A plane traveled 5525 miles with the wind in 8.5 hours and 4505 miles against the wind in the same amount of time. Find the speed of the plane in still air and the speed of the wind. The speed of the plane in still air is ____(hours.miles.mph) ​(Simplify your​ answer.)

Answer:

(-4, y) and (4, y), where y is any real number.

Step-by-step explanation:

The point (-4; 7.5) is 4 units from the y axis.

All points that lie on the line x = -4 and the line x = 4 have the same distance from the y-axis of 4 units.

Answer:

Hope should not pull her defender.

Step-by-step explanation:

When Hope has pulled her defender:

The team had lost 4 times, tied 2 times, and won 3 times.

Hence, the total number of times she meets her goal is:

6 times (Since the goal is to either tie or win the game )

Hence, the probability that she meets her goal is =   6/9=2/3=0.66

When she  left her defender in the game:

The team has lost 1 time, tied 3 times, and won 6 times.

Hence, the total number of times she meets her goal is: 9

Hence, the probability that she meets her goal is: 9/10=0.9

As the probability of meeting her goal is more when she left her defender in the game is more.

 Hence, Hope should not pull her defender.

Answer:

B

Step-by-step explanation:

to find the inverse of a function, repalace f(x) with x, and replace x with y, proceed to solve for y and the answer you get is B

Answer:

B

Step-by-step explanation:

f(x)=5x/3+5

y=5x/3+5

x=5y/3+5

now solve for y

3x=5y+15

5y=3x-15

y=3x/5-3 or 3(x-5)/5

Answer:

The correct option is

This is a polynomial function of degree 7 with a leading coefficient of -1

Step-by-step explanation:

Functions that consist of a variable such as x raised to positive integer powers which are equal to or larger than zero added together to make the function are known as polynomial functions

Therefore, the function in the question which is f(X) = x⁴ × (2 - x³) + 1

Which can be expanded as follows

f(x) = 2·x⁴ - x⁷ + 1, which is the same as given as follow equation;

f(x) = -x⁷ + 2·x⁴ + 1

Which is  polynomial function with a leading coefficient of -1 as it consists of only whole number positive powers of x including the powers of x 4 and 7  

Therefore, the correct option is that f(x) is a polynomial function of degree 7 with a leading coefficient of -1.

Answer:

[tex]2ab - 6a + 5b - 15[/tex]

Step-by-step explanation:

Given

[tex]2ab - 6a + 5b + \_[/tex]

Required

Fill in the gap to produce the product of linear expressions

[tex]2ab - 6a + 5b + \_[/tex]

Split to 2

[tex](2ab - 6a) + (5b + \_)[/tex]

Factorize the first bracket

[tex]2a(b - 3) + (5b + \_)[/tex]

Represent the _ with X

[tex]2a(b - 3) + (5b + X)[/tex]

Factorize the second bracket

[tex]2a(b - 3) + 5(b + \frac{X}{5})[/tex]

To result in a linear expression, then the following condition must be satisfied;

[tex]b - 3 = b + \frac{X}{5}[/tex]

Subtract b from both sides

[tex]b - b- 3 = b - b+ \frac{X}{5}[/tex]

[tex]- 3 = \frac{X}{5}[/tex]

Multiply both sides by 5

[tex]- 3 * 5 = \frac{X}{5} * 5[/tex]

[tex]X = -15[/tex]

Substitute -15 for X in [tex]2a(b - 3) + 5(b + \frac{X}{5})[/tex]

[tex]2a(b - 3) + 5(b + \frac{-15}{5})[/tex]

[tex]2a(b - 3) + 5(b - \frac{15}{5})[/tex]

[tex]2a(b - 3) + 5(b - 3)[/tex]

[tex](2a + 5)(b - 3)[/tex]

The two linear expressions are [tex](2a+ 5)[/tex] and [tex](b - 3)[/tex]

Their product will result in [tex]2ab - 6a + 5b - 15[/tex]

Hence, the constant is -15

Answer:

75% (I think)

Step-by-step explanation:

1/4 of babies have no hair

2/4 of babies have little hair

1/4 of babies have a lot of hair

Answer:

£32.4

Step-by-step explanation:

£100 = 216 Swiss francs

x        =  70 francs

70 x 100=7000/216=32.4

Louis traveled 7,144 miles

Answer:

x = -6    x = -1

Step-by-step explanation:

We want to solve using the zero product property

x^2+7x=-6

Add 6 to each side

x^2 +7x +6 = 0

Factor

What 2 numbers multiply to 6 and add to 7

( x+6) (x+1) =0

Using the zero product property

x+6 =0          x+1 =0

x+6-6 =0-6    x+1-1 = 0-1

x = -6    x = -1

Answer:

Step-by-step explanation:

The equation of  a line in slope-intercept form is expressed as y = mx+c

m is the slope of the line

c is the intercept

m = Δy/Δx = y₂-y₁/x₂-x₁

Given the points on a line to be  (3,1) and (−6,4);

x₁ = 3, y₁ = 1, x₂ = -6 and y₂ = 4

m = 4-1/-6-3

m = 3/-9

m = -1/3

To get the intercept c, we will substitute any of the points given and the value of the slope into the equation y = mx+c. Using the point (3, 1) and m = -1/3

1 = -1/3(3)+c

1 = -1+c

c  = 1+1

c =2

Substituting m = -1/3 and c = 2 into the sllpe intercept form of the equation will give;

y = -1/3 x + 2

Hence the  equation for the line in slope-intercept form is y = -1/3 x + 2

Answer:

The answer is b

Step-by-step explanation:

since 2*9=18 and (x)(2x+3)=2x^2+3x

Answer: B

Step-by-step explanation:

Answer:

[tex]P(X_i=2) =\dfrac{1}{6}[/tex]

[tex]P(X_i=-1) =\dfrac{5}{6}[/tex]

Step-by-step explanation:

Given the numbers on the chips = 1, 1, 3 and 5

Miguel chooses two chips.

Condition of winning: Both the chips are same i.e. 1 and 1 are chosen.

Miguel gets $2 on winning and loses $1 on getting different numbers.

To find:

Probability of winning $2 and losing $1 respectively.

Solution:

Here, we are given 4 numbers 1, 1, 3 and 5 out of which 2 numbers are to be chosen.

This is a simple selection problem.

The total number of ways of selecting r numbers from n is given as:

[tex]_nC_r = \frac{n!}{r!(n-r)!}[/tex]

Here, n = 4 and r = 2.

So, total number of ways = [tex]_4C_2 = \frac{4!}{2!\times 2!} = 6[/tex]

Total number of favorable cases in winning = choosing two 1's from two 1's i.e. [tex]_2C_2 = \frac{2!}{2! 0! } = 1[/tex]

Now, let us have a look at the formula of probability of an event E:

[tex]P(E) = \dfrac{\text{Number of favorable ways}}{\text{Total number of ways}}[/tex]

So, the probability of winning.

[tex]P(X_i=2) =\dfrac{1}{6}[/tex]

Total number of favorable cases for -1: (6-1) = 5

So, probability of getting -1:

[tex]P(X_i=-1) =\dfrac{5}{6}[/tex]

Please refer to the attached image for answer table.

Answer:

two = 1/6

and -1 =  5/6

Step-by-step explanation:

Answer: g(1) = 9

Step-by-step explanation:

g(x) = 3(1/4)^(x-2) - 3

g(1) = 3(1/4)^(1-2) - 3

g(1) = 3(1/4)^(-1) - 3

g(1) = 3(4) - 3

g(1) = 12 - 3

g(1) = 9

Answer:

B: 2²

Step-by-step explanation:

3(7+2²) - 5

PEMDAS says parentheses first

Then we do the order of operations inside the parentheses

Exponents are the first thing inside the parentheses

Answer:

46°

Step-by-step explanation:

We can tell that this triangle is an isosceles triangle because 2 of it's sides are the same, therefore, two of it's angles are the same.

Looking at it, we can assume that the two angles not defined (x and the other one) are the two angles that are the same because they look similar.

Now, the angles of all triangles add up to 180°. So, we can subtract 88° from 180 to see what the two angles add up to.

[tex]180-88=92[/tex]

So both of these angles add up to 92 degrees. Since there are two, we divide 92 by 2.

[tex]92 \div 2 = 46[/tex]

Hope this helped!

Answer:

Step-by-step explanation:

Area of trapezoid:

[tex] \frac{1}{2} \times \: sum \: of \: parallel \: sides \: \times height[/tex]

plugging the values:

[tex] \frac{1}{2} \times (21 + 5) \times 2[/tex]

Calculate the sum

[tex] \frac{1}{2} \times 26 \times 2[/tex]

Reduce the numbers with G.C.F 2

[tex]13 \times 2[/tex]

Calculate the product

[tex]26[/tex] feet squared.

Hope this helps...

Best regards!

Answer:

(a) The probability that the average of the draws will be in the range 80 to 120 is 1.

(b) The probability that the average of the draws will be in the range 99 to 101 is 0.6827.

Step-by-step explanation:

According to the Central Limit Theorem if we have an unknown population with mean μ and standard deviation σ and appropriately huge random samples (n > 30) are selected from the population with replacement, then the distribution of the sample mean will be approximately normally distributed.  

Then, the mean of the sample means is given by,

[tex]\mu_{\bar x}=\mu[/tex]

And the standard deviation of the sample means is given by,

[tex]\sigma_{\bar x}=\frac{\sigma}{\sqrt{n}}[/tex]

As the sample selected is quite large, i.e. n = 400 > 30, then the sampling distribution of sample means will be approximately normally distributed.

Compute the mean and standard deviation of sample mean as follows:

[tex]\mu_{\bar x}=\mu=100\\\\\sigma_{\bar x}=\frac{\sigma}{\sqrt{n}}=\frac{20}{\sqrt{400}}=1[/tex]

So, [tex]\bar X\sim N(100, 1)[/tex]

(a)

Compute the probability that the average of the draws will be in the range 80 to 120 as follows:

[tex]P(80<\bar X<120)=P(\frac{80-100}{1}<\frac{\bar X-\mu_{\bar x}}{\sigma_{\bar x}}<\frac{120-100}{1})[/tex]

                            [tex]=P(-20<Z<20)\\\\=P(Z<20)-P(Z<-20)\\\\=(\approx1)-(\approx0)\\\\=1[/tex]

Thus, the probability that the average of the draws will be in the range 80 to 120 is 1.

(b)

Compute the probability that the average of the draws will be in the range 99 to 101 as follows:

[tex]P(99<\bar X<101)=P(\frac{99-100}{1}<\frac{\bar X-\mu_{\bar x}}{\sigma_{\bar x}}<\frac{101-100}{1})[/tex]

                            [tex]=P(-1<Z<1)\\\\=P(Z<1)-P(Z<-1)\\\\=0.6827[/tex]

Thus, the probability that the average of the draws will be in the range 99 to 101 is 0.6827.

Answer: 40 inches

Step-by-step explanation:

The woman weight and the seat will be: 145lb + 5lb = 150lb,

her son weight and the seat will be: 95lb + 5lb = 100lb

her daughter weight and the seat will be: 70lb + 5lb = 75lb

Given that the woman is on the left side of the seesaw, 60 inches from the fulcrum. The moment of the woman will be 150 × 60 = 9000

The daughter and son both get on the right side.

If the son sits 60 inches from the fulcrum, his moment will be:

100 × 60 = 6000

The sum of the moment of the son and daughter must be equal to the moment of their mother.

Let the position of the daughter = X

The moment of the daughter will be:

75 × X = 75X

Equate the moment of the mother to the sum of the moment of her children

9000 = 6000 + 75X

Collect the like terms

75X = 9000 - 6000

75X = 3000

X = 3000/75

X = 40

The position the daughter should sit to balance the seesaw is 40 inches away from seasaw to the right.

Answer:

(3, -3)

Step-by-step explanation:

Given functions:

and

Solution is the Intersect which is found by equalizing the two functions:

Solving for x:

As both values of x for the first function reveal f(x) = -3, the pairs are:

Answer:

Step-by-step explanation:

The easiest way to think about increasing area is by taking a square, if you double the dimensions, let's say they were 1 by 1 and then was made into a 2x2 square, you can fit four of the original cube (1x1) into the 2x2. So when the dimensions are doubled the area is quadrupled.

Even easier shortcut:

Take the cube idea, when the dimensions are messed with for anything, (works for volume too) always think of the smaller piece as 1x1 or 1x1x1. Then if the dimensions are double make it 2x2 or 2x2x2. If the dimensions are tripled then do 3x3 or 3x3x3, etc... 1x1=1x1x1, they are both equal to 1. So think of that as the numerator. the 2x2 in this case is equal to 4 so the smaller piece is 1/4 of the bigger one. Shown with volume if you double the dimensions of a cube that was 1x1x1 into 2x2x2. 1x1x1 still equals 1 so that's still the numerator and 2x2x2 is equal to 8 so the 1x1x1 cube is 1/8 of the 2x2x2, in other words you can fit eight 1x1x1 cubes into the 2x2x2 cube.

Hope this helps with area and volume.

Answer:

Step-by-step explanation:

number of likely voters = 2022

candidate A = 49%

candidate B = 46%

margin of error = 5%

using the concept of a confidence interval to explain

from the result of the poll conducted candidate A scored 49% of the votes while Candidate B scored 46% therefore the difference between the two voters is 3%.

also the margin of error is 5% which is higher than the 3% difference between the candidates. this margin error means that the 5% can vote for either candidate A or candidate B .which makes the results TOO CLOSE TO CALL

Answer: The answer is D . The graph

Step-by-step explanation: It was the answer given on Edge.

Answer:

d

Step-by-step explanation:

Answer:

8.3miles

Step-by-step explanation:

Here Jeff's sister drives 14 miles

his brother only drives 57/10 miles then the question is only asking the difference between their distance of driving to school knowing fully well that Jeff's sister drive farther than his brother, then we find the difference between their drives which is done bow

14miles -57/10 miles

= 83/10

= 8.3miles

Therefore, Jeff's sister drive 8.3miles farther than his brother

Answer:

Step-by-step explanation:

A frequency table can be used to group a raw data. It shows the quantity of each variable in the data.

The required answers to the question can be found in the attachments to this answer.

Answer:

Step-by-step explanation:

If you aren't supposed to do this on your calculator, then you'd have to figure out a way to get the bases of 10 to have the same power somehow in order to use the properties of exponents. This is the problem (you multiply the 2 dimensions together to find area, remember):

[tex](5.5*10^5)(4.2*10^4)[/tex]You cannot simply add the exponents on the 10's and say your power is 9...cuz it's not. It needs to be rewritten so that there is a power of 4 on the 10 in the parenthesis on the left. Do that this way:

[tex](5.5*10^4*10^1)(4.2*10^4)[/tex] Now you've got a common power of 4 between the 2 sets of parenthesis. 10 to the first is the same as 10, so multiplying that into the 5.5 gives us

[tex](55*10^4)(4.2*10^4)[/tex]

55 * 4.2 is 231 and 10 to the 4th times 10 to the 4th is 10 to the 8th.

[tex]231*10^8[/tex] But that's not in correct scientific notation. If we move the decimal to places to the left, we have to add 2 to the exponent of 8, giving us, finally,

[tex]2.31*10^{10}m^2[/tex]

Next use the hint to convert that to kilometers:

[tex]2.31*10^{10}m^2*\frac{1km^2}{1*10^6m^2}[/tex]

Dividing like bases means we subtract the lower exponent from the upper. 10 - 6 = 4, so the equivalent number of km squared is

2.31 × 10⁴ km²

Kilometers are comparable to miles, which is how we measure large things, like pieces of land. So it would be better to measure the forest in kilometers squared instead of meters squared.

Answer:

41/99

Step-by-step explanation:

There are two types of non terminating decimals. These are: Simple and Mixed

The one that you wrote up here is Simple, Since 41 is the only number that goes on repeating itself.

And mixed non terminating decimal is like 0.352 whereas 52 keeps repeating itself.

So when you change a non terminating decimal the denominator is always 9. But it depends on the decimal whether it is simple or mixed.

Since the decimal you wrote is simple and 2 digits keep on repeating themselves the denominator will be 99.

And the numerator will be the decimal number that keeps repeating itself without the repeating bar.

Therefore, the answer is 41/99.

Hope it helps ;) ❤❤❤

Answer:

Triangle in isosceles, scalene or equilateral forms and

quadrilateral in trapezoid, rectangle or square forms

Step-by-step explanation:

Refer to pictures attached

Shapes can be formed are:

when perpendicular  to base

when  angle cross section to base

when base is isosceles triangle and parallel cross section to base,

or angle cross section

when base is scalene triangle and parallel cross section to base,

or angle cross section

when base is equilateral triangle and parallel cross section to base,

or angle cross section

Answer:

h=−6, k=−30

Step-by-step explanation:

did on edge

Considering the equation of the parabola, the coefficients of the vertex are:

h=−6, k=−30

A quadratic equation is modeled by:

[tex]y = ax^2 + bx + c[/tex]

The vertex is given by:

[tex](h,k)[/tex]

In which:

[tex]h = -\frac{b}{2a}[/tex]

[tex]k = -\frac{b^2 - 4ac}{4a}[/tex]

In this problem, the equation is:

[tex]f(x) = x^2 + 12x + 6[/tex]

Hence the coefficients are a = 1, b = 12, c = 6, thus:

[tex]h = -\frac{12}{2} = -6[/tex]

[tex]k = -\frac{120}{4} = -30[/tex]

More can be learned about the equation of a parabola at https://brainly.com/question/24737967

Answer:

x = -7 or x = 2/3

Step-by-step explanation:

I'm assuming you meant solve for x when f(x) = 0.

f(x) = 3x(x + 7) - 2(x + 7)

0 = (x + 7)(3x - 2) -- Both terms have a common factor of (x + 7) so we can group them

x + 7 = 0 or 3x - 2 = 0 -- Use ZPP

x = -7 or x = 2/3 -- Solve