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The speed of the runner calculated by the properties of average speed is given by 33.45 feet and the upper limit is 43.45 feet in the last 3 seconds.

The first three seconds of a race saw a runner's speed rapidly grow.

The time is therefore 3 seconds.

The table provides her speed at half-second intervals.

We are aware,

Distance x Time = Speed

Similarly

Distance equals speed x time.

Δt equals 0.5 seconds

Then, the minimum distance travelled overall is equal to

0.5(0 + 6.7 + 9.2 + 14.1 + 17.5 + 19.4).

Terms are multiplied and added.

= 0.5 × 66.9

= 33.45 feet

The maximum distance travelled is equal to

0.5 (6.7 + 9.2 + 14.1 + 17.5 + 19.4 + 20)

= 0.5 × 86.9

= 43.45 feet

As a result, her maximum distance in three seconds is 43.45 feet, and her maximum distance in three seconds is 33.45 feet.

Velocity is the rate at which an item's position changes as perceived from a certain point of view and as measured by a given unit of time (for example, 60 km/h northbound).

Velocity is also the direction at which an object is travelling. Velocity is a fundamental concept in kinematics, the branch of classical mechanics that deals with the motion of bodies.

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The location of the coin next to the convex side of a thin spherical glass shell is 3.68 cm.

According to the question,

Radius of curvature : 19 cm

Size of image formed : 1.5cm

Distance of coin from glass shell : 6.5cm

The position of the coin placed next to the convex side of a thin spherical glass shell is calculated as follows;

1/d = 1/f - 1/d'

where;

d' is the position of the coin's image

d position of the coin

f is focal length

Focal length = r/2 =19/ 2 = 9.5 cm

=> 1/d = 1/9.5 - (-1/6.5)

=> 1/d = 1/9.5 + 1/6.5

=> 1/d = 0.1052 + 0.1538

=> 1/d = 0.259

=>d = 1/0.259

d = 3.86 cm

Thus, the position of the coin placed next to the convex side of a thin spherical glass shell is 3.86 cm.

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By using the concept of reflection and scaling, it can be calculated that

New equation of parabola is [tex]y = -5x^2[/tex]

What is reflection and scaling?

Reflection is a mathematical transformation in which a mirror image of an object can be obtained without changing the shape and size of an object.

To draw an object of size proportional to the size of the original object, scaling is used

The equation of the parabola is [tex]y = x^2[/tex]

If it is reflected across x axis, its equation is [tex]y = -x^2[/tex]

Now  y  = -[tex]x^2[/tex] is scaled vertically by a factor of 5

New equation of parabola

[tex]y = -5x^2[/tex]

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The power of the test, if the actual average fuel efficiency is 36 miles per gallon, is 0.5675.

What is the standard deviation?

The standard deviation in statistics is a measure of the amount of variation or dispersion in a set of values. A low standard deviation indicates that the values are close to the set's mean, whereas a high standard deviation indicates that the values are spread out over a larger range.

We want to test [tex]\mu_0 > 35[/tex] at the level [tex]\alpha=0.01[/tex], where the true mean is [tex]\mu_1=36,\sigma\approx4, n=100[/tex]

The power of a right-tailed test is given by

[tex]1-\beta=P(Z > [z_\alpha-\frac{\sqrt{n}}{\sigma}(\mu_1-\mu_0)])\\\\1-\beta=P(Z > [2.33- \frac{\sqrt{100}}{4}(36-35)])\\\\1-\beta=P(z > -0.17)\\\\power=0.5675[/tex]

Hence, the power of the test, if the actual average fuel efficiency is 36 miles per gallon, is 0.5675.

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The statement of the given hypothesis condition is False.

What is hypothesis testing?

A type of statistical inference known as hypothesis testing uses data from a sample to make inferences about a population parameter or population probability distribution.

Given this, A researcher wants to test the hypothesis that on average girls perform better on standardized tests than boys.

i.e. [tex]\mu_{1} > \mu_{2}[/tex]

">" sign implies that right-tailed test i.e. one-tailed right-sided.

Hence, the given statement is FALSE.

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Answer:

WE need to factorise (2x+4y)(2x−4y)

Given identity is (x+a)(x+b)=x

2

+(a+b)x+ab

Here x=2x,a=b=4y

Thus we have (2x+4y)(2x−4y)=(2x) 2

+(4y−4y)+(4y)(−4y)=4x2

−16y 2

The average number of hours that Ashley worked per day is obtained as follows:

Mean = sum of relative frequencies x outcome

The relative frequency table shows that absolute frequencies of the number of hours worked, that is, the number of days in which each amount of hours was worked.

Then the relative frequencies are obtained by the division of each of the absolute frequencies by the total number of outcomes, which is the sum of all the relative frequencies.

Finally, the mean value is obtained just like the mean of a discrete distribution, with the multiplication of each outcome by it's relative frequency obtained previously.

The problem is incomplete, hence I gave a general pattern to find the mean of the data-set.

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Answer:

2 2/3

Step-by-step explanation:

Answer:b

Step-by-step explanation:

Answer:

(65) (64)

Step-by-step explanation:

The probability that a randomly chosen death is a white person who died of diabetes is 0.024 determined using the law of total probability.

The law of total probability is a fundamental rule that connects marginal probabilities to conditional probabilities and expresses the total probability of an outcome via several distinct events. The rule states that if the probability of an event is unknown, it can be calculated using the known probabilities of several distinct events. It is given by P(A ∩ B) = P(A|B)P(B)

In order to determine the probability of an event (D) with not enough information to calculate it directly, a related event, say W can be taken and use that to calculate the probability for D.

Let the events that a person from a certain race die be denoted as:

P(W) = 0.86; P(B) = 0.12; P(A) = 0.02

Let the events that a person from a certain race dies of diabetes be denoted as:

P(D/W) = 0.0.028; P(D/B) = 0.044; P(D/A) = 0.035

Probability that a randomly chosen death is a white person who died of diabetes

P(W) x P (D/W) = 0.86 x 0.028 = 0.02408 ≈ 0.024

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A. Poor understanding of HIV

B. Cognitive impairment

C. Substance abuse

D. Unstable housing

The probability of a person guessing the right combination be

1/720.

Given, a small combination lock on a suitcase has ​wheels, each labeled with the 10 digits from 0 to 9.

we have to find the probability of a person guessing the right combination if there is no repeating of any digit.

as, we need three digit number to unlock the suitcase.

total combinations of the lock be,

10×9×8

= 720

only one combination can open the suitcase,

So, the probability of a person guessing the right combination be

1/720.

Hence, the probability of a person guessing the right combination be

1/720.

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As a fraction of c, the length will be 60% at v/c = 0.76

The length of the moving rod = 60%

Using the formula for length contraction-

L = L_o(√(1 - (v²/c²))

Where;

v = The speed of the object

c = The speed of light

L = The length of the object at a moving speed

L_o = The length of the object at rest

Thus,

L = 65%

L_o = 0.65

Substituting the values -

0.65L_o = L_o[√(1 - (v²/c²))]

Dividing both sides by L_o -

0.65 = √(1 - (v²/c²))

Squaring both sides -

0.65² = (1 - (v²/c²))

v²/c² = 1 - 0.65²

v²/c² = 0.5775

Taking the square root of both sides gives;

v/c = 0.76

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Answer:

1

Step-by-step explanation:

9/8.3 = 1.0843, rounded to the nearest whole number is 1

Answer: -2

Step-by-step explanation:

If width i.e. x is 20 ft then the farmer will purchase the land.

Given,

width of land = x ft

length of land = ( x - 8 ) ft

Area of land =240 square feet

To determine x use formula,

Area of land =length * width

[tex]240=(x-8)*x\\\\240=x^2-8x\\\\x^2-8x-240=0\\\\x^2+12x-20x-240=0\\\\x(x+12)-20(x+12)=0\\\\(x+12)(x-20)=0\\\\x=-12\ or\ 20[/tex]

x cannot be negative.

x=20 ft

Thus, if width i.e. x is 20 ft then the farmer will purchase the land.

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The expression that results from applying the law of indices and expression is 5x^(-7/3).

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation. An expression's structure is as follows: (Number/variable, Math Operator, Number/variable) is an expression. An expression, also known as a mathematical expression, is a finite combination of symbols that are well-formed in accordance with context-dependent rules.

Here,

The resulted expression will be,

(125x)^(7/3)^(-1/3)

125=5^3

(a^n)^m = a^mn

(5x)^3^7/3^-1/3

(5x)^7*-1/3

5x^(-7/3)

The resulted expression will be 5x^(-7/3) using the law of indices and expression.

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Answer:

b. 1 1/4

c. 11 3/8

d. 1 4/7

Step-by-step explanation:

b. 3 - 1 3/4

   2 4/4 - 1 3/4

   [4/4 - 3/4 = 1/4] and [2 - 1 = 1]

   1 + 1/4

   1 1/4

c. 7 3/8 + 4

   Add the whole numbers.

   11 3/8

d. 4 - 2 3/7

   3 7/7 - 2 3/7

   [7/7 - 3/7 = 4/7 and 3 - 2 = 1]

   1 + 4/7

   1 4/7

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Answer:

The goal is to make the denominators the same.

[tex]\frac{numerator}{denominator}[/tex]

Here's how to solve "b" (I explained it so you can do the other ones)

b.

[tex]3 - 1\frac{3}{4}[/tex]

Turn the 3 into a fraction (you can put any number over 1 and it will be the same)

[tex]\frac{3}{1} - 1\frac{3}{4}[/tex]

Next, let's turn the [tex]1\frac{3}{4}[/tex] into an "improper fraction". Right now, it is a mixed number. Multiply the denominator by the whole number on the left, and then add it to the numerator. The denominator will stay the same.

4 * 1 = 4

4 + 3 = 7

[tex]1\frac{3}{4}[/tex] → [tex]\frac{7}{4}[/tex]

Okay, so now we have this:

[tex]\frac{3}{1} - \frac{7}{4}[/tex]

This is getting easier! But to subtract, we have to make the denominators the same. Let's multiply the top and bottom of [tex]\frac{3}{1}[/tex] by 4.

[tex]\frac{3 * 4}{1 * 4} = \frac{12}{4}[/tex]

Now we have:

[tex]\frac{12}{4} -\frac{7}{4}[/tex]

One final step, subtract the numerators! Leave the denominators as they are.

12 - 7 = 5

Our answer is:

[tex]\frac{5}{4}[/tex]

Answer: 75%

Step-by-step explanation:

9 + 3 = 12

9/12 = 3/4

3/4 = 75%

Answer:

64

Step-by-step explanation:

16 ÷ 12 = 1.33 (rounded to 2 decimal places)

1.33 = scale factor

1.33² = area scale factor

1.33² × 36 = 64 (rounded to a whole number)

Answer: 64 would be the area

Step-by-step explanation:

If the wheel rotates clockwise, the height function is h(t) = 28.5 + 22.5sin(270 - 36t).

The function's central axis for the height of the Ferris wheel's center is given by h = f(t).

= 6 + 45 ÷ 2 = 6 + 22.5 = 28.5 meters.

The wheel rotates at a speed of 36 degrees per minute since the period of revolution is 10 minutes.

The wheel's direction of rotation—clockwise or counterclockwise—is not specified.

Let's look at both situations:

The present angle, assuming it spins clockwise, is equal to 270 – 36t degrees, where t is the duration in minutes.

Then the height function h = f(t)

= 28.5 + 22.5sin(a)

= 28.5 + 22.5sin(270 - 36t)

If the wheel rotates anti-clockwise, the current angle is

b = 270 + 36t degrees.

Then the height function

h = r(t)

= 28.5 + 22.5sin(b)

= 28.5 + 22.5sin(270 + 36t)

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Answer:48?

Step-by-step explanation:

I as of now am not completely sure of this is the correct answer.

The value of the the function h(x) at x = 4 is given as follows:

8.7.

The quadratic regression equations for each table are given as follows:

The function for the first item is defined as follows:

h(x) = 50/(5.5 + 8e^(-0.9x)).

At x = 4, the value assumed by the function is obtained replacing the lone instance of x by 4, hence:

h(4) = 50/(5.5 + 8e^(-0.9(4))).

Then a calculator is used to obtain the exact value due to the exponential, hence:

h(4) = 8.7.

The regression equations are obtained inserting the points of each table into a quadratic regression calculator.

For the first table, the points are given as follows:

(16, 15), (18, 15.6), (20, 15.7), (21, 15), (23, 13.1), (26, 8.9), (27, 6.6).

Hence the equation is of:

y = -0.127x² + 4.699x - 27.777.

For the second table, the points are given as follows:

(3, 330), (4, 276), (5, 263), (6, 86), (7, 174), (8, 198), (9, 553).

Hence the equation is of:

y = 32.86x² - 379.14x + 1229.14.

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A+B+C=180

55+80+x=180

135+x=180

x=180-135

x=45

Answer: 14

Step-by-step explanation:

The equation to find slope is y2-y1/x2-x1 or in simpler terms is rise over run.

We see that the y increase by 14 so the rise is 14 and the x is the same so the run is 0. So the slope is 14.

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Answer:

b = -3

Step-by-step explanation:

1. Rearrange Terms

-3(3 + 6b) = 36 - 3b

-3(6b + 3) = 36 - 3b

2. Distribute

-3(6b + 3) = 36 - 3b

-18b - 9  = 36 - 3b

3. Rearrange Terms

-18b - 9  = 36 - 3b

-18b - 9 = -3b + 36

4. Add 9 to both sides

-18b - 9 = -3b + 36

-18b - 9 + 9 = -3b + 36 + 9

5. Simplify

-18b - 9 + 9 = -3b + 36 + 9

-18b = -3b + 45

6. Add 3b to both sides

-18b = -3b + 45

-18b +3b = -3b + 45 + 3b

7. Simplify

-15b = 45

8. Divide both sides by the same factor

-15b = 45

[tex]\frac{-15b}{-15}[/tex] = [tex]\frac{45}{-15}[/tex]

9. Simplify

b = -3

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Answer:

WWWWWW

Step-by-step explanation:

Answer:

Yes

Step-by-step explanation:

There are 36^10 ways  that contain only digits and lower-case letters and having the length is 10.

What is password?

A password, also known as a passcode, is private information that typically consists of a string of characters and is used to verify a user's identity.

We have to find the number of ways that contain only digits and lower-case letters and having the length is 10.

Since, there are total 10 digits from '0 to 9' and 26 lower case letters from

'a to z'.

The 10 slots in the password can be anything - digits as lower case letters.

that is,

10 + 26 = 36 options for each slot.

So, the total number of ways are, 36^10.

Hence, there are 36^10 ways  that contain only digits and lower-case letters and having the length is 10.

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Answer:

Step-by-step explanation:

its 20