The smaller train is a scale drawing of the larger train is the length of the tire rod connecting the three tires of the larger chain as shown below is 36 inches right in equation to find the length of the tire rod of the smaller chain interpret your solution in the context of the problem.

Based on the calculations using unit pricing, Toilet paper B has a lower unit price and is the better deal between the two. Customers will save more money if they purchase toilet paper B rather than toilet paper A because the price per mega roll is lower. (option b)

Saving money while shopping is one of the best ways to reduce your expenses and have more disposable income for other things. Unit pricing is a pricing system that displays prices in standard units, allowing customers to compare prices across different brands and package sizes and save money. To determine which toilet paper deal is better, we can use the unit price method, which divides the price by the number of units in the package. The toilet paper with the lower unit price is the better deal.
The formula for unit pricing is as follows:
Unit price = total price ÷ number of units
Using the above formula, we can calculate the unit price of toilet paper A and toilet paper B as follows:
For Toilet paper A:
Unit price = $4.59 ÷ 6 mega rolls
Unit price = $0.765 per mega roll
For Toilet paper B:
Unit price = $9.02 ÷ 12 mega rolls
Unit price = $0.751 per mega roll
Therefore, based on the calculations, Toilet paper B has a lower unit price and is the better deal between the two. Customers will save more money if they purchase toilet paper B rather than toilet paper A because the price per mega roll is lower. (option b)
Unit pricing is a great way to compare prices, and consumers should always use it to determine the better deal between two products, as this will help them save money and stick to their budget.

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dy/dx = (y-3)(y+3) is the autonomous differential equation that satisfies all of the given properties.

The autonomous differential equation that satisfies all of the given properties is dy/dx = (y-3)(y+3). This equation has two equilibrium solutions at y = 0 and y = 3, and is positive for -inf < y < 0, and negative for 0 < y < 3, and positive for 3 < y < inf.

To demonstrate this, let's consider the equation at y=-3. Since y=-3 is less than 0, the equation can be simplified to dy/dx = 6. Since 6 is positive, y' is also positive, meaning that y is increasing. Similarly, if y=3, dy/dx = 0 which is neither positive nor negative, so y remains constant. Finally, for y>3, dy/dx = -6, which is negative, so y is decreasing.

Therefore, dy/dx = (y-3)(y+3) is the autonomous differential equation that satisfies all of the given properties.

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Based on the net present value profile, Project H has a higher NPV than Project E.

To compare the net present value (NPV) of Project E and Project H, we need to calculate the present value of cash flows for each project and determine which one has a higher NPV. The cash flow patterns for the two projects are as follows:

Project E:

Initial investment: -$100,000

Cash flows for Year 1: $40,000

Cash flows for Year 2: $50,000

Cash flows for Year 3: $60,000

Project H:

Initial investment: -$120,000

Cash flows for Year 1: $60,000

Cash flows for Year 2: $50,000

Cash flows for Year 3: $40,000

To calculate the present value of cash flows, we need to discount them using an appropriate discount rate. The discount rate represents the required rate of return or the cost of capital for the company. Let's assume a discount rate of 10%.

Using the formula method, we can calculate the present value (PV) of each cash flow and sum them up to obtain the NPV for each project:

For Project E:

PV = $40,000/(1 + 0.10)^1 + $50,000/(1 + 0.10)^2 + $60,000/(1 + 0.10)^3

PV = $36,363.64 + $41,322.31 + $45,454.55

PV = $123,140.50

For Project H:

PV = $60,000/(1 + 0.10)^1 + $50,000/(1 + 0.10)^2 + $40,000/(1 + 0.10)^3

PV = $54,545.45 + $41,322.31 + $30,251.14

PV = $126,118.90

Using the financial calculator method, we can input the cash flows and the discount rate to calculate the NPV directly. By entering the cash flows for each project and the discount rate of 10%, we find that the NPV for Project E is approximately $123,140.50 and the NPV for Project H is approximately $126,118.90.

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Answer:

The probability that on a particular week, the hospital will receive on high BP pregnant woman is 0.0068

Step-by-step explanation:

We use the Exponential distribution,

Since we are given that on average, 5 pregnant women with high blood pressure come per week,

So, average = m = 5

Now, on average, 5 people come every week, so,

5 women per week,

so, we get 1 woman per (1/5)th week,

Hence, the mean is m = 1/5 for a woman arriving

and λ = 1/m = 5 = λ

we have to find the probability that it takes higher than a week for a high BP pregnant woman to arrive, i.e,

P(X>1) i.e. the probability that it takes more than a week for a high BP pregnant woman to show up,

Now,

P(X>1) = 1 - P(X<1),

Now, the probability density function is,

\(f(x) = \lambda e^{-\lambda x}\)

And the cumulative distribution function (CDF) is,

\(CDF = 1 - e^{-\lambda x}\)

Now, CDF gives the probability of an event occuring within a given time,

so, for 1 week, we have x = 1, and λ = 5, which gives,

P(X<1) = CDF,

so,

\(P(X < 1)=CDF = 1 - e^{-\lambda x}\\P(X < 1)=1-e^{-5(1)}\\P(X < 1)=1-e^{-5}\\P(X < 1) = 1 - 6.738*10^{-3}\\P(X < 1) = 0.9932\\And,\\P(X > 1) = 1 - 0.9932\\P(X > 1) = 6.8*10^{-3}\\P(X > 1) = 0.0068\)

So, the probability that on a particular week, the hospital will receive on high BP pregnant woman is 0.0068

The angle LKN in the rhombus is 62 degrees.

A rhombus is a quadrilateral that has 4 sides equal to each other. The sum of angles in a rhombus is 360 degrees.

Opposite angles are equal in a rhombus. The diagonals bisect each other at 90 degrees. Adjacent angles add up to 180 degrees.

Therefore, let's find ∠LKN as follows:

m∠JMN = (-x + 69)

m∠LMJ = (-6x + 166)

Therefore,

1 / 2 (-6x + 166) = -x + 69

-3x + 83 = -x + 69

-3x + x = 69 - 83

-2x = -14

x = -14 / -2

x = 7

Therefore,

∠LKN = 1 / 2 (-6x + 166)

∠LKN = 1 / 2 (-6(7) + 166)

∠LKN = 1 / 2 (-42 + 166)

∠LKN = 62 degrees

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Answer:

Hello your answer should be A symmetric property

Step-by-step explanation:

hope this helps

Symmetric property of equality to show that 3a = 4b, then 4b = 3a?

The symmetric property of equality is a simple property that says we can interchange the sides of an equation without changing the truth-value of the equation. That is, if a = b, then b = a. Each side of the equation can be thought of as the mirror image of the other

We have the following information available from the question is:

We have to determine the which property can be used to show that if 3a = 4b, then 4b = 3a

Now, According to the question:

3a = 4b

4b = 3a (both are equal)

This property is used to simplify the equations, to reverse the equations, and also for proofs in numerical and non-numerical logic.

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The fence in dead center is about 399 feet from the third base.

The Pythagorean Theorem states that in the case of a right triangle, the square of the length of the hypotenuse, which is the longest side,  is equals to the sum of the squares of the lengths of the other two sides.

Hence the equation for the theorem is given as follows:

c² = a² + b².

In which:

For the triangle in this problem, we have that:

Hence the distance is obtained as follows:

d² + 90² = 409²

\(d = \sqrt{409^2 - 90^2}\)

d = 399 ft.

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Answer:

1) 30 pounds is the weight of the bag all together

2) science book is the heaviest book

Step-by-step explanation:

bag=4 pounds

library book=2 pounds

maths book=2×4=8 pounds

science book=8×2=16 pounds

4+2+8+16=30 pounds all together

heaviest book= science book (16 pounds)

Answer:

( ~ Sure, But i'm slow <3 ~ )

Is it....

x  =  6

Step-by-step explanation:

(( Sorry if i got it wrong- im Dumb. <3 ))

(( But here's a nice picture for u. ^^ ))

Answer: x = 6

Step-by-step explanation: 2x-5=7

                                                 +5 +5

                                              2x = 12                                                                   divide by 2 on both sides        

                                                 x = 6

Answer:

I think 6 mph

Step-by-step explanation:

I needore characters so ingnor this sentence.

Step-by-step explanation:

As my previous answer got deleted for being wrong (in which it was right), I will answer again.

The answer is 1. Why? Just plug it into the equation. F(1) = 2(1) + 5 = 7.

This is proof that it is right, and that there are some corrupt admins on brainly.

How to get to this solution?

Well notice how we are given what f(a) is. It is 2a + 5. So plug this in for f(a).

If we do so, we get 2a + 5 = 7.

Solving this equation, we get a = 1.

Answer:

2×2×2×2×5

Step-by-step explanation:

Express 80 as the product of its prime factors Write the prime factors in ascending order. ​

2 × 2 × 2 × 2 × 5

2×2×2×2×5 = 80

Answer: We have f(x)=3x⁵+6x²-5 and g(x)= 2x⁴+7x²-x+16

                        (f-g)(x)= 3x⁵-2x⁴-x²+x-21

Step-by-step explanation:

Here we have,

Given : f(x)=3x⁵+6x²-5 and g(x)= 2x⁴+7x²-x+16

We know,

(f-g)(x)= f(x)-g(x)

= (3x⁵+6x²-5 ) - ( 2x⁴+7x²-x+16)

On subtracting g(x) from f(x) we get,

(f-g)(x)= (3x⁵+6x²-5  - 2x⁴-7x²+x-16)

On simplify,

 (f-g)(x) =3x⁵-2x⁴-x²+x-21

Hence,

(f-g)(x) = f(x) - g(x) = 3x⁵-2x⁴-x²+x-21

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The discount amount is $213.6

The sale price for the exercise machines is $676.4

The first step is to calculate the discount amount

890 × 24/100

= 890 × 0.24

= 213.6

The next step is to calculate the sale price

890(1-0.24)

890(0.76)

676.4

Hence the discount amount is $213.6 and the sale price of the exercise machine is $676.4

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Lee's TV costs $4.05 to operate for a month of 30 days.

To calculate the cost of operating Lee's TV for a month, we need to find out the total number of kilowatt-hours (kWh) of electricity consumed by the TV during that time.

First, let's find out how many watts Lee's TV consumes in a day:

250 watts/hour x 3 hours/day = 750 watts/day

To convert this to kilowatts, we divide by 1000:

750 watts/day ÷ 1000 = 0.75 kilowatts/day

Now, we can calculate the total number of kilowatt-hours consumed by the TV in a month:

0.75 kilowatts/day x 30 days = 22.5 kilowatt-hours

Finally, we can calculate the cost of operating the TV for a month:

22.5 kilowatt-hours x 18 cents/kilowatt-hour = $4.05

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Answer:

$121.00

Step-by-step explanation:

y = 18.50x + 47.00

y = the total amount in the account

x = the number of weeks

y = 18.50(4) + 47.00

y = 74.00 + 47.00

y = 121

The translation direction is 5 units to the left.

To determine the translation direction and number of units, we can compare the original coordinates of point Q (Q(5, 4)) with the new coordinates of Q' after the translation (Q'(0, 4)).

By comparing the x-coordinates, we can see that the x-coordinate of Q' is smaller than the x-coordinate of Q, which means the triangle was translated to the left.

By comparing the y-coordinates, we can see that the y-coordinate of Q' is the same as the y-coordinate of Q, which means there was no vertical translation.

Therefore, the translation direction is 5 units to the left.

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1/2 is the probability of getting at least one answer correct

Given that: the exam has 4 multiple choice with 5 possible answers. This means there are 20 possible choices ( 5×4 = 20).

That means each problem has a probability of 1/20 correct answer. The probability of getting at least one answer means you either get one, two, three or four correct answers. Thus:

P (at least one correct) = P(1) + P(2) + P(3) + P(4)

                                      = 1/20 + 2/20 + 3/20 + 4/20

                                      = (1+2+3+4)/20

                                     = 10/20

                                     =   1/2

Therefore, the probability of getting at least one answer correct is 1/2

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The probability of getting at least one answer correct is equal to 7

That I guess at least one answer correctly means that I could get all four answers correct or three answers correct or two answers correct or only one answer correct. The probability of getting any one answer is 1/4 and probability of not getting an answer is 1 - 1/4=3/4. Or implies addition.

probability of getting all four answers correct = 1/4 +1/4 + 1/4 + 1/4 = 4/4 = 1

probability of getting three answers correct = 1/4 +1/4 + 1/4 + 3/4 = 6/4 = 3/2

probability of getting two answers correct = 1/4 +1/4 + 3/4 + 3/4 = 8/4 = 2

probability of getting all four answers correct = 1/4 +3/4 + 3/4 + 3/4 = 10/4 = 5/2

The probability of getting at least one answer correct = 1 + 3/2 + 2 + 5/2

The probability of getting at least one answer correct = (2 + 3 + 4 + 5)/2

The probability of getting at least one answer correct = 14/2

Thefore, the probability of getting at least one answer correctly is the whole number 7

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Answer:

You are correct

Step-by-step explanation:

x - 8 < 23

Add 8 to both sides

x - 8 + 8 < 23 + 8

Simplify

x < 31

Yes, you are correct.

Answer:

b) Y =5.73X +4.36

C)  =5.73225*(21)X +4.359

    124.73625

D) 163.728 = 5.73X +4.36  

     X = (163.728 - 4.36)/5.73

     X = 27.81291449

  Year would be 2027

Step-by-step explanation:

x1 y1  x2 y2

4 27.288  16 96.075

(Y2-Y1) (96.075)-(27.288)=   68.787  ΔY 68.787

(X2-X1) (16)-(4)=    12  ΔX 12

slope= 5 41/56    

B= 4 14/39    

Y =5.73X +4.36      

Answer:

Step-by-step explanation:

Step(i):-

Given first random sample size n₁ = 500

Given  Roper survey reported that 65 out of 500 women ages 18-29 said that they had the most say when purchasing a computer.

First sample proportion

                             \(p^{-} _{1} = \frac{65}{500} = 0.13\)

Given second sample size n₂ = 700

Given a sample of 700 men (unrelated to the women) ages 18-29 found that 133 men said that they had the most say when purchasing a computer.

second sample proportion

                             \(p^{-} _{2} = \frac{133}{700} = 0.19\)

Level of significance = α = 0.05

critical value = 1.96

Step(ii):-

Null hypothesis : H₀: There  is no significance difference between these proportions

Alternative Hypothesis :H₁: There  is significance difference between these proportions

Test statistic

\(Z = \frac{p_{1} ^{-}-p^{-} _{2} }{\sqrt{PQ(\frac{1}{n_{1} } +\frac{1}{n_{2} } )} }\)

where

        \(P = \frac{n_{1} p^{-} _{1}+n_{2} p^{-} _{2} }{n_{1}+ n_{2} } = \frac{500 X 0.13+700 X0.19 }{500 + 700 } = 0.165\)

       Q = 1 - P = 1 - 0.165 = 0.835

\(Z = \frac{0.13-0.19 }{\sqrt{0.165 X0.835(\frac{1}{500 } +\frac{1}{700 } )} }\)

Z =  -2.76

|Z| = |-2.76| = 2.76 > 1.96 at 0.05 level of significance

Null hypothesis is rejected at 0.05 level of significance

Alternative hypothesis is accepted at 0.05 level of significance

Conclusion:-

There is there is a difference between these proportions at α = 0.05

According to the question,

Women,

            \(= 0.13\)

Men,

            \(= 0.19\)

Now,

The pooled estimate of the proportion will be:

→ \(\hat p=\frac{x_1+x_2}{n_1+n_2}\)

By substituting the values,

      \(= \frac{65+133}{500+700}\)

      \(= 0.165\)

then,

→ \(\hat q = 1- \hat p\)

     \(= 1- 0.165\)

     \(= 0.835\)

hence,

The test statistics:

→ \(Z = \frac{\hat p_1- \hat p_2}{\sqrt{\hat p\times \hat q\times (\frac{1}{n_1} +\frac{1}{n_2} )} }\)

By putting the values, we get

      \(= \frac{0.13-0.19}{\sqrt{0.165\times 0.835\times (\frac{1}{500} +\frac{1}{700} )} }\)

      \(= -2.76\)

Thus the above response is right.  

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Answer:

The solution is (3, -3)

Step-by-step explanation:

5x + 2y = 9

2x - 3y = 15

Use elimination by addition/subtraction.  Multiply the first equation by 3 and the second by 2, obtaining:

15x + 6y = 27

4x   - 6y  =  30

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

19x        = 57

This yields x = 3.

Substituting 3 for x into 5x + 2y = 9, we get  5(3) + 2y = 9, or

15 + 2y = 9, or

2y = -6

This yields y = -3.

The solution is (3, -3)

Answer:

$35,000

Step-by-step explanation:

In a proposed business venture, Serena estimates that there is a 65% chance that she will make $70,000

And also a 35% chance that she will loose $30,000

Therefore the expected value can be calculated as follows

E= 65/100 × 70,000 + 35/100 × (-30,000)

= 0.65 × 70,000 + 0.35(-30,000)

= 45,500 - 10,500

= $35,000

Hence the expected value is $35,000

Based on the probability of the payoffs, we can calculate that the expected value is $35,000.

The expected value is calculated as:

= ∑(Probability of payoff x Payoff)

The expected value here is therefore:

= (65% x 70,000) + (35% x -30,000)

= 45,500 - 10,500

= $35,000

In conclusion, the expected value is $35,000.

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Answer:

1) \(\int\limits^{16}_{2} {\frac{dx}{2\cdot x \cdot \sqrt{\ln x}} } \approx 1.665\)

2) \(\frac{dy}{dx} = \pm \frac{1}{\sqrt{4\cdot x^{2}+7\cdot x +3}}\)

3) \(\int\limits^{2\sqrt{3}}_{0} {\frac{dx}{\sqrt{4 + x^{2}}} } \approx 1.317\)

Step-by-step explanation:

1) \(\int\limits^{16}_{2} {\frac{dx}{2\cdot x \cdot \sqrt{\ln x}} }\)

This integral can be solved easily by using algebraic substitutions:

\(u = \ln x\), \(du = \frac{dx}{x}\)

Then, the integral can rewritten as follows:

\(\int {\frac{dx}{2\cdot x\cdot \sqrt{\ln x}} } = \frac{1}{2}\int {\frac{du}{u^{1/2}} } = \frac{1}{2}\int {u^{-1/2}} \, du\)

\(\int {u^{-1/2}} \, du = 2\cdot u^{1/2} + C = 2\cdot \sqrt{\ln x} + C\)

Where \(C\) is the integration constant.

\(\int\limits^{16}_{2} {\frac{dx}{2\cdot x \cdot \sqrt{\ln x}} } = F(16) - F(2)\)

\(F(16) - F(2) = 2\cdot (\sqrt{\ln 16}-\sqrt{\ln 2})\)

\(F(16) - F(2) \approx 1.665\)

2) Let be \(y = \cosh^{-1} (2\cdot \sqrt{x+1})\), then we obtain the expression by the definition of the derivative for the inverse hyperbolic cosine and the chain rule:

\(\frac{dy}{dx} = \pm\frac{1}{\sqrt{4\cdot x + 3}}\cdot \left(\frac{1}{\sqrt{x+1}} \right)\)

\(\frac{dy}{dx} = \pm \frac{1}{\sqrt{(4\cdot x + 3)\cdot (x+1)}}\)

\(\frac{dy}{dx} = \pm \frac{1}{\sqrt{4\cdot x^{2}+7\cdot x +3}}\)

3) \(\int\limits^{2\sqrt{3}}_{0} {\frac{dx}{\sqrt{4 + x^{2}}} }\)

This integral can be solved by the following trigonometric substitutions:

\(\frac{2}{\sqrt{4 + x^{2}}} = \cos \theta\)

\(\frac{1}{\sqrt{4+x^{2}}} = \frac{\cos \theta}{2}\)

\(\frac{x}{2} = \tan \theta\)

\(x = 2\cdot \tan \theta\)

\(dx = 2\cdot \sec^{2}\theta \,d \theta\)

\(\int {\frac{dx}{\sqrt{4+x^{2}}} } = \int {\left(\frac{\cos \theta}{2} \right)\cdot (2\cdot \sec^{2}\theta)} \, d\theta = \int {\sec \theta} \, d\theta\)

\(\int {\sec \theta}\,d\theta = \ln |\sec \theta + \tan \theta| + C\)

\(\ln \left|\frac{\sqrt{4+x^{2}}}{2} + \frac{x}{2} \right| + C\)

Where \(C\) is the integration constant.

\(\int\limits^{2\sqrt{3}}_{0} {\frac{dx}{\sqrt{4 + x^{2}}} } = F(2\sqrt{3}) - F(0)\)

\(F(2\sqrt{3}) - F(0) = \ln \left|2+\sqrt{3}\right|-\ln \left|1\right|\)

\(F(2\sqrt{3}) - F(0) \approx 1.317\)

Answer:

Red grapes.

Step-by-step explanation:

If you find how much one bag of each grape cost which is:

$13.00 ÷ 5 = 2.60 (1 bag of red grapes)

$5.08 ÷ 2 = $2.54 (1 bag of green grapes)

See the price and you'll know it is red grapes.

To find the total time it takes for the airplane to travel from Mumbai to Tokyo via Seoul, we need to add the time taken for the Mumbai-Seoul leg and the Seoul-Tokyo leg.

The airplane takes 3.2 hours to fly from Mumbai to Seoul.

The airplane takes 1 1/3 hours to fly from Seoul to Tokyo, which is equivalent to 1.33 hours.

To find the total time, we add the two durations:

3.2 hours + 1.33 hours = 4.53 hours

Therefore, it takes approximately 4.53 hours for the airplane to travel from Mumbai to Tokyo if it flies through Seoul.

Answer:

-1 7/10 and -1.7

Step-by-step explanation:

The equation to represent this situation is given by 0.65x = 282.75 .

In the various mathematical formulas that are used, the equals sign is used to show that two expressions on either side of the equal sign are equal.  The meaning of the word equation and its cognates might vary slightly depending on the language.

Finding the exact values of the unknown variables that result in the given equality is the very first step in the solving of a variable equation. The values of the unknown variables that fulfil the equality are the equation's solutions, also known as the variables for which the equation must be solved. There are two sorts of equations.

Le t the original cost of the bike be x dollars.

After 35% reduction the new cost is x - (35% of x) = 0.65 x

Therefore 0.65 x = 282.75

or, x = 435

Therefore the cost of the bike is $435.

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We have shown that C is the image of A by dilation with center B and ratio 3.

Now, To show that C is the image of A by dilation with center B and ratio 3, we need to follow these steps:

Firstly, Find the vector AB by subtracting the coordinates of B from the coordinates of A:

AB = A - B = (6 - 3, 4 - 7) = (3, -3)

Multiply the vector AB by the dilation ratio of 3:

3 AB = 3 (3, -3)  = (9, -9)

Add the resulting vector to the coordinates of the center B:

BC = B + 3 AB = (3, 7) + (9, -9)

BC = (12, -2)

Hence, Compare the resulting point BC to the coordinates of C to show that they are the same:

BC = (12, -2) = C

Therefore, we have shown that C is the image of A by dilation with center B and ratio 3.

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Answer: 3.8

Step-by-step explanation: