a) how far has the beam diverged from its assigned target when it reaches the moon? (the distance from the earth to the moon is 240,000 mi. round your answer to the nearest mile.)

For a set of data in which the sample mean is 83.3 and the sample standard deviation is 6.3 the z-score given that x = 79.8 would be -0.555

We know that the formula for calculating a z-score is :

z = (x - μ) / σ

where z is the standard z - score

x is the observed value

μ is the mean of the sample

σis the standard deviation of the sample

here, set of data in which the sample mean is 83.3 and the sample standard deviation is 6.3

i.e., μ = 83.3,  σ = 6.3

We calculate the z-score for x = 79.8

Using above formula,

z = (x - μ) / σ

z = (79.8 - 83.3) / (6.3)

z = (-3.5) / (6.3)

z = -0.555

Therefore, the z-score is:  -0.555

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a must be the least upper bound of S because it satisfies both conditions: it is an upper bound of S, and any other upper bound b for S must be greater than or equal to a.

What is the difference between the least upper bound and upper bound?

An upper bound of a set S of real numbers is any real number that is greater or equal to all numbers in S. A lower bound is any which is less than or equal to all numbers in S. A least upper bound is an upper bound that is less than or equal to all upper bounds.

To prove that a is the least upper bound (LUB) of the set S, we need to show that a satisfies two conditions:

a is an upper bound of S, meaning that for every element x in S, x <= a.

If there is another upper bound b for S, then a <= b.

First, we already know that a is an upper bound of S because it is given that a is an upper bound of the set S.

Next, suppose there is another upper bound b for S such that b > a. Then, since the sequence xₙ converges to a, there exists a positive integer N such that for all n >= N, xₙ is arbitrarily close to a, meaning that |xₙ - a| < (b - a)/2. This means that xₙ < b for all n >= N, which contradicts the assumption that b is an upper bound of S, since xₙ is an element of S and xₙ < b.

Therefore, a must be the least upper bound of S because it satisfies both conditions: it is an upper bound of S, and any other upper bound b for S must be greater than or equal to a.

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Answer: To find the distance fallen after 1.6 seconds, we simply plug this value into the function and solve for h:

h = t^2 * 16

h = 1.6^2 * 16

h = 2.56 * 16

h = 40.96 feet

So, the object has fallen 40.96 feet after 1.6 seconds.

Step-by-step explanation:

A fully inflated professional basketball has a circumference of 78 centimetres, hence the football's radius is 12.42 cm.

A circle is created when almost every point there in plane that is a specific distance away from another point does so (center). As a conclusion, it is a curve made up of segments that are spaced from each other in the plane. It is rotationally homogeneous about the centre in anyway angles. All pair of points in the grid that make up a circle are evenly spaced away from the "centre" and create a closed, two-dimensional object. A specular parity line is generated by a line that passes through circle. It is rotationally symmetric about just the centre at all angles.

given

The football's circumference is 12.42 cm.

Football's circumference is 78 cm.

The formula for the football's circumference is C = 2pir

= 78 r

= 78/2pi r

= 12.42 cm.

A fully inflated professional basketball has a circumference of 78 centimetres, hence the football's radius is 12.42 cm.

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Answer:

we on top

Step-by-step explanation:

Answer:

Step-by-step explanation:

you gotta be kidding me right now b r u h.  Aint no way bro is posting this hahahha get it i guess

Answer:

B. False

Step-by-step explanation:

The domain is the set of values of x.

There is no restriction on the value of x.

x can be any real number.

Answer: B. False

A system of equations in standard form to model this scenario include the following:

2x + 10y = 74.

x + y = 17.

In order to write a system of linear equations that could be used to model the situation and determine the number of small boxes shipped and the number of large boxes shipped, we would assign variables to the number of small boxes that were shipped, the number of large boxes that were shipped respectively as follows:

Next, we would translate the word problem into system of linear equations as follows:

Since x small boxes weigh 2 pounds each and y large boxes weigh 10 pounds each and  all the boxes she ships is 74 pounds;

2x + 10y = 74.

Additionally, she is shipping 17 boxes altogether;

x + y = 17.

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The smallest integer value for IK is (c) 14

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

The parallelogram

The value of IK can be calculated as

IK^2 = 5^2 + 12^2 - 5 * 12cos(J)

IK^2 = 169 - 60cos(J)

If J is obtuse, then cos(J) is a negative value,

This means that IK^2 must be greater than 169 and therefore IK must be greater than 13.

The smallest integer value greater than 13 is 14,

So your answer is (c). IK = 14

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On solving the provided question, we can say that Probability(x>11) = 1 - P(x[tex]\leq 11[/tex])\ = 0.9645 and Probability(5<x<9) = P(x<9) - P(x<5) = 0.0101 and P(x<9) = 0.0106

Probability theory, a subfield of mathematics, gauges the likelihood of an occurrence or a claim being true. An event's probability is a number between 0 and 1, where approximately 0 indicates how unlikely the event is to occur and 1 indicates certainty. A probability is a numerical representation of the likelihood or likelihood that a particular event will occur. Alternative ways to express probabilities are as percentages from 0% to 100% or from 0 to 1. the percentage of occurrences in a complete set of equally likely possibilities that result in a certain occurrence compared to the total number of outcomes.

Probability(x>11) = 1 - P(x[tex]\leq 11[/tex])\

= 0.9645

Probability(5<x<9) = P(x<9) - P(x<5)

= 0.0101

P(x<9) = 0.0106

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The solutions to the system of equations are the values of x for which f(x) and g(x) have the same value according to the table.

When a system of equations is plotted on graph, the solutions are the intersection points of all the functions that compose the system.

At these intersections point, the functions have the same numeric value, which are the points looked at to find the solution on a table.

From the table given by the image presented at the end of the answer, the solutions are given as follows:

The problem is incomplete, hence the solution was given in general terms, with an example problem solved.

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Answer:

Step-by-step explanation:

Sorry I don’t know

As a result, the length is 8.5 cm and the breadth is 3.5 cm, and the total perimeter is 22 cm.

what is perimeter ?

An enclosed line that surrounds, distinguishes, or incorporates a two-dimensional contour or a three-dimensional length is referred to as a boundary. The edge of an ellipse or circle refers to its broadest area. The perimeter calculation has many useful properties. The rim of a form is its edge's radius. Understand how to determine the perimeter by adding the lengths of such sides of various forms. You can always measure the perimeter of a shape by multiplying its side lengths. The perimeter of an object is the space around it. At your house, any enclosed terrace is one illustration. The border of anything is the area encircling it. For a 50 feet x 50 feet yard, a 200 foot fence is required.

given

let the length of the rectangular wallet be x

the width be x - 5

perimeter = sum of all the sides = 22

x + x - 5 = 22

2x - 5 = 22

2x = 17

x = 8.5

length is 8.5 and width is 8.5 - 5 = 3.5

As a result, the length is 8.5 cm and the breadth is 3.5 cm, and the total perimeter is 22 cm.

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The amount of commission Yemi gets is, ₦51

Percentage is a way to express a number as a fraction of 100. It is often used to represent ratios and proportions in a more convenient and understandable form, especially in financial and statistical contexts. For example, 50% means 50 per 100, or half of a given quantity. It is denoted using the symbol "%".

Given that,

Yemi sold 100 books at ₦4.25 each,

So,

the total sales revenue is,

⇒ 100 x ₦4.25

⇒  ₦425

The publishing company gives a 12% commission on sales,

So, Yemi's commission would be,

⇒ 12/100 x ₦425

⇒  ₦51

Therefore, Yemi would get a commission of ₦51.

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I believe its 44,880

10 divided by 0 problem would NOT have a solution.

Given:

a. 10 divided by 2

b. 10 divided by 5

c. 10 divided by 0

d. 0 divided by 10

We know that ,

Integer divided by an integer is an integer

Therefore (a) and (b) will have a proper solution

We also know that ,

Zero divided by anything is Zero

Therefore (d) also have a unique answer that is zero

Now , We know that

Any numeric value divided by Zero tends to infinity .

Hence, 10 divided by 0 problem would NOT have a solution.

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Answer:

Step-by-step explanation:

you take away 1 from 2 and that leaves you with 1

Answer:

Let's say I have two apples. You want one too! I give you one, and how many do I have left? 1

What I am explaining here is that if you take one away from two, it becomes one.

Answer:

4 events

Step-by-step explanation:

you divide 12.50 by 50 then you get 4

The probability in decimal form of getting a parking spot is, 0.2

The term probability refers to the likelihood of an event occurring. Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one.

Given that;

A parking lot is arranged with 9 parking spots in the first row, 15 parking spots in the second row, and 21 parking spots in the third row.

Hence, Total parkin spots = 9 + 15 + 21

                                        = 45

And, Number of spots in first row = 9

Thus, The probability in decimal form of getting a parking spot when a person is aiming to park in first row is,

⇒ 9 / 45

⇒ 1/5

⇒ 0.2

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The number in question is 28.

To make solving this problem easier, we need to consider the number.

Let the number is ab.

So that,

4 × a = b

4a = b

We spread the numbers on the options.

28

(4 × 2 = 8) → True

32

(4 × 3 = 2) → False

15

(4 × 1 = 5) → False

25

(4 × 2 = 5) → False

We prove what number of 28 is when the digits is reversed to be greater than 54.

28 ⇄ 82

It is proved that the number 82 is greater than the number 54.

So, the number in question is 28.

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The following statements are either true or false;

Mutation can be defined as the altering or the change in the DNA sequence or arrangement of a cell.

variation can be defined as any difference between cells, organisms, or groups of organisms of any species caused by genetic differences or environmental factors.

Fossils refers to the remains of plants and animals whose bodies were buried in sand, mud, seas, lakes and rivers over a long period of time.

Therefore, the statement Fossils cannot be dated is false because fossils can be dated to upto 10,000 years ago.

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Answer:

40h = e

Step-by-step explanation:

40 x 11 = 440

a ) Work is needed to stretch the spring from 41 cm to 45 cm is 0.58J

b ) 1445 cm far beyond its natural length will a force of 30 N keep the spring stretched.

A spring has a spring constant k,

It takes force kx to extend the spring's length.

A spring stretched length x has energy kx²/2.

Work of 3J gave the spring energy k(53-36)²/2.

Therefore,

3 = k(53-36)²/2

k = 6/289 N/cm

Work is needed to stretch the spring from 41 cm to 45 cm

At 41 cm the spring has energy k(41-36)²/2.

At 45 cm the spring has energy k(45-36)²/2.

The extra energy is given by,

(6/289)(45-36)²/2 - (6/289)(41-36)²/2

= (6/289) * 81/2 - (6/289) * 25/2

= 243/289 - 75/289

= 168/289

= 0.58J

Work is needed to stretch the spring from 41 cm to 45 cm is 0.58J

The natural length will a force of 30 N keep the spring stretched,

30 = kx

x = 30/k

= 1445 cm

1445 cm far beyond its natural length will a force of 30 N keep the spring stretched.

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Answer:

$26.50

Step-by-step explanation:

Helicopter is $20.

The battery is 25% of 20.

25% of 20

= .25 • 20

= 5

The battery will be $5.

The total purchase will be 20 + 5, that is,

$25

Calculating the tax:

6% of $25

= .06 • 25

= 1.5

Add the tax onto the total.



$25 + $1.50

= 26.50

The helicopter, battery and tax all adds up to $26.50

Answer: The answer is D

Answer:

Step-by-step explanation:

We can find the rental cost for each movie and each video game by dividing the total cost by the number of movies and video games rented, respectively.

For the movies:

Rental cost for each movie = Total cost of movies rented / Number of movies rented

= $33 + $24 = $57

= $57 / 6 = $9.50 per movie

For the video games:

Rental cost for each video game = Total cost of video games rented / Number of video games rented

= $18 + $24 = $42

= $42 / 4 = $10.50 per video game.

The value of f(-7) from the graoh is 1/128

Exponential function typically refers to the positive-valued function of a real variable, although it can be extended to complex numbers or generalized to other mathematical objects like matrices.

From the given graph, we need to determine then value f(-7). The function f(-7), is the equivalent value on the y-axis if the value of x is -7.

The standard exponential equation is y = ab^x

Using the coordinate points (0, 1) and (-2, 4), the resulting equations are:

1 = ab^0

4 = ab^-2

From equation 1, a = 1

4 = b^-2

b^2 = 1/4

b = 1/2

The exponential function will be y = (1/2)^x

f(-7) = (1/2)^-7
f(-7) = 1/128

Hence the resulting value of f(-7) is 1/128

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The probabilities are obtained as -

a) P(X = 1) = 0.006377

b) P(X ≤ 2) = 0.0296075

c) P(X = 4) = 0.091137

d) P(X = 8) = 0.130251

What is Poisson Distribution?

The Poisson distribution is a discrete probability function that means the variable can only take specific values in a given list of numbers, probably infinite. A Poisson distribution measures how many times an event is likely to occur within “x” period of time.

The mean of the Poisson distribution is given by λ.

The cumative distribution function is -

P(X = π) = (e^(-λ)λ^π) / π!, where π = 0,1,2,...

a) So, putting π = 1, λ = 7 in the above formula -

P(X = 1) = (e^(-7)7^1) / 1!

P(X = 1) = (0.000911 × 7) / 1

P(X = 1) = 0.006377

Therefore, the value is P(X = 1) = 0.006377.

b) P(X ≤ 2) = P(X = 0) + P(X = 1) + P(X = 2)

P(X ≤ 2) = (e^(-7)7^0) / 0! + (e^(-7)7^1) / 1! + (e^(-7)7^2) / 2!

P(X ≤ 2) = 0.000911 + 0.006377 + 0.022319

P(X ≤ 2) = 0.0296075

Therefore, the value is P(X ≤ 2) = 0.0296075.

c) So, putting π = 4, λ = 7 in the above formula -

P(X = 4) = (e^(-7)7^4) / 4!

P(X = 4) = (0.000911 × 2401) / 24

P(X = 4) = 0.091137

Therefore, the value is P(X = 4) = 0.091137.

c) So, putting π = 8, λ = 7 in the above formula -

P(X = 8) = (e^(-7)7^8) / 8!

P(X = 8) = (0.000911 × 5764801) / 24

P(X = 8) = 0.130251

Therefore, the value is P(X = 8) = 0.130251.

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The translation of the sentence 'The sum of 15 and Delia’s age is 65'

is 15 + d = 65.

A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.

Let, The age of Delia be 'd'.

Therefore, The equation for the statement 'The sum of 15 and Delia’s age is 65'  can be expressed as,'

15 + d = 65.

d = 65 - 15.

d = 50.

So, The age of Delia is 50 years.

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Therefore , the solution of the given problem of test statistic comes out to be rounding to two decimal places, the z-score is -0.26.

The Z-statistic, which demonstrates that the ordinary ordinary neutral hypothesis is true, has been used as the statistic for anything resembling a Z-test. Let's say you run two separate X-y tests with a 0.05 level of significance, and the variable results show that you got a 2.5 R t. (also  Z-value). The p-value for this Z-value is 0.0124.

Here,

To find the z-scores corresponding to the oldest and youngest senators of age 86% and 41%, respectively, we can use the standard normal distribution formula:

z = (x - μ) / σ

where z is the z-score, x is the given value, μ is the mean, and σ is the standard deviation.

For the oldest senators of age 86%, we can find the corresponding z-score as follows:

z = (x - μ) / σ

z = (0.86 - 0.5) / 0.3413

z = 1.055

Rounding to two decimal places, the z-score is 1.06.

For the youngest senators of age 41%, we can find the corresponding z-score as follows:

z = (x - μ) / σ

z = (0.41 - 0.5) / 0.3413

z = -0.264

Rounding to two decimal places, the z-score is -0.26.

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There are 353925 committees of 10 persons that can be chosen with exactly 8 men.

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

People = 15 men and 11 women

Committee = 10 persons (8 men)

The number of ways is then calculated as

Ways = Men * Women

So, we have

Ways = C(15, 8) * C(11, 2)

Evaluate the products

Ways = 353925

Hence, the number of committee is 353925

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