an airplane travels 5032 kilometers against the wind in 8 hours and 6152 kilometers with the wind in the same amount of time. what is the rate of the plane in still air and what is the rate of the wind?

y= x² - 4 is the function symmetric about the point (0,3).

Graph is a mathematical representation of a network and it describes the relationship between lines and points.

We need to find the  function's graph is symmetric about the point (0,3)

You want a parabola with a vertex at the point (0,3) so that is symmetrical on each side of that point.

Using the point (0,3),

The equation for a parabola in vertex form and then simplify:

Vertex = (h,k)

Vertex = (0,3)

y = (x - h)² + k

= (x - 0)² +3

y= x² - 4

Hence, y= x² - 4 is the function symmetric about the point (0,3).

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Answer:
1.80

Step-by-step explanation:

Answer:

Volume of a cylinder (v) = πr²h

Step-by-step explanation:

Given V = 5m³

r = 0.7m and π = 3.14

h= ?

using V = πr²h

5 = 3.14 x 0.7² x h

5 = 3.14 x 0.49 xh

5= 1.5386h

divide both side by 1.5386

5/1.5386 = h

h= 3.24970

h= 3.25m ( nearest hundredth)

Please refer to the photo taken.

Answer:

  -(√2 +√6)/4

Step-by-step explanation:

You want the exact value of sin(17π/12).

The sine can be written as ...

  sin(17π/12) = sin(π +5/12π)

  = -sin(5/12π) = -sin(2/12π +3/12π)

  = -sin(π/6 +π/4)

  = -(sin(π/6)cos(π/4) +cos(π/6)sin(π/4))

  = -((1/2)(√2/2) +(√3/2)(√2/2))

  = -(√2 +√6)/4

The sine of 17π/12 is -(√2+√6)/4.

Answer:

x = 12

Step-by-step explanation:

6x = 72 ( isolate x by dividing both sides by 6 )

x = 72 ÷ 6 = 12

Answer:

Step-by-step explanation:

6x = 72

Here, 6 is in multiplication with the variable x.

We will move 6 to the right side. With this the 6 which was in multiplication with x will now go in division with 72, by rule.

x = 72/6

x = 12

therefore, x = 12

The train does not always go the same distance each minute.

Predicted amount of time to travel 30 kilometers is equal to 47.52 minutes.

In order to determine a linear equation for the line of best fit (trend line) that models the data points contained in the table, we would have to use a graphing calculator (scatter plot).

In this scenario, the time (in minutes) would be plotted on the x-axis of the scatter plot while the distance (km) would be plotted on the y-axis of the scatter plot.

On the Excel worksheet, you should right click on any data point on the scatter plot, select format trend line, and then tick the box to display an equation for the line of best fit (trend line) on the scatter plot.

From the scatter plot (see attachment) which models the relationship between the distance (km) and time (in minutes), a linear equation for the line of best fit is given by:

y = 1.40x + 5.52

Next, we would determine the predicted amount of time to travel 30 kilometers:

y = 1.40(30) + 5.52

y = 42 + 5.52

y = 47.52 minutes.

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Answer:

a 22950

b 4590

Step-by-step explanation:

7.5% of 306,000 is 22950

20% of 22950 is 4590

The exponential equation of the given statement will be equal to, 1262 ×[tex](2)^x[/tex].

Mathematical expressions with two algebraic symbols on either side of the equal (=) sign are called equations.

This relationship is illustrated by the left and right expressions being equal. The left-hand side equals the right-hand side is a basic, straightforward equation.

As per the given information in the question,

Total number of downloads initially = 1,262

Let the number of months be x.

Then, the equation will be,

y = 1262[tex](2)^x[/tex]

Here, y is the total number of songs.

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In a deck of playing cards has 52 cards of which 12 are face cards, The odds are 33 / 3315 or 0.01 that the top 3 are face cards.

The total number of cards was 52, and there were 12 face cards.

Probability equals the number of possible outcomes divided by the total number of possibilities.

The first attempt had a probability of 12/52,

the second attempt had a probability of 11/51,

and the third attempt had a probability of 10/50.

Therefore, the probability that each of the three cards are face cards is equal to 12 / 52 × 11 / 51 × 10 / 50 = 1320 / 132600 = 132 / 13260 = 33 / 3315

the probability that all three are face cards = 0.00995475113 ≈ 0.01

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The expression represent a trinomial polynomial with three terms. The constant term is 1 , the leading term is 5, and the leading coefficient is 1 / 7.

A polynomial is defined as an expression which is composed of variables, constants and exponents, that are combined using operations such as addition, subtraction, multiplication and division.

Trinomials are the algebraic expressions with three unlike terms.  Trinomial has three terms.

A constant term is a term in an algebraic expression that does not contain any variables and therefore is constant.

The leading term is the term with the highest power of x.

The leading coefficient of a polynomial is the coefficient found with the variable that has the largest exponent.

Therefore, the expression is a trinomial polynomial. This means it has 3 terms.

The constant term of the polynomial is 1 ,

The leading term is 5, and the leading coefficient is 1 / 7.

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If 5 guests are randomly selected from 17 guest and all 5 prizes are identical, there are 89107200 ways in which the prizes can be awarded.

It is given to us that -

17 guests are in attendance at a baby shower

5 of them are randomly selected for a prize

All the 5 prizes are identical

We have to find out the number of ways in which the prizes can be awarded.

In this case, we have to use the combination formula to find the required answer.

We know that the combinations of n number of objects taken r at a time can be represented by the formula as -

[tex]C(n,r) = r!\frac{n!}{(n-r)!}[/tex]   ------ (1)

where,

n = total objects in the given set

r = total chosen objects from the given set

According to the given information, we have -

n = 17

r = 5

Substituting these values in equation (1), we have

[tex]C(n,r) = r!\frac{n!}{(n-r)!}\\= > C(n,r) = 5!*\frac{17!}{(17-5)!}\\= > C(n,r) = 5!*\frac{17!}{12!}\\= > C(n,r) = 89107200[/tex]

Therefore, if 5 guests are randomly selected from 17 guest and all 5 prizes are identical, there are 89107200 ways in which the prizes can be awarded.

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The variables (x, y) have the solution (1, -3) in the system of linear inequality

A system of linear inequalities in two variables consists of at least two linear inequalities in the same variables. The solution of a linear inequality is the ordered pair that is a solution to all inequalities in the system and the graph of the linear inequality is the graph of all solutions of the system.

In the question given

y ≥ -x + 2 ...eq(i)

y > -5x - 2 ...eq(ii)

Plotting this on a graphing calculator to find the point of intersection which will determine the solution of the graph;

The solutions to the variables (x, y) in the linear inequalities are (1 , -3)

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Note that assuming that the instrument used was exogenous, one can conclude about the endogeneity of an explanatory variable if the OLS and 2SLS estimates are significantly different: "The explanatory variable is endogenous and therefore 2SLS should be considered." (Option C)

Two-stage least squares (2SLS) regression analysis is a statistical approach used in structural equation analysis. The OLS approach has been extended using this methodology. It is employed when the error terms of the dependent variable are associated with the independent variables.

The ordinary least squares (OLS) approach is a linear regression methodology used to estimate a model's unknown parameters. The strategy is based on reducing the sum of squared residuals between the expected and actual values.

2SLS is utilized as an alternate strategy when we encounter endogeneity Problems in OLS. Endogeneity arises when the explanatory variable correlates with the error word. Then we utilize 2SLS, which employs an instrumental variable. The outcome will be different because if there is endogeneity in the model, OLS will produce biased results.

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Full Question:
What can we conclude about the endogeneity of an explanatory variable if the OLS and 2SLS estimates are significantly different? Assume that the instrument used was exogenous. Select one:

a. The explanatory variable is not endogenous and therefore using 2SLS is ill-advised.

b. The explanatory variable is not endogenous and therefore OLS should not be used.

c. The explanatory variable is endogenous and therefore using 2SLS should be considered.

d. The explanatory variable is endogenous and therefore OLS should be used.

It looks like you are supposed to match those 20 given equations to their respective graph that the assignment gave you. Do you need help plotting them? If so, I can edit my answer and add a picture of the equations graphed.

Answer:

11 cm

Step-by-step explanation:

2x+x+6+x+4=30

4x+10=30

   -10.  -10

4x=20

/4.  /4

x=5

now we find each length to find the longest

2(5)

10 cm

5+6

11 cm

5+4

9 cm

11 is the biggest one

Hopes this helps have a wonderful day

By comparing the speeds of all the people, Bob picked apple the fastest.

Speed is generally the change in distance per unit time. In this case instead of distance we can use the number of apples.

For this question, speed of picking apples = no of apples / time (in minutes). For Bob, speed = 15/8 = 1.88 apples/minute

For Mary, speed = 16/16 = 1 apples/minute

For Suie, speed = 10/19 = 0.526 apples/minute

This shows that Bob picked apples the fastest.

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Answer:

-6x (x-3)

Step-by-step explanation:

Branliest Pls!

Answer: The two expressions that represent the perimeter of the rectangular pool include the following:

A. x + 3x + 1 + x + 3x + 1

E. 8x + 2

How to calculate the perimeter of a rectangle?

Mathematically, the perimeter of a rectangle can be calculated by using this equation;

P = 2(L + x)

Where:

P represents the perimeter of a rectangle.

L represents the length of a rectangle.

x represents the width of a rectangle.

Since the length is 1 more than 3 times the​ width, we have;

Length, L = 3x + 1

Therefore, the two expressions for the perimeter of this rectangle is given by:

P = 2(3x + 1 + x) = x + 3x + 1 + x + 3x + 1

P = 2(4x + 1) = 8x + 2

Next, we would determine the total cost as follows;

P = 8x + 2

P = 8(20) + 2

P = 162 feet.

Total cost = 1.86 × 162

Total cost = $301.32

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Complete Question:

A hotel manager is adding a tile border around the​ hotel's rectangular pool. Let x represent the width of the​ pool, in feet. The length is 1 more than 3 times the​ width, as shown. Find two expressions that represent the perimeter of the pool. Use the expressions to describe two ways to find the perimeter. The length of each tile is 1 foot. If the width of the pool is 20 ​feet, and each tile costs ​$1.86​, what would be the total cost of the tile for the​ border?

A. x + 3x + 1 + x + 3x + 1

B. x + 3x + 1

C. 2x + 3x + 1

D. 8x + 1

E. 8x + 2

F. 4x + 1

Step-by-step explanation:

Answer:

C,   47°

Step-by-step explanation:

All triangles equal 180°

To find the measure of angle 1, subtract the other angles from 180°

180 - 70 - 63 = 47

Based on the correlation coefficient from the technology data given, the data has a strong negative association.

The correlation coefficient is defined as a statistical measure of the strength of a linear relationship that exists between two variables.

The possible range of values for correlation coefficient is from -1.0 to 1.0. This tells us that the values cannot be more than 1.0 nor be less than -1.0.

Thus, a correlation coefficient of -1.0 shows a perfect negative correlation, while a correlation coefficient of 1.0 shows a perfect positive correlation.

We are given a correlation coefficient of r = -0.9478.

Now, the closer the negative correlation is to -1 indicates a strong negative correlation while the farther it is from -1 indicates a weak negative correlation.

Thus, we can conclude that in this case where the  negative correlation is closer to -1 than farther, it can be said to be a strong negative correlation.

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formula: y = mx + b

current points we know:

m = 1/2

x = 10

y = 0

so we solve for the b value.

0 = 1/2 (10) + b

0 = 5 + b

(inverse operation we subtracted 5 on both sides)

-5 = b

so the equation for a line with slope 1/2 passing through the point (10,0) is

y = (1/2)x + (-5) or y = (1/2)x - 5

(not sure if this is correct...)

The graph meets the vertical line test requirement, it must represent a function (C) The vertical line test shows that the graph is correct, hence the answer is yes.

According to the function, every value in the domain is associated to exactly one value in the range, and they have a predefined domain and range. It is characterized as a certain kind of relationship.

Please refer to the image instead of the graph, which is related to it.

The graphic displays a graph.

A parabola is seen on the graph.

The vertical line test determines if a graph can be a function, as is common knowledge.

The graph passes the vertical line test option, indicating that it does in fact represent a function (C) The vertical line test shows that the graph is correct, hence the answer is yes.

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Comparing both given functions, we can state that: B. Function 1 has the greater rate of change; the slope is 2.

Another name for the rate of change of a function is the slope. It is calculated using the formula:

Slope / rate of change = change in y / change in x.

If the equation of a linear function is given in slope-intercept form as y = mx + b, the rate of change or the slope is represented by "m".

Given the first function as an equation, y = 2x - 6, the slope of this function is represented as 2. This means, the rate of change is m = 2.

To find the rate of change of function 2, use two points from the table, (1, -4) and (2, -5):

Rate of change / slope (m) = (-5 - (-4)) / (2 - 1) = -1/1

m = -1.

The slope value of 2 is greater than the slope value of -1, therefore, we can conclude that: B. Function 1 has the greater rate of change; the slope is 2.

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Answer: 39 mm

Step-by-step explanation:

1 cm = 10 mm

3.9 cm = 39 mm

I just need to take 3.9 times 10 and you will get 39 mm

Answer:

-7/3

Step-by-step explanation:

The formula for finding the slope of a line using two points is:

[tex]\frac{y2 - y1}{x2 - x1}[/tex]

For this case, 9 is x1, 10 is y1

6 is x2 and 17 is y2

Insert these values in the formula and solve:

[tex]\frac{y2 - y1}{x2 - x1}[/tex]

17 - 10          7

----------   =   ---   = -7/3

6 - 9          - 3

The expression for the total amount earned in t hours is 24t.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

Amount earned per hour = $12

Amount earned in t hour = 12t

The amount is double.

The amount earned per hour.

= 2 x 12t

= 24t

Thus,

The total amount earned in t hours is 24t.

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Answer:

194 minutes

Step-by-step explanation:

First you subtract $7 from $20.58 because that was the start fee and get 13.58. Then divide 13.58 by 0.07, and get 194.

By using the squeeze theorem, we conclude that, [tex]$$\lim _{x \rightarrow a} f(x)=b .$$[/tex]

Limit of a function, Squeeze Law:

The squeeze theorem states that if f(x) ≤ g(x) ≤ h(x) for all numbers, and at some point x=k we have f(k)=h(k), then g(k) must also be equal to them. We can use the theorem to find tricky limits like sin(x)/x at x=0, by "squeezing" sin(x)/x between two nicer functions and ​using them to find the limit at x=0

We say that a function f(x) approaches a limit L approaches a, or, [tex]$\lim _{x \rightarrow a} f(x)=L$[/tex]

if, for every number [tex]$\epsilon > 0$[/tex], however small, such that [tex]$|f(x)-L| < \epsilon$[/tex],

there always exists a number δ>0 such that

[tex]|x-a| < \delta \text {. }[/tex]

The Squeeze Law:

Suppose that g(x) ≤ f(x) ≤h(x) in some neighborhood of a and also that

[tex]$$\lim _{x \rightarrow a} g(x)=L=\lim _{x \rightarrow a} h(x)$,[/tex]

then,

[tex]$$\lim _{x \rightarrow a} f(x)=L .$$[/tex]

We have to find the limit of f(x) as x approaches to x.

Let [tex]$b-|x-a|=g(x)$[/tex] and [tex]$b+|x-a|=h(x)$[/tex].

Then we have the inequality, g(x) ≤ f(x) ≤h(x)

Let us see what happens to g(x) and h(x) as [tex]$$x \rightarrow a$.[/tex]

[tex]$$\begin{aligned}g(x) & =b-|x-a| \\\\lim _{x \rightarrow a} g(x) & =\lim _{x \rightarrow a} b-|x-a| . \\& =b\end{aligned}$$[/tex]

Similarly,

[tex]$$\begin{aligned}h(x) & =b+|x-a| \\\lim _{x \rightarrow a} h(x) & =\lim _{x \rightarrow a} b+|x-a| . \\& =b\end{aligned}$$[/tex]

We have the conditions required by the Squeeze law,

[tex]$$\lim _{x \rightarrow a} g(x)=b=\lim _{x \rightarrow a} h(x)$$[/tex]

so we conclude that, [tex]$$\lim _{x \rightarrow a} f(x)=b .$$[/tex]

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The system of inequalities to represent the situation is 2x + 5y ≤ 77, x + y ≥ 19

You are in charge of getting food for the class from the corner store.  You can buy chips for $2 or a hoagie for $5.

There are 19 students in the class, so you need to buy at least 19 items, and you have $77 total.

Hence, the system of inequality to represent this situation is as follows:

let

x = number of chips

y = number of hoagies

Therefore, the inequalities is as follows:

2x + 5y ≤ 77

x + y ≥ 19

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Answer:

$102.72

Step-by-step explanation:

If the mp3 player typically costs $120 and was on sale for 20% off, then the sale price would be 120 * (1 - 0.2) = $96.

If Siddhu had to pay 7% sales tax on the sale price, then the total tax he paid would be 96 * 0.07 = $6.72.

Therefore, Siddhu paid a total of 96 + 6.72 = $102.72 for the mp3 player when it was on sale with the sales tax included.

Answer:

Step-by-step explanation: It looks like Leo is trying to prove that the measure of an exterior angle of a triangle is equal to the sum of the measures of the two remote interior angles of the triangle. From the equations given, it seems that Leo is using the fact that the sum of the measures of supplementary angles is 180 degrees, and the sum of the measures of the angles of any triangle is 180 degrees, to try to prove his statement. Some equations that Leo could use to complete his argument might include:

x = p + q, which follows from the equation r + x = 180 and the substitution of p + q + r = 180

p + q = 180 - r, which follows from the equation p + q + r = 180 and the substitution of r + x = 180

x = p + q + 2r, which follows from the equation x + r = p + q + r and the substitution of r + x = 180

It's not clear from the information given whether these equations are sufficient to prove Leo's statement, as we don't have any information about the values of p, q, r, or x. However, these equations might be a good starting point for Leo to continue his argument.