After my salary was increased by 12%, it was $62,720. What was my salary before the increase?
I'll mark brainliest!

The formula for allocation deviation is as follows:σA = (w1σ1^2 + w2σ2^2 + … + wσn^2)^(1/2)σB = (w1σ1^2 + w2σ2^2 + … + wσn^2)^(1/2)

Here,

σ1 = 15%

σ2 = 10%

w1 = 50%,

w2 = 50%

Substituting the values in the above formula:

σA = (0.5 × 0.15^2 + 0.5 × 0.10^2)^(1/2)

= (0.0225 + 0.0100)^(1/2)

= 0.0158 = 1.58%σB

= (0.5 × 0.15^2 + 0.5 × 0.10^2)^(1/2)

= (0.0225 + 0.0100)^(1/2)

= 0.0158

= 1.58%

Hence, the correct option is

D. σ(A) = 14.14%;

σ(B) = 16.33%.

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The total number of students in the sample who visited campus bars on the weekend before the final exam week is an example of a discrete random variable.

Discrete Random Variable: A discrete random variable is a statistical variable that takes a finite or countable number of values. For instance, the number of cars on a street, the number of people in a movie theatre, and the number of students in a class are all examples of discrete random variables. For example, the total number of students in the sample who visited campus bars on the weekend before the final exam week can take a finite set of values from 0 to 250, making it a discrete random variable.

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Answer:

\(45^{o}\)

Step-by-step explanation:

The intersection of two straight lines forms two sets of opposing angles, with each set of opposing angles having the same value.  Angles A and B will have the same value.  If angle A is \(45^{o}\), then angle B will also be  \(45^{o}\).

The mass of the sample after four hours is 6426.5 grams.

Given,

The biologist has an 8535-gram sample of a radioactive substance.

Relative rate of decay = 13% per hour.

Using exponential decay formula :N(t) = N_0*e^(-rt)

Here, N(t) = mass of the sample after t hours = N_0*e^(-rt)

N_0 = initial mass of the sample = 8535 grams

r = relative rate of decay = 13% per hour = 0.13

t = time in hours = 4 hours

We need to find mass of the sample after 4 hours i.e. N(t).

We can use the formula, N(t) = N_0*e^(-rt)

Substituting the given values,

N(t) = 8535*e^(-0.13*4)

≈ 6426.5 grams (rounding off to nearest tenth)

Therefore, the mass of the sample after four hours is 6426.5 grams.

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The algebraic expression that represents the cost of the purchase made by Cameron can be written as 0.99x + 1.29y

Writing an Algebraic Expression for the Cost of a Purchase:

To write an algebraic expression for the cost of a purchase made by Cameron, we first need to identify the variables involved and the cost per unit of each item. In this case, Cameron purchased x pounds of apples for $0.99 per pound and y pounds of oranges for $1.29 per pound. Therefore, we can represent the cost of the apples as 0.99x and the cost of the oranges as 1.29y.

To find the total cost of the purchase, we need to add the cost of the apples and the cost of the oranges. Therefore, the algebraic expression that represents the cost of the purchase made by Cameron can be written as:

0.99x + 1.29y

This expression represents the sum of the cost of x pounds of apples at $0.99 per pound and y pounds of oranges at $1.29 per pound. By substituting the values of x and y into the expression, we can calculate the actual cost of the purchase.

For example, if Cameron purchased 2 pounds of apples and 3 pounds of oranges, the expression would become:

0.99(2) + 1.29(3) = 1.98 + 3.87 = $5.85

Therefore, the total cost of the purchase made by Cameron would be $5.85.

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Answer:

40

Step-by-step explanation:

4*5=20

5*8=40

I hope you got it....

Answer:

Step-by-step explanation:  Hello!

I don't remember all of the postulates to these, but I hope this will help you! Vertical angles are congruent, so both angles SRT and PRQ are congruent.  This also means that line segments PQ and ST are congruent.  You also know that angles Q and S are congruent which is given.  By the ASA Theorem, when two angles and a side are congruent, then the triangles are congruent.

Answer:

x:b116.67

Step-by-step explanation:

120/100

140×100/120

Answer:

Step-by-step explanation:

The best way to measure an angle is to use a protractor. To do this, you'll start by lining up one ray along the 0-degree line on the protractor. Then, line up the vertex with the midpoint of the protractor. Follow the second ray to determine the angle's measurement to the nearest degree.

Pythagoras was an ancient Greek mathematician who founded the Pythagorean school of thought. The Pythagorean theorem is a fundamental concept in mathematics that is attributed to Pythagoras and his followers.

It states that in a right-angled triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the other two sides. While this theorem is considered a cornerstone of mathematics today, it is important to understand that Pythagoras did not have access to the advanced mathematical tools and methods that we have today.

He had to rely on geometric constructions and reasoning to prove his theorem. Furthermore, Pythagoras believed that all numbers could be expressed as ratios of whole numbers, which is not always true in reality. Despite these limitations, the Pythagorean theorem has stood the test of time and continues to be a crucial tool in mathematics and other fields.

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The boat should travel 12 kilometers in 3 hours. The solution has been obtained by using unitary method.

What is a unitary method?

In the unitary approach, the value of a single unit is estimated before the value of the required number of units is established. Simply expressed, the unitary technique is used to calculate the value of a single unit given a multiple.

We are given that the boat covers total distance of 20 kilometers during the 5-hour tour.

This means that

Distance = 20 kilometers

Time taken = 5 hours

So, using unitary method,

Distance covered in 1 hour = 20/5 = 4km

Distance covered in 3 hours = 4*3 = 12 kilometers

Hence, the boat should travel 12 kilometers in 3 hours.

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Answer:

Assuming that the person does not account for probability changes when counters are not replaced, the answer is 20 counters.

Step-by-step explanation:

Please refer to the picture above.

Disclaimer: Probability is not used to deduce the question. The knowledge of fraction is used instead to avoid excess complexity.

Assuming the number of dabbed counters follow the ratio of 1/4 as deduced from the number of dabbed counters in 200 counters, you would expect the number of dabbed counters in 80 counters to follow the same ratio of 1/4. Hence the answer is 20.

Answer:

option d

Step-by-step explanation:

root of 29 = 5.39 (rounded)

in the line, point B is closest to that value.

The value of x is a counter example to the student's conjecture (x = 2).

What is an expression?

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that x is a non-negative number, a student conjectured that x + 4 < x².

Since x is a non-negative number, A and B are eliminated.

This leaves C and D at the value of x = 2,

2 + 4 < 2²

6 < 4 is false.

Therefore, the value of x is a counterexample to the student's conjecture (x = 2).

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Answer:

I’F’ = 21

Step-by-step explanation:

To find the length of I’F’

We perform the dilation on IF using the given dilation factor

All we have to do here is to multiply the length of IF by the dilation factor

We have this as ;

28 * 3/4 = 21

Answer:

B) 23

Step-by-step explanation:

We need to find the pattern of the table. As seen on the other parts of the table, the pattern is 2x + 3. Here, x is the input. So, we substitute 10 for x, giving us:

2 * 10 + 3 = 20 + 3 = 23

So, the missing value in the table is B) 23.

Hope this helped!

Answer:

B. 23

Step-by-step explanation:

Answer:

1/4

Step-by-step explanation:

Take unknown number as x

-5/4+x=-1

x=-1+5/4

x=1/4

Each box will contain 1 chocolate donut, 1 strawberry donut, and 1 caramel donut, there will be a Total of 4 boxes, and each box will contain 1 chocolate donut, 1 strawberry donut, and 1 caramel donut.

The number of boxes and the distribution of donuts in each box, we need to find the greatest common divisor (GCD) of the total number of chocolate, strawberry, and caramel donuts available. The GCD will represent the maximum number of donuts that can be included in each box.

First, let's find the GCD of 36, 27, and 18. By calculating the GCD, we can determine the maximum number of donuts that can be included in each box.

GCD(36, 27, 18) = 9

Therefore, the maximum number of donuts that can be included in each box is 9.

Next, we need to determine the number of boxes. To do this, we divide the total number of each donut type by the maximum number of donuts per box.

Number of boxes for chocolate donuts = 36 / 9 = 4 boxes

Number of boxes for strawberry donuts = 27 / 9 = 3 boxes

Number of boxes for caramel donuts = 18 / 9 = 2 boxes

Since each box contains the same total number of donuts, we can conclude that there will be 4 boxes with chocolate donuts, 3 boxes with strawberry donuts, and 2 boxes with caramel donuts.

To find the distribution of donuts in each box, we divide the maximum number of donuts per box by the GCD:

Distribution in each box: 9 = 1 × 9

Therefore, each box will contain 1 chocolate donut, 1 strawberry donut, and 1 caramel donut, there will be a total of 4 boxes, and each box will contain 1 chocolate donut, 1 strawberry donut, and 1 caramel donut.

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Answer:

23 and 31

Step-by-step explanation:

substitute x = 2 into f(x) and x = 4 into g(x)

f(2) = 2(2) - 3 = 4 - 3 = 1

g(4) = 5(4) + 2 = 20 + 2 = 22

Then

f(2) + g(4) = 1 + 22 = 23

----------------------------------------------

substitute x = 8 into f(x) and x = 2 into g(x)

f(8) = 5(8) - 3 = 40 - 3 = 37

g(2) = 3(2) = 6

Then

f(8) - g(2) = 37 - 6 = 31

Answer:

integers and rational

Step-by-step explanation:

it's because integers are only negative and rational are only fractions or decimals

Hope this helps!

The relationship between the expressions is that these are inverses.

Here we want to find the relationship between:

logₐ(n) = logₙ(a)

(I changed the variable b for n)

Remember the definition of a logarithm with a base, we can rewrite it as:

logₐ(n) = ln(n)/ln(a)

If we write both of the expressions in that form, we will get:

logₐ(n) = logₙ(a)

ln(n)/ln(a) = ln(a)/ln(n)

So, as you can see, the two expressions are inverses, that is the relation.

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Answer:

wouldn't it be 3:20 P.M.?

Answer:

3:20

Step-by-step explanation:

4:40- 1 hour 3:40- 20 equals 3:20

Answer: x=4 y=14

Step-by-step explanation:

15x-5-125=180(adjacent angles)

15x=180+5-125

15x=60

x=4

7y+27=125( exterior angles of different sides)

7y=125-27

7y=98

y=14

The values of the probability from spinning the spinner and rolling the cube are;

Probability that the spinner lands on an even number = 2/5

Probability of rolling a 5 on the number cube = 1/6

the joint probability of the spinner landing on an even number and rolling a 5 = 1/15

Probability is a measure of the likelihood that an event will occur. The probability of an event = Number of times the event occurs ÷ Sum of the frequencies of all possible events.

Probability has many uses in both analysis and games. Probability is used in sectors of real life and business where making predictions is important. The utilization of probability principles is necessary for forecasting market prices and cricket team performance. Additionally, the branch of modern technology known as artificial intelligence heavily relies on probability.

Numbers on the spinner are; 1, 2, 3, 4, and 5

Numbers in the number cube = 1, 2, 3, 4, 5, and 6

The probability of an event = The number of required outcomes ÷ The number of possible outcomes

The possible even numbers on the spinner = 2 and 4

The number of even numbers in the spinner = 2

The number of possible numbers on the spinner = 5

The ratio of the number of even numbers to the number of possible numbers, which is the probability of spinning an even number, therefore is; P(E) = 2/5

The number of 5s on the cube = 1

The number of possible numbers on the cube = 6

The probability of rolling a 5 on the number cube is therefore, p(5) = 1/6

The probability of landing on an even number and rolling a 5, P(E) × P(5) is therefore;

∴ P(E) × P(5) = (2/5) × (1/6) = 2/30 = 1/15

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First, we want to note two things:

We can describe this with an inequality:  x ≥ -10
Be sure you use ≥ and not >, since -10 is included.

We can describe this with interval notation: [ -10, infty )
Be sure you use [ and not ( on -10, since -10 is included.

You can also use set-builder notation: { x | x ≥ -10 }

The Board of Trustees can choose a president and a provost in 1000 different ways because there are 1000 professors on the college's faculty. The concept used in this is permutations and combinations.

What are combinations?

A combination in mathematics is a choice made from a group of separate elements where the order of the selection is irrelevant (unlike permutations). Three fruits, such as an apple, an orange, and a pear, for instance, can be combined into three different pairs: an apple and a pear, an apple and an orange, or a pear and an orange. A k-combination of a set S is officially defined as a subset of S's k unique elements. So, if and only if each combination contains the same elements, two combinations are said to be identical.

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Correct question:

Suppose that a college has 1000 professors.

a) In how many ways can the Board of Trustees pick a president? The president should be one of the 1000 professors.

The mode of the given data values is N/A (not applicable).Hence, the mean, median, and mode of the given data values are:Mean = 54.36Median = 55.5Mode = N/A (not applicable)

Given data values are 55, 56, 70, 61, 53, 57, 50, 73, 52, 69, and 2. We need to calculate the mean, median, and mode of this sample.So, let's first arrange the data values in ascending order:2, 50, 52, 53, 55, 56, 57, 61, 69, 70, 73

Mean:The mean is the sum of all the data values divided by the total number of data values. So, we can use the following formula to calculate the mean:

Mean = (sum of all the data values) / (total number of data values)Sum of all the data values = 55 + 56 + 70 + 61 + 53 + 57 + 50 + 73 + 52 + 69 + 2 = 598Total number of data values = 11

Therefore,Mean = (sum of all the data values) / (total number of data values) = 598 / 11 = 54.36 (rounded to two decimal places)Therefore, the mean of the given data values is 54.36.

Median:The median is the middle value of a sorted data set. Since the data set has 11 data values, the median is the average of the 6th and 7th values (counting from smallest to largest).

Therefore, the median is :Median = (55 + 56) / 2 = 55.5Therefore, the median of the given data values is 55.5.

Mode:The mode is the data value that appears most frequently in the data set. In this case, there is no data value that appears more than once. So, there is no mode.

Therefore, the mode of the given data values is N/A (not applicable).Hence, the mean, median, and mode of the given data values are:Mean = 54.36Median = 55.5Mode = N/A (not applicable)

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These economic analyses enable the car manufacturer to optimize its business operations, adapt to market conditions, and strategically plan its growth and expansion in the United States.

The company aims to assess the overall economic health of the United States, including factors such as GDP growth, consumer spending, inflation rates, and employment levels. By conducting these analyses, the car manufacturer seeks to make informed decisions regarding its pricing strategies, production levels, and market positioning.

The economic analyses provide the car manufacturer with valuable insights into the current and projected economic conditions in the United States. For instance, by monitoring GDP growth, the company can gauge the overall market demand for cars and adjust its production accordingly. Understanding consumer spending patterns helps the manufacturer determine the affordability and demand for its vehicles in different segments. Additionally, analyzing inflation rates allows the company to anticipate cost fluctuations and make pricing decisions that align with market trends. Employment levels provide insights into the purchasing power of consumers and their propensity to buy new cars.

Overall, these economic analyses enable the car manufacturer to optimize its business operations, adapt to market conditions, and strategically plan its growth and expansion in the United States. By staying informed about economic indicators and trends, the company can position itself competitively and make informed decisions that align with the prevailing economic climate.

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