Answer:
[tex]\frac{27}{20}[/tex]
Step-by-step explanation:
[tex]\frac{3}{5} + \frac{6}{8}[/tex]
adjust the denominators;
= [tex]\frac{3*8}{5*8} + \frac{6*5}{8*5}[/tex]
[tex]=\frac{24}{40} + \frac{30}{40} \\\\=\frac{24+30}{40} \\\\=\frac{54}{40} \\\\simplify\\\\=\frac{27}{20}[/tex]
Which data set has the same standard deviation as the data set {1, 1, 3, 5, 8} ?
{9, 8, 9, 8, 9}
{2, 2, 4, 6, 9}
{1, 2, 6, 6, 9}
{1, 1, 1, 2, 2}
The data set that has the same standard deviation with the given data set is: B. {2, 2, 4, 6, 9}.
How to Find the Standard Deviation of a Data Set?Given the data set, {1, 1, 3, 5, 8}, the standard deviation (σ) is calculated as shown below:
Standard deviation (σ) = √(SS/n)
Count (n) = 5
Mean (μ) = 3.6
Sum of Squares (SS) = 35.2
Standard deviation (σ) = (√35.2/5)
Standard deviation (σ) = √7.04
Standard deviation (σ) ≈ 2.7
Also, the standard deviation of {2, 2, 4, 6, 9} is calculated as shown below:
Count (n) = 5
Mean (μ) = 4.6
Sum of Squares (SS) = 35.2
Standard deviation (σ) = (√35.2/5)
Standard deviation (σ) = √7.04
Standard deviation (σ) ≈ 2.7
Therefore, the data set that has the same standard deviation with the given data set is: B. {2, 2, 4, 6, 9}.
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Evaluate the expression when x=10, y=−2, and z=−5.
|xz−y|=
Answer:
it would be 52
Step-by-step explanation:
if x = 10 y = -2 and z= -5
x * z = 10 * -5 = -50
-50 - (-2) = -52
|-52| this would make it positive so the answer is 52
In the addition problems below A, B, and C are digits. If C is placed in the tens
column instead of the ones column as shown at the right, the sum is 97. What are
the values of A, B, and C?
AB + C = 52
AB+ (C x 10) = 97
The values of A, B, and C are mathematically given as
A=48/BB=48/AC=5This is further explained below.
What are the values of A, B, and C?Generally, the equation for the statement is mathematically given as
AB + C = 52
AB+ (C x 10) = 97....1
Using the substitution technique we have
AB = 52- C ....2
Subbing 2 in 1
AB+ (C x 10) = 97
Therefore
52- C + 10C = 97
9C=97-52
9C=45
C=5
In conclusion,
AB = 52- C
AB = 52- 5
AB=48
A=48/B
Hence
B=48/A
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Solve the equation and determine the solution(s) or any extraneous solution.
Answer:
Solution: x = 9 Extraneous solution: x = 1
Step-by-step explanation:
Given equation:
[tex]\sqrt{4x}=x-3[/tex]
Square both sides:
[tex]\implies \left(\sqrt{4x}\right)^2=\left(x-3\right)^2[/tex]
[tex]\implies 4x=x^2-6x+9[/tex]
Subtract 4x from both sides:
[tex]\implies 4x-4x=x^2-6x+9-4x[/tex]
[tex]\implies 0=x^2-10x+9[/tex]
[tex]\implies x^2-10x+9=0[/tex]
Split the term in x:
[tex]\implies x^2-x-9x+9=0[/tex]
Factor the first two terms and the last two terms separately:
[tex]\implies x(x-1)-9(x-1)=0[/tex]
Factor out the common term (x - 1):
[tex]\implies (x-9)(x-1)=0[/tex]
Apply the zero-product property:
[tex](x-9)=0 \implies x = 9[/tex]
[tex](x-1)=0 \implies x=1[/tex]
Substitute the found values of x into the original equation to verify the solutions:
[tex]\begin{aligned}x=9 \implies \sqrt{4 \cdot 9} & = 9-3\\\sqrt{36} & = 6\\6 & = 6\end{aligned}[/tex]
[tex]\begin{aligned}x=1 \implies \sqrt{4 \cdot 1} & = 1-3\\\sqrt{4} & = -2\\ 2 & = -2\end{aligned}[/tex]
Therefore, the only valid solution is x = 9:
Solution: x = 9Extraneous solution: x = 1Extraneous solution: A solution from the process of solving the equation that is not a valid solution to the original equation.
the class was required to draw plan for the foundation day. Mary and tess was assigned to draw buildings. mary draw buildings twice as much as tess. if the total buildings are 99, how many buildings was draw by mary and tess
Answer:
Mary drew 66 buildings and Tess drew 33 buildings.
Step-by-step explanation:
Let's label the number of buildings drawn by Mary as x and the number of buildings drawn by Tess as y.
We know there are 99 buildings drawn. This means
99=x+y
We also know that Mary drew twice as many buildings as Tess. We can represent this as
x=2y
Now, let's substitute x for 2y, since that would put us in common terms
99=2y+y
Add common variables together and you get
99=3y
Solve for y by dividing 99 by 3
y=33
We now know that Tess drew 33 buildings, as well as y=33. Substitute y in the equation for how many buildings Mary drew:
x=2(33)
Now we know that Mary drew 66 buildings.
To check our work,
99=x+y
99=66+33
99=99
f(x)=x+2
g(x) = 3x² - 5
Find (f ·g)(x).
Step-by-step explanation:
f(x) = x + 2
g(x) = 3x² - 5
= (f.g)(x)
= (x + 2).(3x² - 5)
= 3x³ - 5x + 6x² - 10
= 3x³ + 6x² - 5x - 10
According to a survey conducted by a city’s chamber of commerce, approximately 41.5% of city residents prefer local businesses over national chains. The survey had a margin of error of ±3.8%. Round to the nearest tenth, if necessary.
The values in percentages will be 37.7% and the maximum will be: 45.3%
How to illustrate the information?From the information, the approximately 41.5% of city residents prefer local businesses over national chains and the survey had a margin of error of ±3.8%.
Therefore, the minimum number will be:
= 41.5% - 3.8%
= 37.7%
The maximum will be:
= 41.5% + 3.8%
= 45.3%
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List the interval(s) on which f is increasing.
The interval(s) in which f is increasing is/are: _____________.
(Type your answer in interval notation. Use a comma to separate answers as needed.)
The intervals on which the function f of x is increasing is:
(6, 0) U (2, 4) U (7, 9)
In which intervals is the function increasing?When we have the graph of a function, we can identify if it is increasing if, reading from left to right, we can see that the graph of the function goes upwards.
For the graphed function, we can see that it increases for the values:
-6 < x < 0
2 < x < 4
7 < x < 9
Writing this in interval notation, we have:
(6, 0) U (2, 4) U (7, 9)
This is the list of intervals on which the function f(x) is increasing.
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Angle DFG and angleJKL are complementary angles. If the measure if the angle DFG=x+2 and the measure of the angle JKL =x+9 then find x.
complementary angles m < DFG = 48, m < JKL = 42 is value of x .
What is the opposing angle to the above example?
Complementary angles are those whose combined angle is exactly 90 degrees. 30 degrees and 60 degrees, for instance, are complimentary angles.
∠DFG and ∠JKL are complementary angles. m∠DFG = x + 5,
and m∠JKL = x − 1
When two angles are complementary then the sum of angles is 90 degrees
∠DFG and ∠JKL are complementary angles.
So m < DFG < + m < JKL = 90
Now replace the expressions and solve for x
x + 5 +x - 1 =90
2x + 4 = 90
2x = 90 - 4
2x = 86
x = 43
Now replace x with 43 and find out each angle
m < DFG = x + 5
m < DFG = 43 + 5 = 48
m < DFG = 48
m < JKL = x - 1 = 43 - 1 = 42
m < DFG = 48
m < JKL = 42
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You are getting on a plane to visit family 1200 miles away. The plane you are boarding will travel on
average 500 miles per hour. How long will the trip take you?
Answer:
2.4 hours or 2 hours and 24 minutes
Step-by-step explanation:
Distance = rate times time
d = rt
1200 = 500t Divide both sides by 500
2.4 = t
It will take 2.4 hours. We can convert the .4 into minutes by using a unit multiplier 60 minutes = 1 hour.
[tex]\frac{.4hours}{1}[/tex] x [tex]\frac{60minutes}{1hour}[/tex] The words hours cancel out and we are left with
.4 x 60 = 24 minutes.
The base rate for workers compensation insurance for roofers in one state is $16.95 per $100 paid to employees. The total monthly payroll for Certified Roofing Contractors is $15,738. What is the monthly premium for workers compensation insurance?
Answer:
3.3972 repeating dbbdeebebbbebe
Step-by-step explanation:
wvehhww3g33gg3g33vv3hh333h33hhh3
Answer:
C. not covered by workers' compensation and could recover damages from the employer.
Step-by-step explanation:
Solve x/4>_-1 and -4x-4<_-3 and write the solution in interval notation. If there is no solution, type the no solution symbol.
The solution interval for x is x ∈ (-1/4 , ∞)
An inequality shows the relationship of a non-equal comparison between two numbers or mathematical expressions.
Here, we are given two inequalities
x/4 > -1 and -4x - 4 < -3
Let us take the first equation
x/4 > -1
⇒ x > 4(-1)
x > -4
Now, the second equation
-4x - 4 < -3
-4x < -3 + 4
-4x < 1
Now since we are dividing both sides by a negative number, that is 4, the sign of the inequality will be reversed,
x > 1/-4
x > -1/4
Thus, we get x > -4 and x > -1/4
This means that all values of x greater than -1/4 will satisfy.
Thus, x ∈ (-1/4 , ∞)
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PLEASE HELP!!! ASAP!! FIND THE DOMAIN AND RANGE OF THEESE GRAPHS
Answer:
Domain: [-2, infinity)
Range: [-4, infinity)
Step-by-step explanation:
There's only one graph I see.
Domain is how far the graph extends on the x axis.
Range is how far the graph extends on the y axis.
26) Jody earns $8.00 per hour.
Michael earns $10.00 per hour.
They each earn a 2% commission on what they sell.
Jody sold $6000. She worked 30 hours.
Michael sold $5000. He worked 40 hours.
What were each of their earnings for the week?
What was the difference in their earnings?
Jody's weekly earning is $360 and Michael's weekly earning is $500
The difference between their earning is $140
Jody sold $6000
2% commission of $6000 is (2/100)x 6000
Jody's commission is $120
He earns $8 per hour and he worked for 30 hours
= 8 x 30
=$240
Jody's total earning = 240 + 120 = $360
Michael sold $5000
2% commission of $5000 is (2/100)x 5000
Michael's commission is $100
He earns $10 per hour and he worked for 40 hours
= 10 x 40
=$400
Michael's total earning = 400 + 100 = $500
Difference in there earnings= Michael's earning - Jody's earning
= 500- 360
= $140
Therefore, Jody's weekly earning is $360 and Michael's weekly earning is $500
The difference in their earning is $140
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Write the expression 3x + 4 using words
Answer:
three times "x" plus four
Step-by-step explanation:
three times "x" plus four
Hope this helps!
4x-6*x=238
solve for x
Answer:
x=-119
Step-by-step explanation:
[tex]4x-6x=238[/tex]
[tex]-2x=238[/tex]
[tex]\frac{-2x}{-2}=\frac{238}{-2}[/tex]
[tex]x=-119[/tex]
Please show me how to solve this: Katie and Tara are making crafts for their school's craft fair. For every 7 Tara makes, Katie makes 9. If they made a total of 240 crafts, how many did each girl
make?
Answer:
Tara makes 7x =7*15 = 105 crafts and Katie made 9x = 9*15 = 135 crafts.
Step-by-step explanation:
Crafts tara and katie make resoectively are in the ratiob 7:9. Let's say 7x and 9x.
Now,
7x + 9x = 240
so, x = 240/16
so, x = 15
−12 + −9 = ? I need an answer!
Answer: -21
Step-by-step explanation:
what is the value of 10 to the power of -16 written as a fraction
Answer: 1e-16
Step-by-step explanation:
Steps
(x)n = (10)-16
=
1
10 x 10 x .... x 10
=
1
10000000000000000
= 1e-16
Given the fallowing function find (-3),f(1)
Answer:
12 ,-3, -8
Step-by-step explanation:
1: f(-3)= -5(-3)-3
2: f(0)= -5(0)-3
3: f(1)= -5(1)-3
Hope this helps!
What is the area?
34 cm
39 cm
square centimeters
The area of the shape will be 1326 cm².
How to calculate the area?It should be noted that the area is calculated by multiplying the dimensions that are given.
Therefore the area will be:
= Length × Width
= 34 × 39.
= 1326 cm²
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What is the solution of −|t+3| + 3 ≥ −4?
Answer:
[tex]-1t+31 +3 \geq -4[/tex]
[tex]-1t +34 \geq -4[/tex]
[tex]-1t \geq 30[/tex]
[tex]t \geq -30[/tex]
A recipe calls for the following spices:1/4 teaspoon of turmeric,1/8 teaspoon of ginger, and 1/4 teaspoon of cumin. What is the total quantity of these three spices?
There were 256 farmers in the county 30 years ago 5/8 of those farmers have changed occupations how many of the 256 farmers changed occupations
The answer is 27 for your math
Step-by-step explanation:
A company asks an investor for an investment of $800,000 in exchange for 15% equity in the business. What is the implied valuation of the business?
If a company asks an investor for an investment of $800,000 in exchange for 15% equity in the business. The implied valuation of the business is: $4,533,333.
Implied valuationFirst step is to calculate the equity valuation
Using this formula
Equity valuation=Amount invested/Equity rate
Let plug in the formula
Equity valuation=$800,000/.15
Equity valuation=$5,333,333
Second step is to calculate the implied valuation
Implied valuation=Equity valuation-Amount invested
Let plug in the formula
Implied valuation=$5,333,333-$800,000
Implied valuation=$4,533,333
Therefore If a company asks an investor for an investment of $800,000 in exchange for 15% equity in the business. The implied valuation of the business is: $4,533,333.
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Malcolm got his first job. His wage in his first year was $8.65 an hour. In year 2, it was raised to $10 an hour. What was the percent increase in his hourly wage between year 1 and year 2
O 15.61%
O 13.5%
O 1.35%
O 0.16%
The percentage increase is the ratio of value increased to the original value and multiplied by 100.
The percentage increase in his hourly wage between year 1 and year 2 is 15.61%.
Option A is the correct answer.
What is a percentage increase?The percentage increase is the ratio of value increased to the original value and multiplied by 100.
It is expressed in percentage.
If there is an increase in the value of anything, then there is an increase in percentage.
We have,
Wage in the first year per hour = $8.65
Wage in the second year per hour = $10
The percentage increase in hourly wage:
= [ (10 - 8.65) / 8.65 ] x 100
= ( 1.35 / 8.65 ) x 100
= 15.6069 %
= 15.61 %
Thus the percentage increase in his hourly wage between year 1 and year 2 is 15.61%.
Option A is the correct answer.
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If you only have a 1/3 measuring cup and a recipe calls for 12 2/3 cups of flour, how many 1/3 cups would you need to use? 1/3 * t th cups
If we have a 1/3 measuring cup and a recipe calls for 12 and 2/3 cups of flour,then we would need 38 number of cups.
Given that we have a 1/3 measuring cup and a recipe calls for 12 and 2/3 cups of flour.
We are required to find the number of cups that are needed.
Fraction is the combination of two numbers,one above the division sign and other one below the division sign. The number which is above the division sign is known as numerator and the number which is below the division sign is known as denominator.
Measuring cup=1/3
Number of cups needed in recipe=12+2/3=38/3
Number of cups needed=38/3/1/3
=38 cups
Hence if we have a 1/3 measuring cup and a recipe calls for 12 and 2/3 cups of flour,then we would need 38 number of cups.
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is 35 over 56 a improper fraction and is 144 over 196 a improper fraction
Given that the curves are formed from
quarter circles,
find the area of the shaded region.
Give your answer in terms of TT.
4m
4m
The diagram is not drawn to scale
The area of the shaded region is 8π-16.
The side of the square is 4 m. Imagine a diagonal of the given square, which divides the shaded region into two equal parts due to symmetry. The radius of the quarter circle formed by one of the arcs and the two sides of the square is 4 m. The area of the quarter circle = 1/4πr²The area of the quarter circle = 1/4π4²The area of the quarter circle is 4π m². The diagonal and the two adjacent sides of the square form a right-angled triangle with a base of 4 m and a height of 4 m. The area of the triangle is 1/2*base*height. The area of the triangle is 1/2*4*4. The area of the triangle is 8 m². The area of the shaded region bisected by the diagonal = Area of quarter circle - Area of triangleThe area of the shaded region bisected by the diagonal = 4π-8 m²The area of the shaded region is twice the area of the shaded region bisected by the diagonal. The area of the shaded region = 2 * (4π-8)The area of the shaded region is 8π-16 m².To learn more about area, visit :
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Translate this phrase into an algebraic expression.
Three less than the product of 15 and Chrissy's score
Use the variable c to represent Chrissy's score.
Answer:
15c - 3
Step-by-step explanation:
Product means 'The answer when you Multiply' So we are working in multiplication ( x )
15 x c can also be written as 15c
'3 less than' means subtracting 3 off the answer.
So therefore the answer is:
15c - 3