Mattie Evans drove 350 miles in the same amount of time that it took a turbo propeller plane to travel 1200 miles. The speed of the plane was 170 mph faster than the speed of the car. Find the speed of the plane.

Opposite rays are two rays that both start from a common point and go off in exactly opposite directions. Because of this the two rays (QA and QB in the figure above) form a single straight line through the common endpoint Q. When the two rays are opposite, the points A,Q and B are collinear.

There are 625 possible combinations.

According to the multiplication principle, if an event A can happen in x different ways and an event B can happen in y different ways, then there are x y possibilities for both events to happen at once.

To determine the number of combinations possible with 4 cards and a spinner with 5 numbers, we can use the concept of the multiplication principle.

For the spinner, we have 5 possible numbers that can be selected.

For the 4 cards, each card can have any one of the 5 possible numbers from the spinner.

Using the multiplication principle, we multiply the number of choices for each item together to find the total number of combinations.

Number of combinations = Number of choices for the spinner × Number of choices for each card

                       = 5 × 5 × 5 × 5

                       = 625

Therefore, there are 625 possible combinations.

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Answer:

A = 4, B = 3, C = 7, D = 6

Step-by-step explanation:

A = 4 because A represents the number of people who didn't visit either place. This means that B + C + D = 20 - 4 = 16. To find C, which is the overlap we can do 10 + 13 - 16 = 7 so C = 7 which means B = 10 - 7 = 3 and D = 13 - 7 = 6.

Answer:

A = 4, B = 3, C = 7, D = 6

Step-by-step explanation:

Answer:

0.22

Step-by-step explanation:

True. Recursion is often necessary to solve certain types of problems that exhibit a recursive structure or require repeated subproblem solving.

Recursion is a programming technique where a function calls itself in its own definition. It allows for the decomposition of complex problems into smaller, more manageable subproblems that can be solved recursively. Recursion is particularly useful when problems exhibit a recursive structure, such as tree traversal, backtracking, or divide-and-conquer algorithms.

For example, problems like computing the factorial of a number, calculating Fibonacci numbers, or traversing a binary tree can be elegantly and efficiently solved using recursion. These problems can be broken down into smaller instances of the same problem until a base case is reached, and then the solutions are combined to solve the original problem.

However, it's worth noting that not all problems require recursion for their solution. There are alternative approaches, such as iterative loops or dynamic programming, which can be used depending on the problem's characteristics and requirements.

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1.28571428571 this is the answer thank you please give me 5 stars.plis

Answer:

Fraction form:

\(\frac{3}{4}\)

For every 3 dollars, there are 4 cookies

Step-by-step explanation:

To find the constant, find the rise (y-direction) and the run (x-direction). Of the two points on the line, the rise is 3 and the run 4. The constant is rise over run. So, it’s \(\frac{3}{4}\). This means that for every 3 dollars, there are 4 cookies.

Hope this helps! :)

Answer:

A, C and D

Step-by-step explanation:

In this question, we are asked to select which of the options is/are example(s) of compound event(s)

The easiest way to answer this is to have an idea of what we mean by a compound event. When we talk about a compound event, we are referring to an event that has more than one outcome. This is a direct contrast to a simple event where we have only one outcome. To find the probability of a compound event, we shall need to add up the probabilities of all the single events that lies there in

In answering this question, we shall be considering the options one after the other.

A. It is a compound event

This is because we are looking at more than one event happening

B. It is not a compound event

It is not a compound event as we have only one outcome

C. This is a compound event

We have more than one outcome here. In fact, we are dealing with more than one sample space here

D. It is a compound event

We are working on different simple events here

E. It is not a compound event

It is not because we are only focused on a particular type of outcome

Answer:

A, C, D

A: drawing an ace and then a king from a deck of cards

C: rolling a 1 on a number cube and then tossing a coin and landing on tails

D: choosing a banana, then an apple, and then an orange from a fruit basket

Step-by-step explanation:

just did it on edge 2020 hope it helps

:)

Answer:

x = 6

Step-by-step explanation:

11 = 1/2x + 8

-> Move 8 to left side

11 - 8 = 1/2x

3 = 1/2x

->We can switch sides so 1/2x is on the left and 3 is on the right

1/2x = 3

x = 3 x 2/1

x = 6

Answer:

x=6

Step-by-step explanation:

11=1/2x+8

subtract 8 from both sides first.

11-8=1/2x

3=1/2x

Now, multiply by 2 or divide by 1/2 from both sides (your pick)

3*2=x

Therefore the answer is x=6

Answer:

slope= y²-y¹

x²-x¹

0-6

3-0

-6

3

= -2

Answer:

C

Step-by-step explanation:

You just need to convert some of the mixed numbers so that they have a denominator (of the fraction part) as 8:

10 4/8 = 10 1/2

10 6/8 = 10 3/4

11 2/8 = 11 1/4

To find f'(4), we need to differentiate the given expression y = \((f(u) 3x)^2\) and evaluate it at x = 4, using the given information about f(4) and dy/dx.

Let's start by finding the derivative of y with respect to x using the chain rule. We have y = \((f(u) 3x)^2\), where u = \(x^3\)- 2x. Applying the chain rule, we get:

dy/dx = 2(f(u) 3x) * (f'(u) * u' + 3)

Now we are given that dy/dx = 18 when x = 2. Plugging these values into the derivative expression, we get:

18 = 2(f(u) 3(2)) * (f'(u) * u' + 3)

Simplifying further, we have:

9(f(u) + 3) = f'(u) * u' + 3

Now, we know that f(4) = 6. Since u = \(x^3\)- 2x, when x = 4, u = \(4^3\) - 2(4) = 56. Substituting these values into the equation, we have:

9(f(56) + 3) = f'(56) * (3(\(4^3\) - 2)) + 3

Simplifying and solving for f'(56), we can find the value of f'(4) using the given information.

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Kenny will use 2 3/4 chocolates syrup bottle to produce 44 scoops of ice cream.

Given data

for 1 scoop of ice-cream Kenny uses 1/16 of the chocolate syrup bottle

quantity of chocolates used = 2 3/4

let the scoops of ice-cream be x

this is represented mathematically as

1 = 1/16

x = 2 3/4

we cross multiply to have

x/16 = 2 3 /4

x = 44

Therefore Kenny will use 2 3/4 chocolates syrup bottle to produce 44 scoops of ice cream.

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The slope of the line is  5/6.

From the graph:

Slope : a surface of which one end or side is at a higher level than another rising or falling surface.

Points are (-3,-2) and (3,3)

slope m = y2-y1 / x2-x1

= 3 - (-2) / 3 - (-3)

= 3 + 2 / 3 + 3

m =  5/6.

Therefore  the slope of the line is  5/6.

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Answer:

25 advance

20 same day

Step-by-step explanation:

1700=40x+35y

*40 45=x+y

1700=40x+35y

- 1800=40x+40y

-100= -5y

y=20 tickets

45-20=25

25*40 + 35*20= 1700

1000. + 700 = 1700

Answer:

see explanation

Step-by-step explanation:

Using the trigonometric identity

tan²x + 1 = sec²x

Consider the left side

\(\frac{1+sin^4A}{cos^4A}\)

= \(\frac{1}{cos^4A}\) + \(\frac{sin^4A}{cos^4A}\)

= \(sec^{4}\) A + \(tan^{4}\) A

= (tan²A + 1)² + \(tan^{4}\) A

= \(tan^{4}\) A + 2tan²A + 1 + \(tan^{4}\) A

= 1 + 2tan²A + 2\(tan^{4}\) A ← factor out 2tan²A

= 1 + 2tan²A(1 + tan²A)

= 1 + 2tan²A sec²A

= right side , thus verified

Therefore , the solution of the given problem of probability comes out to be the experimental likelihood that a reggae CD will be the next one lent out is roughly 0.4615, or 46.15%.

Any considerations technique's main objective is to determine the likelihood event that a claim is true or that a particular incident will happen. Any number from 0 to 1, where 0 traditionally represents a percentage and 1 typically denotes the degree of certainty, can be used to represent chance. A probability illustration shows the likelihood that a particular event will occur.

Here,

Given: 86 Latin CDs were lent out, 16 were rock CDs, 45 were hip-hop CDs, and 126 were reggae CDs.

=> CDs loaned out in total: 86 + 16 + 45 + 126 = 273

=> 126 reggae CDs were lent out.

Number of reggae CDs loaned out relative to the total number of CDs loaned out, experimental likelihood of lending a reggae CD

=> A reggae CD's experimental chance of being lent out  = 126/273.

We may calculate the experimental probability's approximation using a calculator as follows:

=> A reggae CD will be lent out with an experimental probability of 0.4615.

Therefore, the experimental likelihood that a reggae CD will be the next one lent out is roughly 0.4615, or 46.15%.

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Answer:

126/273

Step-by-step explanation:

Given:

Table of values.

The train travels at a constant speed.

To find:

The speed of train in miles per hour.

Solution:

From the given table consider any two points, i.e., (0.5,22.5) and (1,45).

The train travels at a constant speed. It means, there is a linear relationship between time and distance.

The average rate of change (Slope) of a linear relationship is

\(m=\dfrac{y_2-y_1}{x_2-x_1}\)

\(m=\dfrac{45-22.5}{1-0.5}\)

\(m=\dfrac{22.5}{0.5}\)

\(m=\dfrac{225}{5}\)

\(m=45\)

So, average rate of change in distance with respect to time is 45.

Therefore, the speed of the train is 45 miles per hour.

Answer:

2,095,426.517

Step-by-step explanation:

From the question above we are required to find the product of 698475.50585057 and 3

Therefore the product can be calculated as follows

698475.50585057 × 3

= 2,095,426.517

Hence 698475.50585057 multiplied by 3 is 2,095,426.517

Answer:

Which expression is equivalent to ((4^((5)/(4)).4^((1)/(4)))/(4^((1)/(2))))^((1)/(2))?

The number of feet in the length of the handrail is 17.3 ft.

The easiest way to see this is to imagine that we can "unfold" the spiral to create a rectangle

The bottom side of the rectangle is just the arc length of a circle with a radius of 3 ft  turned through 270°= (3/4) of a whole revolution

(3/4) (2pi) (3)  =  (9/2)pi ft =   4.5 pi ft

The side of the rectangle will be the rise of the staircase = 10ft

And the diagonal of the rectangle will be the length of the handrail

We can use the Pythagorean Theorem to solve this

Handrail length = √ [ (4.5 pi)^2 + 10^2 ]  ≈  17.3 ft

Pythagorean theorem is the well-known geometric theorem that the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse.

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Answer:

Square root2 /3

Step-by-step explanation:

1. Multiply both numerator and denominator by square root of 2.

2. Square root 2 times itself is just 2 that so denominator is 5-2

3. 1 times Square root 2 is just Square root 2. So numerator is Square root 2

4. 5-2=3 so final answer is Square root 2 over 3

Answer:

I would say A. as a best guess but the question is odd it does not add up to 101 students it adds up to 101 plus all of them are female juniors so they would be picked every time it would be 101/101

The approximate solution of x in log eˣ ⁻ ³ = 7 is 16

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

log eˣ ⁻ ³ = 7

This can be expressed as

(x - 3)log(e) = 7

Divide both sides of the equation by log(e)

So, we have

x - 3 = 7/log(e)

Evaluate the quotient and approximate

x - 3 = 16

Add 3 to both sides of the equation

x = 19

This means that the approximate solution of x in log eˣ ⁻ ³ = 7 is 16

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Complete question

What is the solution to log eˣ ⁻ ³ = 7

The series diverges according to the Root Test.

To test the convergence of the series using the Root Test, we need to evaluate the limit of the absolute value of the nth term raised to the power of 1/n as n approaches infinity. In this case, our series is:

∑(n=1 to ∞) ((2n + 6)/(3n + 1))^n

Let's simplify the limit:

lim(n → ∞) |((2n + 6)/(3n + 1))^n| = lim(n → ∞) ((2n + 6)/(3n + 1))^n

To simplify further, we can take the natural logarithm of both sides:

ln [lim(n → ∞) ((2n + 6)/(3n + 1))^n] = ln [lim(n → ∞) ((2n + 6)/(3n + 1))^n]

Using the properties of logarithms, we can bring the exponent down:

lim(n → ∞) n ln ((2n + 6)/(3n + 1))

Next, we can divide both the numerator and denominator of the logarithm by n:

lim(n → ∞) ln ((2 + 6/n)/(3 + 1/n))

As n approaches infinity, the terms 6/n and 1/n approach zero. Therefore, we have:

lim(n → ∞) ln (2/3)

The natural logarithm of 2/3 is a negative value.Thus, we have:ln (2/3) <0.

Since the limit is a negative value, the series diverges according to the Root Test.

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The probable question may be:
Test the series below for convergence using the Root Test.

sum n = 1 to ∞ ((2n + 6)/(3n + 1)) ^ n

The limit of the root test simplifies to lim n → ∞  |f(n)| where

f(n) =

The limit is:

(enter oo for infinity if needed)

Based on this, the series

Diverges

Converges

Answer: -3

Step-by-step explanation:

a. The number of bricks required for the top step is 795.

b. The total number of bricks required for all the steps is 2250.

(a) To find the number of bricks required for the top step, we need to use the information that each successive step requires two less bricks than the prior step.

So, we can start by finding the total number of bricks required for all the steps and then subtracting the number of bricks required for the bottom 29 steps.

The total number of bricks required for all the steps can be found using the formula for the sum of an arithmetic sequence:

S = n/2 * (a1 + an)

where S is the sum, n is the number of terms, a1 is the first term, and an is the nth term.

In this case, we have:

n = 30 (since there are 30 steps)

a1 = 100 (since the bottom step requires 100 bricks)

d = -2 (since each successive step requires 2 less bricks than the prior step)

an = a1 + (n-1)d = 100 + (30-1)(-2) = 40.

Plugging these values into the formula, we get:

S = 30/2 * (100 + 40) = 2250

So, the total number of bricks required for all the steps is 2250.

To find the number of bricks required for the top step, we subtract the number of bricks required for the bottom 29 steps from the total number of bricks required for all the steps:

number of bricks required for top step = total number of bricks - number of bricks for bottom 29 steps

= 2250 - [100 + 98 + 96 + ... + 6 + 4 + 2]

= 2250 - 1455

= 795

Therefore, the number of bricks required for the top step is 795.

(b) To find the total number of bricks required to build the staircase, we simply add up the number of bricks required for each step. We can use the formula for the sum of an arithmetic series again to simplify the calculation:

S = n/2 * (a1 + an)

where S is the sum, n is the number of terms, a1 is the first term, and an is the nth term.

In this case, we have:

n = 30 (since there are 30 steps)

a1 = 100 (since the bottom step requires 100 bricks)

d = -2 (since each successive step requires 2 less bricks than the prior step)

an = a1 + (n-1)d = 100 + (30-1)(-2) = 40

Plugging these values into the formula, we get:

S = 30/2 * (100 + 40) = 2250

Therefore, the total number of bricks required to build the staircase is 2250.

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