I don't understand someone please help. :(

Answer: b = 11.62

Step-by-step explanation:

We can use this formula to solve for b:

\(b^{2} =\) \(\sqrt{c^{2}-a^{2} }\)

\(b^{2} =\) \(\sqrt{12^{2}-3^2 }\)

\(b^2= \sqrt{144-9}\)

= 11.61895004

We can round that to 11.62.

Hope this helped!

If John solved the equation x² - 10x + 8 = 0 by completing the square, one of the steps in his process would be: A. (x - 5)² = 17.

In Mathematics, the standard form of a quadratic equation is represented by the following equation;

ax² + bx + c = 0

Next, we would solve the given quadratic equation by using the completing the square method;

x² - 10x + 8 = 0

x² - 10x = -8

In order to complete the square, we would have to add (half the coefficient of the x-term)² to both sides of the quadratic equation as follows:

x² - 10x + (-10/2)² = 8 + (-10/2)²

x² - 10x + 25 = -8 + 25

x² - 10x + 25 = 17

By simplifying, we have;

(x - 5)² = 17

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Answer:

Step-by-step explanation:

Probability of landing on pink:

If spun 10 times then possible outcomes with pink:

Answer:

3 times, or \(\frac{3}{10}\)

Step-by-step explanation:

There are 3 out of 10.

Answer:

x = 15 , y = 21

Step-by-step explanation:

using Pythagoras' identity

in Δ ABD

x² + 8² = 17²

x² + 64 = 289 ( subtract 64 from both sides )

x² = 225 ( take square root of both sides )

x = \(\sqrt{226}\) = 15

in Δ ADC

8² + DC² = 10²

64 + DC² = 100 ( subtract 64 from both sides )

DC² = 36 ( take square root of both sides )

DC = \(\sqrt{36}\) = 6

then

y = x + DC = 15 + 6 = 21

Answer:

y = 12x + 35

95 pages

Step-by-step explanation:

Let y represent the total number of pages

Let x represent the total number of months

x = 5 (months)

so..

y = 12(5) + 35

y = 60 + 35

y = 95

Answer:

The linear equation satisfying the given condition is,

\(x=t+15\)

where x is Ravi's age and t is the number of years

(after 10 years (t=10) his age becomes 25)

Step-by-step explanation:

Let x be Ravi's age

Now, his  current age is unknown, but if you add 10 to it, then it becomes 25, so

x + 10 =25

so, his current age is x = 25 =10

x = 15

Now, we find the linear equation satisfying the given condition,

Let t be the number of years that have passed since the present time

so, if 0 years have passed, his age will be 15 years

after 1 year, his age will be 16 years

after 10 years, his age will be 25 years and so on

so

\(x = t + 15\)

this satisfies the given condition, since if we add ten years i.e t = 10,

then we get 25

The equation is:

Work/explanation:

Here's the linear equation for Ravi's age.

Ravi's age is x.

If you add 10 to x you get x + 10.

That gives 25.

So the linear equation is x + 10 = 25.

Answer:

\( 3.45 \times {10}^{11} \)

Step-by-step Explanation:

\(345,000,000,000 = 3.45 \times {10}^{11} \\ \)

Answer:

(1) \(P(Heart\ and\ Club) = 0.0494\)

(2) \(S = \{B,B,B,B,R,R,R,R,R,Y,Y,Y,Y,Y,Y,Y,Y\}\)

Step-by-step explanation:

Question 1:

Given

\(Hearts = 8\)

\(Diamond = 3\)

\(Club=2\)

\(Spade = 5\)

\(Total = 18\)

Required

Probability of 1 heart and 1 club

This probability is calculated as:

\(P(Heart\ and\ Club) = P(Heart) * P(Club)\)

\(P(Heart\ and\ Club) = \frac{n(Heart)}{Total} * \frac{n(Club)}{Total}\)

\(P(Heart\ and\ Club) = \frac{8}{18} * \frac{2}{18}\)

\(P(Heart\ and\ Club) = \frac{8*2}{18*18}\)

\(P(Heart\ and\ Club) = \frac{16}{324}\)

\(P(Heart\ and\ Club) = 0.0494\) -- approximated

Question 2:

Given

\(Blue = 4\)

\(Red= 5\)

\(Yellow = 8\)

Required

Determine the sample space

Represent the blue balls with B, the red with R and the yellow with Y.

The sample space (S) is:

\(S = \{B,B,B,B,R,R,R,R,R,Y,Y,Y,Y,Y,Y,Y,Y\}\)

Answer:

4/12

Step-by-step explanation:

Answer:

Need to see the problem, but the "zero of the function" is the x value when y=0.

Substitute '0' for y.

Solve for x

Answer: D

Step-by-step explanation:

Answer:

c. The period is 2π

Step-by-step explanation:

The period of a function is the smallest value of $p$ for which\( f(x+p) = f(x)\) for all x.

For the function f(x) = 2cos(x^2), we can see that f(x+2π) = f(x) for all x.

This is because the cosine function has a period of 2π. Therefore, the period of f(x) = 2cos(x^2) is \(\boxed{2\pi}\)

Therefore , the solution of the given problem of slope comes out to be  y = 7x - 17 is the equation in slope-intercept form.

A line's steepness is determined by its slope. In gradient-based equations, a situation known as gradient overflow can happen. One can determine the slope by dividing the sum of a run (width differential) and rise (climbing distinction) between two places. The equation with the hill variation, y = mx + b, is used to model the fixed path issue. where grade is mm, a = bc, and the line's y-intercept is situated; (0, b).

Here,

Given :

=> -7x + y = -17

7x both faces together

=>  -7x + 7x + y = 7x - 17

Condense: y = 7x - 17

So,

=>  y = 7x - 17 is the equation in slope-intercept form.

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Answer:

C. she is not beautiful and not clever.

Step-by-step explanation:

A. she is beautiful but not clever. B. she is beautiful and clever

C. she is not beautiful and not clever.

D. she is beautiful or not clever.

p: she is beautiful

q :she is clever

~p^ (~q) in verbal form

~p = she is not beautiful

~q = she is not clever

~p^ (~q) = she is not beautiful and not clever.

C. she is not beautiful and not clever.

A triangle JKL has vertices at J(−1, −5), K(−2, −2), and L(2, −4) and J′ at (−3, −5). The translation direction is 2 units to the left. The number of units of the image of triangle JKL is 2 units to the left only.

Given that a triangle JKL has vertices at J(−1, −5), K(−2, −2), and L(2, −4) and J′ at (−3, −5). We have to determine the translation direction and the number of units of the image of triangle JKL. Let's first find the translation direction to determine the image of triangle JKL.

Seeing the position of J and J', we can determine that the translation was made in the left direction because J has moved from the point (-1,-5) to (-3,-5). Thus, the translation direction is 2 units to the left. Now, let's calculate the number of units of the image of triangle JKL.

Let's draw a rough sketch of the triangle JKL and locate its vertices J(-1,-5), K(-2,-2), and L(2,-4).To find the number of units of the image of triangle JKL, we need to find the horizontal and vertical distances between the vertices of the original triangle and its image.

We can use the horizontal distance between J and J′ as a reference to calculate the remaining distances. J has moved 2 units to the left, so the horizontal distance between J and J′ is 2. Now, let's calculate the vertical distance between J and J′. The coordinates of J and J′ are (-1,-5) and (-3,-5), respectively.

The difference between the y-coordinates of J and J′ is 0, which means that J and J′ are on the same horizontal line. Therefore, the vertical distance between J and J′ is 0. Hence, the image of the triangle JKL has moved 2 units to the left and 0 units vertically. Thus, the number of units of the image of triangle JKL is 2 units to the left only.

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The solution is : 22 meters would be saved if it were possible to walk through the pond.

Here, we have,

There is a pond between two points A and B.

To avoid the pond, one must walk to the south from point A to point C (say) by 34 meters and then to the east from point C to point B by 41 meters.

Now, it is clear that Δ ABC is a right triangle with AB as the hypotenuse that is the minimum distance from A to B through the pond.

The two legs of the right triangle are AC and CB.

Applying Pythagoras Theorem,

AB² = AC² + CB²

      = 34² + 41²

      = 2837

⇒ AB = 53 meters (Rounded to the nearest meter)

Therefore, (34 + 41) - 53 = 22 meters will be saved if it were possible to walk through the pond.

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complete question:

To get from point A to point B you must avoid walking through a pond. To

avoid the pond, you must walk 34 meters south and 41 meters east. To the

nearest meter, how many meters would be saved if it were possible to walk

through the pond?

Answer:

r is wrong, t is wrong,

Step-by-step explanation:

dum gio

Answer:

0,2 0r 2/2

Step-by-step explanation:

Answer:

Step-by-step explanation:

First, you put it into slope intercept form

y = mx + b

m is the slope

b is the y intercept

y = 2/3 + 4

Answer:

Kindly check explanation

Step-by-step explanation:

Given the data:

Number of Home alone movies (X)

Watched probability, p(x)

X : ___ 0 ____ 1 ____ 2 ____ 3 ___ 4 ___ 5

P(x) : _0.15 __ 0.42 __0.32 __? ___0.02 _0.01

a. Write the event "the student has seen 3 Home Alone movies" using probability notation. Then find this probability.

P(x = 3)

Since Σp(x) = 1

P(x =3) = 1 - (p(0)+p(1)+p(2)+p(4)+p(5))

P(x = 3) = 1 - (0.15 + 0.42 + 0.32 + 0.02 + 0.01)

P(x = 3) = 1 - 0.92

P(x = 3) = 0.08

b. Explain in words what P(X > 3) means. What is this probability?

P(x > 3) is the probability they a randomly chosen student has watched more than 3 home alone movies.

P(x > 3) = p(4) + p(5)

P( x > 3) = 0.02 + 0.01 = 0.04

d. Calculate and interpret the expected value of X.

E(X) = [Σ(X * p(x)]

(0*0.15) + (1*0.42) + (2*0.32) + (3*0.08) + (4*0.02) + (5*0.01) = 1.43

The avereage number of home alone movies watched is 1.43

Probability distributions are used to represent the probability of events.

The distribution is given as:

\(\mathbf{Homes \to Probability}\)

\(\mathbf{0 \to 0.15}\)

\(\mathbf{1 \to 0.42}\)

\(\mathbf{2 \to 0.32}\)

\(\mathbf{3 \to ?}\)

\(\mathbf{4 \to 0.02}\)

\(\mathbf{5 \to 0.01}\)

(a) The event using probability notation

When a student sees 3 home alone movies, it means x = 3.

So, the probability notation is: \(\mathbf{P(x = 3)}\)

(b) Explain P(x > 3)

It means the event that a student has seen more than 3 home alone movies.

It is calculated as:

\(\mathbf{P(x > 3) = P(4) + P(5) }\)

So, we have:

\(\mathbf{P(x > 3) = 0.02 + 0.01}\)

\(\mathbf{P(x > 3) = 0.03}\)

Hence, the value of P(x > 3) is 0.03

(c) Histogram

Start by calculating P(x = 3).

Using the complement rule, we have:

\(\mathbf{P(x = 3) = 1 - P(0)- P(1) - P(2) - P(x > 3)}\)

So, we have:

\(\mathbf{P(x = 3) = 1 - 0.15 - 0.42 - 0.32 - 0.03}\)

\(\mathbf{P(x = 3) = 0.08}\)

See attachment for the histogram

The shape is right-symmetric

(d) The expected value

This is calculated as:

\(\mathbf{E(x) = \sum x P(x)}\)

So, we have:

\(\mathbf{E(x) = 0 \times 0.15 + 1 \times 0.42 + 2 \times 0.32 + 3 \times 0.08 + 4 \times 0.02 + 5 \times 0.01}\)

This gives

\(\mathbf{E(x) = 1.43}\)

It means that a student has seen the home alone movies an average time o 1.43 times

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Answer:

That is true but still remember that playing the knight at the start can be very useful.

The annualized return for the entire period is the closest to 10.5%.

To calculate the annualized return for the entire period, we need to consider the returns for each year and the return in the first quarter of Year 4. Since the returns are given for each period, we can use the geometric mean to calculate the annualized return.

The formula for calculating the geometric mean return is:

Geometric Mean Return = [(1 + R1) * (1 + R2) * (1 + R3) * (1 + R4)]^(1/n) - 1

Where R1, R2, R3, and R4 are the returns for each respective period, and n is the number of periods.

Given the returns:

Year 1 return: 5% or 0.05

Year 2 return: 12% or 0.12

Year 3 return: -6% or -0.06

First quarter of Year 4 return: 2% or 0.02

Using the formula, we can calculate the annualized return:

Annualized Return = [(1 + 0.05) * (1 + 0.12) * (1 - 0.06) * (1 + 0.02)]^(1/3) - 1

Annualized Return = (1.05 * 1.12 * 0.94 * 1.02)^(1/3) - 1

Annualized Return = 1.121485^(1/3) - 1

Annualized Return ≈ 0.105 or 10.5%

Therefore, the annualized return for the entire period is approximately 10.5%.

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The inequality that is graphed on the number line is:

x > -2

Here we can see the graph of an inequality on a number line, on it, we can see a blue line that starts with a open circle (which means that we need to use the symbols < or >) at x = -2

Then the line extends to the right of that number, so the allowed values of x are larger than -2, then the inequality graphed is:

x > -2

Thus the correct option is the fourt one.

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Answer:

£1651.38

Step-by-step explanation:

100%+9%=109%

£1800 ÷ 109=1651.37614...

1651.37614... rounded up to the nearest penny is 1651.38

Answer:

A(t)  =  27.86 in²

Dimensions of the paper:

L =  3.73 in

w = 7.47 in

Step-by-step explanation:

The total area of a rectangular page  A  = ( x + 2)* (y + 4 )         x  is the length and  y the wide. x  and  y  are the dimensions of the print area

The print area of the paper is  A =  6 in²       6 = x*y     y  =  6/x

Then print area as a function of x is

A(x)  =  ( x + 2 ) * ( 6/x + 4 )    ⇒  A(x)  =  6  +  4*x  + 12/x + 8

Taking derivatives on both sides of the equation:

A´(x)  =  4  - 12/x²        A´(x)  =  0     4  =  12 /x²

x²  = 12/4       x =√3    x  =  1.73  in  and   y  =  6 / 1.73

y  =  3.47 in

Then the dimensions of the paper  are.

Length  L =  x  + 2  = 3.73 in      and   w  =  3.47 + 4  = 7.47 in

And the least amount of paper is

A(t)  =  3.73* 7.47  =  27.86 in²

To find out if x = 1.73 is an x coordinate for a minimum we get the second derivative

A´´(x)  =  24/x³    is always positive   A´´(x) > 0  then we have a minimum for A at  x = 1.73

Answer:

If the base and the negative exponent is in the denominator already

Step-by-step explanation:

Normally, a base with a negative exponent moves to the denominator.

Example: (2^-3 = 1 / (2)^3 = 1/8)

However, if the base and the negative exponent is already in the denominator, the base would move to the numerator and the exponent would become positive.

Example:  2 / (3)^-3 = 2 * 3^3 = 2 * 27 = 54

Answer:

C is the answer, please choose the letter C that's the answer

Answer:

C

Step-by-step explanation:

The interquartile range is the difference between the upper quartile Q₃ and the lower quartile Q₁

From the five- number summary , then

Q₃ = 24.5 and Q₁ = 11.1

interquartile range = 24.5 - 11.1 = 13.4 → C

Answer:

r=2q-6

Step-by-step explanation:

10q-5r=30

Subtract 10q from both sides:

-5r=30-10q

Divide both sides by -5:

r=2q-6

Hope this helps!