Example: Add 1/4 + 2/4
Solution: Let us add these fractions using the following steps.
Step 1: Check if the denominators are the same. (Here, the denominators are the same, so we move to the next step)
Step 2: Add the numerators and place the sum over the common denominator. This means (1 + 2)/4 = 3/4
Step 3: Simplify the fraction to its lowest form, if needed. Here, it is not needed. So, the sum of the given fractions is, 1/4 + 2/4 = 3/4
If f (x) = 5x - 4 find f(2).
10
48
2
6
Answer:
6
Step-by-step explanation:
f(2) = 10-4 = 6
Answer:
[tex] \sf \: d) \: 6[/tex]
Step-by-step explanation:
Given function,
→ f(x) = 5x - 4
We have to find,
→ The required value of f(2).
Now value of f(2) will be,
→ f(x) = 5x - 4
→ f(2) = 5(2) - 4
→ f(2) = 10 - 4
→ [ f(2) = 6 ]
Therefore, the answer is 6.
One cubic foot holds 7.48 gallons of water, and 1 gallon of water weighs 8.33 pounds. How much does 4.4 cubic feet of water weigh in pounds? In tons?
Answer:
4.4 cubic feet of water weighs approximately 273.5016 pounds or 0.13676 tons.
Step-by-step explanation:
To find the weight of 4.4 cubic feet of water in pounds, we need to find the number of gallons it contains and then multiply it by the weight of one gallon of water.
1 cubic foot = 7.48 gallons
So, 4.4 cubic feet = 4.4 * 7.48 = 32.912 gallons
And the weight of 32.912 gallons of water in pounds is:
32.912 gallons * 8.33 pounds/gallon = 273.5016 pounds
To convert this weight to tons, we divide the weight in pounds by 2000:
273.5016 pounds / 2000 = 0.13676 tons
So, 4.4 cubic feet of water weighs approximately 273.5016 pounds or 0.13676 tons.
Help with question 6:
If the quotient of two functions f(x) and g(x) is a constant, then their derivatives are proportional to each other.
How are g.f' and f.g' related?A function is an expression that shows the relationship between the independent variable and the dependent variable. A function is usually denoted by letters such as f, g, etc.
If the quotient of two functions f(x) and g(x) is a constant k, meaning f(x)/g(x) = k for all x, then it follows that:
f(x) = k.g(x)
Taking the derivative of both sides with respect to x, we get:
f'(x) = k.g'(x) + g(x).d(k)/dx
Since the constant k is a constant and not a function of x, its derivative with respect to x is zero, so we can simplify the equation to:
f'(x) = k.g'(x)
Thus, we can see that if the quotient of two functions f(x) and g(x) is a constant, then their derivatives are proportional to each other, with the constant of proportionality equal to k.
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What are the answers to these?
The values of the vacant spaces are $3.75, 4 oranges, 10 oranges, $15 and 20 percent of 160 is 32
What are the values?The table can be completed using the following values
If 8 oranges cost $10,
Then 1 orange will cost 10/8 = $1.25
This means that 3 oranges will cost 1.25*3 = $3.75
$5 can buy 8/10*5 = 40/10 = 4 oranges
In the same way, $12.50 will buy 8/10 * 12.50 = 10 Oranges
In the same manner, 12 oranges will cost 1.25*12 = $15
20% of 160 can be calculated as follows
Recall that percentage is a proportion of 100
This implies that 20/100 * 160 = 3200/100 = 32
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Selma wants to take her money out of the bank account with simple interest rate of 5% annually and put it in another account with compound interest rate of 8% compounded quarterly if the bank says closing the current account has a penalty of 5% at least how many years she let the money stay at the new account in order to recover the penalty paid using extra interest of the second?
Selma needs to leave the money in the new account for at least one year, option A. 1 to recover the penalty paid.
How did we get this assertion?Assuming Selma wants to recover the penalty paid using the extra interest earned in the new account, she needs to calculate the amount of time it will take for the new account's interest to make up for the penalty paid.
Let P be the initial amount of money in Selma's current account. The penalty for closing the account is 5% of P, which is 0.05P.
If Selma leaves the money in the current account for one year, she will earn simple interest of 5% of P, which is 0.05P. So at the end of the year, the balance in the current account will be P + 0.05P = 1.05P.
If Selma transfers the money to the new account, it will earn compound interest of 8% per year, compounded quarterly. The quarterly interest rate is 8%/4 = 2%.
After one quarter, the balance in the new account will be:
P*(1 + 2%/4) = P*1.02
After two quarters, the balance will be:
P1.02(1 + 2%/4) = P*1.02^2
After three quarters, the balance will be:
P1.02^2(1 + 2%/4) = P*1.02^3
After four quarters (i.e., one year), the balance will be:
P1.02^3(1 + 2%/4) = P*1.02^4
So at the end of one year, Selma will have 1.05P in the current account and P*1.02^4 in the new account.
To recover the penalty of 0.05P, Selma needs the balance in the new account to be at least 1.05P. That is,
P*1.02^4 >= 1.05P
Simplifying, we get:
1.02^4 >= 1.05
Taking the fourth root of both sides, we get:
1.02 >= 1.05^(1/4)
Using a calculator, we get:
1.02 >= 1.01298
So Selma needs to leave the money in the new account for at least one year to recover the penalty paid.
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A random sample of 40 hotel reviews is drawn from a large population of hotel customers. It's known that 30% of the population left the hotel 1 star, 20% left 2 stars, 20% left 3 stars, and 30% left 4 stars. Give the standard deviation of the hotel's star rating.The choices are:0.18910.18930.19040.1934
The closest answer choice is 0.76, which corresponds to 0.1934. So the answer is 0.1934.
We can calculate the variance of the hotel's star rating by using the formula:
variance = sum[(xi - mean)^2 * pi]
where xi is the rating (1, 2, 3, or 4), mean is the expected value of the rating, and pi is the proportion of the population that left that rating. Since we know the proportions of the population that left each rating, we can calculate the expected value of the rating as:
mean = 1(0.3) + 2(0.2) + 3(0.2) + 4(0.3) = 2.9
Then, we can calculate the variance as:
variance = (1 - 2.9)^2 * 0.3 + (2 - 2.9)^2 * 0.2 + (3 - 2.9)^2 * 0.2 + (4 - 2.9)^2 * 0.3
variance ≈ 0.57
Finally, the standard deviation is the square root of the variance:
standard deviation = sqrt(0.57) ≈ 0.756
Therefore, the closest answer choice is 0.76, which corresponds to 0.1934.
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Find the perimeter of the triangle whose vertices are the following specified points in the plane.
(-9,-6), (-5, 0) and (10,-7)
The required perimeter of the triangle with vertices (-9,-6), (-5, 0), and (10,-7) is 42.72 units.
What is Distance?The distance between two points (x₁, y₁) and (x₂, y₂) in the plane can be found using the distance formula,
d = √((x₂- x₁² + (y₂ - y₁)²)
Here
Using the above formula, we can find the length of each side of the triangle:
Length of the first side:
d = √((-5 - (-9))² + (0 - (-6))²)
= √(4² + 6²)
= √52 = 7.2
Similarly, the length of the second and third sides:
d =√274 = 16.5
Length of the third side:
d = √362 = 19.02
Finally, the perimeter of the triangle is the sum of the lengths of its sides, P = 7.2 + 16.5 + 19.02
P = 42.72 units
So, the perimeter of the triangle is approximately 42.72 units.
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7x7+24x5(1x+24)=1
SOlve for x
Marsha deposited $7,000 into a savings account 4 years ago. The simple interest rate is 2%. How much money did Marsha eam in interest?
Answer:
$560
Step-by-step explanation:
The formula for simple interest is:
I = Prt, where P is the principal, r is the interest rate, and t is the time (in years).
Plugging in the values, we get:
I = $7,000 * 2% * 4 years = $560
So, Marsha earned $560 in interest.
Need help really please
Answer:
Step-by-step explanation:
No pressure. You just need to look for the number that when added to the other given number, will give the same as the sum on the other side.
For instance, The top-left question:
4+6 = x+8 (let x be the box)
x= 4+6-8
x=2.
OR, since 4 + 6 =10,
you look for a number when added to 8, that gives 10.
That number is 2.
Hope this helps :]
9 Mr Karim had 2740 sacks of rice at first Mr Dani had 3560 sacks of rice at first. Mr Karim gave some sacks of rice to Mr Dani. In the end, Mr Dani had 4 times as many sacks of rice as Mr Karim. How many sacks of rice did Mr Karim have in the end?
Answer:
**DUE TOMORROW, NEED ANSWER ASAP**
NASA has asked you to evaluate a number of proposals for telescopes. These proposals include information about where the telescope would be built and what wavelengths it intends to observe at. Based only on these factors, evaluate whether NASA should consider funding each proposal. Justify your recommendations. (Some telescopes may have more than one "correct" answer depending on how you justify it).
a.) An ultraviolet telescope in space
b.) An optical telescope in a remote location in Michigan's upper peninsula
c.) A radio telescope in the Mojave desert in Arizona
d.) An x-ray telescope in the Andes mountains in Chile
e.) An optical telescope in space
Step-by-step explanation:
9. In a cranberry punch recipe, four cups of cranberry juice and one quart of pineapple juice make up half of the punch. How many cups of punch does the recipe make?
On solving the provided question, we can say that by fraction, 4/3 (orange Juice) + 3/4 apple juice + 2/3 cranberry juice + 3/4 lemon lime juice.
what is fraction?Any number of equal portions, or fractions, can be used to represent a whole. Fractions in standard English indicate how many units of a certain size there are. 8, 3/4. A whole includes fractions. The ratio of the numerator to the denominator is how numbers are expressed in mathematics. Each of these is an integer in simple fractions. In the numerator or denominator of a complex fraction is a fraction. True fractions have numerators that are less than their denominators. A fraction is a sum that constitutes a portion of a total. By breaking the entire up into smaller bits, you can evaluate it. Half of a full number or item, for instance, is represented as 12.
by fraction
4/3 (orange Juice) + 3/4 apple juice + 2/3 cranberry juice + 3/4 lemon lime juice.
16/12+9/12+8/12+9/12=42/12=3 and 1/2 cups.
20/3.5=5.7 or 6
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All numbers less than 17 and greater than or equal to -8. into SET BUILDER NOTATION!!
In set builder notation, the set of all numbers larger than or equal to -8 and less than 17 can be written as:
{x | -8 <= x < 17}
An explanation of set builder notation?
A set of items can be mathematically expressed using the set builder notation. The set builder notation's syntax is {x | }, where x stands for one of the set's elements and the condition outlines the requirements that an element must meet in order to be included in the set.
In this instance, the set consists of all numbers higher than or equal to -8 and less than 17 in total. The set must satisfy the constraint
-8 <= x < 17,where x is a real value. This implies that x must exceed or equal to -8 and must be less than 17 to be a part of the set.
As a result, in set builder notation, the set of all numbers greater than or equal to -8 and less than 17 can be written as follows: {x | -8 <= x < 17}
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Evaluate the limit limx approches 0 x square+ x over x
Step-by-step explanation:
If we use direct substitution, we will get
[tex] \frac{0}{0} [/tex]
Which is intermediate from so we must use.algebraic manipulation
Let's divide everything by x
We would get
[tex] \frac{x + 1}{1} [/tex]
So the limit as x approaches 0 is
[tex]1[/tex]
Proof using a graph:
As x gets close and closer to 0, f(x) approaches 1. Limits does not care about discontinuity, only what the function gets closer to.
Is the graph of y = x² + 2 a straight line? Explain.
O No. The graph does not pass through (0, 0), so it is not a straight line.
O No. The graph passes through the points (0, 2), (1, 3), and (2, 6), which do not all lie on a straight line.
O Yes. The graph passes through (0, 0), so it is a straight line.
O Yes. The graph passes through the points (0, 2), (1, 3), and (2, 6), which all lie on a straight line.
Answer: No, the graph of y = x² + 2 is not a straight line. The graph is a parabola that opens upwards and has its vertex at (0, 2).
A straight line is defined by a linear equation, which is an equation that can be written in the form y = mx + b, where m and b are constants. In this equation, the coefficient of x (m) represents the slope of the line, and the constant term (b) represents the y-intercept. A straight line has a constant slope, which means that the rate of change of y with respect to x is constant.
In the case of y = x² + 2, the coefficient of x (x) is not a constant, but rather a variable, which means that the slope of the line changes as x changes. The graph of y = x² + 2 is a parabolic shape that opens upwards and has its vertex at (0, 2). The slope of the graph is not constant, but rather increases as x increases. This means that the graph does not represent a straight line, but rather a parabolic curve.
Step-by-step explanation:
The lengths of the three sides of a triangle are x + 15 , 2x + 15 and x + 12 (where x cannot equal zero). What is the perimeter of the triangle? use the drop-down menu to complete the answer.
Answer:
4x + 42
Step-by-step explanation:
[tex]\text{Perimeter}=(x+15)+(2x+15)+(x+12)=4x+42[/tex]
f(1) = 25
f(n) = f(n-1)(-1/5)
f(3) = ??
Answer: = 1 (look at the image for the solution)
Step-by-step explanation:
examine whether you can construct a triangle PQR such that QR=3 cm, PQ=6 cm, PR=3 cm. Justify your answer
You cannot construct a triangle PQR such that QR=3 cm, PQ=6 cm, PR=3 cm, as the sum of the lengths of the two smaller sides is not greater than the length of the larger side.
What is the condition for 3 lengths to represent a triangle?In a triangle, the sum of the lengths of the two smaller sides has to be greater than the length of the greater side.
The lengths for this problem are given as follows:
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There are 12 consecutive parking slots available in a hotel parking lot in how many ways can four distinct cars be packed so that at least one parking slot remains vacant between into cars
Answer:
4 different spots
Step-by-step explanation:
12 - 4 spaces in between = 8 spaces
8 spaces / 4 cars = 4 spots
4 spots and 4 cars = 4 different spots for each car
16
5. Sarah makes a sculpture of a sunflower that is 33 inches tall. She also makes a sculpture of a tulip that is as tall as the sunflower. How tall is the sculpture of the tulip?
The height of the tulip sculpture is 66 inches, which is twice the height of the sunflower sculpture.
How tall is the sculpture of the tulip?From the question, we have the following parameters that can be used in our computation:
Sunflower = 33 inches
Tulip = Twice of sunflower
Using the above as a guide, we have the following:
Tulip = 2 * Sunflower
substitute the known values in the above equation, so, we have the following representation
Tulip = 2 * 33
Evaluate
Tulip = 66
Therefore, the height of the tulip sculpture is 66 inches.
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Graph the following conditions. Click on the graphic to choose the correct answer. [(x, y): x + y = 5) 4 -3 -2 -1 YA 6 5 4 3 2 + T -2 -3 A 5 19 - K 2 3 4 5 6 X
A graph of the equation under this condition {(x, y): x + y = 5)} is shown in the image attached below.
What is an ordered pair?In Mathematics, an ordered pair simply refers to a pair of two (2) elements or data points that are commonly written in a fixed order within parentheses as (x, y), which represents the x-coordinate (abscissa) and the y-coordinate (ordinate) on the coordinate plane of any graph.
Next, we would determine the ordered pairs that satisfies the given linear function in standard form.
When the value of x = 1, the output value of this linear function is given by;
y = 5 - x
y = 5 - 1
y = 4 ⇒ (1, 4)
When the value of x = 0, the output value of this linear function is given by;
y = 5 - x
y = 5 - 0
y = 5 ⇒ (0, 5).
When the value of x = 2, the output value of this linear function is given by;
y = 5 - x
y = 5 - 2
y = 0 ⇒ (2, 3).
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19. The mass of a radioactive element is 35
milligrams. The mass of the element decreases by
12.9% every year.
a. Write a function that represents this situation.
b. Predict the mass of the element in 4 years. Round
your answer to the nearest tenth.
c. Will the mass of the radioactive element ever be 0
milligrams? Explain.
a) The function that represents this situation is,
⇒ y = 35 (1 - 12.9%)ⁿ
Where, 'n' is number of years and 'y' is mass of element.
b) For 4 years, the mass of the element is, 19.95 milligrams
c) No, the mass of the radioactive element will never be 0 milligrams.
What is expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Now,
The function that represents this situation is,
⇒ y = 35 (1 - 12.9%)ⁿ
Where, 'n' is number of years and 'y' is mass of element.
Now, For 4 years, the mass of the element is,
⇒ y = 35 (1 - 12.9%)ⁿ
⇒ y = 35 (1 - 12.9%)⁴
⇒ y = 35 (1 - 0.129)⁴
⇒ y = 35 (0.87)⁴
⇒ y = 35 × 0.57
⇒ y = 19.95 milligrams
No, the mass of the radioactive element will never be 0 milligrams.
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Point V is somewhere on the line segment . If UV = 8, then find the length of .
Answer:
it is 3
Step-by-step explanation:
just subtract
1. Items a company has purchased and paid for, but has not used are called
A. advanced
B.purchased
C.prepaid
D. long-term liability
items.
Answer:
the ans is advanced
I hope you get your ans
Could anyone help with #1 and #2 PLEASE.
URGENT! DUE TOMORROW!!
Answer:
Do the graph Then Solve for y
Answer:
1. Yes, a graph of this relationship will be linear.
2. The y-intercept of the graph is (0, 2).
Step-by-step explanation:
1. The equation will be linear because it can be written in the standard form for the equation of a line. The standard form for the equation of a line is Ax + By = C. Eight can be subtracted from both sides of the equation to get 3x - 4y = -8, which fits the format for standard form. A, B, and C are integers, which includes negative numbers, zero, and whole numbers.
2. 3x - 4y + 8 = 0
3(0) - 4y + 8 = 0
-4y + 8 = 0
-4y = -8
y = 2
Hello can you help me solve
Answer:
(p o q) = 54
(q o p) = 68
Step-by-step explanation:
Another way to write is (p o q)(3) is p(q(3)). As you can see, you start with the inner function and 3 is an input in the q(x) function. Then, the output of this becomes the input of p(x) (the outer function), which yields a final output and the answer:
[tex]p(x) = 4x + 2\\q(x)=5x-2\\\\p(q(3))\\\\q(3)=5(3)-2=13\\p(13)=4(13)+2=54[/tex]
You do the same process for (q o p)(3), which can be written as q(p(3)), where you start with p(3) and then plug in this result as the input for q(x):
[tex]p(x)=4x+2\\q(x)=5x-2\\\\q(p(3))\\\\p(3)=4(3)+2=14\\q(14)=5(14)-2=68[/tex]
Hasten plans to choose a book from the section of the store where everything is 25% off he likes expression D -0.25 days to find the sale price of the book it if there is a YZ dollars below correctly write another expression 0.7 5D that will also find the surprise of the book if the original price is de dollars
Another form of representing the cost of the book is (75/100)×D.
What is a numerical expression?A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.
We know, Percentages and decimals are related.
10% in decimal form is equivalent to (10/100) - 0.1 in decimal.
An expression that represents the sale day book price is 0.75D.
Another expression that would represent the cost of the book priced 'D' would be,
= (75/100)×D.
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Location Number Percent
Illinois 669,000 24%
Indiana 419,000 27%
Iowa 141,000 20%
Kentucky 307,000 31%
Michigan 556,000 26%
Missouri 352,000 26%
Ohio 678,000 26%
Wisconsin 266,000 21%
a. Use Excel functions to find the mean, median, mode, maximum, and minimum descriptive statistics for
the number column of the table. Clearly label these values in Excel.
b. Use Excel functions to find the mean, median, mode, maximum, and minimum descriptive statistics for
the percent column of the table.
c. Write a paragraph about your findings regarding the statistics on children whose parents do not have
secure employment. Make sure to answer the following in your paragraph: How does the state of
Indiana compare to the surrounding states? Which state has the best or worst data (explain your
reasoning)? Which value gives a better comparison, the number or the percentage (explain your
reasoning)?
Answer: I can explain the steps for calculating descriptive statistics for the given data.
For the "number" column:
Mean: To find the mean, add up all the values and divide by the number of values.
Median: To find the median, arrange the values in numerical order and find the middle value. If there is an even number of values, take the average of the two middle values.
Mode: To find the mode, find the value that appears most frequently. If there is no value that appears more than once, then there is no mode.
Maximum: To find the maximum, find the largest value in the list.
Minimum: To find the minimum, find the smallest value in the list.
For the "percent" column:
Mean: To find the mean, add up all the values and divide by the number of values.
Median: To find the median, arrange the values in numerical order and find the middle value. If there is an even number of values, take the average of the two middle values.
Mode: To find the mode, find the value that appears most frequently. If there is no value that appears more than once, then there is no mode.
Maximum: To find the maximum, find the largest value in the list.
Minimum: To find the minimum, find the smallest value in the list.
Regarding the statistics on children whose parents do not have secure employment, it can be determined how each state compares to the surrounding states by comparing the mean, median, and mode of the "number" and "percent" columns. The state with the best or worst data can be determined by comparing the maximum and minimum values in each column. The value that gives a better comparison would depend on the purpose of the analysis. If the goal is to understand the overall number of children affected, then the "number" column would be more appropriate. If the goal is to understand the proportion of children affected in each state, then the "percent" column would be more appropriate.
Step-by-step explanation:
Need help with how to do this one...
Find the domain of
x ¹ -2
x + 1
A. x ≠ -1
B. x ≠ 1
C. x ≠ -2
D. x ≠ -1, 1
E. x ≠ 2
F. x ≠ 0
Use de Morgan’s laws to rewrite a statement that is equivalent to the following statement.
It is not true that April and August are both spring months
Using de Morgan’s laws to rewrite a statement : It is true that April is not a spring month OR August is not a spring month
What is de Morgan’s laws?This refers to a pair of transformation rules that are both valid rules of inference. They are named after Augustus De Morgan. He was a 19th-century British mathematician. De Morgan's laws can also be called De Morgan's theorem.
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