Mathematics College

NO LINKS!! Please help me with these graphs. Part 4

Answers

Answer 1

Answer:

1. 17.5 units²

2. 16 units²

Step-by-step explanation:

Question 1

Given vertices of ΔABC:

A = (-3, 2)B = (4, 2)C = (4, -3)

Plot the vertices on the given graph paper and join with line segments to create the triangle.

As point B and C share the same x-coordinate, and points A and B share the same y-coordinate, ΔABC is a right triangle with base AB and height BC.

[tex]\begin{aligned}\textsf{Area of a triangle} & = \sf \dfrac{1}{2} \times base \times height\\\implies \textsf{Area of $\triangle$ ABC} & = \sf \dfrac{1}{2} \times AB \times BC\\& = \sf \dfrac{1}{2} \times 7 \times 5\\& = \sf \dfrac{35}{2}\\& = \sf 17.5 \:\:units^2\end{aligned}[/tex]

Question 2

Given vertices of rectangle WXYZ:

W = (0, 0)X = (2, 2)Y = (6, -2)Z = (4, -4)

Plot the vertices on the given graph paper and join with line segments to create the rectangle.

The area of a rectangle is found by multiplying the length by the width. To find the area of rectangle WXYZ, find the length (WZ or XY) and the width (WX or ZY) using the distance formula, then multiply them.

Distance between two points

[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

[tex]\textsf{where $(x_1,y_1)$ and $(x_2,y_2)$ are the two points}.[/tex]

[tex]\begin{aligned}WZ & =\sqrt{(x_Z-x_W)^2+(y_Z-y_W)^2}\\& =\sqrt{(4-0)^2+(-4-0)^2}\\& =\sqrt{(4)^2+(-4)^2}\\& =\sqrt{16+16}\\& =\sqrt{32}\sf \:\:units\\\end{aligned}[/tex]

[tex]\begin{aligned}WX & =\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\\& =\sqrt{(x_X-x_W)^2+(y_X-y_W)^2}\\& =\sqrt{(2-0)^2+(2-0)^2}\\& =\sqrt{(2)^2+(2)^2}\\& =\sqrt{4+4}\\& =\sqrt{8}\sf \:\:units\end{aligned}[/tex]

[tex]\begin{aligned}\textsf{Area $WXYZ$} & = WZ \times WX\\& = \sqrt{32} \times \sqrt{8}\\& = \sqrt{32 \cdot 8}\\& = \sqrt{256}\\& = 16\sf \:\:units^2\end{aligned}[/tex]

Related Questions

A water faucet leaked 3 2/6 liters of water every 3/5 of an hour. It leaked at a rate of how many liters per hour?

Answers

Our water faucet leaked 3 2/6 liters of water every 3/5 of a hour.
We are to find the rate in liter per hour at which the water faucet leaked.

First, use the number of liters the water faucet leaked in 3/5 of a hour.

This is 3 2/6 = 20/6

Therefore, the number of liters of water faucet leaked in 1 hour is

(20/6) / (3/5)

Before we solve this, we should simplify,

20/6 can be simplified to 10/3

3/5 cannot be simplified

Then, we should modify our problem to use reciprocation instead of a complex fraction,

(10 • 5) / (3 • 3)

This equals 50/9

Now, solve 50/9 for 5.555555555556

This rounds to 5.6

Thus, the required rate at which the water faucet leaked is 5.6 liters per hour.

What is the slope of the line that passes through the points (2,-6) and (6,-12)
Write your answer in simplest form.

Answers

Mathaway said -3/2
Because yes

Also I’m was dong this ?

Answer:

the answer is -3/2

Step-by-step explanation:

-12-(-6) = -6

6-2=4

-6/4 simplified is -3/2

At Elmo's, an old-fashioned barber shop in Melbourne, Florida, 66% of all customers get a haircut, 49% get a shave, and 40% get both.

a) What is the probability that a randomly selected person doesn't get a shave and doesn't get a haircut? Your answer should have at least 3 decimal places.

b) What is the probability that a randomly selected person gets a shave, given that they get a haircut? Your answer should have at least 3 decimal places.

Answers

a)0.250

b)0.606

In the given question , we observe that

at Elmo's an old-fashioned barber shop in Melbourne, Florida ,66% of all customers get a haircut ,49% get a save and 40% get both.

Probability is simply how likely something is to happen.

Whenever we are unsure about the outcome of an event, we can talk about the probabilities of certain outcomes—how likely they are. The analysis of events governed by probability is called statistics.

The best example for understanding probability is flipping a coin:

There are two possible outcomes—heads or tails.

Independent event:

If two events, A and B are independent then the joint probability is

P(A and B)=P(A∩B)=P(A)P(B)

For example, if two coins are flipped, then the chance of both being heads is 1/2*1/2=1/4

probabilities of different events are:

P(Haircut)=66%=66/100=0.66

P(Shave)=49%=49/100=0.49

P(both)=40%=40/100=0.40

a) we have to find the probability that a randomly selected person doesn't get a shave and doesn't get a haircut.

P(no haircut ∩ no shave)=1-P(haircut ∪ shave)

=1-[P(haircut)+P(shave)-P(both)]

=1-[0.66+0.49-0.40]

=1-0.75

=0.250

b) we have to find the probability that a randomly selected person gets a shave, given that they get a haircut.

P(Shave/Haircut)=P(Both)/P(Haircut)

=0.40/0.66

=0.606

Hence, final answer is

a) the probability that a randomly selected person doesn't get a shave and doesn't get a haircut=0.250

b)the probability that a randomly selected person gets a shave, given that they get a haircut=0.606

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Easton broke a cell sample into 8 batches, each weighing 3.9 x 10^-5 grams. How
much did the original sample weigh? Use scientific notation to express your answer.

Answers

The weight of the original sample from which all eight batches which each weighed 3.9 × 10-⁵ are obtained as required in the task content is; 3.12 × 10-⁴.

What is the weight of the original sample from which the eight batches were obtained?

It follows from the task content that the weight of the original sample from which the eight batches were obtained be determined.

Hence, since each of the eight batches weighs;

3.9 × 10-⁵

Therefore, the weight of the original sample can be obtained as follows;

= 8 × 3.9 × 10-⁵

= 31.2 × 10-⁵.

However, when the weight is expressed in scientific notation, the weight of the original sample is;

3.12 × 10-⁴.

Ultimately, The weight of the original sample from which all eight batches which each weighed 3.9 × 10-⁵ are obtained as required in the task content is; 3.12 × 10-⁴.

Answers

The standard deviation of both sets of data is the same, at 3.67,and adding the same constant c to each data value results in the standard deviation remaining the same.

Define Standard deviation?

In statistics, the standard deviation is a measure of the amount of variation or dispersion of a set of values. A low standard deviation indicates that the values tend to be close to the mean of the set, while a high standard deviation indicates that the values are spread out over a wider range.

We have a data set:

14, 12, 16, 8, 6

As we know the standard deviation formula is :

σ = √[∑(xi-X)/n]

σ = population standard deviation

Here ,

xi = value from the data set

X = mean of the data set

n = number of observation in data set.

X = (14+12+16+8+6)/5

X = 56/5

Where, n = 5

After calculating the standard deviation will be:

σ = 11.2

Add 8 to each data value to get the new data set 14, 12, 16, 8, 6.

We can write,

14+8=22

12+8=20

16+8=24

8+8=16

6+8=14

Then,

New data set is ⇒ 22,20,24,16,14

New standard deviation:

σ(new) = 11.2

Since both sets of data have the same standard deviation, we can conclude that adding a constant to each data value has no effect on the standard deviation.

Adding the same constant c to each data value results in the standard deviation remaining the same.

Thus, the standard deviation of both the data are the same which is 11.2 and adding the same constant c to each data value results in the standard deviation remaining the same.

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Suppose elementary students are asked their favorite color, and these are the
results:
28% chose blue
. 25% chose red
. 17% chose yellow
What percentage chose something other than red, blue, or yellow? (Each student
was only allowed to choose one favorite color.)

Answers

Answer:

30% of students chose something other

28+25+17=70
100-70 = 30
answer- 30 percent

Which of the terms best describes the following sequence?

13, 26, 39, 52, ...

Group of answer choices

Arithmetic

Geometric

Neither

Answers

Answer:

It's both an A. P and a G. P series.

Step-by-step explanation:

Let's prove using A.P with a common difference (d) = 13

Let's say we want to find the second number

a + (n - 1)d

a = 13, n = 4, d = 13

.: S2= 13 + ( 2- 1)13

S2= 13 + (1) 13

S2= 13 + 13 = 26

Let's show using a G. P series.

S2 = arⁿ—¹

S2 = 13 × 2²—¹

S2 = 13 × 2¹

S2 = 13 × 2 = 26

dogs to cats is 2:7 there are 90 animals how many are cats

Answers

[tex]cats = \frac{90}{2 + 7} \times 2 = 20 \: cats[/tex]

Information to answer the question.
This data represents the number of jumps in a row 10 students made during a jump-rope competition.
30, 36, 38, 45, 57, 60, 77, 86, 88, 88
What is the interquartile range? Enter the answer in the box.
Jumps

Answers

Answer: 48

So, to find out the interquartile range, we must first find the median of the lower and upper half of the data. So, 30, 36, 38, 45, 57 | 60, 77, 86, 88, 88 For the first half, the median is 38, and for the upper half, the median is 86. The median of the lower half is known as the quartile 1, and the median of the upper half is known as the quartile 3. The interquartile range is found by the difference between Q3 and Q1. So, 86 - 38 = 48.

There were 48 jumps.

Hops this helps :)

What is the inverse of conditional w=v

Answers

The inverse of the conditional statement w = v is the same as ~w = ~v

What is the inverse of a conditional statement?

This is the term that is used to refer to the statement that is written in mathematics as well as in logic that tells us the negation of the hypothesis that has been made in a statement and the conclusion that has been made as well of that statement.

For instance when we say that it is snowing, the opposite would be it is not snowing.

Hence the way that we would be able to write the statement that we have here would be same as ~w = ~v

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ABCD is a quadrilateral

Answers

A) 6x + 90 = 360
360 - 90= 270
270/6 = 45
x = 45

B) Lines AD and BC are not parallel
lines as they will eventually meet.

For the function
f
(
x
)
=
−
2
x
+
4
, evaluate and simplify the difference quotient.

Answers

the difference quotient for the given function is 2.

How to evaluate the difference quotient?

For any function f(x), we define the difference quotient as:

( f(x + h) - f(x))/h

And we take the limit as h tends to zero.

Here our function is:

f(x) = 2x + 4

Replacing it in the difference quotient we get:

(2*(x + h) + 4 - 2x - 4)/h = ( 2x + 2h + 4 - 2x - 4)/h = 2h/h = 2

So we conclude that the difference quotient for the given function is 2.

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James and Bethany Morrison are celebrating their 10th anniversary by having a reception at a local reception hall. They have budgeted $2,000 for their reception. If the reception hall charges a $100 cleanup fee plus $37 per person, find the greatest number of people that they may invite and still stay within their budget.

Answers

The greatest number of persons that would be invited is 51.

How to solve for the number of invitees

In order to get the greatest number of person that they would be inviting we would have this equation

100+37x ≤ 2,000

Where we have money budgeted to be 2000 dollars

cleanup fee = 100 dollars

Amount per person = 37 dollars

Then we would have

100+37x ≤ 2,000

37x ≤ 2000 - 100

37x ≤ 1900

we have to divide through by 37

37/37 = 1900 / 37

x = 51.3

Hence we would say that the greatest number of persons that would be invited is 51.

Answers

Answer:

Step-by-step explanation:

you just add all of them together

I believe it should be -2

Amanda and her friend worked together selling lemonade. They eamed x dollars. After splitting the money evenly between the two of them, they each had $30.25. What is x?

Answers

X=60.5 because 30.25 is half of x meaning you need to multiply 30.25 by 2. Which gets you 60.5

Answer:

x = $60.50

Step-by-step explanation:

It’s $60.50 because there are 2 people so u multiply $30.25 by 2 and you get $60.50

3.5 ft
3
6 ft
21. Hot Tub The inside of a circular hot tub is lined
with 1-inch by 1-inch tiles.
a. Explain how to estimate the number of tiles
needed for the hot tub.
b. The hot tub is 3.5 feet deep and has a diameter
of 6 feet. What is the minimum number of tiles
needed? (The formula for the circumference of
a circle is C= md.)

Answers

Answer: ?

comfusing

Step-by-step explanation:

Joe needs to make a total of 20 deliveries this week. So far he has completed 19 of them. What percentage of his total deliveries has Joe completed?

Answers

Answer:

He has completed 95% of deliveries

Step-by-step explanation:

What is n?
…………………..

Answers

Answer:

n=25

Step-by-step explanation:

5n-2+2n+7=180

combine like terms

7n+5=180

subtract 5 on both sides

7n=175

divide 7 on both sides

n= 25

A scientist studies a pond and finds that it has 18 fish and 24 turtles. What is the ratio of turtles to fish in the pond? Responses 4:34:3 3:43:4 7:47:4 4:7

Answers

Answer:

4:3

Step-by-step explanation:

They list first first but then ask for turtles to fish.

[tex]\frac{24}{18}[/tex] Divide the top and the bottom by 6 to get [tex]\frac{4}{3}[/tex] or 4:3

Can someone help me on this question? It's due tomorrow :(

Answers

Answer: option 1

Step-by-step explanation:

A company reports that 2000 sem electronics parts where found defective. if this represents 5% of the total shipments how many of these parts were shipped?

Answers

The company shipped altogether 40,000 sem electronic parts. Out of which 2000 parts were reported as defective.

Given, we know that 2000 electronic parts we declared as defective.

from the question, the defective parts represented 5% of the total shipments.

let the total parts be 'x'.

therefore, 5% of total parts = 2000

⇒ 5% of x = 2000

⇒ 5/100 × x = 2000

⇒ 5x/100 = 2000

⇒ 5x = 200000

⇒ x = 200000/5

⇒ x = 40,000

total parts shipped = 40,000

hence we get the total electronic which were shipped as 40,000.

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Please Help I’m struggling

Answers

The inequality for the given statement is 0<n≤8 and the solution set the inequality -8 ≤ w < 2 are w=-8, w=-5 and w=0.

The given inequality is -8 ≤ w < 2.

What is the solution set of inequality?

The solution set of inequality is the set of all solutions. Typically an inequality has infinitely many solutions and the solution set is easily described using interval notation.

a) The solution set the inequality -8 ≤ w < 2 is {-8, -7, -6, -5, -4, -3, -2, -1, 0, 1}

So, the solution sets from the options are w=-8, w=-5 and w=0.

b) The given equation is "a number n is greater than 0, and less than or equal to 8"

The inequality for the given statement is 0<n≤8.

Therefore, the inequality for the given statement is 0<n≤8 and the solution set the inequality -8 ≤ w < 2 are w=-8, w=-5 and w=0.

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Which is the graph of the equation y- 1 = 2/3(x - 3) ?

Answers

Step-by-step explanation:

To graph an equation using the slope and y-intercept, 1) Write the equation in the form y = mx + b to find the slope m and the y-intercept (0, b). 2) Next, plot the y-intercept. 3) From the y-intercept, move up or down and left or right, depending on whether the slope is positive or negative.

Divide 64.5 by 0.015 leaving your answer in a standard form

Answers

Answer:

4300

Step-by-step explanation:

A colony of bacteria doubles in population every hour. Approximately how many hours will it take until the colony is 32
size?

Answers

Answer:23 hours

Step-by-step explanation:23 hours

Solve 9x-2y = 15 for y.
y= ?
(Use integers or fractions for any numbers in the expression.)

Answers

Answer:

[tex]\frac92x - \frac{15}2 = y[/tex]

Step-by-step explanation:

[tex]9x - 2y = 15 \text{ / Add 2y} \\9x - 2y + 2y = 15 + 2y \\\to 9x = 15 + 2y \text{ / Subtract 15} \\9x - 15 = 15 + 2y - 15 \\\to 9x - 15 = 2y \text{ / Divide by 2} \\\frac{9x - 15}2 = \frac{2y}2 \\ \\\frac92x - \frac{15}2 = y[/tex]

.
A family wants to fence in a rectangular area for a garden. One side of the garden will
border their house and will not be fenced. Find the dimensions of the garden with greatest area that can be enclosed with 64 ft of fencing.
A) 16 ft by 16 ft
B) 32 ft by 32 ft
OC) 8 ft by 8 ft
OD) 16 ft by 32 ft

Answers

I think it is c but I’m not sure

Write an equation for the transformation of y=x
vertical compression by a factor of 1/11

Answers

The equation which results from the transformation of the equation given; y = x in the task content is; y = (1/11)x.

What is the resulting equation for the transformation given in the task content?

It follows from the task content that the resulting equation from the transformation of the graph of y =x after a vertical compression by a factor of 1/11 as given in the task content is to be determined.

On this note, since the compression is vertical, the resulting vertical component is; (1/11)• y.

Hence, the resulting graph upon compression is; (1/11)• y.

Ultimately, the resulting graph upon the vertical compression is; y = (1/11) x.

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Mr. Wolfe wrote a number on the board in expanded form.

He asked his math students to write the number in standard or word form. Some students and their answers are shown.

Belen: 4.096
Kara: four and sixty-nine thousandths
Liam: 4.609
Sam: four and six hundred nine thousandths
Which students wrote the number correctly?

A.
Belen and Sam

B.
Kara and Belen

C.
Kara and Liam

D.
Liam and Sam

Answers

Liam and Sam write the correct number.

Option D is true.

What is Expanded form of a number?

The splitting of numbers based on the place value is called Expanded form of a number.

The number is given as;

4×1 + 6 × 1/10 + 9 × 1/1000

Now, The number is written in standard form as;

⇒ 4×1 + 6 × 1/10 + 9 × 1/1000

⇒ 4 + 0.6 + 0.009

⇒ 4.609

Then write the number in word form,

⇒ 4.609 = Four and six hundred nine thousandths.

So, Liam and Sam write the correct number.

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Solve and classify the given system of linear equations. -9x+2y=-4. -x+4y=-2

Answers

The solution to the system is x = 6/17 and y = -7/17

What are linear equations?

Linear equations are equations that have constant average rates of change. Note that the constant average rates of change can also be regarded as the slope or the gradient

How to determine the solution to the system?

A system of linear equations is a collection of at least two linear equations.

In this case, the system of equations is given as

-9x+2y=-4

-x+4y=-2

Multiply -9x+2y=-4 by 2

So, we have

-18x + 4y = -8

Subtract -18x + 4y = -8 from the equation -x+4y=-2

-x + 18x + 4y - 4y = -2 + 8

Evaluate the like terms

17x = 6

Divide both sides of the equation by 17

x = 6/17

Substitute x = 6/17 in -x + 4y = -2

-6/17 + 4y = -2

This gives

4y = -2 + 6/17

Evaluate

4y = -28/17

Divide by 4

y = -7/17

Hence. the solution to the system is x = 6/17 and y = -7/17

NO LINKS!! Please help me with these graphs. Part 4​

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NO LINKS!! Please help me with these graphs. Part 4