Given right ΔABC, if tan A = [tex]\frac{3}{2}[/tex] and b=5, determine the exact lengths of sides a and c.

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 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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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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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 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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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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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:

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

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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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?

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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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

Answer: 151 minutes

Step-by-step explanation:

95.40 - 35 =

60.40

60.40/.40 = 151

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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Answer:

The value of x is 12.

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.

Thus, 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 256 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

= Hypotenuse² = adjacent² + opposite²

From the question

Hypotenuse = 20

Adjacent = x

Opposite = 16.

The value for x

= 20² = x² + 16²

= 400 = x² + 256

= 400-256 = x²

= 144 = x²

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

Therefore adjacent (X) = 12

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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Answer:

Step-by-step explanation:

Answer:

7.8

Step-by-step explanation:

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]

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.

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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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?

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.

Answer:

213 km

Step-by-step explanation:

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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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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Answer:

3:31

Step-by-step explanation:

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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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:

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).