its for 100 points please
Answer: The first choice.
Step-by-step explanation:
As you can see in the diagram, the line passes through the points[tex](x, y) = (4, -4)[/tex] and [tex](x, y) = (-4, 8)[/tex] . Thus, the slope of the line is [tex]\frac{8-(-4)}{-4-(4)} = \frac{12}{-8} = -\frac{3}{2}.[/tex] Thus, the correct answer is the first choice, as that line has a slope of [tex]-\frac64=-\frac32.[/tex]
Use a system of two equations in two variables, and d, to write a formula for the general term (the nth term) of the arithmetic sequence whose fourth term, a4, is 10 and whose sixth term, a6, is 18.
The formula for the nth term of the arithmetic sequence is an = 4n + 2
How to write a formula for the general term (the nth term) of the arithmetic sequence?Let d be the common difference of the arithmetic sequence, and let a1 be the first term. Then we have:
a4 = a1 + 3d = 10
a6 = a1 + 5d = 18
We can solve this system of equations to find a1 and d. Subtracting the first equation from the second, we get:
2d = 8
d = 4
Substituting this into either of the original equations, we get:
a1 + 12 = 18
a1 = 6.
So the arithmetic sequence is:
6, 10, 14, 18, ...
To find the nth term of this sequence, we can use the formula:
an = a1 + (n - 1)d
Substituting in the values of a1 and d, we get:
an = 6 + 4(n - 1)
Simplifying, we get:
an = 4n + 2
Therefore, the formula for the nth term of the arithmetic sequence whose fourth term is 10 and sixth term is 18 is:
an = 4n + 2
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A right triangle has sides 14 and 48. Use the Pythagorean Theorem to find the length of the hypotenuse.
Answer:
According to the Pythagorean Theorem, in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides. So we have:
c^2 = a^2 + b^2
where c is the length of the hypotenuse and a and b are the lengths of the other two sides.
Substituting the given values, we get:
c^2 = 14^2 + 48^2
c^2 = 196 + 2304
c^2 = 2500
Taking the square root of both sides, we get:
c = 50
Therefore, the length of the hypotenuse is 50 units.
50 Points! Multiple choice algebra question. Photo attached. Thank you!
g°f = -9 So, the correct answer is (B) -9.To find g°f, we need to first apply the function f to -3, and then apply the function g to the result.
what is function ?
In mathematics, a function is a relation between two sets, called the domain and the range, that assigns to each element of the domain exactly one element of the range.
In the given question,
To find g°f, we need to first apply the function f to -3, and then apply the function g to the result.
Step 1: Apply f to -3
f(x) = 3x + 7
f(-3) = 3(-3) + 7 = -2
Step 2: Apply g to the result of f(-3)
g(x) = 2x - 5
g(-2) = 2(-2) - 5 = -9
Therefore, g°f = -9.
So, the correct answer is (B) -9.
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The table shows several input and output values of a quadratic function f(x)
x f(x)
3.0 3.00
4.0 5.00
4.5 5.25
5.0 5.00
6.0 3.00
Which statements is tru about the function?
a) The maximum value of f(x) is 6
b) The maximum value of f(x) is 5.25
c) The zeroes of the function are 2 and 4
d) The zeroes of the function are 4 and 5
Answer:-by-step explanation:
the function has the x-intercept of (-2, 0)
the function has the y-intercept of (0, -8)
the function has the x-intercept of (4, 0)
a varies inverselv as b^3. If a =
3/2 when b = 2, find a
when b is 3
If a varies inversely as b³, the value of a when b=3 is 4/9.
Given that, a varies inversely as b³.
Here, a∝1/b³
a=k/b³
Substitute a=3/2 and b=2 in a=k/b³, we get
3/2 = k/2³
3/2 = k/8
3 = k/4
k = 12
Substitute k = 12 in a=k/b³, we get
a=12/b³
When b=3
a = 12/3³
a=12/27
a=4/9
Therefore, if a varies inversely as b³, the value of a when b=3 is 4/9.
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what is 5x-9 and 3x+9
Answer:
5x - 9 and 3x + 9 are two mathematical expressions. The first expression, 5x - 9, represents a value obtained by multiplying 5 by x and then subtracting 9. The second expression, 3x + 9, represents a value obtained by multiplying 3 by x and then adding 9. Both expressions can be simplified further or used in various mathematical operations depending on the context of the problem or equation in which they are being used.
Answer:-45 and -3
Step-by-step explanation:
What is the probability that either event will occur?
15
A
B
12 18
21
P(A or B)=P(A) + P(B) - P(A and B)
P(A or B) = [?]
Enter as a decimal rounded to the nearest hundredth.
Enter
The probability that either event will occur is given as follows:
P(A or B) = 0.83.
How to calculate a probability?A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.
The "or probability" is defined as follows:
P(A or B)=P(A) + P(B) - P(A and B).
From the Venn Diagram, the probabilities of each event are given as follows:
P(A) = 18/(18 + 12 + 6) = 0.5.P(B) = 12/(18 + 12 + 6) = 0.3333.P(A and B) = 0 -> no intersecton.Hence the or probability is given as follows:
P(A or B) = 0.5 + 0.3333 + 0
P(A or B) = 0.83. (rounded to the nearest hundredth).
Missing Information
The Venn diagram is given by the image presented at the end of the answer.
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Find the area ___m^2
Answer: 28.27m^2
Step-by-step explanation:
Area of a circle: [tex]A = \pi r^{2} \\[/tex]
Given the diameter of 6m, we can divide that by 2 to get the radius and plug that into the formula.
6/2 = 3m
[tex]A = \pi (3)^2\\A= 28.27m^{2}[/tex]
Angular speed describes how fast something is turning. Linear speed describes how far it travels while it is turning. Linear speed depends on the circumference of a circle (C = 27r) and the number of revolutions per minute. Vinyl records were not the same size. A 45 rpm record had a diameter of 7 inches, a 33+ a diameter of 12 inches, and a 78 had a diameter of 10 inches. a. If a fly landed on the outer edge of a 45 rpm record, how far would it travel in 1 minute? b. How far if it was perched on the outside edge of a 33 rpm record? c. How far if it was perched on the outside edge of a 78 rpm record?
a. On a 45 rpm record (7-inch diameter), the fly would travel 990 inches in 1 minute.
b. On a 33 rpm record (12-inch diameter), the fly would travel 1,245.6 inches in 1 minute.
c. On a 78 rpm record (10-inch diameter), the fly would travel 2,430 inches in 1 minute.
How to solveRadius of 45 rpm record = 3.5 inches (7/2)
Circumference = 2 * π * r = 2 * π * 3.5 ≈ 22 inches
Distance in 1 minute = Circumference * rpm = 22 * 45 = 990 inches
Thus, it can be seen that On a 45 rpm record (7-inch diameter), the fly would travel 990 inches in 1 minute.
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9x7x9x9x7x9 (I tried the answer 9^4 x 7^2 and it’s not correct
Answer:
321489
Step-by-step explanation:
Which of the following equations represents a quadratic function?
a. x=y^2-2y+4
b. y=3x^2-5x+9
c. y=-2x^2+16√x-64
d. -5x+3y=-4
The equation that represents a quadratic function is option b: [tex]y=3x^2-5x+9[/tex]
What is a quadratic function ?
A quadratic function is a function that can be written in the form of f(x) = [tex]ax^2 + bx + c[/tex] , where a, b, and c are constants, and a is not equal to 0. The graph of a quadratic function is a parabola, which can open upwards or downwards, depending on the sign of the coefficient a.
In option b, we can see that the equation is in the form of [tex]f(x) = 3x^2 - 5x + 9[/tex] , which is a quadratic function. The coefficient of [tex]x^2[/tex] is a non-zero constant (a=3), which means that the graph of this function is a parabola.
Option a is not a quadratic function, as it is in the form of [tex]x=y^2-2y+4[/tex], which is a quadratic equation in terms of y, but not in terms of x.
Option c is a little more complicated, as it contains a radical term. However, if we simplify it, we can see that it is also a quadratic function, in terms of x.
Option d is a linear equation, not a quadratic function, because it does not have an [tex]x^2[/tex] term.
Therefore, the quadratic function is [tex]y=3x^2-5x+9[/tex], option b.
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PLEASE I NEED HELP THIS DEPENDS ON WETHER I STAY IN MY SOFTBALL TEAM
Answer:
Circumference/Diameter = π
If the diameter is 2, then the circumference is 2π.
If the diameter is 6, then the circumference is 6π.
Please help me. Giving Brainliest to whoever answers ALL of them!!!
Answer:
First problem:
The correct pairs are 16 and 30, 26 and 38, and 22 and 34.
16 = 2 × 2 × 2 × 2, 30 = 2 × 3 = 5
26 = 2 × 13, 38 = 2 × 19
12 = 2 × 2 × 3, 28 = 2 × 2 × 7
22 = 2 × 11, 34 = 2 × 17
24 = 2 × 2 × 2 × 3,
32 = 2 × 2 × 2 × 2 × 2
gcf(16, 30) = gcf(26, 38) =
gcf(22, 34) = 2
gcf(12, 28) = 4
gcf(24, 32) = 8
Second problem:
f(x) = 3x - 5
f(2) = 3(2) - 5 = 6 - 5 = 1
f(3) = 3(3) - 5 = 9 - 5 = 4
f(4) = 3(4) - 5 = 12 - 5 = 7
f(5) = 3(5) - 5 = 15 - 5 = 10
Find the error. A student was finding the measure angle 5 in the figure below. She concluded that m angle 5=86
The answer is Option 2: The measure of angle 5 is corresponding to angle 1. Angle 1 is supplementary to 86. So, measure angle 1 = 94. Since corresponding angles are equal angle 5 = 94.
What is a supplementary angle?An angle that, when combined with another angle, creates a straight angle (measuring 180 degrees), is known as a supplementary angle. In other words, if the sum of the measurements of two angles is 180 degrees, they are supplementary. Contrarily, a complimentary angle is one that, when combined with another angle, creates a right angle (which has a 90-degree angle). In other words, if the sum of the measurements of two angles is 90 degrees, they are complimentary. A straight angle and a right angle are not the same thing, hence it is crucial to understand that one angle cannot be both supplementary and complimentary at the same time.
From the given figure we see that the measure of angle 5 is corresponding to angle 1. Angle 1 is supplementary to 86. So, measure angle 1 = 94. Since corresponding angles are equal angle 5 = 94.
Hence, option 2 is correct.
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The complete question is:
Find the surface area
Round to the nearest tenth
There are [tex]144 + 336 = 480[/tex] square units of surface area overall. The shape has a surface area of 480.0 square units, rounded to the closest tenth.
what is surface area ?The dimensions and shape of the object are taken into account while calculating surface area. The volume of water of a cube, for instance, can be computed by adding the areas of the all six of its equal-sized faces. The surface temperature of something like a sphere, while on the other hand, must be calculated using mathematical methods that take into consideration its radius. The concept of surface area is crucial to many branches of mathematics, science, & engineering.
given
The area of each of the two triangles is [tex](1/2) * 3 * 8 = 12[/tex] square units since each triangle has a base of 3 and a height of 8, respectively.
The trapezium features an 8-inch height, a 6-inch top base, a 12-inch bottom base, and a 10-inch slant height.
two rectangles, each measuring 72 square units: 144 square units (2 x 72)
Four trapezoidal sides, each with a surface area of 12 + 72 = 84 square units 336 square units (4 x 84)
There are [tex]144 + 336 = 480[/tex] square units of surface area overall. The shape has a surface area of 480.0 square units, rounded to the closest tenth.
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A sociologist polled a random sample of people and asked them their age and annual income. The two-way frequency table below shows the results.
Annual income vs. age group
Less than
$
50
,
000
$50,000dollar sign, 50, comma, 000 At least
$
50
,
000
$50,000dollar sign, 50, comma, 000 Total
Ages
44
4444 and under
148
148148
68
6868
216
216216
Ages
45
4545 and above
38
3838
94
9494
132
132132
Total
186
186186
162
162162
348
348348
Which of the following statements is true of those polled?
According to the information, we can infer that the correct sentences about the graph is A person with annual income of at least $50,000 is more likely to be 45 years old or above.
How to find the correct sentence?To find the correct sentence we have to analyze the information of the graph and read the options. Once we make this procedure, we can compare each sentence with the information of the graph to establish the correct one.
According to the information the correct option would be A person with annual income of at least $50,000 is more likely to be 45 years old or above (option C).
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On the SAT exam a total of 25 minutes is allotted for students to answer 20 math questions without the use of a calculator. A guidance counselor would like to know if the students in his school are prepared to complete this portion of the exam in the timeframe allotted. To investigate, the counselor selects a random sample of 35 students and administers this portion of the test. The students are instructed to turn in their test as soon as they have completed the questions. The mean amount of time taken by the students is 23.5 minutes with a standard deviation of 4.8 minutes. The counselor would like to know if the data provide convincing evidence that the true mean amount of time needed for all students of this school to complete this portion of the test is less than 25 minutes and therefore tests the hypotheses H0: μ = 25 versus Ha: μ < 25, where μ = the true mean amount of time needed by students at this school to complete this portion of the exam. The conditions for inference are met. What are the appropriate test statistic and P-value?
The P-value is between 0.025 and 0.05. and t = -1.85
On the SAT exam a total of 25 minutes is allotted for students to answer 20 math questions without the use of a calculator.
Therefore tests the hypotheses:
[tex]H_0[/tex] : μ = 25 versus Ha: μ < 25,
where μ = the true mean amount of time needed by students at this school to complete this portion of the exam.
The alternative hypothesis is:
[tex]H_1:\mu < 25[/tex]
The test statistic is given by:
[tex]t=\frac{x-\mu}{\frac{s}{\sqrt{n} } }[/tex]
The parameters are:
'x' is the sample mean. [tex]\mu[/tex] is the value tested at the null hypothesis.s is the standard deviation of the sample.n is the sample size.the values of the parameters are:
x = 23.5 , [tex]\mu=25[/tex] , s = 4.8, n = 35
Plug all the values in above formula of t- statistic is:
[tex]t = \frac{23.5-25}{\frac{4.8}{\sqrt{35} } }[/tex]
t = -1.85
Using a t-distribution , with a left-tailed test, as we are testing if the mean is less than a value and 35 - 1 = 34 df, the p-value is of 0.0365.
t = –1.85; the P-value is between 0.025 and 0.05.
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An Internet provider is trying to gain advertising deals and claims that the mean time online per day is than minutes. You are asked to test this claim.
(a) How would you write the null and alternative hypotheses if you represent the Internet provider and want to support the claim?
(b) How would you write the null and alternative hypotheses if you represent a competing advertiser and want to reject the claim?
a. Null hypothesis (H0): The mean time online per day is 30 minutes or more.
Alternative hypothesis (Ha): The mean time online per day is less than or equal to 30 minutes.
b. Null hypothesis (H0): The mean time online per day is less than or equal to 30 minutes.
Alternative hypothesis (Ha): The mean time online per day is more than 30 minutes.
What is null hypothesis?A type of statistical hypothesis known as a "null hypothesis" makes the case that a given set of observations does not have any statistical significance.
A type of statistical hypothesis known as a "null hypothesis" makes the case that a given set of observations does not have any statistical significance.
a) The following is how you can write the null and alternative hypotheses if you are the Internet service provider and want to back up your claim that people spend less than 30 minutes online on average per day:
Null hypothesis (H0): The mean time online per day is 30 minutes or more.
Alternative hypothesis (Ha): The mean time online per day is less than or equal to 30 minutes.
(b)If you address a contending promoter and need to dismiss the case that the interim online each day is not exactly or equivalent to 30 minutes, the invalid and elective speculations can be composed as follows:
Null hypothesis (H0): The mean time online per day is less than or equal to 30 minutes.
Alternative hypothesis (Ha): The mean time online per day is more than 30 minutes.
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Two numbers to have a hcf of 4 one of the numbers is between 10 and 20 and the other is between 20 and 40 what are the two numbers find all possible answers
To find all possible answers, we can start by listing all the numbers between 10 and 20, and all the numbers between 20 and 40, and then check which pairs of numbers have a highest common factor of 4.
Numbers between 10 and 20: 10, 11, 12, 13, 14, 15, 16, 17, 18, 19
Numbers between 20 and 40: 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40
To have a highest common factor of 4, both numbers must be divisible by 4. Therefore, we can eliminate any numbers in these lists that are not divisible by 4.
Numbers between 10 and 20 that are divisible by 4: 12, 16, 20
Numbers between 20 and 40 that are divisible by 4: 20, 24, 28, 32, 36, 40
Now we can check which pairs of these numbers have a highest common factor of 4.
some possible answers are:
12 and 20
12 and 24
12 and 28
12 and 32
12 and 40
16 and 20
16 and 24
16 and 28
16 and 32
16 and 40
20 and 24
20 and 28
20 and 32
20 and 36
20 and 40
there are more answers, all you have to do is to pair 2 numbers.
if you do not want to include 20 and 40 make sure to not chose them.
Hope this could help.
The mean life of a new smart LED bulb is 20,000 running hours with a standard deviation is 2,250 hours. The data is normally distributed. If a home improvement store sold 18,000 of these light bulbs in the first year of production, how many light bulbs would you expect to last longer than 22,250 hours?
Answer: The expected number of bulbs that would last longer than 22,250 hours is approximately 2,857.
Step-by-step explanation:
To solve this problem, we can start by finding the z-score for 22,250 using the formula:z = (x - mean) / standard deviationz = (22,250 - 20,000) / 2,250 = 1Next, we need to find the proportion of bulbs lasting longer than 22,250. We can look up this proportion in a standard normal distribution table or use a calculator, which gives us a probability of 0.1587.Finally, we can use this probability to find the expected number of bulbs that will last longer than 22,250:Expected number of bulbs = probability * total number of bulbs sold Expected number of bulbs = 0.1587 * 18,000 = 2,857Therefore, we can expect that approximately 2,857 of the 18,000 bulbs sold will last longer than 22,250 running hours.
Answer:
the afternoon is the right one
Is (3, 5) a solution to this system of equations?
y = 5
Y= -5/3x+10
yes
E
Answer:
no
Step-by-step explanation:
-5/3x+10=5
-5/3x=5-10=-5
3x=-5/-5=1
=>x=1/3
Hassim's Fireworks & Cycles had free cash flow of R129 550 this year, and expects this to grow by 3% each year for the foreseeable future. The company has a weighted average cost of capital of 8%. What is the value of the company today? 01R 119 186 O2 R 139 914 4. R1 271 945 R2 668 730
Answer:
To calculate the value of Hassim's Fireworks & Cycles today, we can use the formula for the present value of a growing perpetuity:
PV = FCF / (r - g)
where PV is the present value, FCF is the free cash flow, r is the weighted average cost of capital, and g is the growth rate.
Substituting the given values, we get:
PV = 129550 / (0.08 - 0.03)
PV = 2591000
Therefore, the value of Hassim's Fireworks & Cycles today is R2,591,000.
Find the mean, median and mode of the data set. If there is no mode, enter the words "no mode". 72, 65, 68, 68, 73, 45, 68, 71
Answer:
Step-by-step explanation:
72+65+68+68+73+45+68+71 = 530
530/8 because there are 8 numbers
mean: 66.25
for the median, you line the numbers up from small to big and find the center number. But since there are 2 of them (68 and 68) , add 68+68 and divide by 2 which is still 68!
45,65,68,68,68,71,72,73
the mode is 68 because it is the most occurring number.
ok yea
A grain silo can be modeled as a right cylinder topped with a hemisphere. Find the
volume of the silo if it has a height of 31 m and a radius of 5 m. Round your answer to
the nearest tenth if necessary. (Note: diagram is not drawn to scale.)
I hope this helps you.
Please help with this question A circle is separated into eight sectors of equal area. These eight sectors are arranged to form a shape similar to a parallelogram.
The area of the circle (πr2
) is equal to the area of the parallelogram (bh
).
Select from the drop-down lists to correctly complete each sentence.
The height of the parallelogram is equal to the
of the circle. The base of the parallelogram is equal to
of the circle. Therefore, the area of the circle (πr2
) is equal to the
, and the circumference of the circle is equal to
.
The height of the parallelogram is equal to the diameter of the circle. The base of the parallelogram is equal to half of the circumference of the circle. Therefore, the area of the circle (πr2) is equal to bh and the circumference of the circle is equal to 2b.
The height of the parallelogram is equal to the diameter of the circle. This can be seen because each of the eight sectors has the same area, so they are all the same size. If we place them next to each other in the shape of a parallelogram, we can see that the height of the parallelogram is equal to the diameter of the circle.
The base of the parallelogram is equal to half of the circumference of the circle. This is because the circumference of the circle is divided equally into eight sectors, and the base of the parallelogram is formed by placing two adjacent sectors together. Therefore, the base of the parallelogram is equal to the arc length of one sector plus the arc length of its adjacent sector. Each sector is 1/8th of the circle, so the arc length of one sector is 1/8th of the circumference. Adding the arc lengths of two adjacent sectors gives 1/4th of the circumference, which is half of the base of the parallelogram.
Therefore, the area of the circle (πr2) is equal to the area of the parallelogram (bh), where h is the diameter of the circle and b is half of the circumference of the circle. Additionally, the circumference of the circle is equal to the base of the parallelogram multiplied by 2.
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I really need help on question (if you solve your very smart ) . If answers correct I'll rate 5 stars , a thanks and maybe even brainy.
Billy has x pounds. Liam has twice as much money as billy. Nicola has 3 times as much money as liam. The total amount of money they have is £180 pounds.
A) form an expression in terms of x and find out how much money they have.
Answer:
Billy has £20, Liam has £40, and Nicola has £120. The total amount of money they have is £180, as given in the problem.
Step-by-step explanation:
Let's start by defining the variables:
Billy's money: x pounds
Liam's money: 2x pounds (twice as much as Billy)
Nicola's money: 3(2x) = 6x pounds (three times as much as Liam)
The total amount of money they have is £180, so we can write an equation:
x + 2x + 6x = 180
Simplifying the left side of the equation:
9x = 180
Solving for x:
x = 20
Now we can find out how much money each person has:
Billy: x = 20 pounds
Liam: 2x = 2(20) = 40 pounds
Nicola: 6x = 6(20) = 120 pounds
Given A and b to the right, write the augmented matrix for the linear system that corresponds to the matrix equation Axequals
b.
Then solve the system and write the solution as a vector.
Aequals
left bracket Start 3 By 3 Matrix 1st Row 1st Column 1 2nd Column 2 3rd Column negative 3 2nd Row 1st Column negative 3 2nd Column negative 3 3rd Column 3 3rd Row 1st Column 4 2nd Column 2 3rd Column 4 EndMatrix right bracket,
bequals
left bracket Start 3 By 1 Matrix 1st Row 1st Column negative 7 2nd Row 1st Column 15 3rd Row 1st Column negative 4 EndMatrix right bracket
Question content area bottom
Part 1
Write the augmented matrix for the linear system that corresponds to the matrix equation Upper A Bold x equals Bold b
.
The system has the following solution: [tex]x_1=-4,\ x_2=3,\ x_3=1[/tex]. The vector xequals can be used to represent the answer.
What is equation?A statement in mathematics demonstrating the equality of two expressions is called an equation. Two phrases with the same value are normally separated by the equals sign (=). Finding the area of a circle and predicting planetary motion are only two examples of the many practical issues that equations are used to address.
The linear system's augmented matrix, which is determined by the matrix equation A x = b is given by:
Aequals
[tex]\left[\begin{array}{ccc}1&-3&4\\2&-3&2\\-3&3&4\\-7&15&-4\end{array}\right][/tex]
Part 2:
Aequals
Write the system's solution as a vector after solving it.
We can use Gaussian Elimination to solve this system.
Step 1:
[tex]\left[\begin{array}{ccc}1&1&0\\2&-1&1\\-3&0&1\\-7&8&3\end{array}\right][/tex]
Step 2:
Aequals
[tex]\left[\begin{array}{ccc}1&0&0\\0&1&0\\3&1&0\\-4&3&1\end{array}\right][/tex]
The system's solution is [tex]x_1=-4,\ x_2=3,\ x_3=1[/tex]. The vector xequals represents the answer.
The matrix is,
[tex]\left[\begin{array}{ccc}-4\\3\\1\end{array}\right][/tex]
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Working together, Mike and Stephanie can wash a car in 8.24 minutes. Had she done it alone it would have taken Stephanie 17 minutes. How long would it take Mike to do it alone?
It would take Mike approximately 0.989 minutes (or about 59 seconds) to wash the car alone.
We have,
Let's start by assigning variables to unknown quantities.
Let m be the time it takes for Mike to wash the car alone (in minutes).
We know that Stephanie takes 17 minutes to wash the car alone, so her rate of work is 1/17 car per minute.
Working together, their combined rate of work is 1/8.24 car per minute.
Using the formula:
(rate of work) = (amount of work) / (time)
we can set up the following equation to represent the work they do together:
1/8.24 = (1 car) / t
where t is the time it takes them to wash the car together.
We can also set up a similar equation for Stephanie's work alone:
1/17 = (1 car) / (t + x)
where x is the extra time it takes Mike to wash the car alone.
Since they are working on the same car, the amount of work done in both cases is the same, so we can set the two equations equal to each other and solve for x:
1/8.24 = 1/(t + x) + 1/17
Multiplying both sides by the least common multiple of the denominators (8.2417(t+x)).
17*(t+x) + 8.24*(t+x) = 8.24*17
Simplifying.
25.24t + 17x = 139.68
We also know that Mike's rate of work is 1/m car per minute.
Since we know the combined rate of work when they work together, we can set up another equation:
1/m + 1/17 = 1/8.24
Multiplying both sides by the least common multiple of the denominators (8.2417m).
178.24m + 8.2417m = 8.2417m + m8.24m
Simplifying.
141.08m = 139.68
Solving for m.
m = 0.989
Therefore,
It would take Mike approximately 0.989 minutes (or about 59 seconds) to wash the car alone.
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1. What is Maxwell's filing status?
a. Single
b. Married filing jointly
c. Head of household
d. Dependent
Maxwell's filing status can be described as: b. Married filing jointly.
What is a filing status?A filing status is a category that defines your tax-filing status based on your marital status and family situation. The filing status determines tax rate and standard deduction, as well as the eligibility for certain credits, deductions, and exemptions.
Maxwell can be described as married filing jointly because he and his spouse combined their income, deductions, and credits on one tax return. This status generally results in lower tax rates and a larger standard deduction compared to filing separately.
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