The estimate for the **mean** book **thickness** is **3.2 mm.**

**What is mean?**

In **arithmetic**, **mean** is the sum of all the added values of all the data in a set divided by the number of data in the set.

To find the mean book thickness, we can use the formula for the mean (also known as the average):

mean = (sum of all data points) / (number of data points)

Since we don't have the exact thickness of each book, but rather intervals of thickness and the number of books in each interval, we can use a **weighted mean** to estimate the **mean** **thickness**.

Here is the calculation:

First, we'll find the midpoint of each **interval**:

Interval 1: [0, 2] -> midpoint: x1 = 1

Interval 2: [2, 4] -> midpoint: x2 = 3

Interval 3: [4, 6] -> midpoint: x3 = 5

Next, we'll find the weight of each interval by multiplying the midpoint by the **frequency**:

Interval 1: x1 * f1 = 1 * 5 = 5

Interval 2: x2 * f2 = 3 * 8 = 24

Interval 3: x3 * f3 = 5 * 7 = 35

Finally, we'll sum up the **w**eights and divide by the **total** **frequency** to find the weighted mean:

**Weighted mean **= (5 + 24 + 35) / (5 + 8 + 7) = 64 / 20 = 3.2

So, the estimate for the **mean **book thickness is 3.2 mm.

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Davis will plant seeds in row that are 3 feet apart. In each row he will plant seeds about 4 to 6 inches apart. Estimate the number of corn seeds Davis can plant in section 1

Davis** **can plant a total of about 1555 **corn seeds **in the section one.

**Davis **wants to **plant **in a row that are 3 ft apart each row, plant are about 4 to 6 inches apart from each other.

We have to find out that how many plant can be planted.** Section 1 **has 12 **columns **18 rows.

Each block formed by a **row **and column will have an area of 9 square feet. Each row will have a total of 86.4 seeds of corn seeds in it.

The total number of columns in the section 1 are 54. So, multiplying the number by 54 will get the total number of counts,

Total corn seeds = 86.4 x 54.3

= 1555 corns seeds.

So, a total of 1555 **corn seeds** can be planted.

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The cellular phone service for a business executive is $35 per month plus $0.40 per minute of phone use over 900 min. For a month in which the executive's cellular phone bill was $95.40, how many minutes did the executive use the phone?

**Answer: 151 minutes**

**Step-by-step explanation: **

95.40 - 35 =

60.40

60.40/.40 = 151

Find the roots of the equation

x² − 2(a² + b²)x + (a²-b²)² = 0

**Answer:**

We can solve the above mathematical problem with the following approach.

We know that (a²-b²) = (a + b) (a - b).

So the given equation can be written as:

helppppppppppppppppppppppppppp

**Answer: x = 6 (look at the image for the solution) **

**Step-by-step explanation:**

**Answer: the answer is 35 **

**Step-by-step explanation:**

find the pythageoran theorem of the thing and then solve

Draw one candy

from the bag.

Pink=10

Purple= 6

Blue= 4

If you replace the candy each time,

predict how many times a purple

candy will be chosen out of 80 draws.

[?] times

**Answer:**

24 times out of 80 draws

**Step-by-step explanation:**

The probability of choosing a purple candy is 6 out of 20 candies, or 6/20, which simplifies to 3/10 or 0.3.

If you make 80 draws and replace the candy each time, the number of purple candies selected can be estimated using the expected value formula:

Expected value = number of trials * probability of success

In this case, the expected value is 80 * 0.3 = 24.

So, it can be estimated that a purple candy will be chosen 24 times out of 80 draws.

Correct each of the following errors by circling the error, describing what is wrong, entering what should be there instead, and entering the correct answer.

1. (3x²)(-2x⁴)=3(-2)x²•⁴=6x⁸

2. 4a²•3a⁵=(4+3)a²+⁵=7a⁷

3. x⁶•x•x³=x⁶+³=x⁹

4. 3⁴•2³=6⁴+³

**Answer:The error in #1 is that it should read "3x²•(-2x⁴)=3•(-2)•x²⁴=6x⁸". The error in #2 is that it should read "4a²•3a⁵=4•a²•3•a⁵=12a⁷". The error in #3 is that it should read "x⁶•x³=x⁶•x³=x⁹". The error in #4 is that it should read "3⁴•2³=3⁴•2³=24".**

**Step-by-step explanation:**

easy

can someone help it’s due today

do the work by using the formula

a bakery sells blueberry muffins for 2.50 each. it costs c dollars to make each muttij the profit for selling m muffins is described by the expression below in the expression what is the meaning of (2.5-c)

**Answer:**

7.8

**Step-by-step explanation:**

explain the differences between the 3rd angle projection and the 1st angle projection in terms of the orthographic projection.

In **third**-**angle projection**, the view of a component is drawn next to where the view was taken. In **first**-**angle projection**, the view is drawn on the other end of the component, at the opposite end from where the view was taken.

First angle Protuberance is a system of creating a **2D **delineation of a **3D **object. It's substantially used in Europe and Asia and has not been officially used in Australia for numerous times. In Australia, third angle **protuberance **is the favored system of orthographic protuberance. Note the **symbol **for first angle **orthographic** protuberance

Third Angle Projection the Object is placed in the **Third Quadrant**. This means that the Vertical Aeroplane is in front of the object and the **Vertical Aeroplane** is above the object. These changes in the position of the views are the only difference between **protuberance** **styles**.

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4.21 game of dreidel. a dreidel is a four-sided spinning top with the hebrew letters nun, gimel, hei, and shin, one on each side. each side is equally likely to come up in a single spin of the dreidel. suppose you spin a dreidel three times. calculate the probability of getting

**The probability** of getting at least one nun in **three spins** of a dreidel is approximately 0.578

The probability is the ratio of number of **favorable outcomes** to the total number of outcomes

The probability of getting no nuns in a single spin is 3/4, since there are three **non-nun letters** (Gimel, Hei, Shin) and four total letters.

The probability of getting** **no nuns in three spins is then (3/4)^3, since the spins are** independent** and we can multiply probabilities of independent events.

So the probability of getting **at least one nun** in three spins is

= 1 - (3/4)^3

= 1 - 0.421875

= 0.578125

Therefore, the probability of getting at least one nun is 0.578

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The given question is incomplete, the complete question is:

A dreidel is a four-sided spinning top with the Hebrew letters nun, gimel, hei, and shin, one on each side. Each side is equally likely to come up in a single spin of the dreidel. Suppose you spin a dreidel three times. Calculate the probability of getting (a) at least one nun?

PLEASE HELP I HAVE 2 MINUTES

PLEASE THIS IS VERY EASY.

The **number **of **green **rugs is **more **than the number of purple** **rugs. Then the **amount **of blue rug will be 29/4 square units.

**Algebra **is the study of abstract symbols, while **logic **is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This **approach **is used to answer the problem **correctly **and completely.

Nina buys a new rug that matches **three colors **in her bedroom. The rug is a rectangle. There are **eight **squares on the rug. Four-eighths of the squares are green. **One**-**fourth **of the squares are purple.

The **amount **of **green **rug is given as,

⇒ 4/8

⇒ 1/2 square units

The **amount **of **purple **rug is given as,

⇒ 1/4 square units

The number of **green **rugs is **more **than the number of **purple **rugs.

The **amount **of blue rug is given as,

⇒ 8 - 1/4 - 4/8

⇒ (64 - 2 - 4) / 8

⇒ 29/4 square units

The **number **of green rugs is **more **than the number of **purple **rugs. Then the **amount **of blue rug will be 29/4 square units.

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Solve for n !

[tex] \large{ \gray{ \frak{3x+5= 4(n - 5) \frac{6}{3} }}}[/tex]

Thank You!

**Answer:**

n = (3/8)x+(45/8)

**Step-by-step explanation:**

3x+5 = 4(n-5)*(6/3)

Is this written correctly?

3x+5 = 4(n-5)*(6/3)

3x+5 = 8(n-5) [Simplify: {4*(6/3) = 8)]

3x+5 = 8n-40 [Expand the parentheses]

8n-40 = 3x+5 [Rearrange]

8n = 3x+5 + 40 [Rearrange]

8n = 3x+45 [Simplify]

n = (3x+45)/8 [Divide both sides by 8]

n = (3/8)x+(45/8) [Rearrange]

There are 423 athletes at the vollyball tournament another 9 teams were added with 6 athletes on each team

There are a total of 477 **athletes **after the 9 new teams with 6 athletes on each **team **were added.

If there were 423 athletes at the volleyball tournament and 9 teams with 6 athletes each were added, we can **calculate **the total number of athletes as follows:

Number of athletes at the tournament: 423

Number of athletes in each new team: 6

Number of new teams: 9

The total number of new athletes is the **product **of the number of new teams and the number of athletes in each new team:

Total number of new athletes = 9 x 6 = 54

To find the total number of athletes after the new teams were **added**, we add the number of athletes at the tournament to the total number of new athletes:

Total number of athletes = 423 + 54 = 477

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**Complete question** is:

There are 423 athletes at the volleyball tournament another 9 teams were added with 6 athletes on each team. How many total atheletes are present?

Graph the line that represents this equation:

3x - 4y = 8

Drawing Tools

Select

Point

Line

X

Click on a tool to begin drawing.

-10

-8

-6

-4

-2

10-

4

8

2

S

A

2

2

Delete

++

**Answer:**

**Step-by-step explanation:**

The Serenity and the Mystic are sail boats. The Serenity and the Mystic start at the same point and travel away from each other in opposite directions. The Serenity travels at 14 mph and the Mystic travels at 21 mph. How far apart will they be in 3 hours?

They will be 74 km **apart** after 2 hours.

**What is the relative speed of two moving objects?**

For two objects, the **relative speed** between them equals the change in distance between them divided by the change in time. If two bodies are going in **opposite directions**, their relative speed is equal to the sum of their individual speeds. If they are moving in the same direction, their relative speed is equal to the difference in their individual speeds.

Given here, the Serenity travels at 17 mph and the Mystic travels at 20 mph in the opposite direction .

therefore, the relative speed is sum of their speeds = 17 + 20 = 37 mph

After 2 hours the **distance** between them would be = 37 × 2 = 74 mph

Hence, they will be 74 km **apart** after 2 hours.

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The figure shows the size of a pool. 6 ft 4 ft 16 ft What is the volume of the pool? A. 60 ft³ B. 224 ft3³ 12 ft O C. 1728 ft³ D. 3136 ft³ 8 ft 14 ft h

The **volume **of the pool is **768 cubic feet**.

**What is the Volume?**

In **mathematics**, volume refers to the amount of space occupied by a **three-dimensional **object. It is a measure of the total amount of space enclosed within the boundaries of an object. The **volume **of an object is usually measured in cubic units, such as cubic meters **(m³),** cubic feet** (ft³)**, or cubic centimeters **(cm³)**.

To find the **volume **of the **pool**, we need to multiply its length, width, and depth. Looking at the figure, we see that the **length **of the **pool **is **16 ft,** the width is** 6 ft,** and the depth is **8 ft.**

So, the **volume **of the **pool **is:

V = length x width x depth = 16 ft x 6 ft x 8 ft = 768 cubic feet

Hence, the **volume **of the pool is **768 cubic feet**.

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the histogram below gives the length of service of members of the department of chemistry at a particular university. the classes, in years of service, are 0-4.9, 5-9.9, etc., and the vertical axis represents the number of faculty. (a) what percent of the department faculty have 5 or more years of service? (b) if a member of the department is chosen at random to serve on a university committee, what is the probability (in decimal form) that the chosen representative will have between 5 and 35 years of service? (c) what is the probability the representative above will have less than 5 years of service given that the person has less than 15 years of service?

a. The **percentage** of the department faculty have 5 or more years of service is 76%

b. Probability that a faculty member chosen at **random** has between 5 and 35 years of service is 0.4.

c. The **probability** the representative will have less than 5 years of service given that the person has less than 15 years of service is 0.7.

The histogram is used to estimate **probability** of a categorical variable or probability of frequency of a particular class interval, and there is no gap among the bars of the histogram.

(a) The per cent of the **department faculty **have 5 or more years of service is calculated as follows,

The number of department faculty have 5 or more years of service is 38 and total **frequency** 50, therefore the required probability is:

P(x > 5) = 38/50 = 0.76 = 76%

(b) The **probability** (in decimal form) of representative will have between 5 and 35 years of service is given as,

P(5 < X < 35) = 20/50 = 0.4 = 40%

(c) The probability the representative above will have less than 5 years of service given that the person has less than 15 years of **service** is calculated as follows,

P(X < 5 | X < 15) = 28/40 = 0.7

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For complete question, see the figure.

The length of a shadow of a building is 98 ft when the sun is 66° above the horizon. Find the height of the building. Round your answer to the nearest tenth.

000

000

66°

98

If the **length **of a shadow of a **building **is 98 ft when the **sun **is 66° above the horizon then the height of the building is, 267.7 ft.

An angle is a mathematical term, which we can define, when two straight **lines **or rays meet at a common **endpoint**. The common point is called the **vertex **of an angle. The word angle comes from a Latin word named ‘angulus,’.

Interior angles:- The inner angle made by the intersection of two polygonal sides.

Exterior angles:- The outer angle made by the intersection of two polygonal sides.

We can use the **tangent **function to solve for the height of the building.

tan(66°) = height of building / 98 ft

Solving for the height of the building,

we get:

**height **of building = 98 ft x tan(66°)

Using a calculator, the value of tan(66°) is approximately 2.73.

So,

height of building = 98 ft x 2.73

height of building = 267.74 ft

Rounding to the nearest tenth, the height of the building is approximately 267.7 ft.

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the mean cost for a pint of strawberries is $2.20, with a standard deviation of $0.50. what is the value of the variance? a.) $0.50 b.) $1.00 c.) $1.70 d.) $0.25

The mean cost for a pint of strawberries is $2.20, with a standard deviation of $0.50. The value of the **variance** will be 0.25.

The **variance** (σ2) is a measure of how ways each value inside the information set is from the mean.

A **standard deviation** (or σ) is a measure of the way dispersed the records are in terms of the suggested.

The formula for standard deviation is given, the **square root **of variance by determining each data point's deviation relative to the mean.

Standard deviation = $0.10

Variance = (standard deviation)²

**Variance** = ( 0.50 )^2 = 0.25

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Jeremiah has three more than twice as many pencils as Spencer. If s represents how many pencils Spencer has, which is an algebraic expression that represents the

number of crayons that Jeremiah has?

O 3s +2

O 28 +3

O 58

O 68

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8:3

An **algebraic expression** that represents the number of crayons that **Jeremiah** has is: B. 2s + 3.

In order to write an **equation** that model this situation, we would assign variables to the total number of pencils that Jeremiah has and the total number of pencils that **Spencer** has respectively, and then translate the word problem into algebraic equation as follows:

Since Jeremiah has three more than twice as many pencils as **Spencer**, a linear **equation** that models this situation correctly include the following:

J = 2s + 3

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There are 3 female teachers and 31 male teachers at Eddie's high school. What is the ratio of the number of female teachers to the number of male teachers?

**Answer:**

3:31

**Step-by-step explanation:**

Joule Heating

Consider a metal at uniform temperature in a static uniform electric field E. An electron experiences a collision, and then, after a time t, a second collision. In the Drude model, energy is not conserved in collisions, for the mean speed of an electron emerging from a collision does not depend on the energy that the electron acquired from the field since the time of the preceding collision (assumption 4. Page 6).

(a) Show that the average energy lost to ions in the second of two collisions separated by a time t is (eEt)2 2m. (The average is over all directions in which the electron emerged from the first collision. )

(b) Show, using the result of Problem 1(b), that the average energy loss to the ions per collision is (eEt)2/m, and hence that the average loss per cubic centimeter per second is (ne2Ï„/m)E2=ÏƒE2. Deduce that the power loss in a wire of length L and cross section A is I2R, where I is the current flowing and R is the resistance of the wire

A) The **average **energy lost to ions in the second of two collisions separated by a time t is (eEt)2 2m is **(1/3) (eEt)2 / m**

B) The average energy loss to the ions per collision is (eEt)2/m is **(ne2 / m) E2**

In the Drude model, **collisions **between electrons and ions can cause energy loss, and this loss can be calculated using the average energy lost per collision. Specifically, if an **electron **experiences two collisions separated by a time t, the **average **energy lost to the ions in the second collision can be calculated.

We can use the formula for the **energy **gained by an electron in a uniform electric field: ΔE = eEt, where e is the charge of an electron, E is the electric field strength, and t is the time during which the electron experiences the field.

To do this, we can use the fact that the **mean **free path of an electron in a metal, before it experiences a collision, is given by λ = vτ, where v is the mean speed of the electron and τ is the average time between collisions.

The average energy lost in the second **collision**, over all directions of motion, is then given by:

(1/4π) ∫∫ ΔE2 (cosθ) dΩ

where θ is the angle between the direction of motion before the first collision and the direction of motion after the second collision, and dΩ is an element of solid **angle**. The factor (cosθ) accounts for the projection of the energy loss along the direction of motion.

After some calculations, we obtain the result:

(1/3) (eEt)2 / m

where m is the mass of an **electron**. This is the average energy lost to the ions in the second collision, over all possible directions of motion.

To answer part (b) of the question, we need to use the result of Problem 1(b), which states that the average time between collisions is given by τ = m/(ne2), where n is the number **density **of electrons in the metal. Using this formula, we can express the average energy loss per collision as:

(eEt)2 / mτ = (eEt)2 / (m^2 / ne2) = ne2 (eEt)2 / m

This is the average energy lost to the ions per collision, and we can use it to calculate the **average **loss per unit volume of the metal, which is given by:

(ne2 / m) E2

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In Orange County, 51% of the adults are males, and 49% are females. Also, 9. 5% of males smoke cigars, whereas 1. 7% of females smoke cigars (based on data from the Substance Abuse and Mental Health Services Administration). One adult is randomly selected for a survey involving credit card usage. If the selected person smokes cigars, nd the probability that the person is a male

a) The prior **probability **that the selected person is a male is **0.51**

b) The probability that the selected subject is a **male **is** 92.9%.**

We start by using the given information that 51% of adults in Orange County are males. We can interpret this as the prior **probability **of selecting a male adult randomly, which we denote by P(M). Since we know that there are only two genders, the probability of selecting a **female **adult is simply 1 - P(M), which is 49%.

a) To find the prior probability that the **selected **person is a male, we simply use the information given to us. Thus, P(M) = 0.51 and P(F) = 0.49, where F denotes the event of selecting a female adult.

b) We are given new information that the selected survey subject was smoking a cigar. We denote the event of selecting a smoker by S. We are also given the **conditional **probabilities of cigar smoking given the gender of the adult. Specifically, P(S|M) = 0.095 and P(S|F) = 0.017, where the vertical bar denotes the conditional probability.

We want to find the probability that the selected subject is a male given that they were smoking a cigar, denoted by P(M|S). We can use Bayes' theorem to update our prior probability based on this new information:

P(M|S) = P(S|M) x P(M) / P(S)

To find P(S), we can use the law of total probability, which states that the probability of an event can be obtained by summing over all possible ways it can occur. Thus,

P(S) = P(S|M) x P(M) + P(S|F) x P(F)

We can **substitute **the values given to us to find that:

P(S) = 0.095 x 0.51 + 0.017 x 0.49

P(S) = 0.05212

Using this value, we can now calculate the probability that the selected subject is a **male **given that they were smoking a cigar:

P(M|S) = P(S|M) * P(M) / P(S)

P(M|S) = 0.095 * 0.51 / 0.05212

P(M|S) = 0.929

This means that given the new information that the selected subject was smoking a cigar, the **probability **that they are a male is 92.9%.

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**Complete question:**

In Orange County, 51% of the adults are males. (It doesn't take too much advanced mathematics to deduce that the other 49% are females.) One adult is randomly selected for a survey involving credit card usage.

a) Find the prior probability that the selected person is a male.

b) It is later learned that the selected survey subject was smoking a cigar. Also, 9.5% of males smoke cigars, whereas 1.7% of females smoke cigars (based on data from the Substance Abuse and Mental Health Services Administration).

Use this additional information to find the probability that the selected subject is a male.

what is the area of this figure?

**Answer:**

213 km

**Step-by-step explanation:**

HELP PLEASE

The blood platelet count of a group of women have bell-shaped distribution with a mean of 245.5 and a standard deviation of 68.2 (all units are 1000 cells/ L) Using the empirical rule, fill in the blanks below (Round to the nearest hundredth):

a. Approximately 95% of healthy women in this group

b. Approximately 99.7% of healthy women in this have blood platelet counts between

group have blood platelet counts between

and(1000 cells/ ML). and (1000 cells/ ML).

**Answer:**

a) Approximately 95% of healthy women in this group have blood platelet counts between **109.1** and** 381.9** (1000 cells/*μL*).

b) Approximately 99.7% of healthy women in this group have blood platelet counts between **40.9** and **450.1 **(1000 cells/*μL*).

**Step-by-step explanation:**

The **Empirical Rule** (also known is the "68-95-99.7" rule) states that nearly all of the data within a **normal distribution **will fall within three standard deviations of the mean.

Given the blood platelet count of a group of women has a bell-shaped distribution with:

Mean μ = 245.5 (1000 cells/To determine the lower and upper bounds for blood platelet counts for **95%** of the women, subtract and add **two standard deviations** to the mean:

[tex]\begin{aligned}\text{Lower bound}&= \mu - 2\sigma \\&= 245.5 - 2(68.2)\\&=245.5-136.4\\&=109.1\end{aligned} \qquad \begin{aligned}\text{Upper bound}&= \mu + 2\sigma \\&= 245.5 + 2(68.2)\\&=245.5+136.4\\&=381.9\end{aligned}[/tex]

Therefore, approximately 95% of healthy women in this group have blood platelet counts between **109.1** and** 381.9** (1000 cells/*μL*).

To determine the lower and upper bounds for blood platelet counts for **99.7%** of the women, subtract and add **three standard deviations** to the mean:

[tex]\begin{aligned}\text{Lower bound}&= \mu - 3\sigma \\&= 245.5 - 3(68.2)\\&=245.5-204.6\\&=40.9\end{aligned} \qquad \begin{aligned}\text{Upper bound}&= \mu + 3\sigma \\&= 245.5 + 3(68.2)\\&=245.5+204.6\\&=450.1\end{aligned}[/tex]

Therefore, approximately 99.7% of healthy women in this group have blood platelet counts between **40.9** and **450.1 **(1000 cells/*μL*).

8. A In rectangle ABCD, AC and BD are diagonals. If m/1 = 55, find ABD.

The **value** of m∠ABD is **equals** to 125 degrees.

**Rectangle **can be defined in which opposite sides are **equal**.

AC and BD are **diagonals** of the rectangle ABCD.

Angle ABD is **adjacent** to angle 1 and angle ABO, where O is the intersection of diagonals AC and BD.

We know that m∠1 = 55, and we can find m∠ABO using the fact that the diagonals of a **rectangle bisect** each other. Since angle AOB is opposite to side AB, which is congruent to side CD, we have:

**m∠ABO = 180 - m∠AOB**

= 180 - (180 - m∠1) / 2

= 180 - (180 - 55) / 2

**= 62.5**

Therefore, we can find m∠ABD by adding m∠ABO and m∠DBO, where DBO is congruent to ABO:

**m∠ABD = m∠ABO + m∠DBO**

= m∠ABO + m∠ABO

= 2m∠ABO

= 2(62.5)

**= 125**

Hence, The value of m∠ABD is 125 **degrees.**

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What is the value of x

**Answer:**

**T****h****e**** **value of **x **is **1****2****.**

Greetings!!!

Firstly, recall the **Pythagoras' theorem** states that for all right-angled triangles, 'The square on the hypotenuse is equal to the sum of the squares on the other two sides'. The hypotenuse is the longest side and it's always opposite the right angle. In this triangle **a² = b²+ c²** and angle is a right angle.

a, b, and c represent the lengths of sides of a triangle, then: a2+b2=c2 if and only if **the triangle is a right triangle.**

**T****h****u****s****,**** **on this question

the hypotenuse is **a****=**** **20

the value of **b****=**** **16

so the required value is **c**

[tex]a {}^{2} = b {}^{2} + c {}^{2} [/tex]

substitute known variables into the equation

[tex](20 ){}^{2} = (16) {}^{2} +( c) {}^{2} [/tex]

evaluate both sides

[tex]400 = 256 +( c) {}^{2} [/tex]

minus **2****5****6**** **from both sides

[tex]400 - 256 = (c) {}^{2} [/tex]

[tex]144 = (c) \frac{2}{} [/tex]

write bothe sides under radical in order to erase the square

[tex] \sqrt{144} = \sqrt{c {}^{2} } [/tex]

solve for **c**

[tex]c = 12[/tex]

Hope it helps

**Answer:**

x = 12

**Step-by-step explanation:**

**Pythagoras**** ****Theorem**

**=**** ****Hypotenuse****²**** ****=**** ****adjacent****²**** ****+**** ****opposite****²**

**From**** ****the**** ****question**** **

**Hypotenuse**** ****=**** ****20**

**Adjacent**** ****=**** ****x**

**Opposite**** ****=**** ****16****.**

**The**** ****value**** ****for**** ****x**

**=**** ****20****²**** ****=**** ****x****²**** **** ****+**** **** ****16****²**

**=**** ****40****0**** ****=**** ****x****²**** **** ****+**** ****256**

**=**** ****400-256**** ****=**** ****x****²**

**=**** ****144**** **** ****=**** ****x****²**

**[tex] \sqrt{144} = { \sqrt{x} }^{2} \\ \sqrt{144} = x \\ 12 = x[/tex]**

**Therefore**** ****adjacent**** ****(****X****)**** ****=**** ****12**

a sample of 250 rdns was randomly selected from a list of all rdns in the state of california for a california policy study. which sampling method was used?

If **a sample **of 250 RDNS was randomly selected from a** list of all RDNS** in the state of California for a California policy study, then the sampling method was simple random sample

Here a sample of 250 RDNS was randomly selected from a list of all RDNS.

**Sampling **is defined as the selecting the individual members or the group that you will actually collect data from in your research. There are five types of **sampling method**. They are Random, Systematic, Convenience, Cluster, and Stratified.

In the** simple random sampling** the researchers select the random samples from the population. Here a sample of 250 RDNS was randomly selected from a list of all RDNS.

Therefore, the sampling method that used is simple random sample

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surface area of a rectangular prism with sides of 5,4,3,3.7

Surface area of a **rectangular prism** is 444 square unit.

A rectangular prism is a **three-dimensional shape **with six faces (two at the top and bottom and four are lateral faces). The prism's faces are all rectangular. As an outcome, there really are three sets of exactly equal faces here. A rectangular prism is also recognized as a cuboid due to its shape.

The sides of a** rectangular prism** is 5, 4, 3, 3.7.

This can be calculated by multiplying each of the side lengths together and then multiplying that result by two.

**Surface area **of a rectangular prism = 2 × (5 × 4 × 3 × 3.7)

Surface area of a rectangular prism = 2 × 222

Surface area of a rectangular prism = 444 square unit

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a license plate consists of 2 letters followed by 4 digits. (1) how many license plates are possible? (2) how many license plates are possible if the digits must be different? (3) how many license plates are there that begin with a and don't have a 7?

26 possible **letters** for each of the first two positions and 10 possible digits for each of the last 4 **positions **gives a total of 676,000,000 license plates.

(1) 26 **possible **letters for each of the first two positions and 10 possible digits for each of the last 4 positions gives a total of

26 x 26 x 10 x 10 x 10 x 10 = 676,000,000 license plates.

(2) The number of possible license plates where the digits must be different is the number of **permutations **of 10 items taken 4 at a time, or 10P4 = 5040. Multiplying by 26 x 26 gives a total of

5040 x 26 x 26 = 3,636,160 possible license plates.

(3) To find the number of license plates that begin with "A" and don't have a 7, we first find the **number **of license plates that start with "A" and don't have any restriction on the last 4 digits. This is

26 x 10 x 10 x 10 x 10 = 676,000

Then, we find the number of license plates that have a 7, which is

9 x 26 x 10 x 10 = 23,760

Subtracting this from the total number of **license **plates that start with "A" gives us

676,000 - 23,760 = 652,240 possible license plates.

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