A deck of cards contains 52 cards, of which 4 are aces. You are offered the following wager: Draw one card at random from the deck. You win $10 if the card drawn is an ace. Otherwise, you lose $1.

If you make this wager vary many times, what will be the mean amount you win?

[tex]A=Pe^{rt} \\ \\ 15000000=10000000e^{12r} \\ \\ 1.5=e^{12r} \\ \\ \ln(1.5)=12r \\ \\ r=\frac{\ln(1.5)}{12} \\ \\ r \approx \boxed{0.0338}[/tex]

The exponential growth rate of the population of the country is given by the relation r = 1.8595 %

The exponential growth or decay formula is given by

x ( t ) = x₀ × ( 1 + r )ⁿ

x ( t ) is the value at time t

x₀ is the initial value at time t = 0.

r is the growth rate when r>0 or decay rate when r<0, in percent

t is the time in discrete intervals and selected time units

Given data ,

Let the initial population of the country in 2010 be = 12 million

Let the final population of the country in 2022 = 15 million

Now , let the growth rate be represented as r

And , growth rate r = [ ln( final population - ln (initial population ) / no of years ] x 100

Growth Rate = (ln(15 ) - ln(12 )) / (2022 - 2010)

r = (2.70805 - 2.48491) / 12

r = 0.018595

r = 1.8595 %

Hence , the growth rate r = 1.8595 %

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The solution to the matrix equations A and B are X = (-2 0 4) and X = (-5 1)

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

Solving matrix A, we have the following representations

2X=(-4 0 8)

Rewrite the equation properly

So, we have

2X = (-4 0 8)

Divide through the matrix by 2

This gives

X = (-2 0 4)

Solving matrix B, we have the following representations

3 X-(1 7)=(-16 -4)

Rewrite the equation properly

So, we have

3X - (1 7) = (-16 -4)

Add (1 7) to both sides of the equation

This gives

3X = (-15 3)

Divide through the matrix by 3

This gives

X = (-5 1)

Hence, the solutions are X = (-2 0 4) and X = (-5 1)

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Answer: Graphed: f(x)=-9x+14gx     Answer: =-3x2

Use the given functions to set up and simplify .

Exact Form: x=0,-1/3

Decimal Form: x=0,-0.3

Step-by-step explanation:

[tex]\begin{array}{ccll} \$&hours\\ \cline{1-2} 44 & 6\\ x& 9 \end{array} \implies \cfrac{44}{x}~~=~~\cfrac{6}{9} \\\\\\ \cfrac{ 44 }{ x } ~~=~~ \cfrac{ 2 }{ 3 }\implies 132=2x\implies \cfrac{132}{2}=x\implies 66=x[/tex]

Answer:

B. [tex]BC \cong FC[/tex]

Step-by-step explanation:

For triangles to be congruent by HL, the hypotenuses must be congruent.

Answer: it describe the steepness of the line

Step-by-step explanation:

need brainliest

Answer:

x = 7

Step-by-step explanation:

Given equation,

→ -14 - x = -21

Now the value of x will be,

→ -14 - x = -21

→ -x = -21 + 14

→ -x = -7

→ [ x = 7 ]

Hence, the value of x is 7.

Answer:

x=7

Step-by-step explanation:

Isolate the variable by dividing each side by factors that dont contain the variable

The 125 is the median number of calories per serving for the breakfast cereals.

What is median?

The middle value in a sorted, ascending or descending list of numbers is known as the median, and it has the potential to describe a data set more accurately than the average does. It represents the midpoint of the data because it is the point above and below which half (50%) of the observed data falls.

Given:

The box-and-whisker plot below shows the distribution of the numbers of calories per serving for a selection of breakfast cereals.

We have to find the median.

Since median is the middle most number of the given list of numbers.

In the given list there are 11 numbers.

The middle most number is occur at 5th number.

The number on 5th place is 125.

Hence, the 125 is the median number of calories per serving for the breakfast cereals.

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The tomato plant is 49 cm tall 22 days after Allie bought it.

What are Functions?

A function from a set X to a set Y allocates precisely one element of Y to each element of X. The set X is termed the domain of the function and the set Y is called the codomain of the function.

The function is H(d) = 16 + 1.5d

Since, all the options talks aabout the height of the plant after 22 days

We need to put the value of d as 22 in the function for calculating the height of the function

H(22) = 16 + 1.5(22)

H(22) = 16 + 33 = 49

The tomato plant is 49 cm tall 22 days after Allie bought it.

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Standard deviation of given data corrected to one decimal place is 6.9(rounding off)

The average degree of variability in your datasets is represented by the standard deviation. It reveals the average deviation of each statistic from the mean.

In general, values with a large standard deviation are spread out from the mean, and those with a low standard deviation are grouped together near to the mean.

Given: Data values = 13,2,16,18,19

Mean of data is given as m,

[tex]=\frac{13+2+16+18+19}{5} \\=\frac{68}{5}\\ =13.6[/tex]

Standard deviation, σ

[tex]=\sqrt{\frac{(m-x)^{2} }{n-1} } \\=\sqrt{\frac{(13.6-13)^{2} +(13.6-2)^{2}+(13.6-16)^{2} +(13.6-18)^{2} +(13.6-19)^{2} }{4} }\\ =\sqrt{\frac{0.36+134.56+5.76+19.36+29.16}{4} }\\ =\sqrt{\frac{189.2}{4} }\\ =6.87[/tex]

Hence, standard deviation of given data is 6.9(rounding off)

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The probability that an individual will take far longer than 21 days to complete it is 0.12.

In the descriptive analysis, the standard deviation is the amount of scatter or dispersal of the pieces of data in relation to their mean. It provides information on the distribution of values within the sample data and serves as a gauge for how widely apart the measured values are from the mean.

As per the information available in the question,

Meantime, μ = 14 days

Standard deviation, ρ = 6 days

Assume the time to pass the kidney stone be x.

The probability that it will take someone more time than 21 days to complete it.

Let's find out the Z-score first,

Z-score = (x - μ)/ρ

Substitute values in above equation,

= (21 - 14)/6

Z-score = 1.166.

The probability that it will take someone more time than 21 days to complete it :

P(x > Z) = P(x > 1.16) = 0.12

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k(n) is also the number of partitions of n into distinct, odd parts. We begin with the generating function P(x) = ∑p(n) x_n which counts all partitions of all numbers n, with weight x_n for a partition of n.

How do you explain partitioning numbers?

By breaking huge numbers into smaller parts, partitioning helps to simplify the solution of arithmetic issues involving large numbers. 782, for instance, may be divided into: 700 + 80 + 2. It aids children in understanding the real value of each digit. They will perceive 782 as 700, 80, and 2, rather than as a terrifying number.

The numbers of partitions of 10 with number of parts {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} are respectively {1, 5, 8, 9, 7, 5, 3, 2, 1, 1}. (There are 20 partitions of 10 into an odd number of parts and 22 partitions of 10 into an even number of parts.)

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The equation of the line passing through the points (-3,-15/2) and(1,-3/2) is  3x - 2y - 6 = 0.

What is the equation of a line?

An algebraic way to represent a collection of points that together make a line in a coordinate system is called the equation of a line. An algebraic equation, commonly known as the equation of a line, can be created using the various points that together make up a line in the coordinate axis as a collection of variables (x, y). It is possible to determine whether a specific point lies on a line by utilising the equation of a line.

The equation of a line passing through two points [tex](x_{1} ,y_{1} )[/tex] & [tex](x_{2},y_{2})[/tex] is given by

               [tex]\frac{y-y_{1} }{x-x_{1} } = \frac{y_{2} -y_{1} }{x_{2} -x_{1} }[/tex]

Given, two points are  (-3,-15/2) and(1,-3/2).

[tex](x_{1} ,y_{1} )[/tex] = (-3,-15/2) and  [tex](x_{2},y_{2})[/tex] = (1,-3/2).

So, The equation of line passing through (-3,-15/2) and (1,-3/2) is given by

or, [tex]\frac{y+\frac{15}{2} }{x+3 } = \frac{-\frac{3}{2} +\frac{15}{2} }{1 +3 }[/tex]

or, [tex]\frac{y+\frac{15}{2} }{x+3 } = \frac{6}{4 } =\frac{3}{2}[/tex]

or, 2(y+7.5) = 3(x+3)

or, 2y + 15 = 3x + 9

or, 3x - 2y - 6 = 0

Hence, the required equation of the line is 3x - 2y - 6 = 0.

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Answer: see below

Step-by-step explanation:

slope intercept form

y=mx+b

m=slope

The first question:-5/2 is the sloop

second question: 5/2 is the sloop

Answer:

[tex]\frac{39}{15}[/tex] a - [tex]\frac{8}{5}[/tex]

Step-by-step explanation:

Frist combine your like terms

[tex]\frac{7}{3}[/tex] a + [tex]\frac{4}{15}[/tex] a  The common denominator will be 15

[tex]\frac{35}{15}[/tex] a+ [tex]\frac{4}{15}[/tex] a= [tex]\frac{39}{15}[/tex]a

You cannot combine this with [tex]\frac{8}{5}[/tex] because these are not like terms.  

Answer:

base = 8

Step-by-step explanation:

In an isosceles triangle, the legs are equal.

P = 28 = 2L + 8

2L + 8 = 28

2L = 20

L = 20/2 = 10 (length of each leg)

P = 2L + b  (sum of the lengths of the 2 legs and the base)

28 = 2(10) + b

b = 28 - 20 = 8

All angles are:

a = 37

b = 143

c = 37

d = 58

e = 37

f = 53

g = 48

h = 94

k = 96

m = 26

p = 69

r = 111

s =  69

What is sum of angles of a triangle?

A triangle's total angles equal the straight angle (180 degrees, radians, two right angles, or a half-turn) in a Euclidean space. Three angles, one at each vertex and bounded by two neighbouring sides, make up a triangle.

For a very long period, it was unknown if there were any alternative geometries for which the total is different. During the 19th century, this issue had a particularly significant impact on mathematics. Ultimately, it was determined that the response was correct: in other geometries, this total can be higher or smaller, but it must then depend on the triangle. Its deviation from 180° represents an instance of an angular defect and is a crucial distinction for geometric systems.

From the fig.

we know,

e=37

b= 143 (vertically opposite angle)

143  +  a = 180 (Linear pair)

a =  180 - 143

a  =  37

e = 37

So,  c = 37 (Vertically opposite angle)

c + d + 85 = 180 (Sum of angles on straight line)

37 + d +  85 = 180

d = 180 - 122

d = 58

e + 90 + f = 180 (Sum of all angles of a triangle)

37 + 90 + f = 180

f = 180 - 127

f = 53

g = 48 (if two sides are equal , then the two angles opposite to the equal    

             sides will also be equal.)

48 + 48 + h = 180 (Sum of angles of a triangle)

h = 180 - 96

h = 94

h+ k = 180 (Linear pair)

94 + k = 180

k = 180 - 94

k = 96

d + k + m = 180 (Sum of angles of a triangle)

58 + 96 + m = 180

m = 180 - 154

m = 26

26 + 85 + p = 180 (Sum of angles of a triangle)

p = 180 - 111

p = 69

p + r = 180 (Linear pair)

r = 180 - 69

r = 111

p = s (corresponding angles)

s = 69

Hence all angles are:

a = 37

b = 143

c = 37

d = 58

e = 37

f = 53

g = 48

h = 94

k = 96

m = 26

p = 69

r = 111

s =  69

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By solving linear inequation, it can be calculated that

x < 8 is the solution of the inequality -5x+30 >-10

What is linear inequation?

At first, it is important to know about algebraic expression.

Algebraic expression consist of variables and numbers connected with addition, subtraction, multiplication and division.

Now, algebraic expressions are of different types. They are-

Monomial, Binomial and trinomial.

Algebraic expression with only one term is called monomial

Algebraic expression with two terms are called binomial

Algebraic expressions with three terms are called trinomial.

Algebraic expressions with more than three terms are called polynomial.

Based on degree, algebraic expression may be called as linear, quadratic, cubic and so on

Algebraic expression of degree one is called linear

Algebraic expression of degree two is called quadratic

Algebraic expression of degree one is called cubic

Inequation shows the comparison between two algebraic expressions by connecting the two algebraic expressions by >,<, ≥, ≤

A one degree inequation is known as linear inequation.

Here the given inequality is-

-5x+30 >-10

Now,

-5x + 30 > -10

-5x > -10 - 30

-5x > -40

x < [tex]\frac{-40}{-5}[/tex]

x < 8

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Step-by-step explanation:

a.

correct, the population was 18.5 million in 2000.

why ?

t = years after 2000.

so, if the year is 2000, t = 0.

A(0) = 18.5e^(0.1708 × 0)

you remember, a⁰ = 1 for any a.

so,

A(0) = 18.5×e⁰ = 18.5×1 = 18.5 million.

b.

we need to find the value of t for which A(t) = 26.6.

26.6 = 18.5e^(0.1708 × t)

26.6/18.5 = e^(0.1708 × t)

ln(26.6/18.5) = 0.1708 × t

t = ln(26.6/18.5)/0.1708 = 2.126115244... years

≈ 2 years

2 years after 2000 is 2002.

it will reach 26.6 million in the year 2002.

The value of x for the given triangle is x = 86°.

What is triangle?

Three edges and three vertices make up a triangle, which is a polygon. It is among the fundamental shapes in geometry. Triangle ABC refers to a triangle with the vertices A, B, and C. In Euclidean geometry, any three points that are not collinear determine a singular triangle and a singular plane at the same time.

From the given triangle we have to find the value of x.

By triangle's property.

(x - 45)° + (x + 3)° = (x + 44)°

              2x - 42 = x + 44

                 2x -x = 44 + 42

                       x = 86°

Hence, the value of x for the given triangle is x = 86°.

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Answer:

a) 53.33 miles per hour

b) 1.7 pages per minute

c)2.25 $ per avocado

Step-by-step explanation:

a) 320/6 = 53.33333

b) 68/40 = 1.7

c) 27 /12 = 2.25

Answer:im assuming you need to know the difference and its nine

Step-by-step explanation: 34-25=9

Answer:

-3/2

Step-by-step explanation:

[tex]-\frac{7}{12}=1 \frac{5}{6}+d \\ \\ -\frac{7}{12}=\frac{11}{12}+d \\ \\ -7=11+12d \\ \\ -18=12d \\ \\ d=-3/2[/tex]

The absolute difference rounded to three decimal places is 2.674.

What is polynomial?

An expression that consists of variables, constants, and exponents and is combined using mathematical operations like addition, subtraction, multiplication, and division is referred to as a polynomial.

Given: f(x) = tan(2x)

Then f(5.4) = tan(2 x 5.4) = tan(10.8) = tan(54/5)

The second degree Taylor polynomial centered at x =  5 is given by,

T2(x) = Σ(n = 0, 2) f^n(5)/5!(x - 5)^n

Now,

f°(x) = f(x) = tan(2x)

f(5) = tan(2 x 5) = tan(10)

f'(x) = d/dx(tan(2x))

f'(x) = 2 sec^2x = 2( 1 + tan^2(x))

f'(5) = 2(1 + tan^2(10))

f"(x) = d/dx[2(1 + tan^2(2x)]

f"(x) = 0 + 2(2tan(2x)(2sec^2(2x))

f"(x) = 8 tan(2x)(1 + tan^2(2x))

f"(5) = 8 tan(10)(1 + tan^2(10)

Then

[tex]T_2(x) = \frac{tan(10)}{0!}(x - 5)^0 + \frac{2 + 2tan^210}{1!}(x - 5)^1 + \frac{8(tan(10)(1+tan^2(10)}{2!}(x - 5)^2 \\T_2(5.4) = tan(10) + 2(1 + tan^2(10)) (5.4 - 9) +4tan(10)(1 + tan^2(10)(5.4 - 5)^2\\T_2(5.4) = \frac{16}{25} tan^310 + \frac{4}{5}tan^2(10) + \frac{41}{25} tan(10) + \frac{4}{5}[/tex]

The absolute difference is,

[tex]|f(5.4) - T_2(5.4)| = 2.673745[/tex]

|f(5.4) - T2(5.4)| ≈ 2.674

Hence, the absolute difference rounded to three decimal places is 2.674.

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you might want to write an essay on, but it's your choice.

Answer:

x = 2

Step-by-step explanation:

Given equation,

→ 4x - 22 = -14

Now the value of x will be,

→ 4x - 22 = -14

→ 4x = -14 + 22

→ 4x = 8

→ x = 8/4

→ [ x = 2 ]

Hence, the value of x is 2.

the Answer is: 34

explanat

Answer:

3(3a+1)

Step-by-step explanation:

2a + 3 + 7a

9a + 3

3(3a + 1)