Marvin wrote down all of the numbers from 1 to 100. How many times did the digit 8 appear in Marvins's list?

Answer:

36

Step-by-step explanation:

4/9 x = 16

9/4 * 4/9 x = 16 * 9/4

x = 36

The solution are,

The solution is, the measure of the, inscribed angle: 30°, and,

central angle: 60°.

here, we have,

from the given figure, we get,

The central angle is double the inscribed angle for the same intercepted arc.

Since doubling the angle adds 30° to it,

the original inscribed angle must be 30°.

so, we get,

Then the central angle is 30°+30° = 2·30° = 60°.

The solution are,

the measure of angle C is 52°

the measure of angle B is 52°

the measure of angle BSD is 71°

the measure of angle CSE is 71°

the measure of angle E is 57°

the measure of arc BC 57°.

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The result for the given 14 length bit string is-

(a) The bit strings of length 14 which have exactly three 0s is 2184.

(b) The bit strings of length 14 which have same number of 0s as 1s is 17297280.

(c) The bit strings of length 14 which have at least three 1s is 4472832.

A bit-string would be a binary digit sequence (bits). The size of the value is the amount of bits contained in the sequence.

A null string is a bit-string with no length.

The concept used here is permutation;

ⁿPₓ = n!/(n-x)!

Where, n is the total samples.

x is the selected samples.

(a) Because there are exactly three 0s, its other digits have always been one, hence the total of permutations is equal to;

n = 14 and x = 3 digits.

¹⁴P₃ = 14!/(14-3)!

¹⁴P₃ = 2184.

Thus, the bit strings of length 14 which have exactly three 0s is 2184.

(b) Because it is a bit string with 14 digits and it can only have digits 0 or 1, we must choose 7 0s and the remaining 7 1s, hence the number possible permutations is equal to;

n = 14 and x = 7 digits.

¹⁴P₇ = 14!/(14-7)!

¹⁴P₇ = 17297280.

Thus, the bit strings of length 14 which have same number of 0s as 1s is 17297280.

(c) The answer is identical to problem a, but the rest of a digits could be either 0 or 1, hence it must be doubled by 2¹¹ because there are 11 digits, each of which can be one of two options;

= 2184×2¹¹

= 4472832

Thus, he bit strings of length 14 which have at least three 1s is 4472832.

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The correct question is-

How many bit strings of length 14 have:

(a) Exactly three 0s?

(b) The same number of 0s as 1s?

(d) At least three 1s?

Pythagoras was an ancient Greek mathematician who founded the Pythagorean school of thought. The Pythagorean theorem is a fundamental concept in mathematics that is attributed to Pythagoras and his followers.

It states that in a right-angled triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the other two sides. While this theorem is considered a cornerstone of mathematics today, it is important to understand that Pythagoras did not have access to the advanced mathematical tools and methods that we have today.

He had to rely on geometric constructions and reasoning to prove his theorem. Furthermore, Pythagoras believed that all numbers could be expressed as ratios of whole numbers, which is not always true in reality. Despite these limitations, the Pythagorean theorem has stood the test of time and continues to be a crucial tool in mathematics and other fields.

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Answer:

I believe the answer would be C. Point G.

Answer:

Point F

Step-by-step explanation:

Start from 5 u have to count 8 backwards.

(a) Power series representation for f(x) = 1 / (8 + x)², we can differentiate the geometric series representation of 1 / (8 + x). The geometric series representation of 1 / (8 + x) is:

1 / (8 + x) = 1/8 * (1 / (1 + x/8)) = 1/8 * (1 - x/8 + (x/8)² - (x/8)^3 + ...)

Differentiating this series term by term, we get:

f'(x) = -1/64 * (1 - x/8 + (x/8)² - (x/8)² + ...)' = -1/64 * (-1/8 + 2(x/8²) - 3(x/8³) + ...)

f'(x) = 1 / (8 + x)² = 1/64 * (1/8 - 2(x/8²) + 3(x/8³) - ...)

Therefore, the power series representation for f(x) = 1 / (8 + x)² is:

f(x) = Σ [n=0 to ∞]\((-1)^n\) * (n+1) * \((x/8)^{(n+1)\).

The radius of convergence, R, can be determined using the ratio test. By applying the ratio test to the power series, we find that the radius of convergence is 8.

(b) Using the result from part (a), we can find a power series representation for f(x) = 1 / (8 + x)³. To do this, we differentiate the power series representation for f(x) = 1 / (8 + x)².

f'(x) = Σ [n=0 to ∞]\((-1)^n\) * (n+1) * (n+2) * \((x/8)^{(n)\)

Next, we integrate the resulting series term by term to obtain the power series for f(x) = 1 / (8 + x)³:

f(x) = Σ [n=0 to ∞]\((-1)^n\) * (n+1) * (n+2) * \((x/8)^{(n+1)\) / (n+1)

f(x) = Σ [n=0 to ∞] (-1)^n * (n+2) *\((x/8)^{(n+1\).

The radius of convergence, R, remains 8, as it is inherited from the radius of convergence of the original power series.

(c) Using the result from part (b), we can find a power series representation for f(x) = x² / (8 + x)³. We multiply each term of the power series for f(x) = 1 / (8 + x)³ by x²:

f(x) = x² * Σ [n=0 to ∞] \((-1)^n\) * (n+2) * \((x/8)^{(n+1)\).

f(x) = Σ [n=0 to ∞] \((-1)^n\) * (n+2) *\((x/8)^{(n+3)\).

The radius of convergence, R, remains 8, as it is inherited from the radius of convergence of the original power series.

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Answer:

3

Step-by-step explanation:

Answer:

98 is ur answer

xd hope it help u :)

Solution:

Given:

The radius and tangent to a circle at the point of intersection are perpendicular to each other.

Hence, considering the right triangle;

Hence, the length of the missing side can be gotten using the Pythagorean theorem.

Therefore, to the nearest tenth, the length of the missing side is 6.3

Answer:

2/12 is equivalent fraction for 2/3 divided by 4

Step-by-step explanation:

2

3

&

4

2

3

÷

4= ?

step 2 Multiply 2/3 with reciprocal of 4

=2

3

x1

4

=2

12

The Quotient is 1/3.

One of the four fundamental mathematical operations, along with addition, subtraction, and multiplication, is division. Division is the process of dividing a larger group into smaller groups so that each group contains an equal number of things.

Given:

2/3 divided by 4

As, division is not possible in fraction so we will perform the multiplication

= 2/3  ÷ 4

= 2/3 x 1/4

= 2/6

= 1/3

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Step-by-step explanation:

I hope this helps you if you have any questions please feel free to contact me

The ratio of corresponding sides for the given similar triangles is 2/5.

In the given options, the ratio of corresponding sides is provided for each set of similar triangles. Let's analyze each option to determine the correct ratio:

a. 10

This option only provides a single number and does not specify the ratio of corresponding sides. Therefore, it is not the correct answer.

b. 4/5

This option provides the ratio 4/5 for the corresponding sides of the similar triangles. However, the ratio can be simplified further.

To simplify the ratio, we divide both the numerator and denominator by their greatest common divisor (GCD). In this case, the GCD of 4 and 5 is 1.

Dividing 4 and 5 by 1, we get:

4 ÷ 1 = 4

5 ÷ 1 = 5

Therefore, the simplified ratio is 4/5.

c. 10/85

This option provides the ratio 10/85 for the corresponding sides of the similar triangles. However, this ratio cannot be simplified further, as 10 and 85 do not have a common factor other than 1.

Therefore, the correct ratio of corresponding sides for the given similar triangles is 2/5, as determined in option b.

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i think this is correct

Answer:

x = sqrt(11 - y) - 2 or x = -sqrt(11 - y) - 2

Step-by-step explanation:

Solve for x:

y = -x^2 - 4 x + 7

y = -x^2 - 4 x + 7 is equivalent to -x^2 - 4 x + 7 = y:

-x^2 - 4 x + 7 = y

Multiply both sides by -1:

x^2 + 4 x - 7 = -y

Add 7 to both sides:

x^2 + 4 x = 7 - y

Add 4 to both sides:

x^2 + 4 x + 4 = 11 - y

Write the left hand side as a square:

(x + 2)^2 = 11 - y

Take the square root of both sides:

x + 2 = sqrt(11 - y) or x + 2 = -sqrt(11 - y)

Subtract 2 from both sides:

x = sqrt(11 - y) - 2 or x + 2 = -sqrt(11 - y)

Subtract 2 from both sides:

Answer: x = sqrt(11 - y) - 2 or x = -sqrt(11 - y) - 2

Answer:

The measure of angle WVX is 140°.

Step-by-step explanation:

Let x be the measure of angle WVX.

\( \frac{14}{9} \pi = 2x\)

\( x = \frac{7}{9} \pi( \frac{180}{\pi}) = 140 \: degrees\)

Answer:

angle = arc length/radius
in this case, the arc length is 14/9*\(\pi\) and the radius is 2. Upon multiplying these, you get 140.

so, the answer is 140 degrees.

The required value of the given function  f(a) = -2a^2 - 5a + 4 at a = -3 is 1

Function is characterized as a connection between a bunch of data sources having one result each. In straightforward words, a capability is a connection between inputs where each info is connected with precisely one result. Each Function has a domain and co-domain or range. A capability is by and large meant by f(x) where x is the information.

Function, f(a) = -2a^2 - 5a + 4

To find value of f(-3),

f(a) = -2a^2 - 5a + 4

Put a = -3 in th function

F(-3) = -2(-3)^2-5×-3+4

F(-3) = -18+15+4=1

F(-3) = 1

Thus, required value of f(-3) is 1

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Coorect Question:

What is f(-3) for the function f(a) = -2a2 - 5a + 4?

Answer:

A

Step-by-step explanation:

A.

at 1.5 seconds

h=-16(1.5)²+30(1.5)+6

=-16×2.25+45+6

=-36+45+6

=15 ft

which is correct.

B.

h=-16(t²-30/16 t)+6

=-16(t²-30/16t+(15/16)²-(15/16)²)+6

=-16(t-15/16)²-16(-225/256)+6

=-16(t-15/16)²+225/16 +6

=-16(t-15/16)²+(225+96)/16

=-16(t-15/16)²+321/16

it is at maximum height when t=15/16 seconds

so B is not true.

C.

when t=15/16 seconds

h=321/16 ft=20 1/16 ft

height of fence=20 ft

so it will clear the fence.

C is not true.

D.

when h=0

-16t²+30t+6=0

8t²-15t-3=0

\(t=\frac{15\pm\sqrt{225-4 \times 8 \times (-3)} }{2 \times 8} \\=\frac{15 \pm \sqrt{225+96} }{16} \\=\frac{15\pm \sqrt{321} }{16} \\rejecting~negative~sign\\t=\frac{15+\sqrt{321}}{16} \approx. 2.057 seconds\)

it hits the ground in 2.057 seconds

so D is not true.

Answer:

By definition, atoms have no overall electrical charge. That means that there must be a balance between the positively charged protons and the negatively charged electrons. Atoms must have equal numbers of protons and electrons. In our example, an atom of krypton must contain 36 electrons since it contains 36 protons.

Answer:

5 red, 5 yellow, and 4 blue

Step-by-step explanation:

Answer:

5 red, 5 yellow, and 4 blue :)

Step-by-step explanation:

Answer:

x = -2

y = -10

( -2, -10)

Step-by-step explanation:

set them equal

5x = 9x + 8

subtract 9x

-4x = 8

divide by -4

x = -2

plug in x

y = 5(-2)

y = -10

The person must score 136 to be in the top 5% of all scores in wechsler adult intelligence scale.

The formula for the normal distribution is;

z = (x - μ)/σ

where,

If we want to be in the top 5%, we must outperform 95% of the remaining scores. So we must investigate.

In with us standard normal probability table, look up 0.95 and get the Z score that corresponds to that.

z = 1.7

Put the value in formula ad find x.

1. 7 = (x - 110)/15

x = 25.5 + 110

x = 135.5

x = 136 (whole number)

Thus, the person must score 136 to be in the top 5% of all scores in wechsler adult intelligence scale.

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Answer:

b

Step-by-step explanation:

I had this exactl question a while ago

Answer:

8/25

Step-by-step explanation:

Since there are only three possible outcomes on the spinner (1, 2, or 3), we can find the probability of spinning a 2 by subtracting the probabilities of spinning a 1 or a 3 from 1

P(2) = 1 - P(1) - P(3)

P(2) = 1 - 7/25 - 2/5

P(2) = 1 - 35/125 - 50/125

P(2) = 1 - 85/125

P(2) = 40/125

P(2) = 8/25

Therefore, the experimental probability of spinning a 2 is 8/25 or 0.32.

Probability that |x - 15| ≤ 3 is approximately 0.9772.

Given: x is a normal random variable with mean 15.0 and standard deviation 1.25.

We need to calculate: P(|x - 15| ≤ 3)

We know that |x - 15| represents the distance between the value of x and its mean, so we can rewrite the above expression as:

P(-3 ≤ x - 15 ≤ 3)

We can further simplify this by subtracting 15 from all terms:

P(-3 + 15 ≤ x ≤ 3 + 15)

P(12 ≤ x ≤ 18)

Now, we need to find the probability that x falls between 12 and 18. We can use the standard normal distribution by standardizing the values of x:

z1 = (12 - 15)/1.25 = -2.4

z2 = (18 - 15)/1.25 = 2.4

Using a standard normal distribution table or calculator, we can find the probability that z falls between -2.4 and 2.4:

P(-2.4 ≤ z ≤ 2.4) ≈ 0.9772

Therefore, the probability that |x - 15| ≤ 3 is approximately 0.9772.

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Answer: F. :)

Step-by-step explanation:

The required power-series representation of `h(x)` is given by: \($$\boxed{\sum_{n=0}^{\infty} \frac{135}{8} (-1)^n (3x^{2})^{n}}$$\), for the given a function `f(x) = 2−x⁴`, centered at `c = -4`.

The power series representation of the function `f(x)` centered at `c = -4` is given as:

\($$\begin{aligned}f(x) &= \sum_{n=0}^{\infty} \frac{f^{(n)}(-4)}{n!}(x+4)^n\\&= \sum_{n=0}^{\infty} \frac{(-1)^n\cdot 4x^n}{2^n\cdot n!} + 2\end{aligned}$$\)

Thus, we can write the power series of the given function as:

\($$f(x) = \sum_{n=0}^{\infty} \frac{(-1)^n\cdot 4x^n}{2^n\cdot n!} + 2$$\)

The interval of convergence of the power series representation of `f(x)` centered at `c = -4` can be found using the ratio test.

\($$\begin{aligned}\lim_{n\to\infty} \left|\frac{a_{n+1}}{a_n}\right| &= \lim_{n\to\infty} \frac{|(-1)^{n+1}4(x+4)^{n+1}|}{2^{n+1}(n+1)|(-1)^n4(x+4)^n|}\\&= \lim_{n\to\infty} \frac{2}{n+1}\cdot|x+4|\end{aligned}$$\)

where `a_n` is the nth term of the given series.

From the above expression, we can see that the series will converge if the limit is less than 1, and diverge if the limit is greater than 1. Thus, we have:

\($$\begin{aligned}\frac{2}{n+1}\cdot|x+4| &< 1\\\Rightarrow |x+4| &< \frac{n+1}{2}\end{aligned}$$\)

Since `n` can take any non-negative integer value, the interval of convergence is the set of all `x` such that `|x+4| < ∞`.

Thus, the interval of convergence is given by:

\($$\boxed{(-\infty, \infty)}$$\)

Now, we need to expand the function `g(x) = 1/(1-x)` about the point `c=0` using the formula

`1/(1-x) = \sum_{n=0}^{\infty} x^n`.

To expand the function in a power series with center `c=0`, we can write:

\($$\begin{aligned}g(x) &= \frac{1}{1-x}\\&= \frac{1}{1-(-x)}\\&= \sum_{n=0}^{\infty} (-x)^n && (\text{by using } \frac{1}{1-x} = \sum_{n=0}^{\infty} x^n)\\&= \sum_{n=0}^{\infty} (-1)^n x^n\end{aligned}$$\)

Now, we need to use the above result to expand the function

`h(x) = \frac{135}{3-x^2}` in a power series with center `c=0`.Let `t = 3x^2`.

Then, `x^2 = t/3`, and `h(x)` becomes:

$$
\begin{aligned}
h(x) &= \frac{135}{3-x^2}\\
&= \frac{135}{3-\frac{t}{3}}\\
&= \frac{135}{\frac{8}{3}(3-\frac{t}{8})}\\
&= \frac{405}{8}\cdot \frac{1}{1-\frac{t}{8}}\\
&= \frac{405}{8}\cdot \sum_{n=0}^{\infty} \left(\frac{t}{8}\right)^n && (\text{by using } \frac{1}{1-x} = \sum_{n=0}^{\infty} x^n)\\
&= \sum_{n=0}^{\infty} \frac{405}{8}\cdot \left(\frac{t}{8}\right)^n\\
&= \sum_{n=0}^{\infty} \frac{405}{8}\cdot \left(\frac{3x^2}{8}\right)^n\\
&= \sum_{n=0}^{\infty} \frac{135}{8} (-1)^n (3x^2)^n\\
&= \sum_{n=0}^{\infty} \frac{135}{8} (-1)^n (3^n\cdot x^{2n})\\
&= \boxed{\sum_{n=0}^{\infty} \frac{135}{8} (-1)^n (3x^{2})^{n}}
\end{aligned}
$$

Thus, the required power series representation of `h(x)` is given by:

\($$\boxed{\sum_{n=0}^{\infty} \frac{135}{8} (-1)^n (3x^{2})^{n}}$$\)

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The power series expansion of the function is \(\sum_{n=0}^{\infty} 135(-1)^n (3^n x^{3n}) - \sum_{n=0}^{\infty} x^2\).

To find a power series for the function \(f(x) = 2 - \frac{x^4}{4}\) centered at \(c = -4\), we can express it as a summation:

\[f(x) = \sum_{n=0}^{\infty} 2n4(x+4)^n\]

The interval of convergence of this power series can be determined using the ratio test. Let's apply the ratio test to find the interval of convergence:

First, let's calculate the ratio:

\[R = \lim_{n \to \infty} \left|\frac{2(n+1)4(x+4)^{n+1}}{2n4(x+4)^n}\right|\]

Simplifying the ratio:

\[R = \lim_{n \to \infty} \left|\frac{(n+1)(x+4)}{n}\right|\]

Taking the limit as \(n\) approaches infinity:

\[R = |x+4|\]

For the series to converge, we need \(|x+4| < 1\). Therefore, the interval of convergence is \((-5, -3)\) in interval notation.

Next, for the function \(f(x) = \frac{1}{1-x}\), we can use the formula \(1 - x^{-1} = \sum_{n=0}^{\infty} x^n\) for \(|x| < 1\) to expand the function in a power series with the center \(c = 0\).

Using the given function \(\sum_{n=0}^{\infty} 135(-1)^n (3x)^{3n} - x^2\), we can rewrite it as:

\[\sum_{n=0}^{\infty} 135(-1)^n (3^n x^{3n}) - x^2\]

Thus, the power series expansion of the function is \(\sum_{n=0}^{\infty} 135(-1)^n (3^n x^{3n}) - \sum_{n=0}^{\infty} x^2\).

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Answer:

tje second option (3,6) and (5,6)

The second option is correct because you are subtracting 2 from both sides of the graphing system.

Step-by-step explanation:

n/10+6=11

n/10=11-6

n/10=5

n=5x10

n=50

Answer: n=50

Answer:

ok

Step-by-step explanation: