The side of an equilateral triangle is 14 meters. What is the height of the triangle?.

The probability is that out of 12 customers, 7 will order a non-alcoholic beverage, and the remaining 5 will order an alcoholic beverage.

The likelihood that a client will arrange a non-alcoholic refreshment is given as 48%, which implies that the likelihood that a client will arrange an alcoholic refreshment is (100 - 48) = 52%.

Out of 12 customers, 5 will arrange liquor, which suggests that the remaining clients will arrange a non-alcoholic refreshment. We are able to calculate the number of clients who will arrange a non-alcoholic refreshment as takes after:

Number of clients who will arrange a non-alcoholic refreshment =

Add up to a number of clients - Number of clients who will arrange liquor

= 12 - 5

= 7

Subsequently, out of 12 clients, 7 will arrange a non-alcoholic refreshment, and the remaining 5 will arrange an alcoholic refreshment.

It is critical to note that these calculations are based on the presumption that each client will as it were arrange one refreshment. 

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We have to determine whether the given series converges or diverges. The given series is as follows: `(n+4)! / 4!(n!)` Let's use the ratio test to find out if this series converges or diverges.

The Ratio Test: It is one of the tests that can be used to determine whether a series is convergent or divergent. It compares each term in the series to the term before it. We can use the ratio test to determine the convergence or divergence of series that have positive terms only. Here, a series `Σan` is convergent if and only if the limit of the ratio test is less than one, and it is divergent if and only if the limit of the ratio test is greater than one or infinity. The ratio test is inconclusive if the limit is equal to one. The limit of the ratio test is `lim n→∞ |(an+1)/(an)|` Let's apply the Ratio test to the given series.

`lim n→∞ [(n+5)! / 4!(n+1)!] * [n!(n+1)] / (n+4)!` `lim n→∞ [(n+5)/4] * [1/(n+1)]` `lim n→∞ [(n^2 + 9n + 20) / 4(n^2 + 5n + 4)]` `lim n→∞ (n^2 + 9n + 20) / (4n^2 + 20n + 16)`

As we can see, the limit exists and is equal to 1/4. We can say that the given series converges. The series converges. To determine the convergence of the given series, we use the ratio test. The ratio test is a convergence test for infinite series. It works by computing the limit of the ratio of consecutive terms of a series. A series converges if the limit of this ratio is less than one, and it diverges if the limit is greater than one or does not exist. In the given series `(n+4)! / 4!(n!)`, the ratio test can be applied. Using the ratio test, we get: `

lim n→∞ |(an+1)/(an)| = lim n→∞ [(n+5)! / 4!(n+1)!] * [n!(n+1)] / (n+4)!` `= lim n→∞ [(n+5)/4] * [1/(n+1)]` `= lim n→∞ [(n^2 + 9n + 20) / 4(n^2 + 5n + 4)]` `= 1/4`

Since the limit of the ratio test is less than one, the given series converges.

The series converges to some finite value, which means that it has a sum that can be calculated. Therefore, the answer is a).

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Answer:

9*x=7

7/9=0.78(aprox)

Hope This Helps!!!

Answer: Let's write an equation to represent the cost of s square feet of fabric during the sale, considering the 10% discount.

The regular price of the fabric is $4.90 per square foot. The discount reduces the price by 10%. To calculate the sale price, we need to subtract the discount amount from the regular price.

Let's denote the cost of s square feet of fabric during the sale as C(s).

The regular price per square foot is $4.90. Therefore, the discount amount per square foot is (10/100) * $4.90 = $0.49.

The sale price per square foot is the regular price minus the discount amount:

Sale price per square foot = $4.90 - $0.49 = $4.41.

Now, we can write the equation for the cost of s square feet of fabric during the sale:

C(s) = $4.41 * s

This equation represents the cost of s square feet of fabric during the sale.

To show the change in the cost of fabric, we can write a transformation from the regular price to the sale price:

Regular price: $4.90 per square foot

Sale price: $4.41 per square foot

The transformation can be expressed as:

Sale price = (1 - 10/100) * Regular price

This shows that the sale price is obtained by multiplying the regular price by (1 - 10/100), which represents the 10% discount.

Answer:

4.41

Step-by-step explanation:

4.90 *.90 = 4.41

Answer:

heyyyy octo... i missed u a lot

Step-by-step explanation:

this is my mom's phone and yeah my tab broke ... Sorry couldnt talk... that's really hard for me...

Answer:

B. The second graph ! :)

Answer:

-3(n+8)=-3n-54

Step-by-step explanation:

-3xn=-3n

-3x8=-54

so put them together -3n-54

mistake i think you were meant to type 54 instead of 31

If we remove an arbitrary edge from a tree, the resulting graph will still be connected and acyclic (meaning it does not contain any cycles). This is because a tree is defined as a connected and acyclic graph. Removing an edge will not disconnect the graph since there is always at least one path between any two vertices in a tree. However, the resulting graph will no longer be a tree, as a tree must have exactly one fewer edge than vertices.

If we remove an arbitrary edge from a tree, then the resulting graph will be:

1. A disconnected graph: Since a tree is a connected graph with no cycles, removing an edge will separate it into two components.
2. The components will be trees: Each component will still have no cycles and will remain connected.

So, when you remove an arbitrary edge from a tree, the resulting graph will be a disconnected graph with two tree components.

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Answer:

5% of 30 is 1.5

25% of 30 is 7.5

25% is one quarter. 5% is a fifth of a quarter.

Answer:

5% of 30 is = 30 x 0.05 = 1.5

25% of 30 is 30 x 0.25 = 7.5

The difference is 6

The given series can be evaluated and determined whether it converges or diverges. In this case, the series diverges.

To explain the divergence, let's analyze each term in the series individually. The first term is 101.21/n, which tends to zero as n approaches infinity. The second term is 21/(n+1), which also tends to zero as n approaches infinity. The third term is n, which grows without bound as n increases. The fourth term is 1/102(n+1), which tends to zero as n approaches infinity. The fifth term is 13/103, which is a constant value. Finally, the sixth term is (sin n * sin(n+1))/104, which oscillates between -1 and 1 as n increases.

The divergence of the series can be attributed to the fact that the terms do not approach a finite value as n approaches infinity. The terms oscillate, grow without bound, or tend to zero at different rates. Therefore, the series does not converge to a specific value and is classified as divergent.

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a) If the \(n\)-th term is \(x_n = cn+d\), then

\(x_1 = c + d = 16\)

\(x_2 = 2c + d = 19\)

Eliminating \(d\),

\((2c+d) - (c+d) = 19-16 \implies c = 3\)

Solving for \(d\),

\(3 + d = 16 \implies d = 13\)

Then

\(\boxed{x_n = 3n + 13}\)

b) When \(n=11\), we get

\(x_{11} = 3\cdot11 + 13 = \boxed{46}\)

To determine the addition and multiplication tables for the congruence-class ring F[x]/(p(x)), we first need to find the congruence-class representatives for the polynomials modulo p(x). In this case, we have F = Z3 and p(x) = \(x^{2}\) + 1.

The congruence-class representatives for F[x]/(p(x)) are given by the polynomials of degree at most 1: 0, 1, 2, x, x + 1, x + 2. These representatives will be used to construct the addition and multiplication tables.

Addition table:

+  |  0   1   2   x  x+1 x+2

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

0  |  0   1   2   x  x+1 x+2

1  |  1   2   x  x+1 x+2  0

2  |  2   x  x+1 x+2  0   1

x  |  x  x+1 x+2  0   1   2

x+1| x+1 x+2  0   1   2   x

x+2| x+2  0   1   2   x  x+1

Multiplication table:

*  |  0   1   2   x  x+1 x+2

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

0  |  0   0   0   0   0   0

1  |  0   1   2   x  x+1 x+2

2  |  0   2   1  x+2 x+1  x

x  |  0   x  x+2 x+1  2   1

x+1|  0 x+1 x+1  2   1  x+2

x+2|  0 x+2  x  1  x+2 x+1

To determine if F[x]/(p(x)) is a field, we need to check if every non-zero element in the ring has a multiplicative inverse. In this case, we can see that the element x does not have a multiplicative inverse since it is not possible to find a polynomial y(x) such that x * y(x) ≡ 1 (mod p(x)). Therefore, F[x]/(p(x)) is not a field for F = Z3 and p(x) = \(x^{2}\) + 1.

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There are 225 prime-looking numbers less than 1000. To determine this, we need to find composite numbers that are not divisible by 2, 3, or 5.

We know that there are 168 prime numbers less than 1000. To find the prime-looking numbers, we can subtract the number of prime numbers from the total number of composite numbers less than 1000.

There are a total of 999 - 168 = 831 composite numbers less than 1000.

Next, we need to remove the composite numbers that are divisible by 2, 3, or 5.

Out of the 831 composite numbers, we can identify those divisible by 2, 3, or 5 by checking their last digit. If the last digit is 0, 2, 4, 5, 6, or 8, the number is divisible by 2 or 5. If the sum of its digits is divisible by 3, the number is divisible by 3. By removing these numbers, we can find prime-looking numbers.

After performing these calculations, we find that there are 225 prime-looking numbers less than 1000.

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Using the concept of the angle the conditions are solved. For any whole number n, 360+58n is coterminal with 418°. option C is correct.

Angle is the space between the line or the surface that meets.  And the angle is measured in degree. For complete 1 rotation, the angle is 360 degrees.

Given

The measures of all angles are coterminal with a 418° angle.

a.  360+58n, for any whole number n.

For any whole number n, 360+58n is not coterminal with 418° except one.

b.  58+360n, for any integer n.

For any integer number n, 360+58n is coterminal with 418° except zero.

c.  58+360n, for any whole number n.

For any whole number n, 360+58n is coterminal with 418°.

d.  360 58n, for any integer n.

For any integer number n, 360+58n is not coterminal with 418° except one.

Thus, for any whole number n, 360+58n is coterminal with 418°. option C is correct.

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Answer:

Step-by-step explanation:

122444

The DC current gain (βdc) of the transistor is 73.

The DC current gain (βdc) of a transistor is the ratio of the collector current (IC) to the base current (IB) at DC conditions. Therefore, to determine the βdc of a transistor with IB = 50 µA and IC = 3.65 mA, we simply substitute these values into the equation:

βdc = IC / IB

βdc = 3.65 mA / 50 µA

βdc = 73

Therefore, the DC current gain (βdc) of the transistor is 73.

This result indicates that for every 1 µA of base current, the transistor can allow 73 µA of collector current to flow. A high βdc value indicates that the transistor can provide significant amplification in a circuit. In addition, the βdc value is essential in selecting the appropriate biasing resistors and determining the operating point of the transistor in amplifier circuits.

Thus, by determining the βdc value, we can gain valuable insights into the performance characteristics of a transistor and how it can be used in various circuit designs.

Therefore, The DC current gain (βdc) of the transistor is 73.

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Answer:

C. x = 2

Step-by-step explanation:

In the given triangle,

The measure of angle O is 56°

The length of side MO is approximately 14.5 cm

The length of side NO is approximately 8.1 cm

From the question, we are to solve the given triangle

First, we will determine the measure of angle O

m ∠O + m ∠M = 90° (Complementary angles)

Thus,

m ∠O + 34° = 90°

m ∠O = 90° - 34°

m ∠O = 56°

Using SOH CAH TOA, we can determine the lengths of sides MO and NO

cos (34°) = 12/MO

MO = 12 / cos (34°)

MO = 14.47 cm

MO ≈ 14.5 cm

Also,

tan (34°) = NO / 12

NO = 12 × tan (34°)

NO = 8.09 cm

NO ≈ 8.1 cm

Hence, the length of NO is 8.1 cm

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Answer:

8 - x

Step-by-step explanation:

Answer:

between 10 and 12

Step-by-step explanation:

Given the measure of angles:

m∠B = 70°

m∠C = 60°

m∠A = 50°

Following this information, since the side lengths are directly proportional to the angle measure they see:

Angle B is the largest angle. Therefore, side AC is the longest side of the triangle since it is opposite of the largest angle.

Angle C is the smallest angle, so the side AB is the shortest side.

Therefore, side BC must be between 10 and 12 inches.

Answer:

Step-by-step explanation:

is an opposite angle, therefore congruent, same value 45°

Answer:

45

Step-by-step explanation:

hello, the answer is 45

Answer:

392?

Step-by-step explanation:

to find perimeter you add each side I think, so...

50 + 50 + 50 + 50 + 96 + 96 = 392

No clue if I did this properly but based on my math I did it right not sure the formula you are using/ should be using to figure this out.

The linear correlation between the given two variables be,

4.5y + 5.2x = 168.34

Given, data for a classroom of students who measured each (approximately) in inches.

Femur Length 18.7 14.2 20.5 15.9 16.2 13.1 15.0 12.4 19.0 16.2 21.3

Tibia Length  15.8 21.0 16.2 14.3 12.1 15.8 13.0 18.8 14.3 18.7 13.8

we have to find a linear correlation between the two variables,

linear correlation be,

(y - 15.8)/(x - 18.7) = (15.8 - 21.0)/(18.7 - 14.2)

(y - 15.8)/(x - 18.7) = (- 5.2)/4.5

4.5y - 71.1 = -5.2x + 97.24

4.5y + 5.2x = 168.34

So, the linear correlation between the given two variables be,

4.5y + 5.2x = 168.34

Hence, the linear correlation between the given two variables be,

4.5y + 5.2x = 168.34

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The approximated area of the pentagon that has side lengths of 14.1 cm and an apothem of 12 cm is 342 square centimeters

The given parameters are:

Length, l = 14.1 cm

Apothem, a = 12 cm

The area of the pentagon is calculated using:

\(A= 0.25 * \sqrt{5 * (5 + 2\sqrt 5)} * l^2\)

So, we have:

\(A= 0.25 * \sqrt{5 * (5 + 2\sqrt 5)} * 14.1^2\)

Evaluate

A = 342

Hence, the approximated area of the pentagon is 342 square centimeters

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Answer:

342 cm2  B)

Step-by-step explanation:

edg2022

Answer:

28125

Step-by-step explanation:

The \(n\)th term of your geometric sequence is \(9\cdot5^{n-1}\). This means that the 6th term is \(9\cdot5^{6-1}=28125\).

Answer:

10a - 3b +6c

Step-by-step explanation:

The surveyor is located about 239.6 feet away from the base of the Willis Tower.

The height of the Willis Tower is 165 feet.

The angle of elevation from the surveyor to the top of the antenna is about 3.41°.

The height of the antenna is about 135.9 feet.

Let's call the distance from the surveyor to the base of the Willis Tower "x", and let's call the height of the Willis Tower "h".

We can use trigonometry to solve for x and h. First, let's find x:

tan(34°) = h/x

x = h/tan(34°)

Now we can use the distance from the surveyor to the top of the building to solve for h:

h + 2595 = 2760

h = 165

So the height of the Willis Tower is 165 feet. Now we can solve for x:

x = 165/tan(34°) ≈ 239.6 feet

So the surveyor is located about 239.6 feet away from the base of the Willis Tower.

To find the angle of elevation from the surveyor to the top of the antenna, we can use trigonometry again:

tan(θ) = h/2760

θ = tan^(-1)(h/2760)

θ ≈ 3.41°

So the angle of elevation from the surveyor to the top of the antenna is about 3.41°.

Finally, we can use the height of the Willis Tower and the distance from the surveyor to the top of the antenna to solve for the height of the antenna:

tan(34°) = (h + a)/2760

a ≈ 135.9

So the height of the antenna is about 135.9 feet.

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Answer: 6 and 6

6 + 6 = 12 and 6 * 6 = 36

Answer:

x-3=6

Step-by-step explanation:

Answer:

D and E are both greater than 1

Step-by-step explanation:

2(-6)+7=-5

2(-5)+7=-3

2(2)+7=11

2(3)+7=13

One final test that lasts three hours is given in addition to four-hour exams that are given by the teacher. The student's last grade is an 83.29.

The final exam result was an 80, which counts as 31 hour examinations if the exam scores range from 60 to 81, which totals to 97,87. In order to accomplish this, we must multiply three eighty by 62, 81, 97, and 87, which equals a 31-hour exam.

The whole time for the final exam, which is 31 hours, will be added up and divided by 7, giving us an average final grade for the student of 81.To reduce the number's number of significant digits in order to approximate it. Rounding down from 15.4 to 15.5, from 15.51 to 15.5 or 16, from 0.499 to 0, and from 970,000 to 1 million.

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