9. Seven more than the quotient of a number b
and 45 is greater than 5.

the HCF of x, 2y, 3y, 4z, x², 3z, and 5, where x, y, z are

distinct prime numbers is 1.

To find the highest common factor (HCF) of the given numbers, we need to find the common factors of each pair of numbers and then find the highest common factor of all the resulting common factors.

First, let's find the prime factors of the given numbers:

x = a prime number (distinct from y and z)

2y = 2 × y

3y = 3 × y

4z = 2² × z

3z = 3 × z

x² = a prime number squared (distinct from y and z)

5 = a prime number

Next, we can pair up the numbers and find their common factors:

Common factors of x and 2y: 1, 2, y

Common factors of 3y and 4z: 1, 2, 3, y, z, 6

Common factors of x² and 3z: 1, 3, x, z, xz

Common factors of 5 and 2: 1

Finally, we find the highest common factor of all the resulting common factors:

The highest common factor of x, 2y, 3y, 4z, x², 3z, and 5 is 1, since it is the only factor that is common to all the pairs.

Therefore, the HCF of x, 2y, 3y, 4z, x², 3z, and 5 is 1.

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By the congruence postulate, we have shown that the quadrilateral is  ΔAED ≅ ΔCED.

Let's start by showing that AD = CD. Since AB = AD and BC = CD, we can rewrite AB + BC as AD + CD. This means that AD = AB + BC - CD. But we know that AB = AD, so we can substitute AD for AB to get AD + BC = 2AD + CD. Simplifying this equation, we get AD = CD.

Next, we can show that AE = CE. Since AC is a diagonal of the kite, we know that AC bisects angle BAD and angle BCD. This means that angle BAC = angle DAC and angle BDC = angle CDC. Since AD = CD, we know that triangle ACD is isosceles, so angle ACD = angle CAD.

Using these angle equalities, we can conclude that angle CAE = angle CDE. Since AC ⊥ BD, we know that angle CAD = angle CDE, so we can conclude that triangle ACE is isosceles, which means that AE = CE.

Finally, we need to show that angle AED = angle CED. Since AD = CD and AE = CE, we know that triangles AED and CED have two pairs of congruent sides. Additionally, we know that AC is a common side of the triangles.

Since AC is perpendicular to BD, we know that angle ACD and angle BDC are complementary angles.

This means that angle ACD = 90 - angle BDC and angle CAD = 90 - angle BAC. Using these angle equalities, we can conclude that angle AED = angle CED.

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Answer:

1 minute = 1/6

2 minutes = 1/3

3 minutes =1/2

Step-by-step explanation:

one can eat a bag in 15 minutes so in 1 minute this cat can eat 1/15 of a bag

the other cat can eat a bag in 10 minutes so in 1 minute the cat can eat 1/10 of the bag

to find how much they can eat in 1 minute, add 1/10 and 1/15 which gives you 1/6. to find 2 and 3 minutes just multiply by 1/6 by 2 or 3

The coordinates of point C are: C = (2 + (3/2) * √(13), 2 + (3/2) *√ ((13))

How to find coordinates of point?

To find the coordinates of point C, we can use the midpoint formula, which gives the coordinates of the midpoint of a line segment. We know that point C is 3/4 of the way from point A to point B, so it is closer to B than to A. Therefore, we can find the coordinates of C by finding the midpoint of the line segment AB and then moving 3/4 of the distance from the midpoint to B.

The midpoint of AB can be found by averaging the x-coordinates and the y-coordinates of A and B, respectively:

Midpoint M = ((-4 + 8)/2 , (-2 + 6)/2) = (2, 2)

Now, we need to find the distance from M to B and move 3/4 of that distance in the direction of B. We can use the distance formula to find the distance between two points:

distance MB = √((8 - 2)² + (6 - 2)²) = √(36 + 16) = √(52)

So, the distance from M to C is 3/4 of √(52), which is:

distance MC = (3/4) * √(52) = (3/4) * 2 * √(13) = (3/2) * √(13)

To move in the direction of B, we need to add the x-component and y-component of the distance MC to the x-coordinate and y-coordinate of M, respectively:

x-coordinate of C = 2 + (3/2) * √(13)

y-coordinate of C = 2 + (3/2) * √(13)

Therefore, the coordinates of point C are:

C = (2 + (3/2) * √(13), 2 + (3/2) * √(13))

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120 is 30 percent of 400

We are interested in the population proportion of drivers who claim they always buckle upa.i. x = 320 ii. n = 400 iii. p′ = 0.8

b. The random variable X represents the number of drivers out of the sample of 400 who claim they always buckle up, while P′ represents the sample proportion of drivers who claim they always buckle up.

c. The distribution to use for this problem is the normal distribution because the sample size is large enough (n=400) and the population proportion is not known.

d. i. The 95% confidence interval for the population proportion who claim they always buckle up is (0.7709, 0.8291).

ii. The graph is a normal distribution curve with mean p′ = 0.8 and standard deviation σ = sqrt[p′(1-p′)/n].

iii. The error bound is 0.0291.

e. Three difficulties the insurance companies might have in obtaining random results from a telephone survey are:

Selection bias: The survey might not be truly random if the telephone numbers selected are not representative of the population of interest.

Nonresponse bias: People may choose not to participate in the survey or may not be reached, which could bias the results.

Social desirability bias: Respondents may give socially desirable answers rather than their true opinions, which could also bias the results.

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We have that, if they put 40 chips in a hat, each one with the numbers 1, 2, 3, 4, 5, 6, 7, 8, 9 or 10, and each number is put on four chips. Four tokens are drawn from the hat at random and without replacement, the value of q/p, q,p as probabilities, will be given by 360, therefore, the correct option is (D) 360

The probability that all four tokens have the same number (p) is equal to the total number of possible outcomes that meet that criterion divided by the total number of possible outcomes.

In this case, there are 10 possible numbers that could come up (1-10). Therefore, there are 10 possible outcomes for the four slips of paper that have the same number. Each outcome has the same probability of 1/10, so p = (1/10)^4 = 1/10000.

The probability that two of the slips have a number a and the other two have a number b (q) is equal to the total number of possible outcomes meeting that criterion divided by the total number of possible outcomes.

In this case, there are 10 possible numbers that could be drawn (1-10) and 2 ways to choose 2 different numbers out of 10, so there are 20 possible outcomes for two of the slips bearing a number and the other two bearing a number b. Each outcome has the same probability of 1/20, so q = (1/20)^4 = 1/3200000.

The ratio of q to p is q/p = 3200000/10000 = 360. Therefore, the value of q/p is 360.

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Answer:

The system has one point because when the system is graphed the lines will intersect at exactly one point. Therefore, there is only one solution to this system of equations.

The probability density function (PDF) of Y can be determined by the transformation of the PDF of X. Using the transformation rule, we can calculate that fy(y) = fx(x) |dx/dy|, where x is a function of y, since y = Fx(x).

We can use the Chain Rule to determine the derivative of x with respect to y. Since Fx is a monotone increasing function, dx/dy = 1/F'x(x). Substituting this into the transformation rule, fy(y) = fx(x) / F'x(x).

Therefore, to find fy(y), we need to calculate F'x(x). Fx is the cumulative distribution function, which means that its derivative F'x(x) is the probability density function of X, or fx(x). Substituting this into the transformation rule, fy(y) = fx(x) / fx(x). Since fx(x) = fx(2) and fx(2) is a constant, fy(y) = 1/fx(2).

To summarize, the probability density function of Y is given by fy(y) = 1/fx(2).

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Answer: To solve the problem, we need to use the given time to find Michaela's swimming rate in meters per second, and then use that rate to calculate the distance she will swim in 10 minutes.

1 minute = 60 seconds

4 minutes and 50 seconds = 4 x 60 + 50 = 290 seconds

So, Michaela's rate is:

distance / time = x / 290 seconds

where x is the distance she can swim in 290 seconds.

Simplifying the equation:

x = distance = (time x distance) / time = (290 seconds x distance) / 290 seconds = distance

We know that Michaela can swim 500 meters in 290 seconds:

500 meters / 290 seconds = 1.724 meters per second

Therefore, in 10 minutes (600 seconds), she will swim:

distance = rate x time = 1.724 meters/second x 600 seconds = 1034.4 meters

So, Michaela will swim 1034.4 meters in 10 minutes.

Step-by-step explanation:

Answer:

6/11 = 0.54

Step-by-step explanation:

Answer: Yes you are correct

Step-by-step explanation:

Let n be a positive integer. We can use the properties of modular arithmetic to calculate this remainder. Let's start with a = (32n + 4)-1 mod 9. We can rewrite this as a = 9 - (32n + 4)-1 because 9 = 0 mod 9.

We can use Fermat's Little Theorem to calculate (32n + 4)-1. This theorem states that (32n + 4)-1 mod 9 = (32n + 4)8 mod 9.

Using the identity (a + b)n mod m = ((a mod m) + (b mod m))n mod m, we can simplify the equation to (32n mod 9 + 4 mod 9)8 mod 9.

32n mod 9 = 0, so (32n mod 9 + 4 mod 9)8 mod 9 = 48 mod 9 = 1.

Finally, a = 9 - 1 = 8 mod 9, so the remainder when a is divided by 9 is 8.

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The daily dose is 40mg, this dose per kilogram per day is within the therapeutic range of 2-3mg/kg/day, which means that the medication is within the safe and effective range for this patient's weight.

The weight of the patient is 20kg, and the prescribed dosage is 10mg every 6 hours. To calculate the daily dose, we need to multiply the prescribed dosage by the number of doses per day. Since the medication is prescribed every 6 hours, this means that the patient will take it 4 times a day.

=> (10mg x 4 doses) = 40 mg

The therapeutic range is the range of doses at which the medication is most effective and safe. In this case, the therapeutic range is 2-3mg/kg/day. To determine if the daily dose is within the therapeutic range, we need to divide the daily dose (40mg) by the patient's weight (20kg) to get the dose per kilogram per day, which is 2mg/kg/day.

However, it's important to note that the therapeutic range is a general guideline and may vary depending on the patient's individual circumstances and medical history.

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The given square with a side length of one unit is known to contain five points. One must prove that at least two of these points are within square root 2/2 units of each other.

According to the Pigeonhole principle, "if n items are put into m containers, with n > m, then at least one container must contain more than one item."In this context, the square is the container, and the points inside it are the objects. If more than four points are picked, the theorem is true, and two points are nearer to each other than the square root of 2/2 units.

Let's place four points on the square's four corners. The distance between any two of these points is the square root of two units since the square's side length is 1.

Let's add another point to the mix. That point is either inside the square or outside it. Without loss of generality, let us assume that the point is inside the square. It must then be within the perimeter outlined by joining the square's corners to the point that was not a corner already.

The perimeter of the square described above is a square with a side length of square root 2 units.

Since we have five points in the square, at least two of them must be in the same smaller square, due to the pigeonhole principle. Without loss of generality, let's assume that two of the points are in the upper-left square. As a result, any points within this square are within the square root 2 units of any of the other four points. Hence, at least two points of the five selected are within the square root of 2/2 units of each other.

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The probability that a continuous random variable is equal to a single number zero because the area under a continuous probability density function (pdf) between any two points, even two extremely close points, is never equal to zero.

In other words, since the continuous random variable is infinite and continuous, the probability that it is equal to a single value is almost zero.

Steps in Hypothesis Testing:State the null and alternative hypotheses.Calculate the test statistic.

Determine the critical value or p-value.Calculate the p-value, if necessary.Make a decision and interpret the results.

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Answer:

Second choice
∠BCA ≅ ∠DCA

Step-by-step explanation:

This logically follows from the fact that both ∠BCA and ∠DCA are right angles from the previous step. And the reason given is "All right angles are ≅)

So they are congruent

The probability that a randomly selected quartz timepiece will have a replacement time less than 13.3 years is approximately 0.015 with a mean of 17 years and a standard deviation of 1.7 years.

To find the probability that a randomly selected quartz timepiece will have a replacement time of less than 13.3 years, we need to use the standard normal distribution formula which is as follows:

[tex]Z =\frac{X -μ }{σ}[/tex]

Where Z is the standard score

X is the variable value

μ is the mean

σ is the standard deviation

Given that the mean (μ) of the replacement times for the quartz timepieces is 17 years, the standard deviation (σ) is 1.7 years, and the variable value (X) we are looking for is 13.3 years.

Substitute the values into the standard normal distribution formula to get:

[tex]Z = \frac{13.3-17}{1.7} = -2.17[/tex]

Looking at the standard normal distribution table, we can find the probability of the standard score Z = -2.17 to be 0.015.

Therefore, the probability that a randomly selected quartz timepiece will have a replacement time less than 13.3 years is approximately 0.015.

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Answer:

x = 24 and y = 24

Step-by-step explanation:

Let's use algebra to solve this optimization problem.

Let x be the first number, and y be the second number. Then we have the following two equations based on the problem statement:

x + y = 48 (sum of the two numbers is 48)

xy = ? (product of the two numbers, which we want to maximize)

To solve for x and y in terms of each other, we can use the fact that:

(x + y)^2 = x^2 + 2xy + y^2

Expanding the left side of the equation gives:

x^2 + 2xy + y^2 = 2304

And substituting xy for its value in terms of x and y gives:

x^2 + 2xy + y^2 = x^2 + 2(48 - x)y + y^2 = 2304

Simplifying this equation gives:

2y^2 - 96y + x^2 - 2304 = 0

To maximize the product xy, we need to maximize the value of xy = x(48 - x) = 48x - x^2. This function is a quadratic that opens downwards, and therefore, its maximum value occurs at the vertex of the parabola, which is located at x = -b/2a = -48/(2*-1) = 24.

Thus, the two positive real numbers that sum up to 48 and their product is a maximum are x = 24 and y = 24.

The volume of the solid is 2160ft^3

Volume of Cuboid is the multiplication of length breath and height.

We know that, Volume of Cuboid = l×b×h

put the given values from figure,

= 12×10×15

=1800ft^3

Volume of top = Area of triangle × length

= 1/2 × 4× 12× 15

=360ft^3

Total volume= 1800 + 360

= 2160ft^3

Therefore, the volume of the solid is 2160ft^3

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Cuboid: According to the question the volume of the solid is [tex]2160ft^3[/tex].

A cuboid is a three-dimensional geometric shape which is composed of six rectangular faces. It has 12 edges and 8 vertices. It is also referred to as a rectangular prism. The three dimensions of a cuboid are its length, width, and height. The cuboid is a versatile shape that can be used in many different ways and can be seen in everyday objects such as boxes, desks, and bookshelves. It is also a common shape for mathematically-based problems such as calculating the volume of a cuboid.

We know that, Volume of Cuboid = l×b×h
put the given values from figure,
= 12×10×15
=[tex]1800ft^3[/tex]
Volume of top = Area of triangle × length
= 1/2 × 4× 12× 15
=[tex]360ft^3[/tex]
Total volume= 1800 + 360
= [tex]2160ft^3[/tex]
Therefore, the volume of the solid is [tex]2160ft^3[/tex]

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The percent markup is 25%.

Markup percentage is calculated by dividing the gross profit of a unit (its sales price minus it's cost to make or purchase for resale) by the cost of that unit.

Given that, A department store buys 300 shirts for a total cost of $7,200 and sells them for $30 each.

Cost of one shirt [tex]= 7200 \div 300 = \$24[/tex]

And they sold at $30 each,

Percent markup [tex]= 30-24 \div 24 \times 100[/tex]

[tex]= 25\%[/tex]

Hence, the percent markup is 25%.

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The number of minutes needed to complete a job, m, varies inversely with the number of workers, w.

Three workers can complete a job in 30 minutes.

To find, out how many minutes would it take 6 workers to complete the job.

The formula used for inverse variation is, m1w1 = m2w2

Where, m1 = 30,

w1 = 3,

m2 = ?

and w2 = 6

Substitute the given values in the above formula, 30 × 3 = m2 × 6

Simplify the above expression,90 = 6m2

Divide both sides by 6,90 / 6 = m2m2 = 15

Hence, it will take 15 minutes for 6 workers to complete the job.

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Parachutist's rate during free fall is 40 meters per second and will fall approximately 490 meters during 10 seconds of free fall.

First, we need to convert 132 feet per second to meters per second. We know that 1 meter is equal to 3.3 feet, so we can use the following conversion factor:

[tex]$\frac{3meter}{3.3 feet}[/tex]

To convert feet per second to meters per second, we can multiply by the conversion factor:

[tex]132 (\frac{1}{3.3} ) = 40 meters/second[/tex]

Therefore, the parachutist's rate during free fall is 40 meters per second.

Next, we can use the following formula to find the distance the parachutist falls during 10 seconds of free fall:

distance =[tex]\frac{1}{2}[/tex] * acceleration * time²

where acceleration due to gravity is approximately 9.8 meters/second^2.

Substituting the given values, we get:

distance = [tex]\frac{1}{2}[/tex] * 9.8 meters/second² * (10 seconds)²

distance = 490 meters

Therefore, the parachutist will fall approximately 490 meters during 10 seconds of free fall.

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The suggest that the method is effective.

Assuming different groups of couples use a particular method of gender selection and each couple gives birth to one baby, the probability of a girl is 0.5, and the groups consist of 17 couples, then:

a. The mean is μ= 8.5, and the standard deviation is σ= 3.5.

b. The values separating results that are significantly low or significantly high are 8.5 girls or fewer are significantly low, and 11.5 girls or greater are significantly high.

c. The result of 15 girls is significantly high, because 15 girls is greater than 11.5 girls. This would suggest that the method is effective.

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The experimental likelihood that probability the incoming train will be fully occupied is 0.56, or 56%.

It's simple to calculate the likelihood of a simple event occurring by adding the probabilities together. Your overall odds to win something, for instance, are 10% + 25% = 35% if your chances of winning $10 or $20, respectively, are 10% and 25%, respectively.

In this instance, 14 of the 25 arriving trains were completely full.

The following train's likelihood of being full is determined by the proportion of full trains to all other trains.

14/25 are in favor of the upcoming train being fully loaded.

The likelihood that the following train will have every seat taken is 0.56, or 56%.

It either happens or it doesn't, according to the four significant rules of probability. The chance of an event occurring when the probability of it not occurring is put together is always 1. The same principles apply to empirical probability.

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In the given diagram, ΔHIJ ≈ ΔFIG, the value of u in triangle FIG is calculated as: IG = 8 yd

A triangle is a geometric shape that is formed by three line segments that intersect at three non-collinear points. The three line segments are called the sides of the triangle, while the three points where they intersect are called the vertices of the triangle.

A triangle is a three-sided polygon formed by three line segments intersecting at three non-collinear points, and it can be classified based on the length of its sides and the measure of its angles.

∆HIJ similar to ∆FIG

HI/FI = IJ/IG

5/10 = 4/IG

IG = 8 yd

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In the given diagram, ΔHIJ ≈ ΔFIG, the value of u in triangle FIG is calculated as: IG = 8 yd

A triangle is a geometric shape that is formed by three line segments that intersect at three non-collinear points. The three line segments are called the sides of the triangle, while the three points where they intersect are called the vertices of the triangle.

A triangle is a three-sided polygon formed by three line segments intersecting at three non-collinear points, and it can be classified based on the length of its sides and the measure of its angles.

∆HIJ similar to ∆FIG
HI/FI = IJ/IG
5/10 = 4/IG
IG = 8 yd

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The product of two random variables that follows the normal distribution with mean 0 and variance 1 is expected 0.

To compute the product of two random variables that are normal distributed with a mean of 0 and a variance of 1, the following procedure can be employed:

Thus, we can write the probability density function of the normal distribution as:

f(x) = (1/√2π) * e^(-x^2/2)

E[X] = ∫x * f(x) dx, where the integral is taken over the entire range of X.

E[Y] = ∫y * f(y) dy, where the integral is taken over the entire range of Y.

E[XY] = E[X] * E[Y]

E[X] = ∫x * f(x) dx = ∫x * (1/√2π) * e^(-x^2/2) dx = 0

E[Y] = ∫y * f(y) dy = ∫y * (1/√2π) * e^(-y^2/2) dy = 0

E[XY] = E[X] * E[Y]

= 0 * 0 ⇒ 0

Therefore, the product of two random variables that follow a normal distribution with mean 0 and variance 1 has an expected value of 0.

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The expected value of x is 1.80, the variance is 0.72, and the standard deviation is 0.85.

Calculate the expected value, variance, and standard deviation of the random variable x as follows. Round all answers to two decimal places, and keep in mind that x is the number of red marbles that Suzan has in her hand after selecting three marbles from a bag containing three red marbles and two green ones.

Expected Value: Since there are 3 red marbles and 2 green marbles in the bag, the probability of drawing a red marble is: P(R) = 3/5The probability of drawing a green marble is P(G) = 2/5Therefore, the expected value of the random variable X is: E(X) = μ = np = 3/5 * 3 = 1.80

Variance can be calculated using the following formula: Var(X) = npq, where p is the probability of success and q is the probability of failure of the event. In this scenario, the probability of drawing a red marble is P(R) = 3/5, and the probability of drawing a green marble is P(G) = 2/5.

Therefore, Var(X) = npq Var(X) = (3/5)*(2/5)*3Var(X) = 1.80 * 0.4Var(X) = 0.72Standard Deviation: The square root of the variance is equal to the standard deviation. Hence, the formula for standard deviation is: S.D. = √Var(X)S.D. = √0.72S.D. = 0.85

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Answer:

Let the height of the parallelogram be h

From :the formula of finding Area of the parallelogram

Answer: 4

Step-by-step explanation:

4. shift the boundary line up 1

According to the solving  the annual rate of depreciation is approximately 4.77%.

Annual percentage rate (APR) is the word used to define the annual interest that is generated by a payment that is due to investors or assessed to borrowers. The annual percentage rate, or APR, is a gauge of how much it actually costs to borrow cash over the duration of a loan or the income from an investment.

V = V0 * e[tex]^(^-^r^t^)[/tex]

where:

V0 is the initial value of the asset (in this case, $35,000)

V is the current value of the asset (in this case, $26,796.88)

r is the annual rate of depreciation (what we want to find)

t is the time elapsed (in years)

We know that the time elapsed is 2021 - 2014 = 7 years.

26,796.88 = 35,000 * e[tex]^(^-^7^r^)[/tex]

Dividing both sides by 35,000, we get:

0.766195 = e[tex]^(^-^7^r^)[/tex]

ln(0.766195) = -7r

Solving for "r", we get:

r = -ln(0.766195) / 7

r ≈ 0.0477

the annual rate of depreciation is approximately 4.77%.

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