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.

The **probability **that a **randomly selected person **doesn't get a **shave **and doesn't get a **haircut **is 0.250.

The **probability **that a randomly selected person gets a **shave**, given that they get a **haircut **is 0.606.

The **probability **that a person selected at **random **would not get a **shave **or a **haircut **can be found as:

= 1 - (Prob. of haircut + Prob. of shave - Prob. of both)

= 1 - (0.66 + 0.49 - .40)

= 0.250

The **probability **that a random person would get a **shave **given they have gotten a **haircut **is:

= Probability of both / Probability of getting a haircut

= 0.40 / 0.66

= 0.606

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When a constant force acts upon an object, the acceleration of the object varies Inversely with its mass. When a certain constant force acts upon an object with

mass 7 kg, the acceleration of the object is 10 m/s². If the same force acts upon another object whose mass is 5 kg, what is this object's acceleration?

The **acceleration** of the** object **is found as 14 m/s².

Newton's second law states that acceleration of an object is determined by two variables: the net force acting on it and its mass.

The acceleration of the body isThe formula for the Newton's second law is;

**F = ma**

F = acting force in Newton

m = mass of the body in Kg.

a is the acceleration in m/s².

The mass of 7 kg accelerates with 10m/s².

Force acting on it is;

F = ma

F = 7×10

F = 10 N.

The same **force** is acting on the body of mass 5 kg.

F = ma

a = F/m

a = 70/5

a = 14 m/s².

Therefore, the** acceleration **of the body is found as 14 m/s².

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SOS, is for today!!!!

Given that the total length of the **piece **of **steel **is 25in, the **numerical lengths **of the **first**, **second **and **third piece **of the **steel **are **3in**, **6in **and **16in **respectively.

Given the data in the question, let x represent the length of the first piece.

Length of first piece = xLength of second piece = 2xLength of third piece = 5x + 1Total length of the steel = 25 inTo determine the **length **of **each piece**, we **equate **the **sum **of the **pieces **to the **total length **of the **steel **( 25in ).

x + 2x + ( 5x + 1 ) = 25

3x + 5x + 1 = 25

8x + 1 = 25

8x = 25 - 1

8x = 24

x = 24/8

**x = 3**

Hence,

**Length **of **first piece **= x = **3 inch**

**Length **of **second piece **= 2x = 2(3) = **6 inch**

**Length **of **third piece **= 5x + 1 = 5(3) + 1 = 15 + 1 = **16 inch**

Given that the total length of the **piece **of **steel **is 25in, the **numerical lengths **of the **first**, **second **and **third piece **of the **steel **are **3in**, **6in **and **16in **respectively.

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Mathematical connection A lighthouse casts a revolving beam of light as far as the pier

The light's coverage **area** is given mathematically as i.e. Area=[tex]\pi d^{2}[/tex]

Given that a lighthouse casts a revolving beam of light as far as they peir and asked the **area** is covered.

The revolving beam of light covers the whole space i.e entirely 360°

I.e. it forms a **circle**-like region

**Area** of **circle** = [tex]\pi r^{2}[/tex]{ where r is the radius of **circle**}

Let's assume the distance traveled by light as "d"

as it forms a **circular** region, it forms a **circle** of radius "d"

Mathematical connection i.e. **area** of the region

⇒**area** of circular region=[tex]\pi d^{2}[/tex] {where d is the radius of region}

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A couch with a list price of $2200 will be discounted 35 % at the time of purchase. What is the sale price before taxes?

The **sale price** before taxes and after discount is $1,430.

Given that A couch with a list price of $2200 will be discounted 35 % at the time of purchase and asked to find the **sale price** before taxes.

The original cost of the couch=$2200

The discount percentage=35 %

I.e. 35 % of $2200 is $770

The discount given to the customer will be 35% i.e. $770

⇒The** selling price** will be $770 less than the original cost price.

As a result, the **selling price** will be =$2200-$770

The **Selling price** of the couch is $1,430

Therefore,The **sale price** before taxes and after discount is $1,430.

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How many centimeters are in 2 miles?

**Answer:**

321,800 cm. (Rounded)

**Step-by-step explanation:**

2 × 160,900 = 321,800

There are 160,900 centimeters in one mile, so you must multiply that by 2 and round.

Please help, I don’t know how to solve this!

Carry the 4 and to the exponent of 2

Multiply the rational expressions

3(x-4)² 5(x + 4)5

8(x+4)³ 3(x-4)5

1) 75x^3-300x^2-1200x+4800

Ig

Ig

A company asks an investor for an investment of $800,000 in exchange for 15% equity in the business. What is the implied valuation of the business?

If a company asks an investor for an investment of $800,000 in exchange for 15% **equity **in the business. The implied **valuation **of the business is: $4,533,333.

First step is to calculate the **equity **valuation

Using this formula

Equity valuation=Amount invested/Equity rate

Let plug in the formula

Equity valuation=$800,000/.15

Equity valuation=$5,333,333

Second step is to calculate the **implied** valuation

Implied valuation=Equity valuation-Amount invested

Let plug in the formula

Implied valuation=$5,333,333-$800,000

Implied valuation=$4,533,333

Therefore If a company asks an investor for an investment of $800,000 in exchange for 15% **equity **in the business. The implied **valuation **of the business is: $4,533,333.

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Question 6 (10 points)

=) Listen

The ratio of outdoor outdoor swimmers to indoor swimmers at the recreation center

is 3:2. If the center has 55 swimmers altogether, how many of them are indoor

swimmers?

22

44

none

33

**Answer:**

22

**Step-by-step explanation:**

The ratio tells us 2/5 of the swimmers are indoor swimmers.

55(2/5)=22

li has a jar full of marbles. In the jar there are 15bblue marbles, 10 red marbles and 16 purple marbles. a. She selects a marble at random from the jar. She does not replace the marble. She selects a second marble from the jar. What is the probability that both marbles are red? What is the correct interpretation of this question?

The **probability **that both marbles are **red **will be 0.055.

Its basic premise is that something will almost certainly **happen**. The percentage of **favorable **events to the **total **number of occurrences. The probability is given as,

P = (Favorable event) / (Total event)

A jar full of **marbles **is kept by Li. There are 16 **purple **marbles, 10 **red **marbles, and 15 **blue **marbles in the jar. A stone is chosen at **random **by her from the jar. She leaves the marble alone. She **takes **another stone **out **of the jar.

The **total **number of event = 16 + 10 + 15 = 41

Then the probability of both marble should be **red **will be given as,

P = (10 / 41) x (9 / 40)

P = 0.055

Thus, the probability that **both **marbles are **red **will be 0.055.

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Determine if the following radical expression is a real number. If it is, you are to evaluate the expression.

3√-27

Answer

Selecting an option will display any text boxes needed to complete your answer.

Real Number

O Not a Real Number

No Es Un Número Real

is 7 1/2 equal to 1/10, 1/5 or 4/5?

7y+2=3x-5 is the given equation. Finding the point that does not lie on the specified** line**, 7y+2=3x-5, is the next step.

To determine whether or not the point meets the provided equation, we will simply enter in the supplied point.

Check for (2,-1/7)

Connect it to 7y+2=3x–5.

7(-1/7)+2=3(2)-5

-1+2=6-5

**1=1**

Which is correct; as a result, this point is on the **line** 7y+2=3x-5.

Verify (3,-2/7)

Connect it to 7y+2=3x–5.

7(-2/7)+2=3(3)-5

-2+2=09-5

1=4

Which is False; as a result, the supplied line 7y+2=3x-5 does not include this point.

Connect it to 7y+2=3x–5.

7(-1)+2=3(0)-5

-7+2=0-5

-5=-5

Which is correct; as a result, this point is on the **line **7y+2=3x-5.

Verify (1, -4, 7)

Connect it to 7y+2=3x–5.

7(-4/7)+2=3(1)-5

-4+2=3-5

-2=**-2**

This is why I'm making this point

lies on the line 7y+2=3x-5 that is presented.

Verify (-1, -10/7)

Connect it to 7y+2=3x–5.

7(-10/7)+2=3(-1)-5

-10+2=-3-5

-8=**-8**

Which is correct; as a result, this point is on the line 7y+2=3x-5.

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Which characteristics are appropriate for the Brand of camcorder? Choose all that apply

Question options:

O Nominal

O Scale

O String

O Numeric

**Answer:**

numeric

**Step-by-step explanation:**

what is 4.32 x 10^4 written in standard form

**Answer:**

43,200

**Step-by-step explanation:**

4.32 x 10∧4

10 x 10 x 10 x 10

4.32 x 10000

43,200

If f(x) = -2x² + 4 and g(x) = 3x - 3, find f (4) + g(-6).

**Answer:**

(-2[tex]x^{2}[/tex]+3x+1)

**Step-by-step explanation:**

f(x) = -2x² + 4 g(x) = 3x - 3 find f (4) + g(-6).

f(x)+g(x)

(-2[tex]x^{2}[/tex]+4) +(3x-3)

(-2[tex]x^{2}[/tex]+3x+4-3)

(-2[tex]x^{2}[/tex]+3x+1)

1 + 1 = 2

this is the answer to 1 plus 1

IT'S NOT 3???????????????

Answer:no it 11

Step-by-step explanation:

1+1 = 11

I’m kidding btw

A group of exchange students from Japan went to a convalescent home to sing songs for the seniors and to demonstrate origami. Groups of students and seniors sat together at tables so the students could teach the seniors to fold some origami figures. As it turned out, at each table there was either 1 student and 3 seniors, or 2 students and 4 seniors. There were 23 students and 61 seniors in all. How many tables were being used?

**Answer:**

19 tables

**Step-by-step explanation:**

Let X represent the number of tables that have 1 student and 3 seniors

Let Y represent the number of tables that have 2 student2 and 4 seniors

Therefore number students total

1X + 2Y =23 (1)

Number of seniors total

3X + 4Y = 61 (2)

Multiply equation (1) by 2 giving

2X + 4Y = 46 (3)

Subtract (3) from (2)

3X + 4Y - (2X+4y) = 61-46

3X + 4Y - 2X -4Y = 15

3X-2X = 15

X = 15

Plugging this value into equation (1) gives

1(15) + 2Y = 23

15 + 2Y = 23

Subtract 15 from both sides

2Y = 23 - 15

2Y = 8

Divide by 2 both sides

Y = 4

Thus total number of tables used = X +Y = 15+4 = **19**

A 20-year U.S. Treasury bond has a 3.50 percent interest rate, while a same maturity corporate bond has a 5.25 percent interest rate. Real interest rates and inflation rate expectations would be the same for the two bonds. If a default risk premium of 1.50 percentage points is estimated for the corporate bond, determine the liquidity premium for the corporate bond.

The **liquidity** premium for the corporate bond is 0.25%.

Any **additional** compensation needed to stimulate investment in assets that cannot be quickly and effectively converted into cash at fair **market** value is known as a liquidity premium. For instance, due to its relative **illiquidity**, a long-term bond will have a higher interest rate than a short-term bond.

Liquidity premium for corporate **bond** will be:

= 5.25 - 3.5 - 1.5

= Interest - Treasury - Default risk

= 0.25%.

Therefore, the **liquidity** is 1.25%.

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describe a sequence of transformation that takes abcd to a'b'c'd'

The **quadrilateral** A'B'C'D' is the result of reflecting and translating the **quadrilateral** ABCD.

What kind of rigid transformations were done to transform ABCD to A'B'C'D'?

In this problem we find a representation of a **quadrilateral** and its **image** on a **Cartesian plane**. That **image** is the result of the following **rigid transformations**, that is, **transformations** applied on **geometric loci** such that **Euclidean distance** is conserved at every **point** of the **locus**.

After a careful inspection, we find that the following two **rigid transformations** were done:

Now let is prove this steps:

**Given:** A(x, y) = (- 5, - 7), B(x, y) = (- 5, - 2), C(x, y) = (- 3, - 4), D(x, y) = (- 3, - 7)

**Reflection:**

A''(x, y) = (- 5, - 7) + (0, 14)

A''(x, y) = (- 5, 7)

B''(x, y) = (- 5, - 2) + (0, 4)

B''(x, y) = (- 5, 2)

C''(x, y) = (- 3, - 4) + (0, 8)

C''(x, y) = (- 3, 4)

D''(x, y) = (- 3, - 7) + (0, 14)

D''(x, y) = (- 3, 7)

**Translation**

A'(x, y) = (- 5, 7) + (7, 0)

A'(x, y) = (2, 7)

B'(x, y) = (- 5, 2) + (7, 0)

B'(x, y) = (2, 2)

C'(x, y) = (- 3, 4) + (7, 0)

C'(x, y) = (4, 4)

D'(x, y) = (- 3, 7) + (7, 0)

D'(x, y) = (4, 7)

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Determine the domain of the following graph

the domain of the following graph= [-5,10)

**Domain :**

The domain of a function is the set of its possible inputs, i.e., the set of input values where for which the function is defined. In the function machine metaphor, the domain is the set of objects that the machine will accept as inputs.

For example, when we use the **function notation** f: R→R, we mean that f is a function from the real numbers to the real numbers. In other words, the domain of f is the set of real numbers R (and its set of possible outputs or codomain is also the set of real numbers R).

To, identify the domain and range of functions by using graphs. Because the domain refers to the set of possible input values, the domain of a graph consists of all the input values shown on the

x-axis. The range is the set of possible output values, which are shown on the

y-axis. Keep in mind that if the graph continues beyond the portion of the graph we can see, the domain and range may be greater than the visible values.

We can observe that the horizontal extent of the graph is -5 to 10, so the domain of f is [-5,10)

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Help on this question please

the parameter!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

How many jelly beans are in a 2-liter jar? HELP ME PLEASE

1. The **number** of sample size 1 jelly beans in a 2-liter jar is 645.

2. The **number** of sample size 2 jelly beans in a 2-liter jar is 640.

3. The **number** of sample size 3 jelly beans in a 2-liter jar is 637.

A **mathematical operation** is an expression involving the use of mathematical operands and operators to compute values.

**Mathematical operations** use variables, **numbers**, and operators (addition, subtraction, division, and multiplication).

Total weight = 1,150g

Weight of the jar = 440g

The total weight of the jelly beans = 710g (1,150 - 440)

Sample Size 1: the number of jelly beans = 645 (710/22.0 x 20)

Sample Size 2: the number of jelly beans = 640 (710/22.2 x 20)

Sample Size 3: the number of jelly beans = 637 (710/22.3 x 20)

Thus, the **number** of jelly beans in a 2-liter jar depends on the sample size of the jelly beans.

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A rectangular garden is 6 ft longer than it is wide. Its area is 667 ft2. What are its dimensions?

The dimensions of the **rectangular **garden are 29 feet by 23 feet .

A rectangle is a quadrilateral with parallel opposite sides and equal angles. There are a lot of rectangular objects all around us. Any rectangular form's two defining characteristics are its length and width. A rectangle's longer and shorter sides are its width and length, respectively.

The area of a **rectangle **is given by length × width

Now the given area of the **rectangle **is 667 ft² .

Let the width of the **rectangle **is x ft. Therefore length = x + 6

Now area of the **rectangle **is x (x+6) = x² + 6 x

Therefore x² + 6 x = 667

or, x² + 6 x - 667 = 0

or, (x-23)(x+29) = 0

Either x = 23 or x = -29(not possible)

Hence the width is 23 feet.

Length = 23 + 6 = 29 feet

Therefore the dimensions of the **rectangle **are 29 feet by 23 feet .

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HELP PLEASE I WILL GIVE BRAINLYEST! ALGEBRA 1 HW

Figure 2 is the answer bc it is

Evaluate Log2 11 x Log6 2

The **logarithmic expression **is equal to:

Log₂(11)*log₆(2) = 1.34

Here we have the** logarithmic expression**:

Log₂(11)*log₆(2)

Now, remember that we can rewrite:

Logₐ(b) = Ln(b)/Ln(a)

Using that we can rewrite the **expression**:

Log₂(11)*log₆(2) = (Ln(11)/Ln(2))*(Ln(2)/Ln(6)) = Ln(11)/Ln(6)

Now using a calculator you can find these two** natural logarithms:**

Ln(11)/Ln(6) = 1.34

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????????????????????

**Answer: **120 minutes, 105 km, proportional

**Step-by-step explanation:**

90 km/hr

180 km * 1 hr/90 km=

180 km/90 km * 1 hr=** **

2 hours=**120 minutes**

1 hour=60 minutes

70/60=x/90

7/6=x/90

7*90/6=x

x=7*15

**x=105 km**

How is subtracting integers related to adding integers

**Integer** addition is the addition of integers with the same signs, whereas integer subtraction is the addition of integers with the opposite signs.

**Are there any consistent rules for adding and subtracting integers?**

**What in math is an integer?**

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the function f multiplies it’s input by 2 and then subtracts 17 to produce its output. What is the symbolic representation of this operation

**Answer:**

f(x)= 2x-17

**Step-by-step explanation:**

Let, input be x,

Multiplying input by 2: 2x

then subtracting it by 17: 2x-17

Therefore, Symbolic representation required is : f(x)= 2x-17

The symbolic representation of the **function **defined is f(x) = 2x-17

A **function **is a relation from a set of inputs to a set of possible **outputs **where each input is related to exactly one **output**.

Given that, the **function **f multiplies it’s **input **by 2 and then subtracts 17 to produce its **output**. we need to express the operation into symbolic representation.

Let the **input **be x, then the **output **will be the value of f(x).

Therefore, it is given, the input is multiplied by 2, that mean,

f(x) = 2x

Then 17 is **subtracted **from it, that will give,

f(x) = 2x-17

Hence, the symbolic representation of the given operation is f(x) = 2x-17

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The average temperature in the mountains is 61° in April. The average temperature in that same spot is −2° in December. Determine how much warmer this location is in April than in December, and determine which temperature is the farthest away from 0°.

**Answer: 59 degrees warmer and -2 is farther away form 0 than 61 degrees.**

**Step-by-step explanation: 59+2=61 so, that's how I got the answer. The rest is really easy.**

The absolute value of 61°F is greater than the absolute value of 2°F. Therefore, the **temperature** of 61°F in April is the farthest away from 0°F.

To determine how much warmer the location is in April than in December, you can calculate the difference between the two temperatures:

Temperature difference = April temperature - December temperature

Temperature difference = 61°F - (-2°F)

Temperature difference = 61°F + 2°F

Temperature **difference** = 63°F

So, the location is 63 degrees **Fahrenheit** warmer in April than in December.

To determine which temperature is the farthest away from 0°F, you can calculate the absolute value of the difference between each temperature and 0°F and then compare them:

Absolute value of (61°F - 0°F) = 61°F

Absolute value of (-2°F - 0°F) = 2°F

The absolute value of 61°F is greater than the absolute value of 2°F. Therefore, the temperature of 61°F in April is the farthest away from 0°F.

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Which situation describes a non-proportional relationship?

The circumference of a circle with a radius of x units can be represented by y = 2zx.

The perimeter of an equilateral triangle with a side length of x units can be represented by y = 3x.

The total surface area of a cylinder with a radius of 1 unit and height of x units can be represented by

y = 2x + 2.

The radius of a circle with a diameter of x units can be represented by y=x.

Situation of** non- proportional **relationship :

The circumference of a circle with a radius of **x** units can be represented by = 2nx.

The perimeter of an equilateral triangle with a side length of x units can be represented by y = 3x

The total surface area of a cylinder with a radius of 1 unit and height of x units can be represented by y = 2xx + 2x

The radius of a circle with a diameter of x units can be represented by y = [tex]\frac{1}{2}x[/tex]

a **proportional** relationship is a relationship between two quantities in which the ratio of one quantity to the other quantity is constant. The graph of a proportional relationship is a line through the origin.

When ratios between quantities are not constant, a relationship may be linear but not proportional and the graph does not pass through the origin.

The graph shows the sales tax charged based

on the amount spent at a video game store in

a particular city. Does the graph show a linear

relationship? Is the relationship proportional

or nonproportional?

The graph shows a linear **proportional**

relationship because it is a line that contains

the origin.

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