needed.
The time it takes them to paint the living room together is 2 hours. Expressing this as a fraction reduced to lowest terms 2 hours is 2/1.
What is time working together?Time working together refers to the amount of time that two or more people need to work together to complete a certain task. It is often used in situations where people are working collaboratively or cooperatively to achieve a common goal.
According to question:Let's denote the time it takes Marie to paint the living room alone by M and the time it takes Fran to paint the living room alone by F.
From the problem, we know that:
M = 3 hours
F = 6 hours
To determine the time it takes them to paint the living room together, we can use the following formula:
1 / (time working together) = 1 / M + 1 / F
Substituting the values we have:
1 / (time working together) = 1 / 3 + 1 / 6
Simplifying the right-hand side of the equation:
1 / (time working together) = 2 / 6 + 1 / 6
1 / (time working together) = 3 / 6
1 / (time working together) = 1 / 2
Therefore, the time it takes them to paint the living room together is 2 hours. Expressing this as a fraction reduced to lowest terms:
2 hours = 2/1
So the answer is: 1 / (time working together) = 1 / 2, or equivalently, the time working together is 2/1.
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change 3 5 to a decimal fraction
Answer:
7/20
its the answer to your question