Denzel earned money after school delivering newspapers and doing yardwork. He put - of this month's earnings into his savings. He took the rest to spend at the amusement park. He spent of this amount on popcorn and of it on rides. What fraction of his amusement park money did he spend on rides and popcorn?

In order to maximize the chances that experimental groups represent the population of interest, researchers should conduct  random sampling and random group assignment

Explanation:

The terms Random sampling and Random group assignment are greatly different in process of the sample selection.  The study related to the determination of how sample participants can be drawn from the population refers to the process of Random sampling. The sample participants are subjected to a treatment by the usage of a random procedure comprises the Random group assignment.

When a researcher wants validate externally then random selection can be used. When a researcher wants to determine the effects of treatment within that group which is known as determination of internal validity then he can opt for Random group assignment.

Answer:

In order to maximize the chances that experimental groups represent the population of interest, researchers should conduct random sampling/random group assignment.

Explanation:

Random selection is a representation of the sample of people for your research from a community. Random assignment is the assigning of the sample that describes various groups or operations in the study.

Reasons:

Thus we can say in order to maximize the chances that experimental groups represent the population of interest, researchers should conduct random sampling/random group assignment.

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Answer:Area is 50 cm^2

Step-by-step explanation:

Let L represent the length of the rectangle.

Let W represent the width of the rectangle.

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

Area = LW

The length of a rectangle Is twice the width of the rectangle. This means that

L = 2W

The length of a diagonal of the rectangle is 25cm. This is the hypotenuse of the right angle triangle that is formed. Applying Pythagoras theorem,

25^2 = L^2 + W^2 - - - - - - - 1

Substituting L = 2W into equation 1, it becomes

25^2 = (2W)^2 + W^2

25^2 = 4W^2 + W^2 = 5W^2

Taking square of both sides,

W = √25 = 5

L = 2W = 3×5 = 10

Area = LW = 10×5 = 50 cm^2

The length of a rectangle is twice the width. Using the Pythagorean Theorem, we can find the dimensions of the rectangle and calculate its area. Hence the final answer is 248 cm².

To find the area of a rectangle, we need to know both the length and the width of the rectangle.

Let's assume the width of the rectangle is 'w'.

According to the question, the length of the rectangle is twice the width, so the length of the rectangle is '2w'.

We can use the Pythagorean Theorem to find the length of the diagonal:

Using the formula a^2 + b^2 = c^2, where 'a' and 'b' are the length and width of the rectangle, and 'c' is the length of the diagonal, we can set up the equation:

w^2 + (2w)^2 = 25^2.

Simplifying the equation, we get: 5w^2 = 625

Dividing both sides of the equation by 5, we get: w^2 = 125

Taking the square root of both sides, we get: w = 11.18

The area of the rectangle is length times width, so the area is: 2w * w = 2 * 11.18 * 11.18 = 248.27

Rounding to the nearest integer, the area of the rectangle is approximately 248 cm².

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Answer:

31.0 grams.

Step-by-step explanation:

According to the given information

Half-life of a substance = 37 years

Initial amount = 202 gram

The exponential function for half-life of a substance is

[tex]A(t)=A_0(0.5)^{\frac{t}{h}}[/tex]

where, A₀ is initial amount, t is time and h is half life.

Substitute A₀=202 and h=37 in the above function.

[tex]A(t)=202(0.5)^{\frac{t}{37}}[/tex]

We need to find the amount of the substance remaining after 100 years.

Substitute t=100 in the above function.

[tex]A(100)=202(0.5)^{\frac{100}{37}}[/tex]

[tex]A(100)=31.0282146[/tex]

Round the answer to the nearest tenth.

[tex]A(100)\approx 31.0[/tex]

Therefore, the amount of the substance remaining after 100 years is 31.0 grams.

Answer:

The Amount after 18 years is $66,942,391.5

Step-by-step explanation:

Given as :

The principal invested in saving bond = p = $150

The Time period for the bond = t = 18 years

The rate of interest applied on bond = 106%

Let The Amount after 18 years = $A

Now, From compound interest

Amount = Principal × [tex](1+\dfrac{\textrm rate}{100})^{\textrm time}[/tex]

Or, A = p × [tex](1+\dfrac{\textrm r}{100})^{\textrm t}[/tex]

Or, A = $150 × [tex](1+\dfrac{\textrm 106}{100})^{\textrm 18}[/tex]

Or, A = $150 × [tex](2.06)^{\textrm 18}[/tex]

Or, A = $150 × 446,282.61

∴ A = $66,942,391.5

So,The Amount after 18 years = A = $66,942,391.5

Hence,The Amount after 18 years is $66,942,391.5 Answer

Answer:

Step-by-step explanation:

Shane spends $2,000 each week for supplies and labor to run his car detailing business. This means that his total cost of running his car detailing business is $2000

Let x represent the number of cars that he would need. If he charges $30 for each car, the total amount charged for x cars would be 30×x = $30x

Let y represent the number of trucks that he would need. If he charges $45 for each car, the total amount charged for y trucks would be 45×y = $45y

In order to make profit, the inequality would be

30x + 45y greater than 2000

Final answer:

Shane can use the inequality 30c + 45t > 2000 to calculate the combination of cars (c) and trucks (t) he needs to detail in order to make a profit, where the costs are $2,000 weekly and charges are $30 and $45 respectively.

Explanation:

To calculate the number of cars (c) and trucks (t) Shane needs to detail in order to make a profit, we can set up an inequality based on his weekly costs and his charges for detailing cars and trucks.

With $2,000 for supplies and labor as his weekly expenses and charging $30 for each car and $45 for each truck, Shane's profit inequality would look like:

30c + 45t > 2000

This inequality states that the total revenue from detailing c cars and t trucks must be greater than his weekly expenses of $2,000 to make a profit.

Answer:

y = -5/3 + 5/3x

Step-by-step explanation:

Solve for y. View image.

Answer: the low temperature on Tuesday is 0 degree Fahrenheit

Step-by-step explanation:

The low temperature on Monday was 6 degrees warmer than Sunday's low of -9°F. This means that the temperature on Monday would be

- 9 + 6 = - 3 degrees Fahrenheit

The low temperature on Tuesday was 3 degrees warmer than Monday's low temperature. This means that the low temperature on Tuesday would be

- 3 + 3 = 0 degree Fahrenheit

Final answer:

By sequentially adding the temperature differences to each day's low, we find that Sunday's low was -9°F, Monday's was -3°F, and Tuesday's was 0°F.  So the low temperature on Tuesday was 0°F.

Explanation:

The student's question involves calculating temperature changes over consecutive days. Here's the step-by-step explanation:

The low temperature on Sunday was -9°F.

Monday's low was 6 degrees warmer than Sunday's, so we add 6 to -9°F, resulting in -3°F for Monday's low.

Tuesday's low was 3 degrees warmer than Monday's, so we add 3 to -3°F, which is 0°F.

Therefore, the low temperature on Tuesday was 0°F.

Yes. Micheal and Ashley bought same amount of turkey which is 6 pounds.

Step-by-step explanation:

The question requires to you to form simultaneous equations and solve them.

Take the number of pounds for turkey to be x and that for ham to be y

For store A where michael spent $18

turkey cost $3 per pound ---- 3x

ham cost $4 per pound------4x

The equation for cost will be ; 3x+4y =18

For store B where Ashley spent $27

turkey cost $4.5 per pound

ham cost $6 per pound

The equation for cost is : 4.5x +6y=27

The two equations are;

3x+4y=18

4.5x+6y=27

Solving the equations by graph you get ;

x=6 and y=4.5 for both linear graphs. This means both equations produce similar amounts of turkey and ham . Micheal and Ashley bought same amount of turkey which is 6 pounds.

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Answer: the number is 3

Step-by-step explanation:

Let the number be represented by x.

If 4 more than 4 times a certain number is the same as 4 more than the product of 3 and 4, it means that

4x + 4 = 4 + 3×4

4x + 4 = 4 + 12

4x + 4 = 16

Subtracting 4 from the left hand side and the right hand side of the equation, it becomes

4x + 4 - 4 = 16 - 4

4x = 12

Dividing the left hand side and the right hand side of the equation by 4, it becomes

x = 12/4 = 3

Answer:

$1,828,669

Step-by-step explanation:

For the original lump sum of $28,000 is our principal, P, the annual interest rate r, compounded monthly for n=12 months throughout  a period of 35 years (t) will have a final Accrued Amount of investment A given by the formula:

A= (Principal + Interest)  = P(1 + r/n)^nt  =28000(1+0.12/12)^35*12

=28000(1.01)^420=

28000*65.3096= $1828669

Answer:

Approximately 4,000 times

Step-by-step explanation:

If you're flipping a coin to get 4 heads out of 10 and you times it by 10,000 then you would have a probable win rate of 4,000.

Answer:

894.19 mi/hr

Step-by-step explanation:

Total distance of the trip = 3990 mi

Let the speed of the sound be 'x' miles per hour

Now,

Total distance = Speed × Time

Therefore,

According to the question

3,990 mi = [ ( x - 120 ) × 0.1 ] + [ ( x + 410 ) × 3.0 ]

or

3,990 mi = 0.1x - 12 + 3x + 1230

or

0.1x + 3x = 2772

or

3.1x = 2772

or

x = 894.19 mi/hr

Answer:

  see attached

Step-by-step explanation:

For the figure A, the figure is symmetrical about a vertical line through its center. It has line symmetry.

__

For the figure O, it is symmetrical about both vertical and horizontal lines, as well as being symmetrical about its center point. It has line and point symmetry.

Answer: The slope of the line would be -5/2, and the whole fraction would be negative.  

Step-by-step explanation:

Technically just the 5 is negative because the new slope is going down 5, yet on paper its just safer to write the whole fraction as a negative.

Answer:

True, see proof below.

Step-by-step explanation:

Remember two theorems about continuity:

If f is differentiable in [0,4], then f is continuous in [0,4] (by 1). Now, f(0)=-1<0 and f(4)=3>0. Thus, we have the inequality f(0)<0<f(4). By Bolzano's theorem, there exists some c∈[0,4] such that f(c)=0.

The question is about the intermediate value theorem in calculus, which states a function takes on every value between f(a) and f(b) in a closed interval [a, b]. Given the function's values at 0 and 4, it must cross the x-axis, or equal zero, somewhere in the interval [0, 4].

This is a question about intermediate value theorem, a fundamental theorem in calculus. The intermediate value theorem states that if a function is continuous on a closed interval [a, b], then it takes on every value between f(a) and f(b) at some point within that interval. If we know that f(0) = -1 and f(4) = 3, this means the function f crosses the x-axis (or, in other words, f(c) = 0 for some c) somewhere in the interval [0, 4] because zero lies between -1 and 3 (the function's values at 0 and 4 respectively).

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Answer:

Option A) (x, y) = (4, -3)

Step-by-step explanation:

we know that

A function is a relation from a set of inputs (independent variable) to a set of possible outputs (dependent variable) where each input is related to exactly one output

we know that

The set of the function is { (-4, 2), (3, 6), (4, 3), (x, y) }

The ordered pair (x, y) = (4, -3)

could not be included, because for the input value of x=4, the function would have two output values (y=-3,y=3) and remember that each input is related to exactly one output

Answer:

The expression written by Emma  to represent the amount of the money that Juan earned  is WRONG.

Step-by-step explanation:

Here, the amount earned by Juan by walking dogs = w

The amount earned byJuan lowing lawns  = (2w - 6)

Now, the total amount earned by Juan

= Amount  earned from (Mowing Lawn +  Walking dogs)

= w +  (2 w - 6)

On further simplification, we get:

w +  (2 w - 6)  =  w +  2w - 6   =  3w-6 =  3(w-2)

So, the total amount earned by Juan = 3(w-2)

Now, the expression written by Emma = 2(3w-6)

and 2(3w-6) ≠ 3(w-2)

Hence, the expression written by Emma  to represent the amount of the money that Juan earned  is WRONG.

Answer:

Solar Eclipse will required 30 mins to travel Distance of 1150 miles.

Step-by-step explanation:

Given:

Total Distance = 2300 miles

Time required = 1 hr

we will convert hour in minutes.

1 hr = 60 mins

hence Time = 60 mins

We need to find the time required to travel 1150 miles.

We will first find the speed at which solar eclipse travels.

Speed can be calculated by dividing Distance with time.

Speed = [tex]\frac{Distance}{time}[/tex]

Substituting the values we get;

Speed = [tex]\frac{2300}{60}=38.33\ mi/hr[/tex]

Now to find Time required to travel 1150 miles we will divide 1150 miles with Speed.

Time required to travel 1150 miles = [tex]\frac{1150}{38.33}= 30\ mins[/tex]

Hence Solar Eclipse will required 30 mins to travel Distance of 1150 miles.

Answer:

The probability is %13,5

Step-by-step explanation:

If it is a binomial distribution function than we can find a probability of earning less or more than 35000$ in this certain large city. Lets assume that p is probability of earning less than 35000$ and q is earning more than 35000$.:

p=0,45

q=0,55

So general formula of n families that earning less than 35000$ is:

[tex]P(X=n)=combination(30,n)*0,45^n*0,55^{30-n}[/tex]

Probability of 10 or less families out of 30 families that earning less than 35000$ is:

[tex]combination(30,10)*0.45^{10}*0.55^{20}+combination(30,9)*0.45^9*0.55^{21}+combination(30,8)*0.45^8*0.55^{22}+combination(30,7)*0.45^7*0.55^{23}+combination(30,6)*0.45^6*0.55^{24}+combination(30,5)*0.45^5*0.55^{25}+combination(30,4)*0.45^4*0.55^{26}+combination(30,3)*0.45^3*0.55^{27}+combination(30,2)*0.45^2*0.55^{28}+combination(30,1)*0.45^{1}*0.55^{29}+combination(30,0)*0.45^0*0.55^{30}=0,135[/tex]

The correct probability that a simple random sample of 30 families will have 10 or fewer families earning less than $35,000 per year, using the exact binomial calculation, is approximately 0.0674.

To solve this problem, we will use the binomial probability formula, which is given by:

 [tex]\[ P(X = k) = \binom{n}{k} p^k (1-p)^{n-k} \][/tex]

 Given that 45% of families earn less than $35,000 per year, we have p = 0.45.

The number of families in the sample is n = 30

We want to find the probability that 10 or fewer families earn less than $35,000 per year, so k will range from 0 to 10.

Then, we sum these probabilities to find the cumulative probability of 10 or fewer families earning less than $35,000 per year.

Using the binomial probability formula, we calculate:

[tex]\[ P(X \leq 10) = \sum_{k=0}^{10} \binom{30}{k} (0.45)^k (0.55)^{30-k} \][/tex]

This calculation can be done using statistical software or a calculator that supports binomial probability calculations.

 After performing the exact binomial calculation, we find that the probability is approximately 0.0674.

This is the probability that, in a random sample of 30 families from this city, 10 or fewer families will earn less than $35,000 per year.

The function graphed below is

y = x³ - 3, x ≤ 2

   = x² + 6, x > 2 ⇒ C

Step-by-step explanation:

The graph has two parts:

∴ The graph represents two functions:

→ Quadratic function y = ax² + bx + c with domain x > 2

→ Cubic function y = ax³ + bx² + cx + d with domain x ≤ 2

∵ The answers have two functions:

→ y = x³ - 3 ⇒ cubic function

→ y = x² + 6 ⇒ quadratic function

∵ The domain of the cubic function is x ≤ 2

∵ The domain of the quadratic function is x > 2

∴ The answer is

y = x³ - 3, x ≤ 2

     x² + 6, x > 2

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Answer:

y={x^3-3, x ≤ 2

   {x^2+6, x>2

Step-by-step explanation:

a pex :)

Answer:

B. 7 in.

Step-by-step explanation:

Area = A =pi r^2

r^2 = A / pi

r = √(A / 3.14)

= √(153.9 / 3.14)

= 7 in.

Answer:

3n+2

Step-by-step explanation:

[where, a and b are some constants and x is a variable ( input values)]

so, a+b=5

so,2a+b=8

subtract the first equation from second:

2a+b-a-b=8-5

a=3.

by substituting the value of a in one of the above equations,

you will get b as 2

so, when the input is n, output will be : 3n+2

Answer:

293 feet

Step-by-step explanation:

The distance the wire is attached in the tower is 200 feet

the angle between the wire and the tower is 47 degrees

The length of the wire (x) is the hypotenuse of the triangles formed

The formed triangle is a right angle triangle

For 47 degree angle the adjacent side is 200 feet and hypotenuse is x

[tex]cos(theta)=\frac{adjacent}{hypotenuse}[/tex]

[tex]cos(47)=\frac{200}{x}[/tex]

Cross multiply it

[tex]xcos(47)= 200[/tex]

divide by cos on both sides

[tex]x=\frac{200}{cos(47)}[/tex]

x=293.25 feet

At t = 4, the distance traveled is 68 miles. This means that after the break, Joanna traveled 48 miles.

A function is an assertion, concept, or principle that establishes an association between two variables. Functions may be found throughout mathematics and are essential for the development of significant links.

The linear function is given below.

d(t) = 12t + 20

The distance traveled when t = 4 is calculated as,

d(4) = 12 x 4 + 20

d(4) = 48 + 20

d(4) = 68 miles

So, at t = 4, the distance traveled is 68 miles. This means that after the break, Joanna traveled 48 miles.

More about the function link is given below.

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Answer: x = 28/33, y = 25/23

( 28/23, 25/23)

Step-by-step explanation:

3x + 4y = 8 ----------------------(1)

-2x + 5y = 3 ---------------------(2)

Using elimination method

Consider the coefficient of y in equation 1 and 2

Therefore multiply as follows

(1) x 5 -------- 15x + 20y = 40.

(2) x 4 -------- -8x + 20y = 12

Therefore carry out subtraction on the two equations

23x + 0y = 28

23x = 28

x = 28/23.

Now substitute for x in any of the equations above to get y

3(28/23) +4y = 8

84/23 +4y = 8

Multiply through by 23 to have s simple linear equation

84 + 92y = 184

Collect like terms

92y = 184 - 84

92y = 100

y = 100/92

Reduce to lowest term by dividing by 4

y = 25/33.

(28/23, 25/23)------ solution

Check

Substitute for x and y values in any equations above.

3(28/23) + 4(25/23)

84/23 + 100/23

Resolved into fraction with 23 as the common LCM

184/23

= 8

Answer:

The Conclusion is

Diagonals AC and BD,

a. Bisect each other

b. Not Congruent

c. Not Perpendicular

Step-by-step explanation:

Given:

[]ABCD is Quadrilateral having Vertices as

A(-1, 1),

B(2, 3),

C(6, 0) and

D(3, -2).

So the Diagonal are AC and BD

To Check

The diagonals AC and BD

a. Bisect each other. B. Are congruent. C. Are perpendicular.

Solution:

For a. Bisect each other

We will use Mid Point Formula,

If The mid point of diagonals AC and BD are Same Then

Diagonal, Bisect each other,

For mid point of AC

[tex]Mid\ point(AC)=(\dfrac{x_{1}+x_{2} }{2},\dfrac{y_{1}+y_{2} }{2})[/tex]

Substituting the coordinates of A and C we get

[tex]Mid\ point(AC)=(\dfrac{-1+6}{2},\dfrac{1+0}{2})=(\dfrac{5}{2},\dfrac{1}{2})[/tex]

Similarly, For mid point of BD

Substituting the coordinates of B and D we get

[tex]Mid\ point(BD)=(\dfrac{2+3}{2},\dfrac{3-2}{2})=(\dfrac{5}{2},\dfrac{1}{2})[/tex]

Therefore The Mid point of diagonals AC and BD are Same

Hence Diagonals,

a. Bisect each other

B. Are congruent

For Diagonals to be Congruent We use Distance Formula

For Diagonal AC

[tex]l(AC) = \sqrt{((x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2} )}[/tex]

Substituting A and C we get

[tex]l(AC) = \sqrt{((6-(-1))^{2}+(0-1)^{2} )}=\sqrt{(49+1)}=\sqrt{50}[/tex]

Similarly ,For Diagonal BD

Substituting Band D we get

[tex]l(BD) = \sqrt{((3-2))^{2}+(-2-3)^{2} )}=\sqrt{(1+25)}=\sqrt{26}[/tex]

Therefore Diagonals Not Congruent

For C. Are perpendicular.

For Diagonals to be perpendicular we need to have the Product of slopes must be - 1

For Slope we have

[tex]Slope(AC)=\dfrac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

Substituting A and C we get

[tex]Slope(AC)=\dfrac{0-1}{6--1}\\\\Slope(AC)=\dfrac{-1}{7}[/tex]

Similarly, for BD we have

[tex]Slope(BD)=\dfrac{-2-3}{3-2}\\\\Slope(BD)=\dfrac{-5}{1}[/tex]

The Product of slope is not -1

Hence Diagonals are Not Perpendicular.

Answer:

(a)

Use random selection to pick 10 calves to inoculate.(you didn't mention this option in the question instead you mix it with other option)

(B).No placebo is being used.

(F).After inoculation, test all calves to see if there is a difference in resistance to infection between the two groups.

(b)

(C).No placebo is being used.

(E).Use random selection to pick nine schools to visit.

(A).After the police visits, survey all the schools to see if there is a difference in views between the two groups.

(c)

(F.)A placebo patch is used for the remaining 35 volunteers in the second group.

(E).Use random selection to pick 40 volunteers for the skin patch with the drug.

(G).Then record the smoking habits of all volunteers to see if a difference exists between the two groups.

Step-by-step explanation:

In question one the answer is mixed with other option so the correct answer statements are provided along with the option for all questions. Placebo is not used in question (a) scenario because it is mentioned in the statement that there is enough vaccine is present and sample of 10 calves is selected from 22 calves and we test all calves after the inoculation because it is mention that blood test should be done on all calves.

Placebo is not used in question (b) scenario because it is mentioned in the statement that the police department can visit half of 18 schools and random sample of 9 schools are selected and it is mentioned in the statement that survey is sent to all 18 school so after the police visit all schools are surveyed to see the difference in views

Placebo patch is used in question (c) because it is mentioned in the statement that 40 out of 75 received the new skin patch so, the remaining 35 received placebo patch and random sample of 40 volunteers are selected for new skin patch. It is mentioned in the statement that each subject is survey so in the end smoking habits of all volunteers are recorded.

In the given settings, a completely randomized experiment can be used to test the effects of different interventions. Placebo is not being used in these experiments.

In a completely randomized experiment, the researcher randomly assigns subjects to different treatment groups to determine the effect of the treatment. In the given settings:

(a) A veterinarian wants to test a strain of antibiotic on calves. A completely randomized experiment can be conducted by randomly selecting 5 calves from the pasture to inoculate with the antibiotic while the remaining 17 serve as the control group with no placebo being used. After inoculation, the resistance to infection can be tested on both groups to compare the difference.

(b) The Denver Police Department wants to improve its image with teenagers. A completely randomized experiment can be conducted by randomly selecting half of the 18 schools to receive the visits from the police officer while the other half serve as the control group with no placebo being used. Then, a survey can be sent to all 18 schools at the end of the semester to compare the views between the two groups.

(c) A skin patch contains a new drug to help people quit smoking. A completely randomized experiment can be conducted by randomly selecting 40 volunteers to receive the skin patch with the drug while the remaining 35 volunteers receive the placebo patch with no drugs. The smoking habits of both groups can be surveyed at the end of the two months to see if a difference exists between the two groups.

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We know that 70 sixth graders had an average weight of 90 pounds, and 30 seventh graders had an average weight of 100 pounds.

We know that the weight of all 70 sixth graders will be 70*90, since we're multiplying the total amount of students by the average.

Using this same logic tells us that the total weight for the 30 seventh graders is 30*100

The average weight for all 100 students will be the total weight of the sixth graders (which is 70*90) added with the total weight of the seventh graders (which is 30*100), then finally divided by the total amount of students in the sample space (which is 100).

[tex]\dfrac{70(90)+30(100)}{100}[/tex]

[tex]=\dfrac{6300+3000}{100}[/tex]

[tex]=\dfrac{9300}{100}[/tex]

[tex]=93[/tex]

The average of all 100 students is 93 pounds.

Let me know if you need any clarifications, thanks!

Answer:

The description of the company's is marketing mix.

Step-by-step explanation:

Consider the provided information.

Jakubowski Farms Gourmet Bread Base is the brand name for a mix designed for use in bread making machines which is the product.

We have given that the price is $14.99 plus shipping.

The promotion is word of mouth and public demonstrations.

The place is mail.

The marketing mix is defined as the set of actions or tactics that a company uses to market its brand or product. The 4Ps constitute a standard marketing mix-price, product, promotion and venue.

These four elements are the marketing mix—product, price, promotion, and place.

Hence, the description of the company's is marketing mix.

Answer:

t = 1

Step-by-step explanation:

3 (8 - 3t) = 5 (2 + t)

24 - 9t = 10 + 5t

- 9t - 5t = 10 - 24

- 14t = - 14

- t = - 14/14

- t = - 1

t = 1