*MidpointIn The Figure Below, N Is The Midpoint RT.If RN = 5x - 10 And NT = 2 + 18, Find The Value Of (2024)

The radius of the Sphere is ∛9/4 meter.

What is Sphere ?

A sphere is a geometrical object that is a three-dimensional analogue to a two-dimensional circle. A sphere is the set of points that are all at the same distance r from a given point in three-dimensional space.

The formula of the volume of the sphere is given below :

Volume of Sphere 'V' = (4/3)πr³

We have given the volume of the sphere which is 3π m³,

So, (4/3)πr³ = 3π

r³ = 9/4

r = ∛9/4

Therefore, the radius of the sphere will be ∛9/4 meter.

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A study was conducted in order to explore the relationship between the number of beers a person drinks, and his/her blood alcohol content. This is an example of Case Q→Q.

In the given question, a study was conducted in order to explore the relationship between the number of beers a person drinks, and his/her blood alcohol content. We have to explain this study is an example of.

As the quantity of beer cans increases, the BAC readings rise as well. All points are also getting closer to a linear pattern. As a result, x and y have a moderately positive and high association.

This is an example of Case Q→Q since the explanatory (number of beers) and response (BAC) variables in this case are both quantitative.

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The two nonadjacent angles are formed by two intersecting lines. these angles are congruent, is the meaning of congruent nonadjacent angles

congruent nonadjacent angles are two angles that are not next to each other but have the same measure. They are formed when two lines intersect each other at a single point. A line bisects two angles at the point of intersection, creating two angles on each side of the intersection. These angles are referred to as adjacent angles. However, the two angles at the ends of the intersection are considered nonadjacent angles and are congruent if the two lines intersect at a right angle. The angles are said to be congruent if the measure of one angle is equal to the measure of the other angle. This means that the two angles must have the same degree measure for them to be congruent. Congruent nonadjacent angles are important in geometrical proofs, especially when two parallel lines are intersected by a third line. The angles formed at the intersection point can be used to prove the parallel lines are congruent.

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The polynomial such that each expression can be written as the square of the difference of 2 polynomials is x^2-a^2

What is a polynomial with an example?

Sums of terms of the form kxn, where k is any number and n is a positive integer, make up polynomials. For instance, the polynomial 3x+2x-5. a description of polynomials.

How do you identify a polynomial?

By noticing which formulas only contain the operations of addition, subtraction, multiplication, and non-negative integer exponents, the polynomials may be located. Expressions with additional operations are considered non-polynomial expressions.

Usually we use the polynomial x^2-a^2 to make it look as the difference of other 2 polynomials,

Because it itself is a difference of 2 polynomials.

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Hello,

I hope you and your family are doing well!

To write the equation of a line in slope-intercept form, you need to find the slope of the line and the y-intercept (the point at which the line crosses the y-axis).

To find the slope of the line, you can use the formula:

slope = (y2 - y1) / (x2 - x1)

Plugging in the coordinates of the two points given in the problem, we have:

slope = (3 - 7) / (6 - 4)

= -4 / 2

= -2

To find the y-intercept, you can use the formula:

y-intercept = y - slope * x

Plugging in the coordinates of the point (4, 7) and the slope we just calculated, we have:

y-intercept = 7 - (-2) * 4

= 7 + 8

= 15

So the equation of the line that goes through (4, 7) and (6, 3) in slope-intercept form is y = -2x + 15.

----

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Answer:

[tex]\frac{49}{81}[/tex]

Step-by-step explanation:

It is the scale factor squared.

He will travel around 75 miles if he drives for one hour at the same rate.

What is unitary method?

The unitary approach is a methodology for solving problems that involves first determining the value of a single unit and then multiplying that value by the required value. The term unitary refers to a single or unique entity. As a result, the goal of this approach is to determine values in reference to a single unit. For example, if a car travels 44 kilometers on two litres of gasoline, we may use the unitary technique to calculate how far it will go on one litre of gasoline. The unitary method is a technique that involves determining the value of a single unit and then calculating the value of the requisite number of units based on that value.

Here,

If he drove 15 miles in 12 minutes,

In 60 minutes, he will drive,

=60*15/12

=75 miles

He will go about 75 miles when he drove one hour in total at the same rate.

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a. The maximum of the equation Q = 5x + 3y is; 24.

The minimum of the equation Q is; 14.

b) The way the maximum and minimum would change in the new equation compared to the original equation is;

-24 ≤ -5x - 3y ≤ -14.

How to maximize and Minimize Functions?

We are given the equation as; Q = 5x + 3y

The constraints:

3y + 6 ≥ 5x

y ≤ 3

4x ≥ 8

The constraint 4x ≥ 8 is basically telling us that x ≥ 2, and then;

3y + 6 ≥ 5x and both together tells us that 10 ≤ 5x ≤ 3y + 6

Thus, we have;

10 + 3y ≤

5x + 3y ≤

6y + 6 ≤

6*3 + 6

= 18 + 6

= 24

Due to the fact that we are given that y ≤ 3, then we must get 10 + 3y ≤ 6y + 6, which suggests that 4 + 3y ≤ 6y.

Thus, 4 ≤ 3y

Now, we have;

14 = 10 + 4 ≤

10 + 3y ≤

5x + 3y ≤ 24, and then also the following:

a. The maximum of Q = 5x + 3y is 24, and the minimum of Q is 14.

b. If the equation Q = 5x + 3y was changed to Q = -5x - 3y, the new maximum would definitely now be the negative of the first original minimum, and as such it means that the new minimum would be the negative of it's original maximum.

This is because from 14 ≤ 5x + 3y ≤ 24, we obtain;

14 ≤ 5x + 3y and 5x + 3y ≤ 24

We can multiply both sides of both inequalities by -1, and then switch the direction of inequalities, and so we now have;

-24 ≤ -5x - 3y ≤ -14.

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The amount that a $90,000 loan cost Lauren than Demarcus will be $8280.

Simple interest is a quick and easy method of calculating the interest charge on a loan. Simple interest is determined by multiplying the daily interest rate by the principal by the number of days that elapse between payments.

From the information, Demarcus and Lauren each take out a $90,000 loan for a new condo and each has to repay the loan in 10 years. It should be noted that 10 years in months will be:

= 10 × 12 = 120 months

The difference in the amount paid as a result of the credit score will be:

= ($840 × 120) - ($771 × 120)

= $100800 - $92520

= $8280

Therefore, the amount is $8280.

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The expected value of the distribution = 2

For the given problem it is given observation and probability of observations.

The median of a random variable x is m

Such that

[tex]$$P(x \leqslant m) \geqslant 1 / 2 \text { and } P(x \geqslant m) \geqslant 1 / 2 \text {. }$$[/tex]

The sum of probability which exceeds halt is 2, and the sum of probabilities which exceed by half is 2.

[tex]$$\begin{aligned}& \therefore \quad P(x \leqslant 2) \geqslant 1 / 2 \\& \Rightarrow[P(x=1)+P(x=2)] \geqslant 1 / 2 \\& =[0.29+0.44] \geqslant 1 / 2 \\& =0.73 \geqslant 1 / 2 \\& \end{aligned}$$[/tex]

So, value of M=2 .

In words, the expected value of the distribution is nothing but the sum, over all possible values x, of x times its probability P(X = x).

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Yes, the situation is modeled by a linear equation.

A linear model that represents the distance traveled as a function of time is y=5x.

Given,

Time(seconds) = 1,4,7,10,13

Distance(miles) = 5,20,35,50,65

m(slope) = y2-y1 / x2 - x1 = 20-5 / 4-1 = 15/3= 5 ( all the values of time are given within a gap of 3 so we can assume any value as x1 and x2 the answer will be the same and likewise all the values of distance are given within a gap of 15)

Linear equation => y-y1= m(x-x1) => y-5= 5(x-1) => y-5 = 5x-5 => y = 5x

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A sketch with dimension 2 inches by 6.9 inches has the closest ratio to the actual billboard.

In this question we have been given that an ad campaign manager for McDonalds made some sketches for a billboard design on a sheet of paper. The actual board is 14 feet by 48 feet.

we need to select the measurement that has the closest ratio to the actual billboard.

The dimensions of the actual billboard:

length = 48 feet

width = 14 feet

The length to width ratio is:

48/14 = 3.43

Now we find the ratio of length and width for each given dimension of the sketch.

1) 8 inches by 11 inches

r1 = 11/8

r1 = 1.375

2) 1.7 inches by 9.2 inches

r2 = 9.2/1.7

r2 = 5.41

3) 2 inches by 6.9 inches

r3 = 6.9/2

r3 = 3.45

4) 2.4 inches by 7 inches

r4 = 7/2.4

r4 = 2.92

Therefore, 2 inches by 6.9 inches has the closest ratio to the actual billboard.

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Answer:

Cary is 70 and Dan is 61

Step-by-step explanation:

c = Cary's age

d= Dan's age

c+d+7=75

C= d+7

Rewrite this with one variable

d+7+d+7=75

Simplify and solve for d (dan's current age)

d +14 = 75

d = 61

Cary is 7 years older, so just add 7 to Dan's age, resulting in 70.

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By forming and solving the equation according to the given situation, we know that 120 workers is needed to clear 50 acres in 5 days.

What are equations?

A mathematical equation is a formula that uses the equals sign to represent the equality of two expressions.

Ax+By=C is the usual form for two-variable linear equations.

A standard form linear equation is, for instance, 2x+3y=5. When an equation is given in this format, finding both intercepts is rather simple (x and y).

When attempting to solve systems involving two linear equations, this form is also quite helpful.

So, to find the number of workers needed, form the equation:

8/20 - 3 = x/50 - 5

Now, solve the above equation as follows:

8/20 - 3 = x/50 - 5

8 - 3*20/20 = x - 5*50/20

8 - 60/20 = x - 250/50

(8 - 60)50 = (x - 250)20

400 - 3000 = 20x - 5000

20x = 400 - 3000 + 5000

20x = 400 + 2000

20x = 2400

x = 2400/20

x = 120

Therefore, by forming and solving the equation according to the given situation, we know that 120 workers is needed to clear 50 acres in 5 days.

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The range of the function will be;

⇒ { - 10, - 7, - 4, - 1, 2 }

What is Domain?

The set of all inputs of the function is called Domain of set.

Given that;

The function is,

⇒ f (x) = 3x - 4

And, The domain = {- 2, - 1, 0, 1, 2}

Now,

Since, The function is,

⇒ f (x) = 3x - 4

And, The domain = {- 2, - 1, 0, 1, 2}

We know that;

The range of the function is the value of f(x).

So, We get;

The function is,

⇒ f (x) = 3x - 4

Put x = - 2,

⇒ f (-2) = 3 × - 2 - 4

= - 6 - 4

= - 10

Put x = - 1,

⇒ f (- 1) = 3 × - 1 - 4

= -3 - 4

= - 7

Put x = 0;

⇒ f (x) = 3 × 0 - 4

= -4

Put x = 1;

⇒ f (x) = 3 × 1 - 4

= 3 - 4

= - 1

Put x = 2;

⇒ f (x) = 3 × 2 - 4

= 6 - 4

= 2

Thus, The range of the function = { - 10, - 7, - 4, - 1, 2 }

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Answer:

Remember your good memories

and just relax drink a water it can

comfort u

Answer:

Here's the 10 tips goodluck and be safe okay?

Choose comfortable clothing and footwear: Wear loose, breathable clothing and comfortable shoes to help reduce discomfort during long periods of sitting or walking.Bring a neck pillow: A neck pillow can help support your head and neck while you sleep on long flights or car rides.Use a lumbar support: A lumbar support can help reduce strain on your lower back while sitting for extended periods of time.Take breaks: If you are on a long car or train ride, take breaks to stretch your legs and move around to reduce stiffness and discomfort.Stay hydrated: Drink plenty of water and avoid alcohol and caffeine, which can dehydrate you.Bring healthy snacks: Pack healthy snacks, such as nuts, fruits, and granola bars, to help keep you energized and satisfied during your travels.Use earplugs and a sleep mask: Earplugs can help block out noise, and a sleep mask can help you sleep better on long flights or in bright hotel rooms.Use a travel pillow: A travel pillow can help support your neck and head while sitting or sleeping in an upright position.Choose a comfortable seat: If you are flying, consider upgrading to a more comfortable seat or booking a seat with more legroom to increase your comfort level.Practice relaxation techniques: Techniques such as deep breathing, meditation, or yoga can help you relax and manage stress during travel.

Frank has to drive 142 miles more to after spending his money, he should save it.

Define inequality.

In mathematics, inequalities specify the connection between two non-equal numbers. Equal does not imply inequality. Typically, we use the "not equal sign (≠)" to indicate that two values are not equal. But several inequalities are utilized to compare the numbers, whether it is less than or higher than.

Given

Training and license cost = $495

Insurance cost = $4

Payment on delivery = $353 + $5

Let distance be x

Inequality,

495 + 4x ≥ 353 + 5x

495 - 353 ≥ x

142 ≥ x

Frank has to drive 142 miles more to after spending his money, he should save it.

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Answer:

x² - 11x + 13

Δ = (-11)² - 4*1*13 = 121 - 52 = 69

therefore :

x1 = [-(-11) + √69]/2*1

<=> x1 = (11 + √69)/2

and

x2 = [-(-11) - √69]/2*1

<=> x2 = (11 - √69)/2

so the correct answers are : C & E

The value added and subtracted from a point estimate in order to develop an interval estimate of the population parameter is known as the margin of error. The correct answer is the last option.

What is margin of error?

A margin of error is a statistical measurement that accounts for the difference between actual and projected results in a random survey sample. In simpler terms, the margin of error allows you to gauge the level of unpredictability in data and research outcomes.

The formula for the margin of error is calculated by multiplying a critical factor (for a certain confidence level) with the population standard deviation. Then the result is divided by the square root of the number of observations in the sample.

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The percentage of students at this school who take either calculus or physics (or both) is 90%

In mathematics, a percentage is a number or ratio that can be expressed as a fraction of 100. If we have to calculate the percent of a number, divide the number by the whole and multiply by 100. Hence, the percentage means, a part per hundred. The word percent means per 100. It is represented by the symbol “%”.

Given,

No. of students taking calculus = 40%

No. of students taking physics = 30%

Chances of students taking both =20%

Assuming the total number of students = 100%

The percentage of students at this school who take either calculus or physics (or both) is (40+30+20)% = 90%

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probability of getting a number larger than 9 for the first time on the third roll=25/216

In a particular roll of the two dice,

the probability of obtaining a sum of 10=3/36

The probability of obtaining a sum of 11=2/36

The probability of obtaining a sum of 12=1/36

∴The probability of obtaining a sum greater than 9, in a roll of two dice =33/6+23/6+13/6=6/36=1/6

Hence, the probability of not obtaining a sum greater than 9 in a particular roll of the pair of dice =1−16=56

If we are to obtain a total greater than 9 for the first time on the third roll, we should get totals lesser than or equal to 9 in the first two rolls and a total greater than 9 on the third.

The probability of this happening is =5/6×5/6×1/6 =25/216

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Answer:

Step-by-step explanation:

(i) The enrollment in 2016 year will be 7500.

(ii)In 2026 the enrollment will reach 10000.

The act of putting yourself or someone else onto the official list of members of a course, college or university, or group.To build support among women, politicians can propose and implement a number of different programmes that directly or indirectly affect female enrolment.During the enrolment period on average 3700 of the eligible 4822 persons were available for screening.

Given,

f(x) = 250x + 6000, where x is the number of years since 2010

(i) In 2016 the value of x will be = 6 years

So, f(x) = 250*6 + 6000

f(x) = 1500+6000

f(x) = 7500

Thus, the enrollment in 2016 year will be 7500.

(ii) Given the enrollment will be 10000

So, f(x) =10000

250x + 6000 =10000

x=16

Therefore, in 2026 year the enrollment will reach 10000.

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The inequality can be used to determine the number is C . 0.40x > x/2 - 15

Given :

Forty percent of a number is greater than one-half the number decreased by 15.

And we need to find the number that is used to determine the inequality.

Now, According to the question:

What is Inequality?

An inequality is a relation which makes a non-equal comparison between two numbers or other mathematical expressions. It is used most often to compare two numbers on the number line by their size.

Let us consider x be that unknown number.

We have divide it into two parts.

First, forty percent of the number and it can be written as 40%x or 0.40x.

Next is one-half the number is 1/2 x or x/2

When we combine the whole statement,

Then we get the inequality,

=> 0.40x > x/2 - 15

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The inverse of the matrix as calculated from the data with a scalar coefficient is,

[ -7 ]

[ -1 ]

x -6y = -1

−2x9y=5

which can be written as ,

[ 1 -6 -1 ]

[ -2 9 5 ]

A = [ 1 -6

-2 9 ]

A' = 1 / ( ad - bc ) [ 9 6 ]

[ 2 1 ]

= [ -3 - 2 ]

[-2/3 -1/3 ]

on solving them we get the coefficient as ,

[ -7 ]

[ -1 ]

The quantity of rows and columns in a matrix determines its size. As long as they are positive integers, there is no restriction on how many rows and columns a matrix (in the conventional sense) can have. An m n matrix, also known as an m-by-n matrix, is a matrix having m rows and n columns. M and n are referred to as the matrix's dimensions.

Row and column vectors are terms used to describe matrices with a single row or column. A square matrix is one that has the same number of rows and columns.

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Answer: I believe the answer is: A(subscript)n = n^2 + 2n + 5

Step-by-step explanation:

After solving, the length of o is 1173 in.

In the given question,

In ΔNOP, n = 800 inches, ∠P=97° and ∠N=32°.

We have to find the length of o, to the nearest inch.

As we know that the sum of all sides in triangle is 180 degree. So the measure of angle O is;

O + N + P = 180

O + 32 + 97 = 180

Subtract 32 and 97 on both side, we get;

O = 180° -32° -97°

After simplifying, we get;

O = 51°

Now using the sine law to find the length of O.

The law of sine tells us;

o/sin(O) = n/sin(N)

Multiply by sin(O) on both side, we get;

o = n·sin(O)/sin(N)

Now putting the value;

o = (800 in)·sin(51°)/sin(32°)

After solving

o ≈ 1173 in

Hence, the length of o is 1173 in.

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The probability using distribution table for (a) to right of 2.120 is 0.025 and (b) to left of 1.337 is 0.9

When the estimated standard deviation rather than the actual standard deviation is used as the denominator, the t-distribution is a continuous probability distribution of the z-score.

Similar to the normal distribution, the t-distribution is bell-shaped and symmetric, but due to its heavier tails, it is more likely to yield values that deviate greatly from the mean.

In statistics, t-tests are used to calculate significance.

A t distribution curve's total area under it is 1.0, or 100%.

According to the question,

Degree of freedom of t-distribution = 16

We have to calculate the probability in given region

(a) To the right of 2.120

Using T-distribution table,

P( T₁₆ > 2.120) = 0.025

(b) To the left of 1.337

P( T₁₆ < 1.337) = 0.9

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The probability that it will take less than 4 minutes to complete the test is 0.11.

For a normally distributed set of data, given the mean and standard deviation, the probability can be determined by solving the z-score and using the z-table.

First, solve for the z-score using the formula below.

z-score = (x – μ) / σ

where x = individual data value = 4

μ = mean = 15

σ = standard deviation = 9

z-score = (4 - 15) / 9

z-score = -11 / 9

z-score = -1.22

Find the probability that corresponds to the z-score in the z-table. (see attached images)

z-score = -1.22

probability = 0.11144

p ≅ 0.11

Hence, the probability that it will take less than 4 minutes to complete the test is 0.11.

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Claritin, a medication for allergy patients that was made to prevent drowsiness, was given away as free samples to doctors by its maker because of following reasons

1) One method of performing advertising is by giving samples to doctors. The business is not required to provide further product information in this type of advertisem*nt. Samples of the product are available for customers or audiences to immediately use and evaluate the product's quality and suitability. Consequently, choosing this alternative is the best choice.

2) A common antihistamine is loratadine (Claritin). It inhibits histamine, a substance your body naturally produces that may cause allergy symptoms including itchy eyes.

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