The total direct labor hours for each product to get the total direct labor hours required for the projected sales during the coming year.
To determine the contribution margin per direct-labor hour expended on each product, you will need to calculate the contribution margin for each product and divide it by the number of direct labor hours required to produce that product.
Contribution Margin = Sales Revenue - Variable Costs
Once you have calculated the contribution margin for each product, you can divide it by the number of direct labor hours required to produce that product to get the contribution margin per direct-labor hour.
To prepare a schedule showing the total direct labor hours that will be required to produce the projected sales during the coming year, you will need to estimate the number of units that will be sold for each product and the number of direct labor hours required to produce each unit.
Multiply the number of units by the number of direct labor hours per unit to get the total direct labor hours required for each product.
Contribution Margin = $40 - $20 - $5 - $3 = $12
Direct Labor Hours per unit = 2
Contribution Margin per Direct-Labor Hour = $12 / 2 = $6 MMK YU GHTJUIO7U
Contribution Margin = $60 - $25 - $10 - $5 = $20
Direct Labor Hours per unit = 4
Contribution Margin per Direct-Labor Hour = $20 / 4 = $5
Contribution Margin = $80 - $30 - $15 - $10 = $25
Direct Labor Hours per unit = 5
Contribution Margin per Direct-Labor Hour = $25 / 5 = $5
To prepare a schedule showing the total direct labor hours that will be required to produce the projected sales during the coming year, we need to estimate the number of units that will be sold for each product and the number of direct labor hours required to produce each unit.
Assuming that the projected sales for the coming year are as follows:
Product A: 10,000 units
Product B: 8,000 units
Product C: 5,000 units
And the number of direct labor hours required to produce each unit are as follows:
Product A: 2 hours per unit
Product B: 4 hours per unitF
Product C: 5 hours per unit
For similar question on direct labor hours :
https://brainly.com/question/14300447
#SPJ11
cant answer this question
The value of k, considering the numeric value of the derivative at x = 0, is given as follows:
b) k = -2 or k = 2.
How to obtain the value of k?The function in the context of this problem is defined as follows:
y = (x + k)³.
Applying the power of x rule followed by the chain rule, the derivative of the function is given as follows:
y' = 3(x + k)².
When x = 0, the numeric value of the derivative is of 12, hence the value of k is obtained as follows:
3k² = 12
k² = 4
k = -2 or k = 2.
More can be learned about the derivative of a function at https://brainly.com/question/5313449
#SPJ1
what is the volume of 1 1/2 and 1 and 3 3/4
Answer: 5.625 Cubed
Step-by-step explanation: First you will times 3.75 and 1.5. Which should get you 5.625 squared. Next you will just times 5.625 squared by 1. Which will get you 5.625 cubed.
A roasted turkey is taken from an oven when its temperature has reached 185 Fahrenheit and is placed on a
table in a room where the temperature is 75 Fahrenheit. Give answers accurate to at least 2 decimal
places.
(a) If the temperature of the turkey is 153 Fahrenheit after half an hour, what is its temperature after 45
minutes?
Fahrenheit
(b) When will the turkey cool to 100 Fahrenheit?
hours.
After answering the presented question, we can conclude that As a equation result, the turkey's temperature after 45 minutes is roughly 134.43 Fahrenheit.
What is equation?In mathematics, an equation is a statement that states the equality of two expressions. An equation consists of two sides separated by an algebraic equation (=). The argument "[tex]2x + 3 = 9,[/tex]" for example, states that the sentence "[tex]2x + 3[/tex]" equals the value "9." The goal of solving equations is to find the value or values of the variable(s) that will allow the equation to be true. Equations can be simple or complex, linear or nonlinear, and contain one or more parts. In the equation "[tex]x2 + 2x - 3 = 0[/tex]," the variable x is raised to the second power. Lines are used in many areas of mathematics, including algebra, calculus, and geometry.
a. [tex]dT/dt=-k(T-Ts)[/tex]
[tex]-kdt=(DT/(T-Ts)[/tex][tex])[/tex]
When both sides are combined, the following results:
[tex]-kt + C = ln|T - Ts|[/tex]
where C is the integration constant. To calculate C, we can start with the assumption that the turkey is 185 degrees Fahrenheit when it comes out of the oven:
[tex]ln|185 - 75| = -k(0) + C[/tex]
[tex]C = ln(110) (110)[/tex]
As a result, the equation relating the temperature of the turkey to time is:
[tex]-kt+In|T-75|=-kt+In(110)[/tex]
[tex]T=e(-ktIn(110)+75[/tex]
[tex]T=110e(-0.5k)+75[/tex]
[tex]T=110e(-0.75k+75 T134.43[/tex] degrees Fahrenheit
As a result, the turkey's temperature after 45 minutes is roughly 134.43 Fahrenheit.
To know more about equation visit:
brainly.com/question/649785
#SPJ9
A grain silo has a cylindrical shape. Its diameter is 19ft, and its height is 49ft . What is the volume of the silo? Use the value 3.14 for pi , and round your answer to the nearest whole number. Be sure to include the correct unit in your answer.
The Volume of Silo is. V= 13886 ft cube
A grain Silo is cylindrical in shape.
Height (h) = 49 ft.
Diameter (d) = 19 ft.
We need to find the Volume of silo.
We will first find the radius.
Radius can be given as half of the diameter.
hence Radius (r) = 9.5
Since Silo is in Cylindrical Shape we will find the volume of a cylinder.
Now We know that the Volume of a cylinder can be calculated by multiplying π with the square of the radius and height.
Volume of Cylinder = πr²h
V= 3.14×9.5×9.5×49
v=13885.865 ft cube
Rounding to the nearest whole number we get;
Hence, the Volume of the Silo is. V= 13886 ft cube
learn more about Volume
https://brainly.com/question/1578538
#SPJ1
In 1960 the avrege price of a car was about 2500 this may sound inxpensive but the avrage income was much less then it is now. to compare doller amounts ovr time use the formula V = a/s c where A is the old dollor amount S is the starting years consumer price index cpi ,C is converting year's cpi and V is the curent value of the old dollar amount. Buying a car for 2500 in 1960 was like buying a car for how much money in 2004
Buying a car for $2,500 in 1960 would be like buying a car for $539.23 in 2004 dollars .we can solve by using formula by substituting all details along with consumer price index
what is consumer price index ?
The Consumer Price Index (CPI) is a measure of the average change over time in the prices paid by urban consumers for a basket of goods and services. The CPI is often used as an indicator of inflation
In the given question,
To compare the dollar amounts over time, we can use the formula V = (A/S) x (C/C'), where:
V = the current value of the old dollar amount
A = the old dollar amount ($2,500 in this case)
S = the starting year's consumer price index (CPI) for the old dollar amount (1960 CPI)
C = the converting year's CPI (2004 CPI)
C' = the starting year's CPI for the converting year (1960 CPI)
Using the formula, we can calculate the current value of $2,500 in 1960 dollars as:
V = (A/S) x (C/C')
V = (2,500/29.6) x (188.9/29.6)
V = 84.46 x 6.380
V = $539.23
Therefore, buying a car for $2,500 in 1960 would be like buying a car for $539.23 in 2004 dollars.
To know more about consumer price index , visit:
https://brainly.com/question/4513076
#SPJ1
What is the best way to display data on the average temperature each month?
A.) Histogram
B.) Circle graph
C.) Line graph
D.) frequency tabel
Answer:
A line graph would best show the average temperatures each month
David has a 32 ounce energy drink he drinks 10 ounces Enter the percentage of Ounces he has left of his energy drink.
Answer:
He has 68.8% of his drink left
Step-by-step explanation:
do 32 oz - 10 oz = 22 oz to get how much of his drink is left
To get the percentage, just do what left divided by original amount
so 22/32 = 0.6875 and in percent, that is about 68.8%
Drag each number to the correct location on the statement. Not all numbers will be used. Consider the sequence below. -34, -21, -8, 5, ...
Complete the recursively defined function to describe this sequence.
34
-21
-13
15
13
-34
f(1) = [ ]
f(n) = f(n-1) + [ ]for n = 2, 3, 4, ...
The sequence of the function is -34,-34 -8
Define common differenceIn mathematics, the common difference is a term used in arithmetic sequences to refer to the fixed difference between any two consecutive terms in the sequence.
An arithmetic sequence is a sequence of numbers in which each term is obtained by adding a fixed value, called the common difference, to the preceding term.
-34 -21 -8 5 ...
f(1) = -34
f(n) = f(n-1) + [n-2]*13 for n = 2, 3, 4, ...
The common difference between consecutive terms of the sequence is 13.
The first term of the sequence is -34, which is f(1).
To get the nth term of the sequence, we add (n-2)*13 to the (n-1)th term of the sequence.
For example, to get the 2nd term of the sequence, we add (2-2)*13 = 0 to the 1st term, -34, which gives us -34.
To get the 3rd term, we add (3-2)*13 = 13 to the 2nd term, which gives us -21+13 = -8.
To know more about consecutive, visit:
https://brainly.com/question/1769190
#SPJ1
What is the equation of the
circle with centre (0,-1) and
radius 4?
Answer:
Step-by-step explanation:
Equation of a circle: [tex](x-a)^2+(y-b)^2=r^2[/tex] with centre [tex](a,b)[/tex], radius [tex]r[/tex].
[tex](x-0)^2+(y+1)^2=4^2[/tex]
[tex]x^2+(y+1)^2=16[/tex]
Use the grid on the whiteboard to solve the following system of inequalities by graphing:
y≥-1/2x-8
y<8x+2
Graph the two inequalities,
The region shaded in black satisfies both inequalities
A parallelogram has coordinates of (5, 17), (10, 20), (18, 9), and (13, 6). Which right triangle represents one of the cutouts from the box method?
A right triangle is shown. The length of one side is 5, and another is 17.
A right triangle is shown. The length of one side is 5, and another is 8.
A right triangle is shown. The length of one side is 8, and another is 11.
A right triangle is shown. The length of one side is 3, and another is 8.
The answer is right angle with leg 3 and 8.
To use the box method to find the area of the parallelogram, we need to divide it into two triangles. One possible way to do this is by drawing a diagonal from (5, 17) to (18, 9), and creating two triangles with vertices (5, 17), (10, 20), and (18, 9), and (5, 17), (13, 6), and (18, 9).
The length of the diagonal can be found using the distance formula:
d = √[(18 - 5)^2 + (9 - 17)^2]
d = √[(13)^2 + (-8)^2]
d = √(169 + 64)
d = √233
Now, the area of the parallelogram is equal to the product of the length of the diagonal and half the height of the parallelogram. One of the cutouts from the box method will be a right triangle with legs equal to half the height and half the length of the diagonal.
Half the height can be found by taking the difference in y-coordinates between (5, 17) and (18, 9) and dividing by 2:
h = (17 - 9)/2
h = 4
Half the length of the diagonal is:
l = √233/2
Using these values, we can check each of the given right triangles to see which one matches the dimensions of the cutout:
A right triangle with legs 5 and 17 does not match, since the legs should be half the diagonal and half the height.
A right triangle with legs 5 and 8 does not match, since the legs should be half the diagonal and half the height.
A right triangle with legs 8 and 11 does not match, since the legs are not proportional to the dimensions of the parallelogram.
A right triangle with legs 3 and 8 matches, since half the diagonal is approximately 7.66 and half the height is 4, and 3 and 8 are proportional to these values.
Therefore, the correct answer is the right triangle with legs of 3 and 8.
To know more about triangle visit : https://brainly.com/question/2773823
#SPJ1
Answer:
its the middle one ( 8,11)
Step-by-step explanation:
Assume that Lavonia's marginal tax rate is 20%. If a city of Tampa bond pays 8% interest, what interest rate would a corporate bond have to offer for Lavonia to be indifferent between the two bonds?
The interest rate would a corporate bond have to offer for Lavonia to be indifferent between the two bonds is 6.35%.
What is an interest rate?
The amount that the lender charges the borrower over and beyond the principal amount is referred to as the interest rate. A person who deposits money in a bank or other financial institution also earns additional income in terms of the recipient, known as interest, taking into account the time value of money.
Here, we have
Given: Assume that Lavonia's marginal tax rate is 20%. If a city of Tampa bond pays 8% interest.
We have to find the interest rate would a corporate bond have to offer for Lavonia to be indifferent between the two bonds.
= Interest rate/(1-Tax rate)
= 5%/(1-0.20)
= 6.25%
Hence, the interest rate would a corporate bond have to offer for Lavonia to be indifferent between the two bonds is 6.35%.
To learn more about the interest rate from the given link
https://brainly.com/question/25793394
#SPJ1
Question 3 In a science class everyone study Physics, Chemistry, Biology or combination of any of the three courses. 22 students study Physics and Biology, 21 students study Chemistry and Biology, 18 students study Chemistry and Physics. If only 6 students study pure Chemistry (15 marl 10 students study pure Physics and 8 students study pure Biology, then; a) Find the total number of students in the class.
Answer:
Step-by-step explanation:
Let's use a Venn diagram to help us visualize the information given in the problem. We can start with three overlapping circles representing Physics (P), Chemistry (C), and Biology (B), and then fill in the numbers given:
P
/ \
/ \
/ \
CP BP
\ /
\ /
\ /
B
We know that 6 students study pure Chemistry, so we can write this number in the circle for Chemistry (C). We also know that 10 students study pure Physics and 8 students study pure Biology, so we can write these numbers in the circles for Physics (P) and Biology (B), respectively:
P (10)
/ \
/ \
/ \
CP (18) BP (21)
\ /
\ /
\ /
B (8)
C (6)
Now we can use the information given in the problem to fill in the remaining numbers:
22 students study Physics and Biology, so this number goes in the overlap between P and B: PB = 22
21 students study Chemistry and Biology, so this number goes in the overlap between C and B: CB = 21
We don't know the number of students who study Physics and Chemistry only, but we can use the fact that 6 students study pure Chemistry to figure it out. Since 18 students study Chemistry and Physics in total, and 6 of them study pure Chemistry, the remaining 18 - 6 = 12 students must study both Chemistry and Physics but not Biology. We can write this number in the overlap between C and P: CP = 12.
P (10)
/ \
/ \
/ \
CP (12) BP (21)
\ /
\ /
\ /
B (8)
C (6)
Now we can find the total number of students by adding up all the numbers in the Venn diagram:
Total = P + C + B - (CP + CB + PB) + (CPB)
Total = 10 + 6 + 8 - (12 + 21 + 22) + 0
Total = 19
Therefore, the total number of students in the class is 19.
5 A teacher needs to buy batteries for 32 calculators. ● There are 20 basic calculators that each require 3 batteries. There are 12 advanced calculators that each require 4 batteries. The batteries are sold in packages of 24. The teacher thinks that 6 packages of batteries will be needed and that there will be 12 batteries left over after the calculators are filled. Provide a solution path that shows whether the teacher is correct or incorrect. Explain what each step in the solution path represents in terms of the situation. Enter your answer and your work or explanation in the space provided.
Answer: The teacher is incorrect
Step-by-step explanation: 20x3=60 4x12=48 60+48=108 108/24=4.5
4.5 does not equal 6. 5 packs of battery's will be needed and there will be 12 battery's left over.
A right triangle has legs which measure 14 inches and 18 inches. Find the length of the
hypotenuse.
answers:
13 inches
25 inches
32 inches
22.8 inches
Answer:
22.8 Inches
Step-by-step explanation:
To find the hypotenuse, the formula is √c=√a^2+b^2
Lets input our values now:
c=√14^2+18^2
Now, let's solve:
c=√196+324
c=√520
The square root of 520 equals about 22.8, so our answer would be 22.8 inches.
Which statement best describes the mean of the data listed below? 10, 7, 9, 5, 8, 6, 7, 3, 10, 5, 7 Responses The middle value of the ordered data set is 7. The middle value of the ordered data set is 7. The value that occurs most often in the set is 7. The value that occurs most often in the set is 7. The difference between the smallest value and the largest value is 7. The difference between the smallest value and the largest value is 7. The sum of all the data values divided by the number of data values is 7. The sum of all the data values divided by the number of data values is 7.
Answer: The sum of all the data values divided by the number of data values is 7.
18. The lengths of Atlantic croaker fish are normally distributed, with a mean of 10 inches and a standard deviation
of 2 inches. An Atlantic croaker fish is randomly selected.
a) Find the probability that the length of the croaker fish is less than 7 inches.
b) Find the probability that the length of the fish is between 7 and 15 inches
Answer:
a) To find the probability that the length of the croaker fish is less than 7 inches, we need to calculate the z-score of 7 inches using the formula:
z = (x - mu) / sigma
where x is the length of the fish we are interested in, mu is the mean length of the population, and sigma is the standard deviation of the population.
In this case, x = 7, mu = 10, and sigma = 2. So the z-score is:
z = (7 - 10) / 2 = -1.5
We can look up the probability of a z-score less than -1.5 in a standard normal distribution table or use a calculator. The probability is approximately 0.0668 or 6.68%.
Therefore, the probability that the length of the croaker fish is less than 7 inches is 0.0668 or 6.68%.
b) To find the probability that the length of the fish is between 7 and 15 inches, we need to calculate the z-scores of 7 inches and 15 inches using the same formula as above:
z1 = (7 - 10) / 2 = -1.5
z2 = (15 - 10) / 2 = 2.5
We can look up the probability of a z-score between -1.5 and 2.5 in a standard normal distribution table or use a calculator. The probability is approximately 0.9332 or 93.32%.
Therefore, the probability that the length of the fish is between 7 and 15 inches is 0.9332 or 93.32%.
Find the final amount of money in an account if $ 2 ,100 is deposited at 2 % interest compounded annually and the money is left for 5 years.
[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$2100\\ r=rate\to 2\%\to \frac{2}{100}\dotfill &0.02\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{annually, thus once} \end{array}\dotfill &1\\ t=years\dotfill &5 \end{cases} \\\\\\ A = 2100\left(1+\frac{0.02}{1}\right)^{1\cdot 5}\implies A=2100(1.02)^5 \implies A \approx 2318.57[/tex]
Please provide the answer
Answer:
your answer is the second one.
what is the result of 4:3x
Answer:
Step-by-step explanation:
-5
Find the LCD of the given rational equation:
2x
x²-25 6x+30
+
-3 8
-
6x
OA. (x+5)(x-5)
OB. (x2-25)(6x+30)(6x)
OC. 6x(x+5)(x - 5)
OD. -48x
The LCD of the given rational function is option B (x²-25)(6x + 30)(6x).
What is rational equation?An equation containing one or more rational expressions is referred to as a rational equation. A fraction with polynomials as the numerator and denominator is known as a rational expression. A rational expression is, in other words, the ratio of two polynomials. Finding the LCD (Least Common Denominator) of the fractions, removing the denominators, and then simplifying the resultant equation can be used to solve rational equations. By resolving the resultant equation, which may require factoring, simplification, or the use of other algebraic strategies, the solutions of rational equations can be discovered. In order to simulate complicated systems and events, rational equations are frequently employed in physics, engineering, and other disciplines.
For the given rational equation the LCD will be the multiplication of all the denominators in the given rational equation.
Thus,
(x²-25)(6x + 30)(6x)
Hence, the LCD of the given rational function is option B (x²-25)(6x + 30)(6x).
Learn more about rational function here:
https://brainly.com/question/8177326
#SPJ1
Which of the following is the *best* way to rewrite
44 x 50
so that the exact answer can be found mentally?
Answer:
22 × 100
(which is 2200)
Step-by-step explanation:
44 × 50 may not look like a problem you can do in your head. But if you notice that there is a 2 in the 44 that you can "move over" to the 50 instead, you totally can do this multiplication in your head.
44 × 50
= 22 × 2 × 50
= 22 × 100
= 2200
Learning Task 2 : Find the area of each shaded region. Assume that all angles that appear to be right triangle (3 points each).
Step by step answer
PLS
Answer:
Step-by-step explanation:
1●area of shaded region = area of big rectangle -area of small rectangle
=(12×7)-(8×3)
=84-24
=60ft²
2● Area of shaded region =sum of area of all three rectangle
=9×3.5+9×3.5+16×7
=63+112
=175ft²
Answer:
Step-by-step explanation:
Formula of a square Area=[tex]x^{2}[/tex]
1)Area of a Rectangle =l*w
area=(12)(7)
=84 ft
solution for the area non shaded=(8)(3)
= 24 ft
solution for area shaded=84-64
=60 ft
find the length of each arc
The arc length of the each arc are 14π cm, 95π/6 ft, 7π cm, 39π/4 ft.
What is arc length of a circle?
The arc length formula for a circle is given by L = rθ, where L is the arc length, r is the radius, and θ is the central angle measured in radians.
9) Here angle= 315° and radius= 8cm.
First, we need to convert the angle to radians: 315° × (π/180°) = 7π/4.
Then we can use the arc length formula,
L = 8 × 7π/4 = 14π cm.
10) Here angle = 150° and radius= 19 ft.
First, we need to convert the angle to radians: 150° × (π/180°) = 5π/6.
Then we can use the arc length formula,
L = 19 × 5π/6 = 95π/6 ft
11) Here angle = π/2 and radius= 14 cm.
According to the arc length formula,
L = 14 × π/2 = 7π cm .
12) Here angle= 3π/4 and radius= 13 ft.
According to the arc length formula,
L = 13 × 3π/4 = 39π/4 ft.
Learn more about circle here:
https://brainly.com/question/24375372
#SPJ1
12 charms representing the 12 months of the year are attached in order on to a chain bracelet find the probability that the clasp is between the charms of June and July include a diagram with your solution
There are 11 possible positions for the clasp, as it can be between any two adjacent charms. If we want the clasp to be between the charms of June and July, we need to count how many of these positions satisfy this condition.
Since there are 12 charms in total, we can arrange them in 12! ways. However, since the order of the charms doesn't matter except for the position of the clasp, we need to divide by 12 to account for the different arrangements of the same set of charms.
Now, we can fix the charms of June and July in their correct positions, which leaves us with 10 remaining charms to arrange. There are 10! ways to do this. However, since we want the clasp to be between the charms of June and July, we need to treat them as a single block and arrange the 10 remaining charms and this block. There are 11 ways to do this.
Therefore, the total number of arrangements where the clasp is between the charms of June and July is 11 × 10!.
The probability of the clasp being between the charms of June and July is:
P = (number of favorable outcomes) / (total number of possible outcomes)
= (11 × 10!) / (12!)
= 11/66
We can represent the possible positions of the clasp using a diagram as follows:
Charm 1 - Charm 2 - Charm 3 - Charm 4 - Charm 5 - Charm 6 - Charm 7 - Charm 8 - Charm 9 - Charm 10 - Charm 11 - Charm 12
|---------------------|
Which describes the graph of y = −(x − 3)2 − 8?
The vertex of the parabola is (h, k) = (3, -8), The graph in red has vertex (3, -8), thus, the red parabola is correct.
What is the quadratic functions?A quadratic function is a polynomial function of the form f(x) = ax² + bx + c, where a, b, and c are constants and a is not equal to 0.
We know that the standard form of the parabola is y=ax²+bx+c. Thus, the vertex form of a parabola is y = a(x-h)² + k, and the vertex is given by (h, k)
here, y = −(x − (3))² (−8) is already in vertex form.
Then,
h = 3
k = -8
Thus, the vertex of the parabola is (h, k) = (3, -8), The graph in red has vertex (3, -8), thus, the red parabola is correct.
To learn more about quadratic functions, Visit
https://brainly.com/question/1214333
#SPJ1
Complete question:
Which line describes the graph of y = −(x − 3)2 − 8?
NEED HELP ASAP!!!
A student missed 11 problems on a English test and received a grade of 50%. If all the problems were of equal value, how many problems were on the test? Follow the problem-solving process and round your answer to the nearest integer.
Answer:
22 problems
Step-by-step explanation:
50% is half of 100, so if 100 divided by 2 is 50, then 11 x 2 is 22. 22 is the answer
Write the equation for a parabola with a focus at (2,2) and a directrix at x=8.
x=(blank)
Answer: x=-((y-2)^2)/12 +5
Step-by-step explanation:
Since the directrix is vertical, use the equation of a parabola that opens up or down. Find the vertex.
On a truck, one windshield wiper blade is 80 centimeters long and is connected to a swing arm that is 90 centimeters long from the pivot point to the tip, as shown below. If the swing arm rotates the wiper blade is 120, what is the area of the windshield that is swept by the wiper blade? round your answer to the nearest tenth of a square centimeter
The area of the sector rounding to the nearest tenth is C. 8377.6 [tex]cm^2[/tex].
What is law of cosines?The law of cosines is a formula used to find the length of a side or the measure of an angle in a non-right triangle (a triangle that does not have a 90-degree angle).
According to given information:
To find the area of the windshield swept by the wiper blade, we can consider it as a sector of a circle with radius equal to the length of the segment swept by the wiper blade. The length of this segment can be found using the law of cosines:
[tex]c^2 = a^2 + b^2 - 2ab cos(C)[/tex]
where a and b are the lengths of the sides adjacent to the angle C, and c is the length of the side opposite to the angle C.
In this case, we have:
a = 80 cm (length of the wiper blade)
b = 90 cm (length of the swing arm)
C = 120 degrees (angle swept by the swing arm)
Substituting these values, we get:
[tex]c^2 = 80^2 + 90^2 - 2(80)(90)cos(120)[/tex]
[tex]c^2[/tex] ≈ [tex]20418[/tex]
[tex]c[/tex] ≈ [tex]142.8 cm[/tex]
So the radius of the circle is approximately 142.8 cm. The central angle of the sector is 120 degrees, so its measure in radians is 2π/3. Therefore, the area of the sector is:
A = (1/2) * [tex]r^2[/tex] * θ
A = (1/2) * [tex](142.8)^2[/tex] *[tex](2\pi /3)[/tex]
A ≈ 8377.6 [tex]cm^2[/tex]
Rounding to the nearest tenth, we get the answer as C. 8377.6 [tex]cm^2[/tex].
To know more about law of cosines visit:
https://brainly.com/question/30766161
#SPJ1
What is the solution to 38.4 = 2x
Answer:
19.2
Step-by-step explanation:
You want the solution to 38.4 = 2x.
One-step linear equationWhen you divide both sides of the equation by 2, you will have your answer.
38.4/2 = (2x)/2
19.2 = x
The solution to the equation is x = 19.2.
__
Additional comment
When you learned multiplication and division, you learned that each multiplication fact corresponds to two division facts:
A = B×C . . . . . . . 6 = 2×3
A/B = C . . . . . . . . 6/2 = 3
A/C = B . . . . . . . . 6/3 = 2
We use that relationship here to find the value of one of the factors in the product:
38.4 = 2·x
38.4/2 = x
The other division fact is still true, but isn't useful here for finding the value of x.
38.4/x = 2