An airplane that flies from New York City to Los Angeles for Speedy State Airlines flies at an average speed of
450 mph and uses an average of 0.5 gal of fuel every second.
1. Determine the plane's fuel efficiency, in miles per gallon, by first converting the plane's speed into miles per
second.

According to the equation the given all necessary math work are:

\(A: (x -f)^2 +(y -g)^2 = h^2\)

B:  domain: [-5, 11]; range: [-9, 7]

C:  yes, inside

The hypοtenuse's square is equal tο the sum οf the squares οf the οther twο sides if a triangle has a straight angle (90 degrees), accοrding tο the Pythagοras theοrem. Keep in mind that BC² = AB² + AC² in the triangle ABC signifies this. Base AB, height AC, and hypοtenuse BC are all used in this equatiοn. The lοngest side οf a right-angled triangle is its hypοtenuse, it shοuld be emphasized.

Part A:

Use οf the Pythagοrean theοrem gets yοu tο the equatiοn fοr a circle in essentially οne step:

sum οf squares οf sides = square οf hypοtenuse

\((x -f)^2 +(y -g)^2 = h^2\) . . . . . . circle cantered οn (f, g) with radius h

Part B:

The circle will be defined fοr values οf x in the dοmain f ± h, and fοr values οf y in the range g ± h.

dοmain: 3 ± 8 = [-5, 11]

range: -1 ±8 = [-9, 7]

Part C:

The distance frοm pοint (10, -4) tο (f, g) is ...

\(h^2 = (10 -3)^2 +(-4 -(-1))^2\)

\(h^2 = 7^2 +(-3)^2 = 49 +9 = 58\)

h = √58 < 8 . . . . the distance tο the pοint is less than h=8.

The pοint is inside the circle.

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Answer:

9 x 5

5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 = 5^9

9 x 9 x 9 x 9 x 9 x 9 x 9 x 9 x 9 x 9 = 9 ^ 10

5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 = 5^9

5^9 x 9^10 x 5^9

5^18 x 9^10

Step-by-step explanation:

Answer:

c

Step-by-step explanation:

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

\(\huge\textbf{Original equation/problem:}\)

\(\mathbf{687\times391}\)

\(\mathbf{= 391\times687}\)

\(\mathbf{= 268,617}\)

\(\huge\textbf{Now, we're going to solve for your}\\\huge\textbf{question:}\)

\(\huge\text{Assuming you want us to estimate to the}\\\huge\text{nearest hundred. So we will do so, because}\\\huge\text{it is easier to understand it like that.}\)

\(\mathbf{687 \rightarrow 700}\\\mathbf{391\rightarrow 400}\)

\(\huge\textbf{New equation:}\)

\(\mathbf{700 \times 400}\)

\(\mathbf{= 400\times700}\)

\(\mathbf{= 280,000}\)

\(\huge\text{Therefore, your answer is: \boxed{\mathsf{Option\ A.\ 280,000}}}\huge\checkmark\)

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

Step-by-step explanation:

directly proportional means

y = kx

with k being a constant factor for all values of x.

we get k by using the given data point (10, 15).

15 = k×10

k = 15/10 = 1.5

so, now for the other tree we know k and x and calculate y

y = 1.5×14.4 = 21.6 m

it is 21.6 m tall (its height is 21.6 m).

We can see here that the data set approximately periodic. The period and amplitude is: Periodic with a period of 4 and an amplitude of about 30.

The size or magnitude of a wave or vibration is measured by its amplitude in physics. It describes the greatest deviation of a wave from its equilibrium or rest state, or the greatest intensity of an electromagnetic or sound wave.

When referring to waves, amplitude is commonly calculated as the distance between a wave's peak or trough and its resting position.

We can deduce that the values are being repeated at regular interval of four (4).

For the amplitude:

\(Amplitude: \frac{140 - 74}{2}\)

Amplitude = 33 ≈ 30.

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The values are

a. h(-2) = 20

b. h(-1) = -4

c. h(-x) =x⁴+3x²-8

d. h(3a) = 243a⁴+27a² -8

function, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

h(x) =x⁴+3x²-8

therefore f(-2) = (-2)⁴ + 3(-2)²-8

= 16+12-8

= 20

h(-1) = (-1)⁴+ 3(-1)²-8

h(-1) = 1+3-8

= -4

h(-x) = (-x)⁴ + 3(-x)² -8

= x⁴+3x²-8

h(3a) = 3(3a)⁴ + 3(3a)² -8

= 243a⁴+27a² -8

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Let's begin by listing out the given information:

Triangle ABC is similar to Triangle XYZ. However, Triangle ABC is larger than Triangle XYZ

We will see the ratio by comparing the corresponding sides of both triangles. We have:

From Triangle ABC to Triangle XYZ, observe that the size of the Triangle XYZ is smaller. That shows us that Triangle XYZ is one-fifth of Triangle ABC

Hence, the correct answer is 1/5 (option D)

Answer:

704

Step-by-step explanation:

54 x 12 = 648

648 + 56  = 704

Hope that helps!

Equation: 54 · 12 + 56

Solution: 704

Explanation: Using the Order of Operations (PEMDAS), we know that, in this equation, our first step is to multiply...

1. 54 · 12 = 648

Then, we can add.

2. 648 + 56 = 704

There!!

1. Number of athletes did not own any of the three items = 259 - 228

= 31.

2. Number of athletes own a convertible and a TV but not a store = 44 - 9

= 35.

3. Number of athletes own a convertible or a TV = 110 + 91 - 44

= 157.

4. Number of athletes owned exactly one type of item = 60 + 13 + 71 = 144.

5. Number of athletes owned at least one type of item = 259 - 31

= 228

6. Number of athletes own a TV or a store, but not a convertible = 13 + 34 +71

= 118.

The number of athletes did not own any of the three items need to subtract the number of athletes who own at least one item from the total number of athletes surveyed.

Total number of athletes surveyed = 259

Number of athletes own at least one item = 110 + 91 + 120 - 15 - 43 - 44 + 9 = 228

Number of athletes who did not own any of the three items = 259 - 228 = 31.

The number of athletes who owned a convertible and a TV but not a store need to subtract the number of athletes who own all three items from the number of athletes who own a convertible and a TV.

Number of athletes who own a convertible and a TV = 44

Number of athletes who own all three items = 9

Number of athletes who own a convertible and a TV but not a store = 44 - 9 = 35

The number of athletes who owned a convertible, or a TV need to add the number of athletes who own a convertible to the number of athletes who own a TV and then subtract the number of athletes own both a convertible and a TV.

Number of athletes who own a convertible or a TV = 110 + 91 - 44

= 157.

The number of athletes owned exactly one type of item need to add up the number of athletes who own a convertible only the number of athletes own a TV only and the number of athletes who own a store only.

Number of athletes own a convertible only = 110 - 15 - 9 = 86

Number of athletes own a TV only = 91 - 44 - 9 = 38

Number of athletes own a store only = 120 - 15 - 43 - 9 = 53

Number of athletes owned exactly one type of item = 60 + 13 + 71 = 144.

The number of athletes who owned at least one type of item can use the result from part (1).

Number of athletes who owned at least one type of item = 259 - 31

= 228

The number of athletes who owned a TV or a store but not a convertible need to subtract the number of athletes who own all three items, and the number of athletes own a convertible and a TV from the number of athletes own a TV or a store.

Number of athletes own a TV or a store = 91 + 120 - 43 - 9 = 159

Number of athletes own a TV or a store not a convertible = 13 + 34 +71

= 118.

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3 - 7 = -4

Why?

7 is a bigger number than 3 which makes the answer a negative number.

-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9

that is a number line and if you start from 3 and go back 7 spaces it would be -4.

In conclusion,

-4 is the absolute value of 3 - 7.

Answer: he would be 2 standard deviations above the

Step-by-step explanation:

Option 3 yielded the most money after 10 years is 171.7

Option 1 yielded the most total money by the time you were 60 years old is 8,771.56

A solution of an equation is a value or set of values that satisfy the equation, meaning that when the value(s) is substituted for the variable(s) in the equation, both sides of the equation are equal.

Based on the given equations, Option 1 yielded the most money after 10 years, and Option 3 yielded the most total money by the time you were 60 years old.

After 10 years:

Option 1: 50×(1.09)¹⁰ - 30 =  88.36

Option 2: 50×(1.08)¹⁰ - 20 =  87.94

Option 3: 100×(1.07)¹⁰ - 25 =  171.71

Therefore, Option 3 yielded the most money after 10 years is 171.7

By the time you were 60 years old:

Option 1: 50×(1.09)⁶⁰ - 30 =  8,771.56

Option 2: 50×(1.08)⁶⁰ - 20 =  5,042.85

Option 3: 100×(1.07)⁶⁰ - 25 =  5,769.64

Therefore, Option 1 yielded the most total money by the time you were 60 years old is 8,771.56

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The prime factorization of 2 = 2. The greatest common factor of 20 and 36 is 4. The prime factorization of 9 = 3 x 3. The prime factorization of 15 = 3 x 5. The prime factorization of 10 = 2 x 5.

Prime factorization is factoring the number in the form of its prime factors.

a. We have to find the prime factorization of 2.

Since 2 is the smallest prime number it cannot be factored further.  

So, we have the prime factorization of 2 = 2.

b. We have to find the greatest common factor of 20 and 36

    Let's find the prime factors of each of the numbers 20 and 30 as follows-

factors of 20 = 2 x 2 x 5

factors of 36 = 3 x 3 x 2 x 2

So, the GCD = 2 x 2 = 4

Hence, the greatest common factor of 20 and 36 is 4.

c. We have to find the prime factorization of 9.

Let us find the factors of the 9.

the factors of 9 = 3 x 3.

Hence, the prime factorization of 9 = 3 x 3.

d. We have to find the prime factorization of 15.

Let us find the factors of the 15.

the factors of 15 = 3 x 5.

Hence, the prime factorization of 15 = 3 x 5.

e. We have to find the prime factorization of 10.

Let us find the factors of the 10.

the factors of 10 = 2 x 5.

Hence, the prime factorization of 10 = 2 x 5.

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The complete question is -

a. what is the prime factorization of 2?

b. what is the greatest common factor of 20 and 36?

    2, 4, 5, or 6

c. what is the prime factorization of 9?

d. what is the prime factorization of 15?

e.what is the prime factorization of 10?

Jane received $30025 and Lydia received $60000. Let's assume the amount of money that Jane received as x; then Lydia's share of the money will be twice the share of Jane.

We are to find out the share of each person. Here is the solution in steps:Suppose Jane's share was x dollars, and Lydia's share was y dollars.

Given that the total amount given to the two daughters was $90000. Also, given that Lydia paid off her $75, hence she got $75 less than Jane.

Therefore,  y = 2x - 75; this is because we are given that Lydia got twice the share of Jane, and also, she got $75 less than Jane. Hence, x + y = $90000, this is because the total sum of money shared is $90000.

Substituting y = 2x - 75 into x + y = $90000 gives x + (2x - 75) = $90000.

Simplifying, we have :3x = $90000 + 75 = $90075.

Dividing both sides by 3, we get:x = $30025. Hence, Jane's share is $30025 Lydia's share = 2x - 75 = 2($30025) - $75 = $60075 - $75 = $60000.

Therefore, Jane received $30025 and Lydia received $60000.

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In this manner, the number of wolves changes by around 8 percentage 8% each year based on the given work.

To determine the percentage change within the number of wolves each year, we ought to look at the development rate of the work w(x) = 14 * 1.08^x.

The development rate in this case is given by the example of 1.08, which speaks to the figure by which the number of wolves increments each year. In this work, the coefficient 1.08 speaks to a development rate of 8% per year.

To calculate the percentage change, we subtract 1 from the growth rate and increase by 100 to change over it to a rate:

Percentage change = (1.08 - 1) * 100 = 0.08 * 100 = 8%.

In this manner, the number of wolves changes by around 8 percentage 8% each year based on the given work.

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Step-by-step explanation:

There are 2 variables a and c, and there is only 1 equation. Hence we cannot find both variables.

However if we restrict a and c to be positive integers, we will have:

10a + 5.5c = 31

=> 20a + 11c = 62

Since 62 ≡ 2(mod 20) and 11c <= 62,

we have c = 2.

=> 20a + 11(2) = 62, 20a = 40, a = 2.

Therefore a = 2 and c = 2.

Hopefully this explanation helped!

Answer:

The cost of bagel is $0.8 and that of muffins is $1.25.

Step-by-step explanation:

Let the bagels cost is x and muffins cost is y.

ATQ,

10x+4y=13 ....(1)

5x+8y=14 ....(2)   (it should be 14 instead of 4)

Multiply equation (1) by 2 such that,

20x+8y=26 ...(3)

Now subtract equation (2) and (3).

5x+8y-(20x+8y)=14-26

5x+8y-20x-8y=-12

-15x = -12

x  = $0.8

Put the value of x in equation (1)

10(0.8)+4y=13

8+4y=13

4y = 13-8

4y=5

y = $1.25

So, the cost of bagel is $0.8 and that of muffins is $1.25.

We are given:

Sinθ - √3 Cosθ = 1

Solving for θ:

dividing both the sides by 2

1/2 Sinθ - √3/2 Cosθ = 1/2

Cos(60°)*Sinθ - Sin(60°)Cosθ = Sin(30°)                                                               [Since Cos(60°) = 1/2   and   Sin(60°)=√3/2]

We can see that the LHS resembles the formula:

Sin(A - B) = SinACosB - SinBCosA

Sin(θ - 60°) = Sin(30°)

So, we can say that:

θ - 60 = 30

θ = 90°  or   π/4 radians

Answer:

Step-by-step explanation:

To find the direction of minimum rate of change for the function f(x, y) = x² + xy + y² at the point (5, 2), we need to find the gradient vector (also known as the gradient or the vector of partial derivatives) and then find the direction orthogonal to the gradient vector, as this direction will have the minimum rate of change.

First, let's find the gradient vector by computing the partial derivatives of f(x, y) with respect to x and y:

∂f/∂x = 2x + y

∂f/∂y = x + 2y

Now, evaluate the gradient vector at the point (5, 2):

∇f(5, 2) = (2(5) + 2, 5 + 2(2)) = (12, 9)

The gradient vector is (12, 9). To find the direction orthogonal to the gradient vector, we can swap the x and y components and negate one of them. Since the question asks for a vector with an x-component of 1, 0, or -1, we'll negate the x-component:

Orthogonal vector = (-1, 12)

So, the direction of minimum rate of change at point (5, 2) is given by the vector [-1, 12].

Answer:

The answer is 50.

Step-by-step explanation:

Use MDAS

Multiplication, Division, Addition and Subtraction

2 + 6 * 8 =

Multiply first then add

2 + 6*8 = ?

= 2 + 48

= 50

Answer:

The other endpoint is (7, -5)

Step-by-step explanation:

We can use the formula for the midpoint to find the coordinates of the other endpoint of the segment BC:

xm = x1 + (x2 - x1)/2

ym = y1 + (y2 - y1)/2

For our case, replacing the given coordinates and solving for x2 and y2 (the coordinates of the other endpoint) we get:

For x2:

xm = x1 + (x2 - x1)/2

5 = 3 + (x2 - 3)/2

5 - 3 = (x2 - 3)/2

2 = (x2 - 3)/2

4 = x2 - 3

x2 = 4 + 3 = 7

For y2:

ym = y1 + (y2 - y1)/2

-2 = 1 + (y2 - 1)/2

-2 -1 = (y2 - 1)/2

-3 = (y2 - 1)/2

-6 = y2 - 1

y2 = -6 + 1 = -5

Therefore the other endpoint is (7, -5)

Answer:

the approximate value of m is -0.12, indicating that the value of Ty's computer decreases by 0.12 (or 12%) each year.

Step-by-step explanation:

o express this depreciation rate as a slope in the equation y = mx + b, we need to determine how much the value changes (the "rise") for each year (the "run").

Since the value decreases by 12% per year, the slope (m) would be -12%. However, we need to express the slope as a decimal, so we divide -12% by 100 to convert it to a decimal:

m = -12% / 100 = -0.12

Answer:

5/12<3/6

Step-by-step explanation:

3/6 is 1/2 and 5/12 is smaller than 1/2

Answer:

5/12 < 3/6

Step-by-step explanation:

3/6 is equivalent to 6/12 because 3 times 2 is 6 and 6 times two is 12. 6 (the new numerator of 3/6) is greater than the numerator of 5/12- 5. 5<6. They have the same denominator so 5/12< 6/12 which is the same as 5/12 < 3/6. Hope that helped!

Answer:

Step-by-step explanation:

The line segment joining two points P and Q can be represented by the equation of a straight line in the form y = mx + b, where m is the slope and b is the y-intercept.

To find the equation of the line, we need to find the slope, which can be calculated using the formula:

m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of the points P and Q, respectively.

In this case, the coordinates are:

P = (-3, 2) and Q = (5, 7)

So, the slope is:

m = (7 - 2) / (5 - (-3)) = 5 / 8

Next, we can use either of the points to find the y-intercept. Let's use point P:

b = y - mx, where y and x are the y and x coordinate of the point, respectively.

In this case,

b = 2 - m * (-3) = 2 - (5/8) * (-3) = 2 + 15/8 = 89/8

So, the equation of the line joining the points P and Q is:

y = (5/8)x + 89/8

Now, to find the point where the line crosses the y-axis, we need to find the x-coordinate of the point where y = 0.

So, we have:

0 = (5/8)x + 89/8

Solving for x, we get:

x = -(89/8) / (5/8) = -89 / 5

This means that the line crosses the y-axis at the point (-89/5, 0). To find the ratio in which the line segment is divided by the y-axis, we need to find the ratio of the distance from the y-axis to point P to the distance from the y-axis to point Q.

Let's call the point of intersection with the y-axis R. The distances are then:

PR = (3, 2) and QR = (5 - (-89/5), 7)

The ratio of the distances is then:

PR / QR = (3, 2) / (5 - (-89/5), 7) = 3 / (5 + 89/5) = 3 / (94/5) = 15/47

So, the line segment joining the points P and Q is divided by the y-axis in the ratio 15:47.

Answer & Step-by-step explanation:

In hypothesis testing, the claim being made is called the alternative hypothesis. The null hypothesis is the opposing statement, and it is presumed to be true until sufficient evidence suggests otherwise. The wording of the claim must be specific and precise, and one must clearly state the population, the parameter of interest, and the direction of the hypothesis test (i.e., one-tailed or two-tailed).

For example, a well-worded alternative hypothesis might be "The new teaching method will result in a higher mean test score for students than the traditional teaching method." In this case, the null hypothesis would be "The new teaching method will not result in a higher mean test score for students than the traditional teaching method."

An incorrectly worded claim might be "The new teaching method is better than the traditional teaching method." This claim is too vague because it does not specify in what way the new method is better, nor does it give a direction for the hypothesis test.

In summary, when conducting a hypothesis test to support a claim regarding the mean test score under a new teaching method, the wording of the claim must be specific and precise, and the claim will become the alternative hypothesis.

Answer:

0.3333

Step-by-step explanation:

The experimental probability of pulling a blue marble and then a yellow marble is 0.075 or 7.5%, which is closest to answer option B.

Probability is a statistical term that describes the possibility that something will occur.

here, we have,

Since there is only one blue marble in the bag, the likelihood of getting a blue marble on the first draw is 1/6.

After the blue marble is replaced, the probability of drawing a yellow marble on the second draw is 2/6, since there are now 2 yellow marbles out of a total of 6 marbles in the bag.

The probability of sketching a blue marble and subsequently a yellow marble in the same attempt is:

P(blue then yellow) = P(blue) x P(yellow | blue)

P(blue then yellow) = (1/6) x (2/6)

P(blue then yellow) = 1/18

Since the marbles are replaced after each draw, the probability of drawing a blue marble and then a yellow marble is independent of one attempt to the next.

The experimental probability of pulling a blue marble and then a yellow marble in 40 attempts can be calculated by dividing the number of times it occurred by the total number of attempts:

Experimental probability = number of times blue then yellow was pulled / total number of attempts

Experimental probability = 3 / 40

Experimental probability = 0.075

Therefore, the experimental probability of pulling a blue marble and then a yellow marble is 0.075 or 7.5%.

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complete question:

PLS HELP ASAP WILL MARK BRAINLY!!!. In a bag there are 3 red marbles, 2 yellow marbles and 1 blue marble. After a marble is selected, it is replaced. After 40 attempts at drawing two marbles from the bag, there were three instances where a blue marble then a yellow marble was pulled. What is the experimental probability of pulling a blue marble and then a yellow marble? 0.0556 0.0750 0.0167 0.0333

Step-by-step explanation:

Slope formula:

\( \frac{y2}{x2} - \frac{y1}{x1} = m\)

m = slope

Substitute the points into the formula format:

\( \frac{ - 9}{8} - \frac{ - 3}{ - 4}=m \)

Using Integer rule for subtraction:

\( \frac{ - 9}{8} + \frac{3}{4} = m\)

Solve:

\( \frac{ - 6 \div 6}{12 \div 6} = - \frac{1}{2} = m \)

The slope is -1/2.

Answer:

-1/2 or -0.5

Step-by-step explanation:

You may determine the slope of a line by determining the rise and run of two points on the line. The rise is the vertical change between two places, whereas the run is the horizontal change. The slope is calculated by dividing the increase by the run: Slope equals rise run Slope is short for "raise and ."

Therefore, the slope of the line passing through the points (-4, -3) and (8, -9) is -1/2 or -0.5

~

Hope this helps!

Some of the paper is not shown.

I'll do (26 - 32)

26.

The length of the astronomical seasons varies between 89 and 93 days, while the length of the meteorological seasons is less variable and is fixed at 90 days for winter in a non-leap year (91 days in a leap year), 92 days for spring and summer, and 91 days for autumn.

27. There are 21 cars, each 4m long, so 21x4m = 84 m gives the total length of the cars.

28.  

Cancel out all other squares.

Add A to each section to see how many spaces it could hypothetically take up.

3 each "row" of the square.

3 x 3 = 9

29.

Square A (all squares sides are congruent)

L = 2 W = 2

2 x 2 =4

SQUARE A = 2 (Area)

The large square is 3 blocks a row

so  add 2 + 2  + 2 which is 6

so 6 x 6 = 36

Area of large square = 36

Hint: Cross-sectional area is determined by squaring the radius and then multiplying by 3.14.

32

To find perimeter, add all the lengths and widths up of the square

so the length and width are 6.

So 6 + 6 = 12 + 12 = 24

p = 24

Answer:

78 Sqare Feet

Step-by-step explanation:

Answer:

30 feet

Step-by-step explanation:

Since the area of the rectangle is 56 feet^2 and one side length is 7, the adjacent side lengths must be 8. To find perimeter of a rectangle, add 2L + 2W (double length + double width.

7x2 + 8x2 = 14 + 16 = 30

Answer:

H= -35/4

Decimal form: -8.75

Explanation: