a box of a dozen donuts contains 5 glazed, 3 blueberry, and 4 chocolate donuts. what is the probability that you randomly choose a chocolate donut from the box? state your answer as a reduced fraction.

Answer:

c = 14

Step-by-step explanation:

If 87. 5 percent of a sample of pure 131 I decays in 24 days, then the half-life of 131 i is 8 days.

In this question we have been given 87.5 percent of a sample of pure 131i decays in 24 days

We need to find the the half-life of 131i

We know that the rate constant expression is given as :

k = (2.303/t)*(log (a / a-x))

where, t = 24 days

a = 100

a -x = 100 - 87.5

      = 12.5 g

From the rate constant expression,

k = (2.303 / 24) * (log(100/12.5))

k = 0.0866

Now, the half life is given as :

k = 0.693 / t(1/2)

t1/2 = 0.693 / 0.0866

t1/2 = 8 days.

Therefore, the half-life of 131 i is 8 days.

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The earnings-to-stock-price ratio in simplest terms is 20.

Here given,

Stock price = $55.00

Earnings per share = $2.75

We have to find ratio od earnings,

The formula is,

Ratio is : P/E

By substituting the values,

Ratio = $55.00 / $2.75

         = 20

-3(7f + 3f + 9) - 4f

Distribute.

(−3)(7f) + (−3)(3f) + (−3)(9) + −4f

−21f + −9f + −27 + −4f

Combine like terms.

−21f + −9f + −27 + −4f

(−21f + −9f + −4f) + (−27)

−34f + −27

-34f + -27

The true statements about the circle are

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

x² + y² - 2x - 8 = 0

Generally, To convert this equation to standard form, we need to complete the square.

First, we can rearrange the terms on the left-hand side of the equation so that all the x terms are together and all the y terms are together:

x² - 2x + y² - 8 = 0

Then, we need to add and subtract a value that allows us to rewrite x² - 2x term as a perfect square.

To do this, we take half of the coefficient of the x term (which is -2), square it, and add it to both sides of the equation:

So, we have

x² - 2x + (1²) + y² - 8 = 0 + (1²)

Evaluate

(x - 1)² + y² - 8 = 1

Finally, we can rearrange the terms

So, we have

(x - 1)² + y² = 9

Express 9 as the square of 3

(x - 1)² + y² = 3²

So, the standard form of the equation is (x - 1)² + y² = 3²

The standard equation of a circle is represented as

(x - a)² + (y - b)² = r²

Where

Center = (a, b)

Radius = r

When these equations are compared, we have

Center = (a, b) = (-1, 0)

Radius = r = 3

The point (-1, 0) lies on the x-axis

This means that the center is on the x-axis.

Also, it means that the radius of the circle is 3 units

This radius is the same for a circle that has the form x² + y² = 9

This is so because 9 can be expresses as the square or 3, and r = 3

Hence, the correct statements are (a), (b) and (e)

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Complete Question

Consider a circle whose equation is x2 + y2 – 2x – 8 = 0. Which statements are true?

Select three options.

Presence: a statistical issue, refers to the finding that a systematic relationship exists between the two variables of interest in the population.

The above statement is False.

Presence refers to the finding that there is a systematic relationship between two variables in the population of interest.

Direction means knowing if the relationship is positive or negative.

Strength means knowing how long the relationship will last.

Systematic relationship is also known as Covariance. Covariance is a statistical term that refers to the systematic relationship between two random variables such that changes in the other reflect changes in one.

The relationship between probability and statistics usually falls into one of three categories: deterministic, random, or statistical. Statistical relationships are a hybrid of deterministic and random relationships.

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The total time taken is 24 hours.

What is total time?

Total refers to a whole or full amount, and the verb "to total" means to combine two numbers or to destroy anything. In mathematics, you add integers to get the total; the outcome is the total. The result of adding 8 and 8 is 16. A automobile that has been totalled in an accident is irreparably damaged. Total Time is the result of multiplying the number of minutes in a day by the number of days in a given calendar month.

An inlet pipe takes 8 hours to fill a tank. An outlet pipe takes 12 hours to empty.

[tex]$\Rightarrow$[/tex] Time is taken to fill in 1 hour =1 / 8

[tex]$\Rightarrow$[/tex] Time taken to empty in 1 hour =-1 / 12

[tex]$\Rightarrow$[/tex] If both pipes are opened simultaneously tank be filled in 1 hour =1 / 8-1 / 12 =1 / 24 hours

[tex]$\therefore$[/tex] The total time taken is 24 hours.

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Using the function f(x) = 7+ 4x, -13 is the value of f(-5).

A mathematical phrase, rule, or law that establishes the link between an independent variable and a dependent variable (the dependent variable).

We might create a function with a set of persons as the domain X and a set of numbers as the codomain. For instance, if the codomain Y is the collection of whole integers, then define the function c so that its output, c(x), equals the number of offspring of every given x.

Four main categories may be used to classify different sorts of functions. dependent upon element Function is a one-to-one relationship, a many-to-one relationship, onto function, one-to-one and into function.

Given that,

f(x) = 7 + 4x

now, putting the value of f(-5), we get -

f(-5) = 7 + 4(-5)

or, f(-5) = -13

Using the function f(x) = 7+ 4x, -13 is the value of f(-5).

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this is the explanation above with some examples

Answer:

The 2 numbers are 27 and 30

Step-by-step explanation:

Let call them x and y where x is the larger number and y is the smaller number :

x + y = 57 (obtained from the first line of the question)

x - y = 3 (obtained from the second line of the question)

Now we are going to use the rules of simultaneous equations to find x and y :

I will use elimination method :

Add the 2 equations to eliminate the y :

2x = 60

x = 30

Substitute x into equation 1 :

(30) + y  = 57

Subtract 30 from both sides :

y = 57 - 30

y = 27

So

x = 30 and y = 27

As you can see the difference is also 3

The 2 numbers are 27 and 30

Hope this helped and have a good day

The scale factor, if The original photo is 4 inches by 6 inches, and the new photo is 3 yards by 4.5 yards, is 1.8.

The ratio of one object's scale to that of a new object, which has its representation but is larger, is known as a scale factor (bigger or smaller).

Given:

The original photo is 4 inches by 6 inches, and the new photo is 3 yards by 4.5 yards,

Calculate the scale factor as shown below,

Scale factor = Original dimension / new dimension

Scale factor = (4 × 6) / (3 × 4.5)

Scale factor = 1.8

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The area of the figure in the first, second, and third cases will be 76 square ft, 120 square cm, and 87.5 square in, respectively.

It is a polygon that has four sides. The sum of the internal angle is 360 degrees. In a trapezoid, one pair of opposite sides are parallel.

The area of the trapezoid will be calculated as,

A = 1/2(sum of parallel sides) x height

8. The area of the figure is calculated as,

A = 1/2 (6 + 6 + 7) x 8

A = 76 square ft

9. The area of the figure is calculated as,

A = 1/2 (8 + 4) x 4 + 8 x 12

A = 24 + 96

A = 120 square cm

10. The area of the figure is calculated as,

A = 1/2 (5 + 10) x 5 + 5 x 10

A = 37.5 + 50

A = 87.5 square in

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P(X=12) is the needed probability. P ( X = 12 ) . There is a 0.0042 percent chance that all 12 of them will use their smartphones during courses or meetings.

The possibility or likelihood of an event occurring is expressed numerically as probability. Probabilities are expressed as ratios (0 to 1) and percentages (0 to 100). It is founded on the likelihood that something will occur. The theoretical probability is built on the fundamental principle of probability justification. For instance, there is a 12 percent chance of receiving heads while flipping a coin.

P(X=12) is the needed probability. P ( X = 12 ) . There is a 0.0042 percent chance that all 12 of them will use their smartphones during courses or meetings.

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There are 50 two-point questions and 10 five-point questions on the test.

What is a linear equation in two variables?

A linear equation in two variables is an equation that can be written in the form Ax + By = C, where A, B, and C are constants and x and y are variables. The graph of a linear equation in two variables is a straight line, and the equation represents a linear relationship between the variables.

To solve this problem, you can use the fact that the total number of points on the test is 150 and that some of the questions are worth two points and some are worth five points.

Let x represent the number of two-point questions on the test, and let y represent the number of five-point questions on the test.

We can set up the following system of equations to represent the given information:

2x + 5y = 150

x + y = 60

To solve this system, you can use the substitution method. First, solve the second equation for y:

y = 60 - x

Substitute this expression for y into the first equation:

2x + 5(60 - x) = 150

This simplifies to:

2x + 300 - 5x = 150

Combine like terms:

-3x = -150

Divide both sides by -3:

x = 50

Substitute this value for x into the second equation to find the value of y:

y = 60 - 50 = 10

Hence, there are 50 two-point questions and 10 five-point questions on the test.

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The area of the circle would be 36π.

What is the area of a circle?

If the circle has a radius then the area of the circle can be computed by using the formula

area = π * radius²

The perimeter of the square = 24

4 * side = 24

Side of a square = 24/4 = 6

Side of a square = radius of the circle

Substituting the radius of 6 into this formula gives:

area = π * 6²

Which simplifies to:

area = π * 36

Hence, the area of the circle would be 36π.

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The retail price of the car is  $ 9802.9.

A car dealership pays $8350 for a car.

They mark up the price by 17.4%

8350 * 17.4%  = 1452.9

retail price = 8350 + 1452.9 = $ 9802.9

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Answer: 157.14

Step-by-step explanation: SDHU IK

V = 20,000 * 0.81^2 and V = 20,000 * (1 - 0.19)^2 are the equation(s) that represent the exponential relationship.

The value of the car two years later is represented by the variable V. The initial value of the car is represented by the constant 20,000. The relationship between the value of the car two years later and the initial value of the car is exponential, because the value of the car decreases by a fixed percentage each year.

One equation that represents this relationship is:

V = 20,000 * 0.81^2

This equation says that the value of the car two years later is equal to the initial value of the car multiplied by the decay factor of 0.81 raised to the power of 2. The decay factor represents the percentage by which the value of the car decreases each year.

Another equation that represents this relationship is:

V = 20,000 * (1 - 0.19)^2

This equation says that the value of the car two years later is equal to the initial value of the car multiplied by (1 - 0.19) raised to the power of 2. The term (1 - 0.19) represents the percentage by which the value of the car remains after it has depreciated.

Both of these equations represent the exponential relationship between the value of the car two years later and the initial value of the car.

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The scientific notation of the given number will be equal to 6.48 × 10⁻⁷. Hence, option C is correct.

A way to express numbers that are either too large or too little to be conveniently stated in decimal form is through scientific notation. It is also known as "scientific form" in Britain because researchers, mathematicians, and engineers frequently use it for intricate calculations involving large numbers.

As per the given information in the question,

The given number is,

0.000000648

As we move towards the right of the given point then the power will be in negative form.

So, it can also be written as,

6.48 × 10⁻⁷

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the answer is C:

6.48 × 10−7

Answer:

Step-by-step explanation:7.48521878104

The solution of the system of equation is as follows;

when x = -2 , y = -4

when x = 4, y = 8

System of equation can be solved using different method such as elimination method, substitution method and graphical method.

Let solve the system of equation by substitution method.

Therefore,

y = 2x

y = x² - 8

Using substitution,

2x = x² - 8

x² - 2x - 8 = 0

x² + 2x - 4x - 8 = 0

x(x + 2) - 4(x + 2) = 0

(x - 4)(x + 2) = 0

x = -2 or 4

Hence,

when x = -2

y = 2(-2) = -4

when x = 4

y = 2(4) = 8

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In case A:

The amount to be paid = $41.75

In case B :

The amount to be paid = $41.76

So, the Case A is better option.

Finding the right answer using the round off to nearest hundredth.

How to change any value to it's nearest hundredth ?

Rounding to the nearest hundredth means the rounding of any decimal number to its nearest hundredth value. In decimal, hundredth means 1/100 or 0.01. For example, the rounding of 2.167 to its nearest hundredth is 2.17.

Steps to find nearest hundredth of any value:

Step 1:

Since we need to round the given decimal number to the nearest hundredth, we mark the digit at the hundredths place.

Step 2:

Then, we observe the 'thousandths' place digit, which lies to the right of the hundredths column.

Step 3:

If the digit at the thousandths place is less than 5, we write the hundredths place digit as it is and remove all the digits to its right.

Step 4:

If the digit at the thousandths place is 5 or more than 5, we add 1 to the digit at the hundredths place, that is, we increase the hundredths place by 1 and remove all the digits to its right.

Case A :

The price for each gallon = $3.479

So, the total price for 12 gallon = $41.748

In case A total amount is rounded off

So, the price = $41.75

Case B :

The price for each gallon = $3.479

Rounding off the price for each gallon = $3.48

So, the total amount for 12 gallon = $41.76.

So, the case A is better option.

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A characteristic of quality data which pertains to the expectation for the time between when data are expected and when they are available for use is timeliness of information.

Information's timeliness is a crucial aspect of data quality since incomplete or outdated information can influence people's actions. That consequently costs businesses time, money, and reputational harm.

The term "completeness" describes how thorough the information is. Consider if all the information you require is there when evaluating data completeness; for example, you might just require a customer's first and last name, but their middle initial might be optional.

Reliability in the context of data quality traits refers to the absence of contradiction between one piece of information and another piece of information from a different source or system.

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Answer:

y= -9

Step-by-step explanation:

Subtract 3 from both sides

-2y + 3-3= 21-3

-2y=18

Divide both sides by the same factor

-2y/-2 = 18/-2

y= -9

Answer: y = -9

Step-by-step explanation:

-2y+3=21

-2y=21-3

-2y=18

Divide that by -2:

y=-9

The proportion we get is 0.291 and that matches up with our first choice that we see.

A proportion simply means the amount or quantity of a thing present in another thing taken as whole.

The main purpose of stating stuff in proportions is to compare shares. If 2 people receive shares in a 1:1 proportion, it means they have exactly equal shares. If 2 people invest in something and one partner invests $3 for every $2 the other invested, the major partner would expect the profits to be divided 3:2 in their favor.

This issue informs us that a town's residents were polled by an elected official to see how satisfied they were with the town's services. Both homeowners and renters were included in the survey. The following charts show the percentage of respondents that are unsatisfied with city services. In order to calculate the percentage of surveys with low satisfaction, we only need to consider the third column to the right, which is labeled "low satisfaction," and the number we are interested in is the 1, which corresponds to the row labeled "total," because it represents the total number of survey respondents who have low satisfaction, whether or not they are home owners or renters. This number is 23 points.

But that only represents the whole population of those with low levels of satisfaction. We can find the total number of respondents in the cross section between the total column and the total row, giving us 110 points. We wish to multiply that total for the low level by the entire number of respondents. Therefore, if we want that proportion right away, we need divide 23 by 110 points. When we round off to four decimal places, the result is 0.291, which corresponds to our initial option that we see.

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Answer:

A - 0.2091

Step-by-step explanation:

I took it

The inequality is [tex]115\leq x\leq 495[/tex]

What is inequality?

A connection is termed an inequality if two real numbers or algebraic expressions are connected by the symbols ">", "<", "≥". Inequality is a mathematical statement that uses the inequality symbol to illustrate the relationship between two expressions. An inequality symbol has non-equal expressions on both sides. It indicates that the phrase on the left should be bigger or smaller than the expression on the right, or vice versa. Literal inequalities are relationships between two algebraic expressions that are expressed using the inequality symbols.

Given [tex]60\leq 0.5x+2.5\leq 250[/tex]

splitting the equation:

[tex]60\leq 0.5x +2.5[/tex] and [tex]0.5x +2.5\leq 250[/tex]

[tex]60-2.5\leq 0.5x\\57.5\leq 0.5x\\115\leq x\\x\geq 115[/tex]

also

[tex]0.5x +2.5\leq 250\\0.5x\leq 247.5\\x\leq 495[/tex]

therefore the equation is

[tex]115\leq x\leq 495[/tex]

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Answer:

• Statement of the given problem,

⚫ A man spends 70% of his income and saves Rs. 2550. What is his income?

According to above data,

⚫ the required income of the

given man

= 2550/(1 - 70/10)

☐ = 2550/0.30

= 8,500 (Rs) [Ans]

Answer:4

Step-by-step explanation:i did the quiz