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The length of side BD which is the altitude of the triangle is 2√(70)

The length of BD is solved using similar triangles. This is defined by triangles formed from triangle ABC and they include

Let the altitude be h, hence we have the formula of the proportions as

AD / h = h / DC

plugging the values gives

20 / h = h / 14

h^2 = 20 * 14

h = √(20 * 14 )

h = √(280)

h = 2√(70)

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Answer: slope = \(\frac{1}{2}\)

Step-by-step explanation:

        Since we are given a graph with clear points, we will use "rise over run" by counting the units between points upwards and rightwards.

        Since this line is going up from bottom left to upper right, we have a positive slope.

        Starting at (0, -3) we count up one unit and right two units to (2, -2), giving us a slope of \(\frac{1}{2}\).

Answer:

2 < x < 24

Step-by-step explanation:

Given 2 sides of a triangle then the third side x is in the range

difference of 2 sides < x < sum of 2 sides , that is

13 - 11 < x < 13 + 11

2 < x < 24

What is x equivalent to?

Answer:

IRR = 31.93%

Step-by-step explanation:

Depreciation = 570,000/5 = 114,000

Calculation of Operating cash flow

Operating income = 270000 - 114000 = 156,000

Tax = 156,000 * 35% = 54,600

Operating cash flow = Operating income + Depreciation - Tax = 156,000 + 114,000 - 54,600 = 215,400

Calculation of initial investment

CF0 = Initial investment - Working capital = 570,000 - 73,000 = 497,000

Calculation of the last year cash flow

CF5 = OCF + After tax salvage - Net working capital = 215,400 + 37,000 - 73,000 = 180,100

Calculation of IRR

IRR for the project = IRR(Cashflow from year0, 1, 2,3,4,5) "as attached below picture below"

IRR for the project = 31.93%

Answer:

yes

Step-by-step explanation:

12 + 3t = 72

Let t = 20

12 + 3*20 = 72

12 + 60 = 72

72 = 72

This is a true statement so t =20 is a solution

Answer:

Yes  becauz 12 + 3(20) = 72

12 + 60 = 72

Step-by-step explanation:

If the jobs are sequenced according to the SLACK rule, Job A would be completed on day 12.

The SLACK rule involves calculating the slack time for each job, which is the difference between the due date and the completion time. The job with the least slack time is prioritized and scheduled first. In this case, the due dates for the jobs are as follows: Job A (12), Job B (15), Job C (17), Job D (10), and Job E (8).

Job A has a processing time of 8 days and a due date of 12, so the slack time is 12 - 8 = 4 days. Since Job A has the least slack time among all the jobs, it would be completed on day 12. Therefore, the answer is D. 12.

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Using the weighed mean formula, it is found that Mara's average for the course was of 68.6.

The weighed mean is given by the sum of all elements in a data-set multiplied by it's weight, divided by the sum of the weights.

In this problem, the weights are as follows:

Hence, her weighed mean is given as follows:

\(M = \frac{2(65 + 62 + 60) + (61 + 96 + 80 + 89) + 4(65)}{6 + 4 + 4} = 68.6\)

Mara's average for the course was of 68.6.

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After six​ months, the​ subjects' symptoms are studied and compared. Answer parts​ are given below.

An assumption or concept is given as a hypothesis for the purpose of debating it and testing if it might be true.

Given:

A pharmaceutical company wants to test the effectiveness of a new allergy drug.

The company identifies 250 females​ 30–35 years old who suffer from severe allergies.

The subjects are randomly assigned into two groups.

One group is given the new allergy drug and the other is given a placebo that looks exactly like the new allergy drug.

After six​ months, the​ subjects' symptoms are studied and compared.

Here, 30-35 year-old girls are used to test the new allergy medication's effects.

(a)

Females between the ages of 30 and 35 who are the test subjects are the experimental units.

The new allergy medication, whose results are being studied, is the remedy.

It's best to choose C.

(b)

A bias may develop if a researcher or patient knows whether subjects received a medication or a placebo.

In this case, choice B is preferable.

(c)

If neither the researcher nor the subject knew whether they were receiving a medicine or a placebo, the study would be considered double-blind.

In this case, choice A is preferable.

Therefore, all the correct choices are given above.

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The complete question is given in the image.

Answer:

A. 260°

Step-by-step explanation:

The measure of the arc in the circle given is 260°

A circle is the set of all points in the plane that are a fixed distance (the radius) from a fixed point (the centre). Any interval joining a point on the circle to the centre is called a radius. By the definition of a circle, any two radii have the same length.

Given is a circle, with an inscribed angle of 50°, we need to find the arc ABC,

So, according to the inscribed angle theorem,

∠ BAC = 1/2 arc BC

So, arc BC = 2 x ∠ BAC

arc BC = 2 x 50

∠ BAC = 100°

Now,

arc ABC = 360° - arc BC

Since, we know that the whole circle, measures 360°

So,

arc ABC = 360° - 100°

arc ABC = 260°

Hence, the measure of the arc in the circle given is 260°

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Since none of the 13 classmates had been given math homework between the original survey and Kelly's second survey, the sum of the values in the second data set is the same as the sum of the values in the original data set. Therefore, the change in the means can be determined without calculating the mean of either data set by considering the number of data points in each set.

Since both data sets have the same number of data points, the change in the means will be zero. This is because the mean is calculated by dividing the sum of the values by the number of data points, and since the sum of the values is the same in both data sets, the means will also be the same.

In other words, if the mean of the first data set is x, then the sum of the values in the first data set is 13x (since there are 13 classmates), and the sum of the values in the second data set is also 13x (since none of the values have changed). Therefore, the mean of the second data set will also be x, and the change in the means will be zero.

Answer:

42.78cm2

Step-by-step explanation:

Area =100°/360 * 22/7 * 7^2

=42.78cm2

Answer:

41 inches

Step-by-step explanation:

Let the point at the top of the door on the left be x

Wx + xH = 45

Let the point at the top of the door  on the right be c

Yc + cZ = 37

We know the door is

xH +  plus the width of the tile

The width of the tile is Yc

xH + Yc

On the right door

cZ +  the height of the tile

cZ + Wx

Add the two doors together

xH + Yc + cZ + Wx = 2 times the height of the door

Rewriting

xH +  Wx +  Yc + cZ = 2 times the height of the door

45+ 37 = 2 times the door height

82 = 2 times the door height

Divide by 2

41 = door height

Answer:

First of all you will solve the two equations simultaneously to get the values of a and b after that you use it to find, 3^a /3^b

Step1. a+b=7..... (1)

a-b=3.......(2)

Now take eqn(1) +eqn(2),

Implies 2a=10

Dividing both sides by 2,

Then a=5

Put a=5 into eqn(1),

Implies 5+b=7

b=7-5

b=2

Therefore the values of a and b are 5 and 2

Step2

Now find 3^a/3^b,

Substitute the vaues of a and b into the function.

Implies 3^5/3^2=243/9

=27

Therefore 3^a/3^b=27

Step-by-step explanation:

Above

An equation is formed of two equal expressions. The solution of \(3^a \div 3^b\) is 27 or 3³.

An equation is formed when two equal expressions are equated together with the help of an equal sign '='.

As it is given to us that the sum of a and b is 7, while the difference of a and b is 3, therefore, the two-equation are,

a+b = 7

a-b =3

Now, if we add the two equations we will get, the value of a, therefore,

\((a+b)+(a-b)=7+3\\\\a+b+a-b=10\\\\2a=10\\\\a=5\)

Now, if we substitute the value of a in any one of the equation, then we will get the value of b,

\(a+b=7\\\\5+b=7\\\\b=2\)

Thus, the value of a and b is 5 and 2 respectively.

Now, if we substitute the value of a and b in the problem we will get,

\(3^a \div 3^b\\\\=\dfrac{3^a}{3^b}\\\\=\dfrac{3^5}{3^2}\\\\=3^{5-2}=3^3=27\)

Hence, the solution of \(3^a \div 3^b\) is 27 or 3³.

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Answer:

1.5 or 3/2

Step-by-step explanation:

The scale factor is the factor by which the side lengths of the original shape are multiplied by. In this case, the original shape had side lengths 17 and was multiplied by \(x\) to get the scaled shape.

Now we get the equation \(17\cdot x=51/2\). Solving, we get x=1.5

The rate the level in the tank falling when the height of the syrup level is 3 feet is 8/π feet per minute. The result is obtained by using the rate of change concept.

A conical tank containing syrup is draining.

Find the rate of syrup level falling (dh/dt) when h = 3 ft!

See the picture in the attachment!

By the similar triangles, we get

r/h = 2/6

r/h = 1/3

r = 1/3 h

Find the volume of the syrup left at a certain height.

V = 1/3 πr²h

V = 1/3 π(1/3 h)²h

V = 1/3 π(1/9) h² h

V = 1/27 πh³

The rate of syrup level falling is

dV/dt = dV/dh . dh/dt

dV/dt = d/dt [1/27 πh³] . dh/dt

dV/dt = 1/27 π 3h² dh/dt

8 = 1/27 π 3(3)² dh/dt

8 =  π dh/dt

dh/dt = 8/π ft/min

Hence, the rate of syrup level falling is 8/π feet per minute.

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Suppose f is a uniform continuous function from a metric space X into a metric space Y. We want to prove that for every Cauchy sequence {xn} in X, the sequence {f(xn)} is also a Cauchy sequence in Y.

To prove this, let ε > 0 be given. Since f is uniformly continuous on X, there exists δ > 0 such that for any x, y in X, if d(x, y) < δ, then d(f(x), f(y)) < ε. Now, since {xn} is a Cauchy sequence in X, there exists N in the natural numbers such that for all m, n ≥ N, we have d(xm, xn) < δ.By the definition of uniform continuity, we can conclude that for all m, n ≥ N, we have d(f(xm), f(xn)) < ε. This shows that {f(xn)} is a Cauchy sequence in Y, as it satisfies the definition of a Cauchy sequence.

However, if we only assume that f is continuous on X (not necessarily uniformly continuous), result may not hold. In this case, there could be Cauchy sequences {xn} in X such that the sequence {f(xn)} in Y is not Cauchy. The key difference is the requirement of uniform continuity, which ensures that small changes in input sequence result in small changes in the output sequence, guaranteeing the Cauchy property.

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Answer:

I believe it's A

Step-by-step explanation:

I'm not so sure because I did this a while back

The recurrence relation that describes the sequence {g} is option (b) = (1.1)⋅−1.


The problem states that the population of mice increases by 10% every year. This means that if we start with a population of 100 mice, after one year the population will be 110 (100 + 10% of 100). After two years, the population will be 121 (110 + 10% of 110), and so on.

Let's use the variable g to represent the population of mice after n years. Then, we can write:

g = 1.1g_{n-1}

This recurrence relation says that the population after n years is equal to 1.1 times the population after n-1 years. This makes sense because the population increases by 10% every year.

To find the population after a specific number of years, we can use the recurrence relation repeatedly. For example, to find the population after 3 years, we can write:

g_3 = 1.1g_2
g_2 = 1.1g_1
g_1 = 1.1g_0

If we start with a population of 100 mice (g_0 = 100), then we can find the population after 3 years as follows:

g_1 = 1.1g_0 = 1.1(100) = 110
g_2 = 1.1g_1 = 1.1(110) = 121
g_3 = 1.1g_2 = 1.1(121) = 133.1

So after 3 years, the population of mice would be approximately 133.



the recurrence relation that describes the sequence {g} is (b) = (1.1)⋅−1. This means that the population of mice after n years is equal to 1.1 times the population after n-1 years. To find the population after a specific number of years, we can use the recurrence relation repeatedly.

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Answer:

she didnt put an arrow on the x axis :)

Step-by-step explanation:

The idea that two variables are unrelated in the population is referred to as statistical independence. Therefore, option d is correct.

Statistical independence is a term used in probability theory and statistics to describe the independence of two random variables. If two random variables are independent, the occurrence of one does not have any impact on the probability distribution of the other.Therefore, if we have two random variables X and Y, and they are statistically independent, the occurrence of X has no effect on the likelihood of Y occurring. In other words, the occurrence of X does not affect the occurrence of Y in any way.So, we can say that two variables are said to be statistically independent when the occurrence of one variable does not have any influence on the probability of occurrence of the other variable. We can also say that there is no association between the two variables.In conclusion, we can say that statistical independence is a fundamental concept in probability theory and statistics, which helps to understand the relationship between two random variables and the probability of their occurrence.

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Answer:

\(Pr(x) = \frac{1}{6}\)

Step-by-step explanation:

Given

\(n = 30\) --- number of rolls

Required

The theoretical probability of rolling: (a) 1    (b) 4    (c) 6    (d) 7

Assume the cube is 6 sided.

The sample space is:

\(S = \{1,2,3,4,5,6\}\)

And the probability of each is:

\(Pr(x) = \frac{1}{6}\)

Irrespective of the number of rolls, the theoretical probability of (a). (b), (c) and (d) is:

\(Pr(x) = \frac{1}{6}\)

Answer:

first evening = 21 phone calls

second evening = 11 phone calls

third evening = 84 phone calls

Step-by-step explanation:

Total phone calls = 116

Let

Number of calls in the first evening = x

The second evening = x - 10

The third evening = 4x

Total phone calls = first evening + second evening + third evening

116 = x + (x - 10) + 4x

116 = x + x - 10 + 4x

116 + 10 = 6x

126 = 6x

x = 126 / 6

x = 21 phone calls

Number of calls in the first evening = x

= 21 phone calls

The second evening = x - 10

= 21 - 10

= 11 phone calls

The third evening = 4x

= 4(21)

= 84 phone calls

Let's draw a diagram of this problem:

This triangle can be seen as follows:

We can use the Law of Cosines to find the length of side c, since we know the measure of angle C:

In our case:

Taking the square root of both sides we get:

which, using a calculator or online resource to calculate the right side of the equation will give us:

To the nearest yard, A and B are 101 yards apart, so option A. is correct.

A function to define the area of the triangle is A(b,h) = (1/2)*b*h

A function is a process or a relation that associates each element 'a' of a non-empty set A , at least to a single element 'b' of another non-empty set B. A relation f from a set A (the domain of the function) to another set B (the co-domain of the function) is called a function in math. f = {(a,b)| for all a ∈ A, b ∈ B}.

1) A relation is said to be a function if every element of set A has one and only one image in set B.

2) A function is a relation from a non-empty set B such that the domain of a function is A and no two distinct ordered pairs in f have the same first element.

A function from A → B and (a,b) ∈ f, then f(a) = b, where 'b' is the image of 'a' under 'f' and 'a' is the preimage of 'b' under 'f'.

If there exists a function f: A → B, the set A is called the domain of the function f, and the set B is called its co-domain.

Let us assume that the base of the triangle is b and the height of the triangle is h.

So, a function to define the area of the triangle is

A(b,h) = (1/2)*b*h

This function is a function in two variables.

Thus, a function to define the area of the triangle is A(b,h) = (1/2)*b*h

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The solution to the inequality 4/5p + 9 ≥ 6 is:

p ≥ -15/4.

An inequality is solved similarly to an equality, as the desired variable to find the result is isolated.

The difference, compared to an equality, is that instead of a single value, the solution of an inequality is composed by a range of infinity values in the interval of the solution.

In this problem, the inequality is given as follows:

4/5p + 9 ≥ 6

Then the term with p is isolated as follows:

4/5p ≥ -3

Then p is isolated applying cross multiplication then division, as follows:

4p ≥ -15

p ≥ -15/4

Which is the solution to the given inequality, states as follows:

p is greater than or equal to negative fifteen fourths.

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A because 2 is half of 4 and 18 is half of 36.

Step-by-step explanation: because 2 is half of 4 and 18 is half of 36.

Answer:

Kindly check explanation

Step-by-step explanation:

Given the sound model:

s = 10│x - 4│+ 50

x = measure of music played ; s = sound level I. Decibel

Number measure at which sound level = 80

Plugging values into the equation:

80 = 10│x - 4│+ 50

Subtract 50 from Both sides so as to eliminate the 50 on the right hand side

80 - 50= 10│x - 4│+ 50 -50

30 = 10 |x - 4| + 0

Divide through by 10 so as to isolate the absolute inequality expression

3 = |x - 4|

Eliminate the absolute value sign

±3 = x - 4

Hence,

x = - 3 + 4 = 1

x = 3 + 4 = 7

Hence, x = 1 ; x = 7