The length of a rectangle is 3 inches longer than half of its width. The area of the rectangle is 416 square inches. How many inches in width is the rectangle?

A. 16 inches
B. 19 inches
C. 26 inches
D. 32 inches

The system of equations of Horatio's coins is (c) d = 2n, n + d + q = 57 and 0.05n + 0.10d + 0.25q = 7.25

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

Number of coins = 57

Worth of coins = $7.25

Type of coins = Nickel, dimes and quarters

Twice as many dimes as nickels

Represent the nickels with n, the dimes with d and the quarters with q

So, we have the following representation

n + d + q = 57

When the nickels, dimes and quarters are converted to dollars, we have the following representations

Nickels = $0.05

Dimes = $0.10

Quarters = $0.25

So, we have the following representation

0.05n + 0.10d + 0.25q = 7.25

Recall that

He has twice as many dimes as nickels

This means that

d = 2n

Hence, the system of equations is d = 2n, n + d + q = 57 and 0.05n + 0.10d + 0.25q = 7.25

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Answer: y = -1/3x -1

Step-by-step explanation:

The slope is -1/3, and it crosses the y axis at (0,-1)

Answer:

2-5 will give you -3 then 10 divide by -3 will give you 7

Important functions in Excel;

The SUM function

The TEXT function

The VLOOKUP function

The AVERAGE function

The CONCATENATE Function

Given,

Functions in Excel;

Functions are pre-written formulas that carry out calculations by utilising particular values, referred to as inputs, in a given order, or structure. Calculations of any complexity can be carried out using functions. The Formulas tab on the Ribbon contains the syntax for all of Excel's functions.

The most important five functions in Excel are given below;

Eg; =SUM(A2:A10) Adds the values in cells A2:10. =SUM(A2:A10, C2:C10) Adds the values in cells A2:10, as well as cells C2:C10.

Eg; In Excel, the value 12200000 appears as 12,200,000 if the format string is "#,###". A comma after a placeholder for a digit multiplies the number by 1,000. The format string "#,###. 0," for instance, causes Excel to show the number 12200000 as 12,200.0.

Eg; =VLOOKUP(90,A1:B100,2,TRUE). Exact match - 0/FALSE searches for the exact value in the first column.

Eg;  if the range A1:A20 contains numbers, the formula =AVERAGE(A1:A20) returns the average of those numbers.

Eg; Add double quotation marks with a space between them " ". For example: =CONCATENATE("Hello", " ", "World!").

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70% percentage of the original roland-morris score of 20 was improved to the final score of 6.

Given that,

We have to find what percentage of the original roland-morris score of 20 was improved to the final score of 6.

We know that,

The original roland-morris score of 20 was improved to the final score of 6.

The initial score = 20

Final Score = 6

The improvement is 20 - 6 = 14

So,

The percent improvement is (14/20)* 100 = 70%

Therefore, 70% percentage of the original roland-morris score of 20 was improved to the final score of 6.

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A'(1/2, 1/2), B'(3/4, 3/2), C'(1, 1/2) are the coordinates of the image after dilation.

Given,

Triangle ABC is dilated with a scale factor 2 at the origin.

We have to find the coordinates of the image;

Dilation;

Resizing an item uses a transition called dilation. Dilation is used to enlarge or contract the items. The result of this transformation is an image with the same shape as the original. However, there is a variation in the shape's size.

Here,

The vertices of the triangle;  A(1, 1), B(1.5, 3), C(2, 1).

After the dilation of a scale factor 2, the new point;

A'(1/2, 1/2), B'(3/4, 3/2), C'(1, 1/2).

That is,

The coordinates of the image after dilation is, A'(1/2, 1/2), B'(3/4, 3/2), C'(1, 1/2).

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The given expression is simplified to obtain as (-2.5x - 2).

An algebraic expression can be obtained by doing mathematical operations on the variable and constant terms.

The variable part of an algebraic expression can never be added or subtracted from the constant part.

The given expression is (-5x - 4) ÷ (-3 + 5)

It can be simplified as follows,

(-5x - 4) ÷ (-3 + 5)

= (-5x - 4) ÷ 2

Divide each term of -5x - 4 by 2 as below,

(-5x/2 - 4/2)

= (-2.5x - 2)

Hence, the simplification of the given expression is obtained as (-2.5x - 2).

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Answer:

To determine the number of people who can go to the amusement park, we need to write an inequality that represents the total cost of parking and admission, which is the maximum amount of money that the group has. Let x represent the number of people who can go to the amusement park. The total cost of parking and admission can be represented by the inequality 14.75 + 11.25x ≤ 80. To solve this inequality, we need to find the values of x that make the inequality true. We can do this by isolating the variable on one side of the inequality. To do this, we need to subtract 14.75 from both sides of the inequality: 14.75 + 11.25x ≤ 80

-14.75 -14.75

11.25x ≤ 65.25

Next, we need to divide both sides of the inequality by 11.25 to isolate the variable on one side of the inequality: 11.25x ≤ 65.25

x ≤ 5.77

Since the number of people must be a whole number, we can round down to find the maximum number of people who can go to the amusement park: x ≤ 5

This means that no more than 5 people can go to the amusement park if they want to stay within their budget.

Step-by-step explanation:

DSA is only used for signature purposes but RSA is used for cryptographic purposes.

But somehow DSA uses discrete logarithms for Encryption and in RSA long-term calculations are used which is more secure as compared to DSA.

Now while signing messages with DSA leads to a more time and more memory-consuming process because at every point the message is signed. So the verification of signatures gets complicated.

But in the case of RSA, the calculations are high, but they consume less memory and less need for verification. Because of large calculations, RSA is much slower than DSA.

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Total 12 gallons of fuel was burned

What is the relation between Time, Spped and Diatnce?

The formula speed distance time is used to describe the connection between speed, distance, and time. That is, speed = distance / time. To put it another way, distance divided by speed equals time. You can figure out the third input if you know the first two.

Solution:

10 gallons fuel is burned per hour

Distance Travelled by the Plane = 120 nautical miles

Speed of the Plane = 100 nautical miles per hours

Time = Distance / Speed

Time = 120 / 100 = 1.2 hours

Since 10 gallons of fuel is burned every hour, so total fuel burned in 1.2 hours is 12 gallons

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The equation for circle is 28g + 16f =260

and the equation of tangent to this circle is y = [tex]\frac{6}{12}[/tex] x +29

a) the main equation of circle is ax + by +2gx+ 2fy +c =0     --------- (1)

Now,

putting the points (0,0) , (0,8) and (6,12) one by one, we get,

 For the point (0,0), we get:

                c =o            ----------------------------- (2)

For the point (6,12), we get:

   6x +12y + c = (6)² + (12)²

⇒ 6x +12y +c = 36 +144

⇒ 6x +12y +c = 180          --------------------------- (3)

For the point (0,8), we get,

8y + c = 64                      ----------------------------- (4)

putting c=0,

     8y +0 = 64

⇒ y =64/8

⇒ y = 8

Putting c=0 and y =8, we get,

    6x + 12×8 +0 = 180

⇒ 6x + 96 =180

⇒ 6x = 84

⇒ x = 14

Putting all the values in equation (1), we get:

    (14)² + (8)² +28g +16g + 0 = 0

⇒ 196 + 64 + 28g +16f =0

⇒ 28g + 16f = 260

b) As we know the tangent from the circle:

       y = mx + c

⇒ 8 = -12/6 × 14 +c

⇒ c = 29

Therefore, the equation of the tangent is y = [tex]\frac{6}{12}[/tex]x + 29

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Answer:

arrange them in a triangle shape, and there is a triangle

Step-by-step explanation:

The value of n in the equation is n = s / 180 + 2

The subject of a formula is the variable that is being worked out. Subject of the formula is a variable which is expressed in terms of other variables involved in the formula.

Therefore, we have to make n the subject of the formula in the equation.

Hence,

s = (n - 2)180

open the bracket on the right side

s = 180n - 360

add 360 to both sides of the equation

s = 180n - 360

s + 360 = 180n - 360 + 360

s + 360 = 180n

divide both sides by 180

s + 360 = 180n

s  / 180 + 360 / 180 = 180n / 180

Hence,

n = s / 180 + 2

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Answer: the probability that a person has a positive test result given that person is healthy is 0.01the probability that a patient has a positive test result given that person has COVID is 0.98

Step-by-step What is the probability that a patient has COVID if that person tested positive for COVID?The test seem to have high accuracy. After being tested positive, the probability that you have COVID should be high, right?Before settling down with that guess, let’s use Bayes’ theorem to answer this question.

The linear function that goes through the points (-1, 1) and (3,2) is defined as follows:

y = 0.5x + 1.5.

The slope-intercept of a linear function is given as follows:

y = mx + b.

In which:

The two points on the graph of the function are given as follows:

(-1,1) and (3,2).

Given two points, the slope is calculated as the change in y divided by the change in x, hence:

m = (2 - 1)/(3 - (-1)) = 2/4 = 0.5.

Hence:

y = 0.5x + b.

When x = -1, y = 1, hence the intercept b is obtained as follows:

1 = 0.5(-1) + b

b = 1.5.

Thus the equation is:

y = 0.5x + 1.5.

The problem is incomplete, hence I will suppose that it asks for the definition of the equation, which will help you find whichever the correct statements are.

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The sum of all possible values of N is 336.

What is an integer?

Zero, a positive natural number, or a negative integer denoted by a minus sign are all examples of integers. The inverse additives of the equivalent positive numbers are the negative numbers.

Here, we have

Let the three integers be a, b, and c.

N = abc = 6(a + b + c) and c = a + b.

Then N = ab(a + b) = 6(a + b + a + b) = 12(a + b).

Since a and b are positive, ab = 12

so {a, b} is one of {1, 12}, {2, 6}, {3, 4}

a + b is one of 13, 8, 7

N is one of 12× 13 = 156, 12× 8 = 96, 12×7 = 84

156 + 96 + 84 = 336.

Hence, the sum of all possible values of N is 336.

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The situations represented by 25/9 are "Melanie equally shares 25 meters of paper to create 9 banners" and "Joe makes 9 equal servings from a 25 ounce bag of peanuts".

Expression in mathematics is combination of variables with the use of operations and given rules. It can be in the form of equation, numbers etc.

We have the expression 25/9.

That means 25 divided in 9 equal parts.

Now the expression 1,

Melanie equally shares 25 meters of paper to create 9 banners.

We have to divide 25 meters of paper into 9 equal banners.

The above expression can be written as a mathematical term,

and that is 25/9.

Now the expression 2,

Quill gives away 9 baseball cards from a pack of 25.

In mathematical terms; 25 - 9.

Now the expression 3,

George invites 25 kids and 9 adults to his birthday party.

That means, the total 25 + 9 = 34 people

In mathematical terms : 25 + 9

Now the expression 4,

Becca creates 9 rows with 25 buttons each.

That means, each row has 25 buttons.

So the total 9 rows have 9 x 25 buttons.

In mathematical terms : 9 x 25

Now the expression 5,

Joe makes 9 equal servings from a 25 ounce bag of peanuts.

That means 25 ounce bag of peanuts equally divided into 9 parts.

In mathematical terms : 25/9

Therefore, expression 1 : Melanie equally shares 25 meters of paper to create 9 banners and expression 5: Joe makes 9 equal servings from a 25 ounce bag of peanuts, represented by 25/9.

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Answer:

To find the percentage score for Jude, we need to divide the number of points scored by the total number of points and multiply the result by 100. This can be written as:

Percentage score for Jude = (10/35) * 100 = 28.57%

To find the percentage score for Tom, we need to divide the number of points scored by the total number of points and multiply the result by 100. This can be written as:

Percentage score for Tom = (18/46) * 100 = 39.13%

Since Tom scored a higher percentage of points compared to Jude, Tom got the highest score.

Answer:

2x

x-1

Step-by-step explanation:

Answer:

I will gladly assist you with your problem! (see explanation)

Step-by-step explanation:

Suppose that the tower's height is t and that the necessary distance is x.

To determine the value of t, use comparable triangle ratios:

[tex]t / 10 = (9 + 3) / 3t / 10 = 4t = 40 feet[/tex]

Use Pythagorean Theorem  to find the value of x:  

[tex]x^{2} =40^{2} +(9+3)^{2} \\x^{2} =1600+144\\x^2=1744\\x=\sqrt{1744} \\x= 42 feet[/tex](answer is rounded)

(I hope this helps solve your problem )

Answer:

9 pizzas

Step-by-step explanation:

Since there were 3 boxes which each 3 pizzas, you're gonna need to solve using an easy multiplication problem; 3*3, which is 9. So it's 9 pizzas

The probability that a postdated cheque is forged is 0.8  .

In the question ,

it is given that ,

there is 1 cheque forged in 10000 cheques.

the percent of postdated cheques = 5% ,

So , the number of Post-dated cheque = 0.05*10,000 = 500

the percent of cheques that the postdated cheque is forged is = 80%

the number of Forged cheque that are post-dated = 0.8*500 = 400

So , Probability (post-dated check is forged) = (Forged check that are post-dated)/(post dated checks)

Substituting the values ,

we get ,

= 400/500

= 0.8

Therefore , the required probability is 0.8  .

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The bank you should open a savings account with is Bank A and the bank, should you apply for your vehicle loan is Bank B. Thus the correct option is C.

What is Bank?

A bank is referred to as a financial institution that allows an individual to deposit and withdraw cash and allow them to borrow funds with a fixed interest rate for the purpose of investment.

In the given case, it is explained that Both opening a savings account and getting a car are decisions you have made. You want to borrow money for a car at a cheap interest rate and have the greatest interest rate savings account.

In order to avoid any burden you should make decisions with Bank B for the car loan and Bank A for the savings account and enjoy the assets for a lifetime with appropriate benefits.

Therefore, option C is appropriate.

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1.2 x [tex]10^6[/tex] is 11.5 times smaller than 1.38 x [tex]10^7[/tex]

Option D is the correct answer.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

1.2 x [tex]10^6[/tex] and 1.38 x [tex]10^7[/tex]

We see that,

1.2 x [tex]10^6[/tex] x 11.5 = 1.38 x [tex]10^7[/tex]

This means,

1.2 x [tex]10^6[/tex] is 11.5 times smaller than 1.38 x [tex]10^7[/tex]

Thus,

1.2 x [tex]10^6[/tex] is 11.5 times smaller than 1.38 x [tex]10^7[/tex]

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Answer:

Step-by-step explanation:

x^2-27=4x

x*x (1 x 1)

1-27=4x

-26=4x

divide both sides by 4 and you get...

x=-6.5

(if wrong, i'm sorry.)

Probability of getting 5 notifications in 30 minutes: 0.0625 and Probability of getting 10 or less notifications in one hour: 0.9961

Probability of getting 5 notifications in 30 minutes:

The average number of notifications per hour is 12, so the average number of notifications in 30 minutes is 6.

Therefore, the probability of getting 5 notifications in 30 minutes is

P(5 Notifications) = (6 C 5)*(1/2^6)

P(5 Notifications) = 0.0625

Probability of getting 10 or less notifications in one hour:

The probability of getting 10 or less notifications in one hour is the sum of the probabilities of getting 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, and 10 notifications in one hour.

We can calculate this probability as

P(≤ 10 Notifications) = (12 C 0)(1/2^12) + (12 C 1)(1/2^12) + (12 C 2)(1/2^12) + (12 C 3)(1/2^12) + (12 C 4)(1/2^12) + (12 C 5)(1/2^12) + (12 C 6)(1/2^12) + (12 C 7)(1/2^12) + (12 C 8)(1/2^12) + (12 C 9)(1/2^12) + (12 C 10)*(1/2^12)

P(≤ 10 Notifications) = 0.9961

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The domain value that are significant to the function ie distance the customer rides ; x ≥ 0

What is domain ?

The range of values that we are permitted to enter into our function is known as the domain of a function. The x values for a function like f make up this set (x). A function's range is the collection of values it can take as input. After we enter an x value, the function outputs this sequence of values.

The domain of a graph is made up of all the input values displayed on the x-axis since the term "domain" refers to the set of potential input values. The various output values are represented on the y-axis as the range.

the domain represents the number of miles a customer rides. since distance cannot be negative, the only significant values on this graph are x≥ 0.

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The equation of the line in slope-intercept form y = -1/2x + 6

The slope intercept form of a straight line is one of the most common ways to show the equation of a line. The slope intercept formula can be used to calculate the equation of a line when the y-intercept and slope of the straight line are known ( the y-coordinate of the point where the line intersects the y-axis). The equation of a line is the equation that each point on the line fulfils.

It is represented as y = mx + b

According to the given information

We are given that

Slope m = -1/2

y-intercept ( b ) = 6

Slope Intercept Form

y = mx + b

Putting the values in above equation

y = -1/2x + 6

The equation of the line in slope-intercept form y = -1/2x + 6

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the distinct cubes are possible from the arrangement is 10

What is probability?

By simply dividing the favorable number of possibilities by the entire number of possible outcomes, the probability of an occurrence can be determined using the probability formula. Because the favorable number of outcomes can never exceed the entire number of outcomes, the chance of an event occurring might range from 0 to 1.

each of the six faces of a cube is painted either black or white.

two cubes are considered identical if one cube can be rotated to look like another.

All 6 sides black.

1 side white and 5 side black.

2 adjacent sides white and other 4 sides black.

2 opposite sides white and other 4 sides black.

3 sides with same corner white and other 3 black.

2 opposite sides and 1 center side white and other 3 black.

2 adjacent sides black and other 4 sides white.

2 opposite sides black and other 4 sides white.

1 side black and 5 sides white.

So total is 10

Hence, the distinct cubes are possible from the arrangement is 10.

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