The average yearly salary of the final year is 67000 in dollars.
What is average ?
An average is a single number selected to stand in for a collection of numbers; it is frequently the product of the sum of the numbers divided by the total number of the collection. For example, the average of the integers 2, 3, 4, 7, and 9 is 5.
Let x = the average salary of an individual with the bachelor's degree, in dollars.
Then the average salary of an individual with master's degree is (2x - 35000)in dollars.
According to the sum of these salaries is 118000 dollars:
x + (2x-35000) = 118000
by solving we get
x = 153000/3
x = 51000
Hence, The average salary of an individual with the bachelor's degree is 51000 in dollars.
the average salary of an individual with the master's degree (2*51000 - 35000) = 67000 in dollars.
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Learning
Square TUVW is dilated by a scale factor of with respect to the origin.
Then, it is translated 8 units down to produce TUVw
104-7
units
Submit
d
What is the area of T'U'V'W'?
square units
543211
W
5
4-
3
121
-2
9
4
40
What is the perimeter of T'U'V'W"?
ich d
5
6
7
-8
S
U
78 10
GATHS Stow &
V
Que
Answer:
perimeter: 80area: 400Step-by-step explanation:
Given square TUVW, you want the perimeter and area of square T'U'V'W' after it has been dilated by a factor of 5/2 and translated by (0, -8).
PerimeterCounting grid squares, or reading coordinates, we find the length of a side of square TUVW to be 8 units. Then the perimeter is ...
P = 4s = 4·8 = 32 . . . . units
After dilation, the perimeter of the square is the preimage value multiplied by the dilation factor.
perimeter of T'U'V'W' = (5/2)(perimeter of TUVW) = (5/2)(32 units)
perimeter of T'U'V'W' = 80 units.
AreaThe area is the square of the side length. The side length of T'U'V'W' is ...
s' = (5/2)(8) = 20 . . . . units
Then the area is
A' = (s')² = (20 units)² = 400 units²
area of T'U'V'W' is 400 units².
__
Additional comment
Translation is a rigid transformation. It does not change the dimensions, so does not change the perimeter or area of the dilated square.
Solve
|2x+8 > 10
x < [?] or x >[]
Answer:
x < - 9 or x > 1
Step-by-step explanation:
inequalities of the type | x | > a have a solution of the form
x < - a or x > a
| 2x + 8 | > 10 is of this type , then
2x + 8 < - 10 or 2x + 8 > 10 ( subtract 8 from both sides of each inequality) )
2x < - 18 or 2x > 2 ( divide both sides of each by 2 )
x < - 9 or x > 1
If 7p−4=8, what is the value of p?
Answer:
p =12/7
Step-by-step explanation:
7p -4=87p-4+4=8+47p=127p/7=12/7p=12/7Answer:
p = 12/7
Step-by-step explanation:
7p - 4 = 8
+4 +4
7p = 12
/ /
7 7
p = 12/7
Jamie receives 20 emails total on Monday morning she responds to eight of the emails what is the ratio emails that Jamie received to the mail that she answered
Answer:
5:2
Step-by-step explanation:
A ratio is basically a fraction but horizontally for eg. this: 5:8! This question is asking us to find the ratio of the emails that Jamie received to the emails that she answered.
According to the question, Jamie got 20 emails and responds to 8 of them. The ratio would look like this: 20:8 (because a ratio is just a fraction but horizontal, doesn't mean that there will be mixed numbers!) but not this 8:20. Ratios have a specific order that they have to be in and that will vary depending on the question. If the question says to find the ratio of emails that Jamie responded to to the emails that she received, then in this case 8:20 would be correct.
For now, the answer is 20:8. However, we still need to simplify it by finding its lowest common factor (unless the question asks you to not simplify it, it's better to simplify the answer like a fraction). The lowest common factor would be 4 for 20 and 8. 4 goes in 20 5 times sand 4 goes into 8 2 times.
Your final answer should be: 5:2
If you have any further questions please ask!
Madison and Cindy have a combined age of 65 Cindy is 20 less than four times Madison's age how old are Madison and Cindy
Cindy's age is 40 years and Madison's age is 17 years.
What is an expression?Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also be used to denote the logical syntax's operation order and other properties.
Given that Madison and Cindy have a combined age of 65 Cindy is 20 less than four times Madison's age. The age will be calculated by using the information.
C + M = 65
C = 4M - 20
4M - 20 + M = 65
5M = 65 + 20
5M = 85
M = 85 / 5
M = 17 years
Therefore, Cindy's age is 40 years and Madison's age is 17 years.
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What is 3/25 as an equivalent fraction?
Step-by-step explanation:
equivalent fractions are all fractions with different numbers in numerator and denominator, but after simplifying they have the same value.
like 1/2 and 3/6 are equivalent fractions to each other.
so, the equivalent fractions for 3/25 are
a/a × 3/25
for any "a".
e.g.
6/50, 15/125, 300/2500, ...
270 cal and three servings 450 cal in five servings
Answer:
5 Servings
Step-by-step explanation:
Write the equation of the line that passes through the points ( 7 , − 7 ) (7,−7) and ( 3 , 8 ) (3,8). Put your answer in fully simplified point-slope form, unless it is a vertical or horizontal line.
Answer:
horizontal line isywgwueve
Evaluate the expression when x = -0.75.
1. -x
2. |x| - 0.75
3. 2 • (-x)
4. |x| + |x|
I THINK X IS 2) : -0.75
9<2x +7<15? What does X equal
Answer: X = 2
Step-by-step explanation:
2(2)+7 = 11 --> 9<11<15
Hope this helps you :)
3. An investor received a check in the mall
that was for 6 percent of the amount
invested. If the amount invested was $450.
what was the amount of the check?
(1) $ 24.30
(2) $ 27.00
(3) $ 27.30
(4) $ 75.00
(5) $270.00
The amount of the check with 6 percent of the amount invested was (2) $27.00.
What is the percentage?A percentage is a number or ratio expressed as a fraction of 100 in mathematics. Although the abbreviations "pct.", "pct.", and occasionally "pc" is also used, the percent sign, "%," is frequently used to denote it.Since one percent (symbolized as 1%) is equal to one-hundredth of something, 100 percent stands for everything, and 200 percent refers to twice the amount specified. As an illustration, 1% of 1,000 chickens is equal to 1/100 of 1,000, or 10 chickens, and 20% of the quantity is equal to 20% of 1,000, or 200.So, 6% of $450:
Then,
Therefore, the amount of the check with 6 percent of the amount invested was (2) $27.00.
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A random sample of 100 individuals finds a sample mean value of 22 and sample standard deviation of 3. What is the 99% confidence interval for the population mean? A random sample of 100 individuals finds a sample mean value of 22 and sample standard deviation of 3. What is the 99% confidence interval for the population mean? D. [21.30 , 22.70] B. [21.07 , 22.93] C. [21.01, 22.99] A. [21.23 , 22.77]
If a random sample of 100 individuals finds a sample mean value of 22 and sample standard deviation of 3. The 99% confidence interval for the population mean is: A. [21.23 , 22.77].
Confidence intervalUsing this formula
Confidence interval=Sample means± (z-score× Standard deviation/√Sample size)
Let plug in the formula
The corresponding z-scores for 99% confidence interval is ± 2.575
Hence:
Confidence interval=22± (2.575×3÷√100)
Confidence interval=22± (2.575×3÷10)
Confidence interval=22± (2.575×0.3)
Confidence interval=22± 0.7725
Confidence interval=(22-0.7725); (22+ 0.7725)
Confidence interval=21.23, 22.77
Therefore If a random sample of 100 individuals finds a sample mean value of 22 and sample standard deviation of 3. The 99% confidence interval for the population mean is: A. [21.23 , 22.77].
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Two consecutive multiples of 9 sum up to 63. Fine the numbers
Answer:
27, 36
Step-by-step explanation:
We can write the first number as 9n because it is a multiple of 9, and the second number will be 9(n + 1). We can write:
9n + 9(n + 1) = 63 because they have a sum of 63.
9n + 9n + 9 = 63
18n + 9 = 63
18n = 54
n = 3
This means that the first number is 9 * 3 = 27 and the second is 9 * (3 + 1) = 9 * 4 = 36.
-5/6x =-10/3 solver for x
Answer:
X = 4
Step-by-step explanation:
Remove the fraction first by multiplying with 6 both sides.
Then leave the variable alone by diving with - 5
-------------------------------------------------------------------------------------------------------------
Answer: [tex]\textsf{x= 4}[/tex]
-------------------------------------------------------------------------------------------------------------
Given: [tex]\textsf{-5/6x = -10/3}[/tex]
Find: [tex]\textsf{The value of x}[/tex]
Solution: In order to get the value of x we must multiply both sides by -6/5 to help cancel the coefficient on the left side to leave x by itself.
Multiply both sides by -6/5
[tex]\textsf{-5/6x * -6/5 = -10/3 * -6/5}[/tex][tex]\textsf{x = -10/3 * -6/5}[/tex][tex]\textsf{x = (-10 * -6)/(3 * 5)}[/tex]Simplify the expression
[tex]\textsf{x= 60/15}[/tex][tex]\textsf{x= 4}[/tex]Therefore, the value of the unknown variable x is 4.
Which is bigger, two thirds of 30 or one fifth of 25
Answer:
2/3s of 30
Step-by-step explanation:
2/3s of 30 is 10 and 1/5 of 25 is 5 and 10 is in fact larger than 5
sec(2a + 6°) cos(5a + 3º) = 1
Answer:
Step-by-step explanation:
sec(2a+6)cos (5a+3)=1
[tex]\frac{cos(5a+3)}{cos(2a+6)} =1\\[/tex]
cos(5a+3)=cos(2a+6)
cos(5a+3)-cos(2a+6)=0
[tex]-2sin(\frac{5a+3+2a+6)}{2} )sin(\frac{5a+3-2a-6)}{2} )=0\\-2sin(\frac{7a+9}{2} )sin(\frac{3a-3}{2} )=0\\either sin (\frac{7a+9}{2} )=0=sin ~n\pi \\\frac{7a+9}{2} =n~\pi \\7a+9=2n~\pi \\7a=2n~\pi -9\\a=\frac{2n\pi-9 }{7} \\where~n~is~an~integer.[/tex]
or
[tex]\sin\frac{3a-3}{2} =0=\sin ~n\pi \\3a-3=2n\pi \\3a=2n\pi+3\\a=\frac{2~n\pi+3 }{3}[/tex]
where n is an integer.
Does anyone know how to solve this problem?
Answer:
If you're trying to find the inverse, this is the answer!Step-by-step explanation:
To find the inverse, interchange the variables and solve for y. Hope this helps! <3Students at a local community college have G.P.A.s that are normally distributed with a mean of 2.8 and a standard deviation of 0.5.
The percentage of students at the college have a GPA between 2.3 and 3.3 is C. 68.26%.
How to calculate the percentage?How far is 2.3 from 2.8. This will be:
= (2.3-2.8) = -0.5
That means 2.3 is one standard deviation to the left of the mean.
How far is 3.3 from 2.8? This is (3.3-2.8) = 0.5
That means 3.3 is one standard deviation to the right of the mean.
According to the empirical rule 68% of normally distributed data is within 1 standard deviation of the mean.
Therefore, the correct option is C.
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At one college GPA's are normally distributed with a mean of 2.8 and a standard deviation of .5. What percentage of students at the college have a GPA between 2.3 and 3.3?
a)84.13% b)99.74% c) 68.26% d) 95.44%
In her last gymnastics competition Keri scored a 5.65 on the floor exercise, 5.85 on the vault, and 5.75 on the balance beam. What was Keri’s total score?
Keri's total score in her last gymnastics which had three different types of acts is 17.25.
What is a decimal?A decimal separates the whole part and the integer part of a given number. Decimal can also be written as fractions.
Keri in her last gymnastics competition scored a 5.65 on the floor exercise, 5.85 on the vault, and 5.57 on balance.
∴ Her total score will be the sum of all the scores she obtained in all those three performances which are,
= ( 5.65 + 5.85 + 5.75).
= 17.25.
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ali, ben and clare each played a game. Clare's score was seven times ali's score. ben's score was half of clare's score. write down the ratio of ali's score to ben's score to clare's score. give your answer in its simplest form
The ratio of Ali's score to Ben's score to Clare's score in its simplest form is 1 : 3.5 : 7
Given data:
Claire's score = 7 * Ali's score
Ben's score = 0.5 * Claire's score
How to solve for the ratio of Ali's score to Ben's score to Clare's scorelet Ali's score = x
let Ben's score = y
let Claire's score = z
z = 7 * x = 7x
z = 7x
y = 0.5 * z = 1/2 * z = z / 2
plugging the value of z gives
y = 7x / 2
writing the ratios in terms of x gives
Ali : Ben : Claire
x : y : z
x : 7x/2 : 7x
reducing the terms by dividing through by x
1 : 7/2 : 7
OR
1 : 3.5 : 7
clearing the fraction gives
2 : 7 : 14
Therefore, the ratio of Ali's score to Ben's score to Clare's score in its simplest form is 1 : 3.5 : 7
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is the equation a linear function? explain how you know. 4y = -4x + 2^3
The equation 4y = -4x + 2³ is a linear function
A linear function can be explained as an algebraic equation, whose every term is either a constant or the product of a constant and a variable (raised to the first power only).
The equation 4y = -4x + 2³ is a linear function since both variables x and y meet the criteria, and both constants a and b do comply with rules as well
The exponent of x is 1, that is, it is raised to the first power only and the equation follows the definition of a function: for each input (x) there is only one output (y). The graph of any linear function in one variable is always a straight line.
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HELP!! The equation of the circle is given below. Identify the center and the radius. Then graph the circle. x^2+y^2-6x+2y=6
The center of the circle is (3, -1) and the radius of the circle is 4
How to determine the center of the circle?The equation of the circle is given as
x^2 + y^2 - 6x + 2y = 6
The above equation is the standard equation of a circle
Start by converting the above standard equation of a circle to a form other than the standard equation
Using a graphing calculator, we have the following form
(x - 3)^2 + (y + 1)^2 = 4^2
The equation of a circle is represented as
(x - h)^2 + (y - k)^2 = r^2
Where the center is
Center = (h, k)
So, we have
(h, k) = (3, -1)
This means that
Center = (3, -1)
Hence, the center of the circle is (3, -1)
How to determine the radius of the circle?In (a), we have
Using a graphing calculator, we have the following form
(x - 3)^2 + (y + 1)^2 = 4^2
The equation of a circle is represented as
(x - h)^2 + (y - k)^2 = r^2
Where the radius is
Radius = r
So, we have
r = 4
This means that
Radius = 4
Hence, the radius of the circle is 4
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this picture underneath is my question find length ab
[tex]cos(62) = \frac{ab}{cb} \\ ab = cb.cos(62) \\ ab = 12.cos(62) \approx5.6[/tex]
The relationship between the number of pounds (lb) of egg salad and the
price in dollars is shown in the graph. What is the unit price of salad?
egg
A $5
1 lb
B. 1 lb
$5
C. $1
5 lb
D. $10
2 lb
Based on the number of pounds of egg salad to the price of dollars, the unit price of the salad can be found to be A. $5 / 1 lb
How to find the unit price?The unit price of the pounds of egg salad can be found as:
= Price of egg salad / Weight of egg salad
When the weight is 1, the unit price from the graph is:
= $5 / 1 lb
When the weight is 2, the unit price is:
= 10 / 2
= 5 / 1 in simpler terms
When the weight is 3, the unit price is:
= 15 / 3
= 5 / 1 in simpler terms
In conclusion, the unit price of salad is $5 / 1 lb
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The height of a box is 9 inches. The length is three inches more than the width. Find the width if the volume is 792. Please show step by step
Width of the box is 8 inches and length is 11 inches.
Height of the box is 9 inches given
Length of the box is 3 inches more than the width.
Let the width be x then length = x+3
Volume of the box is = 792 (given)
Volume is the amount of space occupied by the any three dimensional figure. To find the volume of a box we simply multiply length width and height
Volume = length * width * height
792 = (x+3)*x*9
[tex](x^2+3x)*9=792\\9x^2+27x=792\\9x^2+27x-792=0[/tex]
Divide the above equation by 9 as 9 is the common factor
we get
[tex]x^2+3x-88=0[/tex]
now solve this equation by splitting the middle term we get,
[tex]x^2+11x-8x-88=0\\x(x+11)-8(x+11)=0\\(x+11)(x-8)=0\\x=-11,8[/tex]
width is always positive so we consider x = 8
Length = x+3 = 8+3 =11
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Paddy spent $63.00 on three tickets to a concert. Javier spent $76 on four tickets. How much les per ticket did Javier pay compared to paddy. PLEASE HURRY
Answer:The answer is 2
no time for explonations
What is the measure of the largest exterior angle
in the triangle?
The smallest interior angle of a triangle, produces largest exterior angle. Hence, measurement of the exterior largest angle is 359.47°
What is an angle?An angle is the figure formed by the two rays, called the sides of the angle, sharing a common endpoint, called the vertex of the angle. Angles formed by the two rays lie in the plane that contains the rays. Angles are also formed by the intersection of the two planes. These are called the dihedral angles. Two intersecting curves may also define an angle, which is the angle of rays lying tangent to the respective curves at their point of intersection.
Angle is also used to designate the measure of an angle or of rotation. This measure is the ratio of length of a circular arc to its radius. In the case of a geometric angle, arc is centered at the vertex and delimited by the sides. In case of a rotation, the arc is centered at the center of the rotation and delimited by any other point and its image by the rotation.
We know that sum of all the angles of a triangle is equal to 180°
s°+(1/7s+3)°+(1/7s+30)°= 180°
[tex]s+\frac{22}{7}s+\frac{22}{7}s[/tex]= 180°
[tex]\frac{51}{7} s[/tex]=180°
s= 24.7°
both the similar angles =0.53°
Therefore, the largest external angle is:
360°-0.53° = 359.47°
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Unit 1 test study guide(geometry basics)Topic 2: Segment Addition Postulate 9. If DF = 42, find DE. 7x + 1 4x-3 10. In the diagram below, if JL = 10x - 2. JK = 5x - 8, and KL = 7x - 12. find KL.
The required measure of the line DE segment is 29.
What does a line in mathematics mean?
A line is a perfectly straight, one-dimensional shape that extends infinitely in both directions and has no thickness.A line has length but no width, making it a one-dimensional figure. A line is made up of a collection of points that can be stretched indefinitely in opposing directions. Two points in a two-dimensional plane determine it. Collinear points are two points that are located on the same line.(9) Given ,
DF = 42
Here,
DF = DE + EF
From the given put the values of DF = 42, DE = 7x +1 and EF = 4x - 3
42 = 7x + 1 + 4x - 3
42 = 11x - 2
11x = 44
x = 4
DE = 7x + 1
Put the value of x in above equation,
DE = 7 * 4 + 1
DE = 28 + 1
DE = 29
Thus, the required measure of the DE segment is 29.
( 10 ) JL = JK + KL
10x - 2 = ( 5x - 8 ) + ( 7x - 12 )
2x = 18
x = 9
∴KL = 7x - 12 = 7 * 9 - 12 ⇒63 - 12 = 51
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Four friends washed cars all day
on Saturday and earned $66.00.
They shared the work equally, so
they want to share the money they
earned equally. How much money
will each person get?
E
66.00 divided by 4 equals 16.5
Suppose we want to choose 7 letters, without replacement, from 9 distinct letters.
(a) How many ways can this be done, if the order of the choices is relevant?
(b) How many ways can this be done, if the order of the choices is not relevant?
The numbers of ways can this be done, if the order of the choices is relevant is 181,440 ways and the numbers of ways can this be done, if the order of the choices is not relevant is 36 ways.
Number of possible waysa. N permutations
N permutations = nPr = n!/ (n-r)!
N permutations = 9P7 = 9!/(9-7)!
N permutations = 9×8×7×6×5×4×3
N permutations= 181,440
b. N combinations :
N combinations = nCr = n!/((n-r)!r!)
N combinations = 9C7 = 9!/((9-7)!7!)
N combinations =9×8×7×6×5×4×3 ×2!/7!×2!
N combinations = 9×8×7×6×5×4×3 /7!
N combinations =181,440/7!
N combinations =36
Therefore the numbers of ways can this be done, if the order of the choices is relevant is 181,440 ways and the numbers of ways can this be done, if the order of the choices is not relevant is 36 ways.
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