The formula v= u+ atdescribes connections between u: starting velocity a: acceleration t: time v: final velocity a)In a particular situation, u= 0, v= 49 and a= 9.8. Substitute these numbers into the formula to create an equation. b)Solve the equation to find the value of t

The medians are about the same.

Option C is the correct answer.

The median, in statistical terms, refers to the value in the center of a dataset that has been sorted either in ascending or descending order, and it is a commonly used measure of central tendency. This contrasts with the mean, which calculates the total value of all figures, then divides by the number of figures.

We have,

Movie theater 1.

From the box plot given,

The median is 995.

Movie theater 2.

From the box plot given,

The median is 995.

Thus,

The median in both the box plot is the same.

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Answer:

4x^3+x^2-1

Step-by-step explanation:

(3x^2-x^3)-(-5x^3+2x^2+1)

Distribute the minus sign

(3x^2-x^3)+5x^3-2x^2-1

Combine like terms

-x^3 +5x^3  + 3x^2 -2x^2 -1

4x^3+x^2-1

Answer:

your answer is \(4x^{3} + x^{2} -1\).

Step-by-step explanation:

The rate (in km/h) at which the distance from the plane to the radar station is increasing a minute later is 0 km/h (rounded to the nearest whole number).

To solve this problem, we can use the concepts of trigonometry and related rates.

Let's denote the distance from the plane to the radar station as D(t), where t represents time. We want to find the rate at which D is changing with respect to time (dD/dt) one minute later.

Given:

The plane is flying with a constant speed of 360 km/h.

The plane passes over the radar station at an altitude of 1 km.

The plane is climbing at an angle of 30°.

We can visualize the situation as a right triangle, with the ground radar station at one vertex, the plane at another vertex, and the distance between them (D) as the hypotenuse. The altitude of the plane forms a vertical side, and the horizontal distance between the plane and the radar station forms the other side.

We can use the trigonometric relationship of sine to relate the altitude, angle, and hypotenuse:

sin(30°) = 1/D.

To find dD/dt, we can differentiate both sides of this equation with respect to time:

cos(30°) * d(30°)/dt = -1/D^2 * dD/dt.

Since the plane is flying with a constant speed, the rate of change of the angle (d(30°)/dt) is zero. Thus, the equation simplifies to:

cos(30°) * 0 = -1/D^2 * dD/dt.

We can substitute the known values:

cos(30°) = √3/2,

D = 1 km.

Therefore, we have:

√3/2 * 0 = -1/(1^2) * dD/dt.

Simplifying further:

0 = -1 * dD/dt.

This implies that the rate at which the distance from the plane to the radar station is changing is zero. In other words, the distance remains constant.

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Answer:

Step-by-step explanation:

The directional derivative of f at the given point in the direction indicated by the angle θ is expressed as \(\nabla f(x, y)*u\) where u is the unit vector in the direction θ.

Lets first calculate \(\nabla f(x, y)\ at\ (0, 1)\)

\(\nabla = \frac{\delta}{\delta x} i + \frac{\delta}{\delta y} j \\\nabla f(x, y) = \frac{\delta (y cos(xy))}{\delta x} i + \frac{\delta(y cos(xy))}{\delta y} j\\\nabla f(x, y)= -y^{2} sinxy\ i + (cosxy -xysinxy) j\\\)

\(\nabla f(x, y)\ at\ (0, 1)\\= -1^{2}sin0 \ i +(cos 0 - 0sin0) \j\\= 0i+j\\\\\)

The unit vector u in the direction of θ  is expressed as \(cos\theta \ i + sin\theta \ j\)

unit vector u  at θ = π/6 is cos π/6i + sin π/6 j

u= √3/2 i +1/2 j

Taking the dot product i.e \(\nabla f(x, y)*u\)

= (0i+j)*(√3/2 i +1/2 j)

= 1/2

The directional derivative of f is 1/2

The variables are as follows:

x = 4

y = 4.8

The lengths of the sides of the kites are 4.5 and 6.8 units.

A kite is a quadrilateral with 2 pairs of consecutive congruent sides. The diagonals are perpendicular in a kite.

The non vertex angles are congruent.

Therefore,

x + 0.5 = 2x - 3.5

2x - x = 0.5 + 3.5

x = 4

y + 2 = 2y - 2.8

2y - y = 2 + 2.8

y = 4.8

Hence,

length of one pair = 4 + 0.5 = 4.5 units

length of the other pair = 4.8 + 2 = 6.8 units

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To determine how much effort the gas undergoes as it changes from its original condition to its final one, Nora and Bob utilize the area underneath the line separating the two states and the first rule of thermodynamics.

When a gas changes from its initial condition to its final state, Nora and Bob explain how to compute the work that is done. They talk about compressing gas, thus something is being done to the gas.

You suggest using the area under the line separating the final and initial states to calculate the work done as well as the application of the first equation of thermodynamics, q=w.

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Answer:

the perimeter of the rectangle is 26 meters.

Step-by-step explanation:

To find the perimeter of the rectangle, we need to know its width. We can find the width by dividing the area by the length:

width = area / length = 36 / 9 = 4 meters

Now we can use the formula for the perimeter of a rectangle:

perimeter = 2(length + width)

Substituting the given values, we get:

perimeter = 2(9 + 4) = 2(13) = 26 meters

Therefore, the perimeter of the rectangle is 26 meters.

Answer:

uh

Step-by-step explanation:

i do not know

If n is an integer and m + 5 is odd, then n must be even.

To prove this statement using contraposition, we need to show that if n is odd, then m + 5 must be even. Assume that n is odd, which means we can write n = 2k + 1 for some integer k.

Then, we can rewrite m + 5 as (2k + 1) + 5 = 2k + 6 = 2(k + 3), which is even.

Therefore, we have shown that if n is odd, then m + 5 is even.

By contraposition, we can conclude that if m + 5 is odd, then n must be even. Overall, the proof uses the fact that odd + odd = even and even + odd = odd, along with the definition of even and odd integers.

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The function that would have the greatest value at x = 16 include the following: B. y = x² - 17x + 182.

In Mathematics and Geometry, a function is a mathematical equation which defines and represents the relationship that exists between two or more variables such as an ordered pair in tables or relations.

In this exercise, we would determine the corresponding output value for this function of y based on the x-value (x = 16) in simplified form as follows;

\(y = 10^{16}\)

y = 10,000,000,000,000,000.

y = x² - 17x + 182

y = 16² - 17(16) + 182

y = 256 - 272 + 182

y = 166.

\(y = 1.17^x\\\\y = 1.17^{16}\)

y = 12.330304108137675851908392069373.

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Answer:

The two triangles are very similar by them both having the same kind of angles even though they are different in size, like, an acute angle.

I'm not sure if this helped or not hopefully it did good luck.

Answer:

The distance between two points (x₁, y₁) and (x₂, y₂) is given by:

\(d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}\)

Now we know that point D, which we can write as (x, y), is at a distance of 8 units from the origin.

Where the origin is written as (0, 0)

We also know that point D is 6 units away along the y-axis.

Then point D could be:

(x, 6)

or

(x, -6)

Now, let's find the x-value for each case, we need to solve:

\(8 = \sqrt{(x - 0)^2 + (\pm6 - 0)^2}\)

notice that because we have an even power, we will get the same value of x, regardless of which y value we choose.

\(8 = \sqrt{x^2 + 36} \\\\8^2 = x^2 + 36\\64 - 36 = x^2\\28 = x^2\\\pm\sqrt{28} = x\\\pm 5.29 = x\)

So we have two possible values of x.

x = 5.29

and

x = -5.29

Then the points that are at a distance of 8 units from the origin, and that are 6 units away along the y-axis are:

(5.29, 6)

(5.29, -6)

(-5.29, 6)

(-5.29, -6)

Answer:

0.8254 = 82.54% probability that the mean of this sample is between 19.25 hours and 21.0 hours

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean \(\mu\) and standard deviation \(\sigma\), the z-score of a measure X is given by:

\(Z = \frac{X - \mu}{\sigma}\)

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean \(\mu\) and standard deviation \(\sigma\), the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \(\mu\) and standard deviation \(s = \frac{\sigma}{\sqrt{n}}\).

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

Mean of 20 hours, standard deviation of 6:

This means that \(\mu = 20, \sigma = 6\)

Sample of 150:

This means that \(n = 150, s = \frac{6}{\sqrt{150}}\)

What is the probability that the mean of this sample is between 19.25 hours and 21.0 hours?

This is the p-value of Z when X = 21 subtracted by the p-value of Z when X = 19.5. So

X = 21

\(Z = \frac{X - \mu}{\sigma}\)

By the Central Limit Theorem

\(Z = \frac{X - \mu}{s}\)

\(Z = \frac{21 - 20}{\frac{6}{\sqrt{150}}}\)

\(Z = 2.04\)

\(Z = 2.04\) has a p-value of 0.9793

X = 19.5

\(Z = \frac{X - \mu}{s}\)

\(Z = \frac{19.5 - 20}{\frac{6}{\sqrt{150}}}\)

\(Z = -1.02\)

\(Z = -1.02\) has a p-value of 0.1539

0.9793 - 0.1539 = 0.8254

0.8254 = 82.54% probability that the mean of this sample is between 19.25 hours and 21.0 hours

Answer:

a) 1.96cm³

b) 54.32%

Step-by-step explanation:

From the question, we are told that:

The shape of a cancerous tumor is roughly spherical and has volume

V= 4/3 πr^3

a) When first observed, the tumor has radius 0.73 cm, and 45 days later, the radius is 0.95 cm. By how much does the volume of the tumor increase during this period?

Volume of the tumour at a radius of 0.73cm

= V= 4/3 πr^3

V = 4/3 × π × 0.73³

V = 1.6295105991cm³

Approximately = 1.63cm³

After 45 days, radius of the tumour increased to 0.95cm

Volume of the tumour at radius 0.95cm

V= 4/3 πr^3

V = 4/3 × π × 0.95³

V = 3.5913640018cm³

V = 3.59cm³

The percent increase in the volume of the cancerous tumor

= Volume of the tumor after 45days - Volume of the tumour before 45 days

= 3.59 - 1.63

= 1.96cm³

Therefore, the volume of the tumor increases by 1.96cm³

b) After being treated with chemotherapy, the radius of the tumor decreases by 23%. What is the corresponding percentage decrease in the volume of the tumor?

From the question above, we are told that after chemotherapy, the radius of the tumour decreased by 23%

This means the radius of 0.95 decreases by 23%

Therefore,

23% of 0.95cm

= 23% × 0.95 cm = 0.2185cm

Therefore, the radius of the tumour after chemotherapy = 0.95cm - 0.2185cm

= 0.7315cm

The current volume of the tumour is calculated as

= V= 4/3 πr^3

V = 4/3 × π × 0.7315³

V = 1.6395761818cm³

V = approximately 1.64cm³

Volume of the tumour at 0.95cm³ is 3.59cm³

The decrease = 3.59 - 1.64 = 1.95

Percentage decrease = 1.95/3.59 × 100

= 54.317548747 %

Approximately = 54.32%

Answer: –5

Step-by-step explanation:

\(e = -13, f = 8\)

Replace \(e+f\) with their respective values.

\(e + f = -13 + 8 = -5\)

Approximately 37.5% of the data are greater than 28, 33.3% of the data are less than 23, 91.7% of the data are greater than 17.5, and 62.5% of the data are between 17.5 and 28.

To answer the questions, we can analyze the given data set.

First, let's count the number of data points that satisfy each condition:

Greater than 28:

There are 9 data points greater than 28 (29, 29, 29, 30, 29, 29, 28, 28, 28).

Less than 23:

There are 8 data points less than 23 (20, 18, 15, 17, 17, 15, 17, 19).

Greater than 17.5:

There are 22 data points greater than 17.5.

Between 17.5 and 28:

There are 15 data points between 17.5 and 28.

Now, let's calculate the approximate percentage for each condition:

Percent greater than 28:

The total number of data points is 24. Approximately, 9 out of 24 data points are greater than 28.

Percentage =\((9 / 24) \times 100 = 37.5\)%.

Percent less than 23:

Approximately, 8 out of 24 data points are less than 23.

Percentage = \((8 / 24) \times 100 = 33.3\)%.

Percent greater than 17.5:

Approximately, 22 out of 24 data points are greater than 17.5.

Percentage = \((22 / 24) \times 100 = 91.7\)%.

Percent between 17.5 and 28:

Approximately, 15 out of 24 data points are between 17.5 and 28.

Percentage = \((15 / 24) \times 100 = 62.5\)%.

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Answer:

$4.55

Step-by-step explanation:

72.99-68.44=4.55

Answer: 1 4/8

Step-by-step explanation:

Answer:

1 5/8

Step-by-step explanation:

7/8+6/8= 13/8 = 1 5/8

The measures of the cylinder that has a diameter of 4 cm and height of 14 cm are:

i. circumference of the base = 6.29 cm.

ii. area of the base = 12.57 cm²

iii. volume = 176 cm²

The volume of a cylinder is calculated using the formula given as, volume (V) = πr²h, where:

Given the following:

i. The circumference of the base of the cylinder = πr = (22/7) * 2 = 44/7 = 6.29 cm.

ii. The area of the base of the cylinder = πr² = 22/7 * 2² = 88/7 = 12.57 cm²

iii. Volume of the cylinder = πr²h = 22/7 * 2² * 14 = 176 cm²

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Answer:

"Vx: if x is a valid argument with true premises then x has a true conclusion"

In a symbol form

Vx ( P(x) ⇒ 2(x) )

Step-by-step explanation:

The Following statement in the form  âˆ€x ______, if _______ then _______ is a valid argument and this because any valid argument with "true premises" has a "true conclusion" as well

we will rewrite this statement in a universal condition statement form

assume x is a valid argument with true premises

then the following holds true

p(x) : x is a valid argument with true premises

q(x) : x has true conclusion

applying universal conditional statement

"Vx, if x is a valid argument with true premises then x has a true conclusion"

In a symbol form

Vx ( P(x) ⇒ 2(x) )

Answer:

Jumbo burger with fried is 75%

chicken with salad is 65%

Step-by-step explanation:

you first split the burger and sides. You add up the sides to find the salad. Then add up the sides and burgers

Answer:

What is the probability that he order a Jumbo Burger with Regular Fries or a Chicken Sandwich with a Salad? Make an area or tree diagram to help with the problem.

Answer to question: 20% for Jumbo Burger with Regular Fries and 10.5% for Chicken Sandwich with a Salad.

Step-by-step explanation:

You are going to find the probability that he order a Jumbo Burger with Regular Fries or a Chicken Sandwhich with a Salad by using a area model or a tree diagram. Although you ddin't ask me to solve it, I'm gonna help you with it anyways.

Sandwhiches:

50% - Jumbo Burger (JB)

30% - Chicken Sandwich (CS)

20% - Regular Burger (RB)

Sides:

40% - Curly Fries (CF)

35% - Salad (S)

25% - Regular Fries (RF)

Acronyms

Jumbo Burger (JB) + Curly Fries (CF) = JBCF

Jumbo Burger (JB) + Salad (S) = JBS

Jumbo Burger (JB) + Regular Fries (RF) = JBRF

Chicken Sandwich (CS) + Curly Fries (CF) = CSCF

Chicken Sandwich (CS) + Salad (S) = CSS

Chicken Sandwich (CS) + Regular Fries (RF) = CSRF

Regular Burger (RB) + Curly Fries (CF) = RBCF

Regular Burger (RB) + Salad (S) = RBS

Regular Burger (RB) + Regular Fries (RF) = RBRF

Probability of combinations:

JBCF = 0.5 x 0.4 = 0.20

JBS = 0.5 x 0.35 = 17.5

JBRF = 0.5 x 0.25 = 12.5

CSCF = 0.3 x 0.4 = 12

CSS = 0.3 x 0.35 = 10.5

CSRF = 0.3 x 0.25 = 7.5

RBCF = 0.2 x 0.4 = 8

RBS = 0.2 x 0.35 = 7

RBRF = 0.2 x 0.25 = 5

Your tree diagram should look something like this:

         CF(40%)- outcome - JBCF (20%)

          /  

(50%)JB ---  S(35%)-  outcome - JBS (17.5%)

           \            

           RF(25%)-  outcome - JBRF (12.5%)

         CF(40%)- outcome - CSCF (12%)

          /

(30%)CS ---  S(35%)- outcome - CSS (10.5%)

            \

            RF(25%)- outcome - CSRF (7.5%)

           CF(40%)- outcome - RBCF (8%)

           /

(20%)RB ---  S(35%)- outcome - RBS (7%)

          \

          RF(25%)- outcome - RBRF (5%)

Hope this helps because this took forever :D

Answer: will it be 4/13?

Step-by-step explanation:

The answer is (2.5,7)

Answer: x=y/(3b-7)

Step-by-step explanation:

To solve for v, you want to use algebraic properties to isolate x.

y=3bx-7x                [factor out x]

y=x(3b-7)                [divide both sides by 3b-7]

x=y/(3b-7)

Now, we know that x=y/(3b-7).

Answer:

3bx -7x = y

or, x(3b -7) = y

or, x= y/(3b -7)

Answer:  134 miles

Step-by-step explanation:  

f(m) = 16.95 + 0.92m

140.23 = 16.95 + 0.92m

0.92m = 140.23 - 16.95

0.92m = 123.28

m = 123.28/0.92

m = 134 miles

Solution

We are given the expression

The image below shows the definition of a polynomial and some examples as well

Thus, given

Here;

Degree = 0

Leading coefficient = 3

Answer:

Yes

Step-by-step explanation:

To know if a table is a function or not, we have to see if 1 input only has 1 output.

Looking at the table each input only has 1 output, so it is a function.

Answer:

Step-by-step explanation:

Point: 10,-9

k=-2

y=-2x+b

So: 9, -7

8,-5

7,-3

6,-1

5,1

4,3

3,5

2,7

1,9

0,11

y=-2x+11

Answer:

y + 9 = - 2(x - 10)

Step-by-step explanation:

the equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b ) a point on the line

here m = - 2 and (a, b ) = (10, - 9 ) , then

y - (- 9) = - 2(x - 10) , that is

y + 9 = - 2(x - 10)