a. Draw a tree diagram for the results from tossing a fair two-sided coin (H, T) four times
b. How many stages are there in the tree diagram?
c. List all the possible outcomes (the sample space).
d. How many outcomes are there in the sample space?
▪ You must show ALL of your work in order to receive full credit.

Answer:

Step-by-step explanation:

The two numbers are 42 and 49.

Let us suppose the numbers are x and y.

From the above question,

=> x + y = 91 ------(1)

Also,

=> x:y = 6:7

If we express y in terms of x,

Then, x/y = 6/7

It can also be written as,

=> y = 7x/6 ------(2)

On substitution of value from (2) into (1),

We get,

=> x + 7x/6 = 91

=> 13x/6 = 91

=> x = 6*7

=> x = 42

Now, Substituting the value of x in (1),

We get,

=> 42 + y = 91

=> y = 91 - 42

=> y = 49

Therefore, The values of the two numbers are 42 and 49.

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Answer:

19 < x < 53

Step-by-step explanation:

given 2 sides of a triangle then the third side x is in the range

difference of 2 sides < x < sum of 2 sides , that is

36 - 17 < x < 36 + 17

19 < x < 53

The width of rectangle  = 90 m

And, The length of rectangle = 110 m

A rectangle is a two dimension figure with 4 sides, 4 corners and 4 right angles. The opposite sides of the rectangle are equal and parallel to each other.

Given that;

The perimeter of a rectangle is 400 meters.

And, The length is 20 meters longer than the width.

Now, Let the width of rectangle = x

Then, The length of rectangle = x + 20

We know that;

⇒ Perimeter of rectangle = 2 ( Length + width )

Substitute values ,

⇒ 400 = 2 (x + x + 20)

⇒ 400 = 2 (2x + 20)

⇒ 200 = 2x + 20

⇒ 2x = 200 - 20

⇒ 2x = 180

⇒ x = 90

Thus, The width of rectangle = x = 90 m

And, The length of rectangle = x + 20 = 90 + 20 = 110 m

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The area of the wall is 275 ft square

The number of gallon to cover the wall approximately is 3

the price of the paint is $73.5

1. The area of the wall is given as l * w

this is the value that is used to solve for the area of a rectangle

the length is given as 10 ft

the width is given as 22 ft

the area would be 10 * 22

= 220 ft square

find the area of the triangle = rectangular part is given as height = 15 ft - 10 ft = 5 ft

base = 22 ft

area = 1/2 b h

= 0.5 * 22 * 5

= 55

total area = 220 + 55 = 275 ft square

2. If 1 gallon of paint covers 105 ft

the amount that would cover 275 ft would be gotten when we cross multiply

1 = 105 ft

x  = 275 ft

275 ft = 105 x

x = 275 / 105

x = 2.619

x ~ 3 gallons of paint

3. If one gallon is 24.5 dollars, the total amount that you would purchase is 3 * 24.5

= $73.5

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Answer:

Step-by-step explanation:

a) The number of people showing up at the bar during any given minute is a Poisson process with an average rate of 1 person per minute. Let X be the number of people who show up during a random minute. Then X follows a Poisson distribution with parameter λ = 1. The probability of at least 3 people showing up in a random minute is:

P(X >= 3) = 1 - P(X < 3) = 1 - (P(X = 0) + P(X = 1) + P(X = 2))

We can use the Poisson probability mass function to find P(X = k) for k = 0, 1, 2:

P(X = k) = (e^-λ) * (λ^k) / k!

Plugging in λ = 1, we get:

P(X = 0) = e^-1 / 0! = 1/e

P(X = 1) = e^-1 * 1^1 / 1! = 1/e

P(X = 2) = e^-1 * 1^2 / 2! = 1/2e

So, the probability of at least 3 people showing up in a random minute is:

P(X >= 3) = 1 - (P(X = 0) + P(X = 1) + P(X = 2)) = 1 - (1/e + 1/e + 1/2e) = 1 - (2/e + 1/2e) = 1 - (5/2e)

b) The probability of having to wait at least 3 minutes for the next person to show up is equal to the probability of having 0, 1, or 2 people show up during the first three minutes. Using the same calculation as above, we find:

P(X <= 2) = P(X = 0) + P(X = 1) + P(X = 2) = (1/e) + (1/e) + (1/2e) = (2/e + 1/2e) = (5/2e)

So, the probability of having to wait at least 3 minutes for the next person to show up is 1 - (5/2e) = 1 - P(X <= 2).

c) If he has already waited for 1 minute, the probability of having to wait at least 3 more minutes for the next person to show up is equal to the probability of having 0 or 1 people show up during the next 2 minutes. Using the same calculation as above, we find:

P(X <= 1) = P(X = 0) + P(X = 1) = (1/e) + (1/e) = 2/e

So, the probability of having to wait at least 3 more minutes for the next person to show up is 1 - (2/e) = 1 - P(X <= 1).

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Answer:

3ab2+1 = -23

3a^2b-1 =-25

Step-by-step explanation:

Answer:

YOU L HAHA

Step-by-step explanation:

LOS ER

The solution is, the required cost of the used game X= 19.

An equation which can be expressed as a mathematical statement that is made up of two expressions connected by an equal sign.  In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal.

here, we have,

So he bought the $120 game with $82

and 2 equally priced game.

This can be changed to an equation: 120= 82+2X.

The X represents the cost of the used game.

120= 82+2X

-82 -82

——————-

38= 2X

38= 2X

Divide by 2 on both sides

X= 19

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[tex](\stackrel{x_1}{-7}~,~\stackrel{y_1}{5})\qquad (\stackrel{x_2}{g}~,~\stackrel{y_2}{-2}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{-2}-\stackrel{y1}{5}}}{\underset{\textit{\large run}} {\underset{x_2}{g}-\underset{x_1}{(-7)}}} ~~ = ~~\stackrel{\stackrel{\textit{\small slope}}{\downarrow }}{ 7 }\implies \cfrac{-7}{g+7}=7\implies -7=7(g+7) \\\\\\ \cfrac{-7}{7}=g+7\implies -1=g+7\implies \boxed{-8=g}[/tex]

Answer:

Below

Step-by-step explanation:

5.2 * .83     second

(5.2 * .83) * .83   =    5.3 * .83^2     third

.

= 5.2 ( .83)^4        Fifth   = 2.468 ft

The value of k is,

The probability distribution as a table:

r   1     2          3

P(X)   0    1/15  2/15

Probability is a mathematical term, which can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event. The possibility that an event will occur is measured by probability.

Probability of Event = Favorable Outcomes/Total Outcomes = X/n

To find the value of k, we can use the fact that the sum of the probabilities for all possible values of X must equal 1.

Therefore, we have:

P(X = 1) + P(X = 2) + P(X = 3) = k(4(1)(1²) + 4(2)(2²) + 4(3)(3²))

                                              = 24k

Since we also know that P(X = 1) = 0, we have:

P(X = 1) + P(X = 2) + P(X = 3) = P(X = 2) + P(X = 3) = 0.8

Substituting this into the equation above, we get:

0.8 = 24k

k = 0.8/24 = 1/30

Therefore, the probability distribution can be written as:

r 1 2 3

P(X) 0 1/15 2/15

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The value for the Inequality 13x ≤ 200 is x ≤ 15.384.

Mathematical expressions with inequalities are those in which the two sides are not equal. Contrary to equations, we compare two values in inequality. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign.

Given:

13 times a number x is less than or equal to 200.

Now, Writing the Inequality Mathematically

13x ≤ 200

x ≤ 200 / 13

x ≤ 15.384

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The fan should expect the red team to win 8 fewer games than the blue team in a season of 160 games

Probability is defined as the possibility of an event being equal to the ratio of the number of favorable outcomes and the total number of outcomes.

If the probability that the red team wins is 0.55, then the probability that they lose is 1-0.55 = 0.45.

Similarly, if the probability that the blue team wins is 0.60, then the probability that they lose is 1-0.60 = 0.40.

If we assume that the outcomes of each game are independent of each other and that there are no ties, then the expected number of games that the red team will win in a season of 160 games is:

Expected number of wins for the red team = (probability of winning) x (number of games)

= 0.55 x 160

= 88

Similarly, the expected number of wins for the blue team is:

Expected number of wins for the blue team = (probability of winning) x (number of games)

= 0.60 x 160

= 96

Therefore, the fan should expect the red team to win 8 fewer games than the blue team in a season of 160 games (96 - 88 = 8).

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From the table which represents the  exponential function , the multiplicative rate of change of function is (a) 1/5 .

The exponential function is expressed mathematically as : y = a(b)ˣ ;

where "a" is = initial value of function , and "b" is = multiplicative rate of change  ;

We first substitute , the first two values from the exponential table ;

we get ;

⇒ 2 = a(b)¹  

⇒ 2 = ab    ,...,,....equation(1) ;

Now substituting the second value ,

we get ;

⇒ 2/5 = a(b)²    ,....equation(2) ;

On dividing equation(2) by equation(1) ,

we get;

⇒ 2/(2/5) = ab/ab²  ;

⇒ 5 = 1/b ;

⇒ b = 1/5 .

Therefore , the multiplicative rate of change is b = 1/5 .

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The given  question is incomplete , the complete question is

The table represents an exponential function.

What is the multiplicative rate of change of the function ?

(a) 1/5

(b) 2/5

(c) 2

(d) 5

The equation cos (π/6 + β) is solved to get

From the question it was given that sine β = -0.8

solving for β

sine β = -0.8

β = arc sine ( -0.8 )

β = -0.9273

β ≈ -π/3

substituting the value into cos (π/6 + β)

cos (π/6 + β)

cos (π/6 - π/3)

cos (π/6 - π/3)

= √3 / 2

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The inverse of the radical equation x = [√(a + 2) + √(a - 2)] / [√(a + 2) - √(a - 2)] is the equation a = x + 1 / x. (Correct choice: A)

In this problem we find the case of a radical equation in explicit form, that is, a variable x only in terms of a variable a, and we need to obtain the inverse of the function, that is, an expression in terms of a variable x. This problem can be solved by algebra properties.

First, write the original equation:

x = [√(a + 2) + √(a - 2)] / [√(a + 2) - √(a - 2)]

Second, rationalize the expression:

x = [[√(a + 2) + √(a - 2)] · [√(a + 2) + √(a - 2)]] / [[√(a + 2) - √(a - 2)] · [√(a + 2) + √(a - 2)]]

x = [√(a + 2) + √(a - 2)]² / [(a + 2) - (a - 2)]

x = [a + 2 - 2 ·√(a² - 4) + a - 2] / 4

x = [a - √(a² - 4)] / 2

2 · x = a - √(a² - 4)

Third, eliminate the square root operator by algebra properties:

√(a² - 4) = a - 2 · x

a² - 4 = (a - 2 · x)²

Fourth, find the solution to the expression:

a² - 4 = a² - 4 · x · a + 4 · x²

- 4 = - 4 · x · a + 4 · x²

1 = x · a - x²

1 + x² = x · a

a = (1 + x²) / x

a = 1 / x + x

a = x + 1 / x

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Answer:

i got u i have your email

Step-by-step explanation:

Answer:

It would be C.

Step-by-step explanation:

It would be C.

JKP, the smaller triangle, needs to be turned into J'K'P' to show proof the the triangles are similar. So the first thing you would have to do, because J'K'P' is exactly 2 times bigger than JKP, is multiply the x and the y by 2. However, this shifts the triangle, and we need the triangles to overlap to prove they are also the same size. So comparing the x and y values after we increase the sides of JKP, we would see we need to subtract the x value by 3, and the y value by 2.

The number of years, t , after which the value of the company's new equipment will be less than 7500 is 2.64 years

To solve this problem, we can use the formula for exponential growth:

V(t) = V₀ * (1 + r)^t

Given that the parameters are;

To determine time t when the value of the equipment will be less than $7500.

Let's set up an inequality;

V(t) < 7500

Substituting the formula for V(t), we get:

V₀ * (1 + r)^t < 7500

Substitute the values

(1 + 0.159)^t < 0.5

t * log(1 + 0.159) < log(0.5)

t > log(0.5) / log(1 + 0.159)

Using a calculator, we get:

t > 2.64

Hence, the value is 2.64 years.

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There were a total of 95,082 students from country C.

A percentage in mathematics is a figure or ratiο that is stated as a fractiοn of 100. The abbreviatiοns "pct.," "pct," and "pc" are alsο occasionally used. It is frequently denοted using the percent symbol "%," though. The amοunt of percentages has no dimensions. With a denominatοr of 100, percentages are basically fractiοns.

To shοw that a number is a percentage, place a percent symbol (%) next to it. Fοr instance, if you correctly answer 75 out of 100 questiοns on a test (75/100), you receive a 75%. Tο compute percentages, divide the amount by the tοtal and multiply the result by 100. The percentage is calculated using the fοrmula (value/total) x 100%.

x represents the number οf students from cοuntry C.

then 122percent  of x = 116,000

122/100 * x = 116000

x = 116000 * 100/122 = 95,082 students

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Answer:

Step-by-step explanation:

3/2*2/3(6y)=30*3/2

6y=45

6y/y=45/y

y=7.5

Answer:

Step-by-step explanation:

The tide over a 24-hour period can be modeled by a sinusoidal function of the form:

f(x) = A * sin(Bx) + C

where A is the amplitude, B is the frequency, and C is the vertical shift.

To determine the values of A, B, and C, we need three points. Let's use the following points:

(0, 5): This is the value of the tide at midnight, 5 ft.

(12, 9.5): This is the value of the tide at its high, 9.5 ft.

(6, 0.5): This is the value of the tide at its low, 0.5 ft.

Using the first point (0, 5), we can calculate the vertical shift, C:

C = 5

Using the second point (12, 9.5), we can calculate the amplitude, A:

A = (9.5 - 5) / 2 = 2.25

Using the third point (6, 0.5), we can calculate the frequency, B:

0.5 = 2.25 * sin(B * 6) + 5

4.5 = 2.25 * sin(B * 6)

2 = sin(B * 6)

B * 6 = sin^-1(2)

B * 6 = pi / 2

B = pi / (2 * 6) = pi / 12

So, the final equation is:

f(x) = 2.25 * sin(pi * x / 12) + 5

This represents one period of the sinusoidal function that models the tide over a 24-hour period, with time x measured in hours since midnight.

The permutation formula is used when the order matters as it does not remove the combinations with the same elements and different order from the equation.

For the combination formula, the term x! is removed, as it removes all the combinations with the same elements but different order.

The number of different combinations of x objects from a set of n elements is obtained with the formula presented as follows, using factorials.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

The number of possible permutations of x elements from a set of n elements is given by:

[tex]P_{(n,x)} = \frac{n!}{(n-x)!}[/tex]

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The number of years the interest was compounded quarterly is given by the equation b = 9.098 years

Compound interest is interest based on the initial principle plus all prior periods' accumulated interest. The power of compound interest is the ability to generate "interest on interest." Interest can be added at any time, from continuously to daily to annually.

The formula for calculating Compound Interest is

A = P ( 1 + r/n )ⁿᵇ

where A = Final Amount

P = Principal

r = rate of interest

n = number of times interest is applied

b = number of time periods elapsed

Given data ,

Let the amount after b years be A = $ 26,725.00

The number of years be = b

The number of times the interest is applies n = 4 ( quarterly )

Let the principal amount be P = $ 7,000

A = P ( 1 + r/n )ⁿᵇ

Substituting the values in the equation , we get

t = ln ( A/P ) / n [ ln ( 1 + r/n ) ]

t = b = n ( 26,725.00 / 7,000.00 ) / ( 4 × [ ln ( 1 + 0.15/4 ) ] )

On simplifying the equation , we get

b = ln ( 26,725.00 / 7,000.00 ) / ( 4 × [ ln ( 1 + 0.0375 ) ] )

b = ln ( 3.81785714 ) / 4 [ ln ( 1.0375 ) ]

On further simplification , we get

b = 9.098 years

Hence , the number of years the interest was applied is 9 years 1 months

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1) From Given output confidence level, is 95% level of significance = 1-0.95

10.05

2) null hypothesis : M = 150000

=

3) Alternative hypothesis Ha: [M> 150000]

4) since P value = 0.033 is less than d=0.05 Reject null hypothesis.

5) There is sufficient evidence to conclude that the mean life of transmissions is over 1500 comity

6) 95% CI = â ± E

-1519±1.129

=(151.2-1.129, 151.2+1.129)

=(150.071, 152.329)

7) Since M=150 fall out side of the C. We Shoul retect null hypothesis.

8) The null hypothesis value fall outside of the Confidence Interval.

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The composite function has its value to be g o h(x) = -20x^2 - 30x

from the question, we have the following parameters that can be used in our computation:

h(x) = 4x + 6

g(x) = -5x

Using the above as a guide, we have the following:

g o h(x) = g(x) * h(x)

substitute the known values in the above equation, so, we have the following representation

g o h(x) = (4x + 6) * -5x

Evaluate

g o h(x) = -20x^2 - 30x

Hence, the value is g o h(x) = -20x^2 - 30x

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If Mrs. Imperiale's credit card has an APR of 13.2%. The amount she would  save in finance charges Round to the nearest ten dollars is $80.

Finance charge if bought on the first day

Finance charge = (31 × 7400 ÷ 31) × (0.132 ÷ 12)

Finance charge = 7400  ×  0.011

Finance charge= $81.40

Finance charge if bought on the last day

Finance charge = (1 × 7400 ÷ 31) × (0.132 ÷ 12)

Finance charge = 238.709677 ×  0.011

Finance charge= $2.625

Finance charge = $2.63

Savings = $81.40 - $2.63

Savings = $78.77

Savings = $80 ( Approximately)

Therefore the savings is $80.

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The value of the trigonometric equation sin D = 0.923

Trigonometry is the study of the relationships between the angles and the lengths of the sides of triangles

The six trigonometric functions are sin , cos , tan , cosec , sec and cot

Let the angle be θ , such that

sin θ = opposite / hypotenuse

cos θ = adjacent / hypotenuse

tan θ = opposite / adjacent

tan θ = sin θ / cos θ

cosec θ = 1/sin θ

sec θ = 1/cos θ

cot θ = 1/tan θ

Given data ,

Let the triangle be represented as ΔBCD

Now , the measure of BC = 24

The measure of side CD = 10

So , the measure of hypotenuse BD = √ ( BC )² + ( CD )²

Substituting the values in the equation , we get

The measure of BD = √ ( 576 ) + 100

The measure of BD = √ ( 676 )

The measure of BD = 26

Now , from the trigonometric relations ,

sin θ = opposite / hypotenuse

Substituting the values in the equation , we get

sin D = 24 / 26

On simplifying the equation , we get

sin D = 0.923

Hence , the equation is sin D = 0.923

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Answer:

Yes

Step-by-step explanation:

To find this out. If you divide the denominators by each other, they would need to be the same value as if you divide the numerators by each other

[tex]45 \div 9 = 5[/tex]

^ 45 and 9 were the denominators, we divide and get 5

Now for the numerators

[tex]10 \div 2 = 5[/tex]

^ 10 and 2 we're the numerators, dividing also gave 5

Answer:

yes.

Step-by-step explanation:

let us check. to be a proportion they must be equivalent

however, what do we multiply to get there? let us check..

[tex]\frac{2x}{9x} =\frac{10}{45}[/tex]

cross multiply...

2x * 45 = 9x * 10

90x = 90x

yes, they will be proportional!

you can even do it without the X, i just put x in to make it clearer.

Answer:

The surface area of a cylinder can be calculated using the formula:

Surface area = 2πr^2 + 2πrh

Where r is the radius and h is the height of the cylinder.

Plugging in the values we have:

Surface area = 2π(8^2) + 2π(8)(8) = 2π(64) + 2π(64) = 128π

Rounding to the nearest thousandth, we have:

Surface area = 128π = 403.23 in^2 (rounded to the nearest thousandth)

So the surface area of the cylinder with height 8 in and radius 8 in is 403.23 in^2.

Step-by-step explanation: