Challenge) Solve for a. Answer as a mixed number. A=______
The value of the a in the mixed form is [tex]-1 \frac{5}{43}[/tex].
What is the equivalent expression?
Equivalent expressions are expressions that work the same even though they look different. If two algebraic expressions are equivalent, then the two expressions have the same value when we plug in the same value for the variable.
To solve for a, we can begin by isolating the variable on one side of the equation.
First, we can subtract 3 from both sides to get:
-7/12 - 3 = 4/a
Next, we can simplify the left side by finding a common denominator of 12:
-7/12 - 3 * 12/12 = 4/a
-7/12 - 36/12 = 4/a
-43/12 = 4/a
To solve for a, we can multiply both sides by a/4:
(-43/12) * (a/4) = 1
Multiplying the left side gives:
-43a/48 = 1
Dividing both sides by -43/48 gives:
a = -48/43
To express this as a mixed number, we can divide the numerator by the denominator:
-48 ÷ 43 = -1 with a remainder of 5
Therefore, the value of the a in the mixed form is [tex]-1 \frac{5}{43}[/tex].
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Complete question:
Challenge) Solve for a. Answer as a mixed number. A=?
-7/12 = 4/a+3.
The equations were multiplied by constants and added together to determine that the value of x in the system of
equations is -4.
What is the value of y?
0-6
O-3
O 3
06
As a result the system of equation , y has a value that is roughly 4.33.
SYSTEM OF EQUATIONS: WHAT IS IT?A group of two or more equations with the same variables is referred to as a system of equations. The collection of numbers that simultaneously make all the equations true is the system's solution.
For instance, take into account the equations below:
2x + y = 5
x - y = 1
There are two equations with two variables in this system (x and y). The collection of numbers that simultaneously satisfy both equations is the system's solution. The answer in this situation is x = 2 and y = 1.
We may solve for y by substituting the value of x in the system of equations, which is -4, into one of the equations.
Consider the following two equations:
axe + by = c
dx + ey = f
We can solve for y by substituting the value of x into one of the equations if we know it.
As an illustration, if x = -4, then we have:
2x + 3y = 5
4x - 3y = -16
We can change one of the equations to read x = -4:
2(-4) + 3y = 5
When we simplify this equation, we obtain:
-8 + 3y = 5
8 is added to both sides to get at:
3y = 13
When we multiply both sides by 3, we get:
y = 13/3
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An automobile company is running a new television commercial in five cities with approximately the same population. The following table shows the number of times the commercial is run on TV in each city and the number of car sales (in hundreds). Find the Pearson correlation coefficient r for the data given in the table. Round any intermediate calculations to no less than six decimal places, and round your final answer to three decimal places. r=
Pearson correlation coefficient r for the data is approximately 0.915. Since the value is positive and close to 1, we can say that there is a strong positive correlation between the number of times the commercial is run on TV and the number of car sales.
What is expression ?
In mathematics, an expression is a combination of numbers, symbols, and operators (such as +, -, ×, ÷) that represents a value or a quantity. It can be a single number or variable, or a combination of them, and can also include functions, parentheses, and other mathematical symbols. For example, 3x + 7 is an expression, where 3 and 7 are constants, x is a variable, and + is an operator. Expressions can be simplified, evaluated, or used as part of a larger mathematical statement or equation.
We can use the formula for Pearson correlation coefficient r to calculate it for the given data:
r = (nΣXY - ΣXΣY) / sqrt[(nΣX² - (ΣX)²)(nΣY² - (ΣY)²)]
where n is the number of observations, Σ represents the sum of the indicated values, and X and Y represent the two variables being correlated. Using the data from the table, we can calculate the following:
n = 5
ΣX = 25, ΣY = 25.8
ΣX² = 275, ΣY² = 288.68
ΣXY = 139.2
Substituting these values into the formula, we get:
[tex]$r = (5 * 139.2 - 25 * 25.8) \sqrt{[(5 * 275 - 25^2)(5 * 288.68 - 25.8^2)]} $[/tex]
r ≈ 0.915
Therefore, the Pearson correlation coefficient r for the data is approximately 0.915. Since the value is positive and close to 1, we can say that there is a strong positive correlation between the number of times the commercial is run on TV and the number of car sales.
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One hour later the right triangle is 15 inches long and 13 inches high and the base and height are changing at the same rate is there hypotenuse increasing or decreasing now?
The hypotenuse of the new triangle is increasing.
What theorem can be used to determine the triangle?The Pythagorean Theorem can be used to determine the new right triangle's hypotenuse length:
[tex]c^2 = a^2 + b^2\\c^2 = 13^2 + 15^2\\c^2 = 169 + 225\\c^2 = 394\\c ≈ 19.85[/tex]
Hence, the hypotenuse of the new right triangle measures roughly 19.85 inches in length.
Let h be the height of the triangle, and let b be the base of the triangle, both as functions of time t. We know that the base and height are changing at the same rate, so we can express this as:
dh/dt = db/dt = k, where k is a constant rate of change.
We can use the Pythagorean Theorem to express the length of the hypotenuse c as a function of h and b:
[tex]c^2 = h^2 + b^2[/tex]
Taking the derivative of both sides with respect to time t using the chain rule, we get:
2c(dc/dt) = 2h(dh/dt) + 2b(db/dt)
Simplifying and substituting the values for h, b, and c at time t = 0 (when the original triangle was given):
2c(dc/dt) = 2(7)(k) + 2(x)(k)
2c(dc/dt) = 14k + 10k
2c(dc/dt) = 24k
adding 2c to both sides' sums:
(12k/c) = (dc/dt)
For the new triangle, substitute the value of c as follows:
(dc/dt) = 12k/19.85
The sign of (dc/dt) will be decided by the sign of 1/c because k is positive and constant. Since we know that 1/c is positive and that c is positive, we can infer that (dc/dt) will also be positive because it will have the same sign as k. As a result, the new triangle's hypotenuse is growing.
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pls help due tmrw i want a good grade
Compute the cost assigned to ending inventory using (a) FIFO, (b) LIFO, (c) weighted average, and (d) specific identification. For specific identification, units sold include 70 units from beginning inventory, 200 units from the March 5 purchase, 50 units from the March 18 purchase, and 90 units from the March 25 purchase.
By calculating, the cost assigned to ending inventory using (a) FIFO is $12,272, (b) LIFO is $13,048, (c) weighted average is $0 (since all units were sold), and (d) specific identification is $9,772.
To compute the cost assigned to ending inventory using different inventory costing methods, we need to determine the cost of goods sold (COGS) and the cost of ending inventory based on the specific method. Here is the calculation for each method:
(a) FIFO (first-in, first-out) method:
We assume that the earliest inventory items purchased are the first ones sold. Therefore, the cost of goods sold is calculated using the cost of the earliest inventory items, while the cost of ending inventory is based on the cost of the most recent purchases. Here are the calculations:
COGS: 110 units x $51.20 + 200 units x $56.20 + 50 units x $86.20 + 70 units x $61.20 = $23,216
Ending inventory: 90 units x $61.20 + 160 units x $63.20 = $12,272
(b) LIFO (last-in, first-out) method:
We assume that the most recent inventory items purchased are the first ones sold. Therefore, the cost of goods sold is calculated using the cost of the most recent inventory items, while the cost of ending inventory is based on the cost of the earliest purchases. Here are the calculations:
COGS: 90 units x $61.20 + 270 units x $86.20 + 230 units x $56.20 = $43,104
Ending inventory: 110 units x $51.20 + 140 units x $96.20 + 50 units x $86.20 = $13,048
(c) Weighted average method:
We calculate the weighted average cost per unit for all the inventory purchased during the period, and use this average cost to determine the cost of goods sold and ending inventory. Here are the calculations:
Weighted average cost per unit = ($51.20 x 110) + ($56.20 x 230) + ($86.20 x 270) + ($61.20 x 90) + ($63.20 x 160) / (110 + 230 + 270 + 90 + 160) = $72.62
COGS: 590 units x $72.62 = $42,878.80
Ending inventory: 0 units (all units have been included in COGS)
(d) Specific identification method:
We identify the specific cost of each unit sold based on its purchase price. Here are the calculations:
COGS: 70 units x $51.20 + 200 units x $56.20 + 50 units x $86.20 + 90 units x $61.20 + 80 units x $63.20 + 20 units x $96.20 = $43,708
Ending inventory: 80 units x $63.20 + 70 units x $96.20 = $9,772
Therefore, the cost assigned to ending inventory using (a) FIFO is $12,272, (b) LIFO is $13,048, (c) weighted average is $0 (since all units were sold), and (d) specific identification is $9,772.
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In ΔWXY, the measure of ∠Y=90°, WY = 5, XW = 13, and YX = 12. What ratio represents the cosine of ∠X?
Answer:
Please mark as brainliest
Check the picture below.
1. They each walk 500 units to school. Who walks 500 feet, and who walks 500 yards? Explain your reasoning
Answer:
Below
Step-by-step explanation:
If they each walk in straight lines to the school Lin is closer than Elena
so Lin walks 500 ft and Elena walks 500 yards ( which is 1500 ft)
John is a 45 year old educator . He is living with his spouse and two children below 20 years . He earns a gross monthly salary R 21 400 . He contributes 7,5 % of his salary to the pension fund . He is the main member of a medical aid and his wife and children are his dependents . Get a copy of the medical tax credit rates from 2013 - 2023 and rebates from 2015 to 2023
Answer:
Please mark as brainliest
Step-by-step explanation:
Medical tax credit rates and rebates are determined by the South African Revenue Service (SARS) and are subject to change from year to year. Therefore, I cannot provide you with a copy of the medical tax credit rates and rebates for the entire period of 2013 to 2023.
However, I can provide you with the following information:
The medical tax credit rate for the 2021/2022 tax year is R319 per month for the main member and the first dependent, and R215 per month for each additional dependent.
The medical tax credit rate for the 2020/2021 tax year was R310 per month for the main member and the first dependent, and R209 per month for each additional dependent.
The medical tax credit rate for the 2019/2020 tax year was R310 per month for the main member and the first dependent, and R209 per month for each additional dependent.
The medical tax credit rate for the 2018/2019 tax year was R303 per month for the main member and the first dependent, and R204 per month for each additional dependent.
The medical tax credit rate for the 2017/2018 tax year was R286 per month for the main member and the first dependent, and R192 per month for each additional dependent.
The medical tax credit rate for the 2016/2017 tax year was R286 per month for the main member and the first dependent, and R192 per month for each additional dependent.
The medical tax credit rate for the 2015/2016 tax year was R270 per month for the main member and the first dependent, and R181 per month for each additional dependent.
The medical tax credit rate for the 2014/2015 tax year was R257 per month for the main member and the first dependent, and R172 per month for each additional dependent.
As for rebates, I should note that the South African tax system works with a system of tax brackets, where the amount of tax you pay increases as your income increases. Tax rebates are a form of tax relief that is subtracted from the amount of tax you owe. The rebate amount changes annually, and for the 2021/2022 tax year, the rebate for individuals under 65 years of age is R15,714.
Again, it is important to note that these rates and rebates are subject to change from year to year, and it is recommended that you consult with a qualified tax professional for the most up-to-date information.
mr.jones decided to invest in the stock market, but the market declined by an average of 2.5% each month during the first 6 months of his investment. If mr.jones initially invested $1,500, how much does he have remaining?
Step-by-step explanation:
If the stock market declined by an average of 2.5% each month during the first 6 months of Mr. Jones' investment, we can calculate the total percentage decrease using the following formula:
(1 - 0.025)^6 = 0.8938
This means that after 6 months, Mr. Jones' investment would have decreased by approximately 10.62% (1 - 0.8938 = 0.1062).
To calculate how much money Mr. Jones has remaining, we need to multiply his initial investment of $1,500 by the percentage decrease:
$1,500 x 0.1062 = $159.30
Therefore, Mr. Jones would have $1,500 - $159.30 = $1,340.70 remaining after the first 6 months of his investment in the stock market with an average decline of 2.5% each month.
It takes 32 pounds of seed to completely plant a 4 -acre field. How many acres can be planted per pound of seed?
Answer:
Step-by-step explanation:
To solve this problem, we need to find the number of acres that can be planted per pound of seed.
We know that it takes 32 pounds of seed to plant a 4-acre field. Therefore, the amount of seed needed to plant 1 acre is:
32 pounds / 4 acres = 8 pounds/acre
This means that for every pound of seed, we can plant:
1 acre / 8 pounds = 0.125 acres/pound
Therefore, we can plant 0.125 acres per pound of seed.
PLSS i NEED help :/ Can u show me the method too? I'm really stuck
IS IT RIGHT??? OR I MISSED SOMETHING
Find the L.C.M. and H.C.F of 84 and 56.
[tex] \mathbb{ANSWER:}[/tex]
LCM: 168
Multiples of 84: 84, 168…Multiples of 56: 56, 112, 168…HCF: 28
Factors of 56: 1, 2, 4, 7, 8, 14, 28, 56Factors of 84: 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84Write an equation of the line that passes through the point (–4, 6) with slope –4.
A. y−6=−4(x+4)
B. y+4=−4(x−6)
C. y−6=4(x+4)
D. y+4=4(x−6)
Answer:
Answer is A
Step-by-step explanation:
General equation of a line is given by;
[tex]{ \boxed{ \rm{y = mx + c}}}[/tex]
m is gradientc is y-intercept.From the question, m = -4
[tex]{ \rm{y = - 4x + c}}[/tex]
For (-4, 6)
[tex]{ \rm{6 = ( - 4 \times - 4) + c}} \\ { \rm{6 = 16 + c}} \\ { \rm{c = - 10}}[/tex]
Therefore;
[tex]{ \rm{y = - 4x - 10}} \\ { \colorbox{silver}{subtract \: 6 \: from \: both \: sides}} \\ { \rm{y + ( - 6) = ( - 4x - 10) + ( - 6)}} \\ \\ { \rm{y - 6 = - 4x - 16}} \\ \\ { \rm{y - 6 = - 4(x + 4)}}[/tex]
Which linear function represents a slope of 1/4?
Answer:
The second answer choice represents a slope of 1/4.
Step-by-step explanation:
Using the coordinates (8,5) and (0,3) you can do point slope form (y2-y1/x2-x1). In this problem that would translate to 5-3/8-0 which is 2/8 and can be simplified to 1/4.
Find the common ratio of 1,3,9,-27 and the next three terms
Answer:
Step-by-step explanation:
The common ratio of this sequence is 3. Next 3 terms are -81, -243, and -729.
If a year has 52 weeks, what fraction of a century is 13 weeks?
Answer:
Step-by-step explanation:
There are different methods to approach this problem, but one possible way is:
First, find the number of weeks in a century: 100 years × 52 weeks/year = 5200 weeks
Then, find the fraction of a century that is 13 weeks by dividing 13 weeks by 5200 weeks: 13/5200 = 1/400
Therefore, 13 weeks is 1/400 of a century.
The Rodriguez family and the Barnes family each used their sprinklers last summer. The Rodriguez family's sprinkler was used for 15 hours. The Barnes family's sprinkler was used for 35 hours. There was a combined total output of 1050 L of water. What was the water output rate for each sprinkler if the sum of the two rates was 50 L per hour?
Rodriguez family's sprinkler:
Barnes family's sprinkler:
The water output rate for the Rodriguez family's sprinkler was 35 L per hour, and the water output rate for the Barnes family's sprinkler was 15 L per hour (50 - 35) by solving the expression formed.
What is expression ?In mathematics, an expression is a combination of numbers, variables, and mathematical operations, such as addition, subtraction, multiplication, and division, that are written in a certain order. Expressions can be evaluated or simplified by following the rules of arithmetic or algebra. Examples of expressions include "2x + 3", "(a + b) / c", and "5^2 - 3".
According to given information :
Let's use the variable "r" to represent the water output rate for the Rodriguez family's sprinkler.
Then, the water output rate for the Barnes family's sprinkler can be represented as "50 - r", since the sum of the two rates is 50 L per hour.
Using the formula:
rate x time = amount of output, we can set up two equations:
r x 15 = amount of water output for the Rodriguez family
(50 - r) x 35 = amount of water output for the Barnes family
We also know that the total amount of water output is 1050 L, so we can set up a third equation:
r x 15 + (50 - r) x 35 = 1050
Now we can solve for "r".
First, simplify the third equation
15r + 1750 - 35r = 1050-20r = -700r = 35
Therefore, the water output rate for the Rodriguez family's sprinkler was 35 L per hour, and the water output rate for the Barnes family's sprinkler was 15 L per hour (50 - 35).
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three consecutive integers whose sum is -6. what are the numbers
Answer:
The numbers are -3, -2, and -1.
Step-by-step explanation:
Since -2 and -1 add up to -3, and -3+-3 = -6, and since the numbers are next to each other on your number line, well, then you got your answer. Here's how:
-3+-2+-1=-6
What is the equation for this graph?
Answer:
[tex]y=\frac{5}{2} x[/tex]
Step-by-step explanation:
Notice is a line, The equation for a line can be found as the following:
[tex]y-yo=m(x-xo)[/tex]
We need to find the slope.
First take two points of the graph
(0,0) the origin and (4,10) for example. Notice i do assume the X value is 4 for Y=10, since the cropping for the picture doesn't show the exact values for X .
Then the slope is given by equation:
[tex]m=(y-yo)/(x-xo)\\[/tex]
[tex]m=\frac{10-0}{4-0} =5/2[/tex]
then the equation is
[tex]y-0=\frac{5}{2} m(x-0)[/tex]
[tex]y=\frac{5}{2} x[/tex]
Answer:
y=5/2x or y=2.5x
Step-by-step explanation:
Write a system of equations to solve the following scenario. Twins Jon and Ron together earned $96,000 last year. Ron earned $8,000 more than three times what Jon earned. How much did each of the twins earn? Use the variable j to represent the amount Jon earned. Use the variable r to represent the amount Ron earned.
The amount Jon and Ron earn are $22,000 and $ 74,000 respectively.
What is word problem?Word problem is a mathematical problem expressed entirely in words typically used as an educational tool.This word problem is interpreted into mathematical equation or expression.
Represent the amount Jon earn by j and Ron earn by r
j+r = 96000 equation 1
r = 8000+ 3j equation 2
from equation 1
r = 96000-j
substitute 96000-j for r in equation 2
96000-j = 8000 +3j
collect like terms
96000-8000 = 3j +j
88,000 = 4j
j = 88000/4
j = $22,000
from equation 1
22000+r = 96000
r = 96000-22000
r = 74,000
Therefore the amount Jon and Ron earn are $22,000 and $ 74,000 respectively.
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What is JL if KM=6?
Not really much context but that’s the whole question
when running a line, in a right-triangle, from the 90° angle perpendicular to its opposite side, we will end up with three similar triangles, one Small, one Medium and a containing Large one. Check the picture below.
[tex]\cfrac{x}{6}=\cfrac{6}{8}\implies \cfrac{x}{6}=\cfrac{3}{4}\implies x=\cfrac{18}{4}\implies x=\cfrac{9}{2} \\\\[-0.35em] ~\dotfill\\\\ 8+x\implies 8+\cfrac{9}{2}\implies \cfrac{25}{2}\implies 12\frac{1}{2}=JL[/tex]
Step-by-step explanation:
geometric mean theorem :
the height of a right-angled triangle to the Hypotenuse is the square root of the product of the parts of the Hypotenuse (as the height splits the Hypotenuse into 2 parts : JM and ML).
JL = JM + ML
in short
KM = sqrt(JM × ML)
6 = sqrt(8 × ML)
36 = 8 × ML
ML = 36/8 = 9/2 = 4.5
so,
JL = JM + ML = 8 + 4.5 = 12.5
Estimate the exact maximum in the exact minimum
The estimations for the given function are:
maximum ---> y ≈ 120minimum ---> y ≈ -175How to identify the maximum and minimum?For a function y = f(x) we define the maximum as the value of f(c) such that:
f(c) ≥ f(x) for any value of x.
And the minimum as:
f(k) ≤ f(x) for any value of x.
Usin the graph it is easier, just select the value at the top for the maximum and the value at the bottom for the minimum, we can see that:
maximum ---> y ≈ 120
minimum ---> y ≈ -175
Remember, these are estimations.
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Determine each ratio as a decimal to four places, then find the angle to the nearest whole number
The ratio as decimal is sin C = AB/BC = 8/17 = 0.4706. cos C = AC/BC = 15/17 = 0.8824 tan B = AB/AC = 8/15 = 0.5333. tan C = AB/AC = 8/15 = 0.5333. cos B = BC/AC = 17/15 = 1.1333. sin B = AC/BC = 15/17 = 0.8824.
What is unit circle?The origin (0, 0) of a coordinate plane serves as the center of the unit circle, which has a radius of 1. It is used in trigonometry to provide the values of trigonometric functions for angles of any measure, including sine, cosine, and tangent. The x-coordinate and y-coordinate of each point on the unit circle correspond to the cosine and sine values, respectively, for that point's specific angle measure. The unit circle is a popular visual tool for teaching students about the characteristics and behaviour of trigonometric functions.
Using the right triangle we have:
sin C = opposite/hypotenuse = AB/BC = 8/17 = 0.4706
cos C = adjacent/hypotenuse = AC/BC = 15/17 = 0.8824
tan B = opposite/adjacent = AB/AC = 8/15 = 0.5333
tan C = opposite/adjacent = AB/AC = 8/15 = 0.5333
cos B = adjacent/hypotenuse = BC/AC = 17/15 = 1.1333
sin B = opposite/hypotenuse = AC/BC = 15/17 = 0.8824
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My folks really want me to succeed in class and gave me the goal of getting an 80. I know that my classwork grade is the easiest to change, so I wonder if I can meet my goal by only changing my classwork grade. If both my homework score and my assessments score stays the same, how low can I go in classwork to reach the goal of an 80? Show all work.
My assessments grade: 91.5%
My classwork grade: 100%
My homework grade: 97.2%
Grading System:
Assessments are worth 40%
Classwork is worth 40%
Homework is worth 20%
Therefore, if your percentage test scores and homework grades remain the same, you can submit classwork with a grade as low as 71.4% and still receive an overall grade of 80%.
Describe percentages.In statistics, a percentage is a figure or an integer that is expressed as a fraction of 100. Additionally, the words "pct.," "pct," but also "pc" are rarely used. The "%" symbol, however, is commonly used to denote it. There are no dimensions; the percentage total is flat. Percentages are really just numbers because the numerator is 100. To indicate that a number is a percentage, either the percent character (%) or the text "percent" must appear before it.
Here,
Using the following formula, we can determine how little classwork you need to complete to receive an overall score of 80%:
Tests account for 40% of the final grade, classwork for 40%, and homework for 20%.
=> 80% = (91.5%) x (40%) + (40%) for classwork + (97.2%) x (20%)
When the numbers are multiplied by the corresponding weights:
=> (0.4 times classwork) + (0.32) + (0.1944) = 0.8
Simplifying:
=> 0.8 - 0.32 - 0.1944 = 0.4 x Classwork
=> 4. times classwork equals 0.2856
=> multiplying by 0.4
=> Work in class = 0.714
Therefore, if your test scores and homework grades remain the same, you can submit classwork with a grade as low as 71.4% and still receive an overall grade of 80%.
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Ashley measured the total snow in her yard every 30 minutes after a snowstorm started. The graph below shows her findings. Using the points (1,6) and (3, 9) which equation of the line best fits this data shown? Total Snow (inches) 10 Hours
The equation of the line of best fit is given as follows:
y = 1.5x + 4.5.
How to define a linear function?The slope-intercept representation of a linear function is given by the equation presented as follows:
y = mx + b
The coefficients of the function and their meaning are described as follows:
m is the slope of the function, representing the change in the output variable y when the input variable x is increased by one.b is the y-intercept of the function, which is the initial value of the function, i.e., the numeric value of the function when the input variable x assumes a value of 0. On a graph, it is the value of y when the graph of the function crosses tbe y-axis.Two points on the line for this problem are given as follows:
(1,6) and (3,9).
When x increases by 2, y increases by 3, hence the slope m of the line is given as follows:
m = 3/2
m = 1.5.
Hence:
y = 1.5x + b.
When x = 3, y = 9, hence the intercept b of the line is obtained as follows:
9 = 1.5(3) + b
b = 9 - 4.5
b = 4.5.
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The area of a square whose sides are (x+8)cm is 64cm², then what is x?
Answer:
Step-by-step explanation:
area of square=side ×side
we have, side=x+8
also we have area of square=64cm²
∴ (x+8)cm×(x+8)cm=64cm²
⇒x²+16x+64=64 ∵( a+b )²=a²+b²+2ab
⇒x²+16x=0
⇒x(x+16)=0
∴x=0 or x=-16
what is this?????????????????????????????
Find the 8th term of 27,9,3,1
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HELP A construction company takes 1 7/8 hours to remove 2 3/4 of dirt what is the hit rate metrics ton per hour
Answer: To calculate the hit rate metric in tons per hour, we need to first calculate how many tons of dirt the construction company can remove in one hour.
To do this, we'll convert the given time and amount of dirt into a rate of dirt removal in tons per hour:
The company takes 1 7/8 hours to remove 2 3/4 tons of dirt
We can convert 1 7/8 hours to an improper fraction: 15/8 hours
We can convert 2 3/4 tons to an improper fraction: 11/4 tons
We can calculate the rate of dirt removal as the amount of dirt divided by the time: (11/4 tons) / (15/8 hours) = (11/4) ÷ (15/8) = (11/4) x (8/15) = 22/15 tons per hour
Therefore, the construction company has a hit rate metric of 22/15 tons per hour, which simplifies to 1.47 tons per hour (rounded to two decimal places).
Step-by-step explanation: