each day a high school football coach tells his star kicker, brian, that he can go home after he successfully kicks four 35 yard field goals. suppose the probability that brian makes each individual attempt is 0.6. (a) what is the probability that brian kicks his fourth 35 yard field goal on his ninth attempt? (b) what is the expected number of field goals brian will need to attempt to make 4?

We simplified the expression √2(√50 + 7) by rationalizing the denominator using the conjugate. The final result is (-14 + 86√2) / (5√2 - 7).

To simplify and rationalize the denominator of the expression √2(√50 + 7), we need to eliminate the square root in the denominator. This can be achieved by using the conjugate.

First, let's simplify the expression inside the parentheses: √50 + 7.

We can simplify √50 by factoring it as √(25 * 2) = √25 * √2 = 5√2.

Substituting this simplified expression back into the original expression, we have:

√2(5√2 + 7).

To rationalize the denominator, we multiply both the numerator and the denominator by the conjugate of the denominator. The conjugate of 5√2 + 7 is 5√2 - 7.

Multiplying the numerator and denominator by the conjugate, we get:

√2(5√2 + 7) * (5√2 - 7) / (5√2 - 7).

Expanding the numerator using the distributive property, we have:

(√2 * 5√2 + √2 * 7)(5√2 - 7) / (5√2 - 7).

This simplifies to:

(10 * 2 + 7√2)(5√2 - 7) / (5√2 - 7).

Further simplifying the numerator, we get:

(20 + 7√2)(5√2 - 7) / (5√2 - 7).

Expanding the numerator again, we have:

100√2 - 140 + 35√2 - 49√2 / (5√2 - 7).

Combining like terms, we get:

(-14 + 86√2) / (5√2 - 7).

Therefore, the simplified expression with a rationalized denominator is (-14 + 86√2) / (5√2 - 7).

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The probability that a randomly selected board cut by the machine has a length greater than 96.25 inches is approximately 0.3085 or 30.85%.

Probability is a way to gauge how likely something is to happen. Many things are difficult to forecast with absolute confidence.

We can use the z-score formula to find the probability that a randomly selected board cut by the machine has a length greater than 96.25 inches:

z = (x - μ) / σ

where x is the length of the board, μ is the mean length, and σ is the standard deviation.

Substituting the values given in the problem, we have:

z = (96.25 - 96) / 0.5 = 0.5

To find the probability that a randomly selected board has a length greater than 96.25 inches, we need to find the area under the standard normal distribution curve to the right of z = 0.5. We can use a standard normal distribution table or calculator to find this area, which is:

P(Z > 0.5) = 0.3085

Therefore, the probability that a randomly selected board cut by the machine has a length greater than 96.25 inches is approximately 0.3085 or 30.85%.

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Answer:

I believe its A

Step-by-step explanation:

Answer:

8.568cm

Step-by-step explanation:

IF Kenny leaves home and walks 10 blocks east and 24 blocks north to get to the movie theater, his distance from home to the theatre is gotten using the pythagoras theorem as shown;

d² = 23² + 10²

d² = 529 + 100

d² = 629

d = √629

d = 8.568

Hence the required distance is 8.568cm

The integral for calculating the arc length of the curve  \(x = (1/6)(y^2 + 4)^(3/2)\) is: Arc Length = \(∫[0, b] √(1 + y^2(y^2 + 4)/9) dy\), where b represents the upper limit of integration, which depends on the specific problem or given context.

To set up an integral that calculates the arc length of the curve \(x = (1/6)(y^2 + 4)^(3/2)\), we can use the arc length formula:

Arc Length = \(∫[a, b] √(1 + (dx/dy)^2) dy\)

In this case, we have x as a function of y, so we need to find dx/dy. Let's differentiate x with respect to y:

\(dx/dy = d/dy [(1/6)(y^2 + 4)^(3/2)]\\= (3/6)(y^2 + 4)^(1/2) * 2y\\= y(y^2 + 4)^(1/2)/3\)

Now, we can substitute this into the arc length formula:

Arc Length

\(= ∫[a, b] √(1 + (y(y^2 + 4)^(1/2)/3)^2) dy\\= ∫[a, b] √(1 + y^2(y^2 + 4)/9) dy\)

To find the limits of integration [a, b], we need to determine the range of values for y over which the curve is defined. Since the given curve is \(x = (1/6)(y^2 + 4)^(3/2)\), we can set y² + 4 ≥ 0, which means y² ≥ -4. Since y² is always non-negative, the range of values for y is y ≥ 0.

Therefore, the integral for calculating the arc length of the curve\(x = (1/6)(y^2 + 4)^(3/2)\) is:

Arc Length = \(∫[0, b] √(1 + y^2(y^2 + 4)/9) dy\), where b represents the upper limit of integration, which depends on the specific problem or given context.

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Answer:

\( log_{3}( {2x}^{4} + 8 {x}^{3} ) - 3 log_{3}(x) = 2 log_{3}(x) \\ = log_{3}( \frac{2 {x}^{4} + 8 {x}^{3} }{ {x}^{3} + {x}^{2} } ) \\ = log_{3}( \frac{2 {x}^{2} + 8x}{x + 1} )\)

Answer:

c on edge

Step-by-step explanation:

Answer:d?

Step-by-step explanation:

Sam spent two-fifth of his work day by answering email. He works for 9 hours.

Steps to translate and solve a word problem using algebraic expressions:

- Assign the unknowns to variables

- Translate the word into operators plus, less, multiply, or division

- Isolate the unknown

In the given problem, let p is the variable to express the total hours Sam worked yesterday.

He spent two-fifth of hi work day by answering email = 2/5 p

He spent 3.6 hours answering email yesterday, means:

2/5 p = 3.6

p = 5 x 3.6/2 = 9 hours

Hence, Sam worked for 9 hours.

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Answer:

slope= 3/2

Step-by-step explanation:

The equation of g(x) is 24 (3)ˣ when the graph is stretched vertically by a factor of 3 to form the graph g(x).

What is function?

For the parent function f(x) and a constant k >0,

then, the function given by  

g(x) = kf(x) can be sketched by vertically stretching f(x) by a factor of k if k>1 (or)

if 0 < k < 1 , then it is vertically shrinking f(x) by a factor of k

As per the given statement that the graph of f(x) is stretched vertically by a factor of 3 i.e

k = 3 >1

so, by definition

g(x) = 3 f(x) = 3 . 8(3)ˣ

= 8(3)ˣ⁺¹

= 24 (3)ˣ

Hence, the equation of g(x) is 24 (3)ˣ when the graph is stretched vertically by a factor of 3 to form the graph g(x).

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Answer:

Step-by-step explanation:

V of a cone V=3.14* r^2*h/3

942=3.14*r^2*9/3

r^2=942/(3.14*3)=100

r=sqrt100=10

The radius of the cone when the volume of 942 cubic inches and a height of 9 inches should be 10.

Since there is  a volume of 942 cubic inches and a height of 9 inches

We know that

Volume of a cone V=\(3.14* r^2*h/3\)

So,

\(942=3.14*r^2*9/3\\\\r^2=942/(3.14*3)=100\)

r =\(\sqrt 100\)

=10

hence, The radius of the cone when the volume of 942 cubic inches and a height of 9 inches should be 10.

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The least combination of coins and bills that can be used to make the change of $6.60 is:

1 x $5 bill

1 x $1 bill

1 x 50-cent coin

1 x 10-cent coin

To find the least combination of coins and bills that can be used to make the change, we need to subtract the cost of the book from the amount paid and determine the fewest number of bills and coins required.

Change = Amount paid - Cost of the book

Change = $20 - $13.40

Change = $6.60

To determine the least combination of coins and bills, we can start with the largest denominations and work our way down:

$5 bill

$1 bill

50-cent coin

10-cent coin

Using this approach, the least combination of coins and bills that can be used to make the change of $6.60 is:

1 x $5 bill

1 x $1 bill

1 x 50-cent coin

1 x 10-cent coin

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The estimated regression model shows that as advertising increases by $1,000, the estimated mean sales increase by $80,000.

The estimated regression model is a mathematical equation that relates the dependent variable (sales) to the independent variable (advertising) based on a given set of data. In this case, the estimated regression model indicates that for every increase of $1,000 in advertising, the estimated mean sales increase by $80,000. This means that there is a positive correlation between advertising and sales, and the model predicts that increasing advertising expenditure will result in higher sales.

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Answer:

A- Quadrant one.

B- Quadrant three.

Step-by-step explanation:

So, the quadrants go counter-clockwise, starting at the top right which is Quadrant one. Therefore, A is in one. Using that information, we can assume that B is in Quadrant three.

The area under the standard normal curve to the left of z = 1.72 is 0.0427. To find the area to the right of z = 1.72, we can subtract the area to the left from 1.

Subtracting 0.0427 from 1 gives us an area of 0.9573. Therefore, the area under the standard normal curve to the right of z = 1.72 is approximately 0.9573.In the standard normal distribution, the total area under the curve is equal to 1. Since the area to the left of z = 1.72 is given as 0.0427, we can find the area to the right by subtracting this value from 1. This is because the total area under the curve is equal to 1, and the sum of the areas to the left and right of any given z-value is always equal to 1.

By subtracting 0.0427 from 1, we find that the area under the standard normal curve to the right of z = 1.72 is approximately 0.9573. This represents the proportion of values that fall to the right of z = 1.72 in a standard normal distribution.

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All members of set S can be expressed as numbers of the form 2ᵃ3ᵇ, where a and b are non-negative integers.

We will prove by structural induction that all members of set S can be expressed as numbers of the form 2ᵃ3ᵇ, where a and b are non-negative integers.

Base Case:

We start with the base case, where n = 1. In this case, 1∈ S, and we can see that 1 can be expressed as 2⁰3⁰, which is of the desired form.

Inductive Step:

Now, assume that for some positive integer k, if n = k, then k∈ S can be expressed as 2ᵃ3ᵇ for non-negative integers a and b.

We will show that if n = k + 1, then k + 1 can also be expressed as 2ᵃ3ᵇ for non-negative integers a and b.

Case 1: If n = 2k, then we know that 2k∈ S. By the induction hypothesis, we can express 2k as 2ᵃ3ᵇ for some non-negative integers a and b. Now, we can observe that 2k+1 = 2(2k) = 2ᵃ₊₁3ᵇ, which is still of the desired form.

Case 2: If n = 3k, then we know that 3k∈ S. By the induction hypothesis, we can express 3k as 2ᵃ3ᵇ for some non-negative integers a and b. Now, we can observe that 3k+1 = 3(3k) = 2ᵃ3ᵇ₊₁, which is still of the desired form.

Since we have shown that if n = k + 1, then k + 1 can be expressed as 2ᵃ3ᵇ, the proof by structural induction is complete.

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Answer:

AB=PQ

BC=QR

DC=SR

DA=SP

Step-by-step explanation:

Have a nice day!

To find the zeros of the function f(x) = 4x^2 - 10x - 6, we need to solve the equation f(x) = 0. 4x^2 - 10x - 6 = 0
Dividing both sides by 2, we get: 2x^2 - 5x - 3 = 0

Using the quadratic formula: x = (-(-5) ± √((-5)^2 - 4(2)(-3))) / (2(2)) x = (5 ± √49) / 4 x = (5 ± 7) / 4 Therefore, the zeros of the function f are: x = (5 + 7) / 4 = 3 x = (5 - 7) / 4 = -1/2 The zeros of the function f(x) = 4x^2 - 10x - 6 are 3 and -1/2.
To find the zeros of the function f(x) = 4x^2 - 10x - 6, follow these steps: 1. Set f(x) equal to 0: 0 = 4x^2 - 10x - 6 2. Use the quadratic formula, where a = 4, b = -10, and c = -6 x = (-b ± √(b^2 - 4ac)) / 2a 3. Plug the values into the formula: x = (10 ± √((-10)^2 - 4(4)(-6))) / 2(4) 4. Simplify the expression inside the square root: x = (10 ± √(100 + 96)) / 8 5. Calculate the square root: x = (10 ± √196) / 8 6. Simplify further: x = (10 ± 14) / 8 7. Find the two possible values of x: x₁ = (10 + 14) / 8  24 / 8 = 3 x₂ = (10 - 14) / 8 = -4 / 8 = -1/2 So, the zeros of the function f(x) = 4x^2 - 10x - 6 are x = 3 and x = -1/2.

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Using the quadratic formula, the zeros of the function f(x) = 4x^2 - 10x - 6 can be found as: x = (-b ± sqrt(b^2 - 4ac)) / 2a

Plugging in the coefficients a = 4, b = -10, and c = -6, we get: x = (10 ± sqrt(100 + 96)) / 8

x = (10 ± sqrt(196)) / 8

x = (10 ± 14) / 8

x1 = 3/2 and x2 = -1Therefore, the zeros of the function f(x) are x1 = 3/2 and x2 = -1.

The quadratic formula is a standard method to find the zeros of any quadratic equation of the form ax^2 + bx + c. In this case, the function f(x) = 4x^2 - 10x - 6 is a quadratic function, and its zeros represent the x-values where the function intersects the x-axis.  In this case, the zeros are x1 = 3/2 and x2 = -1, which means that the function intersects the x-axis at these two points.

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Answer: The answer is 2

Step-by-step explanation:

Please mark me as Brainiest

Answer: The answer is 2

Step-by-step explanation:

Answer:

y = 2x - 5

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 )

Calculate m using the slope formula

m = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)

with (x₁, y₁ ) = (- 2, - 9) and (x₂, y₂ ) = (13, 21) ← 2 ordered pairs from the table

m = \(\frac{21-(-9)}{13-(-2)}\) = \(\frac{21+9}{13+2}\) = \(\frac{30}{15}\) = 2 , then

y = 2x + c ← is the partial equation

To find c substitute any ordered pair from the table into the partial equation

Using (3, 1 )

1 = 6 + c ⇒ c = 1 - 6 = - 5

y = 2x - 5 ← equation of linear function

Answer:8.5

Step-by-step explanation:I just know it’s

Answer:

13) The ratio is not equivalent

14) The ratio is equivalent

15) The ratio is not equivalent

16) The ratio is equivalent

17) The ratio is equivalent

18) The ratio is not equivalent

I hope this helps

Answer:

name the two things they hoped to achieve when they moved into the interior

Answer: yes

Step-by-step explanation:

Answer:

k < 8

Step-by-step explanation:

-7k + 30k + 25 < 209

23k < 209 - 25

23k < 184 /: 23

k < 8

If you have any questions about the way I solved it, don't hesitate to ask me in the comments below ÷)

Answer:

1.5 °C

Step-by-step explanation:

-2.5, -1, -0.5, 0, 3, 4, 4.5, 5

median is the middle number in the list of numbers

Answer:

1,184.00

Step-by-step explanation:

used a calculator

To evaluate the given surface integral using the Gauss formula, further information is required, specifically the description of the solid for which (S) represents the outside surface.

The Gauss formula, also known as the divergence theorem, relates a surface integral to a volume integral. It states that the flux of a vector field through a closed surface is equal to the triple integral of the divergence of the vector field over the enclosed volume.

In the given problem, we have a surface integral over the outside surface (S) of a solid. However, the description of the solid is missing, so we cannot proceed with evaluating the integral using the Gauss formula.

To apply the Gauss formula, we need to determine the vector field and the solid's volume. Without this information, it is not possible to calculate the integral.

Therefore, without knowing the details of the solid and the vector field involved, we cannot evaluate the surface integral using the Gauss formula.

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