Flying against the wind, a jet travels 4060 miles in 7 hours. Flying with the wind the same jet travels 3760 miles in 4 hours. What is the rate of the jet in still air and what is the rate of the wind?

Answer:

6(8w + 7x)

Step-by-step explanation:

Hello!

The greatest common factor between 48 and 42 is 6. We can factor out 6 from each term.

The expression is 6(8w + 7x).

Answer:

y=1/5x+0

Step-by-step explanation:

answer/explanation:

hope this helps

Answer:

Check the attachment.

Step-by-step explanation:

1) Create a table. Substitute the \(x\) values into the this: \(y=-3x+4\).

\(x\): 0, 1, 2

\(y\): 4, 1, -2

2) Plot the coordinates on the graph and draw a line from one point to the other. Make sure you extend the line, and add the equation beside the line drawn. Check the attachment for a better visual.

Answer:

Given that the vertices of quadrilateral PQRS are P(6,3), Q(4,2), R(2,4) and S(4,5) and the quadrilateral is dilated with a scale factor of 2, about the origin.

Now, let's find the new vertices of the dilated image:

Vertex P is dilated by a scale factor of 2, its new coordinates will be (2 × 6, 2 × 3) = (12, 6). Therefore, the new vertex P' is at (12, 6).

Vertex Q is dilated by a scale factor of 2, its new coordinates will be (2 × 4, 2 × 2) = (8, 4). Therefore, the new vertex Q' is at (8, 4).

Vertex R is dilated by a scale factor of 2, its new coordinates will be (2 × 2, 2 × 4) = (4, 8). Therefore, the new vertex R' is at (4, 8).

Vertex S is dilated by a scale factor of 2, its new coordinates will be (2 × 4, 2 × 5) = (8, 10). Therefore, the new vertex S' is at (8, 10).

Therefore, the coordinates of the vertices of the final image are P’(12, 6), Q’(8, 4), R’(4, 8), and S’(8, 10).So, the correct option is D. P’(12, 6), Q’(8, 4), R’(4, 8), and S’(8, 10).

Step-by-step explanation:

Hope this helps you!! Have a good day/night!!

The average number of students who are afraid of spiders and snakes is 15. (Option C).

To calculate the average number of students who are afraid of spiders and snakes, you need to add the number of students afraid of spiders and the number of students afraid of snakes, and then divide by 2 (since there are two categories being considered: spiders and snakes).

Average = (Number of students afraid of spiders + Number of students afraid of snakes) / 2

Given the information:

Number of students afraid of spiders = 18

Number of students afraid of snakes = a little more than 11 (let's consider 12 for calculation)

Average = (18 + 12) / 2 = 30 / 2 = 15

So, the average number of students who are afraid of spiders and snakes is 15.

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Written without exponents, you'd have

   abbbcc   and    aabbc

Both have one a, two b's, and one c.

The GCF is \(ab^2c\), since those are the greatest factors they all have in common.

The reasonable domain for the function is (b) x > 0

From the question, we have the following parameters that can be used in our computation:

The function f(x) = 75x + 100

Where x is the number of hours

f(x) is the total cost.

In this case, the number of hours cannot be negative or 0

This means that the values of x in the function would be x > 0

These values of x are the domain

So, the reasonable domain for the function os (b) x > 0

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Answer: a= 0.0231

Step-by-step explanation:

n=8

p=0.75

q=1 - 0.75 = 0.25

(p=x)

p(5) = 8C5 (0.25)^5 (0.75)^8-5

p(5)= 0.0231

Or 2.31%

The probability that exactly 3 people  from that group will go to Ches Tahoe restaurant is 2.11%

The probability that at least 35 people will go to Ches Tahoe  the restaurant is -1.88.

Given that,

When you select a random person, the probability that this person will go to Ches Tahoe restaurant is 75%,

We have to determine,

You randomly select 8 people. What is the probability that exactly 3 people

from that group will go to Ches Tahoe restaurant.

You randomly select 50 people. Use the normal approximation to the binomial distribution to find the probability that at least 35 people will go to Ches Tahoe restaurant.

According to the question,

When you select a random person, the probability that this person will go to Ches Tahoe restaurant is 75%,

You randomly select 8 people.

Then,

The probability that exactly 3 people

from that group will go to Ches Tahoe restaurant is,

\(P(x) = ^nC_x \times q^x \times p^{n-x}\)

Where n = 8, x = 5, q = 1 - 0.75 = 0.25, and p = 0.75

Substitute all the values in the expression,

\(P(5) = ^8C_5 \times (0.25)^5 \times (0.75)^{8-5}\\\\P(5) = \dfrac{8!}{(8-5)!. 5!} \times 0.00097 \times (0.75)^3\\\\P(5) = \dfrac{8 \times 7 \times 6}{3 \times 2} \times 0.00097 \times 0.42\\\\P(5) = 0.2118\\\\P(5) = 2.11 \ Percent\)

The probability that exactly 3 people from that group will go to Ches Tahoe restaurant is 2.11%.

You randomly select 50 people. Use the normal approximation to the binomial  distribution

Then, the probability that at least 35 people will go to Ches Tahoe  restaurant is,

Mean for that at least 35 people will go to Ches Tahoe  restaurant is,

\(\mu = n \times p \\\\\mu = 8 \times 0.75\\\\\mu = 6\)

And standard deviation that at least 35 people will go to Ches Tahoe  restaurant is,

\(\sigma = \sqrt{n \times p \times q} \\\\\sigma = \sqrt{0.75 \times 0.25 \times 8}\\\\\sigma = \sqrt{1.5}\\\\\sigma = 0.53\)

Normal approximation to the binomial distribution is,

\(z = \dfrac{x-\mu}{\sigma}\\\\z = \dfrac{5-6}{0.53}\\\\z = \dfraac{-1}{0.53}\\\\z = -1.88\)

The probability that at least 35 people will go to Ches Tahoe  the restaurant is -1.88.

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Answer: A side of a square for the area given 100/9 square meters, then length = 3.33 meters .

Step-by-step explanation:

The area of a square is (100/9) cm.

So, find out the length of the square?

Then,

Define Square:

A square is closed, two-dimensional shape with 4 equal sides. A square is a quadrilateral. We can find the shape of a square in a game board or chess board, a wall clock and in a slice of bread, around us.

The area of any rectangle is length times width. The area of a square is a special case where length equals width, so side times side or side squared is used for area.

Define Area of Square:

Area of a square is defined as the number of square units needed to fill a square. In general, the area is defined as the region occupied inside the boundary of a flat object or 2d figure. The measurement is done in square units with the standard unit being square meters (m²).                    

The area of any rectangle is length times width. The area of a square is a special case where length equals width, so side times side or side squared is used for area.    

Area of a Square = Side ×  Side

Therefore, the area of square = side²  square units                          

                                              A = s²

Means,       A= area of square

You have the area so you need to find the side length that when multiplied by itself equals that area. If you don’t know what number squared is (100/9) you can plug and chug or use a calculator with square roots.

Replace with A=(100/9) values,

We can write,

                        A = s²

               (100/9) = s²

Then we can solve it,

               \(\sqrt{100/9}\) = s

                 \(\sqrt{\frac{(10^{2}) }{3^{2} } }\) = s

We can write, \(\sqrt{10^{2} }\) = 10 , and \(\sqrt{3^{2} }\) = 3

Then,  

                    (10/3) = s

Therefore,   s = (10/3)

                    s = 3.33 meters

So, length = 3.33 meters

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Answer:

It’s  -3

Step-by-step explanation:

\(\huge\text{Hey there!}\)

\(\mathsf{-3^2+ (-4+7) (2)}\)

\(\mathsf{-3^2 = \bf -9}\)

\(\mathsf{-9+(-4+7)(2)}\)

\(\mathsf{(-4+7)=\bf 3}\)

\(\mathsf{-9+ (3)(2)}\)

\(\mathsf{3(2)=\bf 6}\)

\(\mathsf{-9+6}\)

\(\mathsf{-9+6=\bf -3}\)

\(\boxed{\boxed{\large\textsf{Answer: \huge \bf -3}}}\huge\checkmark\)

\(\text{Good luck on your assignment and enjoy your day!}\)

~\(\frak{Amphitrite1040:)}\)

Answer: 33

Step-by-step explanation: When a tangent and radius intersect (as in the diagram) they will always be perpendicular. And using the Triangle Sum Theorem that all angles add up to 180 when get that m<BCA must be 33 degrees.

Answer:

(-1,-4)

Step-by-step explanation:

Because it is near -1 in x axis and -4 y axis

Answer:

The other equation could be: 6y = 4x - 18

Step-by-step explanation:

System with infinite number of solutions:

A linear system has an infinite number of solutions when one equation is a multiple of another.

One of the equations of the system is 3y = 2x - 9. Which could be the other equation?

A multiple of 3y = 2x - 9

Multiplying by 2, the other equation could be: 6y = 4x - 18

Answer:

B: y=2/3 x -3

Step-by-step explanation:

I got it right on Edge

The final result of the integral is:

∫ (log(1 + x²) / (x + 1)²) dx = log(x + 1) - 2 (log(x + 1) / x) - 2Li(x) + C,

where Li(x) is the logarithmic integral function and C is the constant of integration.

We have,

To solve the integral ∫ (log(1 + x²) / (x + 1)²) dx, we can use the method of substitution.

Let's substitute u = x + 1, which implies du = dx. Making this substitution, the integral becomes:

∫ (log(1 + (u-1)²) / u²) du.

Expanding the numerator, we have:

∫ (log(1 + u² - 2u + 1) / u²) du

= ∫ (log(u² - 2u + 2) / u²) du.

Now, let's split the logarithm using the properties of logarithms:

∫ (log(u² - 2u + 2) - log(u²)) / u² du

= ∫ (log(u² - 2u + 2) / u²) du - ∫ (log(u²) / u²) du.

We can simplify the second integral:

∫ (log(u²) / u²) du = ∫ (2 log(u) / u²) du.

Using the power rule for integration, we can integrate both terms:

∫ (log(u² - 2u + 2) / u²) du = log(u² - 2u + 2) / u - 2 ∫ (log(u) / u³) du.

Now, let's focus on the second integral:

∫ (log(u) / u³) du.

This integral does not have a simple closed-form solution in terms of elementary functions.

It can be expressed in terms of a special function called the logarithmic integral, denoted as Li(x).

Therefore,

The final result of the integral is:

∫ (log(1 + x²) / (x + 1)²) dx = log(x + 1) - 2 (log(x + 1) / x) - 2Li(x) + C,

where Li(x) is the logarithmic integral function and C is the constant of integration.

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Answer:

x = 7

Step-by-step explanation:

TV = 17

TV = TU + UV

17 = 2x - 4 + 2x - 7

17 = 4x - 11

28 = 4x

x = 7

Answer:

Step-by-step explanation for Part-2:

We know that:

Work:

Hence, the measure of ∠EGF is 105°.

Step-by-step explanation for Part-3:

We know that:

Work:

Hence, the measure of ∠D is 65°

not clear way ..... clear it

Answer:

b = 8

Step-by-step explanation:

a² + b² = c²

15² + b² = 17²

225 + b² = 289

b² = 64

√b² = 64

b = 8

Step-by-step explanation:

Hope this helps.
If you reflect in the y-axis, it would look like the following.

Answer:

You would be required to pay $587.50

Step-by-step explanation:

Divide $1762.50 by three:

You get $587.50

To find how much you have left:

Subtract 587.50 from 668.72:

You'd be left with

$81.22

Answer:

If you are asking if you can afford to pay rent, then yes you can. Your share of rent would be 1762.50 divided by 3, which equals 587.50. Therefore since 587.50 is less than 668.72, you can afford to pay your rent. Hope this helps!

Step-by-step explanation:

Chuck received a credit of $369.15 for his partial payment.

What is simple interest?

The interest on a loan or principal sum can be easily calculated using simple interest. Simple interest is a notion that is employed across a wide range of industries, including banking, finance, automobiles, and more.

The total cost of the baking potatoes is calculated by multiplying the weight of potatoes by the cost per pound:

800 pounds x $0.85/pound = $680

Since the terms are n/30, Chuck has 30 days to pay the invoice in full to receive the discount. He made a partial payment of $425 within the discount period, which means he has a remaining balance of:

$680 - $425 = $255

To determine how much credit Chuck received for his partial payment, we need to calculate the discount he would have received if he had paid the full amount within the discount period. The discount is calculated by multiplying the total cost by the discount rate, which is calculated by dividing the discount period by the number of days in the year:

Discount rate = discount period / number of days in the year

Discount rate = 30 / 365

Discount rate = 0.0822

Discount = total cost x discount rate

Discount = $680 x 0.0822

Discount = $55.85

Since Chuck only paid $425 within the discount period, he is entitled to a credit for the remaining discount amount:

Credit = Discount - Partial payment

Credit = $55.85 - $425

Credit = -$369.15

Therefore, Chuck received a credit of $369.15 for his partial payment.

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Answer:

$75

Step-by-step explanation:

30% of $250 = amount of money saved

30% of 250 = $75

Answer:

The approximate user base of the social media site 10 months from now would be approximately 52,374.

Step-by-step explanation:

To calculate the approximate user base of the social media site 10 months from now, considering a 4% increase per month, we can use the following steps:

1. Calculate the monthly growth factor: 1 + (4% / 100) = 1 + 0.04 = 1.04

2. Apply the growth factor to the current user base for each month:

  Month 1: 35,930 * 1.04 = 37,387.2 (approx.)

  Month 2: 37,387.2 * 1.04 = 38,868.49 (approx.)

  ...

  Month 10: Previous Month * 1.04

By repeating this calculation for each month, we can determine the approximate user base 10 months from now.

Month 1: 37,387.2

Month 2: 38,868.49

Month 3: 40,391.33

Month 4: 41,957.61

Month 5: 43,569.34

Month 6: 45,228.24

Month 7: 46,936.32

Month 8: 48,695.44

Month 9: 50,507.45

Month 10: 52,374.40 (approx.)

Therefore, the approximate user base of the social media site 10 months from now would be approximately 52,374.

Answer:

a) P(  \(Y^{C}\) | X ) = 0.180

b) P(Y | \(X^{C}\)  ) = 0.998

Step-by-step explanation:

Let

P(X) - Probability that he acts hungry

P(Y) - Probability that he had ate dinner,

Given,

P(X | Y) = 0.5

P(X | \(Y^{C}\)  ) = 0.99

P(Y) = 0.9

a.)

P(  \(Y^{C}\) | X ) =  \(\frac{P( X | Y^{C} ). P(Y^{C} ) }{P( X | Y^{C} ). P(Y^{C} ) + P( X | Y ) . P (Y) }\)

                  = \(\frac{(0.99)(0.1)}{(0.99)(0.1) + (0.5)(0.9)} = \frac{0.099}{0.549}\) = 0.180

⇒P(  \(Y^{C}\) | X ) = 0.180

b.)

P(Y | \(X^{C}\)  ) = \(\frac{(1 - P(X | Y ) ) . P(Y)}{P( X^{C} ) } = \frac{(1 - P(X | Y ) ) . P(Y)}{ 1 - P( X ) }\)

                 = \(\frac{(1 - 0.5)(0.9)}{1 - [(0.99)(0.1) + (0.5)(0.9) ]} = \frac{(0.5)(0.9)}{1 - [(0.099) + (0.45) ]} = \frac{0.45}{1 - [0.540]} = \frac{0.45}{0.451}\) = 0.998

⇒P(Y | \(X^{C}\)  ) = 0.998

Answer:

7√2

7√2 is irrational since √2 is irrational

Step-by-step explanation:

3√2 + 2√8 = 3√2 + 2 × 2√2 = 3√2 + 4√2 = 7√2

7√2 is irrational since √2 is irrational

Answer:

18 Bowls of Candy

Step-by-step explanation:

Camila has 6 bags of candy, and she can pour 1/3 of a bag into a bowl. To determine how many bowls of candy she can make in total, we need to divide the total amount of candy by the amount of candy per bowl.

Since Camila can pour 1/3 of a bag into a bowl, it means she can make 3 bowls of candy with a full bag.

Now, we can calculate the total number of bowls of candy:

Total bowls of candy = (Number of bags) x (Bowls per bag)

Total bowls of candy = 6 bags x 3 bowls per bag

Total bowls of candy = 18 bowls

Therefore, Camila can make a total of 18 bowls of candy with her 6 bags of candy.