[tex]a_n=n^2-n\\\\\text{Put}\ n=1,\ n=2,\ n=3,\ n=4,\ n=5\ \text{to the equation}.\\\\n=1\to a_1=1^2-1=1-1=0\\\\n=2\to a_2=2^2-2=4-2=2\\\\n=3\to a_3=3^2-3=9-3=6\\\\n=4\to a_4=4^2-4=16-4=12\\\\n=5\to a_5=5^2-5=25-5=20\\\\Answer:\ \boxed{0,\ 2,\ 6,\ 12,\ 20}[/tex]
Answer: -1, 2, 7, 14, 23
Step-by-step explanation:
aₙ = n² - 2
for n=1
a₁ = 1² - 2 = 1-2= -1
for n=2
a₂ = 2² - 2 = 4-2 =2
for n= 3
a₃ =3² - 2 = 9-2=7
for n=4
a₄= 4² - 2 = 16-2=14
for n=5
a₅= 5² - 2=25-2=23
Therefore, the first five terms of the sequence are; -1, 2, 7, 14 and 23
How would you name line segment AH?
Answer:
last one
Step-by-step explanation:
Answer:
d
Step-by-step explanation:
Given: ∆AKL, AK = 9 m∠K = 90° m∠A = 60° Find: P∆AKL The area of ∆AKL
The perimeter (P∆AKL) of triangle AKL is 21.294 m, and the area is 20.25 m². Triangle AKL is a 30-60-90 triangle, with sides in the ratio 1:√3:2, allowing for straightforward calculations of the perimeter and area using the given side lengths and right triangle properties.
Explanation:To find the perimeter (P∆AKL) and the area of triangle AKL (∆AKL), we can use the properties of a right triangle. Since we have one angle of 60°, and the right angle 90°, the remaining angle must be 30°. With this information, we recognize that triangle AKL is a 30-60-90 special right triangle.
For a 30-60-90 triangle, the lengths of the sides are in the ratio 1:√3:2. Knowing one side, AK (the side opposite the 60° angle), is 9 m, we determine the side opposite the 30° angle (AL) is half that length, so AL = 9m / 2 = 4.5 m. The side opposite the 90° angle (KL) is √3 times the side opposite the 30° angle, so KL = 4.5m * √3 = 7.794 m.
Now we can find the perimeter (P) by adding all the sides:
AK + AL + KL = 9m + 4.5m + 7.794m = 21.294 mThe area (A) of a right triangle is (½)*base*height.
A = (½) * AK * AL = (½) * 9m * 4.5m = 20.25 m²An online ticket seller charges $44 for each ticket to a concert plus a fix and handling fee of 12 to find the define the unknown variables and write the equation to model the situation
Final answer:
To model the cost of purchasing concert tickets where each ticket is $44 and there's a fixed handling fee of $12, the equation is T = 44n + 12, with T representing the total cost and n the number of tickets.
Explanation:
The question deals with constructing a mathematical model for the situation where an online ticket seller charges a fixed price for a concert ticket plus a handling fee. Here, the unknown variable is the total cost (T) for purchasing a certain number of tickets (n). The fixed price for each ticket is $44, and there is a flat handling fee of $12 regardless of the number of tickets purchased. Therefore, the equation to model the total cost would be:
T = 44n + 12
This equation clearly defines how the total cost is determined by the number of tickets purchased, with n representing the number of tickets and T the total cost.
A market buys mixed nuts at $15 per pound.They want to make a 20% profit. What would you pay for 1 pound of nuts
Answer:
Step-by-step explanation:
100% = $15
20% = 1.2*15 = $18
Quick check
emma is planning a surprise party. she is considering.......
Answer:
Step-by-step explanation:
what is she considering? I would need more information to complete the probolem
Answer:
Nothing...
Step-by-step explanation: Do you have choices, because if you do, please edit your question so I could help you :)
At a county fair, 9 people out of 1,000 earned a perfect score in a carnival game. What decimal represents the number of people who earned a perfect score?
Answer:
Decimal represents the number of people who earned a perfect score is 0.009 .
Step-by-step explanation:
As given
At a county fair, 9 people out of 1,000 earned a perfect score in a carnival game.
[tex]Number\ of\ people\ who\ earned\ a\ perfect\ score = \frac{People\ who\ earned\ perfect\ score}{Total\ number\ people}[/tex]
people who earned a perfect score = 9
Total number of people = 1000
Put in the above
[tex]Number\ of\ people\ who\ earned\ a\ perfect\ score = \frac{9}{1000}[/tex]
Number of people who earned a perfect score = 0.009
Therefore decimal represents the number of people who earned a perfect score is 0.009 .
There were 200 people who voted at the Town council meeting all these people 40% voted for a new basketball court in the park how many people voted against building a new basketball court use numbers in words to explain your answer
Answer:
120 people voted against building the new basketball court.
Step-by-step explanation:
if you divide 200 by 100 then you know how many people equal 1 percent of the 200. knowing that for every 2 people they are equal to 1 percent. so if you do 100 -40 you get 60. the 100 represents the 100 percent and you subtract 40 because these are the people who are voting for the basketball court. The 60 represents the percent of people who are voting against building the basketball court. then you multiply 60 by 2 and you get 120.
A jet ski company charges a flat fee of $26 plus $3.25 per hour to rent a jet ski another company charges a fee of $24 plus $3.50 per hour to rent the same jet ski find number of hours for which the cost are the same round your number to the nearest whole hour
Answer: 8 hours
Step-by-step explanation:
Company 1: 3.25x + 26
Company 2: 3.50x + 24
3.50x + 24 = 3.25x + 26
0.25x +24 = 26 subtracted 3.25x from both sides
0.25x = 2 subtracted 24 from both sides
x = 8 divided both sides by 0.25
Check:
Company 1: 3.25x + 26 = 3.25(8) + 26 = $52
Company 2: 3.50x + 24 = 3.50(8) + 24 = $52
bobby’s christmas list had 3 more than twice as many items on it than johnny’s list. johnny asked for 8 fewer items than bobby. how many items were on johnny’s (x) and bobby’s (y) christmas lists?
Answer:
Johnny had 5 items and Bobby had 13 items.
Step-by-step explanation:
Let us assume that Johnny has x items and Bobby has y items in their list.
Bobby had 3 more than twice as many items on it than Johnny. So,
[tex]\Rightarrow y=3+2x[/tex] ----------1
Johnny asked for 8 fewer items than bobby. So,
[tex]\Rightarrow y-8=x[/tex] -----------2
Putting the value of x from equation 2 in equation 1, we get
[tex]\Rightarrow y=3+2(y-8)[/tex]
[tex]\Rightarrow y=3+2y-16[/tex]
[tex]\Rightarrow 2y-y=16-3[/tex]
[tex]\Rightarrow y=13[/tex]
Putting the value of y in equation 2,
[tex]\Rightarrow 13-8=x[/tex]
[tex]\Rightarrow x=5[/tex]
So, Johnny had 5 items and Bobby had 13 items.
Which of the following represents a proportional situation?
x f(x)
–1 4
0 2
1 0
2 –2
x f(x)
–1 –6
0 –3
1 0
2 3
(The two attached files are C and D)
How many rows are needed to seat all students. When there are 846 students and each row holds 18 people
Answer:
The answer is 47 rows.
Step-by-step explanation:
If we have 846 students, and each row can hold 18 people.
We just divide the total students into the number of people sitting by row.
846 ÷ 18 = 47.
63÷10 63÷10^2 63÷10^3. Please answer these equation and type the answer in the space below in the comment section THX and have a awesome day:)
Georges asked five of his friends how long they studied for the last math test and what grade they received. He found a linear regression equation for the data to be y = 9.6x + 65.8. What does the 9.6 mean in the context of this equation? A) His friends on average studied 9.6 hours. B) If they studied 9.6 hours they would get a 0 on the test. C) They should study 9.6 hours in order to get an A on the test. Eliminate D) For every hour they studied their grade would go up 9.6 points.
Answer:
The answer is D
Step-by-step explanation:
Trust me i just did it on USA TP
To determine whether there is a relationship between the type of school attended and verbal reasoning scores for Irish students, three samples with 25 students, in each group, were randomly selected from data used by Raferty and Hout (1985). One group of students attended secondary school, the second group of students attended vocational school, and the third group consisted of students who attended only primary school.
Select one answer.
If we let μ1, μ 2, and μ 3 be the mean verbal reasoning scores for students who attended secondary school, vocational school, and primary school only, respectively, the appropriate hypotheses in this case are:
a. H0: μ1 = μ2 = μ3
Ha: μ1, μ2, μ3, are not all equal
b. H0: μ1, μ2, μ3, are not all equal
Ha: μ1 = μ2 = μ3
c. H0: μ1 = μ2 = μ3
Ha: μ1 μ μ2 μ μ3
d. H0: μ1 μ μ2 μ μ3
Ha: μ1 = μ2 = μ3
e. None of the above are correct.
The correct hypotheses are:
b. [tex]\(H_0: \mu_1 = \mu_2 = \mu_3\) and \(H_a: \mu_1, \mu_2, \mu_3\) are not all equal.[/tex]
To determine the appropriate hypotheses for testing the relationship between the type of school attended and verbal reasoning scores for Irish students, we first need to understand the nature of the comparison being made.
We have three groups of students: those who attended secondary school, vocational school, and primary school only. We want to investigate if there is a difference in the mean verbal reasoning scores among these groups.
The null hypothesis [tex](\(H_0\)) states that there is no difference in the mean verbal reasoning scores among the three types of schools, expressed as \( \mu_1 = \mu_2 = \mu_3 \), where \( \mu_1 \), \( \mu_2 \), and \( \mu_3 \)[/tex] are the population means for students attending secondary school, vocational school, and primary school only, respectively.
The alternative hypothesis [tex](\(H_a\)) suggests that at least one of the population means is different from the others, expressed as \( \mu_1, \mu_2, \mu_3 \)[/tex] are not all equal.
Option b correctly represents these hypotheses:
[tex]\(H_0: \mu_1 = \mu_2 = \mu_3\) \(H_a: \mu_1, \mu_2, \mu_3\) are not all equal.[/tex]
This formulation allows for the testing of differences in mean verbal reasoning scores across the three types of schools. The null hypothesis assumes equality among the means, while the alternative hypothesis considers the possibility of inequality.
Anthony has 18 stickers.He wants to give 3 to each of his friends.How many friends can he give stickers to?
Huilan is 9 years older than Thomas. The sum of their ages is 53 . What is Thomas's age?
Answer:
The answer is 43. Hope this helps!!!!!
Step-by-step explanation:
Answer:
The correct answer is that Thomas's age is 44.
Step-by-step explanation:
If the sum of their ages is 53 and Huilan is 9 years older all we have to do is subtract 9 from 53, which equals 44.
Hope this helps,
Davinia.
which statement is true of normally distributed data ??
a. approximately 68% of the data falls within 2 standard deviations (+-2) of the mean
b. approximately 68% of the data falls within 1 standard deviation (+-1) of the mean
c. approximately 75% of the data falls within 2 standard deviations (+-2) of the mean
d. approximately 75% of the data falls within 1 standard deviation (+-1) of the mean
Answer:
The correct option is b. approximately 68% of the data falls within 1 standard deviation (+-1) of the mean
Explanation:
According to the empirical rule of normal distribution:
1. Approximately 68% of the data falls within 1 standard deviation [tex]\pm 1[/tex] of the mean
2. Approximately 95% of the data falls within 2 standard deviations [tex]\pm 2[/tex] of the mean
3. Approximately 99.7% of the data falls within 3 standard deviations [tex]\pm 3[/tex] of the mean.
Therefore, among the given options, only option b adheres to the empirical rule of the normal distribution. Therefore, the option b is correct
The true statement about a normally distributed dataset is that approximately 68% of the data falls within 1 standard deviation (±1) of the mean, which is known as the 68-95-99.7 rule or the empirical rule.
Explanation:This question pertains to properties of a normally distributed dataset. In such a distribution, a majority of the data falls within a specific range of the mean (average), defined by the standard deviations. Understanding standard deviations allows us to comprehend how spread out the data is from the average.
In the case of normally distributed data, it is factually correct that approximately 68% of the data falls within 1 standard deviation (±1) of the mean. This is known as the 68-95-99.7 rule or the empirical rule, which states that 68% of data falls within 1 standard deviation, 95% falls within 2 standard deviations, and 99.7% falls within 3 standard deviations of the mean for a normal distribution.
Therefore, the correct statement from the list provided in your question is option (b).
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( 20 PTS HELP FAST PLEASE I DON'T UNDERSTAND HOW TO DO THIS ) Fred Brown and his sister, Nancy, each have $15 in the bank. Every week Nancy plans to add $3 to her account. Fred who loves to spend money when he has it, plans to add $1 to his account each week. How many weeks will it take for Nancy’s account to have twice as much money as Fred’s account? (Explain your thinking using words and numbers.)
It will take 15 weeks for Nancy’s account to have twice as much money as Fred's.
Explanation:We are looking for the number of weeks it will take for Nancy’s account to have twice as much money as Fred’s account. Both Fred and Nancy start with $15. Each week, Nancy adds $3 to her account and Fred adds $1 to his account.
So we have to solve the equation: 15 + 3x = 2 * (15 + x), where x is the number of weeks. Simplifying the equation gives us x = 15 weeks. Thus, it will take 15 weeks for Nancy’s account to have twice as much money as Fred’s account.
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In 1990, a glacier was 400 meters away from a road. Every year since then, it has moved 7 meters closer to the road. At this rate, when will it meet the road?
Answer:
57 years
Step-by-step explanation:
Divide 400 by 7.
What is the probability of spinning a 2 on a spinner that has 8 equal sides numbered 1-8 and rolling a 3 on a die
Answer:
1/48
Step-by-step explanation:
To find the probability of 2 independent events, we multiply their probabilities together.
Probability of getting a 2 on the spinner, 1 of 8 spots
1/8 =
Probability of getting a 3 on the die, 1 of 6
1/6 =
Multiply these probabilities together
1/8 * 1/6 = 1/48
The swimsuit is on sale for 25% off its original price. If the original price was $58. What is the sale price?
When you roll a standard number cube once, what is the probability of rolling a number divisible by 3?
Answer:
[tex]\frac{1}{3}[/tex]
Step-by-step explanation:
On a standard cube there are the numbers 1, 2, 3, 4, 5, 6
Only 2 are divisible by 3, that is 3 and 6, hence
P(divisible by 3 ) = [tex]\frac{2}{6}[/tex] = [tex]\frac{1}{3}[/tex]
Compare the volume of a square pyramid to the volume of a square prism with the same base and height as the pyramid.
Answer:
The Volume of the square pyramid is 1/3 the volume of a square prism with the same base and height
Step-by-step explanation:
The volume of a square pyramid is given by the formula
V = 1/3 s^2 h
where s is the side length of the base
The volume of a square prism given by the formula
V = s^2 h
where s is the side length of the base
So dividing the two, taking the pyramid on top
1/3 s^2 h
---------------------
s^2 h
If the bases are the same, then the side lengths are the same and we know the heights are the same. We will cancel them from the top and the bottom.
1/3
---------------------
1
The Volume of the square pyramid is 1/3 the volume of a square prism with the same base and height
The Volume of the square pyramid is 1/3 the volume of a square prism with the same base and height
Step-by-step explanation:
The volume of a square pyramid is given by the formula
V = 1/3 s^2 h
where s is the side length of the base
The volume of a square prism given by the formula
V = s^2 h
where s is the side length of the base
So dividing the two, taking the pyramid on top
1/3 s^2 h
---------------------
s^2 h
If the bases are the same, then the side lengths are the same and we know the heights are the same. We will cancel them from the top and the bottom.
1/3
---------------------
1
The Volume of the square pyramid is 1/3 the volume of a square prism with the same base and height
50 POINTS!!!!!!!!!
The base (b) of the triangle is _ units.
A) 3 B) 5 C) 8 D) 13
The height (h) of the triangle is units.
A) 3 B) 5 C) 8 D) 13
The area of the triangle is square units.
A) 5 B) 7.5 C) 15 D) 30
I WILL KNOW IF YOU ARE WRONG!!!!!!!
Answer: the base is: 3 units
The height is: 5 units
The area is: 7.5 units
Step-by-step explanation: I just answered this question ❤️
The base of triangle is, 3 units
The height of triangle is, 5 units
And, The area of triangle is, 7.5 units²
What is mean by Triangle?A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.
Given that;
The triangle is shown in image.
Now, We get by graph of triangle;
The base of triangle is, 3 units
The height of triangle is, 5 units
We know that;
⇒ Area of triangle = 1/2 × base × height
⇒ Area of triangle = 1/2 × 3 × 5
⇒ Area of triangle = 7.5 units²
Thus, The base of triangle is, 3 units
The height of triangle is, 5 units
And, The area of triangle is, 7.5 units²
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a flying object's height in the sky can be represented by the equation d= 30+vt+[tex]4t^2\\[/tex] where d is the height in feet, v is the velocity in feet per second, and t is the time in seconds. how long has the flying object been traveling if it has a velocity of 8 feet per second and has risen to a height of 126 ft?
a). 4 seconds
b). 6 seconds
c). 8 seconds
d). 16 seconds
Answer:
t=4 seconds
Step-by-step explanation:
The equation given to us is
d=30 + vt + 4t²
d=126 feet
v= 8 ft per second
to find t =?
Now putting the values in the above equation gives
126 = 30 + 8t + 4t²
126 - 30 = 8t + 4t²
96 = 8t + 4t²
Dividing the whole equation by 4
[tex]\frac{96}{4}=\frac{8t}{4}+\frac{4t^{2} }{4}[/tex]
it will become
24 = 2t + t²
taking 24 to other sides of equality
0 = 2t + t² -24
t²+2t-24=0
Now we will do mid term breaking of the eqaution
t²+6t-4t-24=0
taking common from the equation
t(t+6)-4(t+6)=0
(t+6)(t-4)=0
so it becomes
t+6 = 0 or t-4 =0
t =-6 or t = 4 seconds
as time can not be negative
so t=4 seconds
There are 6,000 products at the store in one hour, 425 products are sold how products are left
Answer:
5575
Step-by-step explanation:
its just subtraction you take the 6000 and subtract 425 and thats how you get whats left they try to trick you using the time im guessing correct me if im wrong
Calculate the sum of the infinite series
Answer:
[tex]\frac{40}{3}[/tex]
Step-by-step explanation:
Here a= 20, r = -1/2
Here, the absolute value of r is 1/2 which is less than 1. So, the series converges.
The sum of an infinite geometric series is given by
S = [tex]\frac{a}{1-r}[/tex]
Substituting the values in the above equation, we have
[tex]S = \frac{20}{1-(-1/2)} =\frac{20}{3/2} =\frac{40}{3}[/tex]
∴ The sum of the given infinite series is 40/3
Answer:
A. 40/3 hope thats helpful
Jonathan worked at mcdonalds 20 hours pet week and earned 195.Use the equation 20h=195 to find jonathan's hourly wage
Answer:
He earns 9.75 per hour.
Step-by-step explanation:
195/20 = 9.75 and 9.75 x 20 = 195.
Answer:
All you will need to do is just divide 195 by 20 and your answer will be $9,75 cents. Hope this helps!!!!!
HELPP! Calculate S22 for the arithmetic sequence in which a12=2.4 and the common difference is d=3.4
Answer:
S22 for the arithmetic sequence is:
First option: 15.4
Step-by-step explanation:
a12=2.4
d=3.4
S22=?
Sn=(a1+an)n/2
n=22
S22=(a1+a22)22/2
S22=(a1+a22)11
ak=aj+(k-j)d
a12=a1+(12-1)d
2.4=a1+11(3.4)
2.4=a1+37.4
Solving for a1: Subtracting 37.4 both sides of the equation:
2.4-37.4=a1+37.4-37.4
Subtracting:
-35=a1
a1=-35
a22=a12+(22-12)d
a22=2.4+10(3.4)
a22=2.4+34
a22=36.4
S22=(a1+a22)11
S22=(-35+36.4)11
S22=(1.4)11
S22=15.4
This table can be used to organize Raj’s credit card balances and payments over 6 months. The annual percentage rate on the card is 18%.
Raj’s Credit Card Payments
(Month) (Balance) (Payment) (Interest Rate) (Interest Charged)
1 $500 $100 0.015 $6.00
2 - $50 0.015 -
3 - $50 0.015 -
4 - $50 0.015 -
5 - $50 0.015 -
6 - $50 0.015 -
What is the amount of total interest charged for the first 6 months?
Answer: 25.90
Step-by-step explanation:
Edge
The total interest charged for the first 6 months is $36.00.
Explanation:The total interest charged for the first 6 months can be calculated by adding up the interest charged for each month. From the table, we can see that the interest charged for each month is $6.00. Since there are 6 months, we can calculate the total interest charged as follows:
Total Interest Charged = Interest Charged per Month x Number of Months
Total Interest Charged = $6.00 x 6
Total Interest Charged = $36.00
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