You have 7,160 grams of a radioactive kind of bismuth. How much will be left after 10 days if
its half-life is 5 days?
grams

The probability of the randomly selected bank being a) guilty of fraud is 0.1 and b) guilty of fraud, it is given it is a private bank is 0.15

Here

let A be the event of the Bank being a fraud

Let B be the event of the bank being private

Here we see that 100 banks have been sampled.

a)

Probability = no. of favorable outcomes/total no. of outcomes

Here we see that under the row of Bank Fraud and Yes section there are

6 + 4

= 10 banks.

Hence,

n(A) = 10

n = 100

Therefore,

P(A) = 10/100

= 0.1

b)

The conditional Probability

P(X|Y) = P(X ∩ Y) / P(Y)

Here,

we need to find the bank is a fraud given that it is a private bank. Hence we need to find,

P(A|B)

= P(A ∩ B) / P(B)

Here we see that the private banks that are fraud are given to be 6.

Hence,

n(A ∩ B) = 6

Therefore,

P(A ∩ B) = 6/100

n(B) = 6 + 34 = 40

P(B) = 40/100

Hence P(A|B) = (6/100) / (40/100

= 6/40

= 3/20

= 0.15

Complete Question

(Information attached as an image)

if an audit company picks a bank at random for audit what is the probability that a bank

(a) is guilty of fraud?

(b) is guilty of fraud given it is a private bank?

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Answer:

let the width be x

perimeter= 2(l+b)

78= 2(7 +x)

78-14= 2x

32= x

this must be the ans

The direct variation equation for the line passing through the points A(4,−2) and B(10,−5) as given in the task content is; y = -2x.

It follows from the task content that the direct variation of equation of the two points given be determined.

On this note, since the relation is said to be a direct variation.

It follows that the ratio of inputs to output in both ordered pairs, k is same and can be determined as;

10/-5 = 4/-2 = k = -2.

Therefore, the required direct variation equation is written as;

y = -2x.

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The points (2, 3)  (6, 3), and  (2, 7) sides corresponds to length of 4 : 4 : 5 and do not form Pythagorean triple hence they do not form a right angle

The distance between the points is calculated and Pythagoras theorem is used to determine if the triple  forms a right angle

let the points be

A (2, 3)  B (6, 3), and  C (2, 7)

using the equation

d = √{(x₁ - x₂)² + (y₁ - y₂)²}

AB = √{(2 - 6)² + (3 - 3)²} = 4

BC = √{(6 - 2)² + (3 - 7)²} = 5

CA = √{(2 - 2)² + (3 - 7)²} = 4

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The ordered pair (5, −6) is a solution to the first and second equations because it makes both equations true.

In mathematics, a linear equation is one that may be written in the form where the variables are alphabets, and the coefficients are frequently real integers. An algebraic equation with simply a constant and a first-order (linear) term, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation. The variables in the previous sentence, y and x, are referred to as a "linear equation with two variables" at times.

The given system of equations is

x + y = -1          ......(1)

3x - y = 21       ......(2)

Rewrite equation (1)

y = - x - 1        ......(3)

Put equation (4) in equation (3)

3x -(-x -1) = 21

3x + x + 1 = 21

4x = 20

x = 20/4

x = 5

Put x= 5 in equation (3)

y = - 5 - 1

y = - 6

So, both the options are correct, (5, -6) is the solution of both equations.

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The percentage increase regarding the change in visitor is 80%.

From the information, the museum had 500 visitors and on Tuesday, it had 900 visitors.

It should be noted that the increase in numbers will be:

= 900 - 500

= 400

The percentage increase will be:

= Increase / initial value × 100

= 400/500 × 100

= 0.8 × 100

= 80%

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If m∠RTG = 5.8° and m∠GTU = 113.6°. Then the measure of the angle ∠RTU will be 119.4°.

The inclination is the separation seen between planes or vectors that meet. Degrees are another way to indicate the slope. For a full rotation, the angle is 360 °.

Adjacent angle - In math, two points are nearby in the event that they have a typical side and a typical vertex.

Angles RTG and GTU are adjacent angles. If m∠RTG = 5.8° and m∠GTU = 113.6°.

∠RTU = ∠RTG + ∠GTU

∠RTU = 5.8° + 113.6°

∠RTU = 119.4°

The measure of the angle ∠RTU will be 119.4°.

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The function has a maximum value of 30 at x = 3.

Given Function:

f(x) = -3+18x+3

here a = -3 , b = 18 , c = 3

a is negative so it has maximum value

x = -b/2a

= -18/2*(-3)

= -18/-6

= 18/6

= 3

f(x) = -3* + 18*3 + 3

= -3*9+54+3

= -27+54+3

= 27+3

= 30

Therefore the function has a maximum value of 30 at x = 3.

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The value of the expression 3(3+5g) is 9 + 15g.

Expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both. Addition, subtraction, multiplication, and division are all possible mathematical operations.

In this case, we want to simplify 3(3 + 5g)

It's important to open the parentheses. This will be:

=3(3 + 5g)

= 9 + 15g

Therefore, the value is 9 + 15g.

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Answer:

144 cm²

Step-by-step explanation:

1.) Find the area of all of the faces

10*4=40 (Top Face)

4*8=32 (Bottom Face)

6*8*0.5=24 (One Triangle)

6*8*.5=24 (Other Triangle)

6*4=24 (Back Face)

2.) Add them all together to get the surface area

40+32+24+24+24= 144

***Don't forget the cm². Some teachers are really annoying about this

Answer:

Step-by-step explanation:

And here is how to use it:

Example: simplify √12

12 is 4 times 3:

√12 = √(4 × 3)

Use the rule:

√(4 × 3) = √4 × √3

And the square root of 4 is 2:

√4 × √3 = 2√3

So √12 is simpler as 2√3

Another example:

Example: simplify √8

√8 = √(4×2) = √4 × √2 = 2√2

(Because the square root of 4 is 2)

And another:

Example: simplify √18

√18 = √(9 × 2) = √9 × √2 = 3√2

It often helps to factor the numbers (into prime numbers is best):

Example: simplify √6 × √15

First we can combine the two numbers:

√6 × √15 = √(6 × 15)

Then we factor them:

√(6 × 15) = √(2 × 3 × 3 × 5)

Then we see two 3s, and decide to "pull them out":

√(2 × 3 × 3 × 5) = √(3 × 3) × √(2 × 5) = 3√10

Fractions

There is a similar rule for fractions:

root a / root b  = root (a / b)

Example: simplify √30 / √10

First we can combine the two numbers:

√30 / √10 = √(30 / 10)

Then simplify:

√(30 / 10) = √3

Some Harder Examples

Example: simplify  

√20 × √5

√2

See if you can follow the steps:

√20 × √5

√2

√(2 × 2 × 5) × √5

√2

√2 × √2 × √5 × √5

√2

√2 × √5 × √5

√2 × 5

5√2

Example: simplify 2√12 + 9√3

First simplify 2√12:

2√12 = 2 × 2√3 = 4√3

Now both terms have √3, we can add them:

4√3 + 9√3 = (4+9)√3 = 13√3

Answer:

1) t = -2

2) t = 8

3) t = -2
4) t = 1

5)t = [tex]\frac{1}{3}[/tex]

Step-by-step explanation:

1)-22t+6 = 11t + 72

 -33t = 66

      t = -2

2) 3t + 4t - 20 = t + 28

 6t = 48

   t = 8

3) -8 -10t - 6t = 3t + 30

   -19t = 38

       t = -2

4) 12t - 6t + 24 = 12t + 12 +6

   -6t = -6

       t = 1

5) -12-21t-3t=48t-36

    -24t - 48t = 12 - 36

    -72t = -24

     t = [tex]\frac{1}{3}[/tex]

The factor most likely results in the loss of genetic variation from a small population is called genetic drift.

Small populations tend to lose genetic variation at a faster rate than large populations due to genetic drift (stochastic sampling error). Genetic drift refers to the change in an existing gene variant frequency in the population due to random chance. Genetic drift may result in the disappearance of gene variants completely and thus decreases genetic variation. Furthermore, it could initially cause rare alleles to become much more frequent, and even fixed. The loss of some versions of a gene due to random chance is more likely to happen when populations are small.

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Answer:

2 : 12 and 3 : 24 are the two equivalent ratios

The newly translated function of  f(x) = 7x + 1 is; g(x) = 7(x - 1) + 1

In transformation of functions, there are different operations such as translation, reflection, dilation, rotation.

Now, we are told that the function is given as;

f ( x ) = 7x + 1

We are told that it is translated by 5 units to the right.

It is pertinent to note that when talking about translation, it is as good as saying moving from one point to the other without changing the dimensions or shape.

Now, when we shift a function f(x) = x - 1 by a units to the left, it means the translated function is; f'(x) = (x + 1) - 1

However, when we shift a function f(x) = x - 1 by a units to the right, it means the translated function is; f'(x) = (x - 1) - 1

Now, applying that translation rule to our given function gives;

g(x) = 7(x - 1) + 1

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The percentage that Richard get is 8%

The statement can be interpreted as:

He answered 52 correctly from a total of 65 questions

From the above statement, we have the following parameters

Dividend = 52

Divisor  = 65

The percentage is then calculated as

Percentage = Dividend/Divisor  x 100%

Substitute the known values in the above equation

So, we have

Percentage = 52/65 x 100%

Evaluate the quotient

Percentage = 0.8x 100%

Evaluate the product

Percentage = 8%

Hence, the percentage is 8%

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Using the concepts of probability, we got that book is independent variable in the experiment in which I randomly assign one group of angelenos to read a book about the history of the Seattle supersonics, and the other to read a book about cheese.

The independent variable is the condition that you actually change in an experiment. It is the variable you control. It is known as independent because its value does not depend on the value and is not affected by the state of any other variable in the experiment.

Hence, when  i randomly assign one group of Angelenos to read a book about the history of the Seattle supersonics, and the other to read a book about cheese and  then give them a quiz about basketball history (including recent events such as the Los Angeles Lakers then  the independent variable in this experiment is the book given by me.

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The probability that exactly two will be replaced under warrant is 0.1937.

The possibility of an event occurring is determined by the probability formula. The ratio of positive outcomes to the total number of outcomes serves as the basis for calculating an event's probability. The probabilities are always between 0 and 1. A probability is a number that expresses the possibility or likelihood that a specific event will take place. Probabilities can be stated as proportions with a range of 0 to 1, or as percentages with a range of 0% to 100%.

Given,

W = Warranty

V = Replaced

P(W) = 20/100

P(W) = 0.20

P(U/W) = 0.40

P(W ∩ U)

= P(U/W) × P(W)

= 0.40 × 0.20

0.-08

P( exactly two will be replaced under warranty)

Using binomial distribution:

= P(X = 2)

= 10/2 (0.0.8)² (0.9)⁸

= 0.1937

The probability that exactly two will be replaced under warrant is 0.1937.

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0.01 is the results of the two-sided significance test  in confidence interval,

What is alpha in statistics?

confidence level = 1 - alpha

so alpha = 1 - confidence level = 1 - 0.99 = 0.01

In statistics, alpha is the number that evaluates the test statistic to see if it is significant or not. In other words, alpha is the allowable type 1 error margin. The significance level, or alpha, is the antithesis of the confidence level. Confusion level + significance level = 1.

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The equation which represents a cubic polynomial function with zeroes 2, 3 and 5 is; f(x) = x³ - 10x² + 31x - 30.

It follows that if a polynomial function has zeroes, a, b and c; The factors of such polynomial function are; (x - a), (x - b) and (x - c).

Therefore, since the given polynomial function has zeroes, 2, 3 and 5, the polynomial function is;

f(x) = (x - 2) (x - 3) (x - 5)

Therefore, by simplification; we have;

f(x) = (x² - 5x + 6) (x - 5)

f(x) = x³ - 5x² + 6x - 5x² + 25x - 30.

f(x) = x³ - 10x² + 31x - 30.

Therefore, the required cubic polynomial function is; f(x) = x³ - 10x² + 31x - 30.

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Answer:

25/0 aka infinity

Step-by-step explanation:

Equation used:

(y2-y1)/(x2-x1)

1. Plug in the values to get (27-2)/(9-9)

2. Simplify to get 25/0

3. This results in an infinity

The  residual value is 0.6.

The estimated value of a fixed asset at the conclusion of its useful life or lease term is known as the residual value, also known as salvage value. In lease agreements, one of the lessor's main methods for figuring out how much the lessee must pay in periodic lease payments is the residual value.

Given:

y = 1.416x − 0.76

For (7, 8):

As, residual value = Measured value - Predicted value

or, residual value = (actual y-coordinate of the point) - (value of y from the

                                                                                                       equation)

When x = 10:

So, the value of y from the equation,

[tex]y_1[/tex] = 1.416 x 10 - 0.76

[tex]y_1[/tex]=  14.16 - 0.76

[tex]y_1[/tex]= 13.4

and, actual y-coordinate of the point, [tex]y_2[/tex]= 14

Residual value = 14 - 13.4

Residual value = 14 - 13.4

Residual value = 0.6

Hence, the residual value is 0.6

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Answer:

0.6

Step-by-step explanation:

im taking the test rn

The perimeter of the isosceles triangle will be P(x) = x√2 + 2x.

A polygon with three sides is known as a triangle. The angles of a triangle add up to form 180° and the sum of all sides of a triangle is known as the perimeter. In an isosceles triangle, the two sides are equal and their opposite angle too. In an isosceles triangle, the hypotenuse side of the triangle can be written as h(x) = x√2. The combined length comes out to be  L(x) = 2x. Using this information the perimeter of the triangle comes out to be,

P(x) = h(x) + L(x).

P(x) =  x√2 + 2x

Hence the perimeter of the triangle comes out to be P(x) =  x√2 + 2x

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Analyzers should use the Alpha aesthetic.

Using the Alpha aesthetic, specific points on a scatterplot are more transparent than others to highlight specific data points.

What is a scatterplot?

A scatter plot is a set of points plotted along a horizontal and vertical axis. In statistics (also known as variables), scatter plots are crucial to demonstrating whether a correlation exists between observational quantities or phenomena.

A scatter plot  plots data points on a horizontal and vertical axis to demonstrate one variable's influence on another. Each row in the data table is represented by a marker whose position is determined by the values of the columns on the X and Y axes.

Using a scatter plot, this line indicates the prevailing direction of a phenomenon. In a scatter plot, a trend line can be used to highlight the direction and speed of price changes.

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The a-values of the business are classified as follows:

The a-value of a business depends on the behavior of the earning function for these business, as follows:

From the table given by the image at the end of the answer, for the lawn care business, a concave down parabola represents the situation, as the earnings start increasing but then during the 3rd month they start to decrease. Hence, the a-value of the business is negative.

For the dog walking and for the house-sitting business, the values are always increasing over the time interval of the table, hence the a-value of these two businesses is positive.

The table is given by the image at the end of the answer.

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8 percentage of her total monthly budget does she plan for savings.

The proportion of value in relation to the original value is measured using the percentage concept. In business, percentages are frequently employed to calculate a company's profit or loss percentage. Additionally, it is used in schools and colleges to show the grades that pupils have earned. A percentage formula can be used to assess the pupils' grades. In general, the definition of a percentage is any ratio of a value to the total value multiplied by 100. The percentage is denoted by the sign %.

Given,

Melissa's monthly budget is shown in the table,

Melissa' s saving = $250

Total amount = 3125

Percentage = Value/ Total × 100

Percentage = 250/3125 × 100

Percentage = 0.08 × 100

Percentage = 8%

8 percentage of her total monthly budget does she plan for savings.

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