If the test scores of a class of 34 students have a mean of 73.1 and the test scores of another class of 26 students have a mean of 66.4, then the mean of the combined group is
The Mean of the combined class is 70.19.
MeanMean is the average of a set of two or more numbers. The arithmetic and geometric mean are the types of mean that can be calculated.
Mean formula[tex]\rm Mean = \dfrac{sum\ of\ the\ term}{total\ number\ of\ term}[/tex]
Given
The test scores of a class of 34 students have a mean of 73.1 and
The test scores of another class of 26 students have a mean of 66.4.
To find
The mean of the combined group.
How to get the mean of the combined group?The sum of the total of the test score = Total number of students x Mean
Class 1 sum will be
The sum of the total test score = 34 x 73.1
The sum of the total test score = 2485.4
Class 2 sum will be
The sum of the total test score = 26 x 66.4
The sum of the total test score = 1726.4
Than Mean for the combine will be
[tex]\rm Mean = \dfrac{sum\ of\ the\ term}{total\ number\ of\ term}\\\\Mean = \dfrac{2485.4+1726.4}{34+26} \\\\Mean = \dfrac{4211.8}{60} \\\\Mean = 70.19[/tex]
Thus the Mean of the combined class is 70.19.
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Suppose given an isosceles triangle with a leg measuring 5 in. Two lines are drawn through some point on the base, each parallel to one of the legs. Find the perimeter of the constructed parallelogram.
Let ΔABC be isosceles triangle with legs AB=BC=5 in. Draw an arbitrary point D on the base AC and spend two lines DE and DF such that DE || BC and DF || AB.
You get the parallelogram BFDE.
1. Consider ΔAED. This triangle is isosceles, because ∠ADE≅∠ACB as corresponding angles at parallel lines. The legs of this triangle are AE=ED.
2. Consider ΔDFC. This triangle is isosceles, because ∠FDC≅∠BAC as corresponding angles at parallel lines. The legs of this triangle are DF=FC.
3. Find the perimeter of parallelogram BFDE.
[tex]P_{BFDE}=BF+FD+ED+BE.[/tex]
Since AE=ED and DF=FC, you have that
[tex]P_{BFDE}=BF+FC+AE+BE=AB+BC=5+5=10\ in.[/tex]
Answer: 10 in.
A circular city park has a sidewolk directly through the rmiddle that is 111- feet long. I each bag of fertilizer covers 50 square feet, then determine how many bags of tertilizer the Parks and Recreation department needs to use to cover the circular park. Ignore oll the sidewalks around and through the park.
The answer should be a fraction
Evaluate g(n-5) if g(x)=x^2-6/2x
Answer: We want to evaluate g(x) in x = n -5, where g(x) = (x^2-6)/2x
then, doing it step by step: [tex]g( n- 5)= \frac{(n-5)^{2} - 6 }{2*(n-5)}= \frac{(n^{2} - 2*5*n + 25) - 6 }{2n - 10} = \frac{n^{2} - 10n + 19 }{2n - 10}[/tex]
where i used that (a - b)^2 = a^2 -2ab + b^2
So the correct option is C.
Solve the equation by completing the square. Round to the nearest hundredth if necessary. x2 – 4x = 5
Answer:
x = 5 or x = -1
Step-by-step explanation:
x^2 – 4x = 5
Solve it by completing the square method
In completing the square method, we take the coefficient of x that is -4, divide it by 2 and then square it
-4/2 = -2
square it (-2)^2 = 4
Now add 4 on both sides
x^2 – 4x +4 = 5+4
x^2 – 4x +4 = 9
Now factor the left hand side
(x-2)(x-2)=9
(x-2)^2 = 9
Take square root on both sides
x-2 = +-3
x-2 = 3 , so x= 5
x-2 = -3, so x= -1
describe the graph of y=3/4x-12 as compared to the graph of y=1/x
Answer:
Parent function is compressed by a factor of 3/4 and shifted to right by 3 units.
Step-by-step explanation:
We are asked to describe the transformation of function [tex]y=\frac{3}{4x-12}[/tex] as compared to the graph of [tex]y=\frac{1}{x}[/tex].
We can write our transformed function as:
[tex]y=\frac{3}{4(x-3)}[/tex]
[tex]y=\frac{3}{4}*\frac{1}{(x-3)}[/tex]
Now let us compare our transformed function with parent function.
Let us see rules of transformation.
[tex]f(x-a)\rightarrow\text{Graph shifted to the right by a units}[/tex],
[tex]f(x+a)\rightarrow\text{Graph shifted to the left by a units}[/tex],
Scaling of a function: [tex]a*f(x)[/tex]
If a>1 , so function is stretched vertically.
If 0<a<1 , so function is compressed vertically.
As our parent function is multiplied by a scale factor of 3/4 and 3/4 is less than 1, so our parent function is compressed vertically by a factor of 3/4.
As 3 is being subtracted from x, so our parent function is shifted to right by 3 units or a horizontal shift to right by 3 units.
Therefore, our parent graph is compressed by a factor of 3/4 and shifted to right by 3 units to get our new graph.
Final answer:
The equation y=3/4x-12 represents a linear function with a straight line graph, while y=1/x depicts a rectangular hyperbola with a curved graph showcasing an inverse relationship. These graphs exhibit fundamentally different behaviors, one being constant and the other varying.
Explanation:
The student's question involves comparing the graph of y=3/4x-12 to the graph of y=1/x. The first equation, y=3/4x-12, describes a linear function with a slope of 3/4 and a y-intercept of -12. This means it is a straight line that increases as x increases, crossing the y-axis at (0, -12).
On the other hand, the graph of y=1/x is a rectangular hyperbola. This curve approaches the x-axis and y-axis but never touches them, known as asymptotes. The hyperbola is divided into two parts, one in the first quadrant where both x and y are positive, and another in the third quadrant where both x and y are negative. This graph does not resemble a straight line at any part.
Comparatively, the key difference lies in the nature of their graphs - one is a straight line and the other a curved hyperbola, showcasing completely different behaviors. The linear equation reflects constant change, whereas the hyperbola’s rate of change varies with x, indicating an inverse relationship.
HELP PLEASE
Translate the answer, T2 = A3, into words:
The BLANK of the orbital period, T, of a
planet is equal to the BLANK of the average distance, A, of the planet from the Sun.
Square
Square Root
Cube
Answer: The square of the orbital period, T, of a planet is equal to the cube of the average distance, A, of the planet from the Sun.
Step-by-step explanation:
In mathematics, A number or variable 'a' to its second power is said to be square of 'a' i.e. [tex]\ a^2[/tex] is the square of a.
A number or variable 'b' to its third power is said to be cube of 'b' i.e. [tex]\ b^3[/tex] is the cube of b.
In the given equation: [tex]T^2 = A^3[/tex]
Here, [tex]T^2 [/tex] is square of T.
And [tex]A^3[/tex] is cube of A.
Therefore, The square of the orbital period, T, of a planet is equal to the cube of the average distance, A, of the planet from the Sun.
HELP ME ANSWER THIS QUESTION!
Boyd (B) is trapped in a soccer training circle. Albert (A) and Carlos (C) kick the ball to Boyd in rotation. Determine how far Boyd needs to kick the ball to Carlos if he is located in the center of his training circle and Carlos is located at the outer rim.
A bank runs a contest to encourage new customers to open accounts. In the contest, each contestant draws a slip representing a different reward—$5, $3, or $x—from a jar. At the beginning of the contest the jar contains 60 slips for $5, 40 slips for $3, and 50 slips for $x.
If the expected value of the first draw from the jar is $5.8, the value of x is__
At one point in the contest, the jar contains 3 slips for $5, 7 slips for $3, and y slips for $x. If the expected value on the next draw is $6, the value of y is __
Which triangle is it ?
a paragraph of; compare savings and investments
Which simplified equation is equivalent to the equation shown below?
4x+x-3-9+4x=6
a.5x-8=6
b.-3x=6
c. 9x-12=6
d. 8x-12=6
We need to group the like terms and combine like terms to get the simplified equation.
[tex] 4x+x-3-9+4x=6\\ \\ Step \; 1: \; Group \; like\; terms\\ \\ 4x+x+4x-3-9=6\\ \\ Step \; 2: \; Combine \; like\; terms\\ \\ 9x-12=6 [/tex]
Conclusion:
Option C is the right answer !!
which of the following is equivalent to the polynomial below
Find geometric mean of the pair of number 6 and 10
The Geometric mean of the pair of number 6 and 10 is [tex]7.74[/tex]
Geometric mean :The geometric mean of two number m and n is given as,
[tex]G.M=\sqrt{m*n}[/tex]
Geometric mean of the pair of number 6 and 10 is,
[tex]G.M=\sqrt{6*10} =\sqrt{60} \\\\G.M=7.74[/tex]
Learn more about the Geometric mean here:
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Can you answer this one for my plz I need before Monday ty
A triangle has one 60 degree angle and one 20 degree angle. The third angle in the triangle must be
a.acute
b.obtuse
c.commplementary
d.straight
PLEASE HELP FAST!!!!!!!!!!!! WILL GIVE BRAINILST OR WHATEVER :)))))))))))
let f(x)=4x+3 and g(x)=-2+5. find (fog) (5)
1.Write equatios to represent the distances the family drove on the given days.
2. construct a math argument to explain why your answer to 5 is correct.
3. How can you check that your answer is reasonable?
The scale on a map is 1 cm:35 mi. The distance on the map between Los Angeles, CA, and San Francisco, CA, is 10.8 cm. What is the actual distance between Los Angeles and San Francisco?
Step 1: Let us assign variable for the unknown that we need to find.
' x ' be the actual distance between Los Angeles and San Francisco
Step 2: Set up an equation based on the given statement "The scale on a map is 1 cm:35 mi. The distance on the map between Los Angeles, CA, and San Francisco, CA, is 10.8 cm."
[tex] \frac{distance \; in \; cm}{distance\; in\; miles}=\frac{1}{35}=\frac{10.8}{x} \\ \\ Cross \; Multiply\\ \\ 1 \cdot x = 35 \cdot 10.8\\ \\ x = 378 [/tex]
Conclusion:
The actual distance between Los Angeles and San Francisco is 378 miles.
A triangle on a coordinate plane is translated according to the rule T–3, 5(x, y). Which is another way to write this rule?
(x, y) → (x – 3, y + 5)
(x, y) → (x – 3, y – 5)
(x, y) → (x + 3, y – 5)
(x, y) → (x + 3, y + 5)
Another way to write the given rule is (x, y) → (x – 3, y + 5).
Given that,
There are the original x and y coordinates that are being moved to the left-hand side by 3 units and go up by 5 units.Based on the information, we can conclude that another way to write the given rule is (x, y) → (x – 3, y + 5).
Hence, the other options are incorrect.
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What is the measure of angle z in this figure?
Enter your answer in the box.
z = ___°
Which shows how the distributive property can be used to evaluate 7×84/5?
The perimeter of a quilt is 34 ft. If the quilt is 8 ft long, what is the area
If you take out a loan that costs $130.50 over nine years at an interest rate of 10%, how much was the loan for?
The original loan amount for which the final amount payable is $130.50 over nine years at an interest rate of 10% was approximately $55.39.
Explanation:To find out the original amount of the loan for which the final amount payable is $130.50 over nine years at an interest rate of 10%, we will use the formula for the present value of a loan.
The formula given is P = A / (1 + r/n)^nt, where P is the principal (initial loan amount), A is the final amount, r is the annual interest rate (expressed as a decimal), n is the number of times that interest is compounded per year, and t is the time the money is borrowed for in years.
As the question doesn't specify how many times the interest is compounded per year, we will assume it is compounded once a year (n=1).
We have:
A = $130.50,r = 10% or 0.10,n = 1,t = 9 years.Plugging these values into the formula:
P = $130.50 / (1 + 0.10/1)^(1*9)
P = $130.50 / (1 + 0.10)^9
P = $130.50 / (1.10)^9
P = $130.50 / 2.35794769
P = $55.39 approximately
Therefore, the original loan amount was approximately $55.39.
factor, x^4y+8x^3y-6x^2y^2-48xy^2
What is the following product? 3 sqrt d x 3 sqrt d x 3 sqrt d
Answer: the first option, d.
Step-by-step explanation:
How to start the problem off. (substitution)
1. A rectangular prism is defined as the drawing shows. Note B at (0, 5, 0) and F (0, 0, 4). The prism is reflected over the xz-plane. The reflected image is then translated 2 units back, 3 units left, and 1 unit up.
a.) Show the results of your calculations for points A, B, C and D from the reflection.
b.) Show the results of your calculations for points A, B, C and D from the translation.
8. The U.S. population was 309 million in 2010. If the U.S. had had the same firearm death rate as Australia in 2010, how many firearm deaths would the U.S. have expected to have that year? Australia’s population was 22.3 million people in 2010. Australia had 236 firearm deaths in 2010. (round to the nearest person)
As per linear equation, in 2010 the expected firearm death U.S. had is 3270.
What is a linear equation?A linear equation represents an equation that has one or multiple variables with the highest power of the variable is 1.
Australia’s population was 22.3 million people in 2010.
Australia had 236 firearm deaths in 2010.
Therefore, portion of Australian population had firearm deaths is
[tex]= \frac{236}{22.3(10)^{6} } \\= 0.000011[/tex]
The U.S. population was 309 million in 2010.
Therefore, the expected firearm deaths in U.S. in 2010 was
[tex]= (309) (10^{6}) (0.000011)\\= 3270.13\\= 3270[/tex]
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