Every year the growth of child is 2.5 inches.
Define linear functionA linear function is a type of mathematical function that produces a straight line when graphed on a coordinate plane. It is defined by an equation of the form y = mx + b, where "m" is the slope of the line and "b" is the y-intercept (the point where the line crosses the y-axis). The slope of a linear function is the rate at which the output value (y) changes with respect to the input value (x).
At 1 year of age,
Height of the child is 27.5inch(from the graph)
At 2 year of age,
Height of the child is 30inch(from the graph)
At 3 year of age,
Height of the child is 37.5inch(from the graph)
Every year the growth of child is=30-27.5/2-1=2.5
Growth of child is linear as per graph, so it will increase accordingly to it.
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labor-hours and its standard cost card per unit is as follows:
Direct material: $ pounds at $11.00 per pound
Direct labor: 3 hours at $12 per hour
Variable overhead: 3 hours at $7 per hour
Total standard variable cost per unit
The company also established the following cost formulas for its selling expenses:
sales salaries and commissions
shipping expenses
Fixed Cost per
Month
$ 280,000
$ 260,000
$ 55.00
36.00
$112.00
Variable
Cost per
Unit Sold
$ 20.00
$ 11.00
The planning budget for March was based on producing and selling 21,000 units. However, during March the company
actually produced and sold 26.600 units and incurred the following costs:
a Purchased 154.000 pounds of raw materials at a cost of $9.50 per pound. All of this material was used in production.
b. Direct laborers worked 63,000 hours at a rate of $13.00 per hour
e Total variable manufacturing overhead for the month was $510,930
d Total advertising sales salaries and commissions, and shipping expenses were $286,000, $495,000, and $195,000,
respectively
6 What direct labor cost would be included in the company's flexible budget for March?
The direct labor cost included in the Preble Company's flexible budget for March is $819,000.
How to compute Preble Company's direct labor cost?To find the direct labor cost included in the company's flexible budget for March, we shall estimate the actual direct labor cost incurred during the period.
Given:
Actual production and sales =n26,600 units
Actual direct labor rate = $13.00 per hour
Actual direct labor hours worked = 63,000 hours
Direct labor cost = Actual direct labor rate × Actual direct labor hours worked
Direct labor cost = $13.00/hour × 63,000 hours
Direct labor cost = $819,000
Hence, the direct labor cost included in the company's flexible budget for March would be $819,000.
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A photograph with a width of 5 inches and a length of 7 inches will be enlarged so that the length is 56 inches. What will the width equal?
A. 35 inches
B. 40 inches
C. 92 inches
D. 180 inches
Answer: B is the answer
Step-by-step explanation:
PLZ HELP
Which is the sum of 3.15 × 10^7 +9.3 × 10^6 ? Write your answer in
scientific notation.
A. 4.08 × 10^7
B. 4.08 × 10^6
C. 0.408 × 10^8
D. 40.8 × 10^6
Answer: A 4.08x10^7
Step-by-step explanation:
Expanded form: 40800000
Gina spent $54 for a total of 15 bags of treats for the cats and dogs at the shelter.She paid $3 for each bag of cat and $4 for each bag of dog treats.
The number of bags of cat treat is 6 and the number of bags of dog treat is 9.
Let
x = number of cat treat
y = number of dog treat
She bought a total of 15 bags for treat for cat and dog. Therefore,
Total number of treats:x + y = 15She spent $54 on the total treats. Therefore,
Total cost of treats: 3x + 4y = 54Therefore,
x + y =15
3x + 4y = 54
3x + 3y = 45
3x + 4y = 54
y = 9
x = 15 - 9
x = 6
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A sample of bacteria is decaying according to a half-life model. If the sample begins with 700 bacteria, and after 13 minutes there are 630 bacteria, after how many minutes will there be 20 bacteria remaining?
When solving this problem, round the value of k to four decimal places and round your final answer to the nearest whole number
The number of minutes for 20 bacteria be left is 439minutes. The decay constant is 0.0081
What is exponential function?An exponential function is a mathematical function, which is used in many real-world situations. It is mainly used to find the exponential decay or exponential growth or to compute investments, model populations and so on.
The No of bacteria left at a particular time t is given as N(t)= Noe^-kt
where No= initial number of bacteria
k= decay constant and t = time
after 13 minutes
630= 700e^-13k
divide both sides by 700
630/700= e^-13k
0.9= e^-13k
ln0.9= -13k
k= ln0.9/-13 = -0.1054/-13 = 0.0081
time for 20 bacteria to be left =
20= 700e^-0.0081t
= 20/700=e^-0.0081t
0.0286= e^-0.0081t
ln0.0286= -0.0081t
-3.554= -0.0081t
divide both sides by -0.0081
t= -3.554/-0.0081= 439 minutes ( nearest minutes)
therefore the time for the bacteria to be left is 439minutes
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what is expanded notation for 2,575,384?
Answer:
2,575,384 =
2,000,000
+ 500,000
+ 70,000
+ 5,000
+ 300
+ 80
+ 4
Step-by-step explanation:
Look back at the plans these students used to solve the word problem below.
Who found a correct solution?
EK BAKI
The entire school, 250 students, went to the soap box derby.
The Math Club went in 2 vans, and each van held 6 students.
How many students from the Math Club went to the soap box
derby?
Paul added vans to students. Eva multiplied students by vans
Since 2+ 6 + 8, eight Math Club Since 6x2 = 12, twelve Math Club
students went to the soap box students went to the soap box
derby
derby
A. Eva
B. Paul
Answer:
A. Eva
Step-by-step explanation:
Given that
The entire school, 250 students, went to the soap box derby.2 vans went to soap box derby and each van held 6 students.
To find the total number of students from the Math Club who went to the soap box derby, we need to add the number of students in each van, the number of times equal to the number of vans.
i.e. by adding 6 (i.e. number of students in each van) 2 (number of vans )number of times, we can get the number of students from Math Club who went to the soap box derby.
Number of Math Club students who went to the soap box derby = 6 + 6 = 12
OR
Simply, multiply number of students in each van with the number of vans .
6 \(\times\) 2 = 12
Therefore, Eva is correct about the calculations.
Cuanto mide el largo de un rectángulo cuyo perímetro es 16cm y su área 12 cm al cuadrado ?
There is a mother-daughter tea that will be attended by 20 mother-daughter pairs, including the hosts. The rules of conduct are very strict; the host mother-daughter will greet everyone, all the guest mothers will greet everyone, and all the guest daughters will greet all the mothers only. How many greetings will there be?
In total, the number of greetings will be 1159.
Why do you use the term "numbers"?Mathematical symbols used to represent quantities or values include numbers. They are employed in the measurement, comparison, addition, subtraction, multiplication, and division processes in mathematics. According to their qualities and properties, numbers can be categorized into a variety of groups, including natural numbers, whole numbers, integers, rational numbers, irrational numbers, real numbers, and complex numbers. There are specific properties and guidelines for mathematical operations for each group of numbers. Mathematics depends on numbers, which are also utilized in many other disciplines, including science, engineering, economics, and statistics.
The number of greetings exchanged between the host and the other mothers and daughters must be counted first. Since there is only one host, the number of mother-daughter pairs is 20 - 1 = 19. There are thus a total of 38 greetings, 19 between the host and the other moms, and 19 between the host and the other daughters.
The number of pleasantries exchanged between the guest mums and everyone else must next be tallied. The host, the other mothers, and the daughters must all be greeted, making a total of 20 - 1 = 19 guest mothers. Thus, each host mother must extend 1 + 19 + 20 = 40 greetings. There will be 760 greetings exchanged between the guest mothers and everyone, or 19 x 40.
The number of pleasantries exchanged between the mothers and the invited girls must also be tallied. Moreover, there are 20 guest girls, so 19 of them must welcome the mothers. As a result, there will be 361 pleasantries exchanged between the mothers and the guest daughters.
In total, the number of greetings will be 38 + 760 + 361 = 1159.
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The diameter of a circle is 8cm. Find its circumference to the nearest tenth.
Answer:
\(C = 25.1 \text{ cm}\)
Step-by-step explanation:
We can find the circumference of the circle by plugging the given radius value 8 cm into the formula:
\(C = \pi d\)
Note: This formula can also be written as \(C = 2\pi r\) because \(2r = d\).
↓ plugging in the given radius
\(C = 8\pi \text{ cm}\)
↓ rounding to the nearest tenth
\(\boxed{C = 25.1 \text{ cm}}\)
What is the value of
O
O
O
O
81
16
16
81
16
81
81
16
(3)*₂
?
The solution of the expression, \((\frac{2}{3} )^{-4}\) is 81 / 16.
How to solve an exponential expression?An algebraic expression is an expression which is made up of variables and constants, along with algebraic operations such as multiplication, subtraction, addition etc.
Therefore, lets solve the expression as follows:
\((\frac{2}{3} )^{-4}\)
Using exponential laws,
b⁻¹ = 1 / b
Let's apply the law to the expression as follows:
\((\frac{2}{3} )^{-4} = \frac{1}{(\frac{2}{3})^{4} }\)
Therefore,
1 ÷ (2 / 3)⁴ = 1 × (3 / 2)⁴ = 3⁴ / 2⁴
Finally,
3⁴ / 2⁴ = 81 / 16
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CAN SOMEONE HELP WITH THIS?✨
4966.5
Step-by-step explanation:
Starting at finding out how the population will increase in 3 years we take 3 and divide it by 4. This produces an increase of 75% every 3 years. If we multiply 2838 by 75% we get 2128.5. If we add it back to 2838, we get 4966.5
The adult skeleton consist of 206 Bones in the school and 30 bones in the arm and legs. Out of the 28th skull bones, 14 are facial bones. Six or ear bones and eight are cardinal bones. How many more bones are there in the arm and legs than in the faceA) 2B) 6C) 14D) 16
We need to compare the number of bones in the arms and legs with the number of bones in the face.
The question says that there are 30 bones in the arms and legs.
The question also says that there are 14 bones on the face.
So, the difference between these will be how many more bones there are in the arms and legs than in the face:
\(30-14=16\)Solve for x, given the equation Vx+9 - 4 = 1.
Is it extraneous or not
Answer:
-4/x it is not
Mrs. Ward baked 840 cookies. She sold them in packets of 24 cookies each. How much did she receive if the selling price per packet was $3.?
Can anyone help me on this
look at picture!! please!!
Answer:
above is the answer to the question
Leo is a barber.
He charges £5 for a haircut.
He charges 10% extra for hair gel.
One day 25 customers have a haircut.
16 of these ask for hair gel.
Work out the total amount that Leo charges his customers that day.
Over the last 3 evenings, Maya received a total of 93 phone calls at the call center. The second evening, she received 4
times as many calls as the third evening. The third evening, she received 9 more calls than the first evening. How many
?
phone calls did she receive each evening?
Number of phone calls the first evening:
By using linear equation, it can be calculated that
Number of calls in the first evening = 8
Number of calls in the second evening = 4(8 + 9) =68
Number of calls in the third evening = 8 + 9 = 17
What is linear equation?
Equation shows the equality between two algebraic expressions by connecting the two algebraic expressions by an equal to sign.
A one degree equation is known as linear equation.
Let the number of calls Maya receives in the first evening be x
Number of calls she receives in third evening = x + 9
Number of calls she receives in the second evening = 4(x + 9)
Total number of phone calls = x + 4(x + 9) + x + 9
By the problem,
The linear equation is
x + 4(x + 9) + x + 9 = 93
x + 5(x + 9) = 93
x + 5x + 45 = 93
6x = 93 - 45
6x = 48
x = \(\frac{48}{6}\)
x = 8
Number of calls in the first evening = 8
Number of calls in the second evening = 4(8 + 9) =68
Number of calls in the third evening = 8 + 9 = 17
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help pls anyone? pls
Name the property illustrated If g = 3h and 3h = 16, then g = 16
3
The property illustrated ca be classified as the transitive property of equality
Transitive property of equalityEquation are expressions separated by an equal sign. For transitive property, if two system of equation are equal, and the first is equal to the second, then they 2nd is equal to the third, they are transitive.
According to the transitive property of equality, two quantities that are equal to the same thing are equal to each other. For instance If x = 10 and 10 = y, then x = y.
Given that g = 3h and 3h = 16, then g = 16, then the property illustrated ca be classified as the transitive property of equality
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Simplify completely
(192x^12/3x^3)^1/3
Show all work for full credit
Answer and Explanation: The answer and explanation is in the image.
A lamp has two bulbs of a type with an average lifetime of 1000 hours. Assuming that we can model the probability of failure of these bulbs by an exponential density function with mean μ = 1000, find the probability that both of the lamp's bulbs fail within 1000 hours.
Answer:
(e-1-1)2=0.3996
Step-by-step explanation:
Solve the problem.
A landscaping team plans to build a rectangular garden that is between 240 yd² and 360 yd2 in area. For aesthetic reasons, they also want the
length to be 1.2 times the width. Determine the restrictions on the width so that the dimensions of the garden will meet the required area. Give exact
values and the approximated values to the nearest tenth of a yard.
The restrictions on the width is that it must be between 14.1 yards and 17.3 yards
How to determine the restrictions on the widthFrom the question, we have the following parameters that can be used in our computation:
Area = between 240 yd² and 360 yd²
Also, we have
Length = 1.2 times the width
This means that
l = 1.2w
The area is then calculated as
Area = lw
So, we have
Area = 1.2w²
This means that
240 < 1.2w² < 360
Divide through by 1.2
200 < w² < 300
Take the square roots
14.14 < w < 17.32
Approximate
14.1 < w < 17.3
Hence, the width must be between 14.1 yards and 17.3 yards
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Mrs. Burke’s mathematics class has 102 students, classified by academic year and major, as illustrated in the table. Mrs. Burke randomly chooses one student to collect yesterday’s work. Mrs. Burke’s Mathematics Class Academic Year Mathematics Majors Non-Mathematics Majors Freshmen 14 16 Sophomores 13 11 Juniors 17 9 Seniors 10 12 Step 1 of 2 : What is the probability that she selects a mathematics major, given that she chooses randomly from only the sophomores? Enter a fraction or round your answer to 4 decimal places, if necessary.
50 POINTS and BRAINLIEST-- A pattern of shaded and unshaded squares is shown below:
Answer:
The number of shaded squares changes by 2 in each figure
Therer will be 90 squares shaded in the 50th figure
Step-by-step explanation:
Brainliest PLS
Answer:
1. I'm not exactly sure but I would say that you add two to every square.
2. 90
Step-by-step explanation:
To find the first answer, you just add and count the squares.
To find the second answer, you just add two to every square, up to 50 squares.
Use the graph that shows the solution to f(x)=g(x). f(x)=x2 g(x)=(12)x−1 What is the solution to f(x)=g(x)?
x=−1
x = 0
x = 1
x = 2
Answer:
To find the solution to f(x)=g(x), we need to find the point(s) where the two curves intersect.
The graph is not provided, but we can find the solution algebraically by setting the two functions equal to each other:
f(x) = g(x)
x^2 = 12^(x-1)
To solve for x, we can take the logarithm of both sides:
log(x^2) = log(12^(x-1))
2log(x) = (x-1)log(12)
2log(x) = xlog(12) - log(12)
2log(x) - xlog(12) = -log(12)
log(x^2) - log(12^x) = -log(12)
log(x^2/12^x) = -log(12)
log(x/12) = -log(12)
log(x) - log(12) = -log(12)
log(x) = 0
x = 1
Therefore, the solution to f(x)=g(x) is x=1.
Step-by-step explanation:
The temperature on Thursday afternoon was 77 °F. A thunderstorm rolled through, and the temperature dropped by 10 °C. What was the temperature after the storm?
Answer:
15 °C
Step-by-step explanation:
°C = (°F - 32) * (5/9)
Given that the initial temperature was 77 °F and it dropped by 10 °C, we can calculate the final temperature.
Initial temperature: 77 °F
Converting to Celsius:
°C = (77 - 32) * (5/9)
°C ≈ 25
The temperature dropped by 10 °C, so the final temperature is:
Final temperature = Initial temperature - Temperature drop
Final temperature ≈ 25 - 10 = 15 °C
Therefore, the temperature after the storm was approximately 15 °C.
5 Katy drew a pentagon, and then she enlarged it by a factor of 2.
Which of the following would NOT change?
A the length of each side
B
the area of the pentagon
C the perimeter of the pentagon
D the measure of each interior angle
Answer:
D. The measure of each interior angle
Step-by-step explanation:
Why? Because if you enlarge the shape, the length, perimeter, and area all change because you're using different lengths for the sides.
The angles do not change because you don't move the sides to create a new angle.
CAN ANYONE HELP ME AND EXPLAIN MY MATH HOMEWORK TO ME
Answer:
i need a picture
or sum
Step-by-step explanation: