STS Solve Applications Involving Normal DistributionsA set of 1200 exam scores is normally distributed with a mean of 84 and standard deviation of 9. Use theEmpirical Rule to complete the statements below.
Answers
Let us upload the bell curve for standard normal distribution
Given that
[tex]\begin{gathered} \mu=84 \\ \sigma=9 \\ \end{gathered}[/tex]15) How many students scored higher than 84
Therefore, the number of students that will score higher than 84 which is the mean will be 50% from the bell curve standard normal distribution.
Hence, the answer is 50%.
19) How many students scored lower than 75?
To get the number of students that score lower than 75, we will subtract 1standard deviation from the mean.
[tex]\begin{gathered} \mu-\sigma=84-9=75 \\ \end{gathered}[/tex]Hence, the number of students will be
[tex]9.2\text{ \%+4.4\%+1.7\%+0.5\%+0.1\%=15.9\%}[/tex]The answer is 15.9%.
20) How many students scored lower than 93?
To get the number of students that score lower than 93, we will add 1standard deviation from the mean.
[tex]\mu+\sigma=84+9=93[/tex]Hence, the number of students will be
[tex]100\text{ \% -(9.2+4.4+1.7+0.5+0.1)\%=100\%-15.9\%=84.1\%}[/tex]The answer is 84.1%.
Related Questions
Need help solving! I got 4x+17 with a remainder of 42 not sure if it is correct!
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Given:
[tex]\frac{4x^2+5x-9}{x-3}[/tex]Using synthetic division we get,
Hence, the answer is,
[tex]4x+17+\frac{42}{x-3}[/tex]-1/15+(-3/5) write in simplest form.
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Answer:
-2/3
Step-by-step explanation:
SEE IMAGE. WILL GIVE BRAINLIEST + POINTS.
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find the hight of a cone with a volume of 150 in 3 and a radius of 10 in.
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we get that:
[tex]150=\frac{1}{3}\pi\cdot10^2\cdot h\rightarrow h=\frac{3\cdot150}{\pi\cdot100}\approx1.4323[/tex]so the height is 1.4323 in
Lacy picks blueberries and raspberries from her garden. She has 1/5 as many pounds of blueberries as raspberries. If she picks 1 4/5 pounds more blueberries, she will have an equal weight of berries. let x represent the weight of raspberries. Which equations could be used to find the weight of the blueberries Lacey has?
Chose all correct answers.
A. [tex]\frac{1}{5} x-1\frac{1}{5}=x[/tex]
B. [tex]x-1\frac{4}{5} =\frac{1}{5}x[/tex]
C. [tex]\frac{1}{5}x=x-1\frac{4}{5}[/tex]
D. [tex]x+1\frac{4}{5}=\frac{1}{5}x-1\frac{4}{5}[/tex]
E. [tex]\frac{1}{5}x+1\frac{4}{5}=x[/tex]
F. [tex]x=1\frac{4}{5}(\frac{1}{5}+x)[/tex]
Answers
The equations that could be used to find the weight of the blueberries Lacey has are given as follows:
B. x - 1 and 4/5 = x/5.
C. x/5 = x - 1 and 4/5.
E. x/5 + 1 and 4/5 = x.
How to obtain the equations?The variable that represents the weight of the raspberries is given as follows:
x.
The variable that represents the weight of the blueberries is given as follows:
b.
She has 1/5 as many pounds of blueberries as raspberries, hence:
b = x/5.
If she picks 1 4/5 pounds more blueberries, she will have an equal weight of berries, hence:
b + 1 and 4/5 = x.
x/5 + 1 and 4/5 = x.
Thus the correct options are given as follows:
Option B, as x - 1 and 4/5 = x/5.Option C, as x/5 = x - 1 and 4/5.Option E, as x/5 + 1 and 4/5 = x.More can be learned about a system of equations at https://brainly.com/question/24342899
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What is the equation in slope -intercept form , of the line that is parallel to the guven line and passes through the point (0, 12
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Answer:
A. y=-5+12
Step-by-step explanation:
It asks for slope intercept form which is y=mx+b. This matches the first option but not the last.
First you can rewrite the given equation (10x+2y=-2) in slope intercept form. That will give you y=-5x=1. (in the slope intercept form the number in front of the X is ur slope and the last number is ur Y intercept).
The question says that ur line is parallel to the given equation line. This means that they have the same slope. In your rewritten equation, y=-5x=1, the slope is -5 because it is in front of the X. A is the only option with -5 in the slope position.
All options are eliminated now but in case u want to know, when it tells you that the line passes through (0,12) that means the X intercept is 12. Because 0 is the x axis, and 12 is the Y. Y intercept just means the point where your line touches the Y axis.
Y intercept goes at the end and that also matches your first equation.
name the polynomials pls
Answers
Answer:
1) B. quadratic trinomial
2) C. linear binomial
3) F. quadratic binomial
4) D. cubic monomial
linear (1 exponent)
quadratic (2 exponent)
cubic (3 exponent)
trinomial (3 terms), quadratic (2 terms), monomial (1 term)
B. A concrete tank has an external diameter of 10 m and an internal height of 3 m. If the walls and bottom of the tank are 30 cm thick, how many cubic meters of concrete are required to make the tank? 10 m 30 cm 3 m 30 cm
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The concrete required to make the tank be 27.4122 m³.
Given, a concrete tank has an external diameter of 10 m and an internal height of 3 m. If the walls and bottom of the tank are 30 cm thick.
External diameter = 10 m
Height = 3 m
Thickness = 0.3 m
External radius = 5 m
Internal radius = 5 - 0.3 = 4.7 m
Volume = πh(e.r² - i.r²)
Volume = (3.14)(3)(5² - 4.7²)
Volume = 9.42(9.7)(0.3)
Volume = 27.4122 m³
Hence, the concrete required to make the tank be 27.4122 m³.
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Which property of addition is shown? −3+ 5 = 5 + (−3)
Associative Property
Commutative Property
Distributive Property
Identity Property.
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This is the Commutative Property. It states that when addition takes place, the addends may switch positions with another addend.
The given expression −3+ 5 = 5 + (−3) is showing the commutative Property. The correct option is B.
What is cumulative property?
The cumulative property states that if the position of the numbers when they are in addition is changed then it will not affect the final result of the addition. If altering the operands' order has no effect on the outcome, the binary operation is commutative in mathematics.
The given expression is −3+ 5 = 5 + (−3).
From the cumulative property, the expression can be solved. The two expressions will have the same value but the frame of writing the expression is different.
This is the Commutative Property. It states that when an addition takes place, the addends may switch positions with another added.
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Potassium-42 has a half-life of 12.4 hours. How much of a 746-gram sample will be left after 62 hours?
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the amount of potassium-42 remaining after 62 hours is approximately 23.31 grams (option B)
Explanation:half life = 12.4 hours
initial amount = 746g
time elapsed = 62 hours
Using the half-life formula:
[tex]\begin{gathered} N(t)=N_0(\frac{1}{2})^{\frac{t}{t_{_{\frac{1}{2}}}}} \\ N(t)\text{ = amount remaining} \\ N_0\text{ = initial amount = 746g} \\ t\text{ = 62 hours} \\ t_{\frac{1}{2}\text{ }}\text{ = 12.4 hours} \end{gathered}[/tex]Substitute for the values:
[tex]\begin{gathered} N(t)=N_0(\frac{1}{2})^{\frac{t}{t_{_{\frac{1}{2}}}}} \\ N(t)\text{ = }746(\frac{1}{2})^{\frac{62}{12.5}} \\ N(t)\text{ = }746(\frac{1}{2})^5 \\ N(t)\text{ = }746(\frac{1}{2^5}) \end{gathered}[/tex][tex]\begin{gathered} N(t)\text{ = }(\frac{746}{32})^{} \\ N(t)\text{ = }23.3125 \end{gathered}[/tex]Hence, the amount of potassium-42 remaining after 62 hours is approximately 23.31 grams (option B)
write a linear function f with the values F (0) = 4 and F (3) = -8
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we have the points (0,4) and (3,-8),
HELP ME PLEASEEEEEEE
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Answer:
A
Step-by-step explanation:
Using the table, the last point has coordinates (120, 190).
Answer:
A
Step-by-step explanation:
the 5th point has the coordinates (129, 190).
120 followers : that is 2 units to the right of 100 on the followers axis.
now we go up to 190 of posts per month.
what point do we find there ? A
The Parkview middle school football team will be playing in the state championship the coach free tickets that he would be distributing to his 52 football players to give to their friends and family if you would like to give each player at least three tickets how many total tickets Must he have?
Answers
He must have 156 total tickets.
According to the question,
We have the following information:
The Parkview middle school football team will be playing in the state championship the coach free tickets that he would be distributing to his 52 football players to give to their friends and family and you would like to give each player at least three tickets.
So, we have the following expression:
1 player = 3 tickets
Now, we will use multiplication to find total number of tickets:
52 players = 52*3 tickets
52 players = 156 tickets
Hence, he must have 156 total tickets.
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Find the missing side length. Show all work.
first right answer with right work gets 500 points
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Answer:
[tex]x=14 \tan 61^{\circ}[/tex]
Step-by-step explanation:
[tex]\tan 61^{\circ}=\frac{x}{14} \\ \\ x=14 \tan 61^{\circ}[/tex]
Estimate the answers to the following calculations by rounding each number to a 1 decimal place and then adding them together. 12.55 and 1.74 = 30.38 and 5.49 = 19.16 and 11.42 =
Answers
Answer:1.7
Step-by-step explanation:
One Decimal Place Rule #1: If the last digit in 1.74 is less than 5, then remove the last digit.
One Decimal Place Rule #2: If the last digit in 1.74 is 5 or more and the second to the last digit in 1.74 is less than 9, then remove the last digit and add 1 to the second to the last digit.
One Decimal Place Rule #3: If the last digit in 1.74 is 5 or more and the second to the last digit in 1.74 is 9, then remove the last digit, make the second to last digit 0, and add 1 to the number to the left of the decimal place.When rounding 1.74 to one decimal place we use
One Decimal Place Rule #1. Therefore, the answer to "What is 1.74 rounded to 1 decimal place?" is:
The estimated answers by rounding each number to a 1 decimal place and then adding them together are 14.3, 35.9, 30.6, respectively.
Here are the estimated answers to the following calculations:
12.55 and 1.74 rounded to 1 decimal place are 12.6 and 1.7. The sum is 14.3.
30.38 and 5.49 rounded to 1 decimal place are 30.4 and 5.5. The sum is 35.9.
19.16 and 11.42 rounded to 1 decimal place are 19.2 and 11.4. The sum is 30.6.
The sum of all three calculations is 14.3 + 35.9 + 30.6 = 80.8.
To estimate the answers, we simply rounded each number to 1 decimal place. This means that we lost some precision, but the overall accuracy of the estimates is still good. For example, the actual sum of 12.55 and 1.74 is 14.29, which is very close to our estimate of 14.3.
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A clerk sold three pieces of one type of ribbon to different customers. One piece was 8 3/8 yards long, another was 6 4/5 yards long, and the third was 15 3/4 yards long. What was the total length of that type of ribbon sold?
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EXPLANATION
If one piece was 8 3/8 yards long, another 6 4/5 and the another 15 3/4 we need to compute the total length as shown as follows:
The total length was:
[tex]\text{Total length=8}\frac{3}{8}+6\frac{4}{5}+15\frac{3}{4}=30\frac{37}{40}=\frac{1237}{40}=30.92\text{ yards long}[/tex]The speed limit on a road is 50 mph. A car drives 19 miles in 22 minutes. Is the car breaking the speed limit? You must show your workings.
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Answer: Yes, the car is breaking the speed limit
Work Shown:
22 min = 22/60 = 0.36667 of an hour approximately
distance = rate*time
rate = distance/time
rate = (19 mi)/( 0.36667 hr)
rate = 51.818 mph approximately
The car is slightly over the 50 mph speed limit.
Which type of angles are described in the second question?
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In the first case:
The angle is an acute angle. It measures more than zero but less than 90 degrees.
Second case:
The angle is an obtuse angle. It measures more than 90 degrees but less than 180 degrees.
Third case:
The angle is a right angle. It measures exactly 90 degrees.
Fourth case:
The angle is a straight angle. It measures exactly 180 degrees.
A town doubles its size every 17 years. If the population is currently 3,070, what will the
population be in 68 years?
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Answer: 49120 would be your answer!
multiply by 2 four times.
The table shows Alejandro's golf scores (relative to par) over a 4-round tournament. Round Score (strokes) 1 +2 2 –4 3 –2 4 +3 What is Alejandro's cumulative score for the tournament?
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Alejandro's cumulative score for the tournament is -1.
What is cumulative score?It is important to note that cumulative score simply has to do with the total score.
From the information, the table shows Alejandro's golf scores over a 4-round tournament.
The scores for the tournament include 2, -4, -2 and 3.
Therefore, the total score will be:
= 2 - 4 - 2 + 3
= -1
The score is -1.
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Find the slope and y-intercept of the line. Graph the line.
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Answer:
Graphing the equation we have;
Explanation:
Given the equation;
[tex]x+5y=40[/tex]the slope of the line can be derived by expressing the equation in slope-intercept form;
[tex]\begin{gathered} 5y=-x+40 \\ y=-\frac{1}{5}x+\frac{40}{5} \\ y=-\frac{1}{5}x+8 \end{gathered}[/tex]So, the slope and y-intercept are;
[tex]\begin{gathered} \text{slope m = -}\frac{1}{5} \\ y-\text{intercept b = 8} \end{gathered}[/tex]to graph the equation, let us find the x-intercept;
[tex]\begin{gathered} at\text{ y=0;} \\ x+5y=40 \\ x+0=40 \\ x=40 \\ (40,0) \\ at\text{ x=0;} \\ (0,8) \end{gathered}[/tex]Graphing the equation we have;
Other points on the graph includes;
[tex]\begin{gathered} at\text{ x=10}; \\ y=-\frac{1}{5}(10)+8=-2+8=6 \\ (10,6) \\ at\text{ x=20;} \\ y=-\frac{1}{5}(20)+8=-4+8=4 \\ (20,4) \end{gathered}[/tex]Determine if each point is a solution to the inequality 2x + 2y > -10 by using the graph shown. Explain. Then justify your answer algebraically.
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The region in the graph shows the solutions for the inequality.
If the point falls on the region, then it is a solution.
The boundary line is a broken line which means, every point on this line is NOT a solution.
a. (-3, -2), Plot this point and check with the region.
That will be :
Since the point is on the boundary, therefore, it is NOT a solution
b (3, -7), plot this point and check with the region :
Since it falls under the region, it is a solution.
Hello hope all is well with you can you help me with this please number 2
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Our equation is:
[tex]4(-x)-2(-x)+2=9+(-x)[/tex]Then we can operate it in the following way, I'll do it step by step
[tex]\Rightarrow4(-x)-2(-x)=(4-2)(-x)=2(-x)[/tex][tex]\begin{gathered} \Rightarrow2(-x)+2=9+(-x) \\ \Rightarrow2(-x)+2-2=9+(-x)-2 \\ \Rightarrow2(-x)=7+(-x) \end{gathered}[/tex][tex]\begin{gathered} \Rightarrow2(-x)-(-x)=7+(-x)-(-x) \\ \Rightarrow(2-1)(-x)=7+(1-1)(-x)=7 \\ \Rightarrow1(-x)=7 \\ \Rightarrow-x=7 \end{gathered}[/tex]And, if -x=7, then
[tex]\begin{gathered} 4(7)-2(7)+2=9+(7) \\ \Rightarrow28-14+2=9+7 \\ \Rightarrow16=16 \end{gathered}[/tex]The denominator of a fraction is three more than the numerator
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Let it be x the numerator. Then we have:
• x + 3: Denominator.
,• x + 9: Numerator increased by nine.
,• (x + 3) + 9: Denominator increased by nine.
Since the simplified result of the fraction is 13/14, we can write and solve for x the following equation.
[tex]\begin{gathered} \frac{x+9}{(x+3)+9}=\frac{13}{14} \\ \frac{x+9}{x+3+9}=\frac{13}{14} \\ \frac{x+9}{x+12}=\frac{13}{14} \\ \text{ Apply cross product} \\ (x+9)\cdot14=13\cdot(x+12) \\ \text{ Apply distributive property} \\ 14\cdot x+9\cdot14=13\cdot x+13\cdot12 \\ 14x+126=13x+156 \\ \text{ Subtract 126 from both sides } \\ 14x=13x+156-126 \\ 14x=13x+30 \\ \text{ Subtract 13x from both sides} \\ 14x-13x=13x+30-13x \\ x=30 \end{gathered}[/tex]Now, we replace the value of x into the left expression from the equation we just solved.
[tex]\begin{gathered} \text{ Original fraction }=\frac{x+9}{(x+3)+9} \\ \text{ Original fraction }=\frac{30+9}{30+3+9} \\ \text{ Original fraction }=\frac{39}{42} \end{gathered}[/tex]Therefore, the original fraction is 39/42.
(3,-1) slope= 2 what is the equation?
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Slope
[tex]m=2[/tex]jack wants to buy a pair of trousers for $60.When he went to the store he found that the price was marked down by 20%. how much do they cost
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Answer:
$48
no idea how working out would go
Answer: $48
Step-by-step explanation: First convert 20% to a decimal which is 0.2 or 0.20.
Then multiply 60 x 0.20 which equals 12.
Because it is a markdown then you must subtract 12 from 60 which gives you the answer $48.
I hope this helps!! Good Luck!
Let f(x) = 4x² + 6.
The quadratic function g(x) is f(x) translated 3 units up.
What is the equation for g(x) in simplest form?
g(x) = ____
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g (x) = 4x² + 10 is the equation for g(x) in the simplest form.
What is a function?A special relationship where each input has a single output is called a function.
Given that, f(x) = 4x² + 6, the quadratic function g(x) is f(x) translated 3 units up.
The translation of a function f (x) in the Cartesian coordinate domain can be done by following the given guidelines:
Translation guidelines ;
Horizontal shifts
Right : f (x) → f (x - a)
Left : f (x) → f (x + a)
Vertical shifts
Up : f (x) → f (x) + b
Down : f (x) → f (x) - b
General shift (Horizontal and Vertical shift) is;
f (x) → f (x ± a) ± b
We will use the guidelines for Vertical shifts, where in this case the magnitude of b = 4.
f (x) = 4x² + 6
g (x) = f (x) + 4
g (x) = 4x² + 6 + 4
g (x) = 4x² + 10
Hence, the equation for g(x) in the simplest form is g (x) = 4x² + 10
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Graph: y = - 4x + 2It’s just on a generic coordinate plane
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The green V function is | x- 4|, so then its necessary to elevate this funtion 2 units , at y axis, to find y = | x - 4| + 2
necessary to elevate this funtion 2 units , at y
axis, to find y = | x - 4 + 2
Anastasia needs to order liquid fertilizer for her landscaping company. She plans to keep the fertilizer in a large cylindrical storage tank, but isn’t sure how much it will hold. The tank is 10 feet tall and the circular base has a diameter of 10 feet. What is the volume of her storage tank?
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785 feet² is the volume of her storage tank .
What is volume ?
Every three-dimensional item takes up space in some way. The volume of this area is what is being measured. The area contained by an object's limits in three-dimensional space is referred to as its volume. It is sometimes referred to as the object's capacity.(V = πr2h)
(V = π * (5)2 * 10)
(V = 250π)
(π) (pi) is approximately equal to (3.14)
V = 250 * 3.14 = 785
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QUICK ANSWERS PLEASE!37. What common angle do AACF and ABCG share?BСAFGA. ZCB. ZFC. ZAD. ZB
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Explanation
as we can see in the picture, after drawing the angles, we can observe the common angles is
[tex]A)\angle C[/tex]I hope this helps you