The probability that extra unleaded gas was requested is 35%.
To find the probability that the next customer requested extra unleaded gas, we need to first find the total probability that any customer requests extra unleaded gas.
Since 35% of customers request extra unleaded gas, the probability that a customer requests it is 35%. Of those customers, 30% fill their tanks, so the probability that a customer requesting extra unleaded gas fills their tank is 30%.
Therefore, the probability that a customer requesting extra unleaded gas fills their tank is (35%) * (30%) = 0.105, or about 10.5%.
This is the probability that the next customer requested extra unleaded gas and fills their tank. To find the probability that the next customer simply requested extra unleaded gas, regardless of whether they fill their tank or not, we need to add the probabilities of them requesting extra unleaded gas and either filling or not filling their tank.
The probability that the next customer requested extra unleaded gas and filled their tank is 0.105, as we calculated above. The probability that the next customer requested extra unleaded gas and did not fill their tank is (35%) * (70%) = 0.245, or about 24.5%.
To find the total probability that the next customer requested extra unleaded gas, we need to add these two probabilities: 0.105 + 0.245 = 0.35, or 35%. This is the probability that the next customer requested extra unleaded gas.
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r(x) = x^2 + 5x + 4 write r(x) in factored form. I would like an explanation as to how you get the answer please!
Answer: (x+1)(x+4)
Step-by-step explanation:
Step 1: Use the sum-product pattern
x^2 + 5x + 4
x^2 + 4x + x + 4
Step 2: Common factor from the two pairs
x(x+4) + x+4
Step 3: Rewrite in factored form
(x+1)(x+4)
f(x) = x²+x-6
g(x) = 4x +9
Find: g(f(x))
The value of the function g(f(x))=4x²+4x-15 if f(x) = x²+x-6
g(x) = 4x +9.
What is meant by a function?An exact one of each element of Y is assigned to each element of X via a mathematical function from a set X to a set Y. The sets X and Y are denoted by the terms "domain" and "codomain," respectively.
The fundamental concept of functions was the connection between fluctuating quantities and other variables. One illustration of this is the impact of time on a planet's position. Beginning at the end of the 17th century and continuing until the 19th century, the concept was developed using the infinitesimal calculus.
Given,
f(x) = x²+x-6
g(x) = 4x +9
f(g(x))=f(4x+9)
g(f(x))=4(x²+x-6)+9
g(f(x))=4x²+4x-24+9
g(f(x))=4x²+4x-15
Therefore, the value of the function g(f(x))=4x²+4x-15 if f(x) = x²+x-6
g(x) = 4x +9.
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Tires A mechanic checked the tire pressures on each car that he worked on
for one week. The random variable x represents the number of tires that
were underinflated.
0
P(x) 0.30
1
2
0.25 0.25
3
0.15
4
0.05
The expected value for the given problem is E(x) = 1.4.
What is expected value?
The expected value is a generalization of the weighted average in probability theory. Informally, the expected value is the arithmetic mean of a significant number of outcomes of a random variable that were independently chosen.
A projected average value for an investment at some point in the future is known as the expected value (EV).
Investors use expected value to gauge an investment's merit, frequently in relation to how risky the investment is.
The formula for to find the expected value is given as,
E ( X ) = μ = ∑ x P ( x ) .
E(x) = 0*0.30 + 1*0.25 + 2*0.25 + 3*0.15 + 4*0.05
E(x) = 1.4
Hence, the expected value for the given problem is E(x) = 1.4.
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Tell whether the point (13, 17) is a solution to the system of linear equations?
y = -x + 30
y = x + 6
yes
no
Answer:
No
Step-by-step explanation:
When the 2 equations are graphed the point (13, 17) is not
a solution to the system of linear equations.
So the answer is no.
If you want to look for the solution**- the solution to the equation is (12, 18)
What is the distance between points m and n? meters
Answer: 9.8
Step-by-step explanation:
Which equation is equivalent to the quadratic equation x^2− 8x +19 = 0 where k represents the absolute value of the maximum value of the function? options:A (x-4)^2+k=0 B:(x-4)^2-k=0 C:(x+4)^2+k=0 D:(x+4)^2-k=0
The equation that is equivalent to quadratic equation x^ 2-8x+19=0 is
(x-4)^ 2+k = 0 using quadratic equation properties .
What is quadratic equation ?
A quadratic equation is a second order equation written as ax2 + bx + c = 0 where a, b, and c are coefficients of real numbers and a ≠ 0.
Properties of graph of quadratic equation :
1. The shape of curve y = f(x) is a parabola.
2. If a>0, the parabola opens upwards.
3. If a<0, the parabola opens downwards.
4.The coordinates of vertex of parabola in all these cases is
(-b/2a , -D/4a).
The given equation is x^ 2-8x+19=0
a = 1,
b = -8,
c = 19.
As a>0, 2nd property is correct i.e. no maximum value , only minimum value can be find that will be at vertex.
So, the vertex = (4,3)
The minimum value = 3 at 4.
So, the value of k = 3,
Given equation can be written as x^ 2-8x+16+3 = 0.
= (x-4)^ 2 +3 = 0.
The option A is correct.
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For what values of x, y, and z is this a parallelogram?
The values of x = 19.5, y= 17, and z=30.6 is not valid for the parallelogram.
What are the Properties of Angles of a Parallelogram?
A parallelogram is a quadrilateral with equal and parallel opposite sides. There are some special properties of a parallelogram that make it different from the other quadrilaterals.
The opposite angles of a parallelogram are congruent (equal). All the angles of a parallelogram add up to 360°. All the respective consecutive angles are supplementary.The consecutive angles are supplementary then,
5y + 7y - 24 = 180
12y = 180 + 24
12y = 204
y = 204/12
y = 17
The opposite angles of a parallelogram are congruent (equal) then,
5y = 4x + 7
5(17) = 4x + 7
85 = 4x + 7
85 -7 = 4x
4x = 78
x = 78/4 = 19.5
x = 19.5
the consecutive angles are supplementary, then
4x + 7 + 3z = 180
4(19.5) + 7 + 3z = 180
78 + 7 + 3z = 180
85 + 3z = 180
3z = 180 - 88
3z = 92
z = 92/3
z = 30.6
All the angles of a parallelogram add up to 360°, then:
4x + 7 + 3z + 5y +7y - 24 = 360
To check is this a parallelogram? put the values of x, y, and z in the above equation:
4(19.5) + 7 + 3(30.6) + 5(17) +7(17) - 24 = 360
356.8 ≠ 360
hence, the values of x = 19.5, y= 17, and z=30.6 is not valid for the parallelogram.
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Sonny has 2x + 3 dollars. Allan has 6x + 4 dollars. How much money did Sonny have if they both had $407 all together?
Answer:
$103
Step-by-step explanation:
In order to determine how much money Sonny has, we need to write a mathematical equation to solve for x. We know how much money Sonny and Allan each have in terms of x, and we can add the two expressions together to equal a total amount of $407. This will be represented and simplified as follows:
2x + 3 + 6x + 4 = 4078x + 7 = 407Now we can solve the equation for x.
8x = 400x = 50We know that x is equal to 50, so we can plug it back into Sonny's expression to find out how much money she has.
2(50) + 3 = 100 + 3 = 103Sonny has $103.We can check our work by solving for the amount of money Allan has and then adding up the two amounts to make sure the total is $407.
6(50) + 4 = 300 + 4 = 304CHECK: $103 + $304 = $407(-20, 12)
(17, 2)
(-11, 8)
(17, 8)
(11, 2)
Is this relation a function?
Answer:
No because x-coordinate 17 appears twice.
Step-by-step explanation:
In a function, no two ordered pairs can have the same x-coordinate.
Here, points (17, 2) and (17, 8) have 17 as the x-coordinate. Since the same x-coordinate, 17, is used more than once, this relation is not a function.
A school is arranging a field trip to the zoo. The school spends 546.53 dollars on passes for 40 students and 3 teachers. The school also spends 351.60 dollars on lunch for just the students. How much money was spent on a pass and lunch for each student?
There are $21.5 money was spent on a pass and lunch for each student.
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that:
The amount spent by school on pass of 40 students and 3 teachers = $546.53
And, the amount spent for the lunch only for students = $351.60
Now,
The money spent for pass of 43 person = $546.53
Then, The amount of pass for each person = 546.53/43
= $12.71
Since, there are 40 student then amount of lunch for each students = ⇒ 351.60/40
⇒ $8.79
Therefore, amount of pass and lunch for each student = 12.71 + 8.79
= $21.5
Thus, $21.5 is the required answer.
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Rufus has collected 100 pounds of aluminum cans to recycle. He plans to collect an additional 25 pounds each week. In how many weeks will Rufus have a total of 400 pounds of cans?
Answer: 12
Step-by-step explanation:
how to find the standard deviate and variance of a discrete random variable in ap stats organic chem tutor
Calculation the variance and standard deviation of the discrete random variable is given by σ² = [tex]\frac{\sum\limits^n_1{(x_{i}-\bar{x}) } \,}{n-1}[/tex] and standard deviation is the square root of Variance 'σ' = [tex]\sqrt{\frac{\sum\limits^n_1{(x_{i}-\bar{x}) } \,}{n-1}}[/tex].
As given in the question,
Variance is used to represent the dispersion of the values in the data from the calculated mean.[tex]( x_{i} - \bar{x})[/tex] represent the dispersion of the given data values from the mean.Variance is given by σ² = [tex]\frac{\sum\limits^n_1{(x_{i}-\bar{x}) } \,}{n-1}[/tex] Standard deviation is the square root of the variance it represents the amount of dispersion of all the given data values.Standard deviation is given by 'σ' = [tex]\sqrt{\frac{\sum\limits^n_1{(x_{i}-\bar{x}) } \,}{n-1}}[/tex].Therefore , the variance and standard deviation of the discrete random variable is calculated with the help of the following formulas:
Variance 'σ²' = [tex]\frac{\sum\limits^n_1{(x_{i}-\bar{x}) } \,}{n-1}[/tex] and standard deviation 'σ' = [tex]\sqrt{\frac{\sum\limits^n_1{(x_{i}-\bar{x}) } \,}{n-1}}[/tex].
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Determine the perimeter of the right triangle shown. Round your final answer to the nearest whole number, if necessary.
Answers: 7 units
14 units
25 units
26 units
answer : 26
steps
get hypotenuse
a² + b² = c²
7² + 8² = c²
49 + 64 = c²
113 = c²
square root of c is √113 which 10.63
7 + 8 + 10.63 = 25.63
In a box of chocolates, of the chocolates are white chocolate, are milk
chocolate, and the rest are dark chocolate.
What fraction of the chocolates are dark chocolate?
......................................................................
HELP PLEASEEEE ASAP
A small publishing company is planning to publish a new book. The production costs will include one-time fixed costs (such as editing) and variable costs (such as printing). The one-time fixed costs will total $29,521. The variable costs will be $12 per book. The publisher will sell the finished product to bookstores at a price of $25.25 per book. How many books must the publisher produce and sell so that the production costs will equal the money from sales?
Answer:
2,228
Step-by-step explanation:
Each unit will make 13.25 in profit before incorporating the one time cost. This means that 29,521/13.25= the amount needed to break even.
Given the side measures, which of the following could form a right triangle?
A. 61 m, 60 m, 11 m
B. 24 in, 34 in, 28 in
C. 55 ft, 45 ft, 35 ft
D. 48 cm, 46 cm, 15 cm
The side measures that could form a right triangle are B (24 in, 34 in, 28 in) and C (55 ft, 45 ft, 35 ft).
What is the right triangle is triangle?
A right triangle is a triangle in which one angle measures 90 degrees. The sides of a right triangle can be used to determine if a triangle is a right triangle using the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
Using this information, we can determine which of the given sets of side measures could form a right triangle:
A. 61 m, 60 m, 11 m: We can use the Pythagorean theorem to see if these sides could form a right triangle. We'll let the hypotenuse be the side with a length of 61 m, and the other two sides are the ones with lengths of 60 m and 11 m. Plugging these values into the Pythagorean theorem, we get:
(61 m)² = (60 m)² + (11 m)²
61² = 60² + 11²
61² ≠ 60² + 11²
Since the left side does not equal the right side, these sides cannot form a right triangle.
B. 24 in, 34 in, 28 in: Using the Pythagorean theorem, we can see that these sides could form a right triangle:
(34 in)² = (24 in)² + (28 in)²
34² = 24² + 28²
34² = 24² + 28²
The left side equals the right side, so these sides could form a right triangle.
C. 55 ft, 45 ft, 35 ft: Using the Pythagorean theorem, we can see that these sides could form a right triangle:
(55 ft)² = (45 ft)² + (35 ft)²
55² = 45² + 35²
55² = 45² + 35²
The left side equals the right side, so these sides could form a right triangle.
D. 48 cm, 46 cm, 15 cm: Using the Pythagorean theorem, we can see that these sides could not form a right triangle:
(48 cm)² ≠ (46 cm)² + (15 cm)²
48² ≠ 46² + 15²
Since the left side does not equal the right side, these sides cannot form a right triangle.
Hence, The side measures that could form a right triangle are B (24 in, 34 in, 28 in) and C (55 ft, 45 ft, 35 ft).
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Please hurry and help!
Graph the following linear equation using the intercepts.
\displaystyle -10 x-12 y=-60−10x−12y=−60
The x−intercept is 6 and the y-intercept is 5.
What is an equation of a line?
In high school algebra, "the equation of a line" is a crucial concept. This refers to an equation in the (x,y) plane with a line as its solution set. The "slope-intercept" form is the most widely used form in algebra. y = mx + b. In essence, x is used as a parameter in this formula, and y is written as a function of x: y = f(x) = mx+b.
Here, we have
The given equation of a line is:
−10x − 12y = −60
10x + 12y = 60
x/6 = y/5 = 1
Hence, the x−intercept is 6 and the y-intercept is 5.
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Write a linear function f with the values.
The equation of the line is f(X)=(-1/6)x—(19/6)
What is equation?
In arithmetic, an equation could be a formula that expresses the equality of 2 expressions, by connecting them with the sign =.
Main body:
first linear functions have their general form as y= mx + c, where y belongs to the range and X belongs to the domain, m is the slope, and c is the y-intercept.
So using f(x) =y
Given that f(—5)=-4 , X=—5 and y=-4, hence by substituting into the general eqn y= mx+c, You get
-4= -5m+c ------(1)
Also given that f(1)=—3, X=1 and y=—3, hence by substituting into the general eqn y= mx+c, You get
-3= m+c --—-(2)
Solve equation (1) and (2), simultaneously to find the value of m and c. After which you will substitute into y=mx+c or f(X)=mx+c to get your f(X).
Note: you will get m=—1/6 and c=-19/6, from the simultaneous equations.
Hence f(X)=(-1/6)x—(19/6) and correct option is D.
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A police officer is estimating the distance from one side of a street to the other. The actual distance is 13.4 m. The police officer’s estimate is 14 m. Find the absolute error and the percent error of the police officer’s estimate.
PLEASE HELP
The absolute error and the percent error of the police officer’s estimate will be 4.29%.
What is the percentage?The amount of any product is given as though it was a proportion of a hundred. The ratio can be expressed as a quarter of 100. The phrase % translates to one hundred percent. It is symbolized by the character '%'.
The percentage is given as,
Percentage (P) = [Final value - Initial value] / Initial value x 100
A cop is assessing the separation from one side of a road to the next. The genuine distance is 13.4 m. The cop's gauge is 14 m.
The absolute error and the percent error of the police officer’s estimate are calculated as,
%error = [(14 - 13.4) / 14] x 100
%error = (0.60 / 14) x 100
%error = 4.29%
The outright mistake and the percent blunder of the cop's gauge will be 4.29%.
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7. Use the Division Property of Equality to write an equation that is
equivalent to 5x = 14.
Answer: x = 14/5 or x = 2.8
Step-by-step explanation:
Step 1: Divide both sides of the equation by five: a common nonzero real number.
(5x)/5= 14/5
Step 2: Simplify
x = 14/5
Which of the following statements is correct for a triangle?
A. triangle can have two obtuse angles
B.The difference of two sides of a triangle is greater than any other side of the same triangle.
C.A triangle can have an obtuse angle and a right angle.
D.None of these
A quadratic function has roots at 2 and 4 and a vertex at (3, −2). What is the equation of the function in vertex form?
Answer:
Step-by-step explanation:
For which situation does one quantity change at a constant rate per unit interval relative to another quantity?
Responses
For every day that passes, a person drives 54 miles.
.
For every month that passes, a savings account earns interest at a rate of 1.5%
For every week that passes, a vine doubles in length 2 times a week.
.
For every year that passes, a population of insects increases by 6%
Answer:
(a) For every day that passes, a person drives 54 miles
Step-by-step explanation:
You want to know the situation in which one quantity changes relative to another at a constant rate.
DrivingThe rate of change is described as 54 miles for each day. This is a constant rate of change. Miles relative to days are described by a linear function.
SavingsWe assume the description means that the balance in the savings account increases by 1.5% with each passing month. While this interest rate is a constant, the amount by which the balance changes each month is not constant. The balance relative to time is described by an exponential function.
VineIf the vine doubles in length twice a week, its length increases by 300% each week. As with savings, this growth rate is constant, but the amount of growth each week is not. The length of the vine is described by an exponential function.
PopulationAs with savings, this growth rate is constant, but the amount of increase each year is not. The population is described by an exponential function.
The situation with a constant rate of change is ...
For every day that passes, a person drives 54 miles.
__
Additional comment
When the quantity is graphed, the "rate of change" refers to the slope of the curve on the graph. The graph of an exponential growth function does not have a constant slope, but has a slope that increases exponentially.
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Please help if possible.
Answer:
$1020.00000$1020.15050$1020.18436$1020.19742$1020.20078Step-by-step explanation:
You want to find the effect of compounding 2% annual interest on $1000 at different intervals for a year. The intervals are ...
1 per year4 per year12 per year52 per year365 per yearCalculatorThe attached calculator display shows the result:
yearly: $1020.00000quarterly: $1020.15050monthly: $1020.18436weekly: $1020.19742daily: $1020.20078There were two candidate A and B conteting for the municipal corporation election in a town. The total number of voter in the town were 80,000. If 90% of the voter had voted and 60% of vote polled were cat in favour of A, find the number of vote received by B
There were two candidate A and B contesting for the municipal corporation election in a town. The total number of voter in the town were 80,000. If 90% of the voter had voted and 60% of vote polled were cat in favour of A, 28,800 the number of vote received by B.
What is municipal corporation election?A state-incorporated city, town, village, or county that has the power to manage local governmental matters, such as creating a police force. A municipal corporation is established by a state's legislature, which also determines its lifespan, privileges, and powers. likewise known as a municipality.
A local governing body, such as cities, counties, towns, townships, charter townships, villages, and boroughs, is referred to legally as a "municipal corporation." Municipally-owned companies can also be referred to as this
Regulation of building construction and land usage. Town planning is included in urban planning. preparing for social and economic progress. water supply for residential, commercial, and industrial uses.
Given that,
Total number voters = 80,000
Total number of votes polled = 90%
Thus,
= (90/100) × 80,000
= 72,000
So, total percent of votes received by B if A gets 60% of polled votes.
= 100% - 60%
= 40%
Hence, total number of votes received by B
= (40/100) × 72,000
= 28,800
Therefore, the number of votes received by B, out of total votes polled is 28,800 votes.
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Part F: Order the integers from least to greatest. 12, -6, 20, -47, -11
The integers are -47, -11, -6, 12, 20 in order of least to greatest.
Explain about the integers?A whole number that can be positive, negative, or zero is called an integer. It is not a fraction. -5, 1, 5, 8, 97, and 3, 043 are some examples of integers. 1.43, 1 3/4, 3.14, and other numbers are examples of non-integer numbers.
Positive numbers, negative numbers, and zero make up integers. Thus, integers include 0 through 3, as well as -1, -2, and -3. No further parts, such as fractions or decimals, are allowed in integers. Therefore, fractional and decimal numbers like 3 1/2 and -7.5 are NOT integers.
Integer is derived from the Latin integer, which means whole or untouched, from the prefix in (for "not") with tangere ("to touch"). The words "entire" and "integer" are both derived from the same root, which is the French word entire.
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Matthew Westhoven deposited $925 in a new regular savings account that earns 5.5% interest compounded semiannually for 1 year. What is the compound interest?
The compound interest received by Matthew Westhoven is $51.80
What is compound interest?The interest you earn on interest is known as compound interest. Simple math may be used to demonstrate this: if you have $100 and it generates 5% interest annually, you will have $105 at the end of the first year. You'll have $110.25 after the second year is over.
Given, the principal amount (P) = $925
Compound interest percentage (r) = 5.5% = 0.055
Time period (t) = 1
Since, it is semiannually compounded (n) = 2*t = 2
Amount (A) = P(1 + r/n)^nt
= 925(1 + 0.055/2)^2
= 925(1.0275)^2
= 925(1.056)
= 976.80
Thus, Interest amount (CI) = A - P
= $976.80 - $925
= $51.80
The compound interest received by Matthew Westhoven is $51.80
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By identifying the vertical asymptote, one can determine the denominator of this
function is
The denominator of function is -x/2 - 1 and vertical asymptote x = -2.
What is vertical asymptote?A vertical line that is not a part of the function's graph but serves as a guide is known as a vertical asymptote. Because it occurs at an x-value outside of the function's domain, the graph cannot cross it. There may be more than one vertical asymptote for a function.
Given graph
the function of graph is F(x) = [tex]2\frac{\left(-\frac{x}{2}\ +\ 1\right)}{\left(\frac{x^{2\ }}{4}-1\right)}[/tex] = 2(1- x/2)/(x²/4 - 1)
reducing the equation
F(x) = 2/(-x/2 - 1)
denominator is -x/2 - 1
for vertical asymptote -x/2 - 1 = 0
x = -2
Therefore for function is -x/2 - 1 and vertical asymptote at x = -2.
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Does 0.010110111011110... represent a
rational number or an irrational number?
Explain your reasoning.
Answer:
This is an irrational number.
Step-by-step explanation:
If you see the decimal, it has the values of 1 and 0, but are not constant.
If it were to be 0.010101010... it would be rational.
But this decimal does not look like that, so its irrational.
Hope this helps.
member c: works 7 hours per week at $7.25 per hour member d: works 9 hours per week at $6.35 per hour a. a and b b. a and c c. b and c d. b and d
Only member B and D will reach their goal.
Given;
Amount to be saved = $285
Total time to save money = 5 weeks
Now,
For member A:
Working hours = 8 per week
per hour earnings = $6.15
Therefore,
The total amount collected
= working hours per week × Total weeks × Earning per hour
= 8 × 5 × 6.15
= $246
For member B:
Working hours = 10 per week
per hour earnings = $5.85
Therefore,
The total amount collected
= working hours per week × Total weeks × Earning per hours
= 10 × 5 × 5.85
= $292.5
For member C:
Working hours = 7 per week
per hour earnings = $7.25
Therefore,
The total amount collected
= working hours per week × Total weeks × Earning per hours
= 7 × 5 × $7.25
= $253.75
For member D:
Working hours = 9 per week
per hour earnings = $6.35
Therefore,
The total amount collected
= working hours per week × Total weeks × Earning per hours
= 9 × 5 × $6.35
= $285.75
Since, the amount earned by member B and D is greater than the goal amount and the amount earned by member A and C is less than the goal amount
therefore,
Only member B and D will reach their goal
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To be able to go on the band trip, four band members each get a part-time job. Each person has 5 weeks in which to save his or her money. Analyze the four individual plans below and decide which of the four people will reach his or her goal of saving $285? Member A: Works 8 hours per week at $6.15 per hour Member B: Works 10 hours per week at $5.85 per hour Member C: Works 7 hours per week at $7.25 per hour Member D: Works 9 hours per week at $6.35 per hour
