A
Step-by-step explanation:
A box contains 20 oranges and 10 grapes what is the probability of picking a grape from the box?
Answer:
[tex]\frac{1}{3}[/tex]
Step-by-step explanation:
First, let's find how many total items there are in the box.
If there are 20 oranges and 10 grapes, then there are [tex]20+10=30[/tex] items in the box.
Now, if there are 10 grapes in this box, we know that the probability of picking a grape is [tex]\frac{10}{30}[/tex] because the total is the denominator and the number of items for that selection is the numerator.
We can simplify this fraction down to [tex]\frac{1}{3}[/tex].
Hope this helped!
Answer:
1/3
Step-by-step explanation:
Use the difference of squares identity to write this polynomial expression in factored form : 9x^2-49
Answer:
The expression in factored form is (3x - 7)(3x + 7)
Step-by-step explanation:
Here in this question, we are interested in using the difference of two squares to factor the given expression.
Mathematically, supposed we have two squares a^2 and b^2, and we are told to factorize a^2-b^2.
By using the difference of two squares;
a^2-b^2 can thus be written as;
(a-b)(a + b)
Now, we can apply same approach to the problem at hand.
9x^2 - 49
kindly note that 9x^2 can be written as ((3x)^2 and 49 can be written as 7^2
So applying what we have said earlier about difference of two squares;
9x^2 - 49 will be ;
(3x-7)(3x + 7)
Answer:
The answer is (3x - 7) (3x +7)
Step-by-step explanation:
Please help with this question!!!!!
===================================
Explanation:
Start with the parent function [tex]y = |x|[/tex]
Replacing x with x-1 shifts the graph 1 unit to the right
Tack a -1 at the end to get [tex]y = |x-1|-1[/tex] which will shift everything down 1 unit.
The vertex started at (0,0) and moved to (1,-1)
show that the point p(-6,2), Q(1,7) and R(6,3) are the vertices of scalene triangle
Answer:
the sides are different lengths as shown in the diagram
Step-by-step explanation:
Plotting the three points, you can see by "inspection" that the middle length side (PQ) is longer than the shortest side (QR) and shorter than the longest side (PR). You could use the distance formula to show this, or you can use a scale to measure the drawing.
A triangle with three unequal sides is a scalene triangle. ∆PQR is scalene.
Manipulate the radius and height of the cone, setting different values for each. Record the radius, height, and exact volume of the cone (in terms of π). The first one has been done for you. Also calculate the decimal value of the volume, and verify that it matches the volume displayed by the tool. (You might see some discrepancies in the tool due to rounding of decimals.)
Answer:
The decimal value of the volume already given= 1885.2 unit³
For radius 11 unit height 12 unit
Volume= 484π unit³
Volume= 1520.73 unit ³
For radius 4 unit height 6 unit
Volume= 32π unit³
Volume= 100.544 unit³
For radius 20 unit height 15 unit
Volume= 2000π unit³
Volume= 6284 unit³
Step-by-step explanation:
The decimal value of the volume already given= 600π
The decimal value of the volume already given= 600*3.142
The decimal value of the volume already given= 1885.2 unit³
For radius 11 unit height 12 unit
Volume= πr²h/3
Volume= 11²*12/3 *π
Volume= 484π unit³
Volume= 1520.73 unit ³
For radius 4 unit height 6 unit
Volume = πr²h/3
Volume= 4²*6/3(π)
Volume= 32π unit³
Volume= 100.544 unit³
For radius 20 unit height 15 unit
Volume= πr²h/3
Volume= 20²*15/3(π)
Volume= 2000π unit³
Volume= 6284 unit³
Here's the right answer.
Raj tested his new flashlight by shining it on his bedroom wall. The beam of light can be described by the equation . How many inches wide is the beam of light on the wall?
Answer:
12 inches
Step-by-step explanation:
Raj tested his new flashlight by shinning it on his bedroom wall the beam of the light can be described by the equation (x^2-2x) + (y^2-4y) - 31=0. how many inches wide is the beam of light on the wall
Solution
Given:
(x^2-2x) + (y^2-4y) - 31=0
By completing the square
(x^2-2x) + (y^2-4y) - 31=0
(x^2-2x+1-1) + (y^2-4y+4-4)-31=0
(x-1)^2 -1 + (y-2)^2 - 4 - 31=0
(x-1)^2 + (y-2)^2 - 1 - 4 - 31=0
(x-1)^2 + (y-2)^2 - 36=0
(x-1)^2 + (y-2)^2=36
Writing the equation in the form: (x-h)^2+(y-k)^2=r^2
(x-1)^2+(y-2)^2=6^2
From the above, r=6
Where,
r=radius
how wide is the diameter ?
radius=6
Diameter= 2 × radius
=2×6
=12 inches
Answer:
12
Step-by-step explanation:
to graph it just scan the equation on photo math!!
9(p−4)=−18 p= I am not great at math, please explain just a little bit
Answer:
[tex]\large \boxed{{p=2}}[/tex]
Step-by-step explanation:
9(p-4) = -18
Expand brackets.
9p -36 = -18
Add 36 on both sides.
9p -36 + 36 = -18 + 36
9p = 18
Divide both sides by 9.
(9p)/9 = 18/9
p = 2
Answer:
p = 2
Step-by-step explanation:
9(p - 4) = -18
You are solving for the variable, p. Note the equal sign, what you do to one side, you do to the other. Do the opposite of PEMDAS.
PEMDAS is the order of operation, and =
Parenthesis
Exponents (& Roots)
Multiplication
Division
Addition
Subtraction
~
First, divide 9 from both sides:
(9(p - 4))/9 = (-18)/9
(p - 4) = -18/9
p - 4 = -2
Isolate the variable, p. Add 4 to both sides:
p - 4 (+4) = -2 (+4)
p = -2 + 4
p = 4 - 2
p = 2
Check. Plug in 2 for p in the equation:
9(p - 4) = -18
9(2 - 4) = -18
9(-2) = - 18
-18 = -18.
~
Sandy’s older sister was given $2,400 and was told to keep the balance of the money after sharing with her siblings. Give Sandy exactly $350. Write Sandy’s portion
Sandy got 350 out of 2400.
Her portion is 350/2400 which can be reduced to:
35/240 = 7/48
The portion is 7/48
Pick out the set of numbers that is not Pythagorean triple
9 40 46
16 30 34
10 24 26
50 120 130
Answer:
[tex]\huge\boxed{9,40,46}[/tex]
Step-by-step explanation:
Let's check it using Pythagorean Theorem:
[tex]c^2 = a^2 + b^2[/tex]
Where c is the longest sides, a and b are rest of the 2 sides
1) 9 , 40 , 46
=> [tex]c^2 = a^2 + b^2[/tex]
=> [tex]46^2 = 9^2 + 40^2[/tex]
=> 2116 = 81 + 1600
=> 2116 ≠ 1681
So, this is not a Pythagorean Triplet
2) 16, 30 and 34
=> [tex]c^2 = a^2 + b^2[/tex]
=> [tex]34^2 = 16^2 + 30^2[/tex]
=> 1156 = 256 + 900
=> 1156 = 1156
No need to check more as we've found the one which is not a Pythagorean Triplet.
Answer:
[tex] \boxed{ \huge{ \boxed{ \sf{ \blue{9 , \: 40 \:, 46 \: }}}}}[/tex]Option A is the correct option.
Step-by-step explanation:
1. Let h , p and b are the hypotenuse , perpendicular and base of a right - angled triangle respectively.
From Pythagoras theorem,
[tex] \sf{ {h}^{2} = {p}^{2} + {b}^{2} }[/tex]
Here, we know that the hypotenuse is always greater than perpendicular and base,
h = 46 , p = 40 , b = 9
⇒[tex] \sf{ {46}^{2} = {40}^{2} + {9}^{2} }[/tex]
⇒[tex]2116 = 1600 + 81[/tex]
⇒[tex] \sf{2116 ≠ 1681}[/tex]
Thus , the relation [tex] \sf{ {h}^{2} = {p}^{2} + {b}^{2} }[/tex] is not satisfied by h = 46 , p = 40 , b = 9
So, The set of numbers 9 , 40 , 46 is not Pythagorean triple.
------------------------------------------------------
2. 16 , 30 , 34
h = 34 , p = 30 , b = 16
[tex] \sf{ {h}^{2} = {p}^{2} + {b}^{2} }[/tex]
⇒[tex] \sf{ {34}^{2} = {30}^{2} + {16}^{2} }[/tex]
⇒[tex] \sf{1156 = 900 + 256}[/tex]
⇒[tex] \sf{1156 = 1156}[/tex]
The relation [tex] \sf{ {h}^{2} = {p}^{2} + {b}^{2} }[/tex] is satisfied by the particular values of h , p and b i.e h = 34 , p = 30 , b = 16
So, the set of numbers 16 , 30 , 34 is a Pythagorean triple.
------------------------------------------------------
3. 10, 24 , 26
h = 26 , p = 24 , b = 10
[tex] \sf{ {h}^{2} = {p}^{2} + {b}^{2} }[/tex]
⇒[tex] \sf{ {26}^{2} = {24}^{2} + {10}^{2} }[/tex]
⇒[tex] \sf{676 = 576 + 100}[/tex]
⇒[tex] \sf{676 = 676}[/tex]
The relation [tex] \sf{ {h}^{2} = {p}^{2} + {b}^{2} }[/tex] is satisfied by the particular values of h , p and h i.e h = 26 , p = 24 , b = 10
So, the set of numbers 10, 24 , 26 is the Pythagorean triple.
-----------------------------------------------------
4. 50 , 120 , 130
h = 130 , p = 120 , b = 50
[tex] \sf{ {h}^{2} = {p}^{2} + {b}^{2} }[/tex]
⇒[tex] \sf{ {130}^{2} = {120}^{2} + {50}^{2} }[/tex]
⇒[tex] \sf{16900 = 14400 + 2500}[/tex]
⇒[tex] \sf{16900 = 16900}[/tex]
The relation [tex] \sf{ {h}^{2} = {p}^{2} + {b}^{2} }[/tex] is satisfied by the particular values of h , p and b i.e h = 130 , p = 120 , b = 50
So, the set of numbers 50, 120 , 130 is the Pythagorean triple.
-----------------------------------------------------
In this way, to satisfy the Pythagoras Theorem , the hypotenuse ( h ) , perpendicular ( p ) and the base ( b ) of a right - angles triangle should have the particular values in order. These values of h , p and b are called Pythagorean triple.
Hope I helped!
Best regards!!
10. Write a word problem for this equation:
n ($25) = $125
Answer:
The word problem is "How many $25 are there in $125?"
Step-by-step explanation:
Given
[tex]n(\$25) = \$125[/tex]
Required
Write a word problem for the expression
We start by solving the given equation
[tex]n(\$25) = \$125[/tex]
Divide both sides by $25
[tex]\frac{n(\$25)}{\$25} = \frac{\$125}{\$25}[/tex]
[tex]n = \frac{\$125}{\$25}[/tex]
[tex]n = 5[/tex]
This implies that there are 5, $25 in $125
Hence; The word problem is "How many $25 are there in $125?"
Please help quickly!!
A truck is driving up a hill with a 24% grade, so it climbs 24 feet vertically for every 100 feet horizontally.
What is the slope of the hill?
Answer:
6/25
Step-by-step explanation:
rise / run
24/100 = 6/25
Answer:
[tex]\frac{6}{25}[/tex]
Step-by-step explanation:
The slope of any relationship is always rise over run. This means the vertical distance traveled over the horizontal distance traveled will get us our slope.
We travels 24 feet vertically for every 100 feet horizontally, so:
[tex]\frac{24}{100}[/tex].
We can simplify this fraction to find the slope in fraction form.
[tex]\frac{24\div4}{100\div4} = \frac{6}{25}[/tex]
So the slope of this equation is [tex]\frac{6}{25}[/tex].
Hope this helped!
Which of the following is the first step when copying a line segment to construct a new line segment?
a. draw a line segment
b. use a straight edge to connect the point not on the line segment to a point in the arc
c. plot a point not on the original line segment
d. draw an arc
Answer:
The correct option is;
c. Plot a point not on the original line segment
Step-by-step explanation:
The steps to copy a line segment are;
1) Plot a point that will be an endpoint of the new line segment
2) With the compass pin at the beginning of the original line segment, open the compass width to the end of the original line segment
3) With the adjusted compass width from the above step place the compass pin at the plotted point of the new line segment and draw an arc in the region the new line segment is to be located
4) Select a point on the arc where the other end of the new line will be
5) From the selected point from the above step, draw a line to the point plotted as the beginning of the new line segment
6) The length of the line drawn above is the same as the length of the original line segment.
I will give brainliest to the right answer!! Find the vertex and the length of the latus rectum. x= 1/2 (y - 5)² + 7
Answer:
(7, 5)2Step-by-step explanation:
When the quadratic is written in vertex form:
x = a(y -k)^2 +h
the vertex is (x, y) = (h, k), and the length of the latus rectum is 1/a.
For your given equation, ...
x = (1/2)(y -5)^2 +7
you have a=1/2, k = 5, h = 7, so ...
the vertex is (7, 5)
the length of the latus rectum is 1/(1/2) = 2
To test the belief that sons are taller than their fathers, a student randomly selects 13 fathers who have adult male children. She records the height of both the father and son in inches and obtains the following data. Are sons taller than their fathers? Use the alphaequals0.10 level of significance. Note: A normal probability plot and boxplot of the data indicate that the differences are approximately normally distributed with no outliers.
Height of Father Height of Son
72.4 77.5
70.6 74.1
73.1 75.6
69.9 71.7
69.4 70.5
69.4 69.9
68.1 68.2
68.9 68.2
70.5 69.3
69.4 67.7
69.5 67
67.2 63.7
70.4 65.5
Which conditions must be met by the sample for this test? Select all that apply.
A. The sample size is no more than 5% of the population size.
B. The differences are normally distributed or the sample size is large.
C. The sample size must be large.
D. The sampling method results in a dependent sample.
E. The sampling method results in an independent sample.
Write the hypotheses for the test. Upper
H 0 :
H 1 :
Calculate the test statistic. t 0=?
(Round to two decimal places as needed.)
Calculate the P-value. P-value=?
(Round to three decimal places as needed.) Should the null hypothesis be rejected?
▼ Do not reject or Reject Upper H 0 because the P-value is ▼ less than or greater than the level of significance. There ▼ is or is not sufficient evidence to conclude that sons ▼ are the same height or are shorter than or are taller than or are not the same height as their fathers at the 0.10 level of significance. Click to select your answer(s).
Answer:
1) B. The differences are normally distributed or the sample size is large
C. The sample size mus be large
E. The sampling method results in an independent sample
2) The null hypothesis H₀: [tex]\bar x_1[/tex] = [tex]\bar x_2[/tex]
The alternative hypothesis Hₐ: [tex]\bar x_1[/tex] < [tex]\bar x_2[/tex]
Test statistic, t = -0.00693
p- value = 0.498
Do not reject Upper H₀ because, the P-value is greater than the level of significance. There is sufficient evidence to conclude that sons are the same height as their fathers at 0.10 level of significance
Step-by-step explanation:
1) B. The differences are normally distributed or the sample size is large
C. The sample size mus be large
E. The sampling method results in an independent sample
2) The null hypothesis H₀: [tex]\bar x_1[/tex] = [tex]\bar x_2[/tex]
The alternative hypothesis Hₐ: [tex]\bar x_1[/tex] < [tex]\bar x_2[/tex]
The test statistic for t test is;
[tex]t=\dfrac{(\bar{x}_1-\bar{x}_2)}{\sqrt{\dfrac{s_{1}^{2} }{n_{1}}-\dfrac{s _{2}^{2}}{n_{2}}}}[/tex]
The mean
Height of Father, h₁, Height of Son h₂
72.4, 77.5
70.6, 74.1
73.1, 75.6
69.9, 71.7
69.4, 70.5
69.4, 69.9
68.1, 68.2
68.9, 68.2
70.5, 69.3
69.4, 67.7
69.5, 67
67.2, 63.7
70.4, 65.5
[tex]\bar x_1[/tex] = 69.6
s₁ = 1.58
[tex]\bar x_2[/tex] = 69.9
s₂ = 3.97
n₁ = 13
n₂ = 13
[tex]t=\dfrac{(69.908-69.915)}{\sqrt{\dfrac{3.97^{2}}{13}-\dfrac{1.58^{2} }{13}}}[/tex]
(We reversed the values in the square root of the denominator therefore, the sign reversal)
t = -0.00693
p- value = 0.498 by graphing calculator function
P-value > α Therefore, we do not reject the null hypothesis
Do not reject Upper H₀ because, the P-value is greater than the level of significance. There is sufficient evidence to conclude that sons are the same height as their fathers at 0.10 lvel of significance
simplify the equation. (5xE2 - 3x) - (5xE2 - 3x+1)
Answer:
[tex]\huge \boxed{\mathrm{-1}}[/tex]
Step-by-step explanation:
[tex](5xe^2 - 3x) - (5xe^2 - 3x+1)[/tex]
Distribute negative sign.
[tex]5xe^2 - 3x- 5xe^2 +3x-1[/tex]
Combine like terms.
[tex]0xe^2 +0x-1[/tex]
[tex]0-1=-1[/tex]
PLEASE ANSWER QUICKLY ASAP
COMPLETE QUESTION B
Answer:
Sector
Step-by-step explanation:
A sector of a circle is the portion of circle enclosed by two radii and arc
What is the equation for the line of symmetry in this figure?
Answer:
x = -1
Step-by-step explanation:
the line of the simetry is x = -1
Answer:
Its x = -1 because it splits the diamond shape perfectly at x -1
Step-by-step explanation:
Translate the following phrase into an algebraic expression using the variable m. Do not simplify,
the cost of renting a car for one day and driving m miles if the rate is $39 per day plus 45 cents per mile
Answer:
y = 0.45X + 39
A company makes nylon and canvas backpacks. The profit on a nylon backpack is $3 and the profit on a canvas backpack is $10. How many backpacks must the company sell to make a profit of more than $250? Write a linear inequality that describes the situation.
Answer:
3x +10y is greater than or equal to 250.
Step-by-step explanation:
The question asks us to write an inequality which shows that both nylon and canvas added should be greater than or equal to 250.
Since we don't know the number of nylon backpacks and canvas backpacks the company makes, we used the variables "x" and "y" to represent the number of backpacks they made from each style.
Answer:
3n + 10c > 250
Step-by-step explanation:
I confirmed it in grandpoint
One type of fabric costs $31.25 for 5 square yards. Another type of fabric costs $71.50 for 11
square yards. Is the relationship between the number of square yards and the cost
proportional between the two types of fabric?
Answer:
as ratio of two type of fabric is different .
hence, the relationship between the number of square yards and the cost
is not proportional between the two types of fabric
Step-by-step explanation:
For a relation to be proportional
a:b = c:d
in other form
a/b = c/d
______________________________________________
Ratio for first type of fabric
cost of fabric/ area of fabric = 31.25/5 = 6.25
Ratio for other type of fabric
cost of fabric/ area of fabric = 71.50/11 = 6.5
as ratio of two type of fabric is different .
hence, the relationship between the number of square yards and the cost
is not proportional between the two types of fabric
if 25% of a number is 75 find the number
Answer:
x = 300
Step-by-step explanation:
of means multiply and is means equals
25% * x = 75
Change to decimal form
.25x = 75
Divide each side by .25
.25x/.25 = 75/.25
x = 300
Answer:
300
Step-by-step explanation:
Assume the unknown value is 'Y'
75 = 25% x Y
75 = 25/100 x Y
Multiplying both sides by 100 and dividing both sides of the equation by 25 we will arrive at:
Y = 3 x 100/25
Y = 300%
Answer: 75 is 25 percent of 300
ABC is an equilateral triangle, solve y
Answer:
y is 60⁰
because all sides are equal
Answer:
60 degrees
Step-by-step explanation:
In an equilateral triangle, the angles are equiangluar and the sides are equal.
180 degrees in a triangle/3 sides =
= 60 degrees per side
n urn contains 3 red balls, 9 green, 2 yellow, 2 orange, and 4 purple balls. Two balls aredrawn, one at a time with replacement. Find the probability of drawing a green ball and an orangeball.
Answer:
[tex]\frac{9}{100}[/tex]
Step-by-step explanation:
Given:
Number of red balls, n(R) = 3
Number of green balls, n(G) = 9
Number of yellow balls, n(Y) = 2
Number of orange balls, n(O) = 2
Number of purple balls, n(P) = 4
Two balls are drawn one at a time with replacement.
To find:
Probability of drawing a green ball and an orange ball ?
Solution:
Total number of balls, n(Total) = 3 + 9 + 2 + 2 + 4 = 20
Formula for probability of an event E is given as:
[tex]P(E) = \dfrac{\text{Number of favorable cases}}{\text {Total number of cases}}[/tex]
Probability that a green ball is drawn at first:
[tex]P(Green) = \dfrac{\text{Number of Green balls}}{\text {Total number of Balls}}[/tex]
[tex]P(Green) = \dfrac{9}{20}[/tex]
Now, the ball is replaced , so total number of balls remain the same i.e. 20.[tex]P(Orange) = \dfrac{\text{Number of Orange balls}}{\text {Total number of Balls}}[/tex]
[tex]P(Orange) = \dfrac{2}{20} = \dfrac{1}{10}[/tex]
[tex]P(Green\ then\ orange) = P(Green) \times P(Orange)\\\Rightarrow P(Green\ then\ orange) = \dfrac{9}{10} \times \dfrac{1}{10}\\\Rightarrow P(Green\ then\ orange) = \bold{ \dfrac{9}{100} }[/tex]
Factorise the following
Answer:
4ny²+4n²-4n-8+y⁴-2y²
Evaluate |3 - 5 + 7|. -5 5 -15 15
Answer:
5
Step-by-step explanation:
|3 - 5 + 7|
= |-2 + 7|
= |5| = 5
Answer:
The correct answer would be 5.
Step-by-step explanation:
What is the perimeter of this polygon?
A(2, 3)
B(-4, 0)
C(0,-4)
D(4,0)
Answer:2,3 hope it help you
Step-by-step explanation:
Answer:
21.627
Step-by-step explanation:
get the distance between all points then add
A
man paid 15600
for a new
car. He
was given a discount of
7%. Find the marked price
of the car
hope it helps.I was reading the same chapter
find the perimeter of the quadrant whose radius is 21cm
Answer:
75 cm
Step-by-step explanation:
∅=90° , r = 21 cm
Arc length= (2πr∅)/360
=(2π×21×90)/360
=33 cm
Perimeter= arc length + 2(radius)
=33+2(21)
=33 + 42
= 75 cm
Astrid is in charge of building a new fleet of ships. Each ship requires 404040 tons of wood, and accommodates 300300300 sailors. She receives a delivery of 444 tons of wood each day. The deliveries can continue for 100100100 days at most, afterwards the weather is too bad to allow them. Overall, she wants to build enough ships to accommodate at least 210021002100 sailors.
To build the fleet of ships, Astrid must consider each of the given rates (i.e. the daily tons of wood, the sailors per ship, etc.). The available deliveries are enough to build ships that can accommodate at least 2100 sailors.
Given that:
Required quantities
[tex]Wood = 40\ tons[/tex]
[tex]Sailors = 300[/tex] per ship
Available quantities
[tex]Wood = 4\ tons[/tex] daily
[tex]Days = 100[/tex] at most
First, we calculate the total tons of woods Astrid can receive.
[tex]Total = Days \times Wood\ Available[/tex]
[tex]Total = 100 \times 4[/tex]
[tex]Total = 400\ tons[/tex] ---- in 100 days
Next, we calculate the number of ships that can be made from the 400 tons.
[tex]Ships = \frac{Total\ tons}{Wood\ Required}[/tex]
So, we have:
[tex]Ships = \frac{400}{40}[/tex]
[tex]Ships = 10[/tex]
This means that Astrid can build up to 10 ships
The number of sailors the ship can accommodate is:
[tex]Sailors = Ships \times Sailors\ per\ ship[/tex]
So, we have:
[tex]Sailors = 10 \times 300[/tex]
[tex]Sailors = 3000[/tex]
It means the 10 ships can accommodate 3000 sailors.
3000 sailors is greater than 2100 sailors.
So, we can conclude that she can build enough ship for the 2100 sailors.
Read more about
https://brainly.com/question/17174491
Answer:
280 tons
Step-by-step explanation:
:)
The Acme Company lost 650 hours due to accidents on the job in the first quarter of the year. The average hourly wage of the employees who contributed to the lost hours was $15.00. The company benefits add 25% to the wages. Using the cost-of-lost-hours formula (employee hours lost X average loaded labour rate = cost), calculate the direct cost of the lost work hours. Discuss the approach you would use to estimate the hidden costs that would also be associated with the lost hours.
Your answer must be at least 200 words in length.
Answer:
Step-by-step explanation:
Given that ;
The Acme Company lost 650 hours due to accidents on the job in the first quarter of the year
The average hourly wage of the employees who contributed to the lost hours was $15.00 . i.e the direct labor cost = $15.00
The company benefits add 25% to the wages. = 0.25
The loaded labor cost = $15.00/hr × 0.25 = $3.75/hour
If we add the additional cost of benefit, then we have the loaded labor cost to be = $15.00/hour + $3.75/hour
= $18.75 / hour
However, the direct labor costs that the workers continued to receive without working. for the first quarter of the year by using the cost-of-lost-hours formula is :
= 650 hours × $15.00 / hours
= $9750
The hidden costs can be estimated from the Acme company's contributions to the employee. Given that the company benefits add 25% to the wage of the employee, therefore, this wage must be incorporated in order to find out the total wage cost for the lost work hours in the Acme company.
As a result of the company benefits, the fully loaded labor cost is 650 hours × $18.75 /hour which gives $12187.5.
Consequently, it is pertinent to determine the cost for additional benefits that the workers are receiving even though they are not working, this is achieved by the difference in the $9750 direct cost paid to labor and the benefits amount of $12187.5
i.e
the cost for additional benefits that the workers are receiving even though they are not working = $12187.5 - $9750 = $2437.5
Other ways the hidden cost can be estimated is by take note of the amount paid to the employee on the day the employee had an emergency, amount paid to the rescue team involved. etc
