The pay increase that was directly deposited into Ken's account is $476.58.
In the question, we are asked to find the pay increase, that was directly posited in Ken's account, given that Ken received his bank statement in the mail and checked it to verify his recent pay increase. He has direct deposit so his paycheck is sent electronically to his account. The previous month's pay was $5,320.10. His account activity showed a $651.22 previous balance, checks of $5,211.39, ATM withdrawals of $250, and a service charger of $4.50. Also, we are informed that his new balance was $982.01.
We assume the pay increase to be $x.
Thus, his this month's pay will be $(5,320.10 + x).
This will be added in his previous month's balance, to get $651.22 + $(5,320.10 + x) = $(5,971.32 + x).
Now, the check of $5,211.39, ATM withdrawal of $250, and the service charge of $4.50 will be deducted from this to get $(5,971.32 + x) - $5,211.39 - $250 - $4.50 = $(505.43 + x).
This is the final balance of Ken's account.
But, we are given that Ken's new balance was $982.01.
Thus, we get an equation 505.43 + x = 982.01, which can be solved by subtracting 505.43 from both sides to get:
505.43 + x - 505.43 = 982.01 - 505.43,
or, x = 476.58.
Thus, the pay increase that was directly deposited into Ken's account is $476.58.
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When an automobile travels uphill or downhill on a highway, it experiences a force due to gravity. This force in pounds is called grade resistance and is modeled by the equation below, where theta is the grade and W is the weight of the automobile.
F = Wsin theta
A 2710-lb car traveling uphill has a grade resistance of 160 lb. What is the angle of the grade?
theta =__.
(Type your answer in degrees. Round to the nearest hundredth as needed.)
Based on the calculations, the angle (θ) of the grade to the nearest hundredth is equal to 3.38 degrees.
What is an equation?An equation can be defined as a mathematical expression which shows that two (2) or more thing are equal.
In Science, grade resistance simply refers to force in pounds and can be modeled by the following equation:
F = Wsinθ
Where:
F represents the grade resistance or force in pounds.θ represents the grade W represents the weight of a physical object.Making theta (θ) the subject of formula, we have:
θ = sin⁻¹(F/W)
Substituting the given parameters into the formula, we have;
θ = sin⁻¹(160/2710)
θ = sin⁻¹(0.0590)
Theta, θ = 3.38 degrees.
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what do i write in the blank and how do i solve
Answer:
I know that the inequality is 85-4x<40
but im not sure on how to solve it, i think the answer is 12
becuase
85-4(12)< 40
85-48<40
37<40
Step-by-step explanation:
Answer: 85 - 4x < 40; 11
Step-by-step explanation:
85 - 4x < 40
-85 -85
- 4x < -45
[When dividing a negative number, change the inequality sign to the opposite sign.]
x > 11.25
The the cars was integer, and x is greater than 11.25, therefore, Mr.Schwantz will need to order more wheels after building 11 cars.
f(1)=30,f(n)=2xf(n-1)-50
Answer: f(0)=40/x
Step-by-step explanation:
f(n)=2xf(n-1)-50
f(1)=2xf(1-1)-50
f(1)=2xf(0)-50
30=2xf(0)-50
2xf(0)=80
f(0)=80/(2x)
f(0)=40/x
Which strategy for multiplying 75 and 63 should result In the correct product
With the partial product method the multiplication answer is 4725.
According to the statement
We have to find that the by which strategy for multiplying 75 and 63 should result In the correct product.
So, For this purpose, we know that the
The partial product method involves multiplying each digit of a number in turn with each digit of another where each digit maintains its place.
From the given information:
We have to multiply the numbers 75 and the 63.
Then
According to the above written strategy,
75 = 70+5 and
63 = 60+3
Then
75*63 = (70*60) + (70*3) + (5*60) + (5*3)
then solve it
75*63 = (4200) + (210) + (300) + (15)
75*63 = 4410 + 315
75*63 = 4725.
So, With the partial product method the multiplication answer is 4725.
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A design for a library has a scale of 1/3 in= 1ft. The height of the library in the drawing is 12 inches. What is the
actual height of the library?
A library's design is scaled at [tex]\frac{1}{3}[/tex] inch = 1 feet. The library in the drawing is 12 inches height. The library's true height is 432 inches, or 36 feet.
Given that,
A library's design is scaled at [tex]\frac{1}{3}[/tex] inch = 1 feet.
The library in the drawing is 12 inches height.
We can take [tex]\frac{1}{3}[/tex] inch = 1 feet
1 inch=3 feet = 36 inches.
36 inches is the actual height .
Now actual height of the library is
Multiplication of the height of the library in the drawing is 12 inches and the new height 36 inches.
12[tex]\times[/tex]36=432 inches
We can say 432 inches is equal to 36 feet.
Therefore, 432 inches or 36 feet is the actual height of the library.
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Which expression is equivalent to
A:4x
B:4x+4
C:x^2+7x+10
D:-x^2-5x-6
Answer:
A
Step-by-step explanation:
x + 2 + [ 4x - [tex]\frac{x^2+6x+8}{x+4}[/tex] ] ← factorise the quadratic on the numerator
= x + 2 + [ 4x - [tex]\frac{(x+4)(x+2)}{x+4}[/tex] ] ← cancel (x + 4) on numerator/denominator
= x + 2 + (4x - (x + 2)
= x + 2 + 4x - x - 2 ← collect like terms
= 4x
Solve -3.5 = x/4 for x using the multiplication property of equality. The operation in the problem is
The operation used in the problem is Multiplication property of equality and the value of x is -14
Property of equality-3.5 = x/4
cross Multiplication- 3.5 × 4 = x
-14 = x
Check:
-3.5 = x/4
- 3.5 = -14 / 4
-3.5 = -3.5
Therefore, the operation used in the problem is Multiplication property of equality and the value of x is -14
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please help if know how to solve
Answer: 12x+17
Step-by-step explanation:
(hog)(x)=
h(g(x))=
h(4x+5)=
3(4x+5)+2=
12x+15+2=12x+17
Answer:
honestly, I don’t think I’m right
Step-by-step explanation:
| (6-x)-9 |
absolute value and i need help solving. do i just combine and make it -3-x? (this problem came from a fog education.
This simplifies to
[tex]|(6-x)-9|\\\\\boxed{|-x-3|}[/tex]
Use z scores to compare the given values.
K
In a recent awards ceremony, the age of the winner for best actor was 31 and the age of the winner for best actress was 42. For all best actors, the mean age is 42.4 years and the
standard deviation is 8.2 years. For all best actresses, the mean age is 31.6 years and the standard deviation is 10.3 years. (All ages are determined at the time of the
awards ceremony.) Relative to their genders, who had the more extreme age when winning the award, the actor or the actress? Explain.
Since the z score for the actor is z= and the z score for the actress is z-, the
had the more extreme age.
So the best actor's age deviates from the mean, he receives the award at the most extreme age.
What is defined as the z score?The z-score of a way of measuring X in a set with mean and standard deviation is given by: z = (x - μ)/σ.The Z-score indicates how far the measure deviates from the mean. After determining the Z-score, we examine the z-score table to determine the p-value connected with this z-score. This p-value represents the probability also that measure's value is less than X, or the percentile of X. Subtracting 1 from the p-value yields the probability that measure's value is greater than X.In response to this question:
Whichever z-score does have the highest absolute value, such that, the one that deviates the most from the mean, has a most extreme age.
Best actor: 31 years old, so.
The mean age of the best actors is 42.2 years, with a standard deviation of 8.2 years.
z = (x - μ)/σ
Put the values;
z = (31 - 42.2)/ 8.2
z = -1.36
Best actress:
So, at the age of 42,
The mean of the best actresses is 31.6 years, with a standard deviation of 10.3 years.
z = (x - μ)/σ
Put the values;
z = (42 - 31.6)/10.3
z = 1.01
Thus, Because the best actor's age is further from the mean, he has the most extreme age when receiving the award.
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Find the value of x the diagram is not a scale
○ 83
○ 97
○ 132
○ 41
Answer:
132
Step-by-step explanation:
.....................................
log 5 = 0.69897, log 3 = 0.47712 and log 2 = 0.30103. evaluate log 4 and log 15
Answer: log4=0.60206 log15=1,17579
Step-by-step explanation:
[tex]log4=\\log2^2=\\2log2=\\2(0.30103)=\\0.60206\\\\log15=\\log(3*5)=\\log3+log5=\\0.47712+0.69897=\\1.17579[/tex]
The cost of a dozen eggs is $2.50. At this store you must by them in packs by the dozen and they do not allow you to buy more than 6 dozen eggs at a time. State a reasonable domain for this situation.
The reasonable domain for this situation is { 1, 2, 3, 4, 5, 6 }.
What is a set ?A set is a well defined collection of objects.Set are represented by many forms two of them are set builder form and roaster form.
According to the given question The cost of a dozen eggs is 2.50 dollars.
At this store you must by them in packs by the dozen and they do not allow you to buy more than 6 dozen eggs at a time,So we can buy eggs in dozen from 1 dozen to 6 dozen.
This can be represented in roaster form by { 1, 2, 3, 4, 5, 6 }.
This can also be represented by set builder form as { x : x ∈ N and 1≤x≤6 }
where x represents no. of dozens of egg.
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In an equilateral triangle, all side lengths are equal and all angle measures are equal. Sketch an equilateral triangle. What are the measures of its angles??
Answer:
every angle equals 60°
Step-by-step explanation:
the sum of angles of any triangle is 180 so the equilateral triangle have all angles equal so 180 ÷ 3 = 60
 If a student has a GPA of 3.0, the student gets the “good student discount”, which is a discount of 20%. Write a function that represents the discount on the monthly premium for a “good student”. call this function S.
S(x) + 0.20(x/12) = 0
S(x) = -0.20(x/12) it is a function that represents the discount on the monthly premium for a “good student.
From the question,
A student has a GPA of 3.0 gets good student discount of 20%
Write a function with ‘S’ that represents the discount of the monthly premium for a good student.
S(x) = -0.20(x ÷ 12)
S(x) is a function and student got a discount of 20%.
i.e., 20/100 = 0.20
The function that represents the discount on the monthly premium so x/12
An expression, rule, or law in mathematics that specifies the relationship between an independent variable and a dependent variable (the dependent variable). In mathematics and the sciences, functions are fundamental for constructing physical relationships.
Hence, it s a function that represents the discount on the monthly premium for a “good student.
S(x) + 0.20(x/12) = 0
S(x) = -0.20(x/12)
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big stonez post the lyrics for brainliest
How do you find the quotient of 45/9
The quotient of the given fraction 45/9 is 5.
What is division?The division is one of the four basic operations of arithmetic, which are the methods by which numbers are combined to form new numbers. Addition, subtraction, and multiplication are the other operations.At the most basic level, the division of two natural numbers is the process of calculating the number of times one number is contained within another.Quotient:
A quotient is a quantity produced by the division of two numbers in arithmetic. The quotient is widely used in mathematics and is also known as the integer part of a division, a fraction, or a ratio.So, the quotient of 45/9 is 5 as:
45 ÷ 9 = 5
(Refer to the picture given below for working)
Therefore, the quotient of the given fraction is 5.
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The length of a certain rectangle is 10m greater than twice its width. If the width were reduced by 20m and the length increased by 100m, the perimeter of the new rectangle would be twice the perimeter of the original rectangle. What are the dimensions of the original rectangle?
The dimensions of the original rectangle is a length of 56.66 meter and width of 23.33 meter.
What is perimeter?Perimeter is the sum of all the sides of a two dimensional polygon or shape.
For first rectangle let x represent width:
Length = 2x + 10; width = x
Perimeter = 2(length + width)
Perimeter = 2(2x + 10 + x) = 6x + 20
For second rectangle:
Length = 2x + 10 + 100 = 2x + 110; width = x - 20
Perimeter = 2(length + width)
Perimeter = 2(2x + 110 + x - 20) = 6x + 180
the perimeter of the new rectangle would be twice the perimeter of the original rectangle. Hence:
6x + 180 = 2(6x + 20)
x = 23.33 m, length = 2x + 10 = 56.66
The dimensions of the original rectangle is a length of 56.66 meter and width of 23.33 meter.
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on the way to the mousetrap car contest the judge drove from Exit 32 on the highway to exit 170 in 2 hours. exita 32 and 170 are 138 miles apart. did the judge follow the speed limit of 65 mph? explain
Answer: The judge did not follow the speed limit of 65mph because if she did she would have not gotten there in 2 hours. The judge was actually going at 85 mph.
Step-by-step explanation:
All my points please help! Given a unit circle, what is the value for y?
the value of y for the given circle will be 1 / 50 ( approx).
We are given a unit circle.
So, we get that:
centre = (0, 0)
Equation of the circle will be
x² + y² = 1
Now, we have a point (- 17 / 20, y)
Substituting the values in the equation, we get that:
(- 17 / 20)² + y² = 1
343 / 400 + y² = 1
y² = 57 / 400
y = 1 / 50 ( approx)
Therefore, we get that, the value of y for the given circle will be 1 / 50 ( approx).
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Answer: top one is 111 dont know bottom
Step-by-step explanation:
<3
A circle has a diameter with endpoints
at A (-3, -12) and B(-7, 4). The point
M(-5, -4) lies on the diameter
What is the distance from A to M (Round to 2 decimal place
What is the distance from B to M (Round to 2 decimal places)
The measure of AM and BM from the given coordinate points are 8.37 units respectively
Distance between coordinatesThe formula for calculating the distance between coordinate points is expressed according to the equation
D = √(x₂-x₁)²+(y₂-y₁)²
Given the coordinate points A (-3, -12) and M(-5, -4). The measure of the distance AM is expressed as:
AM = √(-4+12)²+(-5+3)²
AM = √(8)²+(-2)²
AM = √70
AM = 8.37 units
Similarly;
Given the coordinate points B(-7, 4). and M(-5, -4). The measure of the distance AM is expressed as:
BM = √(-4-4)²+(-5+7)²
BM = √(-8)²+(2)²
BM = √70
BM = 8.37 units
Hence the measure of AM and BM from the given coordinate points are 8.37 units respectively
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Explore and describe the similarities, differences, and interplay between weighted voting, fair division and apportionment.
Weighted vote is the policy of law-making where each representative has a variable voting power.
How to illustrate the information?A policy- or law-making body may use weighted voting, where each representative has a variable voting power (weighted vote) based on the number of principals who have designated them as their proxy or the size of the electorate they represent.
The challenge of distributing resources fairly among a group of individuals is to ensure that each person is given their fair share. This is fair division.
Representatives are apportioned among the states in order to create a fair split or distribution. This is apportionment.
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Determine which integer will make the equation true.
3x + 9 = 24
S = {3, 4, 5, 6}
A: 3
B: 4
C: 5
D: 6
Answer:
c) 5
Step-by-step explanation:
Solving for the value of x,
→ 3x + 9 = 24
→ 3x = 24 - 9
→ x = 15/3
→ [ x = 5 ]
Hence, option (c) is correct.
Can someone help me with this question? It's due tomorrow :(
Answer:1,3
Step-by-step explanation: it is reflecting over the x-axis, not the y-axis. when answering these questions, keep in my what axis you're working with. hope this helps.
What are the solutions to the equation x-7/x=6?
x=-7 and x=1
x=-6 and x=-1
x=-1 and x=7
x=1 and x=6
Answer:
x=7
7-7/7-6=0
0/1=0
Zero divided by anything=0
If AB = 12 and BC = 3, what is AC?
Answer: AC=15
Step-by-step explanation:
AC=AB+BC
AC=12+3
AC=15
Answer:
[tex]\frac{36}{B^2}[/tex]
Step-by-step explanation:
Given:
[tex]AB=12\\BC=3[/tex]
Find:
[tex]AC[/tex]
First, arrange equation 1 to isolate A by dividing both sides by B:
[tex]AB=12\\A=\frac{12}{B}[/tex]
Then, arrange equation 2 to isolate C by dividing both sides by B:
[tex]BC=3\\C=\frac{3}{B}[/tex]
Now, multiply A and C together and simplify:
[tex]AC=\frac{12}{B}*\frac{3}{B}[/tex]
[tex]AC=\frac{36}{B^2}[/tex]
help pleaseeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee
Step-by-step explanation:
f(x) = 4x + 15
6x - 3
if x = -1 (replace x with -1 )
f(-1) = 4(-1) + 15
6(-1) -3
= -4 + 15
-6 -3
= -11
-9
"minus cancel each other when dividing"
Answer = 11
9 or 1.22
Hope this helps ...:-)
Gind the greatest common factor for the list of terms.
98ab^3, 84a, 140b, 112ab
Answer:
14
Step-by-step explanation:
You want the greatest common factor of the terms {98ab^3, 84a, 140b, 112ab}.
Common factorsThere are no variables that are common to all terms. 'a' and 'b' are each common to 3 of the 4 terms, but not all.
The greatest common factor of the constants cannot be larger than the smallest difference of the constants. That difference is ...
98 -84 = 112 -98 = 14
Since 14 is a divisor of all of the constants, 14 is the greatest common factor.
__
Additional comment
Factoring out the greatest common factor, we have ...
= 14{7ab³, 6a, 10b, 8ab}
Dosage 2 tablets, 4x per day 26 tablets per bottle
Select all the expressions equivalent to (81)3/5
((81)1/5)3
0 ((81)1/3)5
((81)1/3)5
((81)5)1/3
3(81)5
5(81)³
