Thus, new coordinates of A'B'C' after the reflection across the y-axis are-
A'(-5, -1), B'(-3,-4), C'(-3, 0).
Explain about the reflection across y-axis:The x-coordinate remains constant when a point is reflected across the x-axis, but the y-coordinate is assumed to be the additive inverse. Point (x, y) is reflected across the x-axis as (x, -y).
The y-coordinate stays the same when a point is reflected across the y-axis, but the x-coordinate is assumed to be the additive inverse. Point (x, y) is reflected across the y-axis as (-x, y).
Given coordinates of ABC.
A(5, -1), B(3,-4), C(3, 0)
Reflection across the y-axis : y coordinates remains same while x coordinate multiplied with -1.
(x,y) -- > (-x, y)
A'(-5, -1), B'(-3,-4), C'(-3, 0)
Thus, new coordinates of A'B'C' after the reflection across the y-axis are-
A'(-5, -1), B'(-3,-4), C'(-3, 0).
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Is (3, 5) a solution to this system of equations?
y=5
y = -5/3x + 10
yes
no
A sum of money has a value of$3000 eight-
een months from now. If money is worth 6%
compounded monthly, what is its equivalent value
(a) now?
(b) one year from now?
(c) three years from now?
Answer:
We can use the formula for compound interest to solve this problem:
A = P(1 + r/n)^(nt)
where A is the future value, P is the present value, r is the interest rate, n is the number of times the interest is compounded per year, and t is the time period in years.
(a) To find the present value of the money, we need to solve for P in the formula above. We are given that A = $3000 and t = 18/12 = 1.5 years. The interest rate is 6% per year, compounded monthly, which means n = 12. Substituting these values into the formula, we get:
3000 = P(1 + 0.06/12)^(12*1.5)
Simplifying and solving for P, we get:
P = 3000 / (1 + 0.06/12)^(12*1.5)
P = $2,572.39
Therefore, the equivalent value of the money now is $2,572.39.
(b) To find the equivalent value of the money one year from now, we need to calculate the future value of $1 after one year, and then multiply it by the present value we found in part (a). The future value of $1 after one year, at 6% per year, compounded monthly, is:
FV = 1*(1 + 0.06/12)^(12*1)
FV = $1.06168
Multiplying this by the present value we found in part (a), we get:
$2,572.39 * $1.06168 = $2,735.92
Therefore, the equivalent value of the money one year from now is $2,735.92.
(c) To find the equivalent value of the money three years from now, we need to calculate the future value of $1 after three years, and then multiply it by the present value we found in part (a). The future value of $1 after three years, at 6% per year, compounded monthly, is:
FV = 1*(1 + 0.06/12)^(12*3)
FV = $1.19102
Multiplying this by the present value we found in part (a), we get:
$2,572.39 * $1.19102 = $3,066.63
Therefore, the equivalent value of the money three years from now is $3,066.63.
Jungle John participates in a reality TV show that features fitness and agility competitions. In order to beat the competitors, John needs to swing from tree A to tree B, completing an arc of at least 60 feet with a central angle of 115∘.
What length of rope (radius) will he need to accomplish this activity?
Round your answer to the nearest foot, and please show your work.
The length of rope Jungle John will he need to accomplish this activity is 30 feet.
How do we calculate?
the formula for arc length is
L = rθ
where L = length of the arc,
r =e radius of the circle,
θ = central angle of the arc in radians.
θ = (115∘/180∘)π = 2.0089 radians
60 feet = r(2.0089 radians)
r = 60 feet / 2.0089 radians
r = 29.85 feet
r is approximated to 30 feet
Therefore, Jungle John will need a rope with a length of at least 30 feet to swing from tree A to tree B and complete an arc of at least 60 feet with a central angle of 115∘.
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find slope and y intercept of -5x = 8 - y
When choosing between a line plot
and a line graph, when is it better to
use a line plot? When is it better to
use a line graph?
Generally, it is better to use a Line Graph if your raw data includes non-numeric values. If your raw data only has numeric values, use a Scatter Plot. You can use a Line Graph if you want to label your horizontal axis with text labels. These labels can represent evenly spaced values as days, weeks, and years.
Somebody please help
Emilee's insurance company pays for 70% of her wrist surgery after she pays a $371
deductible. How much will Emilee pay for her wrist surgery if it costs $12,791?
Round answer to the nearest whole number. Do not include the units. Be sure to
attach work to earn credit.
Emilee will spend around $3,726 for her wrist surgery once her insurance company pays 70% and she meets the $371 deductible.
How much Emilee will pay for her wrist surgery?Calculating out-of-pocket costs for a medical expense after insurance coverage and deductibles often requires simple arithmetic.
The total cost of the medical billSubtraction of the deductibleCompute the insurance coverage amount by multiplying the remaining cost after the deductible by the insurance coverage percentage.To calculate the out-of-pocket cost, subtract the insurance coverage amount from the remaining cost after the deductible.Round the final value to the closest full number if desired.To begin, deduct the deductible from the overall cost of the surgery: $12,791 - $371 = $12,420.
70% of the remaining cost after the deductible is calculated as follows: 70% of $12,420 = $8,694.
Total cost after insurance coverage: $12,420 - $8,694 = $3,726
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12. Mr. Wright is five times as old as
his daughter, Lilly. Lilly is twice
as old as her brother, Micah. If
Micah is 3 years old, how old is
Mr. Wright?
Based on the given data, the age of Mr. Wright currently is 30 years
If Micah is 3 years old, then Lilly is twice as old, which means that
Lilly is 2 * 3 = 6 years old.
Now we know that Mr. Wright is five times as old as his daughter, Lilly, so Mr. Wright's age is:
5 * 6 = 30 years old.
Therefore, Mr. Wright is 30 years old.
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Note: Enter your answer and show all the steps that you use to solve this problem in the space provided.
Find the area of the parallelogram.
check the picture please.
Answer:
[tex]192[/tex] [tex]cm^2[/tex]
Step-by-step explanation:
Recall that the formula for the area of a parallelogram is:
[tex]A=bh[/tex]
Where b is the length of the base, and h is the length of the height.
We are given that the base is 24 cm.
So, b=24.
We are also given that the height is 8 cm.
So, h=8.
Let's plug these values into the formula:
[tex]A=bh=\\A=(24)(8)=\\A=192[/tex]
Since area is a two-dimensional measure, we need to label our answer using units squared.
Thus, the area is [tex]192[/tex] [tex]cm^2[/tex]
Area of a parallelogram => [tex]A=bh[/tex]
Where, b=24 cm and h=8 cm
Plug in the known values and solve.
[tex]\Longrightarrow A=bh \Longrightarrow A=(24 \ cm)(8 \ cm) \Longrightarrow A= \boxed{192 \ cm^2}[/tex]
Scott's employer pays 55% of his health insurance premium and deducts the
remainder from his paycheck. Scott is paid biweekly and the annual premium is
$20,969. How much is deducted from his paycheck for health insurance? Round
answer to the hundredths place. If the answer doesn't have a hundredths place then
use zeros so that it does. Do not include units in the answer.
Your Answer:
Answer:
To calculate how much is deducted from Scott’s paycheck, we need to first find out how much his employer pays for his health insurance premium.
55% of the annual premium is covered by the employer, so we can calculate this as:
0.55 x $20,969 = $11,532.95
Therefore, Scott’s employer pays $11,532.95 towards his health insurance premium.
To find out how much is deducted from Scott’s paycheck, we need to divide the remaining 45% of the premium by the number of pay periods in a year. Since Scott is paid biweekly, he receives 26 paychecks in a year.
45% of the annual premium is not covered by the employer, so we can calculate this as:
0.45 x $20,969 = $9,437.55
To find out how much is deducted from each biweekly paycheck, we can divide $9,437.55 by 26:
$9,437.55 ÷ 26 = $363.75 (rounded to the nearest cent)
Therefore, Scott’s employer pays $11,532.95 towards his health insurance premium and $363.75 is deducted from each of his biweekly paychecks for health insurance.
x^2 + 7y + 12 = ?
x = -1 y = 4
The value of the expression when x = -1 and y = 4 is 41.
Evaluating the expression [tex]x^2[/tex]+7y+12 when x = -1 and y = 4, we get:
[tex]x^2[/tex]+7y+12 = [tex](-1)^2[/tex] + 7(4) + 12 = 1 + 28 + 12 = 41
Therefore, the value of the expression when x = -1 and y = 4 is 41.
Here is the step-by-step solution:
Substitute x = -1 and y = 4 into the expression.
Evaluate the exponent.
Multiply 7 by 4.
Add 1, 28, and 12.
The answer is 41.
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i just dont want to do this
Answer:
B
[tex]6^{-7}[/tex] is equivalent to 1/279936 which is basically [tex]\frac{1}{6^{7}}[/tex]
Prism A is a dilation of Prism B. The height of Prism A is 6
Bis
31/12 ₁²
ft.
61/1/21 ft, and the volume of Prism A is
What is the volume of Prism B?
Enter your answer as a mixed number in simplest form by filling in the boxes.
ft
872/1 T
ft. The height of Prism
S
Therefore, the volume of Prism B is 727/4 ft³ or 181 3/4 ft³ in mixed number form.
How should mixed numbers be done step-by-step?Subtract the denominator from the numerator. The quotient should be expressed as a whole number in step 2. Step 3: Enter the denominator and numerator, respectively, as the remainder and the divisor.
We can write: Using the formula for a prism's volume (V = Bh, where B is the base area):
We must determine Prism B's cross-sectional area in order to get the volume of Prism B. By dividing the height equation of prism A by its volume equation, the following result is obtained:
cross-sectional area of Prism A = (Volume of Prism A) / (height of Prism A) = (872/1 ft³) / (6 ft) = 218/3 ft²
Using the scale factor equation for height, we get:
k = (height of Prism A) / (height of Prism B) = (6 ft) / (31/12 ft) = 24/31
Using the scale factor equation for cross-sectional area, we get:
k² = (cross-sectional area of Prism A) / (cross-sectional area of Prism B) = (218/3 ft²) / (cross-sectional area of Prism B)
Solving for the cross-sectional area of Prism B, we get:
cross-sectional area of Prism B = [tex](218/3 ft^2) / k^2 = (218/3 ft^2) / (24/31)^2 = 59/3 ft^2[/tex]
Finally, substituting the height and cross-sectional area of Prism B into the volume equation of Prism B, we get:
Volume of Prism B = (cross-sectional area of Prism B) * (height of Prism B) = [tex](59/3 ft^2) * (31/12 ft) = 727/4 ft^3.[/tex]
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please answer and explain how to get it.
What is the simplified form of 7 log3x + 4 log3z – 6 log3y?
The simplified form of 7 log3x + 4 log3z - 6 log3y is log3(x^7 z^4 / y^6).
What is the simplified form of the expressionWe can simplify the expression using the following logarithmic rule:
log a + log b = log ab (product rule)
log a - log b = log(a/b) (quotient rule)
c log a = log a^c (power rule)
Using these rules, we can simplify 7 log3x + 4 log3z - 6 log3y as follows:
7 log3x + 4 log3z - 6 log3y
= log3x^7 + log3z^4 - log3y^6 (using the power rule)
= log3(x^7 z^4 / y^6) (using the quotient rule)
Therefore, the simplified form of 7 log3x + 4 log3z - 6 log3y is log3(x^7 z^4 / y^6).
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Is a triangle with sides of 5 meters, 12 meters, and 13 meters a right triangle? Explain/Show your work.
Answer:
[tex]\huge\boxed{\sf Yes.}[/tex]
Step-by-step explanation:
In a right angled triangle, the longest side is called hypotenuse.
So,
Hypotenuse = 13 m
The rest are:
Base = 5 m
Perpendicular = 12 m
Using Pythagoras Theorem to verify:
[tex](Hypotenuse)^2=(Base)^2+(Perpendicular)^2[/tex]
Put the given data
(13)² = (12)² + (5)²
169 = 144 + 25
169 = 169Since, both left hand side and right hand side are equal, this means the triangle is a right-angled triangle.
[tex]\rule[225]{225}{2}[/tex]
NO LINKS!! URGENT HELP PLEASE!!!
Express the statement as an inequality Part 4a^2
The correct answer is B) |x| > 6 for the given statement
What is meant by the statement?
A statement is a declarative sentence that can be either true or false. It is a proposition that can be proven using logical reasoning or evidence. Statements are the building blocks of mathematical proofs and are used to establish the truth of mathematical theories and concepts.
According to the given information
The statement “the absolute value of x is greater than 6” can be expressed as an inequality in the following way:
|x| > 6
This means that the distance between x and 0 on the number line is greater than 6 units. In other words, x can be any number that is either less than -6 or greater than 6.
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Musa got 750 bags of coffee
2011 yield dropped by 30%
2012 rose by 15%
A bag of coffee weighs 55kg and he paid 7900 shillings per tonne
Thereafter the price per tonne increased by 10% find his earnings from coffee hence find his total income for the three years
Answer:
2011: 0.3×750= 225
therefore, 750-225=525
2012: 0.15 × 525= 78.75
therefore, 525 + 78.75= 603. 75
bag of coffee: mass (kg)
1: 55
603.75: x
x= 55 × 603.75
=33206.25 Kg
33206.25÷1000= 332.0625
tonne: shillings
1:7900
332.0625: x
hence, x= 2623293.75 shillings
8690× 332.0625= 2885623. 125 shillings
Employees at a factory receive regular raises. The table below shows how an employee's hourly wage increases based on these regular raises. Which linear equation models the relationship shown in the table? A: y=0.5x+0.8 B: y=1.6x+9.75 C: y=9.75+1.6 D: y=0.8x+9.75
A linear equation that models the relationship shown in the table is: D. y = 0.8x + 9.75
How to determine an equation of this line?In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical equation (formula):
y - y₁ = m(x - x₁)
Where:
x and y represent the data points.m represent the slope.First of all, we would determine the slope of this line;
Slope (m) = (y₂ - y₁)/(x₂ - x₁)
Slope (m) = (10.55 - 9.75)/(1 - 0)
Slope (m) = 0.8/1
Slope (m) = 0.8
At data point (0, 9.75) and a slope of 0.8, a linear equation for this line can be calculated by using the point-slope form as follows:
y - y₁ = m(x - x₁)
y - 9.75 = 0.8(x - 0)
y = 0.8x + 9.75
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Missing information:
The question is incomplete and the complete question is shown in the attached picture.
answer is c please help its about limit
Using limits the value of k is c √2
What is the limit of a function?The limit of a function is the valuer the function tends to as the dependent variable tends to a particular value.
Given that the limit lim n → ∞ [x√(x + 1)[1 - √(2x + 3)]/(7 - 6x + kx²) = - 1, we desirte to find the value of k.
So, we proceed as follows
lim n → ∞ [x√(x + 1)[1 - √(2x + 3)]/(7 - 6x + kx²) = - 1
Factorizing out √2x, we have that
lim n → ∞ [x√(x + 1)[1 - √(2x√(1 + 3/√(2x)]/(7 - 6x + kx²) = - 1
lim n → ∞ [x√(x + 1)√(2x[1/√(2x - √(1 + 3/√(2x)]/(7 - 6x + kx²) = - 1
Also, factorizing out √x, we have that
lim n → ∞ [x√x√(1 + 1/√x)√2x[1/√(2x - √(1 + 3/√(2x)]/(7 - 6x + kx²) = - 1
lim n → ∞ [x√x√2x√(1 + 1/√x)[1/√(2x - √(1 + 3/√(2x)]/(7 - 6x + kx²) = - 1
lim n → ∞ [x√2x√(1 + 1/√x)[1/√(2x - √(1 + 3/√(2x)]/(7 - 6x + kx²) = - 1
lim n → ∞ [√2x²√(1 + 1/√x)[1/√(2x - √(1 + 3/√(2x)]/(7 - 6x + kx²) = - 1
Factorizing x² from the denominator, we have that
lim n → ∞ [√2x²√(1 + 1/√x)[1/√(2x - √(1 + 3/√(2x)]/x²(7/x² - 6/x + k) = - 1
lim n → ∞ [√2√(1 + 1/√x)[1/√(2x - √(1 + 3/√(2x)]/(7/x² - 6/x + k) = - 1
Now substituting x = ∞ into the equation, we have that
[√2√(1 + 1/√∞)[1/√(2∞ - √(1 + 3/√(2∞)]/(7/∞² - 6/∞ + k) = - 1
[√2√(1 + 0)[0 - √(1 + 0]/(0 - 0 + k) = - 1
[√2√(1)[- √1]/k = - 1
[√2(1)[- 1]/k = - 1
-√2/k = - 1
k = -√2/-1
k = √2
So, the value of k is c √2
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Olivia mowed 4 lawns in 16 hours. What was her rate of mowing in hours per lawn?
Answer:
Her rate of mowing lawns per hour is 4 lawns to one hour
Step-by-step explanation:so on a table you divide 4÷4=1 then you do the same thing for the 16÷4=4. So Oliva can mow 4 lawns per hour
m^2-6m +9
in factored form?
Answer:
(m-3)^2
Step-by-step explanation:
(m^2-6m+9) is factored by using this formula:
(a-b)^2=a^2-2ab+b^2.
Therefore, we can substitute the values into this equation.
m^2=a^2,
-6m=-2ab,
9=b^2.
Solving for b in the third equation, b is equal to 3 or -3. However, as this equation is negative, then it must be -3.
(m-3)^2
6 A cube-shaped block of cheese has edge lengths of 8 inches. The block of cheese is cut into smaller pieces. Each piece has a volume of 1 cubic inch. How many pieces of cheese will there be? 16 pieces 64 pieces 128 pieces O. 512 pieces
When the block is cut into smaller pieces, 512 pieces of cheese remain.
What is cube and formula of volume of cube?A cube is a solid three-dimensional shape with 6 square faces, 8 vertices and 12 edges. It is also said to be a regular hexahedral.
The volume V of a cube is given by the formula V = a^3, where a = the length of one side of the cube. V = 4 ^ 3 = 64 cubic meters or inches ^ 3. The volume of a cube is 64 cubic meters
The total volume of the cheese block is obtained as follows:
V = edge length³ = 8³ = 512 cubic meters
Since the volume of each piece is 1 cubic inch, the total number of pieces is obtained by dividing the total volume by the volume of each piece:
Number of pieces = V / volume per piece = 512 / 1 = 512 pieces
Therefore, when the block is cut into smaller pieces, 512 pieces of cheese remain.
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Two mechanics worked on a car. The first mechanic worked for 10 hours, and the second mechanic worked for 15 hours. Together they charged a total of 1650 . What was the rate charged per hour by each mechanic if the sum of the two rates was 135 per hour?
Rates of first and second mechanics are 75 and 60 per hour respectively.
What does an equation mean?A mathematical statement or relation between two or more numeric values, variable and mathematical operations via equal sign is called an Equation.
How to solve equations in Elimination Method?Elimination method is a kind of method to solve simultaneous equations in two variables. In elimination method we compare coefficient of one of two variables and in next step we eliminate that variable using addition or subtraction and form another relation with only one variable and find the value for that one variable and then substituting that value initial equation we can get the value of another variable.
Let the rate of first mechanic and second mechanic be x and y per hour respectively.
Sum of the two rates is 135 per hour. So the suitable equation will be,
x+y = 135 ............... (i)
Since they charged together 1650 after working 10 hours by first and 15 hours by second mechanics. So the suitable equation this time will be,
10x+15y = 1650
5(2x+3y) = 1650
2x+3y = 1650/5
2x+3y = 330 ............... (ii)
Multiplying 2 with equation (i) and then subtracting it from equation (ii) we get,
(2x+3y) - 2(x+y) = 330 - 2*135
2x+3y-2x-2y = 330-270
y = 60
Substituting y=60 in equation (i) we get,
x+60 = 135
x = 135-60 = 75
Hence, the rates charged per hour are 75 and 60 per hour respectively.
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ASAAP NEED IT RN PLEASE HELP
Thanks :)
The equation of circle in the standard with given center and radius is [tex](x+3)^{2} + (y-4)^2[/tex] = 49.
What is equation of circle?
Every point in a plane that is at a certain distance from the center point forms a circle. In order to go around a curve while maintaining a constant distance from another point, a moving point in a plane must follow a specific path.
The following is the typical form for expressing the equation of a circle:
[tex](x-h)^{2} + (y-k)^2 = r^2[/tex]
Here,
(h, k) represents the center and r is the radius.
We are given that the center is (-3, 4) and the radius is 7.
Now, using the standard form, we get
⇒ [tex](x-(-3))^{2} + (y-4)^2 = 7^2[/tex]
⇒ [tex](x+3)^{2} + (y-4)^2[/tex] = 49
Hence, the equation of circle in the standard with given center and radius is [tex](x+3)^{2} + (y-4)^2[/tex] = 49.
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Since, there are multiple questions so the question answered above is attached below.
Brian deposited $9,411 into a savings account for which interest is compounded
weekly at a rate of 3.48%. How much interest will he earn after 7 years? Round
answer to the hundredths place. If answer does not have a hundredths place then
include zeros so it does. Do not include units in the answer. Be sure to attach your
work for credit.
Answer:
We can use the formula for compound interest to calculate the amount of interest Brian will earn:
A = P (1 + r/n)^(nt)
where:
A = the total amount after 7 years
P = the principal amount ($9,411)
r = the annual interest rate (3.48%)
n = the number of times the interest is compounded per year (52 weeks in a year, so n = 52)
t = the number of years (7)
Plugging in the values, we get:
A = $9,411 (1 + 0.0348/52)^(52*7)
A = $9,411 (1.0006692302021135)^364
A = $12,471.36
To find the amount of interest earned, we can subtract the principal amount from the total amount:
Interest = $12,471.36 - $9,411 = $3,060.36
Therefore, Brian will earn $3,060.36 in interest after 7 years. Rounded to the nearest cent, this is $3,060.37.
3 divide 2 5ths in a facrtion
When 3 is divided by 2/5 , the answer is 7.5
Let's compare our whole number and fraction so that we can see the issue we are attempting to tackle.
3 divided by 2/5
In this case, creating a new numerator just requires multiplying the numerator by the full number. After that, the original numerator becomes the new denominator.
3*5/2 = 15/2
Most people prefer to express results in decimals, and all you have to do to do so is divide the numerator by the denominator:
15/2 = 7.5
What is Numerator?The portion written above the horizontal line is referred to as the numerator. Example: 2/5 ,here 2 is numerator.
What is Decimal?A decimal number consists of both a whole number and a fractional number. The numerical value of complete and partially whole amounts is expressed using decimal numbers, which are in between integers.
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The complete question is
what happens when 3 divide by 2/5ths in a facrtion?
Need help asap please thanks
The possible rule of the polynomial function is f(x) = 1/2(x + 2)(x + 1)²(x - 1)²
Finding the possible rule of the functionFrom the question, we have the following zeros and multiplicities that can be used to derive the rule of the function
Zeros: x = -2; Multiplicity = 1Zeros: x = -1; Multiplicity = 2Zeros: x = 1; Multiplicity = 2The possible rule of the function is represented as
f(x) = a(x - zero)^multiplicity
So, we have
f(x) = a(x + 2)(x + 1)²(x - 1)²
The graph passes through (0, 1)
So, we have
a(0 + 2)(0 + 1)²(0 - 1)² = 1
This gives
2a = 1
Divide
a = 1/2
Recall that
f(x) = a(x + 2)(x + 1)²(x - 1)²
So, we have
f(x) = 1/2(x + 2)(x + 1)²(x - 1)²
Hence, the function is f(x) = 1/2(x + 2)(x + 1)²(x - 1)²
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The tables show the numbers of lawns mowed by you and your friend each
month for a year.
a. Make a back-to-back stem-and-leaf plot for the data.
b. Use the stem-and-leaf plot to compare the mean and median of the data
for you and your friend. Explain your reasoning.
c. Compare the range of the data for you and your friend.
Lawns Mowed by You
5 12 7 10 25 30
12 8 21 17 20 4
Lawns Mowed by Your Friend
19 32 27 35 40 38
35 29 31 30 32 28
Stem Leaf
0 1 3 4 6
1 0 4
2 5 7
3 1 1 9
4 1 5
Key: 1 | 0 10 plays
Pages Printed
24 32 47 12 31 9
7 10 26 28 20 40
1. A back-to-back stem-and-leaf plot for the data would be
Mowed by you stem mowed by your friend
8 7 5 4 0
7 2 2 0 1 9
5 1 0 2 7 8 9
0 3 0 1 2 2 5 5 8
4 4
KEY: 3 | 1 ⇒ 31
2. The mean for you = 14.25 and your friend 31.3. This means that your friend has a higher mean than you. The median for you is 11 and your friend is 30.5. Given that both the mean and median of your friend is higher than yours, it means that your friend mowed more lawns than you
3. The range of data for you is 26 and for your friend is 21.
How do you find the mean, median and range?To find the mean for each data set, add all the number together and divide it by the set number. For example;
4 + 5 + 7 + 8 + 10 + 12 + 12 + 17 + 20 + 21 + 25 + 30
= 171 / 12
= 14.25
To find the range for the data set, simply take the highest number of a set and minus it by the lowest number. For Example;
For your data set, it is 30 - 4 = 26
To find the median for the data sets, simply look for the number in the middle. However, in your data set, there are two middle numbers. take the sum of the two numbers and divide it by 2.
(10 + 12) / 2 = 11
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A particular employee arrives at work sometime between 8:00 a.m. and 8:50 a.m. Based on past experience the company has determined that the employee is equally likely to arrive at any time between 8:00 a.m. and 8:50 a.m. Find the probability that the employee will arrive between 8:05 a.m. and 8:45 a.m. Round your answer to four decimal places, if necessary.
The probability that the employee will arrive between 8:05 a.m. and 8:45 a.m. is 0.8, or 80% when expressed as a percentage.
HOW TO SOLVE THE PROBABILITY ?To find the probability that the employee will arrive between 8:05 a.m. and 8:45 a.m., we need to calculate the proportion of the total possible time range between 8:00 a.m. and 8:50 a.m. that falls within the specified time interval.
The total time range between 8:00 a.m. and 8:50 a.m. is 50 minutes (8:50 - 8:00 = 50). The time interval between 8:05 a.m. and 8:45 a.m. is 40 minutes (8:45 - 8:05 = 40).
So, the probability that the employee will arrive between 8:05 a.m. and 8:45 a.m. is:
Probability = (Time interval between 8:05 a.m. and 8:45 a.m.) / (Total time range between 8:00 a.m. and 8:50 a.m.)
Probability = 40 minutes / 50 minutes
Probability = 0.8
Therefore, the probability that the employee will arrive between 8:05 a.m. and 8:45 a.m. is 0.8, or 80% when expressed as a percentage.
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solve 3/4 (5x- 3) + 8 = 17. show your work.