Solve the following equation 3x-1=2x -2/3​

Answer:

Hello!

Step-by-step explanation:

Theoretical probability is what's expected to happen

Experimental probability is what's happen based on the experiment

Daisy gets 20 cats delivered to her shelter in the last month She expects to get 20 this month based on the theoretical probability but she actually gets 15 cats this month so her theoretical probability was 5 more then her experimental probability Hope that helps!

Answer:

\(x = 5\), \(y = -2\)

Step-by-step explanation:

\(2x + 5y = 0\)

\(3x - 4y = 23\)

By using substitution:

\(2x + 5y = 0\)

\(2x = -5y\)

\(x = -\frac{5}{2}y\)

\(3x - 4y = 23\)

\(3 (-\frac{5}{2} y) - 4y = 23\)

\(-\frac{23}{2} y = 23\)

\(y = -2\)

\(x = -\frac{5}{2} y\)

\(x = -\frac{5}{2} (-2)\)

\(x = 5\)

Answer:

A

Step-by-step explanation:

Answer:

\(\dfrac{6}{7}\).

Step-by-step explanation:

It is given that the sum of first two terms of an infinite GP is 6.

nth term of a GP is

\(a_n=ar^{n-1}\)

\(a+ar=6\)     ...(1)

Each term is 5 times the sum of the succeeding terms.

\(a_n=5(a_{n+1}+a_{n+2}+...+\infty)\)

\(ar^{n-1}=5(ar^n+ar^{n+1}+...+\infty)\)

\(ar^{n-1}=5ar^n(1+r+r^2+...+\infty)\)

Divide both sides by a.

\(r^{n-1}=5r^n(\dfrac{1}{1-r})\)    \([\text{Sum of infinite GP}=\dfrac{a}{1-r}]\)

\(\dfrac{r^n}{r}=\dfrac{5r^n}{1-r}\)

\(\dfrac{1}{r}=\dfrac{5}{1-r}\)

\(1-r=5r\)

\(1=6r\)

\(\dfrac{1}{6}=r\)

The common ratio is 1/6.

Put r=1/6 in (1).

\(a+a(\dfrac{1}{6})=6\)

\(6a+a=36\)

\(7a=36\)

\(a=\dfrac{36}{7}\)

Second term \(ar=\dfrac{36}{7}\times \dfrac{1}{6}=\dfrac{6}{7}\)

Therefore, the second term is \(\dfrac{6}{7}\).

We know that the score is obtained by subtracting the number of incorrect answers from twice the number of correct answers. Let's use "x" to represent the number of correct answers.

According to the question, the player answered 40 questions in total. This means that the number of incorrect answers is 40 - x.
Now we can use the formula for the score:
Score = 2x - (40 - x)
We also know that the player obtained a score of 50. So we can set up the equation:
50 = 2x - (40 - x)
Simplifying the equation:
50 = 3x - 40
90 = 3x
x = 30
Therefore, the player answered 30 questions correctly.
To check, we can plug this value back into the formula for the score:
Score = 2x - (40 - x)
Score = 2(30) - (40 - 30)
Score = 60 - 10
Score = 50
So the score of 50 is correct and the player answered 30 questions correctly.

To find out how many questions the player answered correctly in the trivia game with a score of 50, we can use the given information to set up an equation:
Let x be the number of correct answers and y be the number of incorrect answers. According to the question, the score is calculated by subtracting the number of incorrect answers (y) from twice the number of correct answers (2x). The player answered 40 questions in total, so we have:
x + y = 40
2x - y = 50
Now we can solve this system of equations step-by-step:
1. Solve the first equation for x:
x = 40 - y
2. Substitute this expression for x in the second equation:
2(40 - y) - y = 50
3. Simplify the equation:
80 - 2y - y = 50
4. Combine like terms:
80 - 3y = 50
5. Subtract 80 from both sides:
-3y = -30
6. Divide both sides by -3:
y = 10
7. Substitute the value of y back into the expression for x:
x = 40 - 10
x = 30
The player answered 30 questions correctly in the trivia game with a score of 50.

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Answer:

1080

Step-by-step explanation:

Answer:

500 liters

Step-by-step explanation:

We want to find the total amount of water that was drained.

He drained 62.5 liters of water per minute and this went on for 8 minutes. The total amount of water drained is:

62.5 * 8 = 500 liters of water

3 Answers: x = 0, x = 1, or x = 2

==================================================

Explanation:

The relation

{(0, 5) (1, 5) (2, 6) (x, 7)}

has points with x coordinates of: 0, 1, 2, and x.

If we repeated any of the x values listed so far, then we will not have a function.

So if we had the points (0,5) and (0,7), then the input x = 0 leads to multiple outputs. A function is only possible when any input x leads to exactly one output y.

This means that if x = 0, 1, or 2, then we won't have a function.

Side note: The y values can repeat, but if they do, then we won't have a one-to-one function. In this case, y = 5 repeats, so this function is not one-to-one (assuming x is not 0, not 1, and not 2).

The runner's rate in miles per hour is D * 4/3 miles per hour.

Distance is a measure of the physical space between two objects or points. It is the length of the shortest path between two points in space. Distance can be measured in different units, such as meters, kilometers, miles, feet, or inches, depending on the scale of the objects or the purpose of the measurement.

In geometry, the distance between two points in a Euclidean space can be calculated using the Pythagorean theorem or the distance formula. The distance formula is expressed as:

d = sqrt((x2 - x1)^2 + (y2 - y1)^2)

where d is the distance between two points (x1, y1) and (x2, y2) in a two-dimensional plane. This formula can be extended to three dimensions by adding a third term to the equation.

Distance can also be calculated using other methods, such as GPS (Global Positioning System) or by measuring the time it takes for an object to travel from one point to another, using the speed of light or sound.

In everyday life, distance is a fundamental concept used in various contexts, such as navigation, transportation, sports, and communication. It plays a significant role in determining the time and effort required to travel between two points and is often used as a basis for making decisions.

We can use the formula:

rate = distance / time

where distance is the distance traveled by the runner and time is the time taken to travel that distance.

Given that the runner travels 2/3 of the marathon distance in 10 minutes, we can find the total distance of the marathon by dividing the distance traveled by 2/3:

total distance = distance traveled / (2/3) = distance traveled * 3/2

Let's denote the total distance of the marathon as D. Then:

D = distance traveled * 3/2

distance traveled = D * 2/3

We know that the time taken to travel 2/3 of the distance is 10 minutes. Let's convert this to hours:

10 minutes = 10/60 hours = 1/6 hours

Now we can calculate the runner's rate:

rate = distance / time = (D * 2/3) / (1/6) = (D * 4/3) / 1 = D * 4/3

So the runner's rate in miles per hour is D * 4/3 miles per hour.

Note that we don't have a specific value for the total distance D of the marathon, so we cannot give a numerical answer. We can only express the runner's rate in terms of D as:

runner's rate = D * 4/3 miles per hour

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The area of the trapezoid is 25. 8 ft²

We can see from information given that the shape is a trapezoid.

Hence, the formula for calculating the area of a trapezoid is expressed as;

A = a + b/2 h

Such that the parameters of the given equation are;

Substitute the value, we have that;

Area = 2.7 + 5.9)/2 × 6

add the values, we have;

Area = 8. 6/2 ×6

Divide the values, we have;

Area = 25. 8 ft²

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When performing a statistical analysis, we work with sample rather than the entire population because, we often lack manpower or resources to gather data. So option D is correct.

Statistical work is usually done with a sample. This is done because, if we try to include and collect data from the whole population, it will be very time consuming and need more manpower and resources. It will become a much tedious process.

So a sample which is representative of the whole population is needed. Selecting a sample size and determining the sample must follow certain criteria. They are population parameters we want to estimate, Cost of sampling, Variability of the population, how hard is it to collect data and how precise we want the final estimates to be. All these are taken into consideration and a sample that properly represent the population is determined without bias.

So, option D is the correct answer.

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The amount that Heather earns if she works 46 hours in one week is; $563.5

Amount she earns per hour if she works for 40 hours a week = $11.5 per hour

If she works over 40 hours, her hourly pay is 1.5 times the previous rate.

Thus;

Amount she earned for 40 hours is;

11.5 × 40 = $460

Amount she earned for the 6 extra hours to make it 46 hours is;

1.5 × 11.5 × 6 = $103.5

Total amount she earned for the 46 hours = $460 + $103.5 = $563.5

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Ellen can make a maximum of 6 batches of Cardamom cookies with her 2 fluid ounces of cardamom.

Ellen has 2 fluid ounces of cardamom in a jar. Her recipe requires 3/10 of a fluid ounce of cardamom for each batch of cardamom cookies.

We can use division to find the number of batches of cardamom cookies that Ellen can make with all of her cardamom:

2 fluid ounces ÷ (3/10 fluid ounce per batch) = (2/1) ÷ (3/10)

= (2/1) x (10/3)

= 20/3

= 6 2/3

Therefore, Ellen can make 6 batches of cardamom cookies with her 2 fluid ounces of cardamom, with 2/3 of a batch remaining.

Since she cannot make a fraction of a batch, Ellen can make a maximum of 6 batches of cardamom cookies with her 2 fluid ounces of cardamom.

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The sides are 20 and 21 in   right triangle.

What defines a right triangle?

The term "right triangle" refers to a triangle with an interior angle of 90 degrees.

                 The hypotenuse, the side of the right triangle that is opposite the right angle and is also its longest side, and the height and base are the two arms of the right angle.The term "right triangle" refers to a triangle with an interior angle of 90 degrees. The hypotenuse, the side of the right triangle that is opposite the right angle and is also its longest side, and the height and base are the two arms of the right angle.

29² = x²  + (x+1)²

x²+ x² +2x +1 = 841

2x² +2x -840 =0

x² + x -420 =0

(x+21)(x-20)=0

x=20

the sides are 20 and 21

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The ordered pair which is solution of 8x+16y > 32 is (-3,5) , the correct option is (b) .

In the question ,

it is given that ,

the linear inequality is 8x+16y > 32 .

to find the solution set ,

we substitute the options that are given

Option(a)

Substituting (0,2) in 8x+16y > 32 ,

we get ,

8(0) + 16(2) > 32

32 > 32 ,

false , hence it is not a solution .

Option(b)

Substituting (-3,5) in 8x+16y > 32 ,

we get ,

8(-3) + 16(5) > 32

-24 + 80 > 32

56 > 32

true , yes it is the solution .

Option(c)

Substituting (-1,1) in 8x+16y > 32 ,

we get ,

8(-1) + 16(1) > 32

-8 + 16 > 32

8 > 32

False , hence it is not a solution .

Option(d)

Substituting (4,0) in 8x+16y > 32 ,

we get ,

8(4) + 16(0) > 32

32 + 0 > 32

32 > 32

False , hence it is not a solution .

The only solution that satisfy the inequality is (-3,5) .

Therefore  , The ordered pair which is solution of 8x+16y > 32 is (-3,5) .

The given question is incomplete , the complete question is

Which ordered pair is in the solution set of 8x+16y > 32 ?

(a) (0,2)

(b) (-3,5)

(c) (-1,1)

(d) (4,0)

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Answer:

There is no common difference between each sequence.

Step-by-step explanation:

The difference between each number increases by 1 each time.

2+3=5

4+4=9

9+5=14

Therefore the next number is 20.

14+6=20

Hii student!

_________________________________________________

\(\multimap\parallel\boldsymbol{Answer.}\parallel\gets\)

there's no common difference in the sequence!

\(\multimap\parallel\boldsymbol{Explanation.}\parallel\gets\)

The common difference is the amount we add or subtract to obtain the next term. It should always be the same amount.

Since in this given sequence we add 3, then 4, then 5, there's no common difference in this sequence.

\(\maltese\boldsymbol{\therefore,\,option\;a\;is\,correct.}\)

Hope that this helped! Best wishes.

\(\textsl{Reach far. Aim high. Dream big.}\)

\(\boldsymbol{-Greetings!-}\)

_______________________________________

Answer:

-4

Step-by-step explanation:

In a nonexperimental method, relationships between variables are studied by making observations or measures of the variables of interest.

Research without either the manipulation of an independent variable, the random assignment of individuals to conditions or orders of conditions, or both, is referred to as non-experimental research.

The non-experimental study is entirely dependent on variables that the researcher has no control over. By whatever means, they cannot manipulate, control, or change the subjects. Thus, all they can do is continue their research while monitoring and interpreting their subjects.

It is safe to assume that a non-experimental research design is used when there is no specific cause-effect study problem and the researcher simply wants to grasp a topic in depth without constraining it with variables. They examine the natural phenomena as they take place.

Therefore, in a nonexperimental method, relationships between variables are studied by observing or measuring the variables of interest.

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The 90% confidence interval for the difference between the dropout rates of the two groups is (-0.366, -0.034).

a. To find the dropout rates for each group of exercisers, we divide the number of dropouts by the total number of exercisers in each group and multiply by 100 to get a percentage.

For the first exercise group:

Dropout rate = (Number of dropouts / Total number of exercisers) * 100

= (15 / 40) * 100

= 37.5%

For the second exercise group:

Dropout rate = (Number of dropouts / Total number of exercisers) * 100

= (23 / 40) * 100

= 57.5%

b. To find the 90% confidence interval for the difference between the dropout rates of the two groups, we can use the formula:

Confidence Interval = (p1 - p2) ± Z * √[(p1 * (1 - p1) / n1) + (p2 * (1 - p2) / n2)]

where p1 and p2 are the dropout rates of the two groups, n1 and n2 are the respective sample sizes, and Z is the Z-score corresponding to a 90% confidence level.

Using the given information, p1 = 0.375, p2 = 0.575, n1 = n2 = 40, and for a 90% confidence level, the Z-score is approximately 1.645.

Substituting these values into the formula, we have:

Confidence Interval = (0.375 - 0.575) ± 1.645 * √[(0.375 * (1 - 0.375) / 40) + (0.575 * (1 - 0.575) / 40)]

Calculating the values within the square root and simplifying, we get:

Confidence Interval = -0.2 ± 1.645 * √(0.003515 + 0.006675)

= -0.2 ± 1.645 * √0.01019

= -0.2 ± 1.645 * 0.100944

= -0.2 ± 0.166063

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Answer:

b

Step-by-step explanation:

Answer:

No, Jaelyn is incorrect because 18 is not equivalent to 24.

Step-by-step explanation:

3(p+2)+9=8+6p

Step 1 : substitute p
3(3+2)+9=8+6x3

Step 2 : distribute 3 into 3 and 2
9+6+9=8+6x3

Step 3 : multiply 6 by 3
9 + 6 + 9 = 18

Step 4: add
24 = 18

Answer:

D. {1}

Step-by-step explanation:

F(x)=3x−1

Let F(x) =2

2 = 3x-1

Add 1 to each side

2+1 = 3x-1+1

3 =3x

Divide by 3

3/3 = 3x/3

1 =x

Answer:

Heres the answer

Step-by-step explanation:

To calculate the ratio of an amount we divide the amount by total number of parts in the ratio then multiply the answer by original ratio.

Answer:

1. Circumference of a circle = 2πr or πd (r=radius and d=diameter)

2. Perimeter = 74 feet

3. 2π*5 = 10π

4. π*20 = 20π

Step-by-step explanation:

1. Diameter is equal to radius*2.

2. 25+25+12+12=74

3. Substitute 5 for r in the formula.

4. Substitute 20 for d in the second formula.

Answer: 80.8

Step-by-step explanation:

Ayee just trust me

No, enough information is not given to prove that triangles are congruent using the SSS congruence theorem.

The SSS congruence theorem  expresses that assuming in two triangles, three sides of one are consistent to three sides of the other, then, at that point, the two triangles are said to be congruent.

Now, we are given that triangle ACB and triangle DEB that share a common vertex b. So, both triangles share a common side. So, one side is same for both of triangles.

From the diagram, we can see that both triangles opposite side are equal. So, second side is equal for both of triangles.

Now, from the diagram, we can see that both triangles vertically opposite angles are equal. So, we have two sides equal and one angle is equal.

So, given triangle is proved to congruent by SAS congruency not by SSS congruency.

Hence, enough information is not given.

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The optimal mix of crops to plant is 1,304 acres of soybeans, 761 acres of corn, and 341 acres of cotton, which will maximize the family's total profit.

3.51 Farm Management problem: Formulate and solve a linear programming model for this problem in a spreadsheet.The given table contains information about the labor-hours and fertilizer needed per acre and the total expected profit per acre for the potential crops under consideration.

Given that Dwight, Hattie, and their children can work at most 6.500 total hours during the upcoming season and have 200 tons of fertilizer available. We need to find the mix of crops that maximizes the family's total profit.Let x1, x2, and x3 be the amount of acres for soybeans, corn, and cotton, respectively.

We need to maximize the profit, which is given byZ = 70x1 + 60x2 + 90x3subject to the constraints given below:2x1 + 3x2 + 4x3 <= 6,500 (labor-hours constraint)3x1 + 2x2 + 4x3 <= 200 (fertilizer constraint)x1, x2, x3 >= 0 (non-negativity constraint)The linear programming model for this problem can be written as follows:maximize Z = 70x1 + 60x2 + 90x3Subject to:2x1 + 3x2 + 4x3 ≤ 6,5003x1 + 2x2 + 4x3 ≤ 200x1, x2, x3 ≥ 0Solving the problem using a spreadsheet, we get the following optimal solution.

 The optimal solution is obtained for x1 = 1,304 acres of soybeans, x2 = 761 acres of corn, and x3 = 341 acres of cotton.

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Answer:

time taken = 850/(8+7) =56.6 second

Answer:

The answer is: 56 2/3

Step-by-step explanation:

First add up the amount of feet they run all together every second. 8+7=15 feet/second. You have to find the total amount of seconds for them to meet so you divide. 850 divided 15 equals 56 2/3 seconds. That's your answer.