Juan is playing a game in which he can win $100 with probability 0.2, $300 with probability 0.3, and $500 with probability 0.5. What is the expected value of Juan's winnings?

Answer: (1/3)x - 8

Step-by-step explanation:

one - third means 1/3

one - third of a number means (1/3)x

       ( x being the number )

Eight less means -8

Eight less than 1/3 of an number is (1/3)x - 8

Step-by-step explanation:

"down by one" means that the y values (the function result values) are all decreased by 1.

so, k = -1

Answer:

9/7 or 1.285714

Step-by-step explanation:

Answer:9/7

Step-by-step explanation:

Answer:

(−∞,1/3)∪(1/3,∞),{yly≠1/3}

Step-by-step explanation:

Means if a number is bigger than other number.

Answer:

13

Step-by-step explanation:

56/7 = 8

13 - 5 = 8

15/7 = 13 - 5

The missing number in the expression is 13.

We have,

To find the missing number in the equation 56 / 7 =? - 5, solve for the unknown value.

Unknown value = x

Starting with the equation 56 / 7 = x - 5, simplify the left side:

56 / 7 = x - 5

8 = x - 5

x = 8 + 5

x = 13

Thus,

The missing number in the expression is 13.

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The mean is 38.5. It tell us that the average distance a heavy ball was thrown is 38.5 feet.

A stem-and-leaf plot is table that displays a data set in ascending order.  used to display a dataset. A stem-and-leaf plot divides a number into a stem and a leaf. In this stem-and-leaf plot, the stem is the tens digit and the leaf is the units digit. For example, in the number 32, 3 is the stem 2 is the leaf.

The mean is a measure of the center of a dataset that is used to determine the average of a set of numbers

Mean = sum of numbers / total numbers in the data set

(20 + 21 + 24 + 31 + 32 + 36 + 41 + 43 + 47 + 51 + 51 + 65) / 12

462 / 12 = 38.5

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The number line with the numbers -3, 1 and 3 is shown by the image at the end of the answer.

The correct statements regarding the number line are given as follows:

Integer numbers are numbers that do not have decimal parts, they are either positive or negative, but exact.

These numbers are plotted marking a symbol such as a X or a circle on the number line.

The number line is increasing, so the negative numbers appear before the positive numbers.

This means that if a number a is to the left another number b, the number a is less than b, hence:

As the order in which the numbers appear is given as follows:

-3, 1 and 3.

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The given graph of the function is increasing in the interval (-∞,-6),(-4,-1)(3,6), and (8,∞).

A function is defined as the expression that set up the relationship between the dependent variable and the independent variable. A graph is the representation of the data on the vertical and horizontal coordinates so we can see the trend of the data.

Given that the graph of the function has increased and decreasing orders on the coordinate plane.

The interval in which the given graph of the function is increasing is,

(-∞,-6)

(-4,-1)

(3,6)

(8,∞)

Therefore, the given graph of the function is increasing in the interval (-∞,-6),(-4,-1)(3,6), and (8,∞).

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The product doubles when one of the factors in a multiplication problem is doubled

A product in mathematics is the result of multiplication, or an expression that identifies the objects to be multiplied, known as factors. For instance, 30 is the sum of 6 and 5.

In mathematics, multiplying means adding equal groups. The number of things in the group grows as we multiply. A multiplication problem includes the two factors and the product.

For example, 2 × 3 = 6. When 2 is doubled, it becomes 4 and the product will be:

= 4 × 3 = 12

Therefore, the product doubles too.

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The amount in the account is $3499. 2

The formula for determining compound interest is given as;

A = P ( 1 + r/ n) ^nt

Given that;

Substitute the values into the formula, we have;

A = $3000 ( 1 + 0. 04 / 0. 5) ^(0.5× 4)

Find the exponential value

A = $3000 ( 1 + 0. 04 / 0. 5) ^2

A =  $3000( 1+ 0. 08)^2

Expand the bracket, we get;

A = $3000 (1. 08)^2

A = $3000(1. 17)

multiply through

A = $3499. 2

Hence, the value is $3499. 2

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Using the points (5, 1273) and (10, 2546), equation for the line is 5y =  1273x.

There are many different ways to define an equation. The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign. Mathematical algebraic equations typically have one or more variables.

Given,

Coordinates (5, 1273) and (10,2546)

For slope, m

m = y₂ - y₁/ x₂ - x₁

m = 2546 - 1273/10 -5

m = 1273/5

Equation in y = mx form,

y = 1273/5 x

Cross multiplying,

5y =  1273x

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If a standardized exam's scores are normally distributed. The z-scores that correspond to each value are 1.22, -0.75, 2.18,- 0.31.

mu = population mean = 1487

sigma = population standard deviation = 314

x =1870

z = (x - mu)/σ

z = (1870-1487)/314

z = 1.22 (approximately)

x =1250

z = (x - mu)/σ

z = (1250-1487)/314

z = -0.75

x =2170

z = (x - mu)/σ

z = (2170-1487)/314

z = 2.18 (approximately)

x =1390

z = (x - mu)/σ

z = (1390-1487)/314

z = -0.31 (approximately)

Therefore the z-scores that correspond to each value are 1.22, -0.75, 2.18,- 0.31.

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When we differentiate the given function with respect to x we get

(30x⁶ + 20x⁵ - 30x⁴ - 24x³)/ (5x²-3)²

what is Differentiation?

Differentiate is used for calculating rates of change.

How to Differentiate function?

Some of the formulas are; Power Rule: (d/dx) (xn ) = nxn⁻¹. Derivative of a constant, a: (d/dx) (a) = 0.

Here, we have

y = 2x⁵ + 2x⁴ / 5x² -3

when we differentiate a given function with respect to x, we get

dy/dx = {(5x² -3)(10x⁴ + 8x³)} - {(2x⁵ + 2x⁴)(10x -3)}/(5x -3)²

dy/dx = (30x⁶ + 20x⁵ - 30x⁴ - 24x³)/ (5x²-3)²

Hence, after differentiating the given function with respect to x, we get

(30x⁶ + 20x⁵ - 30x⁴ - 24x³)/ (5x²-3)²

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The linear equation in the slope-intercept is:

y = (-1/5)*x  - 26/5

And it can be written as:

y = (-1/5)*(x + 1) - 5

We can write the equation for line L as:

y = a*x +b

Where a is the slope and b is the y-intercept.

Two lines are perpendicular if the product between the slopes is equal to -1.

So if we want our line to be perpendicular to y= 5x, then we must have:

a*5 = -1

a = -1/5

So our line is something like:

y = (-1/5)*x + b

And the line passes through (-1, -5), replacing these values:

-5 = (-1/5)*-1 + b

-5 = 1/5 + b

-5 - 1/5 = b

-26/5 = b

The linear equation is:

y = (-1/5)*x  - 26/5

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Answer:156

Step-by-step explanation:

Answer:

Step-by-step explanation:

A=60

B=75

C=45

D=60

E=75

F=45

G=90

Answer:

0=0

Step-by-step explanation:

Answer: Infinite Solutions

Step-by-step explanation:

Hello! Let's solve this equation.

[tex]\sf{6x-5=6x-5}[/tex]

↓

[tex]\sf{6x=6x-5+5}[/tex]

↓

[tex]\sf{6x=6x}[/tex]

[tex]\sf{6x-6x}[/tex]

↓

[tex]\sf{0}[/tex]

[tex]\textbf{So as you see, all the terms \textit{cancel out.}}\\\textbf{The \textsf{given equation} has \textit{\underline{infinite solutions.}}}\\\textbf{The equation is true for any x-value.}[/tex]

[tex]_ < \!\!\!\rule{300}{1}\!\!\!_ >[/tex]

The number of square cm of cheese layers that Anna needs to put on the pizza is  30.25π square cm.

What is the area of a circle?

In geometry, the area of a circle is the space occupied by the circle.

To find the area of a circle having radius "r", we can use the formula.

               Area of a circle = π×r².

In the given question, the diameter of the pizza is 11 cm.

so the radius will be = 11/2 = 5.5 cm.

                Area of the pizza = π×r²

                                              = π×(5.5)²

                                              = 30.25π square cm.

Hence, the number of square cm of cheese layers that need to be put on the pizza is  30.25π square cm.

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The percentage increase in Hayley's fuel bills from 2021 to 2022 is equal to 17.105%.

What is a Percentage Increase?

The phrase "percentage increase" (or "percentage change" in general) refers to the difference between the final and starting values of a quantity, expressed as a percentage of that number's original value.

Steps to Calculate Percentage Increase?

Here, in the question, it is given that,

The original amount (X) or the fuel bill in 2021 is £76.

The new amount (Y) or the fuel bill in 2022 is £89.

So, the Increase (I) in the fuel bills from 2021 and 2022 is calculated as,

[tex]I=Y-X\\\implies I=89-76\\\implies I=13[/tex]

Now, we can calculate the percentage increase in fuel bills from 2021 to 2022 as,

[tex]\%I=\frac{I}{X} \times 100\\\implies \%I=\frac{13}{76} \times 100\\\implies \%I=17.105\%[/tex]

Therefore, the percentage increase in Hayley's fuel bills from 2021 to 2022 is 17.105%.

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The transformations of g(x) that would result in odd functions are (a)-g(x)   , (b)g(2x)  and (d)g(–x) ,

In the question ,

it is given that,

the function is g(x) = 3x³ + x

We know that the function f(x) is called an odd function if f(-x) = -f(x) .

Option(a)

the transformation is given as -g(x)

-g(x)  = -(3x³ + x) = -3x³ - x

g(-x) = 3(-x)³ + (-x) = -3x³ - x

so , this is odd function .

Option (b)

the transformation is given as g(2x)

g(-2x) = 3(-2x)³ + (-2x) = -24x³ - 2x

-g(2x) = -{3(2x)³ + (2x)} = -( 24x³ + 2x ) = -24x³ - 2x

so , this is  odd function .

Option (c)

the transformation is given as g(x)-3

(g(-x) - 3) =  3(-x)³ + (-x) - 3 = -3x³-x-3

-(g(x) - 3) = -{(3x³ + x) -3} = -3x³ - x +3

So, so , this is not an odd function

Option (d)

the transformation is given as g(-x)

g(-(-x)) = g(x) = 3x³+x

-g(-x) = -(3(-x)³ + (-x)) = -(-3x³ - x) = 3x³+x

so , this is odd function .

Therefore, the odd transformations are -g(x)   , g(2x)  and g(–x) ,

The given question is incomplete , the complete question is

The function g(x)=3x³+x is an odd function. Which transformation of g(x) would result in odd functions? Check all that apply

(a) -g(x)

(b) g(2x)

(c) g(x) − 3

(d) g(–x)

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Answer:

B (x = 3 + √5)

Explanation:

x² + 9 = 5

Take square root of both sides

x + 3 = ± √5

Add 3 to both sides

x = 3 + √5 or x = 3 - √5

Sandy earn 306.9 dollars in commission and 1739.1 dollars in hourly wages.

Sandy works at a clothing store. She makes $9 per hour plus earns 15% commission on her sales.

She worked 71 hours over the last two weeks and had a total of $2,046 in sales before taxes.

The amount she will earn in her hourly wages and commission is as follows:

amount earn in commission = 15% of 2046

amount earn in commission = 15 / 100 × 2046

amount earn in commission = 30690 / 100

amount earn in commission = 306.9 dollars

Therefore,

amount earn in hourly wages = 2046 - 306.9

amount earn in hourly wages = 1739.1 dollars.

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The sum of the fraction 74/10 + 42/5 is 15 4/5.

A fraction is simply a piece of a whole. The number is represented mathematically as a quotient where the numerator and denominator are split. In a simple fraction, the numerator as well as the denominator are both integers.

In this case, the fraction will be illustrated as:

= 74/10 + 42/5

Change to mixed numbers

= 7 4/10 + 8 2/5

= 7 4/10 + 8 4/10

= 15 8/10

= 15 4/5

The value is 15 4/5.

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Answer:

81 people

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Answer:

Step-by-step explanation:

$2.40             12.45 mi
___        *        ___          =   ?  ;
1  mi.               1              

The units of miles— "mi" —cancel out to "1" ;

   since:  " mi/ mi = 1 "

  and we have:
    $2.40  * 12.45  =  ?  ;

                             =  $29. 88 ; {using a calculator};

       ⇒ which corresponds to:  Answer choice:  [D]:  $29.88 .
_____
Hope this is helpful!

  Best wishes!
_____

The missing terms in the two column proof are;

Reason 1; Perpendicular bisector

Reason 2; Definition of perpendicular bisector

Statement 3; CO ≅ BO

Reason 3; Segment division

Reason 4; Reflexive Property of Congruence

Reason 5; Definition of Isosceles Triangle

Reason 6; AAS Congruency Postulate

From the given image, we want to use the two column proof to prove that ΔAOB ≅ ΔAOC

Now, we have the two column proof as follows;

Statement 1; AO ⊥ BC

Reason 1; Perpendicular bisector

Statement 2; ∠AOB and ∠AOC are right angles

Reason 2; Definition of perpendicular bisector

Statement 3; CO ≅ BO

Reason 3; Segment division

Statement 4; AO ≅ AO

Reason 4; Reflexive Property of Congruence

Statement 5; AB ≅ AC

Reason 5; Definition of Isosceles Triangle

Statement 6; ΔAOB ≅ ΔAOC

Reason 6; AAS Congruency Postulate

The final proof is AAS Congruency postulate because it has 2 congruent angles and the non-included congruent side.

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Representing length and width relationship of a rectangle, and the perimeter given by length of wire using inequality gives

The perimeter of a rectangle, P is given by the formula

P = 2(L + W) ≤ 57 units of wire

width, W = 2 units

length, L = 1 + W

= 1 + 2

= 3

The perimeter of the rectangle is given by

P = 2(L + W)

plugging the values of L and W

P = 2 (3 + 1)

P = 2 (4 )

P = 8 units

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