set up an equation and solve: the length of a rectangle is 4 feet more than three times the width. the perimeter is 48 feet. find the length and the width of the rectangle.

Using the Fundamental Counting Theorem, it is found that there are 60 possible 3-course meals.

Given,

In the question:

A restaurant offers a choice of 4 salads, 5 main courses, and 3 desserts.

To find the how many possible 3-course meals are there?

Now, According to the question:

Let's know:

What is the Fundamental Counting Theorem?

It is a theorem that states that if there are n things, each with  ways to be done, each thing independent of the other, the number of ways they can be done is:

[tex]N=n_1[/tex] × [tex]n_2[/tex] × [tex]n_3[/tex]... ×[tex]n_n[/tex]

In this problem, considering the number of salads, main courses and desserts, we have that:

[tex]n_1=4 , n_2=5,n_3=3[/tex]

The total number of options is given by:

N = 4 × 5 × 3

N = 60

Hence, Using the Fundamental Counting Theorem, it is found that there are 60 possible 3-course meals.

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Answer:

Step-by-step explanation:

The probability that a student is chosen randomly from the class has a cat or a dog is 26/29.

It is based on the probabilities that something could happen. The theory of probability primarily relies on the justification for probability. A coin is tossed, for instance, and the theoretical likelihood of randomly receiving a head is 1 in 2.

explanation:

The formula of probability is defined as the ratio of a number of favorable outcomes to the total number of outcomes.

P(E) = Number of favorable outcomes / total number of outcomes

The total strength of the class is 29

The probability that a student is chosen randomly from the class has a cat or a dog =  Number of favorable outcomes / total number of outcomes

P(E) = 26/29

Hence, The probability that a student is chosen randomly from the class has a cat or a dog is 26/29.

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[tex]y+4=13 \implies \boxed{y=9}\\\\2x=3x-1 \implies \boxed{x=1}[/tex]

Additionally, [tex]63=3z \implies \boxed{z=21}[/tex]

the equation of the straight line is y = -x-7

What is equation straight line?

Y = mx + c is the general equation for a straight line, where m denotes the line's slope and c the y-intercept. It is the version of the equation for a straight line that is used most frequently in geometry. There are numerous ways to express the equation of a straight line, including point-slope form, slope-intercept form, general form, standard form, etc. A straight line is a geometric object with two dimensions and infinite lengths at both ends. The formulas for the equation of a straight line that are most frequently employed are y = mx + c and axe + by = c. Other versions include point-slope, slope-intercept, standard, general, and others.

In the graph the slope m = -1

the y-intercept will be -7

Hence the equation of the st. line is y = -x-7

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Answer:

Step-by-step explanation:

The number of trials needed to produce results similar to their predicted outcomes is likely to be higher for Kasey's experiment with 20 possible outcomes than for Gerald's experiment with 3 possible outcomes.

Answer:

The distributions of the income of the 3 states are pretty similar. The highest income in Maine is 50s, in Indiana it is pretty evenly spread out and Connecticut is highest in 60/70 and has multiple stragglers in 170 - 200 and a few near 300. The main place where most of the plot points are is 10 - 150.

Not completely sure if this helps, but I hope it does.

The equation that matches this table is  X=Y*k,k=12,  Hence Given table is direct variation.

X=12,Y=1

X=24,Y=2

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Answer:

28 feet long

Step-by-step explanation:

we find the area of the first lawn using recent angle formula (l)(w)=a

(7)(3)

21

Now we multiply this by 4 since the second lawn is four times it

21x4

84

Now we rearrange the rectangle area formula to where length is what we are trying to find

a=(l)(w)

/w. /w

a/w=l

Now we fill in this formula

84/3=a

28

Hopes this helps

The range of the given relation is:

R: {1, 2, 4, 5}

Thus the correct option is A.

A relation maps elements from one set, the set of the inputs called the domain, into elements from another set, the range.

A point in a relationship is written as (x, y), where y is on the range.

Here we have the relation given by the pairs:

(1, 2), (2, 4), (4, 5), (6, 1)

The range is the set given by the second values of each point, thus the range is:

R: {1, 2, 4, 5}

The the correct option is A.

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The annual rate of interest she is charging you is 12%.

Given that, you ask your best friend to lend you $200 to buy your favorite toy.

An interest rate tells you how high the cost of borrowing is, or high the rewards are for saving. So, if you're a borrower, the interest rate is the amount you are charged for borrowing money, shown as a percentage of the total amount of the loan.

Here,

Extra money per month =$2

Extra money per year = $2×12

Extra money per two year = 2×2×12 = 4×12 = $48

Money lend = $200

Money given after two years = $(200+48) = $248

Now, the rate of interest can be find using SI=(P×R×T)/100

48= (200×R×2)/100

⇒ 48= 4R

⇒ R=12%

Hence, the annual rate of interest she is charging you is 12%.

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"Your question is incomplete, probably the complete question/missing part is:"

You ask your best friend to lend you $200 to buy your favorite toy. She says she can lend you the money only if you give her an extra $2 for every month that passes before you return it. What is the total amount you must pay her if you return it after two years? rupees What is the annual rate of interest she is charging you?

1/8, 1/4, 3/8, 2/3, 3/4

By simply dividing the fractions!

In 1/4, we can divide the numbers:

1 ÷ 4 = 0.25.

In 1/8:

1 ÷ 8 = 0.125

In 2/3:

2 ÷ 3 = 0.66

In 3/8:

3 ÷ 8 = 0.375

And in 3/4:

3 ÷ 4 = 0.75

0.125, 0.25, 0.375, 0.66, 0.75

Now, we have to put them into their original fractions, not decimals:

1/8, 1/4, 3/8, 2/3, 3/4

I hope my answer helped you! If you need more information or help, comment down below and I will be sure to respond if I am online. Have a wonderful rest of your day!

The probability that the card has a multiple of 3 is 5/16. We use the concept of probability and multiples to get the answer.

Probability of an event = (no of possible ways it can happen) / (total number of outcomes)

For instance, 20 is a multiple of 4 and 5 if we declare that 4 + 5 = 20. The remaining multiples of four can be written as follows: 4, 8, 12, and so on. Four times one equals four. Numerous other mathematical ideas can be explored with the aid of multiples knowledge.

Given, total number of the cards in the bag is from 1 to 16.

So, total number of cards = 16.

Multiples of 3 below 16 = 3,6,9,12,15.

Number of cards below 16 which are multiples of 3 = 5

Therefore P(E) = No. of possible ways/Total no. of ways

=5/16

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A story that can be represented using the equation y=x+1/5x is "John has an apple and he cut another apple into 5 equal parts and took on part. What's the rural fraction of apple that he has?

An equation is the statement that illustrates the variables given. In this case, two or more components are taken into consideration to describe the scenario. It is vital to note that an equation is a mathematical statement which is made up of two expressions that are connected by an equal sign.

In this case, if John has an apple and he cut another apple into 5 equal parts and took on part.

This can be illustrated as:

y = x + 1/5x

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Observing the cases provided with the formula of probability and implementing it with OR rule , The answer is 0.22.

Simply put, probability is the likelihood that something will occur. When we don't know how an event will turn out, we can discuss the likelihood or likelihood of several outcomes. Statistics is the study of events that follow a probability distribution.

All potential results make up the sample space of a random experiment. A subset of the sample space is an event connected to a random experiment. Any outcome's probability is a value between 0 and 1. The sum of all the outcomes' probabilities is one.

Probability that dice rolled shows a 5 once =  1/36

Probability that dice rolled shows a 5 twice =  2/36

Probability that the sum is 8 = 5/36

Total probability = 1/36 + 2/36 + 5/36 = 0.22

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Answer:
the first term = y-x

and the fourth term= y+x
and the fifth term = 2y+x

Step-by-step explanation:

Answer: y = 1x + 5

Step-by-step explanation:

This is where the equation; y=mx+b comes in handy.

We are given m, 1.

And we are given a coordinate to plug in.

2=1(-3)+b

2=-3+b

b=5

y = 1x + 5

Answer:

Step-by-step explanation:

The standard form of a line is Ax+By=C.  To solve this problem, begin with the point-slope form [tex]y-y_1=m(x-x_1)[/tex].  For this problem, let

[tex](x_1,y_1)=(-3,2)\\m=1[/tex]

Input these values into the point-slope form equation and convert to slope-intercept form,

[tex]y-(2)=(1)[x-(-3)]\\y-2=x+3\\y-2+2=x+3+2\\y=x+5[/tex]

Next, convert slope-intercept form to standard form:

y=x+5

-x+y=5

For standard form, A must be positive.  So,

-(x-y)=5

x-y=-5

Carlos points are 12

Let , Fabio points = x= 31

Carlos points = Y

Fabio had 7 points less than 2 times as many points as Carlos.

X = 2Y - 7

X = 2Y - 7

X + 7 = 2Y

Y = (x + 7)/2

X = (31 - 7)/2

x = 24/2

X = 12

Carlos points are 12

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The numerical  top and bottom limits for a d grade is 68 and 61 respectively

What can we learn from mean and standard deviation?

In statistics, the measurement of variability known as the standard deviation (SD) is frequently utilised. It demonstrates how different things are from the norm (mean). While a high SD shows that the data are dispersed throughout a wide range of values, a low SD suggests that the data points tend to be close to the mean.

Given,

Mean = 75.1

Standard Deviation = 9.1

For a D grade at / 6th Percentile and 78th Percentile critical

Z- Scores are -0.77 and -1.55 respectively

The Corresponding Top grade for d

x + z * σ

75.1 + (-0.77) * 9.1 =68

The Corresponding Bottom grade for d

x + z * σ

75.1 + (-1.55) * 9.1 =61

A d grade has numerical top and bottom limitations of 68 and 61, respectively.

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The slope of the given line is 40 mi/h.

How to find slope of the line in the graph?

The slope of a line is the ratio of rise to run. Hence, here are the steps to find slope from a graph.

Select any two random points on the graph of the line (preferably with integer coordinates).

Label them as A and B (in any order).

Calculate the "rise" from A to B. While going vertically from A to B, if we have to go

"up", then the rise is positive;

"down", then the rise is negative.

Calculate the "run" from A to B. While going horizontally from A to B, if we have to go

"right", then the run is positive;

"left", then the run is negative.

Now, use the formula: slope = rise/run.

According to the given question:

To calculate the slope of the line in given graph let point A be (5, 200) and point B (10, 400).

Run = 5

Rise = 200

Therefore, slope = rise/run = 200/5 = 40 mi/h

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Both a smaller and a bigger number are 25 and 68

The outcome or conclusion we get at when we add two or more integers is known as the SUM. example the total of the addends, 6, and 4, is 10. In other words, we may argue that 8 plus 5 equals 13 or that 8 plus 5 equals 13.

Here, we've been given two numbers, one smaller and one bigger, where the smaller number is X and the larger number is 18  more than twice the smaller number.

2X + 18 is the greater number.

Because the total is now 93, X + (2X+18) = 93

3X = 93 - 18 .

X = 25

larger number will be 2(25) + 18 = 68

Thus the numbers are smaller number is 25 and larger number is 68.

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Answer: 100

Step-by-step explanation:

To solve this expression, we can start by performing the operations inside the parentheses first:

560 divided by 7 + 140 divided by 7

= 80 + 20

= 100

So the result of the expression is 100.

I hope this helps! Let me know if you have any questions.

The equation of the line that passes through the point (5, 4) and is perpendicular to the line whose equation 2x + y = 3 is y = 1/2x + 3/2

The given equation of the line is

2x + y = 3

y = 3 - 2x

y = -2x + 3

The slope of the line is -2

The slope of the original line will be negative inverse of -2

= - 1/-2

= 1/2

The line is passing through the point (5, 4)

The slope intercept form is

y = mx + b

Substitute the values in the equation

4 = 1/2(5) + b

4 = 5/2 + b

b = 4 - (5/2)

b = 3/2

Therefore, the equation of the line is y = 1/2x + 3/2

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The unknown angle of the right angle triangle is as follows:

A right angle triangle is a triangle that has one of its angles as 90 degrees.  The sides of a right angle triangle can be named base on the position of the angles. The sides includes hypotenuse side, opposite side and adjacent side.

The sum of angles in a right angle triangle is 180 degrees.  Therefore, let's find the ∠C in the triangle ABC.

Therefore,

180 = ∠A + ∠B + ∠C

m ∠B = y + 40

m ∠C = 3y - 10

m ∠A = 90°

Hence,

180 = 3y - 10 + y + 40 + 90

180 = 4y + 120

180 - 120 = 4y

y = 60 / 4

y = 15

Hence,

m ∠C = 3(15) - 10

m ∠C = 45 - 10

m ∠C = 35 degrees

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The equation of a line perpendicular to y=4/24x that pass through the point (-8, -4) is -6x-4y=16 where x-intercept is -6 and y-intercept is -4.

A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. The variables in the preceding equation are y and x, and it is occasionally referred to as a "linear equation of two variables.

The formula for a straight line is y=mx+c where c is the height at which the line intersects the y-axis, often known as the y-intercept, and m is the gradient.

Given line ;

y=1x/6

now comparing it with y=mx+c to find the value of m and we found;

m1=1/6

now if two lines are perpendicular then,

m1.m2=-1

m2=-6

now finding the equation of line passing through the point (-8, -4)

x1=-8

y1=-4

(y−y1)=m(x−x1)

Y+4=(-6)(x+4)

Y+4=(-6x/4)

Y=(-6x/4)-4

Y=(-6x-16)/4

4y=-6x-16

rearrange;

-6x-4y=16

this is our required value.

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Answer:

4.5 as a fraction is 9/2.

Step-by-step explanation:

Please give the brainliest.

The equation use to determine the value of [tex]x[/tex] is [tex](2x+5)+3(2x+5)=92[/tex].

The measures of [tex]\angle A, \angle B[/tex] are [tex]23^\circ, 69^\circ.[/tex]

Let us assume the measures of [tex]\angle A, \angle B[/tex] are [tex]z, y[/tex].

Now according to the question, we can write the relation between [tex]\angle A, \angle B[/tex] is [tex]y=3z....(i)[/tex].

We know, the measure of [tex]\angle A[/tex] is [tex]2x+5[/tex] so [tex]2x+5=z....(ii)[/tex]. Now, we will substitute the value of [tex]z[/tex] from equation [tex](ii)[/tex] in equation [tex](i)[/tex].

[tex]y=3z\\= 3 \times (2x+5)\\=6x+15[/tex]

So, the final equation will be [tex](2x+5)+3(2x+5)=92[/tex]

⇒ [tex]6x+15+2x+5=92[/tex]

⇒ [tex]8x+20=92[/tex]

⇒ [tex]8x=72[/tex]

⇒ [tex]x=9[/tex]

[tex]\therefore[/tex] measure of [tex]\angle A[/tex] is [tex]2x+5=(2 \times 9)+1=25[/tex] and measure of [tex]\angle B[/tex] is [tex]2 \times 23 = 69[/tex].

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i hope you understand cause i can write on a screen

Answer: In this scenario, the length of the backpacking trip is the independent variable and the amount of trail mix Wesley will bring is the dependent variable.

The independent variable is the variable that is being changed or controlled in an experiment or study. In this case, the length of the backpacking trip is the independent variable because it is being determined by Wesley and is not influenced by any other factor.

The dependent variable is the variable that is being measured or observed in an experiment or study. In this case, the amount of trail mix Wesley will bring is the dependent variable because it depends on the length of the backpacking trip. Wesley's decision on how much trail mix to bring will be influenced by how long he plans to go backpacking.

For the given equation y=x+1/5x, if the value of x is 40, y will be 48.

An equation is a statement that two expressions, which include variables and/or numbers, are equal. In essence, equations are questions, and efforts to systematically find solutions to these questions have been the driving forces behind the creation of mathematics.

It is given that, the equation is

y=x+1/5x

We have to find the value of y when the value of x is 40.

Substitute the value of x in order to obtain the value of y as

y=40+40/5

y=40+8

y=48

Thus, for the given equation y=x+1/5x, if the value of x is 40, y will be 48

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Answer:

48

Step-by-step explanation:

y = x + 1/5 x

y = 40 + 1/5 × 40

y = 40 + 8

y = 48