Part B: In complete sentences, explain how a circle can be used to find the circumcenter of the triangle graphed below.
Part C: Use a circle to locate the circumcenter of the triangle. Provide the location of the circumcenter.

The topsoil will be 4.05 inches deep

From the question, we are to determine how many inches deep the topsoil will be

From the given information,

The volume of the topsoil = 1 cubic yard

Convert to cubic feet

1 cubic yard = 27 cubic feet

∴ The volume of the topsoil = 27 cubic feet

Then,

The depth of the topsoil will be = 27/(8 ×10)

Depth of topsoil = 27/80

Depth of topsoil = 0.3375 foot

Now, convert to inches

1 foot = 12 inches

∴ 0.3375 foot = 0.3375×12 inches

= 4.05 inches

Hence, the topsoil will be 4.05 inches deep

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Using the hypergeometric distribution, the probabilities are given as follows:

a) 0.0333 = 3.33%.

b) 0.5 = 50%.

c) 0.8333 = 83.33%.

d) 0.9667 = 96.67%.

The formula is:

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

The parameters are:

The values of the parameters are:

N = 10, n = 3, k = 4.

Item a:

The probability is P(X = 3), hence:

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]

[tex]P(X = 3) = h(3,10,3,4) = \frac{C_{4,3}C_{6,0}}{C_{10,3}} = 0.0333[/tex]

Item b:

The probability is P(X = 1), hence:

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]

[tex]P(X = 1) = h(1,10,3,4) = \frac{C_{4,1}C_{6,2}}{C_{10,3}} = 0.5[/tex]

Item c:

The probability is:

[tex]P(X \geq 1) = 1 - P(X = 0)[/tex]

In which:

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]

[tex]P(X = 0) = h(0,10,3,4) = \frac{C_{4,0}C_{6,3}}{C_{10,3}} = 0.1667[/tex]

Then:

[tex]P(X \geq 1) = 1 - P(X = 0) = 1 - 0.1667 = 0.8333[/tex]

Item d:

The probability is:

[tex]P(X \leq 2) = 1 - P(X = 3)[/tex].

Considering item a:

[tex]P(X \leq 2) = 1 - P(X = 3) = 1 - 0.0333 = 0.9667[/tex]

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Let [tex]O[/tex] be the random variable for the number of bad oranges picked out. Then

[tex]P(O=o) = \dfrac{\dbinom6{3-o} \dbinom4o}{\dbinom{10}3}[/tex]

if [tex]o\in\{0,1,2,3\}[/tex] and zero otherwise, where

[tex]\dbinom nk = \dfrac{n!}{k!(n-k)!}[/tex]

is the so-called binomial coefficient.

(a) Of the 6 good oranges, you pick 0. Of the 3 bad oranges, you pick 3. Of the 10 total oranges, you pick 3. So the probability of picking out all bad oranges is

[tex]P(O=3) = \dfrac{\dbinom60 \dbinom43}{\dbinom{10}3} = \boxed{\dfrac1{30}}[/tex]

(b) By similar reasoning, the probability of drawing exactly 1 bad orange is

[tex]P(O=1) = \dfrac{\dbinom62 \dbinom41}{\dbinom{10}3} = \boxed{\dfrac12}[/tex]

(c) "At least 1 bad orange" means you pick out 1, 2, or 3 bad oranges. These events are mutually exclusive, and we already know the probabilities of picking out exactly 1 or all 3 bad oranges. The remaining probability of drawing 2 bad oranges is

[tex]P(O=2) = \dfrac{\dbinom61 \dbinom42}{\dbinom{10}3} = \dfrac3{10}[/tex]

so the overall probability of drawing at least 1 bad orange is

[tex]P(O\ge1) = P(O=1)+P(O=2)+P(O=3) =\dfrac1{30} + \dfrac3{10} + \dfrac12 = \boxed{\dfrac56}[/tex]

(d) I assume you mean "at most 2 bad oranges," meaning you pick out 0, 1, or 2 bad oranges. Again, these events are mutually exclusive, and the probability of picking out no bad oranges is

[tex]P(O=0) = \dfrac{\dbinom63 \dbinom40}{\dbinom{10}3} = \dfrac16[/tex]

hence the probability of drawings at most 2 bad oranges is

[tex]P(O\le2) = P(O=0) + P(O=1) + P(O=2) = \dfrac16 + \dfrac12 + \dfrac3{10} = \boxed{\dfrac{29}{30}}[/tex]

Answer:

c.) aₙ = 5 × 4ⁿ⁻¹

Explanation:

Geometric sequence: aₙ = a(r)ⁿ⁻¹

where 'a' resembles first term of a sequence, 'r' is the common difference.

Here sequence: 5, 20, 80, 320,...

First term (a) = 5

Common difference (d) = second term ÷ first term = 20 ÷ 5 = 4

Hence putting into equation: aₙ = 5(4)ⁿ⁻¹

Answer: [tex]g(x)=\left|\frac{x}{5} \right|[/tex]

Step-by-step explanation:

See atached image.

The Income Statement for Nascar Motors in April and May 2017 under Throughput Costing is given as attached.

This refers a costing technique, also known as super-variable costing, which solely takes direct materials into account when calculating product costs.

The other expenses are all classed as period costs and are all deducted from income in the time period in which they are spent.

It is to be noted that Throughput costing has the lowest operating income in April while having the greatest operating income in May.

More so than either absorption or variable costing, throughput costing emphasizes sales as the source of operational income. See the attached.

It is to be noted that production that doesn't result in a commensurate sale in the same time period is penalized under throughput costing.

When compared to variable costing, costs that are variable with regard to production but are not direct materials are expensed in the period of incurrence.

In contrast to variable costing or absorption costing, throughput costing offers less of motivation to create inventory.

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The expected value of your bet will be the negative $16.27 that mean loses.

Binomial distributions consist of n independent Bernoulli trials.

The expected value will be

E(X) = np

Suppose that you and a friend are playing cards and decide to make a bet.

If you draw two face cards, where a face card is a Jack, a Queen, or a King, in succession from a standard deck of 52 cards replacing the first card, you win $50.

Otherwise, you pay your friend $20.

Then the probability of winning will be

p = (12 / 52)(12 / 52)

p = 9 / 169

Then the probability of loosing will be

q = 1 – p

q = 1 – 9/169

q = 160 / 169

Then the expected value will be

E(x) = (9/169) x 50 + (160/169) x (-20)

E(x) = -$16.27

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Answer:

x + 3

Step-by-step explanation:

x = Anna's age

y = John's age

z = Tamara's age

y = x + 1

z = x - 2

the expression for the sum of Anna's and John's age minus Tamara's age is

x + y - z

and when we use the equations above to simplify that :

x + (x + 1) - (x - 2) = x + x + 1 - x + 2 = x + 3

Answer:

The Prime Factorization of 220 is 22 × 51 × 111.

Step-by-step explanation:

Factors of 220 are integers that can be divided evenly into 220. It has total 12 factors of which 220 is the biggest factor and the prime factors of 220 are 2, 5, 11. There for, the  Prime Factorization of 220 is 22 × 51 × 111.

LCM of 4x²-100 and 4x + 20 is 4(x+5)(x-5)

What is  Least Common Multiple?

Least Common Multiple is defined as the smallest number that is a multiple of two or more numbers.

We have to factorise 4x²-100 which is of the form A²-B²,

= (2x)² -(10)²

= (2x+10)(2x-10)

= 2×2(x+5)(x-5)

= 4(x+5)(x-5).

We have to factorise 4x + 20​

= 4(x+5)

LCM of 4x²-100 and 4x + 20 = 4(x+5)(x-5).

Hence, LCM of 4x²-100 and 4x + 20 is 4(x+5)(x-5)

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Answer:

16

Step-by-step explanation:

The outlier in the given dataset is "16".

Given is a data set 69, 16, 79, 80, 82, we need to determine the outliners of the set,

To identify outliers in a dataset, we generally use a statistical method such as the z-score or the IQR (interquartile range).

Since, the provided dataset is small with only five values, we can manually identify the outliers by observing the data.

An outlier is a value that significantly deviates from the rest of the dataset.

Let's examine the given dataset:

69, 16, 79, 80, 82

To identify outliers, we can consider any data points that are notably different from the others.

In this case, it seems that the value "16" is considerably lower than the other values.

Let's label it as a potential outlier.

Therefore, the outlier in the given dataset is "16".

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Answer: Width = 15cm

              L = 31cm

Step-by-step explanation:

P = 92 cm

L = 1 + 2W

P = 2L + 2W

P = 2(1+2W) + 2W

P = 2+4W+2W

P = 2 + 6W

92cm = 2 + 6W

subtract 2 on both sides to cancel the 2 on the right side.

90cm = 6W

W = 90/6

Width = 15cm

L = 1+2W

L = 1 + 30cm

L = 31 cm

Verification:

P = 2L+2W

P = 2(31)+2(15)

P = 62+30

P = 92cm

Hope I Helped!

Answer:

P = 2(L + W) = 2L + 2W (first part)

L = 2W + 1 (second part)

Step-by-step explanation:

L = length of rectangle
W = width of rectangle
P = perimeter of rectangle = 2 * (L + W)
So P = 2(L + W) = 2L + 2W  (1)

It is also given that length is 2 * width + 1

So we get the equation

L = 2W + 1 for L in terms of W  (2)

This question does not ask you to compute L and W but if you wanted to do that use the following steps
Substitute for L from equation 2 to equation 1 giving
P = 2(2W+1) + 2W = 4W + 2 + 2W = 6W + 2

We know P = 92

So 6W + 2 = 92
Subtracting 2 from both sides we get 6W = 90
Dividing both sides by 6 gives us W = 15
and L = 2 * 15 + 1 = 31

We can check this by finding the perimeter from L and W
perimeter = 2(L+W) = 2(31 + 15) = 2 (46) = 92 which matches the data in the question

The key features of the graph are:

The graph has a minimum value at (-2, -1)

This represents the vertex

The x coordinate of the vertex is the axis of symmetry.

So, we have

x = -2

The graph crosses the y-axis at (0, 3)

This represents the y-intercept

The graph opens up.

This means that the vertex is minimum.

The domain is the set of all real number, because the graph extends in both directions on the x-axis without end

While the range is y >= -1, because it has a minimum at this point

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Step-by-step explanation:

You can't use quadratic formula in this

6.5 s  take the projectile to hit the ground.

A projectile is any object thrown into space upon which the only acting force is gravity.

Given:

speed = 25 m/s

h(t) = -5t² + 25t  + 70

height = 70 m

Time to reach maximum height

( u sin90)/2g

= 25/2*9.8

= 1.275s

Max height = u²Sin²[tex]\theta[/tex]/g

=25*25/9.8

=63.775

So, total height=63.775 + 70 = 133.775 m

Now, time to fall back to the ground

h = ut+(1/2)gt²

t² = (h- ut)2/g

u=0

H= 133.775 m

(133.775*2)/9.8= t²

t² = 27.3010

t= 5.225 s

Total time taken to hit ground

= 5.225 + 1.275

= 6.5 s

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-------------------------------------------------------------------------------------------------------------

Answer:  [tex]\textsf{y = 4/11}[/tex]

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Given: [tex]\textsf{2y + 14 = 6(4y + 1)}[/tex]

Find:  [tex]\textsf{Solve for y}[/tex]

Solution:  In order to solve for y we need to distribute the ride side of the expression, simplify, subtract 14 from both sides, subtract 24y from both sides, and divide both sides by -22.

Distribute and simplify

Subtract 14 from both sides

Subtract 24y from both sides

Divide both sides by -22

Therefore, the expression simplifies down to y = 4/11.

Probability the selected number is even is 7/15

Probability the selected number is a multiple of 4 is 1/5

Probability the selected number is prime = 2/5

Probability is the likelihood of an event happening or an event not happening.

When it is certain an event would happen the probability is 1.

Probability can be independent or mutually exclusive.

Analysis:

Required outcome

A = {2, 4, 6, 8, 10, 12, 14} (even numbers)

Total entry = 7

Total Sample = 15

P(even numbers) = 7/15

B (multiples of 4) = {4, 8, 12}

Total entry = 3

P(B) = 3/15 = 1/5

C(prime numbers) = {2, 3, 5, 7, 11, 13}

Total entry = 6

P(C) = 6/15

P(A and C) = 0.

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Using substitution, the result of the indefinite integral is:

[tex]3\ln{(1 + x^{\frac{1}{3}})} + C[/tex]

The integral is:

[tex]\int \frac{1}{x^{\frac{2}{3}}(1 + x^{\frac{1}{3}})} dx[/tex]

The substitution is:

[tex]u = 1 + x^{\frac{1}{3}}[/tex]

Then the derivative is:

[tex]du = \frac{1}{3}x^{-\frac{2}{3}} dx[/tex]

ttex]dx = 3dux^{-\frac{2}{3}}[/tex]

Hence the integral is:

[tex]\int \frac{1}{x^{\frac{2}{3}}(1 + x^{\frac{1}{3}})} dx[/tex]

[tex]\int \frac{1}{x^{\frac{2}{3}}u} \times 3dux^{-\frac{2}{3}}[/tex]

[tex]\int \frac{3du}{u}[/tex]

[tex]3\ln{u} + C[/tex]

Returning to x:

[tex]3\ln{(1 + x^{\frac{1}{3}})} + C[/tex]

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Step-by-step explanation:

x/7 ≥ -6

we rewrite it as :

x/7 = -6

by cross multiplication

x = -42

In order words:

x ≥ -42

Hope this helps

Good luck ✅

The cost of the file is $6.15 and the cost of the pen is $8.9

The interpretation of the given word problem leads to a system of linear equations.

From the given information:

f + 3p = 32.85 --- (1)

2f + 8p = 83.5 --- (2)

From equation (1)

f = - 3p+32.85

Replace the value of f in the above equation into equation (2)

2(-3p + 32.85) + 8p = 83.5

2p + 65.7 = 83.5

2p = 83.5 -65.7

2p = 17.8

p = 17.8/2

p = 8.9

Replacing the value of p = 8.9 into f = - 3p+32.85

f = -3(8.9)+32.85

f = 6.15

Therefore, we can conclude that the cost of the file is $6.15 and the cost of the pen is $8.9.

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The statement third "Betty wrote an indirect proof using contradiction' and statement fourth "Ken wrote direct proof using deductive evidence" are correct.

When two lines or rays converge at the same point, the measurement between them is called a "Angle."

We have Ken's statements are shown in the table:

Angle AOC = Angle BOD (given)

Angle AOB + Angle BOC = Angle BOC + Angle COD   (angle addition postulate)

Angle AOB = ANgle COD (subtraction property of equality)

Ken wrote direct proof using deductive evidence.

As we can in betty's proof:

Betty wrote an indirect proof using contradiction.

Thus, the statement third "Betty wrote an indirect proof using contradiction' and statement fourth "Ken wrote direct proof using deductive evidence" are correct.

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The equivalent pair of the given expression is; [4.8] and [3.21]

Floor function states that the greatest integer that is less than or equal to x. It is represented by:  ⌊ x ⌋.

Ceiling function states that the least integer that is greater than or equal to x. It is represented by ⌈ x ⌉.

Kareem wrote the expressions;

[3.2] [2.7] [2.9] [4.8]

By definition above;

[3.2] = 4

[2.7] = 2

[2.9] = 3

[4.8] = 4

Thus, the equivalent pair is [4.8] and [3.2]

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The coordinates of the point of intersection of y=3x−3 and y=7−2x is (2, 3)

From the question, we are to graph the given equations.

The graph of the equations is attached below.

In the graph, we can observe that the coordinates of the point of intersection of the is (2, 3)

Hence, the coordinates of the point of intersection of y=3x−3 and y=7−2x is (2, 3)

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It can be concluded that ΔWXY is equivalent to ΔBCD by the SAS rule because the corresponding sides and corresponding angle are congruent. Option D

SAS congruency states that  two triangles are said to be congruent if any two sides or angle between the sides of one triangle are equal to the corresponding two sides and also the angle between the sides of the second triangle.

Thus, it can be concluded that ΔWXY is equivalent to ΔBCD by the SAS rule because the corresponding sides and corresponding angle are congruent. Option D

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Answer:

B. No, because the corresponding congruent angles listed are not the included angles.

Step-by-step explanation:

The number of spoons that can be purchased is 11, whereas the equation is given as 8x + 10 ≤ 100

An equation is an expression that shows the relationship between two or more variables and numbers.

The cost of each spoon is $8, hence A = 8. The cost of painting is 10, hence B = 10. Joshua can spend at most 100$, C = 100

8x + 10 ≤ 100

x ≤ 11.25

The number of spoons that can be purchased is 11, whereas the equation is given as 8x + 10 ≤ 100

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Answer:

92 spoons can be purchased.

Step-by-step explanation:

10x + 8 ≤ 100

10x + 8 ≤ 100

8 - 8 10x 100 - 8

10x ≤ 92

x = 1/5

10 x 1/5 = 92.

<---------------------------------------------------------------------------------------------------------->

 <----------------------------------------------------0---------------------------- 92

Answer:

5621 years

Step-by-step explanation:

Plug everything in first.

[tex]N=N_0e^{-kt}\\\\\implies 0.57 = e^{-0.0001t}\\\\\implies\ln \left(0.57\right)=-0.0001t\\\\t=-\frac{\ln \left(0.57\right)}{0.0001}[/tex]

Round to closest amount of years = 5621 years

The graph is in the attached image.

Answer:

:)\

Step-by-step explanation:

By using the definitions of unit circle and trigonometric functions, we find that the tangent of the terminal point of the angle is equal to 0.

In trigonometry, an unit circle is a circle with a radius of 1 and used to determine the values of trigonometric functions. There are two fundamental trigonometric functions: (i) sine, (ii) cosine, and the tangent is a derivate trigonometric function, which is defined below:

tan θ = y/x     (1)

If we know that x = 1 and y = 0, then the tangent of the terminal point of angle is:

tan θ = 0/1

tan θ = 0

By using the definitions of unit circle and trigonometric functions, we find that the tangent of the terminal point of the angle is equal to 0.

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Answer:

tan= 0

Step-by-step explanation:

^^^correct :)