a) The system of equations modeling this scenario is as follows:
C = 11.50 + 0.9n
C = 13.25 + 0.55n.
b) The number of toppings where the cost is the same at either Pizza Palace or Tasty Pizza is 5.
What is a system of equations?A system of equations is two or more equations solved concurrently.
A system of equations is also called simultaneous equations because the equations are solved at the same time or simultaneously.
Pizza Palace Tasty Pizza
Pizza cost per unit $11.50 $13.25
Topping cost per unit $0.90 $0.55
Let the number of toppings = n
Let the total cost for the pizza at each pizza place = c
Equations:The total cost at Pizza Palace C = 11.50 + 0.9n... Equation 1
The total cost at Tasty Pizza, C = 13.25 + 0.55n... Equation 2
For the total cost, c, to be the same at the pizza places, Equation 1 must equate Equation 2:
That is, C = C.
Substituting the values of C:
11.50 + 0.9n = 13.25 + 0.55n
0.35n = 1.75
n = 5
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what is the value of x
Answer:
D. x = 20
Step-by-step explanation:
All angles equal 180°
x + 5 + 7x -5 + x = 180
Combine like terms
9x = 180
Divide both sides by 9
x =20
If y=(2x-1)/(x+6) what are the values of y when x is equal to 5,0 , and -6 ?
When x is equal to 5, the value of y is equal to 9/11. When x is equal to 0, y is equal to -1/6 and when x is equal to -6, y is undefined since the denominator of the fraction is equal to 0.
A rational function is what?Every function that can be expressed as the ratio of two polynomial functions is referred to as rational. A rational function, then, has the form f(x) = p(x)/q(x), where p(x) and q(x) are polynomial functions and q(x) is not equal to 0. All real numbers fall inside a rational function's domain, with the exception of x values that cause the denominator to be equal to 0. A rational function's graph may include vertical and horizontal asymptotes, or lines that the graph approaches when particular values of x are approached.
The given equation of y is y=(2x-1)/(x+6).
Substituting the given values of x we have:
When x = 5:
y = (2(5) - 1)/(5 + 6) = 9/11
When x = 0:
y = (2(0) - 1)/(0 + 6) = -1/6
When x = -6:
y = (2(-6) - 1)/(-6 + 6) = undefined
Hence, when x is equal to 5, y is equal to 9/11. When x is equal to 0, y is equal to -1/6 and when x is equal to -6, y is undefined since the denominator of the fraction is equal to 0.
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Jennifer bought 14. 75 gallons of gasoline for her car at a cost of $2. 95 a gallon. Which is closest to the amount she paid for the gasoline? HELPPP
The amount Jennifer paid for the gasoline is closest to $43.51.
This is because we can multiply the number of gallons by the cost per gallon to get the total cost, which in this case is 14.75 x 2.95 = 43.5125. Rounding this to two decimal places, we get $43.51, which is the closest answer option.
In general, when calculating the total cost of gasoline, we need to know the number of gallons purchased and the cost per gallon. These two values can be multiplied together to find the total cost of the gasoline. So here the answer is $43.51.
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In one to two sentences, describe an impact that division of labor had on the economic growth of the United States. (2 points)
The division of labor, or specialization of tasks, has boosted efficiency and productivity in the United States, thereby stimulating economic growth. It also facilitates the growth of factories and mass production, which further contributes to the overall economic growth of the country.
Division of labor:
Division of labor is the process of dividing the work of producing goods and services into separate tasks performed by different people or groups of people. Division of labor is an economic concept that states that dividing a production process into stages allows workers to focus on specific tasks. If workers can concentrate on a small aspect of production, as long as sufficient quantities and quantities are produced, overall efficiency will increase.
This division is generally based on the skills, expertise and resources of the worker, as well as the wants and needs of the market.
The purpose of division of labor is to increase efficiency and productivity by allowing workers to specialize in specific tasks and develop expertise in those tasks. This can lead to better quality products and services and lower costs. The division of labor is a key concept in economics and an important factor in the development and growth of societies.
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1/2x35 fractions please help me
Answer:
Step-by-step explanation: 17/5
Please help find values of c and b.
Answer:
c = 21b = -12Step-by-step explanation:
You want the coefficients of the quadratic with roots (3±2i√3)/2 and a leading coefficient of 4.
CoefficientsThe value b/a is the opposite of the sum of the roots.
b/a = -((3+2i√3)/2 +(3-2i√3)/2) = -(3/2 +3/2) = -3
b = -3a = -3(4)
b = -12
The value c/a is the product of the roots. This will be the difference of squares:
c/a = (3+2i√3)/2 × (3-2i√3)/2 = (3² -(2i√3)²)/4 = (9 +12)/4 = 21/4
c = a(21/4) = (4)(21/4)
c = 21
I need help, please!!!!!!!
After answering the provided question, we can conclude that As a result, probability the correct answer is C) A• The expected point value is 0.13, so guessing is advantageous.
What is probability?Probability of how likely an event is to occur. It is represented by a number is for both 0 and 1, with 0 representing an unlikely event and 1 representing an unavoidable event. Shifting a fair coin and coin flips has a probability of 0.5 or 50% because there are two equally likely outcomes. (Heads or tails). Probability theory is a mathematical discipline that investigates random events instead than their properties. It is applied in many fields, including facts and figures, finance, scientific knowledge, and engineering.
After eliminating one of the six possible answers, the remaining five options are equally likely to be correct, so the probability of correctly guessing is now 1/5 and the probability of incorrectly guessing is 4/5.
Point value expected = (probability of gaining points x point value) - (probability of losing points x point value)
(1/5 x 1) is the expected point value. - (4/5 x 1/6)
1/5 - 1/30 = expected point value
5/30 - 1/30 = expected point value
4/30 is the expected point value.
The expected point value is 0.13. (rounded to two decimal places)
It is advantageous to guess because the expected point value is positive.
As a result, the correct answer is C) A• The expected point value is 0.13, so guessing is advantageous.
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How does the value of a in the function effect is graph when compared to the graph of the quadratic parent function G parenthesis experience disease equals 22X squared 2
Changing the value of 'a' changes the shape, position, and concavity of the graph of the function.
What is function?In mathematics, a function is a rule that assigns to each element in a set (called the domain) a unique element in another set (called the range or codomain).
Stretching or compressing the graph: If 'a' is greater than 1, the graph of the function will be stretched vertically, making it thinner and taller. If 'a' is between 0 and 1, the graph will be compressed vertically, making it wider and shorter. If 'a' is negative, the graph will be upside down.
Shifting the graph: If 'a' is positive, the graph will be shifted up or down depending on the value of 'a'. If 'a' is negative, the graph will be shifted down or up.
Changing the concavity of the graph: The graph of the parent function G(x) is an upward-facing parabola, which means it has a positive concavity. If 'a' is positive, the graph of the function will also have a positive concavity. If 'a' is negative, the graph of the function will have a negative concavity, which means it will be a downward-facing parabola.
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Liam bought 2 vintage movie posters, 2 rock posters, and 1 rap poster. He applied a 35$ gift card to the total purchase and a 1/2 off coupon to the rap posters. write and evaluate a numerical expression to show how much Liam paid for the posters.
Answer: $91.25
Step-by-step explanation:
We know that
Vintage movie = $28.5
Rock = $29.75
Rap = $19.5
For the total cost, we get
(2 × 28.5) + (2 × 29.75) + (1 × 19.5) = $136
Recalling that he has a $35 gift card as well as the 1/2 off coupon on rap posters,
136 - 35 - ½(19.5)
$91.25
Pls answerrrrr
with simple working
Question: Is -451 in the sequence bellow?
15, 7, -1, -9, -17, ...
-451 not in the sequence
Numerical sequenceThis question involves the concepts of arithmetic progression.
Which consists of adding the previous term to a certain ratio (r), which will be found the next term.
Let's seeData to calculate
r = 7-15=-8
an = -451
a1= 15
n=?
[tex]\begin{array}{l}\sf a_{n} = a_{1} + ( n-1 )r\\\sf -451 = 15 + ( n-1 )\times(-8)\\\sf -451=15-8x+8\\\sf -451 = 23-8n\\\sf 8n=23+451\\\sf 8n=474\\\sf n=\dfrac{474}{8}\\\sf n=59{,}25\end{array}[/tex]
The result is not an integer, so -451 is not part of the sequence
I need help with payroll accounting. Its in an excel format for multiple months
By following the steps outlined below, you can create a payroll payslip that provides all of the necessary information and helps ensure that your employees are paid accurately and on time.
Open Excel and create a new workbook. In the first row, create headings for the different columns you will need, such as "Employee Name," "Employee ID," "Pay Period," "Gross Pay," "Deductions," "Net Pay," and so on.
Enter the employee's name, ID, and pay period in the appropriate cells.
Calculate the employee's gross pay. Gross pay is the total amount of money the employee earned before any deductions are taken out.
Calculate the employee's deductions. Deductions are the amounts that are taken out of the employee's pay, such as taxes, social security, health insurance, and so on.
Calculate the employee's net pay. Net pay is the amount of money the employee receives after all deductions are taken out. To calculate this, subtract the total amount of deductions from the gross pay.
Once you have calculated all of the necessary amounts, enter them into the appropriate cells on the payslip.
Finally, you can customize the payslip by adding your company logo, address, and other relevant information. You can also format the cells to make the payslip look more professional.
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Complete Question:
How do I create a payroll payslip in Excel?
A park ranger counted the number of squirrels he saw while giving tours in three sections of a national park that have different areas.
Determine the unit rate in terms of the number of squirrels per square mile in the park, and complete the sentences below. Assume the relationship of squirrels to square miles shown in the table can be extended to the entire park.
Fill in the Blank.
The park ranger counted ___ squirrels for every mile in the park.
For every 128 square miles in the park, the park ranger would count ___ squirrels.
For every ___ square miles in the park, the park ranger would count 324 squirrels.
Area is a measure of the size of a two-dimensional surface or region. It is typically measured in square units, such as square meters or square feet. The area of a shape is found by multiplying the length and width of the shape in most cases, although the formula for finding the area may vary depending on the shape.
In the given question,
To find the unit rate in terms of the number of squirrels per square mile, we need to divide the total number of squirrels by the total area of the park.
Total number of squirrels = 20 + 32 + 128 = 180
Total area of the park = 5 + 8 + 32 = 45
Unit rate of squirrels per square mile = 180/45 = 4 squirrels per square mileFor every 128 square miles in the park, the park ranger would count 512 squirrels. (4 squirrels per square mile x 128 square miles = 512 squirrels)For every 40 square miles in the park, the park ranger would count 324 squirrels. (4 squirrels per square mile x 40 square miles = 160 squirrels)Note: The last blank can be filled with 40, as shown above.
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Answer:
1. 4
2. 512
3. 81
Step-by-step explanation:
-3y 2 + 4x when x =-4 and y = 2
Answer: -22
Step-by-step explanation:
replace the variables with their given values and calculate
-3(2) + 4(-4)
5. Which equation below can be transformed into the following equation:
2x + 4 = 6x + 2
2x + ½ = 6x + 1⁄2
2(2x+5)= 4x + x + 2
O2(x+2) = 2 (3x + 1)
Answer:
The equation that can be transformed into the following equation 2x + 4 = 6x + 2 is:
2(2x+5)= 4x + x + 2
Therefore, the equation 2(2x+5)= 4x + x + 2 can be simplified and transformed to the form of 2x + 4 = 6x + 2.
HELP ASAP is the relationship between the amount of dry dog food and the amount of wet dog food proportional the numbers are for dry god food (cups) (Y) there 4.5 6 9
for wet dog food (oz) (x) SHOW WORK THX
Yes, there is direct relatiοn in amοunt οf dry dοg fοοd and the amοunt οf wet dοg fοοd.
If amοunt οf dry dοg fοοd is x and the amοunt οf wet dοg fοοd is y then the relatiοn is given as: x = 3y
Hοw tο find the prοpοrtiοnality?Tο determine whether the relatiοnship between the amοunt οf dry dοg fοοd and the amοunt οf wet dοg fοοd is prοpοrtiοnal, we need tο check whether the ratiο οf the twο quantities remains cοnstant.
A) yes, there is direct relatiοn in amοunt οf dry dοg fοοd and the amοunt οf wet dοg fοοd. as amοunt οf dry dοg fοοd increases there alsο increase in amοunt οf wet gοοd.
if amοunt οf dry dοg fοοd is x and the amοunt οf wet dοg fοοd is y then the relatiοn is given as:
x = 3y
fοr example lets take values frοm first rοw
4.5 = 3 × 1.5
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Complete question:
7) Given: the sequence 4, 8, 16, 32,. . . When using the geometric sequence formula an
determine the 15th term, which variable would be replaced with the number 27
1) a1
2) n
3) an
4) r
Answer:
The correct answer is 3) an.
In a geometric sequence, the term can be calculated by the formula an = a1 × r^(n–1).
In this case, the first term (a1) is 4, the common ratio (r) is 2, and the 15th term (n) is 15. Therefore, replacing an with 27, we get 27 = 4 × 2^(15–1). Solving for the 15th term (n), we get n = 27/4 × 2^(-14). The 15th term is 27.
SOMEONE HELP PLS IF YOU GET ALL OF THE BLANKS RIGHT I'LL GIVE BRAINLIEST AND FIVE STAR
Two trains simultaneously left points M and N and headed toward each other. The distance between point M and N is 380mi. The speed of the train, which started, from point N was 5 mph faster than the speed of the other train. In two hours after the departure the distance between the trains was 30 mi. What is the speed of each train?
Answer: the speed of the train that started from point M is 92.5 mph, and the speed of the train that started from point N is 97.5 mph (92.5 + 5).
Step-by-step explanation:
Let's use the following variables:
x = speed of the train that started from point M
x + 5 = speed of the train that started from point N
We know that:
The total distance between the trains is 380 miles.
In 2 hours, the distance between the trains decreased by 30 miles.
Using the formula: distance = rate x time, we can write two equations:
Equation 1: 2x + 2(x + 5) = 380 (the sum of the distances traveled by the two trains equals the total distance between them)
Equation 2: 2x - 2(x + 5 - 30/2) = 30 (the difference in distances traveled by the two trains in 2 hours equals the decrease in distance between them)
Simplifying Equation 1:
4x + 10 = 380
4x = 370
x = 92.5
Therefore, the speed of the train that started from point M is 92.5 mph, and the speed of the train that started from point N is 97.5 mph (92.5 + 5).
To check, let's substitute these values into Equation 2:
2(92.5) - 2(97.5 - 30/2) = 30
185 - 155 = 30
30 = 30
This confirms that our solution is correct.
A village is hit by malaria. The government decides to give each member in a household a mosquito net to avoid mosquitoes. Each package contains an equal number of nets of six" There are 12 households in the village, whose members are 2,3,4, 5. 3. 7. 9. 8, 11, 12, 8, 10. Determine the number of mosquito nets the government will take to the village
The village will require 14 bundles of mosquito nets to be brought by the government.
There are 12 households in the village with a total of 12 members. To determine the number of mosquito nets needed, we first need to calculate the total number of individuals who require a net:
2 + 3 + 4 + 5 + 3 + 7 + 9 + 8 + 11 + 12 + 8 + 10 = 82 individuals
Since each package contains an equal number of nets of six, we can calculate the number of packages required by dividing the total number of individuals by six:
82 individuals ÷ 6 = 13.67
Since we cannot have a fractional number of packages, we need to round up to the nearest whole number:
14 packages
Therefore, the government will need to take 14 packages of mosquito nets to the village.
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In a group of 15 children, 5 said they are an only child, 3 said they have 1 sibling only, 4 said they have exactly 2 siblings, and 3 said they have exactly 3 siblings.
What is the average number of siblings for this group?
Enter your answer as a decimal, rounded to the nearest tenth, in the blank.
The average number οf siblings fοr this grοup is 1.3.
Tο find the average number οf siblings fοr this grοup, we need tο calculate the tοtal number οf siblings and divide by the tοtal number οf children.
The 5 children whο said they are an οnly child have 0 siblings each, sο they cοntribute 0 tο the tοtal.
The 3 children whο said they have 1 sibling οnly have 1 sibling each, sο they cοntribute 3 tο the tοtal.
The 4 children whο said they have exactly 2 siblings have 2 siblings each, sο they cοntribute 8 tο the tοtal.
The 3 children whο said they have exactly 3 siblings have 3 siblings each, sο they cοntribute 9 tο the tοtal.
Therefοre, the tοtal number οf siblings is 0 + 3 + 8 + 9 = 20.
The tοtal number οf children is 15.
Sο, the average number οf siblings is 20/15, which is apprοximately 1.3 (rοunded tο the nearest tenth).
Therefοre, the average number οf siblings fοr this grοup is 1.3.
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The value of (– 5)2 x (-5)-2 + (-5)2
is:
Answer:50x-12
Step-by-step explanation:
We need to get rid of parentheses in this term.
All the negative factors will change sign.
In our example, we have 2 negative factors.
The sign of the term will not change, since there is an even number of negative factors.
PLEASE HELP I APPRECIATE IT THANK YOU
Determine the value of "a" in the expression below:
[tex]\sqrt[3]{81x^15y^9} =3^ax^5y^3[/tex]
Attached is a photo of the problem too in case I wrote the equation wrong.
Thanks again!!
See below for the explanation
---------------------------------------------------------------
I'll go through the possible answer choices.
A. If we tried a = 3, then 3^a = 3^3 = 27 which is not 81 that we want. This rules out choice A.B. Try a = 1 to get 3^a = 3^1 = 3 which also doesn't match with the 81. Cross choice B off the list.C. Try a = -1 to get 3^a = 3^(-1) = 1/(3^1) = 1/3. Still no, so we cross choice C off as well.D. Try a = 2 and we get 3^a = 3^2 = 9. Choice D is eliminated.E. Lastly, 3^a = 3^0 = 1 which eliminates choice E.To summarize, choices A through E lead to results that aren't 81, so we must eliminate them. There's nothing left to pick, so your teacher must have made a typo somewhere. You'll need to ask her/him for further clarification.
Which sequence is represented by the equation a n =4(3)^ n-1
The sequence represented by means of the equation a n =4(3)^ n-1 is an exponential sequence with a commonplace ratio of 3 and an preliminary term of 4.
To see this, we can plug within the values of n and study the pattern:
Whilst n = 1:
a 1 = 4(3)^0 = 4(1) = 4
Whilst n = 2:
a 2 = 4(3)^1 = 4(3) = 12
Whilst n = 3:
a three = 4(3)^2 = 4(9) = 36
While n = 4:
a 4 = 4(3)^3 = 4(27) = 108
And so on.
We can see that every time period in the sequence is received by way of multiplying the previous term by using 3, and that the first term is 4.
Thus, the sequence is an exponential sequence with a commonplace ratio of 3 and an preliminary term of 4.
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Explore the categorical predictors (excluding the first four)by computing the average fare in each category and using boxplots. Which categorical predictor seems best for predicting fare?
The 'Pclass' predictor seems to be the best predictor of fare, as it was seen that the average fare increases as the passenger class increases.
The average fare in each category can be calculated by calculating the average fare for each category of the categorical predictors (excluding the first four). For example, for the 'Sibsp' predictor, the average fare can be calculated by taking the sum of all fares for each category and dividing it by the total number of passengers in that category.
The boxplots can then be used to visualize the average fares for each category of the categorical predictors. From the boxplots, it can be seen that the 'Pclass' predictor seems to be the best predictor of fare, as the average fare increases as the passenger class increases. Specifically, the average fare for passenger class 1 is much higher than that for passenger class 2 and 3, confirming that 'Pclass' is the best predictor of fare.
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Complete question:
Which categorical predictor is most effective for predicting the fare of an airline ticket?
How much of a 8% salt solution must combined with a 20% salt solution to make 4 gallons of a 15% salt solution? Step 1 of 3 : Identify the variable. Let x= number of gallons of salt solution to add. A
In response to the supplied query, we may state that Consequently, to equation create 4 gallons of a 15% salt solution, we must combine 1.67 gallons of the 8% salt solution with 2.33 gallons of the 20% salt solution.
What is equation?A mathematical equation links two statements and utilises the equals sign (=) to indicate equality. In algebra, an equation is a mathematical assertion that proves the equality of two mathematical expressions. For instance, in the equation 3x + 5 = 14, the equal sign separates the numbers by a gap. A mathematical formula may be used to determine how the two sentences on either side of a letter relate to one another. The logo and the particular piece of software are usually identical. like, for instance, 2x - 4 = 2.
We know that 0.08x gallons of salt, or 8% of x gallons, is in the 8% salt solution.
Since we are adding x gallons of the 8% salt solution to a total of 4 gallons of the final solution, we know that 20% of (4 - x) gallons is salt, or 0.2(4 - x) gallons of salt, for the 20% salt solution.
0.08x + 0.2(4 - x) = 0.15(4) (4)
We can condense things and find x:
0.08x + 0.8 - 0.2x = 0.6
-0.12x = -0.2
x = 1.67
Consequently, to create 4 gallons of a 15% salt solution, we must combine 1.67 gallons of the 8% salt solution with 2.33 gallons of the 20% salt solution.
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find area of compound shape
Answer:
110
Step-by-step explanation:
Basically, in area, we do length x width.
So, All we had to do is do 11 (length) x 10 (width)
And the answer is 110!
(I think this is right?)
you flip a coin 16 times and get heads 7 times. based on this experiment, what is the probability of flipping a coin and getting tails? select the correct answer below:
The probability of flipping a coin and getting tails is 50%.
This is because in a fair coin toss, there is an equal chance of getting heads or tails. This means that the probability of each outcome is 50%.
To prove this experimentally, you flipped the coin 16 times and got heads 7 times. This means that out of the 16 times, you got heads 7 times and tails 9 times. Therefore, the probability of getting tails is 9/16, which is the same as 50%.
In general, the probability of flipping a coin and getting tails is always 50%, no matter how many times the coin is flipped or what the result of previous flips were. This is because each flip of the coin is an independent event and has the same probability of being heads or tails.
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To fence a rectangular cornfield, a farmer uses 1,800 meters of fencing. The length of the field is 500 meters. Complete the equation that can be used to determine the width w of the field in meters. Drag the correct values into each box to complete the equation. Hide Hints
The width of the rectangular cornfield is 400 meters.
How is perimeter used in geometry? What is perimeter?The circumference of a two-dimensional shape's perimeter is its entire length. In geometry, perimeter is used to calculate the length of a polygon's perimeter, such as a circle, square, triangle, or rectangle. By adding up the lengths of each side, one may determine a polygon's perimeter. For instance, the formula P = 2L + 2W may be used to determine the perimeter of a rectangle, where P stands for the perimeter, L for the length, and W for the width. The idea of perimeter is crucial to understanding geometry because it allows us to estimate how much material is required to enclose a form, such as fencing for a rectangular area or carpeting for a room.
Let us suppose the width of the field = w.
The perimeter of the rectangle is given as:
P = 2(l + w)
Substituting the given values, we get:
1,800 = 2(500) + 2w
1,800 = 1,000 + 2w
800 = 2w
w = 400
Therefore, the width of the rectangular cornfield is 400 meters.
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Alfonzo works for a lean service company. It takes him 3/4 hour to mow a lawn. If he works more than 8 hours, he gets 1/2 lunch break. Write and solve an inequality to find the number of lawns he can mow if he works at least 14 hours.
Alfonzo can mow at most 4 lawns if he works at least 14 hours. And we used the "less than or equal to" symbol because Alfonzo may not be able to mow a fraction of a lawn.
What is an Inequality ?
An inequality is a mathematical statement that describes a relationship between two values or expressions that are not necessarily equal.
Let's start by determining how many lawns Alfonzo can mow in 1 hour:
1 hour = 4/4 hours
Lawns mowed in 1 hour = 1 / (3/4) = 4/3
Now, let L be the number of lawns Alfonzo can mow if he works at least 14 hours. Since he works 8 hours without a lunch break, he has (14 - 8 - 1/2) = 5.5 hours left to work after his lunch break. Therefore, we can set up the following inequality to find L:
4/3(L) ≤ 5.5
Multiplying on both sides by 3/4, we get:
L ≤ 5.5 x 3/4
L ≤ 4.125
Therefore, Alfonzo can mow at most 4 lawns if he works at least 14 hours. Note that we used the "less than or equal to" symbol because Alfonzo may not be able to mow a fraction of a lawn.
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I need help with these problems , please and thank you
Therefore, the value of x that satisfies the equation √x = 14i√3 is -588. The answer is (a). The only value of x that satisfies this equation is option (b): which is -2i.
What is the value of xWe can start by squaring both sides of the equation to eliminate the square root:
We have to apply the knowledge of multiplying or squaring a complex number will give us a negative value.
(√x)^2 = (14i√3)^2
x = (14i)^2 x (√3)^2
We have to take the square of the complex number and the square root of 3.
x = -196 x 3
Multiply the value
x = -588
The value of x in the equation is -588.
2. We can factor out x from the expression as follows:
x(x^4 + 6x^2 + 8)
Now, we need to find the value(s) of x that make the expression equal to 0.
We can see that one solution is x = 0, since anything multiplied by 0 is 0.
To find the other solution(s), we can solve the quadratic equation inside the parentheses:
x^4 + 6x^2 + 8 = 0
Substitute y = x^2:
y^2 + 6y + 8 = 0
Factor the quadratic equation:
(y + 4)(y + 2) = 0
Therefore, the possible values of y are -4 and -2. Substituting back y = x^2, we get:
x^2 = -4 or x^2 = -2
Since x^2 cannot be negative for real numbers, there are no real solutions to this equation. However, if we allow complex numbers, we can find the solutions by taking the square roots of -4 and -2:
x = ±2i or x = ±sqrt(2)i
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Let A and B be events with P(A)=0.6, P(B)=0.4, and P(B|A)=0.4. Find P(A and B)
The value of P(A and B) is 0.24.
What is Conditional probability?
Conditional probability is a type of probability that describes the likelihood of an event occurring given that another event has already occurred. It is calculated by dividing the probability of the joint occurrence of both events by the probability of the occurrence of the event that has already occurred.
More formally, if we have two events A and B, the conditional probability of event A given event B is denoted by P(A|B) and is defined as:
P(A|B) = P(A and B) / P(B)
We are given :
P(A)=0.6, P(B)=0.4, and P(B|A)=0.4
We can use the formula for conditional probability to solve :
P(B|A) = P(A and B) / P(A)
We can write it as :
P(A and B) = P(B|A) * P(A)
Now, Substituting in the given values, we get:
P(A and B) = 0.4 * 0.6 = 0.24
Therefore, the probability of both events A and B occurring is 0.24.
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