Using the weighted mean, it is found that Trent can earn scores of at least 62 on the final exam to pass the course if he needs a "C" or better.
What is the missing information?The complete problem is given as follows:
"Trent earns scores of 62, 86, and 80 on three chapter tests for a certain class.
His homework grade is 68 and his grade for a class project is 64.
The overall average for the course is computed as follows: the average of the three chapter tests makes up 50% of the course grade; homework accounts for 10% of the course grade; the project accounts for 20% of the course grade and the final exam accounts for 20% of the course grade.
What range of scores can Trent earn on the final exam to pass the course if he needs a "C" or better?
A "C" or better requires an overall course score of 70 or better, and 100 is the highest score that can be earned on the final exam."
What is the weighted mean?The weighted mean is given by the sum of all elements in a data-set multiplied by it's weight, divided by the sum of the weights.
For this problem, we have that:
The average of the three chapters is of (62 + 86 + 80)/3 = 76, with a weight of 0.5.Homework grade of 68, with a weight of 0.1.Class project grade of 64, with a weight of 0.2.Final exam grade of x, with a weight of 0.2.Hence his weighted mean is given by:
76 x 0.5 + 68 x 0.1 + 64 x 0.2 + 0.2x = 57.6 + 0.2x.
For a grade C, he needs a score of at least 70, hence:
57.6 + 0.2x ≥ 70.
0.2x ≥ 12.4
x ≥ 12.4/0.2
x ≥ 62.
Hence Trent can earn scores of at least 62 on the final exam to pass the course if he needs a "C" or better.
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Tina's refrigerator unexpectedly failed and she had to purchase a replacement for $1,100. Unfortunately, this came at the same time
that she had to pay her real estate taxes. She decided to use the store's credit offer of a 1.2% monthly periodic rate if the balance is not
paid by the second month. If she pays $500 by the second month and plans to pay the balance due at the end of the fourth month, how
much will she have to pay then?
$619.87.
$607.20.
$614.49.
$641.69.
Answer: if my math is correct i think its b
Step-by-step explanation:
The correct option is option C that is the due amount which Tina needs to pay at the end of fourth month is $ 614.4.
What is algebra ?
Algebra is a branch of mathematics that deals with various symbols and the arithmetic operations such as division , multiplication , etc.
It is given that Tina needs to purchase a refrigerator as replacement for $1100.
The monthly periodic rate if balance is not paid by the second month = 1.2 %
The amount she paid by the second month = $500
The due amount is :
= 1100 - 500
= $600
This amount she decided to pay by end of fourth month or after two more months.
Let's assume the amount she had to pay now at the end of fourth month is x then it given by :
= 600 + ( 600 × [tex]\frac{1.2}{100}[/tex] × 2)
= 600 + ( 12 × 1.2 )
= 600 + 14.4
= $ 614.4
Therefore , the correct option is option C that is the due amount which Tina needs to pay at the end of fourth month is $ 614.4.
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What is the price of 0.02percent of it is 0.01£?
Answer:
2*10^-4
Step-by-step explanation:
0.02*0.01
what is the relationship between
a and b are vertically opposite angle ...
☘☘☘...
If P(A)=0.9, P(B)=0.1, and A and B are independent, find P(A and B).
According to the given statement;
If P(A)=0.9, P(B)=0.1, and A and B are independent, P(A and B)=0.09
What is probability of event?The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a proposition is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty. The likelihood that an event will occur increases with its probability. A straightforward illustration is tossing a fair (impartial) coin. Since there are no other possible outcomes and the coin is fair, the odds of both the outcomes, "heads" and "tails," are equally likely to occur. As a result, the probability of either outcome is half.
According to the given value;
P(A) = 0.9
P(B) = 0.1
A and B independent;
We know that independent
P(A∩B) = P(A) · P(B)
= (0.9)*(0.1)
=0.09
P(A∩B) =0.09
hence, If P(A)=0.9, P(B)=0.1, and A and B are independent, P(A and B)=0.09
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7) Mt. Denali in Alaska measures about 5,500 meters from its base to its
highest peak. How high is this in feet? Round your answer to the nearest
thousand.
The measured height in feet of the base to its highest peak is 18045.5 feet
How to determine the measured height in feet?The given parameter is
Length of the base to its highest peak = 5500 meters
As a general rule
1 meter = 3.281 feet
So, we have:
Length of the base to its highest peak = 5500 * 3.281 feet
Evaluate the product
Length of the base to its highest peak = 18045.5 feet
Hence, the measured height in feet of the base to its highest peak is 18045.5 feet
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Simplify 5x - 4x
Show your work
Select the correct answer.
The number of cities in a region over time is represented by the function C(x)=2.9(1.05)^x. The approximate number of people per city is represented by the function P(x) = (1.05) (1.05) 3+5
Which function best describes T (2), the approximate population in the region?
OA. T (2) 2.9(1.05) 3²+5x
OB. T (T) (6.09)^4x+5
OC. T (1) 2.9(1.05)^4x+5
OD. T(x)= (3.045)^x + (1.05)^3x+5
The correct option is option C.
T(x) = 2.9(1.05)⁴ˣ ⁺ ⁵
Given the number of cities in a region is represented by the function:
C(x) = 2.9(1.05)ˣ
The approximate number of people per city is represented by the function P(x) = (1.05)³ˣ⁺⁵
we are asked to determine T(x), the approximate population in the region = ?
combine C(x) and P(x)
therefore, T(x) = C(x)P(x)
T(x) = 2.9(1.05)ˣ(1.05)³ˣ⁺⁵
During multiplication, when bases are same then powers are added.
T(x) = 2.9(1.05)³ˣ⁺ˣ⁺⁵
T(x) = 2.9(1.05)⁴ˣ⁺⁵
Hence we get the approximate function of T(x) as T(x) = 2.9(1.05)⁴ˣ⁺⁵
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Between which two perfect cubes does the cube root 141 lie
125 and 216 are two perfect cubes
A bald eagle flies 43.2 meters in 3 seconds. The graph shows the distance a typical peregrine falcon flies over time. At these rates, What is the difference in the distances flown by these two birds after 3 hours of flight? Show your
. find the rate of each birds speed in kilometers per hour
The difference between the distances flown by these birds is 150 Km.
According to the statement
We have to find that the rate of each birds speed in kilometers per hour.
So, For this purpose, we know that the
Graph is a mathematical representation of a network and it describes the relationship between lines and points.
From the given information:
We have the graph given within the question to understand it please see the image below.
We have to search out the difference within the distances flown by these two birds after 3 hours of flight.
According to the question -
The slope of the road is -
m = 400/5 = 80
The y - intercept of the road is 0.
Therefore c = 0.
Therefore, the equation of the road are -
y = 80x
The distance covered by Bird 1 is
D[1] = initial distance + 80 x 3 = 250 + 240 = 490 Km.
And
The distance covered by Bird 2 is
D[2] = initial distance + 80 x 3 = 400 + 80 x 3 = 400 + 240 = 640 Km.
Then
difference between the distances flown by these birds is D[2] - D[1] = 640 - 490 = 150 Km.
Therefore, The difference between the distances flown by these birds is 150 Km.
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5.6967 rounded to nearest thousandth
Answer
5.6967 rounded up will be 5.697.
Step-by-step explanation:
the sum of 3 consecutive even integers is 36. find the integers
Answer:
12, 12, and 12
Step-by-step explanation:
12 is an even integer, and 12 + 12 + 12 = 36, so it would be logical for 12 to be the unknown integer.
Enter the sum of numbers as a product of their GCF and another sum
25 + 35
The sum of the numbers as a product of their GCF is ___ x ( ___ + ___)
The sum of the numbers as a product of their GCF is 5 x ( 5 + 7 ).
Given,
25 + 35.
We need to find its GCF and another sum.
What is GCF?It is the greatest factor common to both 25 and 35.
Example: 8 and 24
- 4 x 2 = 8
- 4 x 6 = 24
4 is the GCF.
Find the GCF of 25 and 35.
5 x 5 = 25
5 x 7 = 35
5 is the GCF of 25 and 35.
Now,
25 + 35 = 60
5 x ( 5 + 7 ) = 5 x 12 = 60
The sum of the numbers as a product of their GCF is 5 x ( 5 + 7 )
Thus,
The sum of the numbers as a product of their GCF is 5 x ( 5 + 7 ).
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point x is located at (4.8, 0.8) and divides line segment AB in ratio 2:3 select two possible sets of endpoints for segment AB
The possible endpoints are: (i) A(x, y) = (6, - 2) and B(x, y) = (3, 5), (ii) A(x, y) = (4, 4) and B(x, y) = (6, - 4).
What are the possible locations of the endpoints of a line segment?
In this problem we know the location of the midpoint and the line segment ratio. There are two posibilities according to the definition of line segment ratio:
AX / BX = 2 / 3 (1)
BX / AX = 2 / 3 (2)
And now we solve for each case:
Case 1
X(x, y) = A(x, y) + (2 / 5) · [B(x, y) - A(x, y)]
X(x, y) = (3 / 5) · A(x, y) + (2 / 5) · B(x, y)
(4.8, 0.8) = (3 / 5) · A(x, y) + (2 / 5) · B(x, y)
(4.8, 0.8) = 0.6 · A(x, y) + 0.4 · B(x, y)
(4.8, 0.8) - 0.6 · A(x, y) = 0.4 · B(x, y)
(12, 2) - 1.5 · A(x, y) = B(x, y)
B(x, y) = (12, 2) - 1.5 · A(x, y)
Now we proceed to check each choice:
A(x, y) = (6, - 2)
B(x, y) = (12, 2) - 1.5 · (6, - 2)
B(x, y) = (3, 5) TRUE
A(x, y) = (6, 2)
B(x, y) = (12, 2) - 1.5 · (6, 2)
B(x, y) = (3, - 1) FALSE
A(x, y) = (8, 1)
B(x, y) = (12, 2) - 1.5 · (8, 1)
B(x, y) = (0, 0.5) FALSE
A(x, y) = (2.4, 0.4)
B(x, y) = (12, 2) - 1.5 · (2.4, 0.4)
B(x, y) = (8.4, 1.4) FALSE
A(x, y) = (4, 4)
B(x, y) = (12, 2) - 1.5 · (4, 4)
B(x, y) = (6, - 4) TRUE
A(x, y) = (1.8, - 1.2)
B(x, y) = (12, 2) - 1.5 · (1.8, - 1.2)
B(x, y) = (9.3, 3.8) FALSE
Case 2
X(x, y) = B(x, y) + (2 / 5) · [A(x, y) - B(x, y)]
X(x, y) = (2 / 5) · A(x, y) + (3 / 5) · B(x, y)
(4.8, 0.8) = (2 / 5) · A(x, y) + (3 / 5) · B(x, y)
(4.8, 0.8) = 0.4 · A(x, y) + 0.6 · B(x, y)
(4.8, 0.8) - 0.4 · A(x, y) = 0.6 · B(x, y)
(12, 2) - 0.667 · A(x, y) = B(x, y)
B(x, y) = (12, 2) - 0.667 · A(x, y)
Now we proceed to check each choice:
A(x, y) = (6, - 2)
B(x, y) = (12, 2) - 0.667 · (6, - 2)
B(x, y) = (8, 3.334) FALSE
A(x, y) = (6, 2)
B(x, y) = (12, 2) - 0.667 · (6, 2)
B(x, y) = (8, 0.667) FALSE
A(x, y) = (8, 1)
B(x, y) = (12, 2) - 0.667 · (8, 1)
B(x, y) = (6.664, 1.333) FALSE
A(x, y) = (2.4, 0.4)
B(x, y) = (12, 2) - 0.667 · (2.4, 0.4)
B(x, y) = (10.399, 1.733) FALSE
A(x, y) = (4, 4)
B(x, y) = (12, 2) - 0.667 · (4, 4)
B(x, y) = (9.332, - 0.668) FALSE
A(x, y) = (1.8, - 1.2)
B(x, y) = (12, 2) - 0.667 · (1.8, - 1.2)
B(x, y) = (10.8, 2.8) FALSE
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tyler has 14 boards cut to 3/4 yards and one that is 2 1/4 yards. what is the total length of the boards.
Answer:
vhdvbhahshsh
shsljjhsishhgdddndhd
Please I need to know
Answer:
46
Step-by-step explanation:
solve this question 1
HELP!!!! Finding the initial amount and rate of change given a table for a linear function
The initial amount and rate of change given a table for a linear function are $65 and $86, respectively
How to find the initial amount and rate of change given a table for a linear function?The table of linear function represents the given parameter
On the table, we have the following points
(x, y) = (6, 476) and (10, 736)
The rate of change is calculated as
Rate = (y2 - y1)/(x2 - x1)
So, we have
Rate = (736 - 476)/(10 - 6)
Evaluate
Rate = 65
This means that the rate of change is $65
The initial amount is calculated as
y = m(x - x1) + y1
Where
m = 65
So, we have
y = 65(x - x1) + y1
Using one of the points, we have
y = 65(x - 6) + 476
Set x = 0
So, we have
y = 65(0 - 6) + 476
Evaluate
y = 86
Hence, the initial amount and rate of change given a table for a linear function are $65 and $86, respectively
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1
1) Find the average rate of change in height for Chuck. At age 10, Chuck
was 51 inches tall. At age 18, Chuck was 64 inches tall.
I
The average rate of change is 1.625.
How to find the average rate of change?The average rate of change in height for chuck can be found as follows:
The average rate of change is a measure of how much the function changed per unit, on average, over that interval.
Therefore,
average rate of change = change in y / change in x
Therefore,
(10, 51)(18, 64)
average rate of change = y₂ - y₁ / x₂ - x₁
x₁ = 10
x₂ = 18
y₁ = 51
y₂ = 64
Therefore,
average rate of change = 64 - 51 / 18 - 10
average rate of change = 13 / 8
average rate of change = 1.625
Therefore, the average rate of change is 1.625.
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URGENT PLEASE HELP ‼️
After investing a sum of money for 10 years a person accumulated $84 200. The simple interest earned from the investment was $24 600.
(a) What was the initial sum of money invested?
(b) What was the percentage rate of return per annum on the investment?
Answer- A) 59,600 ; B) 4.12% per year.
Explanation
84,200 minus 24,600 is 59,600. This means the originally cost put into the account was 59,600.
Next we have to divide the amount of interest earn into the number of years that the amount was accumulated. 24,600 divided by 10 is 2460. This means that each year 2,460 were earned in interest. 59,600 divided into 2,460 is 0.0412751678. This rounds to .0412 If we move our decimal to a percentage this leaves us with 4.12% This means that annual interest on the investment is 4.12%
Hope this helps! Good Luck!
need to find the value of xp
Answer:
x = 10
Step-by-step explanation:
it is given that: Line m || line n and line t is their transversal.(6x + 10)° is the vertical angle of the interior angle formed by the top line (perhaps line m) and it's transversal.Thus, by interior angles on the same side of the transversal, we have:-> (6x + 10)° + (10x + 10)° = 180° -> (16x + 20)° = 180°-> 16x + 20 = 180-> 16x = 180 - 20-> 16x = 160x = 160/16x = 105 Q1. The multiplicative inverse of - 5/7
(-7/5) is the multiplicative inverse of the number - 5/7.
The answer to the question is (b/a), which is the multiplicative inverse of the fraction number that is (a/b).
So, according to the question:
The reciprocal of (-5/7) is (-7/5).
As a result, (-7/5) is the right response to a multiplicative inverse.
What is inverse multiplicative?The reciprocal of the supplied integer can be used to establish a number's multiplicative inverse. The denominator must not be 0 in order for a multiplicative inverse to exist. And the result of the multiplication should be 1.
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3. How many ways can 10 students line up for lunch?
The 10 students can be lined up for lunch in 3628800 ways.
What is factorial of a number?Factorial of a number n is defined as the product of that number with every number less than or equal to the given number till 1.
The formula is given by:
n! = n(n-1)(n-2)(n-3(n-4)(n-5)(n-6)....3.2.1
We have,
n! = n(n-1)(n-2)(n-3)(n-4)(n-5)......3.2.1
We have to arrange for 10 students so n = 10.
Now,
10! = 10.9.8.7.6.5.4.3.2.1
Multiply each number.
10! = 3628800 ways
Therefore the 10 students can be lined up for lunch in 3628800 ways.
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If your car gets 33 miles per gallon, how much does it cost to drive 350 miles when gasoline costs $3.50 per gallon?
Answer:
$37.12
Step-by-step explanation:
Total cost = $3.50(350/33) = $37.12
passes through (-2,1) perpendicular to y = 4x -11
The equation of a line which is perpendicular to [y = (4x - 11)] and passes through the point (-2, 1) will be [(4y + x) = 2].
As per the question statement, a line is perpendicular to [y = (4x - 11)] and passes through the point (-2, 1).
We are required to determine the equation of the above mentioned line.
Now, we know that, the standard equation of a line goes as [y = (mx + c)] where, "m" is the slope of the line while "c" is the y-intercept.
Comparing [y = (4x - 11)] to the standard form, we can identify that (m = 4), i.e., slope of the given line is 4.
Since the products of the slopes of two perpendicular lines is (-1), and considering the slope of our required line to be "m₁", we can say that,
[tex]4*m_{1}=(-1)\\ or,m_{1}=\frac{-1}{4}[/tex]...[since our required line is perpendicular to [y = (4x - 11)]
and slope of [y = (4x - 11)] is 4]
That is, slope of our required line is [tex](\frac{-1}{4})[/tex].
Another concept we need to know about forming the equation of a line is that, the equation of a line can be written as [tex][(y-y_{1})=m(x-x_{1})][/tex], if the line passes through the point (x₁, y₁).
Here, our concerned line passes through the point (-2, 1) and has a slope of [m = [tex](\frac{-1}{4})[/tex]].
Therefore, equation of our concerned line can be written as
[tex](y-1)=(\frac{-1}{4})[x-(-2)]\\or,(y-1)=(\frac{-1}{4})(x+2)\\or,(y-1)=(\frac{-x}{4})+(\frac{-1}{4}*2)\\ or,(y-1)=(\frac{-x}{4})+(\frac{-1*2}{4})\\or,(y-1)=(\frac{-x}{4})+(\frac{-1}{2})\\or,y=(\frac{-x}{4})+1+(\frac{-1}{2})\\or,y=(\frac{-x}{4})+(1-\frac{1}{2})\\or, y=(\frac{-x}{4})+\frac{1}{2}\\or,4y=(-x)+2\\or,4y+x=2[/tex]
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Si 14 % de un número es 160 ¿cuánto es de 10%
What is the 10% of number in which the 14% is 160
What does percentage mean?Although "pct," "pct," and occasionally "pc" are also used as abbreviations, the percent symbol "%" is most usually used to denote it. A% is a number that has neither dimensions nor a defined unit of measurement.
being that,
14% × x = 160
14/100 × x = 160
x = 160 × 100/14
x = 1142.86
The current value is 1142.86.
10% of the total number must be located.
to say,
10% x 1142.86 = 10 / 100 x 1142.86
= 114.286
Consequently, 114.286 is the value of the 10% of the number.
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Evaluate each expression when x = 2.
Number 31 i will give brainliest
Refer to the graph at the right. Write each equation in the correct column.
The only possible equation of the drawn line is: y - 2 = 1/2(x + 4)
The rest options are not equations of the drawn line.
What is the Equation of a Line in Point-Slope Form?The equation, y - b = m(x - a), is the point-slope form of any given line where m is the slope of the line and any point on the line is given as (a, b).
Slope (m) = rise/run.
Find the slope (m) of the graph at the right.
Slope (m) = rise/run = 1 units/2 units
Slope (m) = 1/2.
Any possible equation of the line should have a slope of 1/2.
y - 2 = 1/2(x - 4), y - 2 = 1/2(x + 4), and y - 4 = 1/2(x - 2) are the only equations that has a slope of 1/2.
Using a point on the line, say (0, 3), substitute x = 0 and y = 3 into each of the three equations to check if the equation is true.
y - 2 = 1/2(x - 4)
3 - 2 = 1/2(0 - 4)
1 = -2 [not true]
y - 2 = 1/2(x + 4)
3 - 2 = 1/2(0 + 4)
1 = 2 [not true]
y - 4 = 1/2(x - 2)
3 - 4 = 1/2(0 - 2)
-1 = -1 [true]
Therefore, the only possible equation of the drawn line is: y - 2 = 1/2(x + 4)
The rest 4 equations are not equations of the drawn line.
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-1/2+1/9 it's supposed to be fractions but I can't figure out how to do it on here
Answer:
-7/18
Step-by-step explanation:
Multiply both the numerator and denominator of each fraction by the number that makes its denominator equal the LCD. This is basically multiplying each fraction by 1.
( -1/2 × 9/9) + (1/9 × 2/2) = ?
Complete the multiplication and the equation becomes:
-9/18 + 2/18 = ?
Then:
-9+2/18 = -7/18
Therefore:
-1/2 + 1/9 = -7/18
A package of 4 pairs of insulated gloves costs $26.36. What is the unit price of the pairs of gloves?
The unit price of the pair of gloves is $6.59
How to find the unit price of the pair of gloves?The package contains 4 pairs of insulated gloves costs $26.36.
The unit price of the pairs of gloves can be found as follows:
Unit price is the price at which a single quantity of a product is being sold.
Therefore, the unit price is the price of a single pair of gloves.
Hence,
unit price of the pair of gloves = total price / number of pairs of gloves
where
total price = $26.36number of pairs of gloves = 4Therefore,
unit price of the pair of gloves = 26.36 / 4
unit price of the pair of gloves = $6.59
Therefore, the unit price of the pair of gloves is $6.59
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a function has an initial value of 5 and a rate of change of 6 PLEASE HELP MEEEEE
