1, 4, 9, 16, 36, 49, 64 find the pattern​

Using Conditional probability,

The probability that after a fair coin is tossed 5 times that the result will contain 3 'heads' given that the first toss was a 'head' is 3/5.

A fair coin is tossed five times .

so, total possible outcomes = 2⁵ = 32

Let A: head observed on first toss

B: 3 heads observed.

Probability that the first toss was head (p) = 1/2

we have to find out probability that on 5 tosses result contain 3 heads given that first toss wss head .

Using Binomial Probability distribution

P (X= x) = ⁿCₓ (p)ˣ (q)⁽ⁿ⁻ˣ⁾

x = 3 , n = 5

we get , P(B) = P(X= 3 ) = ⁵C₃(1/2)³(1/2)²

=> P(B) = 10 ×(1/2)⁵= 5/16

since the first toss is fixed as a head.

P(A ∩ B) =P( X₁ = 1 and X₂+ X₃ + X₄ + X₅) = P(X₁= 1)P(X₂+X₃+X₄+X₅)

= 1/2 × ⁴C₂ (1/2)⁵ = 3 (1/2)⁴

The required probability is , Conditional probability P(B/A) = P(A ∩ B)/P(A)

= 3(1/2)⁴/ 5/16 = 3/5

Hence , the required probability is 3/5.

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According to the division property of equality, if both sides of an equation are divided by a common real integer that is not zero, the quotients remain equal.

Commutative property, associative property, distributive property, and identity property are the four number properties. Only the algebraic operations addition, subtraction, multiplication, and division are linked with number characteristics.

The four key terminology used in the division process are dividend, divisor, quotient and remainder. Dividend Divisor = Quotient + Remainder is the formula for dividing two numbers.

Commutative property, associative property, distributive property, and identity property are the four number properties. Only the algebraic operations addition, subtraction, multiplication, and division are linked with number characteristics.

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Sum and difference identities are formulas in trigonometry that allow us to express the trigonometric functions of the sum or difference of two angles in terms of the trigonometric functions of the individual angles.

The sum identities are:

sin(a + b) = sin(a)cos(b) + cos(a)sin(b)

cos(a + b) = cos(a)cos(b) - sin(a)sin(b)

tan(a + b) = (tan(a) + tan(b)) / (1 - tan(a)tan(b))

The difference identities are:

sin(a - b) = sin(a)cos(b) - cos(a)sin(b)

cos(a - b) = cos(a)cos(b) + sin(a)sin(b)

tan(a - b) = (tan(a) - tan(b)) / (1 + tan(a)tan(b))

For example, if we want to find the value of sin(45 + 30), we can use the sum identity for sine:

sin(45 + 30) = sin(45)cos(30) + cos(45)sin(30)

We know that sin(45) and cos(30) are both equal to √2/2, and that cos(45) and sin(30) are both equal to 1/2, so we can substitute these values into the formula and simplify:

sin(45 + 30) = (√2/2) x (1/2) + (√2/2) x (1/2)

= (√2 + 1)/2

Therefore, sin(45 + 30) = (√2 + 1)/2.

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Answer:

Step-by-step explanation:

the solution can be found in the attachment.

The triangles are used to prove the cosine rule which gives a²=b²-c²+2bcCosA

In trigonometry, the Cosine Rule says that the square of the length of any side of a given triangle is equal to the sum of the squares of the length of the other sides minus twice the product of the other two sides multiplied by the cosine of angle included between them.

From the given parameters

For ΔABD, c²=x²+b² and SinB = x/c

Which yields that x=cCosb

For ΔCBD, a²= h² + (b -x )² = b²-2bx +x²) +h²

Using substitution this yields

a² = b² -c² + 2bc CosA

This gives the cosine rule from the two triangles

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The answer  is that a 400-troy-ounce gold ingot weighs approximately 12.4 kilograms or 27.34 pounds. This weight is equivalent to 3,110 grams or 3.11 kilograms. In summary, a 400-troy-ounce gold ingot weighs around 12.4 kilograms or 27.34 pounds and is equivalent to 3,110 grams or 3.11 kilograms.

The 400-troy-ounce gold ingot weighs, as the name suggests, 400 troy ounces. To provide some context, one troy ounce is equivalent to 31.1035 grams. Therefore, to determine the weight of the gold ingot in grams, you can perform the following calculation: 400 troy ounces x 31.1035 grams/troy ounce = 12,441.4 grams. In summary, the 400-troy-ounce gold ingot weighs 12,441.4 grams.

The weight of a 400-troy-ounce gold ingot can be calculated as follows: One troy ounce is equal to approximately 31.1 grams. The troy ounce is commonly used as a unit of weight for precious metals like gold. To find the weight of a 400-troy-ounce gold ingot, we multiply 400 by the weight of one troy ounce: 400 troy ounces * 31.1 grams per troy ounce = 12,440 grams. Since there are 1,000 grams in a kilogram, we can convert the weight from grams to kilograms:

12,440 grams / 1,000 grams per kilogram = 12.44 kilograms.

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Answer:

You can narrow it down to A or D because it is clear that football gets more attendance. There is typically a large distance between the 2, for example the first 1 has a distance of 80 and second a distance of 44. This means the answer is likely D, that football averages 50 more people in attendance

Step-by-step explanation:

Answer:

Divide 6 miles by 0.5 hour:  6/0.5 = 12 miles per hour.

Step-by-step explanation:

The average speed must she rides her bike to get there on time will be 12 miles per hour.

The distance covered by the particle or the body in an hour is called speed. It is a scalar quantity. It is the ratio of distance to time.

We know that the speed formula

Speed = Distance/Time

In a half-hour, Sarah is meeting her friends at the lake, 6 miles from her house.

The average speed must she rides her bike to get there on time will be

S = 6 / (1/2)

S = 6 x 2

S = 12 miles per hour

The average speed must she rides her bike to get there on time will be 12 miles per hour.

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By using the law of exponent the value of (24)⁻¹ is equal to  1/24.

To simplify (24)⁻¹, we can apply the rule for negative exponents.

The rule states that any non-zero number raised to the power of -n is equal to the reciprocal of that number raised to the power of n.

Applying this rule to (24)⁻¹, we have,

(24)⁻¹

= 1 / (24)¹

= 1 / 24

Therefore, applying the law of exponent (24)⁻¹ simplifies to 1/24.

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The above question is incomplete, the complete question is:

Using laws of exponents with integer exponents ,simplify (24)⁻¹.

one over two raised to the power of negative four one over two raised to the fourth power .

Answer:

I think the answer for this question is 2.24cm

Step-by-step explanation:

Let the number of psychology books be 'x'.

and that of sociology books be 'y'.

x + y = 317 (given)

Number of sociology books sold was 89 less than that of psychology books.

y = x - 89

Which means,

x + x - 89 = 317

2x = 317 + 89

2x = 406

x = 406/2 = 203

y = 203 - 89 = 114

Hence, 203 psychology books and 114 sociology books were sold.

The real distance between the ship and the base is 35 km and the measure of the bearing of B from S would be; 70 degrees.

Scale factor is the factor which is used to enlarge or smaller the original figure. Scale factor is the ratio of representation measurement of the figure to the original figures.

The figure represent the position of the ship(S) and the marine base(B).

a) Real distance between the ship and the base is;

When the distance from ship and the base is measured by rules. It comes out 3.5 cm.

The scale of the diagram is 1 cm, represents 10 km. Thus,

BS = 10/ 1 x 3.5

BS = 35 km

b) Measure the bearing of B from S

With the help of compass, the bearing angle of B from S is measured as the given;

Angle BSN = 70 degree

Thus, the real distance between the ship and the base is 35 km and the measure of the bearing of B from S would be; 70 degrees.

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Answer: I think your answer is B!!

Step-by-step explanation: i might not be right but im pretty sure

Answer:

2/5 is greater than 3/8, so 25 2/5 is greater

Step-by-step explanation:

Find the least common denominator or LCM of the two denominators:

LCM of 5 and 8 is 40

Next, find the equivalent fraction of both fractional numbers with denominator 40

For the 1st fraction, since 5 × 8 = 40,

2/5

=

2 × 8

5 × 8

=

16/40

Likewise, for the 2nd fraction, since 8 × 5 = 40,

3/8

=

3 × 5

8 × 5

=

15/40

Since the denominators are now the same, the fraction with the bigger numerator is the greater fraction

16/40 > 15/ 40 or 2/5 > 3/8

Answer:

  the graph of f has 3 turning points

Step-by-step explanation:

The graph of a function has a turning point (local extreme) where the derivative is zero and changes sign.

The derivative of a function tells you the slope of that function's graph. When the derivative is positive, the function is increasing. When the derivative is negative, the function is decreasing.

Where the derivative changes sign from positive to negative, the graph of the function changes direction from increasing to decreasing. At the point where the derivative is zero (between positive and negative), the graph is neither increasing nor decreasing. A tangent to the function at that point is a horizontal line, and the function itself is at a local maximum, a turning point.

The reverse is also true. When the derivative changes sign from negative to positive, the function changes from decreasing to increasing. The turning point where that occurs is a local minimum.

If the derivative crosses the x-axis (changes sign) 3 times, then there are three local extremes in the graph of f. The graph of f has 3 turning points.

__

Additional comment

In the attached graph, we have constructed a derivative function (red) that crosses the x-axis 3 times. It is the derivative of f(x), which is shown in blue. The purpose is to show the local extremes of f(x) match the zero crossings of the derivative.

Answer:

27976000

Step-by-step explanation:

1.04 x 10^5=104000, and  2.808 x 10^7=28080000

28080000-104000=27976000

that's what I think, did this help

Answer: true

Step-by-step explanation:

Answer: True

Step-by-step explanation: Has to be true if a b and c are all numbers

Answer:sorry for the delate

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

Answer:

-5,3

Step-by-step explanation:

Answer:

$8.45

Step-by-step explanation:

if he has $26 to start and spends 17.55 on his friends, he has 8.45 leftover to spend on himself, but since he bought his friends pancakes for 17.55 their pancakes would have cost 8.775 each which suggests that Jeremiah likely cannot afford his own pancakes

Therefore, the value of n, the number of terms within the geometric  series, is around 104.804.n = 1 + log base 1.0241 (2341106.65 * 0.0241)

Given:

Sum of the third term and the fifth term of the geometric series = 295181

Three consecutive terms: 179x, 21027x, and 31381x

Sum of all terms in the series = 419093072x

To find the number of terms in the series, we need to determine the common ratio (r) of the geometric series and then use it to calculate the number of terms.

Step 1: Find the common ratio (r)

The common ratio (r) can be found by dividing the second term by the first term or the third term by the second term. Let's use the first and second terms:

21027x / 179x = r

Simplifying:

r = 21027 / 179

Step 2: Find the value of x

From the given information, we know that x is equal to the sixth term in the series. Using the formula for the nth term of a geometric series, we can express the sixth term in terms of the first term and the common ratio:

sixth term = first term * (r(n-1))

Plugging in the values:

31381x = 179x * (r⁵)

Simplifying:

(r⁵)= 31381 / 179

Step 3: Find the number of terms

To find the number of terms, we need to determine the value of n in the sixth term formula. We can use the sum of all terms in the series and the formula for the sum of a geometric series:

Sum of all terms = first term * ((rn - 1) / (r - 1))

Plugging in the values:

419093072x = 179x * ((rn - 1) / (r - 1))

We can simplify this equation to:

((r(n - 1) / (r - 1)) = 419093072 / 179

Now, we have two equations:

r⁵ = 31381 / 179

((rn - 1) / (r - 1)) = 419093072 / 179

To solve for n, able to multiply both sides of the equation by 0.0241:

1.0241(n - 1 = 2341106.65 * 0.0241

Presently, we are able solve for n by taking the logarithm of both sides of the condition with base 1.0241:

log base 1.0241 (1.0241(n - 1) = log base 1.0241 (2341106.65 * 0.0241)

n - 1 = log base 1.0241 (2341106.65 * 0.0241)

To confine n, we include 1 to both sides of the equation:

n = 1 + log base 1.0241 (2341106.65 * 0.0241

n ≈ 104.804

Therefore, the value of n, the number of terms within the geometric  series, is around 104.804.n = 1 + log base 1.0241 (2341106.65 * 0.0241)

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Therefore, the value of n, the number of terms within the geometric  series, is around 104.804.n = 1 + log base 1.0241 (2341106.65 * 0.0241)

Given:

Sum of the third term and the fifth term of the geometric series = 295181

Three consecutive terms: 179x, 21027x, and 31381x

Sum of all terms in the series = 419093072x

To find the number of terms in the series, we need to determine the common ratio (r) of the geometric series and then use it to calculate the number of terms.

Step 1: Find the common ratio (r)

The common ratio (r) can be found by dividing the second term by the first term or the third term by the second term. Let's use the first and second terms:

21027x / 179x = r

Simplifying:

r = 21027 / 179

Step 2: Find the value of x

From the given information, we know that x is equal to the sixth term in the series. Using the formula for the nth term of a geometric series, we can express the sixth term in terms of the first term and the common ratio:

sixth term = first term * (r(n-1))

Plugging in the values:

31381x = 179x * (r⁵)

Simplifying:

(r⁵)= 31381 / 179

Step 3: Find the number of terms

To find the number of terms, we need to determine the value of n in the sixth term formula. We can use the sum of all terms in the series and the formula for the sum of a geometric series:

Sum of all terms = first term * ((rn - 1) / (r - 1))

Plugging in the values:

419093072x = 179x * ((rn - 1) / (r - 1))

We can simplify this equation to:

((r(n - 1) / (r - 1)) = 419093072 / 179

Now, we have two equations:

r⁵ = 31381 / 179

((rn - 1) / (r - 1)) = 419093072 / 179

To solve for n, able to multiply both sides of the equation by 0.0241:

1.0241(n - 1 = 2341106.65 * 0.0241

Presently, we are able solve for n by taking the logarithm of both sides of the condition with base 1.0241:

log base 1.0241 (1.0241(n - 1) = log base 1.0241 (2341106.65 * 0.0241)

n - 1 = log base 1.0241 (2341106.65 * 0.0241)

To confine n, we include 1 to both sides of the equation:

n = 1 + log base 1.0241 (2341106.65 * 0.0241

n ≈ 104.804

Therefore, the value of n, the number of terms within the geometric  series, is around 104.804.n = 1 + log base 1.0241 (2341106.65 * 0.0241)

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Answer:

Step-by-step explanation:

The statements are marked as;

I. False

II. False

III. True

IV. False

V. True

To prove the statements, we need to know the following;

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The fraction \($\frac{9}{12}$\) can be expressed as the sum of the smaller fraction \($\frac{3}{4}$\).

Ryan grew \($\frac{1}{2}$\) feet in a year.

1. To express the fraction \($\frac{9}{12}$\) as a sum of smaller fractions, we can simplify it by dividing both the numerator and denominator by their greatest common divisor. In this case, the greatest common divisor of \(9\) and \(12\) is \(3\).

So, we can rewrite \($\frac{9}{12}$\) as:

\($\frac{9}{12} = \frac{3 \times 3}{3 \times 4} = \frac{3}{4}$\)

Therefore, the fraction \($\frac{9}{12}$\) can be expressed as the sum of the smaller fraction \($\frac{3}{4}$\).

2. To find how much Ryan grew in a year, we need to calculate the difference between his height this year and his height last year.

Let's convert the mixed fractions to improper fractions for easier computation:

Last year's height: \($4 \frac{3}{4} = \frac{4 \times 4 + 3}{4} = \frac{19}{4}feet\)

This year's height: \($5 \frac{1}{4} = \frac{5 \times 4 + 1}{4} = \frac{21}{4} feet\)

To determine the growth, we subtract last year's height from this year's height:

\($\frac{21}{4} - \frac{19}{4} = \frac{21 - 19}{4} = \frac{2}{4} = \frac{1}{2}feet\)

Therefore, Ryan grew \($\frac{1}{2}$\) feet in a year.

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Answer: a. b. and c.

Step-by-step explanation:

a.- (f)1=14 is correct in this explanation because 15-

1=14

b.- f(2)=15 is incorrect. 15-2 does not equal 15. It would be 13.

=0

c.- f(12)=3 is correct because 15-12=3

d.- f(15)=0 is correct because 15-5=

Answer:

its d

Step-by-step explanation:

Answer:

y = x + 17

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = - x - 18 ← is in slope- intercept form

with slope m = - 1

given a line with slope m then the slope of a line perpendicular to it is

\(m_{perpendicular}\) = - \(\frac{1}{m}\) = - \(\frac{1}{-1}\) = 1 , then

y = x + c ← is the partial equation of the perpendicular line

to find c substitute (- 6, 11 ) into the partial equation

11 = - 6 + c ⇒ c = 11 + 6 = 17

y = x + 17 ← equation of perpendicular line