A salesman packed 3 shirts and 5 ties. With one shirt, he could wear all 5 ties. With another shirt, he could wear 4 ties. With the third shirt, he could wear only 2 ties. How many different combinations did he have? a) 40 b) 22 c) 11 d) 10

Answer:

The study is an observational study because the study examines individuals in the sample, but does not try to influence the response variable.

Step-by-step explanation:

Final answer:

The described study, which involves asking a sample of people with heart arrhythmias about their caffeine consumption to explore a relationship between the two, is an observational study. In this type of study, there is no manipulation of variables or conditions, just observations and recordings of naturally occurring phenomena.

Explanation:

The study described is investigating if there is a relationship between heart arrhythmias and caffeine consumption by asking a sample of people with heart arrhythmia about their caffeine intake. This corresponds to an observational study, not an experiment. In an observational study, researchers collect data on existing behaviors and outcomes without manipulating any variables or conditions. Participants are observed in their natural settings, and their experiences or characteristics are recorded to find correlations or associations between factors.

By contrast, an experiment involves the researcher actively manipulating one or more independent variables to investigate the effects on a dependent variable, often involving random assignment to different conditions, such as treatment versus control groups.

In the context provided, because there is no manipulation of participants' caffeine consumption and no assignment to different conditions, but rather a collection of data through questionnaires, this study is classified as an observational study.

Answer:

$198779.46

Step-by-step explanation:

We must determine the amount owed for the first 7 years. The monthly compound interest formula is:

[tex]A=P(1+r/12)^1^2^t-Xnt[/tex]

[tex]A=155000(1+0.048/12)^84-888.15[/tex]

[tex]A=216752.23-74604.6[/tex]

[tex]A=142147.63[/tex]

The balance will be $85690.81 after 7 years of paying

He will still have to pay:

[tex]A=142147.63(1+0.048/12)^8^4=198779.46[/tex]

He will have to pay $198779.46 for the last 17 years

Answer:

$123,692.61

Step-by-step explanation:

Answer:

[tex]11x+4y=264[/tex]

Step-by-step explanation:

an equation of the line in the form ax+by=c

y intercept is 66. at y intercept x is 0 . so y intercept point is (0,66)

x intercept is 24. at x intercept y is 0 . so x intercept point is (24,0)

slope m formula is [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

Plug in the values in the formula and find out m

[tex]\frac{66-0}{0-24}=-\frac{11}{4}[/tex]

[tex]y=mx+b[/tex]

b is the y intercept 66

[tex]y=-\frac{11}{4} x+66[/tex]

multiply the whole equation by 4

[tex]4y=-11x+264[/tex]

add 11x on both sides

[tex]11x+4y=264[/tex]

Answer:

(3)4

Step-by-step explanation:

3 x 3 x 3 x 3 can also be written as (3)4 or 3 to the 4th power

Answer:

The distance of the helicopter from the bristol is approximately 12.81 miles

Step-by-step explanation:

Given:

Helicopter flies 10 miles east of bristol.

Then the helicopter flies 8 miles North before landing.

To find the direct distance between the helicopter and bristol.

Solution:

In order to find the distance of the helicopter from the bristol before landing, we will trace the path of the helicopter

The helicopter is first heading 10 miles east of bristol and then going 8 miles due north.

On tracing the path of the helicopter we find that the direct distance of the helicopter from the bristol is the hypotenuse of a right triangle formed by enclosing the path of the helicopter.

Applying Pythagorean theorem to find the hypotenuse of the triangle.

[tex]Hypotenuse^2=Short\ leg^2+Shortest\ leg^2[/tex]

[tex]Hypotenuse^2=10^2+8^2[/tex]

[tex]Hypotenuse^2=100+64\\Hypotenuse^2=164[/tex]

Taking square root both sides.

[tex]\sqrt{Hyptenuse^2}=\sqrt{164}\\Hypotenuse = 12.81\ miles[/tex]

Thus, the distance of the helicopter from the bristol is approximately 12.81 miles

Answer: Is there a question missing?

Step-by-step explanation:

Probability is the numerical measurement of the likeliness of an even to/not to occur. The probability of an event to/not to occur is always less or equal to 1 (It is never above 1).

It is possible to find the probability of success or the probability of failure of an event. Success is whatever is favourable to you, and Failure is the unfavourable occurence(s).

For example:

A coin has two sides, a head, and a tail. If you toss it once, you'll either get a head or a tail, both sides have equal likeliness of occurring. It is also important to know that the addition of the probability of success and the probability of failure of an even is exactly 1.

Probability of Success(p) + Probability of Failure (q) = 1

Simply,

p + q = 1

Which means if we are given the probability of the likeliness of an event, we can easily find the probability of its failure by subtracting it from 1.

Suppose we want to know the probability of having a head when the coin is tossed once, because we can only have one of the two sides at a time, we say the probability of having a head is 1 out of 2 possible outcomes. That is,

Probability of having a head = 1/2 or 0.5, which is less than 1.

Also, the probability of having a tail is 0.5. Suppose we didn't know, we can just say

p + q = 1

0.5 + q = 1

q = 1 - 0.5

= 0.5

In your statement above, the probability that a randomly selected person will have a tattoo is 0.2 tells us that 20%, or 1 out every 5 persons in the industry have a tattoo (0.2 is 20% of 1).

Answer: the expression representing the perimeter of the field is 4x + 280

Step-by-step explanation:

The perimeter of a figure is the distance around it.

The formula for determining the perimeter of a rectangle is expressed as

Perimeter = 2(length + width)

The length of a football field is x. The width of the field is 70 yards less than the length. This means that the width of the football field is x - 70 yards.

an expression that represents the perimeter of the field without parentheses would be

Perimeter = 2(x + x- 70) = 2(2x + 70)

= 4x + 280

Answer:

The probability that he picked 2 purpled socks is 0.33.

Step-by-step explanation:

Given:

Number of purple socks, [tex] n(P) = 6[/tex]

Number of orange socks, [tex] n(O) = 4[/tex]

Two socks are picked without replacement.

Now, total number of socks, [tex]n(T)=N(P)+n(O)=6+4=10[/tex]

Probability of picking the first cap as purple cap is given as:

[tex]P(P1)=\frac{n(P)}{n(T)}\\\\P(P1)=\frac{6}{10}=\frac{3}{5}[/tex]

Since there is no replacement, the number of socks decreases by 1. Also, if the first sock picked is purple, then number of purple socks is also decreased by 1.

Therefore, probability of picking the second cap as purple cap is given as:

[tex]P(P2)=\frac{n(P)-1}{n(T)-1}\\\\P(P2)=\frac{5}{9}[/tex]

Now, probability that both the picked caps are purple is given by their probability product. This gives,

[tex]P(P1\ and\ P2)=P(P1)\times P(P2)\\\\P(P1\ and\ P2)=\frac{3}{5}\times\frac{5}{9}\\\\P(P1\ and\ P2)=\frac{3}{9}=\frac{1}{3}=0.33[/tex]

Therefore, the probability that he picked 2 purpled socks is 0.33

By considering the number of House members who voted in favor and against as variables and applying simple algebra, we find that 242 members voted in favor of the bill and 193 members voted against.

We can solve this question using simple mathematics or algebra. Let's consider the number of members who voted in favor as 'F' and against as 'A'. The total number of House members (435) is their sum (F + A). Moreover, we know there are 49 more members who voted in favor than against (F = A + 49).

Substituting the second equation into the first, we have: A + 49 + A = 435. If we simplify that by combining like terms, we get: 2A + 49 = 435. Subtracting 49 from both sides will result in 2A = 386. Dividing both sides by 2, we get A = 193. As we have 'A', we can now determine 'F' with the equation F = A + 49, which means F = 193 + 49 = 242. Thus, there were 242 members who voted in favor and 193 members who voted against.

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Answer:

C

Step-by-step explanation:

Firstly, we have 1/x as the parent function. 1/x-1 describes the graph of 1/x to shift 1 unit right. -1/x-1, states that it is reflected across the x-axis. And -1/x-1 -10 states that it is shifted 10 units down.

Answer:

[tex]FJ=18\ units[/tex]

Step-by-step explanation:

see the attached figure to better understand the problem

we know that

If two triangles are similar, then the ratio of its corresponding sides is proportional and its corresponding angles are congruent

In this problem

△FEG is similar with △FHJ -----> by AA Similarity Theorem

so

[tex]\frac{FE}{FH}=\frac{FG}{FJ}[/tex]

we have

[tex]FE=HF+EH=12+8=20\ units[/tex]

[tex]FH=HF=12\ units[/tex]

[tex]FG=30\ units[/tex]

substitute the given values

[tex]\frac{20}{12}=\frac{30}{FJ}[/tex]

[tex]FJ=12(30)/20\\FJ=18\ units[/tex]

Answer:

18 from k12

Step-by-step explanation:

Answer:

Step-by-step explanation:

Let x represent the original price of the model.

A builder of tract homes reduced the price of a model by 15%. This means that x was reduced by 15%. The amount by which x was reduced would be

15/100 × x = 0.15 × x = 0.15x

The new price would be

x - 0.15x = 0.85x

If the new price is $425,000, then it means that

0.85x = 425000

x = 425000/0.85

x = $500000

The amount that can be saved by purchasing the model at the new price would be

500000 - 425000 = $75000

Final answer:

The original price of the home was $500,000 before a 15% reduction. The new price is $425,000. Therefore, a buyer would save $75,000 by purchasing the home at the reduced price.

Explanation:

To find the original price of the home before the 15% reduction, we can use the formula for percentage decrease, which is:

Original Price = New Price / (1 - Rate of Decrease)

Here, the New Price is $425,000 and the Rate of Decrease is 15%, or 0.15 when converted to decimal form. Plugging the numbers into the formula gives us:

Original Price = $425,000 / (1 - 0.15) = $425,000 / 0.85

Original Price = $500,000

The amount that can be saved by purchasing the model at the reduced price is the difference between the original price and the new price:

Savings = Original Price - New Price

Savings = $500,000 - $425,000

Savings = $75,000

Answer:

a) [tex] P(-t_o < t_7 <t_o) =0.9[/tex]

Using the symmetrical property we can write this like this:

[tex] 1-2P(t_7<-t_o) =0.9[/tex]

We can solve for the probability like this:

[tex] 2P(t_7<-t_o) = 1-0.9=0.1[/tex]

[tex] P(t_7<-t_o) =0.05[/tex]

And we can find the value using the following excel code: "=T.INV(0.05,7)"

So on this case the answer would be [tex] t_o =\pm 1.895[/tex]

b) For this case we can use the complement rule and we got:

[tex] 1-P(t_7<t_o) = 0.05[/tex]

We can solve for the probability and we got:

[tex] P(t_7 <t_o) = 1-0.05=0.95[/tex]

And we can use the following excel code to find the value"=T.INV(0.95;7)"

And the answer would be [tex] t_o = 1.895[/tex]

Step-by-step explanation:

Previous concepts

The t distribution (Student’s t-distribution) is a "probability distribution that is used to estimate population parameters when the sample size is small (n<30) or when the population variance is unknown".

The shape of the t distribution is determined by its degrees of freedom and when the degrees of freedom increase the t distirbution becomes a normal distribution approximately.  

The degrees of freedom represent "the number of independent observations in a set of data. For example if we estimate a mean score from a single sample, the number of independent observations would be equal to the sample size minus one."

Solution to the problem

For this case we know that [tex] t \sim t(df=7)[/tex]

And we want to find:

Part a

[tex] P(|t|<t_o)=0.9[/tex]

We can rewrite the expression using properties for the absolute value like this:

[tex] P(-t_o < t_7 <t_o) =0.9[/tex]

Using the symmetrical property we can write this like this:

[tex] 1-2P(t_7<-t_o) =0.9[/tex]

We can solve for the probability like this:

[tex] 2P(t_7<-t_o) = 1-0.9=0.1[/tex]

[tex] P(t_7<-t_o) =0.05[/tex]

And we can find the value using the following excel code: "=T.INV(0.05,7)"

So on this case the answer would be [tex] t_o =\pm 1.895[/tex]

Part b

[tex] P(t>t_o) =0.05[/tex]

For this case we can use the complement rule and we got:

[tex] 1-P(t_7<t_o) = 0.05[/tex]

We can solve for the probability and we got:

[tex] P(t_7 <t_o) = 1-0.05=0.95[/tex]

And we can use the following excel code to find the value"=T.INV(0.95;7)"

And the answer would be [tex] t_o = 1.895[/tex]

The t0 values in the queries are the t-values at which certain probabilistic conditions about the t7 distribution are met. These can be obtained from t-distribution tables or calculated with statistical software.

The questions deal with the probabilities under a t-distribution with 7 degrees of freedom. The t-distribution is a type of probability distribution that is symmetric, bell-shaped and has heavier tails compared to the normal distribution. It's often used when the size of the sample is small and/or the population standard deviation is unknown.

(a) In the first case, p(|t | < t0) = .9 means we are looking for the value of t (t0) for which 90% of the distribution lies within -t0 and t0. This induces that each tail beyond these points contains 5% of the distribution as the total probability is 1. This t0 value can be found in standard t-distribution tables or calculated using software like R, Python, or a scientific calculator capable of t-distribution calculations.

(b) For the p(t > t0) = .05 condition, you are looking for the t0 such that 5% of the t-distribution is to the right of this value. This t0 can be referred as the 95th percentile (or the 0.95 quantile) of the t-distribution. This because 95% of the distribution lies to the left of this point. This value can again be found in the t-distribution tables or calculated using relevant software.

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The solution to given system of equations is x = 2 and y = -5

Solution:

Given the system of equations are:

4x + y = 3 ---------- eqn 1

-2x + 3y = -19 ---------- eqn 2

We have to find the solution to above system of equations

We can solve the system by substitution method

From eqn 1,

4x + y = 3

Isolate y to one side

y = 3 - 4x ----------- eqn 3

Substitute eqn 3 in eqn 2

-2x + 3(3 - 4x) = -19

-2x + 9 - 12x = -19

Combine the like terms

-14x = -19 - 9

-14x = -28

Divide both sides of equation by -14

Substitute x = 2 in eqn 3

y = 3 - 4(2)

y = 3 - 8

Thus the solution is x = 2 and y = -5

Answer:

The person must walk 36.36 minutes to use at least 240 calories.

Step-by-step explanation:

Given:

A 150 pound person uses 6.6 calories per minute when walking at a speed of 4 mph.

Now, to find the time the person walk at this speed to use at least 240 calories.

As, given calories used per minute = 6.6.

So, to solve we use unitary method:

If 6.6 calories used in = 1 minute.

So, 1 calorie used in = [tex]\frac{1}{6.6}[/tex]

Thus, 240 calorie used in = [tex]\frac{1}{6.6} \times 240[/tex]

= [tex]\frac{1}{6.6} \times 240[/tex]

= [tex]\frac{240}{6.6}[/tex]

= [tex]36.36\ minutes.[/tex]

Therefore, the person must walk 36.36 minutes to use at least 240 calories.

Answer:

c) 72% is a statistic and 56% is a parameter.

Step-by-step explanation:

Previous concepts

A statistic or sample statistic "is any quantity computed from values in a sample", for example the sample mean, sample proportion and standard deviation

A parameter is "any numerical quantity that characterizes a given population or some aspect of it".

Solution to the problem

For this case we know that they select a sample of 663 registered voters and the sample proportion from these registered voters is:

[tex] \hat p = 0.72[/tex] representing the sample proportion of people who voted in the election

They info that they have is that the true proportion before is [tex] p =0.52[/tex] and that represent a value related to the population.

So on this case the 0.72 represent a statistic since represent the sample and the 0.52 is a value who represent the population for this case is a parameter.

So the correct option is:

c) 72% is a statistic and 56% is a parameter.

Answer:

The answer to your question is     sin 45° = 0.6494      

Step-by-step explanation:

Data

sin 45° = ?

Process

Formula

       sin (15 + 30) = sin (15)cos(30) + cos(15)sin(30)

sin 15 = 0.2334

sin 30 = 0.4540

cos 15 = 0.9723

cos 30 = 0.8910

Substitution

sin(15 + 30) = (0.2334)(0.8910) + (0.9723)(0.4540)

                   = 0.2080 + 0.4414

                   = 0.6494      

None of the options

Answer:

time

Step-by-step explanation:

Answer: The ball will hit the ground 5 seconds after being thrown.

Step-by-step explanation:

The correct function is: [tex]h (t) =-16t^2 +64t+80[/tex]

You can rewrite the Quadratic function given in the exercise with making [tex]h(t)=0[/tex]. Then this is:

[tex]0=-16t^2 +64t+80[/tex]

Now you can simplify the equation dividing both sides by -16. So you get:

 [tex]\frac{0}{-16}=\frac{-16t^2 +64t+80}{-16}\\\\0=t^2-4t-5[/tex]

To find the solution of the Quadratic equation, you can facfor it. In order to do this, it is necessary to find two numbers whose sum is -4 and whose product is -5. These number would be -5 and 1.

Therefore, you get this result:

[tex]0=(t-5)(t+1)\\\\t_1=5\\t_2=-1[/tex]

Since the time cannot be negative, you can conclude that the ball will hit the ground 5 seconds after being thrown.

Answer:

The decomposition is as shown in the attachment below

Step-by-step explanation:

Where A, B, C, D, E, F, G, H, I, J are numerical value of the coefficients that can be determined by method of comparing coefficients. Hence , there are two methods for solving partial fractions ; Cover up method and method of comparing coefficients.

The form of the partial fraction decomposition is as shown in the attachment.

Answer:

Sugar will dissolve to half of it's amount in 2.41 minutes.

Step-by-step explanation:

The given question is incomplete; here is the complete question.

When the sugar is dissolved in water, the amount A that remains undissolved after t minutes satisfies the differential equation

[tex]\frac{dA}{dt}=-kA, (k>0)[/tex]

If 25% of the sugar dissolves after 1 min, how long does it take for half of the sugar to dissolve.

The given differential equation is [tex]\frac{dA}{dt}=-kA[/tex]

In other form, dA = -kA.dt

We further integrate the equation,

[tex]\int\limits {dA}\,=\int{-kA}\, dt[/tex]

[tex]\int\limits{\frac{dA}{A} }\,=-k\int\, dt[/tex]

lnA = -kt + c

Or [tex]A=e^{c-kt}[/tex]

A = [tex]e^{c}.e^{-kt}[/tex] -----(1)

Here [tex]e^{c}[/tex] is a constant.

For t = 0,

[tex]A=e^{c}[/tex]

Let [tex]e^{c}=A_{0}[/tex]

Therefore, equation (1) will become

A = [tex]A_{0}e^{-kt}[/tex]

If sugar dissolves 25% in 1 minutes then undissolved sugar will be

100 - 25 = 75%

Now from the equation

[tex]0.75A_{0}=A_{0}e^{-k\times 1}[/tex]

[tex]e^{-k}=0.75[/tex]

By taking natural log on both the sides

[tex]ln(e^{-k})=ln(0.75)[/tex]

k = 0.2877

Now we have to calculate the time to dissolve half of the sugar, that means half the sugar will be undissolved.

Form the equation,

[tex]0.5A_{0}=A_{0}e^{-0.2877t}[/tex]

[tex]0.5=e^{-0.2877t}[/tex]

ln(0.5) = [tex]ln(e^{-0.2877t})[/tex]

0.6931 = 0.2877t

t = 2.41 minutes

The question deals with logarithmic differential equations. After finding the value of the decay constant (k), it's used to find the time it takes for half of the sugar to dissolve.

The subject you're asking about is logarithmic differential equations. Let's start by writing the differential equation in its general form: dA/dt = -kA. This equation describes an exponentially decaying process, where the amount of undissolved sugar decreases proportionally to the amount of sugar left at any point in time (A).

From the problem, it's known that after 1 min 75% of the sugar remains, which means A = 0.75 and t = 1. We substitute these values into the equation to find the value of k.

Then we can use this information to calculate the time it takes for half of the sugar to dissolve. At this point A will be 0.5. We substitute A = 0.5 and the value of k from earlier into the equation and solve for t.

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Answer:

3y^7/ x 3y^5

Photomath

Answer:

The slope is [tex]4.2\ \frac{tickets}{day}[/tex]

Step-by-step explanation:

The picture of the question in the attached figure

Let

x ----> the number of days

y ---> the number of tickets sold

we have the points

(1,30) and (7,55)

The formula to calculate the slope between two points is equal to

[tex]m=\frac{y2-y1}{x2-x1}[/tex]

substitute the given values in the formula

[tex]m=\frac{55-30}{7-1}[/tex]

[tex]m=\frac{25}{6}[/tex]

[tex]m=4.2\ \frac{tickets}{day}[/tex]

Answer:

36 students got an'A' grade in the quiz.

Step-by-step explanation:

Given:

Total number of students taking the quiz = 132

Fraction of students getting an 'A' grade =  [tex]\frac{3}{11}[/tex]

To find the number of students getting an 'A' grade.

Solution:

In order to find the number of students who got an 'A' grade in the quiz, we will find the fractional part who got an 'A' of the total students taking the quiz.

The fraction of students getting an 'A' is =  [tex]\frac{3}{11}[/tex]

Thus, total number of student getting an 'A' is :

⇒  [tex]\frac{3}{11}[/tex] of [tex]132[/tex]

⇒ [tex]\frac{3}{11}\times 132[/tex]

⇒ [tex]\frac{396}{11}[/tex]

⇒ 36 (Answer)

Answer: x= 1090 y=450

my question was "Tickets to a Broadway show cost $35 for adults and $10 for children. The total receipts for 1540 tickets at one performance were $42,650. How many adult and how many child tickets were sold?"

Step-by-step explanation:

to find y

take the original equation 35x+10y=42,650 and fill in the x which is 1090 in the equation

35(1090) +10y =42,650

38,150 +10y=42,650

-38,150         -38,150

-------------------------------

10y = 4,500

divide 10 by both sides and u get

y= 450

have a great day! :)

Answer:

y=25 and x=30.

Step-by-step explanation:

See picture

Answer:the number of hours that the Simmons family used their sprinklers last summer is 30

the number of hours that the Wright family used their sprinklers last summer is 25

Step-by-step explanation:

Let x represent the number of hours that the Simmons family used their sprinklers last summer.

Let y represent the number of hours that the Wright family used their sprinklers last summer.

The families used their sprinklers for a combined total of 55 hours, it means that

x + y = 55

The water output rate for the Simmons family's sprinkler was 20l per hour. The water output rate for the Wright family's sprinkler was 35l per hour. The total water output was 1475l. It means that

20x + 35y = 1475 - - - - - - - - - - 1

Substituting x = 55 - y into equation 1, it becomes

20(55 - y) + 35y = 1475

1100 - 20y + 35y = 1475

- 20y + 35y = 1475 - 1100

15y = 375

y = 375/15 = 25

x = 55 - y = 55 - 25

x = 30

Answer:

A) True

Step-by-step explanation:

Solution: When values of the ordered pair (v1, v2, ... , vn) are substituted in every equation of the linear system with variables x1, x2, ... , xn and these values satisfy each and every equation then it's called a solution.

Answer:

They sold 16 French fries.

Step-by-step explanation:

Let x represent the number of large burgers that they sold on that day.

Let y represent the number of French fries that they sold on that day.

fast food sells large burgers for five dollars each and french fries for three dollars each that day and their total sales was $98.It means that

5x + 3y = 98 - - - - - - - - - - - - - -1

they sold six more french fries than burgers. It means that

y = x + 6

Substituting y = x+ 6 into equation 1, it becomes

5x + 3(x + 6) = 98

5x + 3x + 18 = 98

8x = 98 - 18 = 80

x = 80/8 = 10

y = x + 6 = 10 + 6

y = 16

Answer:

the apprentice can complete the job in 30 hours by working alone.

Step-by-step explanation:

Given:

Number of hours required to complete a job by welder = 18 hours

Number of hours welder work on job = 6 hours.

Number of hours required by apprentice to complete the job = 14 hours

We need to find Number of hours required to complete a job by apprentice alone.

Solution:

Let Number of hours required to complete a job by apprentice alone be 'a'.

Also let the job completed be = 1

Now we know that ;

Time required on job is equal to sum of Number of hours welder work on job and Number of hours required by apprentice to complete the job.

framing in equation form we get

Time required on job =  [tex]6+14 =20\ hrs[/tex]

Now we can say that;

each has done a fraction of the work so we will add to two fraction as number of hours of work done by Total number of hours required to do the work to complete 1 job.

so we can frame the equation as;

[tex]\frac{6}{18}+\frac{20}{a}=1[/tex]

By reducing the fraction we get;

[tex]\frac{1}{3}+\frac{20}{a}=1[/tex]

Now we will make the denominator common to solve the fraction we get;

[tex]\frac{1\times a}{3\times a}+\frac{20\times3}{a\times3}=1\\\\\frac{a}{3a}+\frac{60}{3a}=1[/tex]

Now denominators are same so we will solve the numerator we get;

[tex]\frac{a+60}{3a}=1[/tex]

Multiplying both side by 3a we get;

[tex]\frac{a+60}{3a}\times3a=1\times 3a\\\\a+60=3a[/tex]

Combining the like terms we get;

[tex]3a-a=60\\\\2a=60[/tex]

Dividing both side by 2 we get;

[tex]\frac{2a}{2}=\frac{60}{2}\\\\a=30\ hrs[/tex]

Hence the apprentice can complete the job in 30 hours by working alone.

Final answer:

The apprentice would take 21 hours to finish the welding job working alone. The problem is solved using the combined work rate of the welder and apprentice and then isolating the apprentice's work rate.

Explanation:

The student is asking how long it would take for an apprentice, working alone, to complete a welding job if the welder requires 18 hours to do the job alone, and together they have worked for 6 hours, after which the apprentice completes the remainder of the job in 14 hours. Let's represent the time it would take the apprentice to complete the job working alone as 'A' hours.

To solve this, we find the combined hourly rate of the welder and apprentice and use it to determine the apprentice's solo hourly rate. The welder completes the job in 18 hours, so his work rate is 1/18 job per hour. Together, they work for 6 hours, so they completed 6/18, or 1/3, of the job. We know that 1 whole job - 1/3 job leaves 2/3 of the job that the apprentice completes alone in 14 hours.

Therefore, the apprentice's rate is 2/3 job per 14 hours or 1/21 job per hour. Now we calculate the time it would take the apprentice to do the whole job alone (A hours) by setting up the equation 1/A = 1/21. By solving this equation for A, we find A = 21, meaning the apprentice would take 21 hours to finish the job working alone.

Answer:

Option C.

Step-by-step explanation:

We need to find the correct definition of like terms.

Like terms :Two or more terms are called like terms if they have the same variables and same powers.  

For example : 4xy and 9xy are like terms.

Option A is incorrect because 3x and 3 are not like terms.

Option B is incorrect because 6x and 9 are not like terms.

Option C is correct because like terms are terms that have the same variable factors as well as the same number of factors of each type. For​ example, 3x and 5x are like terms.

Option D is incorrect because 3x and 5 are not like terms.

Therefore, the correct option is C.