Help my son please!!!

The expression represents the probability of getting exactly 3 heads is,

[tex]C(n,r)(0.5)^3(0.5)^6[/tex]

We have given

Aron flips a penny 9 times.

We have to determine

Which expression represents the probability of getting exactly 3 heads

The binomial distribution is determined as the probability of mass or discrete random variable which yields exactly some values.

The binomial probability formula shown has variables that represent:

[tex]=C\left(n,r\right)\times \left(p\right)^r\times\:\left(1-p\right)^{n-r}[/tex]

Where n is the total number of trials (here, we flip penny 9 times, hence n = 9).

r is the number we want to find (here, we want the probability of 3 heads, so r = 3).

p is the probability of success (here, success means getting heads.

So, in a coin flip the probability of heads is always 1/2, so p = 1/2).

Therefore, The expression represents the probability of getting exactly 3 heads is;

[tex]=C\left(n,r\right)\times \left(p\right)^r\times\:\left(1-p\right)^{n-r}[/tex]

[tex]=C\left(9,3\right)\times \left(0.5\right)^3\times \:\left(0.5\right)^6[/tex]

Hence, the expression represents the probability of getting exactly 3 heads is [tex]C\left(9,3\right)\times \left(0.5\right)^3\times \:\left(0.5\right)^6[/tex].

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The probability that the Wilson family had at least 3 girls is 0.5, while the probability that Wilson family had at most 3 girls is 0.8125.

A common discrete distribution is used in statistics, as opposed to a continuous distribution is called a Binomial distribution. It is given by the formula,

P(x) = ⁿCₓ (pˣ) (q⁽ⁿ⁻ˣ⁾)

Where,

x is the number of successes needed,

n is the number of trials or sample size,

p is the probability of a single success, and

q is the probability of a single failure.

Given the probability of a child being girl is 0.5, therefore, the probability of a child being boy is 0.5. Now, the probability of at least 3 girls out of 5 is,

Probability (x≥3)

= ⁵C₃ (0.5)³(0.5)² + ⁵C₄ (0.5)⁴(0.5)¹ + ⁵C₅(0.5)⁵(0.5)⁰

= 0.5

Probability (x≤3)

= ⁵C₃ (0.5)³(0.5)² + ⁵C₂(0.5)²(0.5)³ + ⁵C₁(0.5)¹(0.5)⁴ + ⁵C₀(0.5)⁰(0.5)⁵

= 0.8125

Hence, the probability that the Wilson family had at least 3 girls is 0.5, while the probability that Wilson family had at most 3 girls is 0.8125.

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The complete question is

"Write the inequality when 3 is less than w and 9 is greater than w."

The inequality become as 3 < w < 9.

Inequality is defined as the relation which makes a non-equal comparison between two given functions.

Given information ;

when 3 is less than w and 9 is greater than w.

Thus, the inequality will be ;

3 < w < 9

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The Actual Question:

What do large differences of the means of each group indicate? Select the correct answer.

A. The large differences do not indicate any Significant meaning in the given context.

B. The peppers with different weights aren't properly distributed between the two groups.

C. There is not enough information to analyze the differences.

D. The peppers with different weights are properly distributed between the two groups

Answer:

B. The peppers with different weights aren't properly distributed between the two groups.

A quantity having a value intermediate between the values of other quantities; an average, especially the arithmetic mean.

The considerable discrepancies in the means of each group imply that: B. the peppers with varying weights are not adequately divided across the two groups.

So in the given situation above in the question, it can be concluded that large differences of the means from each group indicates that the peppers that are not properly distributed between the 2 different groups have different weights.

Answer:

Formula of Trapezoid:

A = (a + b) × h / 2

The formula can be derived in different ways. for now, we have discussed two ways:

1. By using the formula of a triangle

2. By dividing into different sections

Step-by-step explanation:

1. By using the formula of a triangle

One of the ways to explain a formula for an area of a trapezoid using a formula for a triangle can be as follows.

Assume a trapezoid PQRS with lower base SR and upper base PQ (they are parallel) and sides PS and QR.

The image is attached below.

Connect vertices P and R with a diagonal.

Consider triangle ΔPQR as having a base PQ and an altitude from vertex R down to point M on base PQ (RM⊥PQ).

Its area is

S1=[tex]\frac{1}{2} *PQ*RM[/tex]

Consider triangle ΔPRS as having a base SR and an altitude from vertex P up to point N on-base SR (PN⊥SR).

Its area is

S2=[tex]\frac{1}{2} *SR*PN[/tex]

Altitudes RM and PN are equal and constitute the distance between two parallel bases PQ and SR.

They both are equal to the altitude of the trapezoid h.

Therefore, we can represent areas of our two triangles as

S1=[tex]\frac{1}{2}*PQ*h[/tex]

S2=[tex]\frac{1}{2}*SR*h[/tex]

Adding them together, we get the area of the whole trapezoid:

S=S1+S2=[tex]\frac{1}{2} (PQ+SR)h,[/tex]

which is usually represented in words as "half-sum of the bases times the altitude".

2. By dividing into different sections

Trapezoid PQRS is shown below, with PQ parallel to RS.

Figure 1 - Trapezoid PQRS with PQ parallel to RS(image is attached below.)

We are going to derive the area of a trapezoid by dividing it into different sections.

If we drop another line from Q, then we will have two altitudes namely PT and QU.

Figure 2 - Trapezoid PQRS divided into two triangles and a rectangle. (image is attached below.)

From Figure 2, it is clear that Area of PQRS = Area of PST + Area of PQUT + Area of QRU. We have learned that the area of a triangle is the product of its base and altitude divided by 2, and the area of a rectangle is the product of its length and width. Hence, we can easily compute the area of PQRS. It is clear that

=> [tex]A_{PQRS} = (\frac{ah}{2}) + b_{1}h + \frac{ch}{2}[/tex]

Simplifying, we have

=>[tex]A= \frac{ah+2b_{1+C} }{2}[/tex]

Factoring we have,

=> [tex]A_{PQRS} = (a+ 2b_{1} + c)\frac{h}{2} \\= > {(a+ b_{1} + c) + b_{1} }\frac{h}{2}[/tex]

 But, [tex]a+ b_{1} + c[/tex]  is equal to [tex]b_{2}[/tex], the longer base of our trapezoid.

Hence, [tex]A_{PQRS}= (b_{1} + b_{2} )\frac{h}{2}[/tex]

We have discussed two ways by which we can derive area of a trapezoid.

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Answer:

  (d)  The parabola g(x) will open in the same direction of f(x), and the parabola will be wider than f(x).

Step-by-step explanation:

We assume you intend ...

  f(x) = equation of a parabola

  g(x) = 2/3·f(x)

Multiplying a function by a factor of 2/3 will cause it to be compressed vertically to 2/3 of its original height. When the function is a parabola, this has the effect of making it appear wider than before the compression.

__

The compression factor is positive, so points on the graph remain on the same side of the x-axis. The direction in which the graph opens is not changed.

The attachment shows parabolas that open upward and downward, along with the transformed version.

Answer:

D.)  The parabola g(x) will open in the same direction of f(x), and the parabola will be wider than f(x).

Step-by-step explanation:

I got it right on the test :)

stay hydrated.

The depth of the sea bed is 5104 fathom and 1.986 league

The bottom of an ocean , the ocean floor is called Seabed .

It is given that

The depth of a certain part of the Earth's seabed is 36,024 feet

The depth in fathom is given by =  depth in feet / 6

The depth in fathom is = 36024 / 6

= 5104 fathom

1 league = 6046.1 * 3 feet = 18138.1 feet

The depth in League (marine) = Depth in feet / 18138.1

The depth in League (marine) = 36024/18138.1

= 1.986 league

Therefore the depth of the sea bed is 5104 fathom and 1.986 league.

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The population in the year 2023 is 120,780.

The growth is linear hence, the equation of the growth is
y=ax+b where b represents the initial population and a is the number of people growing yearly.

So, according to the question statement, we have that

y=280x+b where x is the number of years past and y is the population in the xth year.

According to the given problem population in 2022 will be 120,500.

Suppose that the initial population is taken at 2000.

Hence, 120,500=280×(2022-2000)+b

⇒b=120,500-280×22

⇒b=120,500-6,160

    =114,340

So, the Linear equation becomes

y=280x+114,340

⇒y=280×(2023-2000)+114,340

⇒y=120,780

Hence, the population in the year 2023 is 120,780.

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Answer: Translate the graph of y=|x| 6 units to the right.

The transformation of a function may involve any change. The transformation of the function is Right shift by 90 units.

The transformation of a function may involve any change.

Usually, these can be shifted horizontally (by transforming inputs) or vertically (by transforming output), stretched (multiplying outputs or inputs) etc.

If the original function is y = f(x), assuming the horizontal axis is the input axis and the vertical is for outputs, then:

Horizontal shift (also called phase shift):

Left shift by c units:

y=f(x+c) (same output, but c units earlier)

Right shift by c units:

y=f(x-c)(same output, but c units late)

Vertical shift:

Up by d units: y = f(x) + d

Down by d units: y = f(x) - d

Stretching:

Vertical stretch by a factor k: [tex]y = k \times f(x)[/tex]

Horizontal stretch by a factor k: [tex]y = f\left(\dfrac{x}{k}\right)[/tex]

Since the function is transformed from f(x)=x to g(x)=x-90, therefore, the transformation of the function is Right shift by 90 units.

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College students (ages 18-26) tend to make decisions that are tentative (more short-range) and support a desire for autonomy. This depicts more permanent choices.

It should be noted that values are a compass that helps us make decisions and choices.

Choices characterize the stage of life we are in. For example 18-26 ages tend to make tentative choices, later 27-31 ages tend to make permanent choices, and ages 32-42 people make stable choices.

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Answer:

[tex]\large \boxed{ \tt{y = - 2x + 5}}[/tex]

Step-by-step explanation:

From the y-intercept og [tex][0,5][/tex], travel five unit south over two unit east. Doing so will get yoy to the endpoint of [tex][1,3][/tex], which tells you that the rate of change is [tex] - 2[/tex], Therefore, your equation, in Solpe Intercept Form , is [tex]y = - 2x + 5[/tex]

[tex] \\ [/tex]

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[tex] \huge\mathbb{ \underline{SOLUTION :}}[/tex]

[tex]\leadsto[/tex] Using the slope-intercept form:

▪ [tex] \bold{y = mx + b}[/tex]

▪ [tex] \bold{y = mx + 5}[/tex]

Finally, we are going to use any point of the line. In this case, I am going to take the point (2, 1). Substituting,

[tex] \sf \longrightarrow{1 =m*2+5}[/tex]

[tex] \sf \longrightarrow{1 - 5 = 2m}[/tex]

[tex] \sf \longrightarrow{ m= - \dfrac{4}{2} = - 4 }[/tex]

[tex]\huge \mathbb{ \underline{ANSWER:}}[/tex]

[tex]\large\boxed{\sf y = 2x + 5}[/tex] ✓

Answer:

[tex](x,y) = (5,-6)[/tex]

Step-by-step explanation:

[tex]\underline{\textbf{Determinant of a matrix.}}\\\\\text{For a}~ 2 \times 2 ~ \text{matrix,}\\\\\begin{vmatrix} a_1&a_2\\b_1&b_2 \end{vmatrix} = a_1b_2 - a_2b_1\\\\\\\text{For a}~ 3 \times 3 ~ \text{matrix,}\\\\\begin{vmatrix} a_1&a_2&a_3\\ b_1&b_2&b_3\\ c_1&c_2&c_3 \end{vmatrix} = a_1\begin{vmatrix} b_2&b_3\\c_2&c_3 \end{vmatrix} - a_2 \begin{vmatrix} b_1&b_3\\c_1&c_3 \end{vmatrix}+ a_3 \begin{vmatrix} b_1&b_2\\c_1&c_2 \end{vmatrix}\\\\\\[/tex]

                     [tex]~~~~~~~~~~~~~~~~~~=a_1(b_2c_3-b_3c_2) -a_2(b_1c_3-b_3c_1) +a_3(b_1c_2-b_2c_1)[/tex]

[tex]\underline{\textbf{Cramer's Rule to solve a system of two equations.}}\\\\\text{Consider the system of two equations:}\\\\~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~a_1x + b_1 y= c_1\\\\~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~a_2x +b_2 y = c_2\\\\\text{Here,}\\\\x = \dfrac{D_x}{D}= \dfrac{\begin{vmatrix} c_1&b_1\\c_2&b_2 \end{vmatrix}}{\begin{vmatrix} a_1&b_1\\a_2&b_2 \end{vmatrix}}\\\\\\ y= \dfrac{D_y}{D}= \dfrac{\begin{vmatrix} a_1&c_1\\a_2&c_2 \end{vmatrix}}{\begin{vmatrix} a_1&b_1\\a_2&b_2 \end{vmatrix}}\\\\[/tex]

[tex]\underline{\textbf{Solution:}}\\\\~~~~~~~~~~~~~~~~~~~~~~~8x-5y = 70~~~~~~...(i)\\\\~~~~~~~~~~~~~~~~~~~~~~~9x +7y = 3~~~~~~~...(ii)\\\\\text{Applying Cramer's rule:}\\\\x = \dfrac{D_x}{D}\\\\\\~~=\dfrac{\begin{vmatrix} 70& -5 \\3&7 \end{vmatrix}}{\begin{vmatrix} 8& -5\\ 9& 7\end{vmatrix}}\\\\\\~~=\dfrac{70(7) -(-5)(3)}{(8)(7)-(-5)(9)}\\\\\\~~=\dfrac{490+15}{56+45}\\\\\\~~=\dfrac{505}{101}\\\\\\~~=5[/tex]

[tex]y = \dfrac{D_y}{D}\\\\\\~~=\dfrac{\begin{vmatrix} 8& 70 \\9&3 \end{vmatrix}}{\begin{vmatrix} 8& -5\\ 9& 7\end{vmatrix}}\\\\\\~~=\dfrac{(8)(3) -(70)(9)}{(8)(7)-(-5)(9)}\\\\\\~~=\dfrac{24-630}{56+45}\\\\\\~~=-\dfrac{606}{101}\\\\\\~~=-6[/tex]

[tex]\textbf{Hence, the solution to the system of equation is}~ (x,y) = (5,-6)[/tex]

Answer : C. 512

step-by-step explanation :

[tex]\qquad\qquad\qquad\boxed{\bf\:\: \: (c) \: 512}[/tex]

[tex] \purple{\bold{\underline{\underline{ Cube \: of \: 8 \: is = 512:}}}}[/tex]

[tex]\red{\bold{\underline{\underline{so \: option \:( c ) \: is \: correct \: \: :}}}}[/tex]

[tex]\orange{\bold{\underline{\underline{ more \: additional \: information \: :}}}}[/tex]

To find Cubes -:

To find Cube Root -:

Answer: (1, -10)

Step-by-step explanation:

Since both of the equations are set equal to y, we can conclude that:

[tex]-x^2 -5x-4=-x^2 + 9x-18\\\\-5x-4=9x-18\\ \\ -14x-4=-18\\\\-14x=-14\\\\x=1[/tex]

If x=1, then [tex]y=-(1)^{2}+9(1)-18=-10[/tex]

Thus, the solution is (1, -10)

Answer:

1) D because the answer to 8.42*10^3=8420

and 8420 lies between 8400 and 8500

2) C because when you take the absolute value of -2.3 and -3.2, they become positive numbers => 2.3 < 3.2

3)D because 6 < 6.3 < 6.6

Hope it helps!

I'll use the method of transformations.

If [tex]f_X(x)[/tex] denotes the PDF of [tex]X[/tex], and [tex]y=g(x)=x^3 \iff x=g^{-1}(y) = y^{1/3}[/tex], we have

[tex]f_Y(y) = f_X\left(g^{-1}(y)\right) \left|\dfrac{dg^{-1}}{dy}\right|[/tex]

[tex]\dfrac{dg^{-1}}{dy} = \dfrac13 y^{-2/3}[/tex]

[tex]\implies f_Y(y) = f_X\left(y^{1/3}\right) \left|\dfrac13 y^{-2/3}\right| = \boxed{\begin{cases} \dfrac53 y^{2/3} & \text{if } 0 \le y \le 1 \\ 0 & \text{otherwise} \end{cases}}[/tex]

Answer:

Yes, she passes with 80%

Step-by-step explanation:

4 divided by 5 = 0.8

0.8 multiplied by 100 = 80%

80% is greater than the required 75% needed to pass

Answer:

Yes

Step-by-step explanation:

First lets establish the key points

We know she needs 75% to pass and she gets 4/5 of the marks

Lets make 4/5 a decimal 4/5 X 2/2 is 8/10 better know as .8

.75 = 75%

.8 = 80%

80% > 75%

Meaning She PASSED!!!

The number of customers I would have expected to win the prize is 6.

Probability determines the chances that an event would happen. The probability the event occurs is 1 and the probability that the event does not occur is 0.

Based on the probability, the number of customers I would have expected to win: 0.18 x 300 = 36

How many more people I would have expected to win : 36 - 30 = 6

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Answer:

already in standard form

Step-by-step explanation:

the equation of a quadratic in standard form is

y = ax² + bx + c ( a ≠ 0 )

y = x² + 4x + 3 ← is in standard form

with a = 1 , b = 4 , c = 3

Answer: A. -3.65

Step-by-step explanation: The best way to figure this out is by using a calculator. One specific rule to remember is the positive/negative rule. When it applies to multiplication, it also applies to division.

[tex](+)*(+)=+\\(+)*(-)=-\\(-)*(+)=-\\(-)*(-)=+\\[/tex]

Knowing this, we can input it into the calculator and find the answer's sign.

[tex]-27.375/7.5=-3.65[/tex]

Therefore, the answer is A. -3.65.

I hope this helps! Pls mark brainliest!! :)

Triangle ABC and triangle XYZ are similar based on angle-side-angle criterion.

Triangle ABC and triangle RQP are similar based on side-angle-side criterion.

An equation is an expression that shows the relationship between two or more numbers and variables.

Two triangles are said to be congruent if they have the same shape and their corresponding sides are congruent.

Triangle ABC and triangle XYZ are similar based on angle-side-angle criterion.

Triangle ABC and triangle RQP are similar based on side-angle-side criterion.

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Answer:

3y= 36×9x

3y=324x

y=324÷3

y=108 ans

The missing reason in Step 8 is substitution

When a triangle is not a right triangle and when either the lengths of two sides and the measurement of the included angle are known (SAS) or the lengths of the three sides are known (SSS), the Law of Cosines is used to discover the remaining pieces of the triangle.

According to the law of cosine, if a, b, and c are any triangle's three sides, then a² = b² + c² - 2bcosa

The x in statement 5 of the preceding proof is changed to c cos A from statement 6 in statement 8 of the proof.

Option C, from the list of alternatives, is the one that best explains statement 8.

Hence  missing reason in Step 8 is substitution

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Answer: OPTION C

Step-by-step explanation:

EDGE22

The slope of the graph is 4/5

Using the formula

Slope = Δ y-axis / Δ x- axis

y2 = -4

y1 = 0

x2 = -5

x1 = 0

Slope = [tex]\frac{y2 - y1}{x2 - x1}[/tex]

Substitute the values into the formula

Slope = [tex]\frac{-4 - 0}{- 5 - 0}[/tex]

Slope = [tex]\frac{-4}{-5}[/tex]

Slope = [tex]\frac{4}{5}[/tex]

Therefore, the slope of the graph is 4/5

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Answer: Choice B) One-sixth

In other words, the fraction 1/6

===========================================================

Explanation:

The base, aka horizontal component, is 6 units long. Count out the spaces from -5 to 1 to get a result of 6.

Or you could subtract and use absolute value in either of these two ways

Where A = -5 and B = 1 are the endpoints mentioned. Absolute value is used to ensure the result of the subtraction isn't negative. Negative distance on a number line doesn't make sense.

----------

However you determine the base, we'll multiply it by the unknown height which we'll call h. This leads to the area of the rectangle. The area is 6h.

Rule: The area under a probability density curve must always be 1.

So the area 6h must be 1 which helps us see that...

6h = 1

h = 1/6

Divide both sides by 6 to isolate h fully.

Answer:

B

Step-by-step explanation:

1200 pounds of protein supplement and 600 pounds of standard protein is used.

Let a be the protein supplement and b be the standard protein.

Given that protein supplement and standard protein make 1800 pounds of high grade protein.

i.e., a+b = 1800 ------- (1)

45% a + 15% b = 35% 1800

0.45a + 0.15b = 1800 (3.5)

By (1), a = 1800 - b

Substituting, we get

0.45 (1800-b) + 0.15b = 630

810 - 0.45 b + 0.15b = 630

- 0.3 b = - 180

b = -180/-0.3

b = 600

Substituting b = 600 in (1),

we get

a = 1200.

Hence, 1200 pounds of protein supplement and 600 pounds of standard protein is used.

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The graph is: On a coordinate plane, a cubic function has a point of inflection at x = 5 and crosses the x-axis at x = 5

A cubic function in mathematics is one with the formula f(x)=ax3+bx2+cx+d, where aneq 0 and the coefficients a, b, c, and d are complex numbers, and the variable x has real values. In other words, it is a real function as well as a polynomial function of degree three.

The function we have is:

y = ∛(x - 5)

So cubic root is given

Here we notice that when x = 0, we have:

y = ∛-5, this is the y-intercept

And when x = 5 we have:

y = ∛0 = 0 which is the x-intercept, and also the inflection point because here we have the change of sign.

Hence option which describes graph best is On a coordinate plane, a cubic function has a point of inflection at x = 5 and crosses the x-axis at x = 5

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Answer:A

Step-by-step explanation: Edge 2022

Answer:

33.33%

Step-by-step explanation:

from 7 to 9 it's 2 hours and you make 500
and 7 to 11 is 4 hours so you make 1000
then do 1000/3000 to find the percentage you have made
1000/3000 is 33.3333333333...% (the 3333.... never ends)

Answer:

29, 36, 38

Step-by-step explanation:

The pattern is add 7 then 2, then 7, then 2, then 7, then 2. You should get the hang of it. All you have to do is just do the same thing for the next three numbers.