13 points) find the area of the largest rectangle that can be inscribed in a right triangle with legs of length 3 and 4 if two sides of the rectangle lie along the legs

For the parent function y = x, the equation of the line has a negative y-intercept and a positive slope will be y = mx + c where c < 0 and m > 0.

What is the slope-intercept form of a line?

When you know the slope of the line to be examined and the point given is also the y-intercept, you can use the slope-intercept formula y = mx + b. (0, b). The y value of the y-intercept point is represented by b in the formula.

For the given parent function y = x.

Comparing with the slope-intercept form y = mx + c, we get

                slope(m) = 1, and the y-intercept is c = 0;

So we can make one line such that it has a negative y-intercept and a positive slope.

                              y = mx + c, where c < 0 and m > 0.

Hence, for the parent function y = x, the equation of the line has a negative y-intercept and a positive slope will be y = mx + c where c < 0 and m > 0.

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The set of ordered pairs that is a function is (c)  {(-2, -6), (-5, -6), (9, -2), (7, 3)}

The list of options represents the given parameter

As a general rule, for an ordered pair to be a function;

The y values on the ordered pair must point to different x values

In (a) the y values -1 and 7 have the same x value of 1

So, it is not a function

In (b) the y values -4 and -6 have the same x value of 3

So, it is not a function

In (c) all the y values have different x values

So, it is a function

In (d) the y values -5 and -1 have the same x value of -6

So, it is not a function

Hence, the ordered pair that is a function is (c)

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Answer:

The answer would be C. {(-2, -6), (-5, -6), (9, -2), (7, 3)\}{(−2,−6),(−5,−6),(9,−2),(7,3)}

Step-by-step explanation:

the circle's area is approximately 2173.22 mm².We can find the radius of the circle by dividing the diameter by 2

what is  diameter ?

Diameter is a straight line passing through the center of a circle or sphere and connecting two points on the circumference. It is the longest chord of the circle.

In the given question,

The diameter of a circle is 52.6 millimeters.

We can find the radius of the circle by dividing the diameter by 2:

radius = diameter/2 = 52.6/2 = 26.3 mm

Now, we can use the formula for the area of a circle:

area = π × radius²

Plugging in the values we have:

area = 3.14 × 26.3² = 3.14 × 691.69 ≈ 2173.21 mm²

Rounding to the nearest hundredth, we get:

area ≈ 2173.21 ≈ 2173.22 mm²

Therefore, the circle's area is approximately 2173.22 mm².

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There are five rules in one group

From the question, we have

25 rules in 5 groups

In one group = 25/5 = 5 rules

There are five rules in one group

Divide:

Repetitive subtraction is the process of division. It is the multiplication operation's opposite. It is described as the process of creating equitable groups. When dividing numbers, we divide a larger number down into smaller ones such that the larger number obtained will be equal to the multiplication of the smaller numbers. One of the four fundamental mathematical operations, along with addition, subtraction, and multiplication, is division. Division is the process of dividing a larger group into smaller groups so that each group contains an equal number of things. It is a mathematical operation used for equal distribution and equal grouping.

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The system of equations to find the smallest number of buses the orchestra can rent will be b + v ≤ 6 and 25b + 12v ≥ 111.

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.

Given that,  Six of the orchestra's 111 musicians hold driving licenses for big, multi-passenger vehicles. 25 people can fit on a bus, but renting one is far more expensive. 12 persons can fit in a passenger van.

The system of equations to find the smallest number of busses the orchestra can rent is,

The total number of buses :

b + v ≤ 6

The total number of passengers.

25b + 12v ≥ 111 - - - - (2)

Thus, the system of equations to find the smallest number of buses the orchestra can rent will be b + v ≤ 6 and 25b + 12v ≥ 111.

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If reserve rate decreases from 5% to 4%  then money supply of $50000

deposits increases .i.e bank can save $2000 and can lend $48000.

The reserve ratio is the percentage of reserves (or cash deposits) that a bank must keep and not lend out. The higher the reserve requirement, the less money a bank can potentially lend—but this extra cash also prevents a bank from failing and strengthens its balance sheet. Still, when the reserve ratio rises, monetary policy is considered contractionary, and when it falls, monetary policy is considered expansionary.

Given this, the reserve rate falls from 5% to 4%.

$50000 is the initial deposit.

If the reserve ratio is 5%, the bank must keep 50000*0.05 = $2500 in reserve and may make loans totaling 50000-2500=$47500.

If the reserve ratio is reduced to 4%, a bank with $50000 in deposits must save 50000*0.04 = $2000 before it can lend $48000.

Thus, if reserve ratio decreases then the money supply increases.

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The size of the garden That Brian need to grow 20 carrots at a time is 5 square feet

The size of the Brian's garden in square feet = x

The number of carrots that he can grow at a time = y

The equation that models the relationship is

y = 4x

The means the number of carrots that he can grow at a time is directly proportional to the size of the Brian's garden,

The number of carrots that he need to grow = 20 carrots

Substitute the values in the equation and find the value of x

20 = 4x

The size of the garden x = 20/4

= 5 square feet

Hence, the size of the garden That Brian need to grow 20 carrots at a time is 5 square feet

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Answer:

y = -1/2x + 4

Step-by-step explanation:

Use the slope formula (change in y divided by change in x) to find the slope. (-1/2). Then pick one of the points and plug it back into the new equation using -1/2 as your slope.

The amount owed is $10865, based on the given parameters

The given parameters about the compound interest are

Principal Amount, P = $5300

Interest Rate, R = 8%

Time, t = 6 years

To calculate the amount owed, we make use of the following formula

A = P + CI

Where

Compound interest, CI = P(1 + R)^t - P

So, the equation becomes

A = P + P(1 + R)^t - P

Evaluate the like terms

A = P(1 + R)^t

In this question, the formula is given as

A = P(1 + r/n)^nt

Where

n = 12, i.e compounded monthly

Substitute the known values in the above equation

A = 5300 * (1 + 8%/12)^(6*12)

Express 8% as decimal

A = 5300 * (1 + 0.08/12)^(6*12)

Evaluate the sum

A = 5300 * (1.01)^(6*12)

Evaluate the exponent

A = 5300 * 2.05

Evaluate the product

A = 10865

Hence, the value of the amount after 6 years is $10865

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Answer:

64

Step-by-step explanation:

Answer:

x = 27.1  y = 62.9  x + y = 90

Explaination:

Let's say you have 2 complimentary angles, x and y

So x + y = 90

if x is 35.8 degrees less than the measure of a complementary angle, then x = y - 35.8

Putting this into our x + y = 90 equation, we get (y - 35.8) + y = 90

2y - 35.8 = 90

2y = 90 + 35.8

2y = 125.8

y = 125.8/2 = 62.9 degrees.

so x = 62.9 - 35.8 = 27.1 degrees.

Answer:

  (a) (x, y) = (2, 5)

  (bi) y = 5, y = 5; the values are the same

  (bii) the values are the same as in part (a)

Step-by-step explanation:

You want the solution and some observations about it for the system of equations ...

The graph shows the lines cross at the point (x, y) = (2, 5).

The solution to the equations is (x, y) = (2, 5).

i) For x=2, the value of y in the first equation is ...

  y = 2(2) +1 = 4 +1 = 5

For x=2, the value of y in the second equation is ...

  y = -(2) +7 = -2 +7 = 5

ii) The values of y are the same, and match the value we found in part (a).

__

Additional comment

The purpose of the exercise is to get you to see that the value of x that is the solution makes both equations have the same value of y, and that is the value of y that is the solution.

The graph is a plot of the y-value for each x-value. Where the lines cross, the y-values are the same for that x-value. That point of intersection of the lines is the solution to the system of equations: the values of x and y satisfy both equations at that point.

[tex]~~~~~~ \textit{Simple Interest Earned} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\dotfill & \$40\\ P=\textit{original amount deposited}\dotfill & \$500\\ r=rate\to r\%\to \frac{r}{100}\\ t=years\dotfill &4 \end{cases} \\\\\\ 40 = (500)(\frac{r}{100})(4) \implies 40=20r\implies \cfrac{40}{20}=r\implies \stackrel{\%}{2}=r[/tex]

Answer:

When x = 3, y = 6,

[tex][3(3)- 12]-[(\frac{1}{2}(3)(6)) -10] = (9-12)-(9-10)[/tex]

                                             [tex]= (-3)-(-1)[/tex]

                                             [tex]= -3+1[/tex]

                                             [tex]=-2[/tex]

The number of candies bought = 10

The number of pretzels bought = 8

What is an equation?

An equation is a mathematical statement that proves two mathematical expressions are equal in algebra, and this is how it is most commonly used. In the equation 3x + 5 = 14, for instance, the two expressions 3x + 5 and 14 are separated.

Let,

x = number of candies bought

y = number of pretzels bought.

The equations that describe the given problem are:

4.75 x + 3.5 y = 75.50..........(1)

x + y = 18

x = 18 - y.................(2)

Substitute equation 2 in equation 1,

4.75 (18 - y) + 3.5 y = 75.50

85.5-4.75y+3.5y=75.50

85.5-1.25y=75.50

1.25y=85.5-75.50=10

y=8

Substitute y=8 into x = 18 - y.

x=18-8=10

The number of candies bought is 10, and the number of pretzels bought is 8.

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I may be incorrect.

Answer: 33.333333333333%

Step-by-step explanation:

The difference is 1/3. Twelve by three is four. Nine by three is three. The different from 9 to 12 is 1/3.

Variance of the given distribution is equal to 0.63.

As given in the question,

Given data for the distribution is equal to :

X:            0          1           2            3

P(x):   0.027   0.189    0.441     0.343

Variance for the given distribution is equal to

= E(x²) - {E(x)}²

Now , Value of E(x) can be calculated using the formula,

E(x) = [tex]\sum x_{i} P( x_{i} )[/tex]

      = (0)(0.027) + (1)(0.189) + (2)(0.441) + (3)(0.343)

      = 0.189 + 0.882 + 1.029

      = 2.1

E(x²) = [tex]\sum x_{i} ^{2} P(x_{i})[/tex]

        =  (0)²(0.027) + (1)²(0.189) + (2)²(0.441) + (3)²(0.343)

        = 0.189 + 1.764 + 3.087

        = 5.04

Variance = E(x²) - {E(x)}²

               = 5.04 - (2.1)²

               = 5.04 - 4.41

               = 0.63

Therefore, variance of the given distribution is equal to 0.63.

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The probability that Alice leaves before Carol is 0.5 according to the given information.

Probability is a branch of mathematics that deals with numerical descriptions of how likely an event or statement is to occur.

If X1 and X2 are both exponential distributions with parameters 1 and 2, respectively, then

P(X₁< X₂)= λ₁/(λ₁+λ₂ )

And P(X>s+t/x>s)=P(X>t), if X≈exp(μ)

Here, Let [tex]X_{A}[/tex], [tex]X_{C}[/tex] denote the service times for Alice and Carol

And also given that,

E[ [tex]X_{A}[/tex]]=1/μ

E[ [tex]X_{A}[/tex]]=4

E[ [tex]X_{C}[/tex]]=4

E[ [tex]X_{A}[/tex]]=E[ [tex]X_{C}[/tex]]=4

So, [tex]X_{A}[/tex], [tex]X_{C}[/tex] ≈exp(1/4)

Now, when Betty completes his service, Alice is still being served, and the remaining time required to complete his service is exp(1/4).

Because the exponential distribution has no memory.

So, P( [tex]X_{A}[/tex]< [tex]X_{C}[/tex] )=  λ₁/ λ₁+ λ₂

=(1/4)/((1/4)+(1/4))

=(1/4)/(1/2)

=0.5

As a result, the probability that Alice leaves before Carol is 0.5.

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Equation that makes it easier to find the number of vertices in an Octahedron is V + F = 14 with 8 faces there are 6 vertices.

Given:

Octahedron has 8 faces

Let F be the faces of octahedron

Let V be the vertices of octahedron

we know that:

V + F = 14

Given F = 8 substitute

V + 8 = 14

V = 14 - 8

V = 6

Therefore Equation that makes it easier to find the number of vertices in an Octahedron is V + F = 14 with 8 faces there are 6 vertices.

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The formula for d is d = v/√48

What is a formula?

In science, a formula is a compact manner of symbolically describing information, such as a mathematical formula or a chemical formula. In physics, the phrase formula refers to the general construct of a connection between given quantities. In mathematics, a formula is an identity that equates one mathematical statement to another, the most significant of which are mathematical theorems. A formula (also known as a well-formed formula) is a logical object that is produced utilizing the symbols and formation rules of a specific logical language. For example, calculating the volume of a sphere necessitates extensive use of integral calculus or its geometrical equivalent, the method of exhaustion.

The equation is given as v= √48d

Hence, the formula for d is, d = v/√48

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The probability that the next consumer will use cash as payment is 85/106

85 customers made cash payments.

5 customers used debit cards in total.

16 customers used credit cards in total.

The probability that the following consumer will make a cash payment must be calculated as a fraction in its simplest form.

Total clients: 85 + 5 + 16 = 106

There were 85 successful outcomes (Customers who paid cash)

Therefore, the probability will be: =85/106 = 0.801

Therefore, the probability that the following customer will pay with cash is 85/106.

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Answer:

≈ 80%

Step-by-step explanation:

Based on these results, express the probability that the next customer will pay with cash as a percent to the nearest whole number.

85 cash, 5 debit card, and 16 credit card.

85+5+16= 106

There were a toal of 106 customers. 85 paid with cash.

Probability the next customer will pay with cash:
85/106= 0.801886...

0.801886... ×100% ≈ 80.1887%

≈ 80%

There are infinitely more possibilities, but the midpoint between 1/2 and 1 is 3/4.

what is fraction?

An element of a whole or, more broadly, any number of equal pieces, is represented by a fraction. When used in conversational English, a fraction indicates the number of components of a particular size, as in one-half, eight-fifths, and three-quarters.

For any two numbers a and b, the average 1/2(a + b) is lies between them.

Here, the given two numbers are 1/2 and 1.

So, to find the fraction between 1/2 and 1 we can form the average:

1/2(1/2 + 1) = 1/2(3/2) = 3/4

Hence, the fraction that fit between 1/2 and 1 is 3/4.

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The percent of times that Emerson hit the ball, given the number of times that he struck out was 68 %

First, find the total number of times that Emerson had at bat:

= Game 1 + Game 2 + Games 3

= 90 + 120 + 140

= 350 times

The number of times Emerson missed was:

= 30 + 40 + 42

= 112 times

The number of times the ball was hit is therefore:

= 350 - 112

= 238 times

The percent of time the ball was hit:

= 238 / 350

= 68 %

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Step-by-step explanation:

6-(2x+4) is less than or equal to 10

6-(2x+4) ≤ 10

6 - 2x - 4 ≤ 10

combine like terms on left side:

2 - 2x  ≤ 10

subtract 2 from both sides:

2 - 2x - 2 ≤ 10 - 2

- 2x  ≤ 8

divide both sides by -2: (remember, when dividing by a negative number you must FLIP the sign direction)

- 2x/-2 ≥ 8/-2

x ≥ 8/-2

x ≥ -4

[-4, ∞)

Step-by-step explanation:

6-(2x+4) is less than or equal to 10

6-(2x+4) ≤ 10

6 - 2x - 4 ≤ 10

combine like terms on left side:

2 - 2x  ≤ 10

subtract 2 from both sides:

2 - 2x - 2 ≤ 10 - 2

- 2x  ≤ 8

divide both sides by -2: (remember, when dividing by a negative number you must FLIP the sign direction)

- 2x/-2 ≥ 8/-2

x ≥ 8/-2

x ≥ -4

[-4, ∞)

The thing to include in the response regarding the sampling include:

Sampling is the process of selecting the group from which you will collect data for your research. For example, if you want to know what students think at your university, you could survey 100 of them. In statistics, sampling allows you to test a hypothesis about a population's characteristics.

The act of deciding how many observations or replicates to include in a statistical sample is known as sample size determination. The sample size is an important aspect of any empirical study.

In this case, the sample size wasn't a true reflection of the customers.

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Answer:

Step-by-step explanation:

-12.4 x 4 = -49.6

n = -49.6

Answer:

n = -49.6

Step-by-step explanation:

1. Multiply both sides of the equation by 4

2. Simplify the expression

The quadratic equation is [tex]x^2+x-12[/tex]

What is quadratic equation?

Quadratics can be defined as a polynomial equation of a second degree, which implies that it comprises a minimum of one term that is squared. It is also called quadratic equations. The general form of the quadratic equation is:

ax² + bx + c = 0

where x is an unknown variable and a, b, c are numerical coefficients.

Given, the roots of quadratic equation as (3,-4).

The formula to find the quadratic equation, as

x2 – (Sum of the roots)x + Product of the roots = 0

Sum of roots = 3-4

=-1

Product of roots = 3(-4) = -12

The quadratic equation is

x²+x-12

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The triangle which are similar to ABC are:

The connecting of three non-collinear points results in a triangle, which is a three-sided closed-plane object. Triangles can be classified into three categories based on their side properties: equilateral, scalene, and isosceles.

We know that the when we sum all the interior angles of a triangle, we get 180°.

Given that, A triangle ABC has ∠A = 35° and ∠B = 20°.

∴ ∠C = 180° - 35° - 20°.

∠C = 125°.

Triangle will be similar if every corresponding angle of different triangles has the same measure. So, Triangles that are similar to triangle ABC is triangle DEF where ∠D is 35° and ∠E is 20° and triangle JKL where ∠J is 35° and ∠L is 125° and triangle MNO where ∠N is 20° and ∠O is 125°.

Therefore, triangle DEF, JKL and MNO are similar to triangle ABC.

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The given question is incomplete. Here is the complete Question:

Answer:-5/4

Step-by-step explanation:

the slope is the number next to the letter X.

Brand B will be the best because it costs less each fork.

Brand B has price of $0.03 per forks .

Here given,

Given that Brand A charges $1,54 for a package of 36forks,

Then the price per fork will be:

= $1.54 / 36

= $0.042

Given that Brand B charges $1.66 for a box of 48 forks,

Then the price per fork will be:

= $1.66 / 48

= $ 0.034

Since brand B  has lower cost per fork ,

Brand B will therefore be the finest brand with $0.03 per forks price.

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