The distance an airplane travels depends on how much time it spends flying. Which expression represents the distance the airplane flies in 20 minutes?

a. 20(distance)
b. distance-20
c. distance+20
d. distance(20)

Based on the given informations, the change in y as t changes from 1 to 6 is approximately 3.870. Therefore the correct option is (A).

To find the change in y as t changes from 1 to 6, we need to integrate the given function with respect to t over the interval [1, 6] and then find the difference between the values of the integral at the two endpoints.

∫₁⁶ 6e\(.^{(-0.08(t-5)^2)}\)  dt

We can use the substitution u = t - 5 to simplify the integral:

∫₋₄¹ 6e\(.^{(-0.08u^2)}\)  du

Unfortunately, there is no closed-form solution for this integral. We can use numerical integration methods, such as Simpson's rule or the trapezoidal rule, to approximate the integral. Using Simpson's rule with a step size of 1, we get:

∫₋₄¹ 6e\(.^{(-0.08u^2)}\) du ≈ 3.870

Therefore, the change in y as t changes from 1 to 6 is approximately 3.870, which corresponds to option (A).

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To identify the two incorrect ways to express that a function f is onto, we need to understand the concept of an onto function. An onto function, also known as a surjective function.

Every element in the codomain has a preimage in the domain." - Correct For every y in the codomain, there exists an x in the domain such that f(x) = y." - Correct The range of the function equals the codomain." - Correct "The function is one-to-one." - Incorrect "The function is invertible." - Correct

Now, let's identify the two incorrect statements: "The function is one-to-one." - This statement is incorrect because an onto function does not have to be one-to-one. It is possible for multiple elements in the domain to map to the same element in the codomain. "The function is invertible." - This statement is also incorrect because an onto function does not have to be invertible. While invertible functions are onto, not all onto functions are invertible.
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The incorrect ways to express that a function f is onto are that the range of f is equal to the codomain and that f is a one-to-one function.

To determine the incorrect ways to express that a function f is onto, we need to understand what it means for a function to be onto.

A function f is said to be onto (or surjective) if every element in the codomain has a corresponding pre-image in the domain. In other words, for every y in the codomain, there exists an x in the domain such that f(x) = y.

Let's analyze each of the given statements and identify the incorrect ones:

1. "f(x) = y for all y in the codomain."
  This statement is correct because it represents the definition of an onto function. The function maps every element in the domain to a unique element in the codomain.

2. "Every y in the codomain has a corresponding x in the domain such that f(x) = y."
  This statement is correct as well. It conveys the same meaning as the definition of an onto function.

3. "The range of f is equal to the codomain."
  This statement is incorrect. While an onto function does cover the entire codomain, the range of the function may be a proper subset of the codomain.

4. "f is a one-to-one function."
  This statement is incorrect. A one-to-one function (or injective) is different from an onto function. A one-to-one function maps distinct elements in the domain to distinct elements in the codomain.

5. "f is a surjective function."
  This statement is correct. "Surjective" is another term for an onto function.

Based on our analysis, the incorrect statements are:
- The range of f is equal to the codomain.
- f is a one-to-one function.

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Answer:

y-9=-5/2(x+6)

Step-by-step explanation:

y-y1=m(x-x1)

y-9=-5/2(x-(-6))

y-9=-5/2(x+6)

An equation in point-slope form for this line would be y-9=-5/2(x+6).

The equation of the straight line has its slope and given point.

If we have a non-vertical line that passes through any point(x1, y1) has gradient m. then general point (x, y) must satisfy the equation

y-y₁ = m(x-x₁)

Which is the required equation of a line in a point-slope form.

Thus,

y-y1= m(x-x1)

A line passes through the point (-6,9) and has a slope of -5/2 So,

y-9=-5/2(x-(-6))

y-9=-5/2(x+6)

Hence, an equation in point-slope form for this line would be y-9=-5/2(x+6).

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We can make the graph through\(\( f(2x+1) \)\) from the graph of\(\( f(x) \),\)two transformations to be made:

1. Dilate the graph by a factor of 2 in the\(\( x \)-\)direction: all the points will be horizontally stretched by 2. The new graph will be narrower compared to the original graph.in each point\(\((x, y)\\))on the graph we multiply the\(\( x \)\)-coordinate by 2 to obtain the new\(\( x \)-\)coordinate.

2. Translate the graph by 1 unit in the negative\(\( x \)-\)direction: This means that every point on the dilated graph will be shifted 1 unit to the left. The new graph will be shifted to the left compared to the dilated graph. At each point \(\((x, y)\)\) on the dilated graph, you subtract 1 from the \(\( x \)-\) we coordinate to find a new coordinate.

We can find the graph of\(\( f(2x+1) \)\)from other graph of\(\( f(x) \),\)by these steps

1. Multiply the\(\( x \)-\) each points co ordinate with 2.

2. Subtract 1 from the\(\( x \)\)-coordinates of each point obtained from step 1.

These transformations will dilate the graph by a factor of 2 in the \(\( x \)-\)direction and translate it 1 unit to the left.

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In a case whereby the sum of two consecutive numbers is 25 the largest of the consecutive numbers is 13.

Given that sum of two consecutive numbers is 25 , ans we were required to locatye the  largest of the consecutive numbers. The we can represent the consecutive numbers as x and x+1. According to the problem, the sum of these two consecutive numbers is 25:

x + (x+1) = 25

Simplifying the left side of the equation:

2x + 1 = 25

2x = 24

Dividing both sides by 2:

x = 12

So the first consecutive number is 12. The second consecutive number is 12 + 1 = 13. Therefore, the largest of the consecutive numbers is 13.

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Walking is not safe on the path whenever rabbits have been seen in the area, and berries are ripe along the path. This is formalized by using the →(if-then) and ∧(logical and) operators.

Given information and corresponding atomic propositions:

We need to formalize the given statements in terms of atomic propositions r, b, and w, which are defined as follows:

r: Rabbits have been seen in the area.

b: Berries are ripe along the path.

w: Walking on the path is safe.

Now, let us formalize each of the given statements in terms of these atomic propositions:

a) Berries are ripe along the path, but rabbits have not been seen in the area.

b: Rabbits have not been seen in the area, and walking on the path is safe, but berries are ripe along the path.

c: If berries are ripe along the path, then walking is safe if and only if rabbits have not been seen in the area.

d: It is not safe to walk along the path, but rabbits have not been seen in the area, and the berries along the path are ripe.

e) For walking on the path to be safe, it is necessary but not sufficient that berries not be ripe along the path and for rabbits not to have been seen in the area.

Walking is not safe on the path whenever rabbits have been seen in the area, and berries are ripe along the path.

The formalizations in terms of atomic propositions are:

a) b ∧ ¬r.b) ¬r ∧ w ∧

b.c) (b → w) ∧ (¬r → w).

d) ¬w ∧ ¬r ∧

b.e) (¬r ∧ ¬b) → w.b ∧

Berries are ripe along the path, but rabbits have not been seen in the area.

This is formalized by using the ∧(logical and) operator.

(¬r ∧ ¬b) → w: It means For walking on the path to be safe, it is necessary but not sufficient that berries not be ripe along the path and for rabbits not to have been seen in the area.

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Mike's claim that (5,28.6) is a point on the exponential function g(x) is incorrect

The points are given as:

(3,6.5) and (4,17.55)

Calculate the rate of change using:

r = y4/y3

This means that:

r = 17.55/6.5

r = 2.7

So, the next point on the graph is:

Next point = 2.7 * y4

Substitute 17.55 for y4

Next point = 2.7 * 17.55

Evaluate

Next point = 47.39

This means that the next point on the graph is (5,47.99)

Hence, Mike's claim that (5,28.6) is a point on the exponential function g(x) is incorrect

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When f = -4, g = 5, and h = 3/4, the value of the expression -8h - 2(5 + f³) + 7g² is 287.

To find the value of the expression -8h - 2(5 + f³) + 7g² when f = -4, g = 5, and h = 3/4, we substitute these values into the expression and simplify step by step.

Let's begin with the given expression:

-8h - 2(5 + f³) + 7g²

Substituting f = -4, g = 5, and h = 3/4, we have:

-8(3/4) - 2(5 + (-4)³) + 7(5)²

Simplifying further:

-6 - 2(5 + (-4)³) + 7(25)

Now, let's simplify the terms inside the parentheses:

-6 - 2(5 + (-4)³) + 175

Inside the parentheses, (-4)³ equals -64:

-6 - 2(5 - 64) + 175

Continuing to simplify:

-6 - 2(-59) + 175

Multiplying -2 by -59 gives us 118:

-6 + 118 + 175

Now, we can add the numbers together:

112 + 175

The sum is:

287

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The Great Dane, being considerably larger than the Chihuahua, weighs a total of 81 kilograms.

Carl, who works at a veterinarian office, encounters two dogs. The first dog is a Chihuahua, and it weighs 3 kilograms.

The second dog, a Great Dane, is significantly larger than the Chihuahua.

To determine the weight of the Great Dane, we can use the given information that it weighs 27 times as much as the Chihuahua.

Since the Chihuahua weighs 3 kilograms, we can multiply this weight by 27 to find the weight of the Great Dane.

By performing this calculation (3 kilograms * 27), we discover that the Great Dane weighs 81 kilograms. Consequently, the Great Dane weighs 81 kilogrammes overall because it is much larger than the Chihuahua.

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Answer: -40

Step-by-step explanation:

So if you put it into an expression, it would be 3(18 + 2) - 100.
Follow pemdas.
3(18 + 2) - 100
3(20) - 100. Parentheses mean multiply the coefficient with the value.
60 - 100.
-40

It is more unusual to have a day with a high temperature of 55 F. A high temerature of 55 F in July is 2.2 std deviation below the mean and a high temperature of 55 F in January is only 1.889 std deviation above the mean.

Which month is more unusual to have a day with a high temperature?

Here z score =(X-mean)/std deviation

Therefore for temperature 55 F ; zscore for January =(55-38)/9=1.889

And for temperature 55 F ; zscore for July =(55-77)/10=-2.2

As z score reflect that 55 F is farthest from the mean of July in terms of std deviation

It is more unusual to have a day with a high temperature of 55 F. A high temperature of 55 F in July is a 2.2 std deviation below the mean, and a high temperature of 55 F in January is only a 1.889 std deviation above the mean.

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The gas station serves 16 vehicles per hour, and 72 vehicles arrive in 4 hours. The vehicles will spend 4.50 hours at the gas station.



To find the total time the vehicles will spend at the gas station, we need to calculate the total number of vehicles that arrive and then divide it by the rate at which the gas station serves vehicles.

Given:

Arrival rate: 18 vehicles per hour

Service rate: 16 vehicles per hour

Time: 4 hours

First, let's calculate the total number of vehicles that arrive during the 4-hour period:

Total number of vehicles = Arrival rate * Time

                      = 18 vehicles/hour * 4 hours

                      = 72 vehicles

Since the gas station can serve 16 vehicles per hour, we can determine the time it takes to serve all the vehicles:

Time to serve all vehicles = Total number of vehicles / Service rate

                         = 72 vehicles / 16 vehicles/hour

                         = 4.5 hours

Therefore, the vehicles will spend 4.5 hours at the gas station. Rounded to 2 decimal places, the answer is 4.50 hours.

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The width of the freezer is 2.25ft

The formula for calculating the volume of rectangular prism is expressed as:

V = lwh

Given the following

length l = 8feet

w is the width

height h = 3feet

Substitute

54 = 8*3w

54 = 24w

w = 54/24

w = 2.25ft

Hence the width of the freezer is 2.25ft

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The derivative of the trigonometric function f(x) = 7x cos(-x) can be found using the product rule and the chain rule.

The product rule states that the derivative of the product of two functions is equal to the derivative of the first function multiplied by the second function, plus the first function multiplied by the derivative of the second function. In this case, let's consider the functions u(x) = 7x and v(x) = cos(-x). Taking the derivatives of these functions, we have u'(x) = 7 and v'(x) = -sin(-x) * (-1) = sin(x).

Applying the product rule, we can find the derivative of f(x):

f'(x) = u'(x) * v(x) + u(x) * v'(x)

= 7 * cos(-x) + 7x * sin(x)

Simplifying the expression, we have: f'(x) = 7cos(-x) + 7xsin(x)

Therefore, the derivative of the trigonometric function f(x) = 7x cos(-x) is f'(x) = 7cos(-x) + 7xsin(x).

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Answer:

58° = measure of arc AC

Step-by-step explanation:

The measure of an angle formed by 2 chords is equal to 1/2 the sum of the measures of the intercepted arcs.

65 = (measure of arc AC + measure of arc BD)/2

     =  (measure of arc AC + 72)/2

130 = measure of arc AC + 72

58° = measure of arc AC

Answer:

-36

Step-by-step explanation:

replace x with -5 and solve for the parenthesis and then take that number which would be -16 and multiply it by 9 which then would give you -144.  So then you would take -144 and divide it by 4 and your answer would be -36.

Answer:

answer 436 tubig is water halimaw is monster ang Ganda mo Sana kaso ang height mo pang kinder

Step-by-step explanation:

answer is 436 I hope it helps

Answer:

Hexagon

Step-by-step explanation:

Because I a cross section

Answer:

1750

Step-by-step explanation:

2000-1750=250

250x7=1750

Answer:

image isn't loading for me :((( can you try replying to me w the question

The scenario where a restaurant gathers data about a new dish by providing free samples to parties of six or more is a sampling bias.

What is sampling bias?

Sampling bias occurs when some members of a population are systematically more likely than others to be chosen for a sample. In the medical world, this is known as ascertainment bias. Because it threatens external validity, specifically population validity, sampling bias reduces the generalizability of findings.

Sampling bias occurs when some people in a community being surveyed are purposefully placed to be chosen or not chosen over others. If a sample process consistently favors some results over others, it is said to be biased. Ascertainment bias particularly in biological areas)/ and systematic bias are other terms for sampling bias. Bias can be intentional, but it is frequently unintentional.

Hence, the scenario where a restaurant gathers data about a new dish by providing free samples to parties of six or more is a sampling bias.

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Josue used 150 square centimeters of wrapping paper to cover the cube-shaped gift box

To determine the amount of wrapping paper used by Josue for the cube-shaped gift box, we need to calculate the surface area of the cube.

The net of the gift box consists of six squares, each representing a face of the cube. The dimensions provided in the figure show that each side of the squares is 5 cm.

Since a cube has six faces, we need to calculate the total surface area by multiplying the area of one square face by six.

The formula to find the area of a square is side length squared, so we can calculate the area of one square face as 5 cm * 5 cm = 25 cm².

Now, to find the total surface area, we multiply the area of one face by six: 25 cm² * 6 = 150 cm².

Therefore, Josue used 150 square centimeters of wrapping paper to cover the cube-shaped gift box.

It's worth noting that this calculation assumes that there is no overlap or excess wrapping paper used while wrapping the gift box. Additionally, we have assumed that the dimensions provided are accurate and refer to the side length of the squares in the net.

Overall, the amount of wrapping paper used can vary based on the wrapping technique employed and any additional decorations or folds added to the gift box.

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Answer:

I believe that x = -3/4 makes the equation true.

Step-by-step explanation:

3(-3/4 - 6)=8x - 3(3x + 7) is a true value equation.

I hoped this helped you answer your question.  

Answer:

The answer is -3/4

Step-by-step explanation:

Feel free to give brainliest

Have an amazing day!

Answer: 64

Step-by-step explanation:

(2 x 2) x (2 x 2) x (2 x 2)= 64

  (4      x     4)    x      4   = 64

           16           x     4   =  64

Hope this helps! If so, could I have a Brainly? I need a few to level up- Thx :3

\(\\\)

\(\large\mathfrak\red{\underline{Step\:by\:step \:explanation}}\)

\(\dashrightarrow\)There are 2 (L and Z) consonants out of 6 letters.

\(\\\)

\(\red\bigstar\)The probability of getting a consonant

\(\pink\implies\) 2/6 = 1/3

\(\\\)

\(:\red\implies\)When we spin the spinner second time, we will get the same probability

= 2/6 = 1/3

\(\dashrightarrow\)The probability that the spinner will stop on a consonant then again on a consonant

= 1/3 x 1/3

= 1/9

\(\red\bigstar\mathfrak \pink{Therefore, the \: answer \: is \: B) 1/9}\)

\(\rule{300px}{.7ex}\)

\(\large\tt\purple{\underline{ElegantLavender~}}\)

Option B is correct - 1/9

Answer:

see explanation

Step-by-step explanation:

Using the identity

cos2Θ = 1 - 2sin²Θ, then

1 - 2sin²(\(\frac{\pi }{4}\) - \(\frac{0}{2}\) )

= cos [2(\(\frac{\pi }{4}\) - \(\frac{0}{2}\) )]

= sos(\(\frac{\pi }{2}\) - Θ )

= cos\(\frac{\pi }{2}\)cosΘ + sin

= 0 × cosΘ + 1 × sinΘ

= 0 + sinΘ

= sinΘ = right side

Answer:  see proof below

Step-by-step explanation:

Use the Difference Identity: sin (A + B) = sin A cos B - cos A sin B

Use the following Half-Angle Identities:  

\(\sin\bigg(\dfrac{A}{2}\bigg)=\sqrt{\dfrac{1-\cos A}{2}}\\\\\cos\bigg(\dfrac{A}{2}\bigg)=\sqrt{\dfrac{1+\cos A}{2}}\)

Use the Pythagorean Identity: cos²A + sin²A = 1   -->   sin²A = 1 - cos²A

Use the Unit Circle to evaluate: \(\cos\dfrac{\pi}{4}=\sin\dfrac{\pi}{4}=\dfrac{1}{\sqrt2}\)

Proof LHS → RHS

\(\text{Given:}\qquad \qquad \qquad 1-2\sin^2\bigg(\dfrac{\pi}{4}-\dfrac{\theta}{2}\bigg)\\\\\text{Difference Identity:}\quad 1-2\bigg(\sin\dfrac{\pi}{4}\cdot \cos \dfrac{\theta}{2}-\cos \dfrac{\pi}{4}\cdot \sin\dfrac{\theta}{2}\bigg)^2\\\\\text{Unit Circle:}\qquad \qquad 1-2\bigg(\dfrac{1}{\sqrt2}\cos \dfrac{\theta}{2}-\dfrac{1}{\sqrt2}\sin \dfrac{\theta}{2}\bigg)^2\\\\\\\text{Half-Angle Identity:}\quad 1-2\bigg(\dfrac{\sqrt{1+\cos A}}{2}-\dfrac{\sqrt{1-\cos A}}{2}\bigg)^2\)

\(\text{Expand Binomial:}\quad 1-2\bigg(\dfrac{1+\cos A}{4}-\dfrac{2\sqrt{1-\cos^2 A}}{4}+\dfrac{1-\cos A}{4}\bigg)\\\\\text{Simplify:}\qquad \qquad \quad 1-2\bigg(\dfrac{2-2\sqrt{1-\cos^2 A}}{4}\bigg)\\\\\text{Pythagorean Identity:}\quad 1-\dfrac{1}{2}\bigg(2-2\sqrt{\sin^2 A}\bigg)\\\\\text{Simplify:}\qquad \qquad \qquad 1-\dfrac{1}{2}(2-2\sin A)\\\\\text{Distribute:}\qquad \qquad \qquad 1-(1-\sin A)\\\\.\qquad \qquad \qquad \qquad \quad =1-1+\sin A\\\\\text{Simplify:}\qquad \qquad \qquad \sin A\)

RHS = LHS:   sin A = sin A  \(\checkmark\)

Answer:

C

Step-by-step explanation:

the three binomial factors are (x+2)(x-1)(x-3)

Answer:

C

Step-by-step explanation:

Given a zero x = a then the corresponding factor is (x - a )

Here the zeros ( where the graph crosses the x- axis ) are at

x = - 2, x = 1 and x = 3

Thus the corresponding binomial factors are

(x - (- 2) ), (x - 1) and (x - 3), that is

(x + 2), (x - 1), (x - 3) → C

If the dimension of the cubicle is 7 ft by 8 ft by 5 ft. Then the volume of the cubicle will be 280 cubic feet.

It deals with the size of geometry, region, and density of the different forms both 2D and 3D.

An office cubicle measures seven feet by eight feet with a five-foot wall.

Then the volume of the cubicle will be

The volume is given as

Volume = length x width x height

We have

Volume = 7 x 8 x 5

Volume = 280 cubic feet

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