Answer:
12.6
Step-by-step explanation:
plug in 5 for b
5*5 = 25
25-12.4=12.6
Answer:
B= -2.48
Step-by-step explanation:
Divide 5 and -12.4 both by 5 then B=-2.48
Which of the following expressions are equivalent to (x+y)^2? There may be more than one correct answer
The equivalent expressions are:
[tex](x+y)^2 = x^2+2xy+y^2[/tex]
[tex](x+y)^2 = x(x+y)+y(x+y)[/tex]
[tex](x+y)^2 = (x+y)(x+y)[/tex]
[tex](x+y)^2=(y+x)^2[/tex]
Solution:
We have to find the equivalent expression for the given expression
Given expression is:
[tex](x+y)^2[/tex]
First equivalent expression:Let us first use the algebraic identity
[tex](a+b)^2=a^2+2ab+b^2[/tex]
Therefore,
[tex](x+y)^2 = x^2+2xy+y^2[/tex]
Second Equivalent expression:From above we get,
[tex](x+y)^2 = x^2+2xy+y^2[/tex]
2xy can be rewritten as xy + xy
Thus we get,
[tex]x^2+2xy + y^2 = x^2+xy+xy+y^2[/tex]
Group the terms we get,
[tex]x^2+2xy + y^2 = (x^2+xy)+(xy+y^2)[/tex]
Factor out "x" from first bracket and "y" from second bracket
[tex]x^2+2xy+y^2 = x(x+y)+y(x+y)[/tex]
Thus the equivalent expression is:
[tex](x+y)^2 = x(x+y)+y(x+y)[/tex]
Third equivalent expression:[tex]\text{We know that } a^2 = a \times a[/tex]
Therefore,
[tex](x+y)^2 = (x+y)(x+y)[/tex]
Fourth equivalent expression:By commutative property we know that,
[tex]a + b = b + a[/tex]
Therefore,
[tex](x+y)^2=(y+x)^2[/tex]
Thus the equivalent expressions are found
Phillip departed from town A with coordinates (1, 6) towards town B with coordinates (7, 6). At the same time Bruce headed from town B to town A. What are the coordinates of point C where they will meet if the ratio of Phillip's to Bruce's rates is 7:5, respectively?
Answer:
(4.5, 6)
Step-by-step explanation:
The distance covered is proportional to the rate, so the distance from A to C compared to the distance from B to C will have the same proportion as Phillip's and Bruce's rates.
__
setup(C -A)/(B -C) = 7/5 . . . . . distance is proportional to rates
solution5(C -A) = 7(B -C) . . . . multiply by 5(B -C)
12C = 7B +5A . . . . . add 7C+5A
C = (7B +5A)/12 = (7(7, 6) +5(1, 6))/12 = (49+5, 42+30)/12 = (4.5, 6)
Phillip and Bruce will meet at C(4.5, 6).
Answer:
he is right but the answer is (4,6) not (4.5,6)
Step-by-step explanation:
Before the three-dimensional structure of DNA was discovered, scientists knew that DNA contained nitrogenous bases. The table below shows the percentages of the nitrogenous bases in a DNA sample. Which rule can be used to determine the percentages of the missing nitrogenous bases? Complete the table AND explain your answer. Base Percent Adenine 23 Thymine Cytosine 27 Guanine
Answer:
Thymine 23
Guanine 27
Step-by-step explanation:
A DNA molecule consists of two long chains of DNA connected to each other through the bonds nitrogenous bases make one with another. However, this bonding is strictly regulated through Chargaff's rule. It basically says that adenine from one DNA chain can only bond with thymine from another chain and vice versa. Additionally, cytosine from one chain only bonds with guanine from another and vice versa:
[A] = [T]
[G] = [C]
That means that there should be an equal number of corresponding bases.
If there were 23% of adenine, there will also be 23% of thymine.
Similarly, if there were 27% of cytosine, there will also be 27% of guanine.
Also note that the sum of non-bonding bases is always 50%, in this case, adenine + cytosine was 23% + 27% = 50%.
The Answer is: Thymine 23
Then Guanine 27
Now Step-by-step explanation:When A DNA molecule consists of two long chains of DNA connected to each other through the bonds nitrogenous are bases to make one with another. When However, this bonding is strictly regulated through Chargaff's rule. It basically says that adenine from one DNA chain can only bond with thymine from another chain and vice versa. Thus that the Additionally, cytosine from one chain only bonds with guanine from another and vice versa:[A] = [T][G] = [C]Now That means there should be an equal number of corresponding bases.When If there were 23% of adenine, there will also be 23% of thymine.So that Similarly, if there were 27% of cytosine, there will also be 27% of guanine.After that Also note that the sum of non-bonding bases is always 50%, but in this case, adenine + cytosine was 23% + 27% = 50%.Learn more about:
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What is the period of the function? y=cos(pi/2)
Answer: period=4
Step-by-step explanation: a=1,b=π/2, c=0
to calculate the period of the function,we use 2π/b
therefore,period=2π/π/2
2π×2/π=4.
which of the following inequalities is represented by the number line
Answer:x > -3
Step-by-step explanation:
The inequality can be written as follows:
x > -3
Given is number line with an open circle at -3 and goes infinitely in right [positive] direction, we need to find the inequality that is represented by the number line.
If there is an open circle at -3 on the number line, it means that -3 is not included in the solution set. The number line continues infinitely in the positive direction.
To represent the inequality using the number line, we use the open circle to indicate that -3 is not included and an arrow pointing to the right to show that the numbers continue infinitely in the positive direction.
The inequality can be written as follows:
x > -3
This inequality indicates that x is greater than -3 and includes all numbers to the right of -3 (but not -3 itself) on the number line.
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Find the perimeter and area of the polygon shown below.
The polygon consists of a rectangle with dimensions 15 ft by 18 ft and a right triangle with a base of 8 ft and a hypotenuse of 17 ft. The perimeter is 76 ft, and the area is 330 sq ft. The correct option is A).
To Find the area of each individual shape.
a. Area of the rectangle:
The area (A) of a rectangle is given by the formula: A = Length × Width.
Area of the rectangle = 18 ft × 15 ft = 270 sq ft
b. Area of the right triangle:
The area (A) of a right triangle is given by the formula: A = 0.5 × Base × Height.
Area of the right triangle = 0.5 × 8 ft × 15 ft = 60 sq ft
To Find the total area of the polygon.
Total area of the polygon = Area of the rectangle + Area of the right triangle = 270 sq ft + 60 sq ft = 330 sq ft
So, the perimeter of the polygon is 106 feet, and the area of the polygon is 330 square feet.
The perimeter of the polygon is the sum of the lengths of all its sides:
Perimeter = 15 ft (rectangle side) + 18 ft (rectangle side) + 18 ft (rectangle side) + 8 ft (triangle base) + 17 ft (triangle hypotenuse) = 76 ft
So, the correct perimeter of the polygon is 76 feet.
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The polygon is made up of a rectangle 15 feet by 18 feet in size and a right triangle with an 8-foot base and a 17-foot hypotenuse. The circumference is 76 feet long, and the size is 330 square feet. The correct answer is A).
Calculate the area of each individual form.
a. Rectangle surface area:
A rectangle's area (A) is provided by the formula: A = Length Width.
The rectangle's area is 18 ft 15 ft = 270 sq ft.
b. The right triangle's area:
The formula for calculating the area (A) of a right triangle is A = 0.5 Base Height.
Right triangle area = 0.5 8 ft 15 ft = 60 sq ft
To determine the polygon's overall area.
Total polygon area equals rectangle area + right triangle area = 270 sq ft + 60 sq ft = 330 sq ft
As a result, the polygon's perimeter is 106 feet, and its size is 330 square feet.
The polygon's perimeter is the sum of the lengths of all its sides:
Perimeter = 15 feet (rectangle side) + 18 feet (rectangle side) + 8 feet (triangle base) + 17 feet (triangle hypotenuse) = 76 feet
As a result, the polygon's correct perimeter is 76 feet.
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What is the equation of the line that contains point(3, -2) and has a slope of 5?
y = 5x - 17
y = 5x - 13
y = 5x + 13
y = 5x + 17
Answer:
y = 5x - 17
Step-by-step explanation:
y = mx + c
m = the gradient/slope = 5
y = 5x + c
Substitute (3, -2) into the equation above to find c.
-2 = 5(3) + c
-2 = 15 + c
-2 - 15 = c
-17 = c
y = 5x - 17
Answer:
Step-by-step explanation:
point(3, -2) and has a slope of 5
Slope m = 5
y1 = -2 and x1 = 3
The equation is
y - y1 = m(x - x1)
y + 2 = 5(x - 3)
y + 2 = 5x - 15
y = 5x - 15 - 2
y = 5x - 17
Which statement correctly describes the solution to the equation below?
-4[x+2]+x= 3x - 8 - 5x
A There is no solution to this equation.
B There are infinitely many solutions to this equation.
C There is exactly one solution to this equation, and the solution is 0 .
D There is exactly one solution to this equation, and the solution is -1 .
Answer:
Option C) There is exactly one solution to this equation, and the solution is 0 is correct
That is the solution x=0
Step-by-step explanation:
Given equation is -4(x+2)+x=3x-8-5x
To find the solution to the given equation :
First to solve the given equation
-4(x+2)+x=3x-8-5x
-4x-8+x=3x-8-5x ( by using the distributive property )
-3x-8=-2x-8 ( adding the like terms )
-3x-8-(-2x-8)=-2x-8-(-2x-8)
-3x-8+2x+8=-2x-8+2x+8 ( adding the like terms )
-x=0
Therefore x=0 is the only solution to the given equation
Option C) There is exactly one solution to this equation, and the solution is 0 is correct
That is the solution x=0
After simplifying and solving the given equation, it is clear that the single solution is x = 0, which corresponds to option C.
To identify the correct statement describing the solution to the given equation, we need to solve the equation step by step:
-4[x+2]+x = 3x - 8 - 5x.
First, distribute the -4 across the terms inside the brackets:
-4x - 8 + x = 3x - 8 - 5x.
Combine like terms:
-3x - 8 = -2x - 8.
Then add 3x to both sides:
-8 = x - 8.
Finally, add 8 to both sides to solve for x:
x = 0.
The equation simplifies to x = 0, which means there is a single solution to this equation. Therefore, the correct option is: C. There is exactly one solution to this equation, and the solution is 0.
what expression simplifies to 8x-5
The value of the equation A = -6x + 7 ( 2x + 1 ) - 12 is A = 8x - 5
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is
A = -6x + 7 ( 2x + 1 ) - 12 be equation (1)
Now , let the equation B = 8x - 5
On simplifying the equation (1) , we get
A = -6x + 7 ( 2x ) + 7 ( 1 ) - 12
A = -6x + 14x + 7 - 12
On further simplification , we get
A = 8x - 5
So , the value of A = B
Therefore , the value of A is 8x - 5
Hence , the equation is A = 8x - 5
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Answer:
The Answer is A = -6x + 7 ( 2x + 1 ) - 12 is A = 8x - 5
Step-by-step explanation:
I got it right
2x + 3y= 22
-2x +5y=-6
The solution is x = 8 and y = 2
Solution:
Given are the system of equations
2x + 3y = 22 -------- eqn 1
-2x + 5y = -6 ----- eqn 2
We can solve the system of equations by elimination method
Add eqn 1 and eqn 2
Eqn 1 + Eqn 2
2x + 3y -2x + 5y = 22 - 6
0x + 3y + 5y = 16
8y = 16
Divide both sides of equation by 8
y = 2Substitute y = 2 in eqn 1
2x + 3(2) = 22
2x = 22 - 6
2x = 16
x = 8Thus the solution is x = 8 and y = 2
Which equation represents the volume of a cone with the same base and height as the cylinder below?
Vcone=(pie)t2k
Vcone=1/3(pie)t2k
Vcone=1/2(pie)t2k
Vcone=3(pie)t2k
Answer:
The equation that represents the volume of a cone with the same base and height as the cylinder is [tex]\frac{1}{3}\pi t^2k[/tex]
Step-by-step explanation:
Given:
The height of the cylinder = k
The Radius of the cylinder = t
To Find:
Equation representing the volume the cone = ?
Solution:
We know that the volume of the cone is
=> [tex]\frac{1}{3}\pi r^2 h[/tex]
where
r is the radius of the cone
h is the height of the cone
Here the radius of the cone = radius of the cylinder = t
and height of the cone = height oft the cylinder = k
then
the volume of the cone will be
=>[tex]\frac{1}{3}\pi t^2k[/tex]
Answer:
its b
Step-by-step explanation:
i took the test
Celebrity A has 400 followers on social media and is gaining 75 followers each day. Celebrity B has 1,000 followers on social media, but is losing 25 followers a day. How many days will it take them to have the same number of followers?
It takes 6 days for both of them to have same number of followers
Solution:
Let "x" be the number of days
Case 1:Celebrity A has 400 followers on social media and is gaining 75 followers each day
We can frame a equation as:
Celebrity A : 400 + 75(number of days)
Celebrity A : 400 + 75x --------- eqn 1
Case 2:Celebrity B has 1,000 followers on social media, but is losing 25 followers a day
We can frame a equation as:
Celebrity B : 1000 - 25(number of days)
Here we use negative sign to denote losing of followers
Celebrity B : 1000 - 25x --------- eqn 2
For both of them to have same number of followers, eqn 1 must be equal to eqn 2
[tex]400 + 75x = 1000 - 25x\\\\\text{Solve the above equation for x}\\\\75x + 25x = 1000 - 400\\\\\text{Combine the like terms }\\\\100x = 600\\\\x = 6[/tex]
Thus it takes 6 days for both of them to have same number of followers
3 and 1 half to the power of 2 simplify
Answer: 49/4
Step-by-step explanation:
3 + 1/2 = (3x2 + 1)/2 = 7/2
(7/2)² = 7²/2² = 49/4
SpymoreTim's phone service charges $23.02 plus an additional $0.19 for each text message sent per month. If Tim's phone bill was $27.77, which equation could be used to find how many text messages, x , Tim sent last month?
A. $0.19x + 23.02 = $27.77
B. $23.02x + $0.19 = $27.77
C. $0.19x - $23.02 = $27.77
D. 23.02x - $0.19 = 27.77
Answer:
Step-by-step explanation:
23.02 plus an additional 0.19 for each text.....x = # of texts
$ 0.19x + 23.02 = 27.77 is ur equation
Answer: B
Step-by-step explanation: i got it wrong trust me
Directions: Solve each of the following equations.
a. Combine like terms
b. Then isolate the variable if necessary
c. Follow rules for signed numbers
1. 15t + 8t - 2t = 16
2. 24m + 24m = 96
3. 26 = 12n + 2n
4. 20a - 3a = 34
5. 170x + 4 = 64
6. 15x - 25 = 200
7. 5s + 3s = 42
8. 10t + 2t = 28
9. 14s + 35s - 7s = 42
10. 124s - 14s + 12s = 12
11. 76x + 23x = 33
12. 140r - 8r - 4r = 216
13. 98c - 99c = 1
14. 104mn + (-84mn) = 36
15. 118j - 234j = 234
(I appreciate all your help
1. 15t + 8t - 2t = 16
t = 0.76
2. 24m + 24m = 96
m = 2
3. 26 = 12n + 2n
n = 1.86
4. 20a - 3a = 34
a = 2
5. 170x + 4 = 64
x = 0.35
6. 15x - 25 = 200
x = 15
7. 5s + 3s = 42
s = 5.25
8. 10t + 2t = 28
t = 2.333333
9. 14s + 35s - 7s = 42
s = 1
10. 124s - 14s + 12s = 12
s = 0.1
Hope this helps, sorry I couldn't get to all of it. :)
Give the equation of the line that is perpendicular to y= (1/2)x -1 and passes through the point (3,4)
Answer: y = -2x + 10
Step-by-step explanation:
Two lines are said to be perpendicular if the product of their slope = -1, that is , if [tex]m_{1}[/tex] is the slope of the first line and [tex]m_{2}[/tex] is the slope of the second line , if the two lines are perpendicular , then [tex]m_{1}[/tex][tex]m_{2}[/tex] = -1
The equation of the line given :
y = 1/2x - 1
comparing with the equation of line in slope intercept form
y = mx + c , where m is the slope and c is the y - intercept , it implies that
[tex]m_{1}[/tex] = 1/2
Therefore :
[tex]m_{2}[/tex] = -2
To find the equation of the line with slope -2 and passes through the point ( 3 , 4 ) we will use the formula
[tex]y-y_{1}[/tex] = m ([tex]x-x_{1}[/tex] )
y - 4 = -2 ( x - 3 )
y - 4 = -2x + 6
y = -2x + 6 + 4
y = -2x + 10
every 10 customer get a free coke at the movie theater. Every 12 customer gets a free popcorn. what number customer will get both a free coke and a free popcorn?
Answer:
The 60th customer will get both a free coke and a free popcorn.
Step-by-step explanation:
i) every 10 customer gets a free coke
ii) every 12 customer gets a free popcorn
iii) therefore the first customer who will get both a free coke and a free popcorn will be given by the Lowest Common Multiple of 10 and 12 which is 60, as 10 goes in to 60 by 6 times and 12 goes into 60 by 5 times.
Answer:
The 60th customer will get both a free coke and a free popcorn.
Step-by-step explanation:
Please this is urgent look at the image!!!
Answer:
y-coordinate
Step-by-step explanation:
Answer:
y coordinate
Step-by-step explanation:
Kelly had a part time job last year. She paid the state $234 in income tax. The state income tax rate is 5.2%. How much did Kelly earn?
Answer
Step-by-step explanation:All you do is multiply $234 by 5.2% or .052 as a decimal
$234×.052×1
Answer:
It's 4500
Step-by-step explanation:
Sari drives 55 miles per hour. Which equation shows the proportional relationship between hours (h) and miles (m)?
Answer:
[tex]m=55h[/tex]
Step-by-step explanation:
we know that
A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form [tex]k=\frac{y}{x}[/tex] or [tex]y=kx[/tex]
In a proportional relationship the constant of proportionality k is equal to the slope m of the line and the line passes through the origin
Let
m ----> the distance in miles (y-coordinate)
h ----> the time in hours (x-coordinate)
In this problem the constant of proportionality k is given and is equal to
[tex]k=55\ \frac{miles}{hour}[/tex] ----> the speed
substitute
[tex]m=55h[/tex]
A 16 oz package of brown rie cost 79 cents and 32 oz package of white rice costs $3.49 . Which package is a better deal?
Answer:
Step-by-step explanation:
Brown rice
16oz = 0.79
Since 16oz is half of 32oz, we can multiply this equation by 2:
32oz = $1.58
Comparing the two, the 16oz package of brown rice is a better deal because it costs less.
if 3x= 27, then x = 9 what algebraic property?
Division property of equality is used
Solution:
Given that,
If 3x = 27 then x = 9
We have to find the algebraic property used here
Division property is used here
The division property of equality is a property that tells us if we divide one side of an equation by a number, we must also divide the other side by the same number so that our equation stays the same.
Given equation is:
3x = 27
Divide both the sides by 3
[tex]\frac{3x}{3} = \frac{27}{3}\\\\x = 9[/tex]
Thus division property of equality is used
The algebraic property used in changing 3x = 27, to x = 9 is the Division Property of Equality. This property means that if both sides of an equal equation are divided by the same nonzero number, then the resulting equation remains true.
Explanation:The algebraic property that applies when rearranging the equation 3x = 27, to x = 9 is known as the Division Property of Equality. This property states that when both sides of an equation are divided by the same nonzero number, the result is an equivalent equation.
To demonstrate this, in the given equation 3x = 27 we can apply the Division Property of Equality by dividing both sides of the equation by 3. This will give: 3x/3 = 27/3 which simplifies to x = 9, thus demonstrating the division property of equality.
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what inverse operation is used to solve the equation 2x=10
A) add 2 to both sides
B) divide by 2 on both sides
C) multiply by 2 on both sides
D) subtract 2 from both sides
Answer:
Step-by-step explanation:
2x = 10.....there are 2 ways to solve this....u can either divide by 2 on both sides, or multiply by 1/2 on both sides. However, the inverse operation would be the dividing by 2 because it is the inverse of multiplying.
so ur answer is : divide by 2 on both sides
Divide by 2 on both sides to get the inverse operation to solve the equation 2x=10.
What is Equation?Two or more expressions with an equal sign is called as Equation.
2x = 10.....there are 2 ways to solve this
Either divide by 2 on both sides, or multiply by 1/2 on both sides. However, the inverse operation would be the dividing by 2 because it is the inverse of multiplying.
Hence divide by 2 on both sides is the operation used to solve the equation 2X=10.
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Help
The output values of a relation are called the _____ of the relation
Answer:
The output values of a relation are called the Range of the relation
Step-by-step explanation:
we know that
For a set of ordered pairs, the first elements of each ordered pair is called the input value or independent variable and represents the domain of the function and second elements of each ordered pair is called the output value or dependent variable and represents the range of the function.
therefore
The output values of a relation are called the Range of the relation
Use sigma notation to represent the sum of the first six terms of the following sequence: 4, 12, 20, …
Answer:
check the photo below for the answer.
Sigma notation is used to represent series of numbers. To find the sum of the first six terms of the sequence 4, 12, 20, ..., you can use the formula Σ(4 + 8(n - 1)).
Sigma notation is a way to represent a series of numbers. In this specific case, we want to find the sum of the first six terms of the sequence 4, 12, 20, ... The sum can be represented as Σ(4 + 8(n - 1)), where n goes from 1 to 6.
2/5,3/10,1/3,2/4 least to greatest
Answer:
3/10, 2/5, 1/3, 2/4
Step-by-step explanation:
the greater the denominator the lower the portion will be depending on the numerator
Which expression is equivalent to |b|>2 ?
b > –2 and b < 2
b < –2 or b > 2
b < –2 and b > 2
b > –2 or b < 2
Answer:
b < –2 or b > 2
Step-by-step explanation:
The given expresion is
[tex] |b| \: > \: 2[/tex]
By the definition of absolute value function.
|x|=x, if x>0
|x|=-x, if x<0
This implies that:
[tex] b \: > \: 2 \: or \: - b \: > \: 2[/tex]
Divide the second inequality by -2 and reverse the sign
[tex]b \: > \: 2 \: or \: b \: < \: - 2[/tex]
Option B is correct
The expression |b| > 2 is equivalent to b < -2 or b > 2, indicating that the value of b is either greater than 2 or less than -2.
The expression |b| > 2 is equivalent to the situation where b is greater than 2 or less than -2. The absolute value sign indicates the distance of b from 0 on a number line, without considering direction. Therefore, if |b| is greater than 2, b must lie outside the interval from -2 to 2, since anything within that interval would have an absolute value less than or equal to 2.
This means that the correct expression equivalent to |b| > 2 is b < -2 or b > 2. When b is positive, it must be greater than 2 to satisfy the inequality. When b is negative, to have an absolute value greater than 2, it must be less than -2.
Adam has created a register for the bank account he opened on April 16th. Unfortunately, Adam has made a mistake and cannot figure out where he went wrong. Use the transaction descriptions below to determine where his error is.
The account was opened on April 16 with a tax refund check of $145.00.
Paid SellUPhone $65.34 on April 18. (Check 794)
Deposited a paycheck on April 23. ($9.76/hour for 35 hours)
Bought $61.32 (4% sales tax not included) in clothes from BargainsRUs on April 24 using a debit card.
Number Date Transaction Description Payment, Fee, Withdrawal (–) Deposit, Credit (+) Balance $
4/16 Open Account $145.00
794 4/18 SellUPhone 65.34 $79.66
4/23 Deposit 338.45 $418.11
4/24 BargainsRUs 63.77 $354.34
He completely forgot to include the clothes he bought from BargainsRUS.
He made an arithmetic error in the balance column.
He recorded one of his withdrawals in the deposit column.
He recorded his paycheck amount for April 23th incorrectly.
Answer:
D. He recorded his paycheck amount for April 23rd incorrectly. Yes, this was Adam's mistake. The correct amount should be 341.60 and not 338.45.
Step-by-step explanation:
1. Let's review the information given to us to help Adam to determine where his error is.
A. He completely forgot to include the clothes he bought from Bargains RUS. No, he didn't. It was recorded properly, including the sales tax amount.
B. He made an arithmetic error in the balance column. No he didn't, the balance was calculated correctly after each transaction.
C. He recorded one of his withdrawals in the deposit column. No, he didn't. All of the withdrawals are in the right column.
D. He recorded his paycheck amount for April 23rd incorrectly. Yes, this was Adam's mistake. The correct amount should be 341.60 and not 338.45.
Adam's error in the register lies in the paycheck amount recorded for the April 23rd deposit. His hourly wage is $9.76 and he worked for 35 hours, which should result in a pay of $341.60, but he recorded it as $338.45.
Explanation:The error in Adam's register appears to be in the paycheck amount recorded for the April 23rd deposit. Here's how we can figure it out
Adam's hourly wage is $9.76 and he worked for 35 hours. So, the total pay should be $9.76 * 35 = $341.60.In the register, however, the deposit amount for April 23rd is listed as $338.45, which does not match the calculation. So, this seems to be where Adam made a mistake.All the other transactions match correctly with the descriptions provided.So, Adam recorded his paycheck amount for April 23rd incorrectly.
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Please help! Pythagoras question.
The length of swimming course is 345.93 meters.
Step-by-step explanation:
Given,
BC = 80 m
AB = 145 m
Using pythagoras theorem to find AC.
[tex]AC^2+BC^2=AB^2\\AC^2+(80)^2=(145)^2\\AC^2+6400=21025\\AC^2=21025-6400\\AC^2=14625[/tex]
Taking square root on both sides
[tex]\sqrt{AC^2}=\sqrt{14625}\\AC=120.93m[/tex]
Length of swimming course = AB + BC + AC
Length of swimming course = 145 + 80 + 120.93 = 345.93 m
The length of swimming course is 345.93 meters.
Keywords: square root, addition
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What is the missing fraction for the equation?
9/10 + ?/? = 99/100
Final answer:
The missing fraction in the equation 9/10 + ?/? = 99/100 is 9/100 because 9/10 is equivalent to 90/100 and 99/100 - 90/100 equals 9/100.
Explanation:
To find the missing fraction in the equation 9/10 + ?/? = 99/100, we need to find a common denominator and then solve for the numerator of the missing fraction. The common denominator for 10 and 100 is 100, so we must convert 9/10 into an equivalent fraction with a denominator of 100, which is 90/100. Now, to find the missing numerator, we subtract 90/100 from 99/100 which gives us 9/100. Therefore, the missing fraction is 9/100.