Suppose that grade point averages of undergraduate students at one university have a bell-shaped distribution with a mean of 2.61 and a standard deviation of 0.39. Using the empirical rule, what percentage of the students have grade point averages that are between 1.83 and 3.39?
As a result, 95% of the students had grade point averages ranging from 1.83 to 3.39.
What exactly is a normal distribution?A normal distribution is a data set design in which the majority of values cluster around the middle of the range and the remainder taper off symmetrically toward either end.
What is the significance of the term "normal distribution"?The normal distribution is also known as the bell curve because the probability density graph resembles a bell. It is also known as the Gaussian distribution, after German mathematician Carl Gauss, who described it initially.
According to the given data:A bell-curve distribution is a normal Distribution.
Let X be the grade point averages of undergraduate students at one university.
X ~ Normal Distribution(2.61,(0.39)2)
P(1.83 < X < 3.39)
= P(X < 3.39) - P(X < 1.83)
= P((X - μ)/σ < (3.39 - 2.61)/.39) - P(((X - μ)/σ)< (1.83 - 2.61)/039)
= P(z < 2) -P(z < -2)
= P(-2 < z < 2)
Thus, given a regular normal distribution (μ=0, σ =1), z is between 2 standard deviations away from the mean.
According to the Empirical Rule, 95% of the data obtained after a normal distribution is within two standard deviations of the mean.
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given the first term and the term-to-term rule, write down the first six terms of each sequence.
b) first term: 2 term-to-term rule add 9
Step-by-step explanation:
a1 = 2
a2 = a1 + 9 = 2 + 9 = 11
a3 = a2 + 9 = 20
a4 = a3 + 9 = 29
a5 = a4 + 9 = 38
a6 = a5 + 9 = 47
help pleaseeeeeeeeeeeeee
Answer:
400
Step-by-step explanation:
[tex]R(x)=\frac{2000x^2}{x^2+4}[/tex]
Since x represents the number of years since publication, the revenue at the end of the first year would be found by just plugging in 1 into the function.
[tex]R(1)=\frac{2000(1)^2}{(1)^2+4} \\\\R(1)=400[/tex]
write an equation for the line that passes through (-4,-4) and (8,5)
Answer:
The equation for this line is (P(x,y)----> P'(2h-x,2k-y), hence h=3 and k=1/2
Step-by-step explanation:
P(x,y)----> P'(2h-x,2k-y)
P(-4,-4)---->P'(8,5)
Now comparing the corresponding sides;
2h+4=8
2h=8-4
2h=4
h=2
Again,
2k-y=5
2k+4=5
2k=5-4
2k=1
k=1/2
Now, checking the answer:
P(-4,-4)----->P'{2*2-(-4),2*1/2-(-4)}
=P'(4+4,1+4)
=P'(8,5)
Find x for this equation
Show clear algebraic fraction
Step-by-step explanation:
cross multiply both sides
2(6x+1)=3(5x–2)
12x+2=15x–6
collect like terms
+2+6=15x–12x
8=3x
divide both sides by 3
8\3=3x\3
therefore, the final answer is
8\3
thank you
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All of the statements are true about the barrier methods of birth control EXCEPT:
A. The female condom is inserted into the vagina before intercourse.
B. When condoms are used correctly they are 80% effective.
C. Both male and female condoms can be used as protection from an STI.
D. Another name for a diaphragm is cervical cap.
Use interval notation to express the following:
The set of all numbers less than or equal to 1
The interval notation that expresses the statement is (-∝, 1]
How to use interval notation to express the statement?The statement is given as:
The set of all numbers less than or equal to 1
The above can be represented as:
<= 1
Represent the set with variable x
So, we have
x <= 1
As an interval notation, we have (-∝, 1]
Hence, the interval notation that expresses the statement is (-∝, 1]
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If , choose the line of reflection between the two congruent triangles.
The line of reflection of the given congruent angles is the y-axis.
What is the line of reflection?
A line of reflection is defined as a line that lies in a position between two identical mirror images so that any point on one image is the same distance from the line as the same point on the other flipped image
Now, from the attached image, we see that the two given congruent triangles are; ΔAHJ and ΔADB
Now, we see that the coordinates are transformed as folllows;
D(5, 2) → H(-5, 2)
B(3, 0) → J(-3, 0)
Now, this type of transformation follows the transformation rule; (x, y) → (−x, y). This means it was reflected over the y-axis.
This the line of reflection of the given congruent angles is the y-axis.
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describe the magnification of a 20x ocular lens and a objective 60x lens
the dimensions of a rectangle are 2x-3 and 5x+1. what is the area in sqaure feet
The area of the rectangle is 10x² - 13x - 3.
How to calculate the area?It should be noted that the area of a rectangle is the length multiplied by the width.
Here, the dimensions of a rectangle are 2x-3 and 5x+1.
The area will be:
= (2x - 3)(5x + 1)
= 10x² + 2x - 15x - 3
= 10x² - 13x - 3
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1.1.2 Show how the catering cost was determined if the cost per person is R225,00.
The catering cost was determined if the cost per person is R225,00. then the cost of 50 people is equal to = 1,125,000 R.
The catering cost was determined if the cost per person is R 225,00.
The cost per person = 225,00 R
To calculate the cost per unit, add all of your fixed costs and all of your variable costs together and then divide this by the total amount of units you produced during that time period.
Let us assume,
Suppose you can find the cost for 50 people.
Then,
We can write,
Catering cost = x
x = 225,00 * 50
x = 1,125,000 R
Therefore,
The catering cost was determined if the cost per person is R225,00. then the cost of 50 people is equal to = 1,125,000 R.
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he table represents a linear equation. A two column table with 5 rows. The first column, x, has the entries, negative 10, negative 5, 10, 15. The second column, y, has the entries, 8, 7. 4, 3. Which equation shows how (–10, 8) can be used to write the equation of this line in point-slope form?
Equation of the line in point slope form passing through (-10,8) for the given coordinates (-10,8), (-5, 7) , (10,4), (15,3) of linear equation is
(y - 8)=(-1/5)(x+ 10).
As given,
Given points of linear equation: (-10,8), (-5, 7) , (10,4), (15,3)
Consider (x₁, y₁)=(-10,8) and (x₂ ,y₂)=(-5,7)
Slope 'm'=(y₂-y₁)/(x₂-x₁)
=(7-8)/(-5+10)
=-1/5
Equation of line passing through (-10,8) in point slope form:
y-y₁=m(x-x₁)
⇒(y -8)=(-1/5)(x+10)
⇒y=1/5(-x+30)
Therefore, equation of the line in point slope form passing through (-10,8) for the given coordinates (-10,8), (-5, 7) , (10,4), (15,3) of linear equation is
(y - 8)=(-1/5)( x + 10).
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ACME movers charges $59 plus $20 per hour to move household goods across town. Hank movers charges$45 per hour. For what length of time does it cost less to
The length of time that it cost less to move good across town will be more than 2.36 hours.
How to explain the information?From the information, ACME movers charges $59 plus $20 per hour to move household goods across town and Hank movers charges $45 per hour.
Let the number of hours be represented by h.
Therefore, the appropriate equation will be:
59 + 20h = 45h
Collect like terms
45h - 20h = 59
25h = 59
h = 59/25
h = 2.36 hours.
Therefore, the length of time that it cost less to move good across town will be more than 2.36 hours.
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ACME movers charges $59 plus $20 per hour to move household goods across town. Hank movers charges $45 per hour. For what length of time does it cost less to move good across town?
Help me pleaseeeeeeeeeeeee
megan buys a 2-quart bottle of juice for $2.56. What is the rate unit of the cost of the juice?
The rate unit of the cost of the juice bought by Megan is $1.28 per quart.
What is defined as the unitary method?The unitary method is a methodology that involves determining the value of a single unit and then calculating the value of the requisite number of units based on that value.The unitary method's formula is to obtain the price of a single unit and afterwards multiply that value by the number of components to get the required value.For the given question;
The price of 2-quart bottle of juice bought by Megan = $2.56.
For calculating the price of 1 bottle, simply divide the total cost by number of bottles.
Price of a single quart bottle = $2.56/2.
Price of a single quart bottle = $1.28 per quart.
Thus, the price of single quart bottle of juice is 1.28 per quart.
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Use the Distributive Property to write 2(-3 + 9) as an equivalent expression. Then evaluate.
O 2(12); 24
O2(-3) + 2(9); 24
O 2(-3) + 2(9); 12
(3 + 9)2; 24
How long, in seconds, should a bus take to travel 5000 m at an average speed of 10 m/s?
Answer:
10 분
Step-by-step explanation:
Calculate the value of x that is positioned between two isosceles triangles. value of each angle is 24.
During an isosceles triangle two angles are identical, adding up to a total of 180, and its x value is 78.
Isosceles triangle: what is it?
In geometry, an isosceles triangle is one with at least two sides of equal length. There are two ways to define it: either as having precisely two sides of equal length or at least two sides of equal length, with the equilateral triangle being an exception to the second definition.
The aforementioned claim states that a triangle's total number of angles is 180.
the total of all angles in a triangle is 180.
⟹24+x+x=180
24+2x=180
12+x=90
x=90−12
x=78
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Question 2
For all rational numbers a and b, a−b = a + (−b).
O True
O False
It is true. For all rational numbers a and b, a−b = a + (−b).
Given that,
To determine whether the statement, "For all rational numbers a and b, a−b = a + (−b)." is true or false.
In mathematics, a rational number is a number that can be described as the result of a fraction of value or does not have face value.
Here,
= a + (-b)
Since in the parenthesis there is a negative value, when we open the parenthesis the sign of the arithmetic operator will change accordingly,
So,
= a - b
So, the condition is true for all rational numbers.
Thus, It is true. For all rational numbers a and b, a−b = a + (−b).
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An airplane’s altitude in feet during its descent for landing can be found using the function f(x) = −300x + 30,000, where x represents the horizontal distance in miles from where the plane begins its descent. After new government regulations become law, the airplane’s
descent will be modeled by the function g(x) = −300x + 30,500. Which statement describes this change?
A. The airplane descends 500 feet per horizontal mile slower
B. The airplane starts its descent from an altitude 500 feet higher
C. The airplane descends 500 feet per horizontal mile faster
D. The airplane starts its descent from an altitude 500 feet lower
Answer:
B. The airplane starts its descent from an altitude 500 feet higher
Step-by-step explanation:
f(x) = −300x + 30,000
the function itself represents the airplane's altitude. the y intercept, 30,000 ft, then represents the initial starting position of the plane.
when it changes
g(x) = −300x + 30,500
only the y intercept changes. it's now 30,500 ft, which is 500 more than before. that means the plane initial position is 500 feet higher.
since the term with x doesn't change, the rate will not be affected. the answers with slower or faster talks about rate, which isn't what changed.
How to solve this math equation, a+2=5
Answer:
a = 3
Hope this helps :)
Explanation and Check part below.
Step-by-step explanation:
1. Isolate the variable by doing the inverse operation which is in this case subtracting 2 on both sides of the equation.
a + 2 = 5
- 2 - 2
a = 3
Check:
1. Substitute a with the solution 3.
3 + 2 = 5
5 = 5 ✓
Your yard is a mess, and you decide to hire a landscaper. The greenhouse charges a $20 consultation fee plus $11 per hour for the actual work. Garden pros does not charge a consulting fee, but charges $15 per hour for the actual work. Write an equation that will help you determine the # of hours at which the 2 companies charge the same. Clearly indicate what the variable represents.
Answer:
5 hoursStep-by-step explanation:
Let the hours of actual work be x and total charge be y.
The greenhouseTotal amount of charge is:
y = 11x + 20Garden prosTotal amount of charge is:
y = 15xSince y is same for both companies, set the equation and solve for x:
11x + 20 = 15x15x - 11x = 204x = 20x = 20/4x = 5Find the product.
654
×
42
=
□
A.
3
,
600
B.
3
,
824
C.
25
,
268
D.
27
,
468
Answer:
D. 27,468
Step-by-step explanation:
654
x42
--------
1,308
+26,160
---------
27,468
Express each fraction as an expression using a negative exponent organ than -1.
1/25=?
Answer:
A negative exponent flips the fraction and turns the exponent positive, and vice versa.
1/121 = 1/1211 = 121-1
As an example, 5-2 = 1/25, and 1/5-2 = 25.
Cheese, bologna, and peanut butter sandwiches were made for a picnic in a ratio of 5 to 7 to 8. If a total of 120 sandwiches were made, how many bologna sandwiches were made?
42 bologna sandwiches were made
How many bologna sandwiches were made?The ratio is given as
Cheese : Bologna : Peanut butter = 5 : 7 : 8
Also, we have
Total = 120 sandwiches
The number of bologna sandwiches made is calculated using
Bologna = bologna ratio/total ratio * 120
So, we have
Bologna = 7/(5 + 7 + 8) * 120
Evaluate
Bologna = 42
Hence, 42 bologna sandwiches were made
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Tom invites Maggie for a party. Maggie knows that on her way to Tom's house, she will come across 4 lanes. There
are five houses at the end of each lane. One of the five houses is Tom's. What is the probability that the first house
that Maggie checks is not Tom's?
Step-by-step explanation:
Given that
Tom invites Maggie for a party. Maggie knows that on her way to Tom's house, she will come across 4 lanes.There are five houses at the end of each lane. One of the five houses is Tom's.To find
The probability that the first house that Maggie checks is not Tom's?So, according to the question
we have,
There are five lanes with five houses at the end of each lane. It is clear that Tom's house is in the fifth lane because Maggie must cross four lanes to get there.Now, there are 5 homes on the first lane, and Tom's is one of them. Thus, there are 1 favorable outcomes and a total of 5 outcomes that could happen. The likelihood is therefore given as follows.We know that,
Probability P(E) = [tex]\frac{possible\;events}{no.\;of\;events}[/tex]
There is,
possible event is 1, and no. of events are 5.
So, we can say that
[tex]P(E) = \frac{1}{5}[/tex]
Answer:
The probability that the first house that Maggie checks is not Tom's is 1/5.To learn more about probability, please click on the link:
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The table shows information about the masses of some dogs.
a) Work out the minimum number of dogs that could have a mass of more than 24 kg.
b) Work out the maximum number of dogs that could have a mass of more than 24 kg.
a) A minimum of number of dogs that could have a mass of more than 24 kg is 6.
b) The maximum number of dogs that could have a mass of more than 18 kg is 20.
What do minimum and maximum value mean?Rearrange the function using fundamental algebraic concepts to get the value of x when the derivative equals 0. This response gives the x-coordinate of the function's vertex, which is where the maximum or minimum will occur. To find the minimum or maximum, rewrite the solution into the original function.
The minimum of the values present in the interval 20 to 40 is 6
The maximum of the values present in the interval 20 to 40 is (12+6) = 18
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Work out 10.3% of 853.93km
Give your answer rounded to 2 DP.
Answer: 87.96 km
Step-by-step explanation:
10.3% of 853.93km= 87.96 km
help me with this question
Answer:3
Step-by-step explanation:
How do I do this: 18 - (-21)
Answer:
39
Step-by-step explanation:
1) Remove parentheses.
18 + 21
2) Simplify.
39
Thanks,
Eddie
Quick hint:
When there is a number and then a - sign outside the parenthesis and on the inside, then it creates a figure similar to the plus sign, that is when you just make it one.
Add the two numbers (both are always positive in this instance),
and there's your answer!
