+
Problem
Step 1
Step 2
Step 3
Step 4
Step 5
3(-4 + x) -5x = 7x + 15
-12 +3x -15x = 7x + 115,
-12 -12x + 12x = 7x + 12x +15
-12 = 19x + 15
-12 -15 = 19x + 15 -151
-27 = 19x
8
Step 6
x= - 1 19

Answer:

Step-by-step explanation:

So first you do y=z and1+2=3 so 6=y=-0 is your answer :)

Answer: y= -4

Step-by-step explanation:

1. Distribute

2(y+5)= 8y + 34

2y+10 = 8y + 34

2. Subtract 10 from both sides

3. Simplify

4. Subtract 8y from both sides

5. simplify

6.Divide both sides by the same factor

7. simplify

Answer:

y = -4

Step-by-step explanation:

Given equation,

→ 2(y + 5) = 8y + 34

Now the value of y will be,

→ 2(y + 5) = 8y + 34

→ 2y + 10 = 8y + 34

→ 2y - 8y = 34 - 10

→ -6y = 24

→ y = 24/-6

→ [ y = -4 ]

Hence, the value of y is -4.

Answer:

b is 36

Step-by-step explanation:

The relationship between x and y with the first data point (2,24) is 1/12.  That is, x is 1/12 of y.  Or we can say y = 12x.  The second point has x = 3.  If the same proportionality holds, then b would be 12*3 or 36.

Answer:

  d.  36

Step-by-step explanation:

You want to know the value of y for x=3 when y=24 and x=2, and the variation is direct.

Direct variation means the ratio of y to x is the same for any x and y.

  y/x = 24/2 = b/3

  b = 3(24/2) = 3(12) = 36

The value of b is 36.

Answer:

Your answer is <, Hope it helps.

The deterministic finite automaton (DFA) M3 for the language L3, where strings have more than 3 'c' symbols and do not end in 'c', is designed with states q0, q1, q2, q3, and q4. Transitions and loops are created to determine acceptance.



To build a deterministic finite automaton (DFA) for the language L3 = {x ∈ {a, b, c}* | x has strictly more than 3 'c' symbols and does not end in 'c'}, we can design the following DFA M3:1. Start with an initial state q0.

2. Create a loop on q0 for 'a', 'b', and 'c' inputs, leading back to q0.

3. From q0, transition to a state q1 on input 'c'. This represents the first 'c' encountered.

4. From q1, create a loop for 'a' and 'b' inputs, leading back to q1.

5. Transition from q1 to q2 on input 'c'. This represents the second 'c' encountered.

6. Similarly, create a loop on q2 for 'a' and 'b' inputs, leading back to q2.

7. Transition from q2 to q3 on input 'c'. This represents the third 'c' encountered.

8. From q3, create a loop for 'a', 'b', and 'c' inputs, leading back to q3.

9. Create a final accepting state q4 and transition from q3 to q4 on 'a' or 'b' inputs.

In this DFA, any string that ends with 'c' or has less than three 'c' symbols will not reach the accepting state q4, hence not belonging to L3.

Therefore, The deterministic finite automaton (DFA) M3 for the language L3, where strings have more than 3 'c' symbols and do not end in 'c', is designed with states q0, q1, q2, q3, and q4. Transitions and loops are created to determine acceptance.

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Answer:

125+2x=y   (take 125 add 2x for $2 a day and then = y for amount saved)

Points on Graph:

(125,0)

(135,5)

(145,10)

(155,15)

(165,20)

(175,25)

(185,30)

(195,35)

(205,40)

(215,45)

(225,50)

Answer:

Step-by-step explanation:

Answer:

35 cm^2

Step-by-step explanation:

a = bh

a = (7)(5)

a = 35 cm^2

Answer:

x/2  - 8x + 15

Step-by-step explanation:

Expand the polynomial using the foil method

The total required cost of downloading books and videos is $57.92

Linear equations are equations that have constant average rates of change. Note that the constant average rates of change can also be regarded as the slope or the gradient

The given parameters are:

Cost of downloading a book = $5.99

Cost of downloading a video = $7.99

The number of books and videos downlaoded are

Books = 3

Videos = 5

So, the total cost of downloading books and videos is

Total cost = Cost of downloading a book * x + Cost of downloading a video *  y

This gives

Total cost = Cost of downloading a book * Books + Cost of downloading a video *  Videos.

This gives

Total cost = 5.99 * 3 + 7.99 * 5

Evaluate

Total cost = 57.92

So, the total cost of downloading books and videos is $57.92

Hence, the total required cost of downloading books and videos is $57.92

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Answer:

1

Step-by-step explanation:

The equation is y = mx + b. so in this case 1 is b

Have a nice day! :-)

It will take 660 minutes, or 11 hours, to correct the chemical concentration in the pool.

The worker should have added 1,000 pounds of chemical,

but added 10,000 pounds instead.

So the excess chemical is,

⇒ 10,000 pounds - 1,000 pounds = 9,000 pounds

Now, we have to find out how much fresh water needs to be added to the pool to dilute the excess chemical.

The pool holds 660,000 gallons of water, but we don't know how much water is currently in the pool.

Let the amount of water in the pool "W".

Set up an equation to solve for W,

⇒ (9,000 pounds of chemical) / (W gallons of water) = (1 pound of chemical) / (66 gallons of water)

Solving for W, we get,

⇒ W = (9,000 pounds of chemical) / ((1 pound of chemical) / (66 gallons of water)) = 594,000 gallons of water

We know that there are 594,000 gallons of water in the pool, and we need to add fresh water to dilute the excess chemical.

We need to add,

⇒ 660,000 gallons - 594,000 gallons = 66,000 gallons

We also know that fresh water can be added and removed from the pool at a rate of 100 gallons per minute.

So it will take,

⇒ 66,000 gallons / 100 gallons per minute = 660 minutes

To add enough fresh water to dilute the excess chemical.

So, 11 hours or 660 minutes will pass until the chemical balance in the pool is restored.

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Confidence Interval = 0.1703 ± 0.0222 Confidence Interval ≈ (0.1481, 0.1925)  We are 95% confident that the true proportion of student loan borrowers with loans totaling more than $40,000 for their undergraduate education falls between approximately 0.1481 and 0.1925.

To construct a confidence interval to estimate the population proportion, we can use the following formula:

Confidence Interval = Sample Proportion ± Margin of Error

First, let's calculate the sample proportion:

Sample Proportion = Number of borrowers with loans > $40,000 / Total number of borrowers

Sample Proportion = 218 / 1280 ≈ 0.1703

Next, we need to determine the margin of error. For a 95% confidence level, we can use the formula:

Margin of Error = Z * sqrt((Sample Proportion * (1 - Sample Proportion)) / n)

Where Z is the z-value corresponding to the desired confidence level (in this case, 95%), and n is the sample size.

For a 95% confidence level, the critical z-value is approximately 1.96.

Margin of Error = 1.96 * sqrt((0.1703 * (1 - 0.1703)) / 1280)

Margin of Error ≈ 0.0222

Now, we can construct the confidence interval:

Confidence Interval = 0.1703 ± 0.0222

Confidence Interval ≈ (0.1481, 0.1925)

We are 95% confident that the true proportion of student loan borrowers with loans totaling more than $40,000 for their undergraduate education falls between approximately 0.1481 and 0.1925.

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Answer and Step-by-step explanation:

The answer will be the first answer choice, in which both lines would be the same lines as the original shape.

This is because the figure is being dilated by the point P, so it will only increase in length one direction, instead of making the entire triangle get bigger and surround the original triangle.

#teamtrees #PAW (Plant And Water)

if we know the context of the problem and the relationship between C and angle A, then we can use trigonometric functions to find the values of cos(A) and sin(A).

For example, if we know that angle A is the angle between the x-axis and the line passing through the origin and point C, we can use the coordinates of C to find the length of the hypotenuse and the adjacent side of a right triangle, and then use the definitions of cosine and sine to find the values of cos(A) and sin(A).

In general, the values of cos(A) and sin(A) depend on the angle A and the unit circle, which is a circle with radius 1 centered at the origin. The x-coordinate of a point on the unit circle represents the value of cosine of the angle formed by the line segment from the origin to the point and the positive x-axis, and the y-coordinate represents the value of sine of the angle.

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Answer:

Step-by-step explanation:

35. 4

36. 4

37. 16

38. 4

39. 2

40. 2

Answer:

35. 4

36. 4

37. 16

38. 4

39. 2

40. 2

Step-by-step explanation:

35. Y/3

= 12/3

= 4

36. x/2

= 8/2

= 4

37. xy/6

= 8 * 12/6

= 96/6

= 16

38. y/6 + x/4

= 12/6 + 8/4

= 2 + 2

= 4

39. 24/x - 1

= 24/8 - 1

= 3 - 1

= 2

40. y + 2/7

= 12 + 2/7

= 14/7

= 2

Answer:

50%

Step-by-step explanation:

50% is equal to 1/2.

1/2 of 60 is 30.

Answer:

50%

Step-by-step explanation:

Work backwards- 30 is half of 60.

That means that 50% of 60 will be 30, because it is the same as dividing 60 by 2.

\(\frac{60}{2}\) = 30, so 50% of 60 is 30

Answer:

£103.70

Step-by-step explanation:

Payment per hour = £8.50

Overtime payment = 1.4 × 8.50

= £11.90

Ben worked for 11 hours.

Normal time = 8 hours

Overtime = 3 hours

Total earnings = (8 hours × 8.50) + (3 hours × 11.90)

= £68 + £35.7

= £103.70

Ben earned £103.70 for working for 11 hours

The maximum amount you can earn is $540

a. y = 13.50x , 10 <= x <= 40
b. x = 10, y = 135; x = 20, y= 270; x = 30, y = 405; x = 40, y = 540
c. Domain: 10 <= x <= 40; Range: 0 <= y <= 540
d. The minimum amount you can earn in a week with this job is $135. The maximum amount you can earn is $540.

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Answer:

Their Ratio

Step-by-step explanation:

You switched the numbers 2 and 3 btw

\(\boldsymbol{\left ( 2 \right )}\) their ratio

A ratio indicates how many times one number contains another.

Two sequences of numbers, often experimental data, are proportional or directly proportional if their corresponding elements have a constant ratio, which is called the coefficient of proportionality or proportionality constant.

When two variables are proportional, \(\boldsymbol{\left ( 2 \right )}\) their ratio is constant.

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Answer:

96,500

Step-by-step explanation:

The plumber bought 10 pieces of copper pipe and 6 pieces of plastic pipe. Let's start by assigning variables to the unknown quantities.

- Let's call the number of copper pipes that the plumber bought "c". Let's call the number of plastic pipes that the plumber bought "p".

We can then use this information to set up two equations:
- The total number of pipes bought is 16:

c + p = 16

- The total length of the pipes bought is 40 meters:

7c + 1p = 40

Now we have two equations with two variables, which we can solve using algebra.

First, let's solve for one of the variables in terms of the other. We'll use the first equation:

c + p = 16

c = 16 - p

Now we can substitute this expression for "c" into the second equation:

7c + 1p = 40

7(16 - p) + p = 40

112 - 6p = 40

-6p = -72

p = 12

So the plumber bought 12 pieces of plastic pipe. We can substitute this value back into our expression for "c":

c = 16 - p

c = 16 - 12

c = 4

So the plumber bought 4 pieces of copper pipe.

To check our answer, we can verify that the total length of the pipes is indeed 40 meters:

7c + 1p = 7(4) + 1(12) = 28 + 12 = 40

So our solution of 4 copper pipes and 12 plastic pipes is correct.

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Answer:

10%

Step-by-step explanation:

(517-470)/470x100

=10%

Find the difference after tax and divide by the original price and times 100%

Answer:

do u mind helping me for school ?

if so check my latest questions pls ty

Step-by-step explanation:

Given that John climbs a height of \($(x + 5)$\) miles in \($(x - 1)$\) hours and Jane climbs a height of \($(x + 11)$\) miles in \($(x + 1)$\) hours. We know that the distance covered by both John and Jane are equal.

Distance covered by John = Distance covered by Jane

Therefore, \($(x + 5) = (x + 11)$\)

Thus, x = 6

Now, we need to find the speed of both, which is given by the formulae:

Speed = Distance / Time

So, speed of John = \($(x + 5) / (x - 1)$\) Speed of John =\($11 / 5$\) mph

Similarly, speed of Jane = \($(x + 11) / (x + 1)$\)

Speed of Jane = \($17 / 7$\) mph

Since both have to be equal, Speed of John = Speed of Jane Therefore,

\($(x + 5) / (x - 1) = (x + 11) / (x + 1)$\)

Solving this equation we get ,x = 2Speed of John = \($7 / 3$\) mph

Speed of Jane = \($7 / 3$\) mph

Thus, their speed was \($7 / 3$\) mph.

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Answer:

x=22

Step-by-step explanation:

Let the unknown number be x

:- the power of x = x³

From the question

x³-15=7 and x²

x³=7+15

x³ * x²= 22

x= 22

The error involved in approximating the sum of the given series by the sum of the first five terms of the series is `R5 = 1/6³ + 1/7³ + ...`.

To estimate the error that is made by approximating the sum of the given series by the series the first 5 terms 1/k³, we can use the remainder term of a convergent series.

The given series is ∑ 1/k³ from k = 1 to infinity.We have to find the error involved in approximating the sum of the given series by the sum of the first five terms of the series.

That is, we need to find the difference between the actual sum of the series and the sum of the first five terms of the series.

The sum of the series is given by: `S = 1/1³ + 1/2³ + 1/3³ + 1/4³ + ... + 1/n³ + ...` We can use the remainder term of the series to find the error in approximation.

The remainder term `Rn` is given by: `Rn = Sn - S` where `Sn` is the sum of the first `n` terms of the series. Thus, we have to find the remainder term for `n = 5`.

The remainder term `Rn` is given by: `Rn = S - Sn = 1/6³ + 1/7³ + ...` Since the given series is convergent, the remainder term `Rn` tends to zero as `n` tends to infinity.

So, if we take the sum of the first five terms of the series, the error involved in approximation is given by the remainder term `R5`.

The error involved in this approximation is very small and can be neglected.

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Comparing with the approximations obtained in parts (a) and (b), we see that the approximation using Euler's method with step size 0.1 is closer to the exact solution

What is the linear equation?

A linear equation is an algebraic equation of the form y=mx+b. where m is the slope and b is the y-intercept.

The given differential equation is:

dy/dx = x + y

with initial condition y(0) = 1.

(a) Using Euler's method with step size 0.2, we have:

x₁ = 0 + 0.2 = 0.2

y₁ = 1 + 0.2(0 + 1) = 1.2

x₂ = 0.2 + 0.2 = 0.4

y₂ = 1.2 + 0.2(0.2 + 1.2) = 1.44

Therefore, the approximation of y(0.4) using Euler's method with step size 0.2 is 1.44.

(b) Using Euler's method with step size 0.1, we have:

x₁ = 0 + 0.1 = 0.1

y₁ = 1 + 0.1(0 + 1) = 1.1

x₂ = 0.1 + 0.1 = 0.2

y₂ = 1.1 + 0.1(0.1 + 1.1) = 1.22

x₃ = 0.2 + 0.1 = 0.3

y₃ = 1.22 + 0.1(0.2 + 1.22) = 1.364

x₄ = 0.3 + 0.1 = 0.4

y₄ = 1.364 + 0.1(0.3 + 1.364) = 1.537

Therefore, the approximation of y(0.4) using Euler's method with step size 0.1 is 1.537.

(c) The given differential equation can be solved exactly by the separation of variables:

dy/(x+y) = dx

ln|x+y| = x + C

\(|x+y| = e^(x+C) = Ce^x\)

\(x+y = \pm Ce^x\)

Using the initial condition y(0) = 1, we have:

0 + 1 = ±C

C = -1

So the solution to the differential equation is:

x + y = -eˣ

Substituting x = 0.4, we get:

\(y(0.4) = -e^{0.4}\)

≈ -1.491

Hence, Comparing with the approximations obtained in parts (a) and (b), we see that the approximation using Euler's method with step size 0.1 is closer to the exact solution.

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Answer:

x = 18

Step-by-step explanation:

x/81 = 4/x

cross-multiply:

x² = 81(4)

x² = 324

x = \(\sqrt{324}\) = 18