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The probability that at least five wear sunglasses is 0.9464

Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and 1, where, roughly speaking, 0 indicates impossibility of the event and 1 indicates certainty. The higher the probability of an event, the more likely it is that the event will occur. A simple example is the tossing of a fair (unbiased) coin. Since the coin is fair, the two outcomes ("heads" and "tails") are both equally probable; the probability of "heads" equals the probability of "tails"; and since no other outcomes are possible, the probability of either "heads" or "tails" is 1/2 (which could also be written as 0.5 or 50%).

In a random sample of 10 adults, the probability that at least five wear sunglasses

P(X ≥ 5) = P(X = 5) + P(X = 6 ) + P(X=7) + P(X=8) + P(X=9) + P(X=10)

P(X ≥ 5) = 10[tex]C_{5}[/tex] × [tex](0.7)^{5}[/tex]×[tex](0.3)^{5}[/tex] +  10[tex]C_{6}[/tex]×[tex](0.7)^{6}[/tex]× [tex](0.3)^{4}[/tex]+ 10[tex]C_{7}[/tex]×[tex](0.7)^{7}[/tex]×[tex](0.3)^{3}[/tex] + 10[tex]C_{8}[/tex]× [tex](0.7)^{8}[/tex]×[tex](0.3)^{2}[/tex] +10[tex]C_{9}[/tex] ×[tex](0.7)^{9}[/tex]×[tex](0.3)^{1}[/tex]+10[tex]C_{10}[/tex]×[tex](0.7)^{10}[/tex]×[tex](0.3)^{0}[/tex]

P(X ≥ 5) = 0.9464

The probability that at least five wear sunglasses is 0.9464

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The equation could be used to solve for charles' rate if it is represented by x is 2x=54.

In the given question wehave to find the equation could be used to solve for charles' rate if it is represented by x.

Bill riding a bicycle at an average rate of 9 mph.

Charles' rate is x.

So the relative rate = x−9 mph

Distance traveled by Bill in 4 hours = 9*4 =36 mph

Charles' overtook Bill in 2 hours. So

Relative Rate = Distance/Time

x−9=36/2

Multiply by 2 on both side. We get

2(x−9)=36

Simplifying

2x−18=36

Add 18 on both side, we get

2x=36+18

2x=54

Hence, the equation could be used to solve for charles' rate if it is represented by x is 2x=54.

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The gcf of 25 and 60 is 5

the lcm of 25 and 60 is 300

The process of determining which prime numbers combine to form the original number is known as prime factorization.

Prime factorization of 25 = 5 * 5

Prime factorization of 60 = 2 × 2 × 3 × 5

the greatest common factor, gcf of 25 and 60 is 5

The lowest common multiple, lcm of 25 and 60

= 2 * 2 * 3 * 5 * 5

= 300

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The expression that represents the width of the box is (x - 1) , the correct option is (b) .

In the question ,

it is given that ,

the Volume of the rectangular prism is = x³ + 9x² + 6x – 16

the measure of the length of the box = x+2

the measure of the height of the box = x+8

formula for Volume of Prism is

Volume = l × w × h

where l = length of the prism,

w = width of the prism and

h = height of the prism.

Substituting the values ,

we get ,

x³ [tex]+[/tex] 9x² [tex]+[/tex] 6x – 16 [tex]=[/tex] (x [tex]+[/tex] 2) * (x [tex]+[/tex] 8) * width

On dividing the equation  (x³ + 9x² + 6x – 16) with (x+2)

and then dividing the result with (x+8) , we get

width = (x-1) .

Therefore , The expression that represents the width of the box is (x - 1) , the correct option is (b) .

The given question is incomplete , the complete question is

The volume of a rectangular prism is represented by the function x³ + 9x² + 6x – 16. The length of the box is x + 2 while the height is x + 8. Find the expression representing the width of the box

(a) x - 4

(b) x - 1

(c) x + 1

(d) x + 4

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Answer:

B

Step-by-step explanation:

Asked my teacher to help me.

Answer:17

Step-by-step explanation:

Answer:

Simplest form = -w - 2

Step-by-step explanation:

Given expression,

→ -24 - 12w

→ -12w - 24

Simplifying the expression,

→ -12w - 24

→ (-12w - 24)/12

→ -w - 2

Hence, the answer is -w -2.

Tanya, who has a Bronze level plan and only goes to the doctor once a year for an annual exam, is likely to pay the least for healthcare. The correct option is A.

Health care refers to the maintenance or improvement of an individual's physical or mental health through the prevention, diagnosis, and treatment of illness, injury, or disease. It encompasses a range of services provided by healthcare professionals.

Based on the information provided, Tanya, who has a Bronze level plan and only goes to the doctor once a year for an annual exam, is likely to pay the least for healthcare.

Bronze level plans typically have lower monthly premiums but higher out-of-pocket costs for healthcare services, such as copays, deductibles, and coinsurance.

Since Tanya only goes to the doctor once a year, she is unlikely to meet her deductible or incur significant out-of-pocket costs.

In contrast, options B, C, and D involve more frequent or more serious healthcare needs, which would likely result in higher out-of-pocket costs for healthcare services.

Thus, the correct option is A.

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The required solution is 24.4 to the given numerical expression 8.54 ÷ 0.35.

In mathematics, divides left-hand operands into right-hand operands in the division operation.

The numerical expression is given in the question as:

8.54 ÷ 0.35

We have to determine the solution to the given expression

As per the question,

8.54 ÷ 0.35

8.54 / 0.35

(854/100) / (35/100)

Reciprocal the terms of numerator

854/100 × 100/35

854/35

Apply the division operation to get the solution

24.4

Thus, the required solution is 24.4 to the given numerical expression.

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The total output of 15 workers will be 105 units per day.Work and time are correlated so using this we could solve the question.

What is work and time?

Time is the duration of any activity or work that occurs or continues.

Work is a task or set of activities designed to achieve a specific result.

Main Body:

This can be done by simply multiplying both number of days and total work in one day.Hence the equation become:

total output = total workers*total work done by one person.

Total output = 7*15

hence,total output = 105 units

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To factorize this,the answer is [tex]\frac{1}{3} x^{4} y^{2} (\frac{1}{4} y^{} -\frac{1}{3} x)[/tex]

Factorization is when you break a number down into smaller numbers that, when multiplied together, give you that original number.

The expression above can only be determined by looking at the common factors and using it to answer the question. [tex]\frac{1}{12} x^{4}y^{3} -\frac{1}{9}x^{5}y^{2}[/tex]

To factorize the fractions by looking at the common factor between the both[tex]\frac{1}{3} (\frac{1}{4} -\frac{1}{3} )[/tex]To factorize the indices by looking at the common factor[tex]x^{4}y^{2} (y-x)[/tex]

So, to factorize the expression above[tex]\frac{1}{3} x^{4} y^{2}(\frac{1}{4} y-\frac{1}{3} x)[/tex]

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Answer: 9+6i√5

Step-by-step explanation:

√4 + √−45 + √49 + √−45

2 + √45i + 7 + √45i

9 + 3i√5 + 3i√5

9+6i√5

Answer: 80 copies can be purchased with $60.00.

Step-by-step explanation:

If it costs $0.75 for each color copy, then you would have to divide $60.00 by $0.75, which equals 80 copies.

The given ordered pair (x, y) represents a linear function

Consider first point (-1, -3) and (0, -1)

The slope of the line is the change in y coordinate with respect to the change in x coordinate of the line.

The slope of the line = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

Substitute the value in the equation

The slope of the line = (-1-(-3)) / (0 -(-1)

= (-1+3) / 1

= 2

Consider the next set of points (1, 1)  and (2, 3)
The slope of the line = (3-1) / (2-1)

= 2

Here slope of the line is same, therefore it is linear function

Hence, the given ordered pair (x, y) represents a linear function

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The inequality shown on the number line is -3 < x ≤ 2

Inequality means when the two values that are not equal is defined by inequalities. Inequality means unequal.

When two values are not equal we will greater than or less than sign .

" < " means less than

" >" means greater than

"≤ " means less than and equal to

"≥ " means greater than and equal to

(a) Inequality -4 < n ≤ 5

here , -4 is not included so, the Number line starts from -3

5 is included so, number line will end on 5

(b) The number line shows ,

line is starting from -3 but the dot is not filled means it is not included

The line ends at 2 so,

Inequality is -3 < n ≤ 2

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Answer:

B

Step-by-step explanation:

product means multiplication and quotient is division , then

product of 8 and the quotient of 6 and w is

8 ([tex]\frac{6}{w}[/tex] )

Number of solutions for the given linear quadratic equation y = x² and

y = 2x+ b is equal to 2.

b. As we change the value of b solution of the linear system of equation get modify. For example b = 0 it passes through origin.

As given in the question,

Given linear quadratic equations are:

y = x² and

y = 2x+ b

⇒ x² = 2x + b

⇒ x² -2x -b = 0

Number of solutions depends on :

Discriminant 'D'  = b² -4ac

Here a = 1 , b = -2 , c= -b

D = (-2)² - 4(1)(-b)

  = 4 + 4b

If D > 0 there are two real solutions.

If D = 0 there is only one solution.

If D < 0 there is no solution.

Value of D depends on the value of 'b' .

Linear quadratic equation has two solutions if D > 0.

Graph is attached for the given quadratic equations.

Therefore, number of solutions for the given linear quadratic equation y = x² and y = 2x+ b is equal to 2.

b. As we change the value of b solution of the linear system of equation get modify. For example b = 0 it passes through origin.

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Answer:

(-2, 3 1/3)

2nd one

Step-by-step explanation:

2/3*-3=-2 so x=-2

2/3*5=10/3= 3 1/3 so y= 3 1/3

(-2, 3 1/3)

The George's integer must be true for option D)I and IV.

What is integer?

 A full number (not a fraction) that can be positive, negative, or zero is called an integer . -5, 1, 5, 8, 97, and 3, 043 are some examples of integers. 1.43, 1 3/4, 3.14, and other numbers are examples of non-integer numbers. Integer, which means full or whole in Latin, is the root of the English term integer. A particular category of numbers called integers includes zero, positive numbers, and negative numbers. All whole numbers, both negative and positive, and 0 are considered integers.

Here the opposite of George integer is -53.

We know that opposite value of x is -x.

Then George integer is 53.

George integer must be true for The given options I. the integer is 53 and IV.The integer has absolute value of 53.

Therefore the correct option is  D) I and IV.

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The speed of the plane is 252 miles per hour and the speed of the wind is 28 miles per hour .

In the question ,

it is given that ,

the airplane covers the distance of 560 miles in 2 hours with the wind,

So , the speed of the airplane with the wind is 560/2 = 280 miles per hour

also given that

airplane covers the distance of 560 miles in 2.5 hours against the wind ,

So , the speed of the plane with the wind = 560/2.5 = 224 miles per hour .

let the speed of the airplane be "a" miles per hour ,

and let the speed of the wind be "b" miles per hour ,

So , equation of speed  with the wind is denoted by

a + b = 280

and the equation of speed against the wind is denoted by

a - b = 224

Adding both the equations , we get

2a = 504

a = 504/2

a = 252 miles per hour

and b = 280 - 252 = 28 miles per hour .

Therefore , The speed of the plane is 252 miles per hour and the speed of the wind is 28 miles per hour .

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The P(X<0.2) with standard beta distribution parameters α = 5 and β = 2 is 0.0016.

How to calculated the probability density function in standard beta distribution?

Beta distribution is one of the continuous probability distributions set at interval (0, 1) intervals with two positive parameters α and β.

Probability density function can be calculated by this formula

[tex]\frac{x^{\alpha -1}(1-x)^{\beta -1}}{B(\alpha ,\beta) }[/tex]

B(α,β) is beta function =  Γ(α)Γ(β)/Γ(α+β)

Γ(α) is gamma function of alpha

Γ(β) is gamma function of beta

P(X<0.2) = [tex]\frac{0.2^{5-1}(1-0.2)^{2-1}}{B(5,2) }[/tex]

= 0.0016

Excel formula for beta distribution is

=BETA.DIST(x;α;β;TRUE)

Thus, the P(X<0.2) with standard beta distribution parameters α = 5 and β = 2 is 0.0016.

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The value of x for the given equation is -20 .

An equation is a combination of different variables, in which two mathematical expressions are equal to each other.

The given equation is,

(5/3)x+(1/3)x=13(1/3)+(8/3)x

Solve equation, to find the value of x,

(5/3+1/3)x=13(1/3)+(8/3)x

-13(1/3)=(8/3)x-(5/3+1/3)x

-40/3=(8/3-2)x

1.(-40/3)=1.(2/3)x

-20=x

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Answer:

See attached "Image 2" for graph

3 points that are in the system

[tex](6,1)\\(8,-2)\\(7,5)[/tex]

3 points that are not in the system:

[tex](0,0)\\(-2,-6)\\(-8,4)[/tex]

Step-by-step explanation:

Start by writing the equation in slope-intercept form so they can be graphed.

[tex]\left \{ {{y+5 < 2x} \atop {3y\geq -2x+6}} \right. \\\\\left \{ {{y < 2x-5} \atop {y\geq -\frac{2}{3} x+2}} \right. \\\\[/tex]

Now, graph just the lines - LIGHTLY- on the coordinate plane. See the first attached image.

Now, you can shade the correct areas. In the first equation y is LESS THAN the function, so you would shade BELOW the line, and draw the line as a dashed line, not a solid line. This is because y is not EQUAL to the function.

In the second equation y is GREATER than or EQUAL to the function, so draw the line as a solid line and you would SHADE above the line.

In a system of inequalities, the correct area to shade is where the two shaded areas overlap. See the attached image 2 to see how that looks.

Some points that are in the system of inequalities are:

[tex](6,1)\\(8,-2)\\(7,5)[/tex]

These points are NOT in the system:

[tex](0,0)\\(-2,-6)\\(-8,4)[/tex]

Answer:

-41.79

Madeline was overdrawn $41.79.

Step-by-step explanation:

If she deposited $29.06 a week for 8 weeks, she put

8 × 29.06

= 232.48

$232.48 into her account. But they're saying she now has only $190.69. Some of the money went to payback the negative balance she had.

Balance+232.48=190.69

Balance=190.69-232.48

Balance = -41.79

Madeline had a negative balance of $41.79.

The integers are  3√25, -185/5, rational = -1/4, 0.75, 3√25, -185/5, 4√8, irrational = √13,

An integer is the number zero (0), a positive natural number (1, 2, 3, etc.) or a negative integer with a minus sign.

A rational number is any number that can be written as a fraction, where both the numerator na demoninator that is the top and the bottom number  are integers, and the denominator is cannot be zero

An irrational number is a type of real number which cannot be represented as a simple fraction.

A integer can always be a rational number but vice versa is not true.

Integer = 3√25 = 3x5 = 15

-185/5 = -37

rational = -1/4, 0.75, 3√25, -185/5, 4√8

irrational = √13,

Therefore, the integers are  3√25, -185/5, rational = -1/4, 0.75, 3√25, -185/5, 4√8, irrational = √13,

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Answer:

4²0=4×5=20=4²0 арлатат

Answer:

4%12

Step-by-step explanation:

Answer:

$85.10

Step-by-step explanation:

115 * .20 = 23

115 - 23 = 92

92 * 0.075 = 6.9

92 - 6.9 + 85.10

Answer:

y= -7/2x-20

Step-by-step explanation:

parallel line so same slope

the equation given is in y=mx+b form so take out m:

m= -7/2

now input the coordinates and slope(m) given into y=mx+b to find b:

-6=-7/2(-4)+b

-6=28/2+b

-6=14+b

-6-14=b

b=-20

now write equation using slope(m) and y intercept(b)

y= -7/2x-20

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The equation in point-slope pass through the given point will be y = -7/2x-20

Equations are mathematical expressions that have two algebras on either side of an equal (=) sign. The expressions on the left and right are shown to be equal to one another, demonstrating this relationship. L.H.S. = R.H.S. (left-hand side = right side) is a fundamental simple equation.

The same slope due to a parallel line,

Take away m from the above equation since it is in the y = mx+b form:

m= -7/2

Now, enter the given coordinates and slope(m) into y=mx+b to determine b:

-6 =-7/2 (-4) + b

-6 = 28/2 + b

-6 = 14 + b

b = -20

Slope(m) and y-intercept are now used to create an equation (b),

y = -7/2x-20

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Answer:

at least 1,408 minutes

Step-by-step explanation:

Let m be the number of minutes.

[tex]17 + .07m \geqslant 115.56[/tex]

[tex].07m \geqslant 98.56[/tex]

[tex]m \geqslant 1408[/tex]

Answer:

51

Step-by-step explanation:

The segments are indicated to be congruent.

[tex]3x+9=5x-19 \\ \\ 9=2x-19 \\ \\ 2x=28 \\ \\ x=14 \\ \\ \implies AB=3(14)+9=51[/tex]

3x + 9 = 5x - 19

+ 19           + 19

3x +28 = 5x

- 3x            -3x

28 = 2x

÷2     ÷2

14 = x

3x + 9

= 3(14) + 9

= 42 + 9