The evaluations are:
i. 11! = 39916800
ii. 24! = 2.045 x 10^37
What is expansion by factorial?Expansion by factorial is a method of expanding a given number from 1 to the number given. An example is given thus;
5! = 5 x 4 x 3 x 2 x 1!
= 120
To evaluate the given expressions;
a. 11! = 11 x 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1!
= 39916800
Also,
b. 24! = 24 x 23 x 22 x 20 x ........ x 5 x 4 x 3 x 2 x 1!
= 204484017332398 x 10 ^23
= 2.045 x 10^37
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Which of the points plotted is farther away from (−7, 8), and what is the distance?
Answer:
(10, -10)
Step-by-step explanation:
This are the farest the graph can go unless you want (100,-100)
Change the values from negative to positive and positive to negative to get the most farest results
Answer: D
Step-by-step explanation:
I graphed so you can see. Count how far each are away.
(5,8) is 12 away
(-7,-5) is 13 away
So you answer is D
Or
You can also think of it as, for, (5, 8) only the x changed so you only moved in the x direction. subtract the numbers 5-(-7)=12
For (-7,-5) you only moved in the y direction, so subtract those 8-(-5)=13
Jazmine has 3 dogs She wants to give each dog 2 treats. How many treats does she need to have total?
Answer: 6
Step-by-step explanation:
you just get those numbers and times them 3 times 2 is 6
Someone help i really need help with this
Step-by-step explanation:
we just need to find out how many percentage of the daily goal each day, so let's assume that $50 is 100% of the daily goal.
ANGELINA
Mr. Black's class sold highlighters and pens to raise money. Every highlighter cost the same amount. Every pen
cost the same amount.
. On day 1, the class made $120 and sold 80 highlighters and 20 pens.
. On day 2, the class made $200 and sold 120 highlighters and 40 pens.
What was the cost per highlighter?
$
1
4
7
0
2
5
8
per highlighter
3
6
9
The cost per highlighter is approximately $1.
To find the cost per highlighter, we can use a system of equations. Let's call the cost per highlighter "h" and the cost per pen "p". Then, we can set up two equations based on the information given;
80h + 20p = 120 (day 1)
120h + 40p = 200 (day 2)
We can simplify these equations by dividing both sides by 20;
4h + p = 6 (day 1)
6h + 2p = 10 (day 2)
Now we can use the first equation to solve for p in terms of h;
p = 6 - 4h
Substitute this expression for p into second equation;
6h + 2(6 - 4h) = 10
Simplify and solve for h;
6h + 12 - 8h = 10
-2h = -2
h = 1
Therefore, the cost per highlighter is $1.
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A charity needs to report its typical donations received. The following is a list of the donations from one week. A histogram is provided to display the data.
10, 11, 35, 39, 40, 42, 42, 45, 49, 49, 51, 51, 52, 53, 53, 54, 56, 59
A graph titled Donations to Charity in Dollars. The x-axis is labeled 10 to 19, 20 to 29, 30 to 39, 40 to 49, and 50 to 59. The y-axis is labeled Frequency. There is a shaded bar up to 2 above 10 to 19, up to 2 above 30 to 39, up to 6 above 40 to 49, and up to 8 above 50 to 59. There is no shaded bar above 20 to 29.
Which measure of variability should the charity use to accurately represent the data? Explain your answer.
The range of 13 is the most accurate to use, since the data is skewed.
The IQR of 49 is the most accurate to use to show that they need more money.
The range of 49 is the most accurate to use to show that they have plenty of money.
The IQR of 13 is the most accurate to use, since the data is skewed.
The most appropriate measure of variability to use in this case is the IQR (Interquartile Range) of 13.
How to determine which measure of variability should the charity use to accurately represent the dataThe reason for this is that the data appears to be skewed towards the higher values, with more donations in the higher range (from 40 to 59 dollars) and fewer in the lower range (from 10 to 39 dollars).
Using the range (which is the difference between the highest and lowest values) would not accurately represent the variability of the data, as it would be heavily influenced by the outliers. On the other hand, the IQR, which is the range of the middle 50% of the data, is a more robust measure of variability that is not influenced by outliers. Therefore, the IQR of 13 is the most appropriate measure of variability to use in this case.
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I need assistance please.
Your Assignment
Mr. Paulsen challenges Olivia and Angelica to move figure ABCDE onto figure A"B"C"D"E" using a series of two different transformations. They give two different answers.
Answer the questions to investigate ways to transform ABCDE.
1. Olivia finds a combination of two different transformations that moves ABCDE onto A"B"C"D"E". What is one way she might have done this? (3 points)
2. Angelica reflects ABCDE over the y-axis and translates it up 8 units. Does her transformed figure match A"B"C"D"E"? If not, describe how her transformed figure compares to A"B"C"D"E". (3 points)
3. Michael says he can move ABCDE onto A"B"C"D"E" with one transformation by translating ABCDE diagonally so that it moves 8 units up and 10 units right. Is he correct? Explain why or why not. (4 points)
Olivia could have used a combination of a rotation and a translation to move ABCDE onto A"B"C"D"E".
Angelica's transformed figure will not match A"B"C"D"E" because reflecting ABCDE over the y-axis will change the order of the letters in the figure.
No, Michael is not correct.
How to explain the transformationTranslating ABCDE diagonally by 8 units up and 10 units right will move each point in ABCDE the same distance horizontally and vertically, which will change the shape of the figure.
In order to match A"B"C"D"E", the transformation must preserve the order of the letters and the angles between the segments.
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For the following right triangle, find the side length x. Round your answer to the nearest hundredth
The side length x of the given right angle triangle is: 14.97
How to use Pythagoras Theorem?When two sides of a right-angled triangle are given and one side is to be found, we can do so using the Pythagoras theorem. In the given triangle the base is x, the perpendicular is 10 and the hypotenuse is 18.
According to the Pythagoras Theorem, the following equation can be written as:
x² = 18² - 10²
x = √224
x = 14.97
Thus, that is the missing length of the given right triangle
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Part A: Is it possible to make a triangle that is both equilateral triangle and a right triangle? Explain
Part B: Is it possible to draw a triangle with side lengths of 15, 15 and 20? Explain.
Answer:
A. No, it is not possible. An equilateral triangle is also an equiangular triangle, meaning all of its angles measure 60°.
B. Yes, it is possible. By the Triangle Inequality Theorem:
15 + 15 > 20, and 20 + 15 > 15
i really don’t understand this so i would really appreciate help
Answer:
[tex]6\sqrt{2}+3\sqrt{10}[/tex]
Step-by-step explanation:
Use the Distributive Property. Remember that you can multiply the numbers under a square root whether or not they're the same. But you can ONLY add square roots when the square root part is the same.
[tex]\sqrt{3}(2\sqrt{6}+\sqrt{30})\\= \sqrt{3}(2\sqrt{6})+\sqrt{3}(\sqrt{30})\\=2\sqrt{18}+\sqrt{90}[/tex]
Simplify each square root part:
[tex]2\sqrt{18}+\sqrt{90}\\=2(3\sqrt{2})+3\sqrt{10}\\=6\sqrt{2}+3\sqrt{10}[/tex]
Since the square root parts are different, you cannot simplify any further.
What is the graph of f(x)=-2^x?
Answer:
exponential graph
Step-by-step explanation:
it is a exponential graph the is negative ,if you substitute x values and find the points to plot you'll see how it is plotted
Answer:
See graph
Step-by-step explanation:
The graph of any function can be identified by making an x-y table.
Choose some values for x (often -2, -1, 0, 1, 2)
f(-2) = - 2^(-2) = - 1/4
f(-1) = - 2^(-1) = - 1/2
f(-0) = - 2^(-0) = - 1
f(1) = - 2^(1) = - 2
f(2) = - 2^(2) = - 4
if you have the answer please reply im having trouble need the steps.
Over a given period of time, Seth sold more water bottles than Hayden.
To compare the number of water bottles sold by Seth and Hayden, we need to find out the equation for Seth's sales rate. Looking at the graph, we can see that Seth sold 10 bottles on day 1, 20 bottles on day 2, 30 bottles on day 3, and 40 bottles on day 4.
We can find the average daily sales rate for Seth by dividing the total bottles sold by the number of days:
Average daily sales rate for Seth = (10+20+30+40)/4 = 25
The equation given for Hayden's sales rate is y = 11x, where y represents the number of bottles sold and x represents the number of days. This equation shows that Hayden sells 11 bottles per day.
Comparing the two sales rates, we can see that Seth sold more water bottles. On average, Seth sold 25 bottles per day, while Hayden sold only 11 bottles per day. Therefore, over a given period of time, Seth sold more water bottles than Hayden.
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System of equations
2x + 3y = 4
3x + 5y = 7
10x + 15y = 20
-9x - 15y = -21
Find the solution of this system of linear
equations. Separate the x- and y- values with a
comma. Enclose them in a pair of parantheses.
Enter the correct answer.
DONE
Answer:-₍1,3₎
Step-by-step explanation:
To solve this system of equations, we can use the method of elimination to eliminate one of the variables. We can multiply the first equation by 5 and the second equation by -3, then add the two equations to eliminate $y$:
$(5)(2x + 3y = 4) \Rightarrow 10x + 15y = 20$
$(-3)(3x + 5y = 7) \Rightarrow -9x - 15y = -21$
Adding the equations, we get:
$10x + 15y - 9x - 15y = 20 - 21$
Simplifying, we get:
$x = -1$
Now we can substitute $x=-1$ into one of the original equations to solve for $y$. Using the first equation, we have:
$2(-1) + 3y = 4$
Solving for $y$, we get:
$y = 2$
Therefore, the solution to the system of equations is $x=-1$ and $y=2$. We can check this solution by substituting $x=-1$ and $y=2$ into the other two equations:
$3(-1) + 5(2) = 7$
$10(-1) + 15(2) = 20$
Both equations are true, so our solution is correct.
A company that sells paper has a tiered pricing model based on how much paper you buy. If you buy less than 10 reams, they charge you $7 per ream and a shipping cost of $8. If you buy 10 or more reams but less than 20 reams, they charge you $6 per ream and a shipping cost of $16. If you buy 20 or more reams, they charge you $6 per ream and shipping is free.
a. Write a function that models the price in terms of the number of reams bought.
b. What is the domain of the function?
c. What is the range of the function?
d. How much will it cost to buy 25 reams of paper?
f. How much paper can you buy for $60?
The function can be defined as price = 6x
It will cost $150 to buy 25 reams of paper.
How to explain the functionThe domain of the function is all non-negative real numbers, since the number of reams bought cannot be negative.
The range of the function is all non-negative real numbers, since the price cannot be negative.
Fir 25 items, price = 6(25) = $150
It will cost $150 to buy 25 reams of paper.
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Someone help i really need help with this
The percentage increase in the number of water bottles from February to April is 19%.
How to find the percentage increase?A company manufactures water bottles. The list describes the amount of water bottles manufactured in three months.
Therefore,
February: 4100 water bottlesMarch: 7% more water bottles than in FebruaryApril: 500 more water bottles than in marchTherefore,
Number of water bottles in march = 4100 + 7% of 4100
Number of water bottles in march =4100 + 7 / 100 × 4100
Number of water bottles in march = 4100 + 287
Number of water bottles in march = 4387
Hence,
Number of water bottles manufactured in April = 4387 + 500 = 4887
Therefore,
percentage increase from February to April = 4887 - 4100 / 4100 × 100
percentage increase from February to April = 787 / 4100 × 100
percentage increase from February to April = 78700 / 4100
percentage increase from February to April = 19.1951219512
percentage increase from February to April = 19%
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what is the solution to
-15x=90
Answer:
option c) x=-6
Step-by-step explanation:
-15x = 90
= x = 90/-15
= x = (-6)
find - 4 - 2 1/2 expression on the number line by drawing an arrow
The resulting arrow should end at -6 1/2. This is because -4 - 2 1/2 is equal to -6 1/2.
In mathematics, an expression is a combination of numbers, variables, and operators that can be evaluated to produce a value. Expressions can be simple or complex and are used to represent mathematical relationships and operations.
How to determine the expression?To find -4 - 2 1/2 expression on the number line by drawing an arrow, we need to start at -4 and then move left by 2 1/2 units.
To do this, we can draw an arrow starting at -4 and then mark off 2 1/2 units to the left. One way to represent 2 1/2 units is to divide the space between -4 and -5 into two equal parts, and then mark off one of those parts.
The resulting arrow should end at -6 1/2. This is because -4 - 2 1/2 is equal to -6 1/2.
Here's an example of what the arrow would look like:
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Based on a survey of 100 households, a newspaper reports that the average number of vehicles per household is 1.8 with a margin of error of ±0.3. The population surveyed is 50,000 households.
How many vehicles are included in the margin of error? Enter your answer in the blank.
Answer:
Step-by-step explanation:
The margin of error is ±0.3. This means that the actual average number of vehicles per household in the population is expected to be between 1.5 (1.8 - 0.3) and 2.1 (1.8 + 0.3).
To calculate the range of the margin of error in terms of the number of vehicles, we can multiply the margin of error by the square root of the sample size (100) to get:
0.3 * sqrt(100) = 3
So the margin of error in terms of the number of vehicles is ±3.
Therefore, the number of vehicles included in the margin of error is between 1.5 * 50,000 = 75,000 and 2.1 * 50,000 = 105,000.
So the range of the margin of error in terms of the number of vehicles is 30,000, and the number of vehicles included in the margin of error is 30,000.
The sum of two numbers is 998
The difference between them is 10
What are the two numbers?
Answer:
The two numbers are 494 and 504
Step-by-step explanation:
Let x = one of the numbers
Let y = the other number
x + y = 998
x - y = 10 or x = y + 10
Substitute y + 10 for x in the first equation and solve for y
x + y = 998
y + 10 + y = 998 Subtract 10 from both sides
y + y = 988 Combine like terms
2y = 988 Divide both sides by 2
y = 494
One of the numbers is 494.
x = y + 10 Substitute 494 for y
x = 494 + 10
x = 504
The other number is 504.
Check:
x + y = 998
504 + 494 = 998
998 = 998 checks
x - y = 10
504 - 494 = 10
10 = 10 checks
Helping in the name of Jesus.
The terminal point of 0 is (0,1). What is tan 0?
Two mechanics worked on a car. The first mechanic worked for 20 hours, and the second mechanic worked for 15 hours. Together they charged a total of $2600. What was the rate charged per hour by each mechanic if the sum of the two rates was $155
per hour?
the first mechanic charged $55 per hour and the second mechanic charged $100 per hour. we solve this by forming equation by by given data.
what is equation ?
An equation is a mathematical statement that shows that two expressions are equal. It typically consists of two sides separated by an equal sign (=). The expressions on each side of the equal sign can contain variables,
In the given question,
Let's assume that the first mechanic charged x dollars per hour and the second mechanic charged y dollars per hour.
From the problem, we know that:
The first mechanic worked for 20 hours, so he charged 20x dollars.
The second mechanic worked for 15 hours, so he charged 15y dollars.
Together, they charged a total of $2600, so we have:
20x + 15y = 2600
The sum of the two rates was $155 per hour, so we have:
x + y = 155
We can use these two equations to solve for x and y. First, we can rewrite the second equation as:
y = 155 - x
Then, we can substitute this expression for y into the first equation:
20x + 15(155 - x) = 2600
Simplifying and solving for x, we get:
20x + 2325 - 15x = 2600
5x = 275
x = 55
Now that we know x, we can use the second equation to find y:
y = 155 - x = 155 - 55 = 100
Therefore, the first mechanic charged $55 per hour and the second mechanic charged $100 per hour.
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Graph and solve y=1/2x-6 and y=1/2x+2
Answer:
No solution.
Step-by-step explanation:
To solve this problem, all you have to do is graph the lines and see where they intersect.
This is what you would do to solve a normal problem. However, these lines are parallel this means that the solution to these lines is no soultion
In a class of 52 students, 13 excel in Science and Mathematics, 16 excel in Science and Arts, 12 excel in Mathematics and Arts, 24 excel in Arts and 2 excel in none. Twice as many students excel in science only as do in mathematics only. The number of students who excel in mathematics only is six times the number of students who excel in Arts only. Determine the number of students who excelled in: (a) All the three subjects (b) Two subjects
14 students excel in all three subjects.
How to solveLet's use the Principle of Inclusion-Exclusion to solve this problem.
Let A be the set of students excelling in Arts, B be the set of students excelling in Science, and C be the set of students excelling in Mathematics.
|A| = 24, |B| = 16, |C| = 13
|A ∩ B| = 16, |B ∩ C| = 13, |A ∩ C| = 12
Let x be the number of students who excel in all three subjects.
|A ∩ B ∩ C| = x
We are given that 2 students excel in none of the subjects.
So, |A ∪ B ∪ C| = 52 - 2 = 50
Using the Principle of Inclusion-Exclusion:
|A ∪ B ∪ C| = |A| + |B| + |C| - |A ∩ B| - |B ∩ C| - |A ∩ C| + |A ∩ B ∩ C|
Substituting the given values, we get:
50 = 24 + 16 + 13 - 16 - 13 - 12 + x
Solving for x, we get:
50 = 24 - 12 + x
x = 38 - 24
x = 14
So, 14 students excel in all three subjects.
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Study the stock market quote , which shows a six month price graph for a software company. What might an investor expect regarding the stock price or the price change in the next 30 days ?
As indicated by the question, the company's prices have been declining. As a result, a sharp increase is not anticipated, nor is a significant change in the following 30 days.
What is stock market?a public market where business stock and its derivatives can be traded at a set price on a regulated exchange. This means that there is little chance of a big shift in the stock price during the next 30 days.
Look at the query to comprehend the printing company's pricing pattern. The price of this printing company's shares has decreased, according tothe inquiry. It has fallen steadily over time.
Investors shouldn't anticipate a sudden increase in the price of this company's shares because the question doesn't indicate one. However, 30 days is a relatively small period of time to indicate any movement in the stock's price.
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Find the distance from G to S.
Answer:
i think its b sorry if it's wrong
Step-by-step explanation:
what is the volume of the rectangular prism with a length of 11 meters, width of 26, and height of 38 meters?
I need help with this AP Stats question.
The probability that the team wins the debate is 0.6475
How to solve the probabilityP(win) = P(win | S)P(S) + P(win | J)P(J) + P(win | R)P(R)
= (0.25)(0.2) + (0.6)(0.35) + (0.85)(0.45)
= 0.6475
Therefore, the probability that the team wins the debate is 0.6475.
In order to simulate the probability that a Sophomore is never selected to give the closing argument in the next 5 debates, we can use the following steps:
Create a table of random digits with enough rows and columns to simulate the 5 debates. Each row represents a debate and each column represents a team member.
Assign the digits 0, 1, and 2 to represent the events that a sophomore, junior, and senior gives the closing argument, respectively.
Starting from the first row and first column, read the digits from the table and determine which team member gives the closing argument for the first debate.
If a sophomore is selected, record a 0 for that debate. Otherwise, record a 1.
Repeat steps 3 and 4 for the remaining debates, filling in the table as you go.
Calculate the proportion of simulations where a Sophomore is never selected to give the closing argument in the next 5 debates.
Repeat steps 1-6 many times (e.g., 10,000 times) to get a more accurate estimate of the probability.
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Find the areas of the trapezoids.
Answer:
Area = ½* height(a+b)
Where;
a=4units
b=8units
h=6units
Therefore Area= ½*6(4+8)
= ½*6*12
=36sq.un
Answer:
24sq²
Step-by-step explanation:
Area = ( b1 + b2) x h
---------------------
2
Area = (8 + 4) x 6
---------------------
2
Area = (12) x 6
---------------------
2
A = 72/2
A = 36
A = 1/2 * b * h
A = (1/2) * 4 * 6
A = (1/2) * 24
A = 12
36 - 12 = 24sq²
I hope this helps!
what could be the value of the point grafted only number line between 0.09 and 0.10
6. Stewart is making fruit punch for
his birthday party. He is filling a
240-ounce bowl with cans of apple
juice and pineapple juice. Each
can of apple juice holds 10 ounces,
while each can of pineapple juice
holds 18 ounces.
Write an inequality in standard
form representing the maximum
number of cans of apple juice, a,
and cans of pineapple juice, p,
Stewart can use.
The inequality in standard form that will represent the maximum number of cans of apple juice and cans of pineapple juice Stewart can use would be = 240ounce = 10a + 18p.
How to determine the inequality in standard form?The total quantity of fruit punch that would be used for the birthday = 240 ounce.
The quantity of juice each can holds for apple juice,a, = 10 ounces.
The quantity of juice each can hold for pineapple juice,p,= 18 ounces.
Therefore the best expression in standard form would be = 240ounce = 10a + 18p.
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Anita’s and Casey’s bills do not vary from month to month. Anita pays $80 more than Casey does each month. Over the course of 4 months, their combined bills are $1,520.
Part A
Write the system of equations that describes this situation. Let a represent Anita's monthly payment and c represent Casey's monthly payment.
a +
c =
a =
+
Part B
Solve the system to find Anita’s and Casey’s monthly payments.
Anita: $
Casey: $
Answer:
Casey's monthly payment is $150.
Anita's monthly payment is $230.
Step-by-step explanation:
Part A:
The system of equations that describes this situation is:
a + c = Total monthly bill
a = c + 80
where a represents Anita's monthly payment, c represents Casey's monthly payment, and Total monthly bill represents the combined bills of Anita and Casey.
Part B:
To solve the system, we can substitute the second equation into the first equation and get:
(c + 80) + c = Total monthly bill
Simplifying this equation, we get:
2c + 80 = Total monthly bill
We also know that over the course of 4 months, their combined bills are $1,520. So we can write:
4(Total monthly bill) = 1520
Substituting the equation for Total monthly bill from the previous step, we get:
4(2c + 80) = 1520
Simplifying this equation, we get:
8c + 320 = 1520
Subtracting 320 from both sides, we get:
8c = 1200
Dividing both sides by 8, we get:
c = 150
So Casey's monthly payment is $150. To find Anita's monthly payment, we can use the second equation from Part A:
a = c + 80
a = 150 + 80
a = 230
Therefore, Anita's monthly payment is $230.