Mathematics College

## Answers

**Answer 1**

The **mean** of the score is 3.4 and the standard deviation is 3.2.

Scores of students = 5, 4, 4, 3 and 1

When determining the **mean **of a group of numbers, add up all the numbers and divide by the total number in the group.

Calculating the **mean** -

= Sum of total values / Total values

= 5 + 4 + 4 + 3 + 1 / 5

= 17/5

= 3.4

By averaging the squared deviations of each integer from the mean, you may get the variance before calculating the** standard deviation.**

Calculating the** Standard deviation** -

σ = √ ∑ (xi - u)²/n

σ² = (1² + (3.4 - 1)² + (3.4 - 4)² + (3.4 - 4)²+ (3.4 - 5)²) / 5

= 3.2

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## Related Questions

ara sells apples at a farmers market she begins the day with 35 1/2 pounds of apples she sells half of the apples in the mornning 4/19 of the apples in the afternoon and 1/4 of the apples in the evening how many pounds of apples dose she have left

### Answers

Ara sells 1/2 of her apples in the morning, so she sells 35.5 / 2 = 17.75 pounds of apples.

She sells 4/19 of the remaining apples in the afternoon, so she sells 17.75 * 4/19 = 2.7 pounds of apples.

She sells 1/4 of the remaining apples in the evening, so she sells (35.5 - 17.75 - 2.7) / 4 = 4.5 pounds of apples.

Ara has 35.5 - 17.75 - 2.7 - 4.5 = 10.5 pounds of apples left

skee ball refer to exercise 4. make a histogram of the probability distribution. describe its shape.

### Answers

Ten to fifty is the range of the **scores**. The most **frequent** result is a 10 with a **right-skewing bias**.

**Probability histogram**

The height of each bar must be equal to the probability, the width of each bar must be the same, and the bars must be centered on the amount of money gathered.

The distribution is skewed to the right **because** the highest bar in the histogram is to the left and there is a tail of lower bars to its right.

The most frequent score is 10 due to the fact that the top bar in the histogram is **centered** at 10.

The result is:

Ten to fifty is the range of the scores.

The most **frequent** result is a 10 with a right-skewing bias.

Ten to fifty is the range of the scores.

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Let A be a 5 by 7 , B be a 7 by 6 and C be a 6 by 5 matrix. How to determine the size of the following matrices ? O AB, BA, O A^TB, BC, O ABC , CA ,O B^TA , BC^T

### Answers

The **matrices **matrix A be a 5 by 7 , matrix B be a 7 by 6 and matrix C be a 6 by 5 matrix.

now, we need to determine the size of the matrices

AB = [tex](AB)_{5*6}[/tex]

BA is undefined

[tex]A^{T}[/tex]B is undefined

BC = [tex](BC)_{7*5}[/tex]

ABC = [tex](ABC)_{5*5}[/tex]

CA = [tex](CA)_{6*7}[/tex]

[tex]B^{T}[/tex]A is undefined.

B[tex]C^{T}[/tex] is undefined.

given that

matrix A is [tex]A_{5*7}[/tex]

matrix B is [tex]B_{7*6}[/tex]

matrix C is [tex]C_{6*5}[/tex]

now, we need to determine the size of the matrices

AB multiplication of two **matrices**

**multiplication** of two **matrices** is possible only when B has the same number of columns as rows in A,

[tex]A_{m*n}[/tex]and [tex]B_{n*p}[/tex]

If it is defined as above, then the matrix AB will have m rows and p **columns**, i.e., A must have n columns and B must have n rows in order for AB to be defined.

[tex](AB)_{m*n}[/tex]

In addition, a matrix gets** transposed **when columns turn into rows and vice versa.

Thus, if

[tex]A_{m*n}[/tex]⇒[tex](AT)_{m*n}[/tex]

So, for this particular question, we have: [tex]A_{5*7}[/tex], [tex]B_{7*6}[/tex] , [tex]C_{6*5}[/tex]

According to the aforementioned idea, AB is therefore [tex](AB)_{5*6}[/tex] in size.

Additionally, BA and [tex]A^{T}[/tex]B are not defined.

[tex](BC)_{7*5}[/tex]

ABC=(AB)C=A(BC) because matrix multiplication is **associative**,

[tex](ABC)_{5*5}[/tex]

[tex](CA)_{6*7}[/tex]

[tex]B^{T}[/tex]A is undefined. because they don't have same number of columns in matrix B and rows in matrix A

B[tex]C^{T}[/tex] is undefined. because they don't have same number of columns in matrix B and rows in matrix C

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I came up with 7 hours and 15 minutes but that is not one of the answer choices?

### Answers

well, as I see it Person1 is faster than Person2, but Person2 doesn't factor in the issue here, let's nevermind Person2.

most of the procedures are 45mins each, namely on average they're 45 mins each.

so Person1 say did 9 procedures, but two of those guys took much longer, too 2 hours each, so two procedures alone ate 4 hours.

Now, Person1 besides doing those two really long procedures, has to also finish the other seven, 2 + 7 = 9, so there are 7 more procedures that on average take 45 mins each.

[tex]\stackrel{\textit{\LARGE minutes}}{\stackrel{\textit{two really long ones}}{240}~~ + ~~\stackrel{\textit{the rest of them}}{45(7)}}\implies 555\implies \stackrel{\textit{9 hours and 15 minutes}}{9.25~hours}[/tex]

It 9 hours and 15 minutes because that is what I got when I did the problem

what is the slope through the line of (4, 7) and (6, 2)

### Answers

The slope through the line of (4, 7) and (6, 2) can be found by using the slope formula:

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

where (x1, y1) and (x2, y2) are the coordinates of the two points on the line.

Substituting the values for (4, 7) and (6, 2) into the formula:

m = (2 - 7) / (6 - 4)

m = -5 / 2

m = -2.5

So, the slope of the line through (4, 7) and (6, 2) is -2.5.

Hello:

--> find the slope between the points (4, 7) and (6, 2)

Let's consider our point given:

--> (x1, y1): (4, 7)

--> (x2, y2): (6, 2)

Let's consider what formula we need:

[tex]\text{Slope}=\dfrac{y2-y1}{x2-x1}=\dfrac{2-7}{6-4}=\dfrac{-5}{2}=-\dfrac{5}{2}[/tex]

Thus our slope is -5/2

**Answer****: -5/2**

Gombak Mega Store is having its Year-End-Sales. Ten percent, five percent and twenty percent discounts were given on shoes, handbags and watches respectively if two or more units of each item were bought. Noor bought three pairs of shoes, two units of handbag and one unit of watch. If the price (per unit) of shoes, handbag and watch is RM150, RM200 and RM250 respectively, how much money does Noor has to pay?

### Answers

**Answer:**

$963.00

**Step-by-step explanation:**

.9(3x150) + .95(2x200) + 250

.9(450) + .95(400) + 250

405 + 308 + 250 = 963

If we are taking 10% off, that is like leaving 90% (.9) on.

If we are taking 5% off, that is like leaving 95% ( .95) on.

No discount for the watch because she only bought one.

What is the solution for the system of linear equations shown in the graph?

a coordinate grid with one line that passes through the points 0 comma 0 and 1 comma negative 3 and another line that passes through the points 0 comma 2 and negative 1 comma 1

negative one half comma three halves

one half comma one half

three halves comma three halves

negative three halves comma one half

### Answers

The **solution **of the** system of equations** is:

(-3/2, 1/2)

**What is the solution of the system of equations?**

Here we have two **lines **of the form:

y = a*x + b

one passes through (0, 0) and (1, -3)

For the first point we know that the constant is 0, and replacing the values of the second point we get:

1 = a*-3

1/-3 = a

The line is:

y = (-1/3)*x

The second line passes through (0, 2) and (-1, 1) from the first point we can see that:

y = a*x + 2

And replacing the values of the second point we get:

1 = a*-1 + 2

1 - 2 = -a

-1 = - a

1 = a

This line is y = x + 2

Then the** system of equations** is:

y = x + 2

y = (-1/3)*x

We can replace use the substitution method to write:

x + 2 = (-1/3)*x

x + 1/3*x = -2

(4/3)*x = -2

x = -2*(3/4)

x = -3/2

And the y-value is:

y = -3/2 + 2

y = 1/2

The solution is (-3/2, 1/2)

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Jenna earned $125 of interest by leaving her money in the bank for 4 years at a 5% interest rate. What was the principle amount that Jenna put in the bank

### Answers

The **principal **amount that Jenna put in the bank is $625.

What is simple interest?

**Borrowers **must pay lenders simple interest as a fee in **exchange **for a loan. **Compound **interest is excluded from the **calculation **and just the original **principal **is used. Simple interest applies to all loans, not just specific ones. **Additionally**, it refers to the kind of **interest **that banks give their customers on their **savings **accounts.

Given **interest **earned = $125

time = 4 years

rate = 5%

let the **principal **be p

this is the case of **simple **interest,

SI = (p*r*t)/100

**substitute **the values

125 (p* 5 * 4)/100

125 x 100 = p x 20

p = 12500/20

p = $625

Hence **principal **amount is $625.

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are y-1/7x-2 & x-7y=4 parallel perpendicular intersecting but not perpendicular

### Answers

y-1/7x-2 & x-7y=4 are intersecting but not parallel or perpendicular lines.

Two lines are parallel if they have the same slope (or no slope at all), and two lines are perpendicular if the product of their slopes is -1. To determine if lines are parallel or perpendicular, you can find their slopes and check if they are equal or if the product of their slopes is -1.

The first line y-1/7x-2 can be rewritten in slope-intercept form y = mx + b as y = 1/7x + 2

The second line x-7y=4 can be rewritten in slope-intercept form y = mx + b as y = x/7 - 4/7

The slopes of the two lines are 1/7 and -1/7 respectively. The product of the slopes of two lines is 1/49 which is not -1, that means that the two lines are not perpendicular. Also, the slopes are not equal, which means that the lines are not parallel.

Therefore, the two lines y-1/7x-2 & x-7y=4 are intersecting but not parallel or perpendicular lines.

Find the x-intercept of the line -5x-2y=15

### Answers

**Answer:**

The x intercept is -3

**Step-by-step explanation:**

To find the **x intercept,** let y = 0 and solve for x.

-5x-2y=15

-5x-2*0=15

-5x=15

Divide each side by -5

-5x/-5 = 15/-5

x = -3

The x intercept is -3

Explain why 96:38 is NOT the same as 38:96.

### Answers

The two **ratios **are inverse of each other that's why 96:38 is not the **same **as 38:96.

What are inverse ratios?

When two **quantities **are inversely related, that is, when an **increase **in one quantity causes a decrease in the other and vice versa, they are said to be in inverse proportion. The product of the given two quantities is equal to a constant value in inverse proportion.

Given that the two ratios are 96:38 and 38:96. The value of the two ratios will not be the same because both the ratios are inverse of each other or are reciprocals of each other.

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**Answer:**

The two ratios are inverse of each other that's why 96:38 is not the same as 38:96.

**Step-by-step explanation:**

I took the quiz.

a scale drawing for a backyard is shown below. In the drawing, 4cm represents 5m. Assuming the patio is rectangular, find the area of the real patio.

### Answers

:

The the **area** of the **real patio** is = 50 m²

How to find the area?

Recall that **area** deals with the **floor space** occupied by the **rectangular **field

The area of the **lawn** is represented by

Area = L*W

2 cm for **length** = 5 m.

4 cm for **width** = 10 m.

Area = width • length. 10•5=50cm²

Having computed the area, we now conclude that the the **area** of the real patio 50cm²

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Find the indefinite integral of each of the following by using [ f'(x)[f(x)"]dx =[ [f(x)]^n+1 / n+1] + c, where n #1

(a) e^x (3 - e^x)^4 dx

(b) 3e^2x √(1 + e²x) dx

(c) 3e^-2x / (1 + e^-2x)^3 dx

(d) 4 cos 2x sin³ 2x dx

(e) sec² 3x tan³ 3x dx

(f) 2+tan ² x / cos² x dx

### Answers

**Answer:**

**a) e^x (3 - e^x)^4 dx**

**Using the formula [ f'(x)[f(x)"]dx =[ [f(x)]^n+1 / n+1] + c, where n = 1,**

**we have:**

**e^x (3 - e^x)^4 dx = (e^x)^5 (3 - e^x)^4 / 5 + c**

**= (e^5x - 4e^4x + 6e^3x - 4e^2x + e^x) / 5 + c**

**b) 3e^2x √(1 + e²x) dx**

**Using the formula [ f'(x)[f(x)"]dx =[ [f(x)]^n+1 / n+1] + c, where n = 1,**

**we have:**

**3e^2x √(1 + e²x) dx = (3e^2x)^2 * (1 + e²x)^(3/2) / 2 + c**

**= (9e^4x + 3e^2x) / 2 + c**

**c) 3e^-2x / (1 + e^-2x)^3 dx**

**Using the formula [ f'(x)[f(x)"]dx =[ [f(x)]^n+1 / n+1] + c, where n = 1,**

**we have:**

**3e^-2x / (1 + e^-2x)^3 dx = -(3e^-2x)^2 / (1 + e^-2x)^2 + c**

**= -(9e^-4x) / (e^-4x + 2e^-2x + 1) + c**

**d) 4 cos 2x sin³ 2x dx**

**Using the formula [ f'(x)[f(x)"]dx =[ [f(x)]^n+1 / n+1] + c, where n = 1,**

**we have:**

**4 cos 2x sin³ 2x dx = -4 cos 2x (sin 2x)^4 / 4 + c**

**= -(cos 2x) (1 - cos 4x)^2 / 2 + c**

**e) sec² 3x tan³ 3x dx**

**Using the formula [ f'(x)[f(x)"]dx =[ [f(x)]^n+1 / n+1] + c, where n = 1,**

**we have:**

**sec² 3x tan³ 3x dx = -sec² 3x (tan 3x)^4 / 4 + c**

**= -sec² 3x (sec² 3x - 1)^2 / 4 + c**

**f) 2+tan ² x / cos² x dx**

**Using the formula [ f'(x)[f(x)"]dx =[ [f(x)]^n+1 / n+1] + c, where n = 1,**

**we have:**

**2+tan ² x / cos² x dx = ln|sec x| + c**

**It's worth noting that all these integrals are indefinite, which means that the constant c is arbitrary, and the actual antiderivative depends on the problem context.**

**Step-by-step explanation:**

if there are 5 people and 2 have to sit next to each other and 2 others cant sit next to each other, how many combinations

### Answers

if there are 5 **people **and 2 have to sit next to each other and 2 others cant sit next to each other, then 30 **combinations **possible

What are **combinations**?

A combination is a calculation that determines the number of **possible arrangements **in a collection of items in which the order of the selection does not matter. In combinations we can select the items in any order.

nn!/r!(n-r)!

Number of ways=5

=5!/2!2!

=5!/2*2

=5*4*3*2/2*2

=30

=30 ways

if there are 5 people and 2 have to sit next to each other and 2 others cant **sit **next to each other, then 30 combinations possible

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The bullseye on an archery target has a radius of 3 inches. The entire target has a radius of 9 inches. To the nearest hundredth, find the area of the target outside of the bullseye. Use 3.14 for π.

### Answers

**Answer:**

226.1 [tex]in^{2}[/tex]

**Step-by-step explanation:**

Thank you to anyone that can help I am ever so appreciative!!

### Answers

**Answer:**

C. Angle Bisector Theorem

x = 5

PO = 34

**Step-by-step explanation:**

The theorem used is C: Angle bisector theorem

A can be eliminated because there is no midsegment here

B can also be eliminated - no perpendicular bisector

D relates to a median and there is no median here

C is the best choice. You can see in the figure that EO bisects ∠NEP.

Because of this angles ∠NEO and ∠OEP are equal

That makes the triangles congruent since we have one common side and two angles that are equal to each other

Therefore PO = NO

8x - 6 = 6x + 4

8x - 6x = 4 + 6

2x = 10

x = 5

PO = 8(5) - 6 = 40 - 6 = 34

The baker made a batch of chocolate chip, oatmeal raisin, and sugar cookies. If P(chocolate chip) = 0.25, interpret the likelihood of randomly selecting a chocolate chip cookie from the batch.

A. Equally likely and unlikely

B. Likely

C. Unlikely

D. This value is not possible to represent probability of a chance event.

### Answers

The baker made a batch of** chocolate **chips, oatmeal raisin, and sugar cookies. If P(chocolate chip) = 0.25, the likelihood of randomly selecting a chocolate chip is **B. Likely.**

What is **probability**?

Generally, **Probability **is a measure of the likelihood of an event occurring. It is a number between 0 and 1, with 0 indicating that an event is impossible and 1 indicating that an event is certain.

A **probability **of 0.5, for example, would indicate that an event has a 50% chance of occurring. Probability can be used to make predictions and inform **decision-making **in a wide range of fields, including statistics, finance, and engineering.

A **probability **of 0.25 represents a 25% chance of a randomly selected cookie from the batch being a chocolate chip cookie, which is considered "likely" to occur.

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a clerk is wrapping two cube-shaped packages and wants to know the smallest amount of wrapping paper that can wrap each package. the edge length of the larger package is 3in. the greater than the length of the smaller package. the surface area of the larger package is 384 in^2. what is the surface area of the smaller package?

### Answers

The surface area of the smaller **cubical **package is given S = 150 inches²

**What is the surface area of cube?**

The formula for surface area of a **cube **is equal to six times of square of length of the sides of **cube**. It is represented by 6a2, where a is the side length of **cube**.It is basically the total surface area.

Surface area S = 6a² ,

where a is the side of the cube

Given data ,

Let the surface area of the smaller **cube **be represented as S

Now , the surface area of the larger **cube **L = 384 inches²

And , side length of smaller cube = side length of larger cube - 3

Now , the **equation **will be

Surface area of the larger **cube **L = 6 ( A )² ,

where A is the side length of the larger cube

So , substituting the values in the **equation **, we get

6 ( A )² = 384

Divide by 6 on both sides of the equation , we get

A² = 64

Taking square roots on both sides of the **equation **, we get

A = 8 inches

Now , side length of smaller **cube **a = 8 - 3 = 5 inches

So , surface area of the smaller cube S = 6 ( a )²

Substituting the values in the **equation **, we get

Surface area of the smaller cube S = 6 ( 5 )²

Surface area of the smaller cube S = 6 x 25

Surface area of the smaller **cube **S = 150 inches²

Hence , the surface area is 150 inches²

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Moshde runs a hairstyling business from her house. She charges $49 for a haircut and style. Her monthly expenses are $1010. She wants to be able to put at least $1,246 per month into her savings account order to open her own salon.

How many "cut & styles" must she do to save at least $1,246 per month?

### Answers

The number of **cut & styles **that Moshde can do is 47.

How many cut and styles can she do?

The total amount that Moshde can **save **is the difference between the total revenue and the total cost.

Amount that can be **saved **= total revenue - total cost

$1246 = (charge per haircut x number of hair cuts) - $1010

$1246 = ($49 x h) - $1010

$1246 = $49h - $1010

In order to determine the value of h, take the following steps:

Combine and add similar terms:

$1246 + $1010 = 49h

2256 = 49h

Divide both sides of the equation by 49

h = 2256 / 49

h = 46.04

h = 47

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Fred is a weightlifter who can lift 800 pounds on 45% of his attempts. Which of these expressions represents the probability Fred will make 30 lifts out of 60? A. B(30,.45,60)B. B(30,800,60)C. N(30, 800,60) D. N(60, 45, 30)E. B(60, 45, 30)

### Answers

**Expression** represents the **probability** of the given number of attempts and the success rate is given by option E.** B( 60 , 45 , 30 ).**

As given in the question,

In the given situation,

Let us consider 'n' represents the number of trials attempt by the weightlifter.

'p' represents the** probability** of success in his number of trials.

And 'r' represents the number of success out of his total number of attempts.

Here n = 60

p = 45%

r = 30

Using **binomial distribution **method we can represents the expression of the probability for the given condition :

B( n , p , r )

Substitute the values we get,

= B( 60, 45, 30 )

Therefore, for the given total number of lifts , success rate the expression represents the** probability ** is given by option E . B ( 60, 45 , 30 ).

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URGENT!!!

Consider the graph of the polynomial function y=f(x) given below. The graph continues forever at both ends. Determine the following features (make sure you write all intervals in interval notation and all intercepts as points):

(A) State the domain and range.

(B) State the x-intercepts.

(C) State the y-intercept.

(D) State the interval(s) for which the function is increasing.

(E) State the interval(s) for which the function is decreasing.

(F) State the interval(s) for which the function is constant.

(G) State any symmetry about any axis and/or the origin.

(H) Determine whether the function is even, odd, or neither.

### Answers

The features of the given polynomial graph are;

A) **Domain**: (-∞, ∞)

**Range**: (-∞, 16)

B) The x-intercepts are; (-2√2, 0), (0, 0), (2√2, 0)

C) The y-intercept is; (0, 0)

D) The interval(s) for which the function is increasing is; (-∞, -2) and (0, 2)

E) The interval(s) for which the function is decreasing. is; (-2, 0) and (2, ∞)

F) The graph has no constant interval.

G) It is symmetrical about the y-axis

H) Even function

How to find the domain and range of a polynomial graph?

The** domain** of a function is defined as the set of all possible input values for which the function holds. The **range** of a function is defined as the set of all possible output values for all possible input values.

A) The x-values intervals we reckon will be positive and negative infinity as the graph extends till infinity. However, the maximum value of the y-values will be 16 while the minimum is negative infinity.

B) The **x-intercepts **are the points where the graph crosses the x-axis and they are; (-2√2, 0), (0, 0), (2√2, 0)

C) The** y-intercepts** are the points where the graph crosses the y-axis and it has the coordinate; (0, 0)

D) Looking at the given graph, it is increasing when the curve rises and in this case it is; (-∞, -2) and (0, 2)

E) Looking at the given graph, it is decreasing when the curve descends and in this case it is; (-2, 0) and (2, ∞)

F) The graph has no constant interval.

G) It is symmetrical about the y-axis

H) The function is an **even function**

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A company sells concrete in batches of 5 cubic yards. The probability distribution of X, the number of cubic yards sold in a single order for concrete from this company, is shown in the table. The expected value of the probability distribution of X is 19.25 and the standard deviation is 5.76. There is a fixed cost to deliver the concrete. The profit Y, in dollars, for a particular order can be described by Y = 75X - 100. What is the standard deviation of Y?

answer choices

O $332.00

O $432.00

O $532.00

O $1,343.75

O $1,400.00

### Answers

The **standard **deviation of Y is **$432.00** and this can be determined by using the formula of standard deviation and the given data.

Given :

A company sells concrete in batches of 5 cubic yards.

The **probability **distribution of X, the number of cubic yards sold in a single order for concrete from this company, is shown in the table below.

The **expected** value of the probability distribution of X is 19.25 and the standard deviation is 5.76.

There is a fixed cost to deliver the concrete. The profit Y, in dollars, for a particular order can be described by (Y = 75X - 100).

The **formula **to obtain the standard deviation is given below:

**SD(Y) = SD(75X - 100)**

Simplify the above expression by substituting the value of SD(X) and SD(100) in the above expression.

SD(Y) = 75SD(X) - SD(100)

SD(Y) = 75 SD(X) - 0

SD(Y) = 75×5.76

**SD(Y) = $432**

Therefore, the correct** option is B.**

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Express the area of the shaded region in the room shown algebraically

### Answers

to find the shaded area you have to subtract the unshaded small rectangles area from the larger rectangles total area

the larger rectangles area (L) is found by multiplying base by height:

(x+3) • 2x = 2x^2 + 6x

the smaller rectangles area (S) is also found by multiplying base by height:

x • 5 = 5x

then to find the unshaded area take the largest rectangle area and subtract the smaller rectangle (L-S):

2x^2 + 6x - 5x = 2x^2 + x

answer: 2x^2 + x

Mr.Honkenberg Is planning for his Superbowl party.If he he buys 18 chicken wings for $15 what is the cost of the wings in wings per dollar?

### Answers

**Answer:**

The cost of the wings per dollar is 18/15 = 1.2 wings per dollar.

**Answer:**

1.2

**Step-by-step explanation:**

A trapezium ABCD is inscribed into a semi-circle of radius l so that the base AD of the trapezium is diameter and the vertices B and C lie on the circumference. Then the value of base angle θ (in degree) of the trapezium ABCD which has the greatest perimeter, is

### Answers

The value of base angle θ (in degree) of the trapezium ABCD which has the greatest **perimeter**, is **60**°

Given, AD = 2I

From ΔABD,

cos∅=[tex]\frac{AB}{AD}[/tex]

⇒ AB = AD cos∅

⇒ AB = 2I cos∅

and x = ABcos∅ = 2I [tex]cos^{2}[/tex]∅

Now **perimeter**,

P = 2I+ 2I - 2x + 2AB

P = 4I - 4I [tex]cos^{2}[/tex]∅ + 4Icos∅

P = 4I (1 - cos²∅ + cos∅)

Differentiating with respect to ∅, we get

dP/d∅= 4I(2 cos∅ sin∅ - sin∅)

For **max**/**min**,

dP/d∅ = O

2 cos∅ sin∅ - sin∅ = 0

⇒ cos∅ = [tex]\frac{1}{2}[/tex] (∅ [tex]\neq[/tex] 0)

= **60**°

[tex]d^{2}[/tex]P/d∅ = 4i(2 cos2∅ - cos∅)

[tex]d^{2}[/tex]P/d∅ < 0

∅ = 60°

Therefore, Perimeter is maximum when ∅ = **60**°

To know more about **Trapezium**:

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HELP!!!

Ivan must choose a number between 55 and 101 that is a multiple of 4, 10, and 20. Write all the numbers that he could choose. If there is more than one number, separate them with commas.

### Answers

**Answer:**

60, 80, 100

**Step-by-step explanation:**

What you need to do in this case is find animver between 55 and 101 that has a first number as an even number and the second number as zero

**Answer:**

60,80,100

**Step-by-step explanation:**

I don't even know

^UVW & ^ UXY are shown below.

Which statement is true ?

### Answers

**Answer:**

**They have to be similar because careful inspection will show all of their angles (the two triangles) are equal. **

**One can start with the fact that the two triangles have a common angle.**

**CAll it x.**

**x * 40 + q = 180**

**x + 50 + r = 180**

**q and r must equal 50 and 40 to satisfy the sum of the interior angles must sum to 180.**

There are 24 four-digit whole numbers that use each of the four digits 2, 4, 5 and 7 exactly once. Only one of these four-digit numbers is a multiple of another one. Which of the following is it?

O 5724 O 7245 O 7254 O 7425

O 7542

### Answers

The **average **four-digit number 7254 is the only one that is a multiple of another one, as it is composed of the digits 2, 4, 5 and 7 used **exactly **once.

To find the four-digit number that is a multiple of another one using the digits 2, 4, 5 and 7, we can list all the possible **combinations **of these digits:

2457, 2475, 2547, 2574, 2745, 2754, 4257, 4275, 4527, 4572, 4725, 4752, 5247, 5274, 5427, 5472, 5724, 5742, 7245, 7254, 7425, 7452, 7524, 7542. as it is **composed **of the digits 2, 4, 5 and 7 used exactly once.

Next, we can check to see which of these **numbers **is a multiple of another one. 7254 is the only one that is a multiple of another one, as it can be **divided **by 2, 4, 5 and 7. Therefore, the answer is 7254.

Learn more about **average **here

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−4≤−2(y−1)<2

Step 2 of 2 : Graph the solution set.

### Answers

**Answer:**

draw a line between an empty point at 0 and a filled point at 3

**Step-by-step explanation:**

To graph this inequality we first want to isolate the y variable to make it a bit easier to deal with. This is a **compound inequality** and when isolating the y variable instead of just doing an operation on both sides, we do it to all sides which follows the same principle of maintaining equality.

We start with the original inequality:

[tex]-4 \le -2(y-1) < 2[/tex]

From here we divide by -2 on all sides, but since we're dividing by a negative we would flip the way the inequality is pointing so we get:

[tex]2\ge y-1 > -1[/tex]

From here we add 1 to all sides.

[tex]3 \ge y > 0[/tex]

Although generally we would write this as:

[tex]0 < y \le 3[/tex]

Now to graph this we would draw a **hole** on the number line at the point zero, and a **filled point** on the number line at 3, since 3 is included (since less than **or equal to 3)** and then just connect the two points. I'll include an image that demonstrates this.

NO LINKS!! Please help me with this Domain and Range

### Answers

**Answer:**

Domain: (-∞, ∞)

Range: [2, ∞)

Input: (f) = 2

Output: f(1) = 3

**Step-by-step explanation:**

Domain

The **domain **is the set of all possible** input values** (x-values).

There are **arrows **at both **endpoints **of the graphed continuous line, indicating that the line **continues indefinitely** in those directions.

Therefore, the **domain **of the relation is **unrestricted**:

Domain: (-∞, ∞)

Range

The **range **is the set of all possible **output values** (y-values).

Assuming that each square is 1 unit, from inspection of the graph, the **minimum y-value** is **y = 2**.

The **arrow** at the **endpoint **in **quadrant I** indicates that the line **continues horizontally** at y = 2.

The **arrow **at the **endpoint **in **quadrant II** indicates that the line **continues indefinitely **towards y = ∞.

Therefore, the **range **of the relation is **restricted**:

Range: [2, ∞)

Input

To find the value of f(4), find x = 4 and trace up to the line then read the **y-value** at that point. Therefore:

f(4) = 2

Output

To find the x-value when y = 3, find y = 3 and trace horizontally to the line then read the **x-value** at that point. Therefore:

f(1) = 3