Answer:
The explicit rule is Ak = 1 + 2 * (k - 1)
Step-by-step explanation:
1. Let's review the information provided to us for finding the explicit rule for the sequence.
The arithmetic sequence 1, 3, 5, 7, 9, . . . represents the set of odd natural numbers.
2. Let's find the solution:
Ak = 1 + 2 * (k - 1)
For k = 1 ⇒ Ak = 1 + 2 * (1 - 1) = 1 + 2 * 0 = 1 + 0 = 1
For k = 2 ⇒ Ak = 1 + 2 * (2 - 1) = 1 + 2 * 1 = 1 + 2 = 3
For k = 3 ⇒ Ak = 1 + 2 * (3 - 1) = 1 + 2 * 2 = 1 + 4 = 5
For k = 4 ⇒ Ak = 1 + 2 * (4 - 1) = 1 + 2 * 3 = 1 + 6 = 7
For k = 5 ⇒ Ak = 1 + 2 * (5 - 1) = 1 + 2 * 4 = 1 + 8 = 9
For k = 6 ⇒ Ak = 1 + 2 * (6 - 1) = 1 + 2 * 5 = 1 + 10 = 11
For k = 7 ⇒ Ak = 1 + 2 * (7 - 1) = 1 + 2 * 6 = 1 + 12 = 13
Answer:
1st: 1+(k-1)2
2nd: 399
3rd: C
4th: 40,000
explanation:
just did it :)
Gabrielle has 3 gallons of paint. She uses 9 quarts to paint her bedroom. How much paint does she have left?
Answer:
3 quarts
Step-by-step explanation:
There are 4 quarts in a gallon
3×4=12
12-9= 3
A textbook costs $65.49 before tax. The tax on the textbook is 6.5%.
What is the total cost of the textbook?
Round your answer to the nearest cent.
Enter your answer in the box.
Answer:
$69.75
Step-by-step explanation:
Given: Cost of textbook before tax=$65.49
The tax on the textbook = 6.5%
The tax amount = 6.5% of $65.49
=\frac{65}{1000}\times65.49=4.25685\approx4.26
⇒The tax amount = $4.26
The total cost of the textbook=Cost of textbook before tax+tax amount
=$65.49+$4.26
=$69.75
The total cost of the textbook is $69.75.
Credit goes to @JeanaShupp
Answer:
Answer is69.75
Step-by-step explanation:
The equation S = -16t2 + 34t + 184 models the height of a ball that is thrown upward from the roof of a 184 foot building and falls to the street below. In this equation S is the height in feet of the ball above the ground and t is the time in seconds the ball has traveled. According to this model, how many seconds did it take the ball to reach a height of 91 feet? (round to 1 decimal place)
Answer:
t=1.6
Step-by-step explanation:
If the equation [tex]S=-16t^2+34t+184[/tex] models the height of a ball above the ground, where t is time the ball travelled.If the height of the ball above the ground is S=91 instead of 184, then the time the ball should take to get to the ground comes from the expression above: [tex]S=-16t^2+34t+91[/tex] (because now we want to know how much time does it takes to reach the ground if it is thrown from 91 foot, not 184). Then, to know when the ball reaches the floor, we must equal the equation to zero [tex]-16t^2+34t+91=0[/tex] (because when the equation is zero, the height of the ball is zero, which means it is in the ground).To obtain the value of t in the expression [tex]-16t^2+34t+91=0[/tex] , we can apply the well known formula [tex]t=\frac{-b(+-)\sqrt{b^2-4ac} }{2a}[/tex], where a is the coefficient that accompanies the quadratic term (in this case a=16), b is the coefficient that accompanies the linear term (b=34 in this case), and c is the constant coefficient (c=91).Because time is always possitive, we only retain the possitive value for t that solves the equation:[tex]\frac{-34(+-)\sqrt{34^2-4\times(-16)\times93} }{2\times16}[/tex]. [tex]t=1.55\simeq1.6[/tex]Three fifths of the members of a hiking club went
on the last hiking trip. It 39 people went on the
trip, how many are in the club?
There are 65 people in the club.
Step-by-step explanation:
Given,
Fraction of people went on hiking = [tex]\frac{3}{5}[/tex]
No. of people went on hiking = 39
Let,
x be the number of people at club.
According to given statement;
[tex]\frac{3}{5}\ of\ x = 39\\\\\frac{3}{5}x=39\\0.6x=39\\[/tex]
Dividing both sides by 0.6
[tex]\frac{0.6x}{0.6}=\frac{39}{0.6}\\x=65[/tex]
There are 65 people in the club.
Keywords: fractions, division
Learn more about fractions at:
brainly.com/question/1234767brainly.com/question/1238144#LearnwithBrainly
There's 5 trees fill with apples. Alex wants 2 off each tree. How much apples do she have?
Answer:
10
Step-by-step explanation:
5 trees * 2 from each = 10 apples
Answer:
10
Step-by-step explanation:
5*2=10
Complete this statement:
45x^3a + 27xa^2= 9xa
Enter the correct answer.
0000
DO
Clear all
DOO
Answer:
[tex]45x^3a+27xa^2= 9xa(5x^2+3a)[/tex]
Step-by-step explanation:
Given:
[tex]45x^3a+27xa^2= 9xa[/tex]
We need to complete this Statement.
By Solving the above equation we get;
We will take some common factor out so we will get;
[tex]45x^3a+27xa^2= 9xa(5x^2+3a)[/tex]
Hence the Complete statement is [tex]45x^3a+27xa^2= 9xa(5x^2+3a)[/tex]
plz help me plz I will mark brainlest for the person who answer first
Answer:
[tex] \frac{16}{20} [/tex]
Step-by-step explanation:
he sold 16 and he was supposed to sell 20. therefore it's 16/20. not relevant, but he sold 80% of the tickets
Answer:
I don't know why but I personally think its 1/4 I'm probably wrong but I'm trying my best well I hope dis helps and stay safe :3
At a music festival, T-shirts are sold for $15 and sweatshirts are sold for $20. The festival organizers pay x dollars for each T-shirt and y dollars for each sweatshirt. The festival sells 53 T-shirts and 39 sweatshirts.
Write and simplify an expression that represents the profit.
Answer:
38.0
Step-by-step explanation:
you have to you's the part and whole number ≤Answer:
53(15) + 39(20) = x
795 + 780
=1,575
Step-by-step explanation:
there are 53 t-shirts 15$ each. Then 39 sweatshirts each 20$. so 53*15 + 39*20 will be your final solution.
Write in vertex form y=x^2+16x-71
Good evening ,
Answer:
x^2+16x-71 = (x+8)²-135
Step-by-step explanation:
x^2+16x-71 = (x+8)²-8²-71
= (x+8)²-(64+71)
= (x+8)²-135.
:)
Find the y intersept of
y=logbase (b)(a-k) based on the constants b and k ?
Answer:
[tex](0, log_{b}(-k)), k < 0[/tex]
Step-by-step explanation:
[tex]y = \log_{b}(a - k)[/tex]
To find the y-intercept, set a = 0 and solve for y.
[tex]y = \log_{b}(0 - k)\\y = \log_{b}(-k)[/tex]
This equation is undefined for k ≥ 0.
There is a y-intercept only if k < 0. Only then can the argument of the log function be positive.
The y-intercept is at
[tex]\mathbf{(0, log_{b}(-k)), k < 0}[/tex]
For example, if b = 2 and k = -3, log₂(3) = 1.585
The intercept is at (0, 1.585).
Five tenths in standard and expanded form
Answer:
Standard form: 5 x 10^-1
Expanded form: 0.5
Step-by-step explanation:
hope this helps
Which three comparisons are true?
1/2 = 2/4
6/8 = 1/4
3/6 = 2/4
2/4 = 4/6
4/8 = 2/4
Answer:
The answer is 4/8=2/4 because 4/8 simplifying is 2/4 or 1/2
The true fraction comparisons are 1/2 = 2/4 and 4/8 = 2/4. The other comparisons are false. Simplifying fractions helps determine their equality.
Comparing Fractions:
Let's determine which of the given fraction comparisons are true:
1/2 = 2/4: To check this, we can simplify 2/4. Dividing both the numerator and the denominator by 2, we get 1/2. Thus, 1/2 equals 2/4. This is a true statement.6/8 = 1/4: We simplify 6/8 by dividing both the numerator and the denominator by 2, which gives us 3/4. This does not equal 1/4. This is a false statement.3/6 = 2/4: Simplifying 3/6 by dividing both the numerator and the denominator by 3, we get 1/2. Simplifying 2/4 gives us 1/2 as well. Therefore, 3/6 equals 2/4. This is a true statement.2/4 = 4/6: Simplifying 2/4 to 1/2 and simplifying 4/6 to 2/3 shows that 2/4 does not equal 4/6. This is a false statement.4/8 = 2/4: Simplifying 4/8 by dividing both the numerator and the denominator by 4, we get 1/2. Simplifying 2/4 also gives us 1/2. Thus, 4/8 equals 2/4. This is a true statement.The three true comparisons are: 1/2 = 2/4, 3/6 = 2/4, 4/8 = 2/4, and none from the rest.
A drawer contains 60 coins consisting of dimes and quarters. If the total value of the coins is $12.30, how many dimes and how many quarters are in the drawer?
Answer:
my mistake sorry
Step-by-step explanation:
Help me please with question 4 b
Answer:
see explanation
Step-by-step explanation:
The second term of sequence P is 2a + b
The third term of sequence Q is 3b + a
Equating gives
2a + b = 3b + a ( subtract a from both sides )
a + b = 3b ( subtract b from both sides )
a = 2b ← as required
Good evening ,
Step-by-step explanation:
4 (b)
The 2nd term of sequence P is 2a+b
The 3rd term of sequence Q is 3b+a
2a+b=3b+a ⇌ (2a-a) = (3b-b) ⇌ a=2b.
:)
In 12 weeks Jim earns $4500 Doing yardwork he earns the same amount each week let M stand for the amount and each week how much does Jim make in one week
Answer:
375
Step-by-step explanation:
Jim earns a total of $4500 over 12 weeks. To find out how much he makes weekly, divide the total earnings by the number of weeks, which is $4500 divided by 12, resulting in Jim earning $375 per week.
To calculate how much Jim makes in one week, we can divide his total earnings over the 12-week period by the number of weeks. Jim earns a total of $4500 over 12 weeks, so we can use the following equation where M stands for the amount Jim earns each week:
M = Total Earnings÷ Number of Weeks
M = $4500÷ 12
By performing the division, we find that Jim earns $375 per week. This is done by dividing 4500 by 12:
M = $375
Therefore, Jim makes $375 each week doing yardwork.
On a coordinate plane, a solid straight line has a positive slope and goes through (negative 4, 0) and (0, 2). Everything to the right of the line is shaded. Which linear inequality is represented by the graph? y ≤ One-halfx + 2 y ≥ One-halfx + 2 y ≤ One-thirdx + 2 y ≥ One-thirdx + 2
Answer:
[tex]y\le\dfrac{1}{2}x+2[/tex]
Step-by-step explanation:
On a coordinate plane, a solid straight line has a positive slope and goes through (negative 4, 0) and (0, 2). This line has the equation
[tex]y-0=\dfrac{2-0}{0-(-4)}(x-(-4))\\ \\y=\dfrac{1}{2}(x+4)\\ \\y=\dfrac{1}{2}x+2[/tex]
The origin belongs to the shaded region, so its coordinates must satisfy the inequality. Since
[tex]\dfrac{1}{2}\cdot 0+2=2\ge 0,[/tex]
then the correct inequality is
[tex]y\le\dfrac{1}{2}x+2[/tex]
Answer:
A
y ≤ [tex]\frac{1}{2}[/tex]x + 2
Step-by-step explanation:
❤❤Solve for the unknown by using the additive inverse. Type the FULL answer in the box, without using any spaces (ex., X=5).
–X + 4 = –2X – 6
Answer:
solve the inequality and enter your solution as an inequality comparing the variable to the solution
-19>x-26
Answer:
x < 7
Step-by-step explanation:
We are given an equation of inequality and we have to solve the equation as an inequality.
The given equation is - 19 > x - 26
⇒ - 19 + 26 > x
⇒ 7 > x
⇒ x < 7 {Since, if a > b then we can write b < a, as they are equivalent}
Hence,the solution of the equation of the inequality is x < 7. (Answer)
Find the value of 9y-9 given that 5y-2=3.
Answer:
0
Step-by-step explanation:
5y-2=3
5y=3+2
5y=5
y=5/5=1
9y-9=9(1)-9=9-9=0
How do I find the slope, y-intercept, and coordinates of (-1,7) (0,5)?
Answer:
The slope for the given points is - 2 , and y- intercept is 5
Step-by-step explanation:
Given points as :
( - 1 , 7 ) and ( 0 , 5 )
Now slope of line in points form as
Slope = m = [tex]\dfrac{y_2-y_1}{x_2-x_1}[/tex]
or, m = [tex]\dfrac{5 - 7}{0 + 1}[/tex]
or, m = - 2
so, Slope of line is - 2
Now equation of line is given as
y - [tex]y_1[/tex] = m × ( x - [tex]x_1[/tex] )
or, y - 7 = ( - 2 ) × ( x + 1)
or, y - 7 = - 2 x - 2
Or, equation of line is
y = - 2 x + 5
Now, for y - intercept , x = 0
So, from line equation
y = - 2 × 0 + 5
Or, y = 0 + 5
∴ y = 5
Hence The slope for the given points is - 2 , and y- intercept is 5 Answer
Which of the following is equivalent to 18 + 36?
A 29+16)
6/3 + 12)
7(2+4)
2+36)
Answer:
None.
Step-by-step explanation:
18+36=54
A) 29+16=45
B) 6/3+12=2+12=14
C) 7(2+4)=7(6)=42
D) 2+36=38
over what interval will the immediate value theorem apply
Answer:
Any [a,b] that does NOT include the x-value 3 in it.
Either an [a,b] entirely to the left of 3, or
an [a,b] entirely to the right of 3
Step-by-step explanation:
The intermediate value theorem requires for the function for which the intermediate value is calculated, to be continuous in a closed interval [a,b]. Therefore, for the graph of the function shown in your problem, the intermediate value theorem will apply as long as the interval [a,b] does NOT contain "3", which is the x-value where the function shows a discontinuity.
Then any [a,b] entirely to the left of 3 (that is any [a,b] where b < 3; or on the other hand any [a,b] completely to the right of 3 (that is any [a,b} where a > 3, will be fine for the intermediate value theorem to apply.
35 is 51% of what number?
Answer:
68.627
Step-by-step explanation:
51%=0.51
35/0.51=68.627
Answer:
68.627 is the answer!
Step-by-step explanation: I just took a test on it like 5 minutes ago!PLEASE MARK BRAINLIEST!!!! PLEASE!!! HAVE A NICE DAY!!!!
What is the product?
(negative 3 s + 2 t)(4 s minus t)
negative 12 s squared minus 2 t squared
negative 12 s squared + 2 t squared
negative 12 s squared + 8 s t minus 2 t squared
negative 12 s squared + 11 s t minus 2 t squared
Answer:
(d) negative 12 s squared + 11 s t minus 2 t squared is the PRODUCT.
Step-by-step explanation:
Here, the given expression is:
(negative 3 s + 2 t)(4 s minus t) = (- 3s + 2t) (4s - t)
Now, by DISTRIBUTIVE PROPERTY:
A(B-C) = AB - AC
Simplifying the given expression ,we get:
[tex](- 3s + 2t) (4s - t) = -3s(4s-t) + 2t(4s -t)\\= -3s(4s) -3s(-t) + 2t(4s) + 2t(-t) = -12s^2 + 3st + 8 st - 2t^2\\= -12s^2 + 11st - 2t^2\\\implies (- 3s + 2t) (4s - t) = -12s^2 + 11st - 2t^2[/tex]
Now, the resultant expression can also be written as
[tex]-12s^2 + 11st - 2t^2[/tex] = negative 12 s squared + 11 s t minus 2 t squared.
Hence, the option (4) is the correct option.
Answer:
option 4 is the answer
Step-by-step explanation:
Find four consecutive numbers whose sum equals 218
Answer: 53, 54, 55, and 56
Step-by-step explanation: This problem states that the sum of 4 consecutive numbers is 218 and it asks us to find the numbers.
4 consecutive numbers can be represented as followed.
X ⇒ first number
X + 1 ⇒ second number
X + 2 ⇒ third number
X + 3 ⇒ fourth number
Since the sum of our 4 consecutive numbers is 218, we can set up an equation to represent this.
X + X + 1 + X + 2 + X + 3 = 218
On the left side of the equation, we can combine our x's and our numbers.
4x + 6 = 218
-6 -6 ← subtract 6 from both sides of the equation
4x = 212
÷4 ÷4 ← divide both sides of the equation by 4
X = 53
X ⇒ first number = 53
X + 1 ⇒ second number = 54
X + 2 ⇒ third number = 55
X + 3 ⇒ fourth number = 56
Therefore, our 4 consecutive numbers are 53, 54, 55, and 56.
please help me first thinks
Answer:
3 minutes
5 minutes.
Step-by-step explanation:
It is given that, Amelia can wash 8 plates in 24 minutes.
So, if this rate remains constant then 1 plate will be washed in [tex] \frac{24}{8} = 3[/tex] minutes.
Again, it is given that, Amelia bakes 12 cookies in 60 minutes.
So, if this rate also remains constant then she will bake 1 cookie in [tex] \frac{60}{12} = 5[/tex] minutes. ( Answer )
Benjamin drove a distance of 301.5 miles in
4.5 h. If Benjamin drove at a constant rate, how
many miles per h did he drive?
Answer: 67 miles per hour
Step-by-step explanation: [tex]v = \frac{s}{t}[/tex] where v is velocity, s is space and t is time;
[tex]\frac{301.5 miles}{4.5 h}[/tex] = 67
What is the value of the expression if m=3 and n=2?
2(m3) + (6-n)n
Be sure to explain all of the steps you used in solving this problem.
Step-by-step explanation:
So fill it in
2(3 times 3)+(6-2)2
so
2(9)+(4)2
then
18+8=26
Answer: 26
hope that is right
Answer:
First plug in for m and n
2(3)(3) +(6-2)(2)
Next solve
18 + 8
Answer= 10
Step-by-step explanation:
using the z table, find the critical value for a=0.024 in a left tailed test
Answer:
Critical value is -1.98.
Step-by-step explanation:
Given:
The value of alpha is, [tex]\alpha=0.024[/tex]
Now, in order to find the critical value, we need to subtract alpha from 1 and then look at the z-score table to find the respective 'z' value for the above result.
The probability of critical value is given as:
[tex]P(critical)=1-\alpha=1-0.024=0.976[/tex]
So, from the z-score table, the value of z-score for probability 0.976 is 1.98.
Now, in a left tailed test, we multiply the z value by negative 1 to arrive at the final answer. We do so because the area to the left of mean in a normal distribution curve is negative.
So, the z-score for critical value 0.024 in a left tailed test is -1.98.
The critical value for α = 0.024 in a left-tailed test is -1.98.
To find this value, we locate α = 0.024 in the z-table. The z-table is a table that shows the probability of obtaining a z-score less than or equal to a certain value.
The z-score is a measure of how many standard deviations a particular data point is away from the mean of the population.
Here is the critical value for α = 0.024 in a left-tailed test: -1.98
In this case, we are looking for the z-score that corresponds to a probability of 0.024. This z-score is -1.98. Therefore, if our test statistic is less than or equal to -1.98, we will reject the null hypothesis.
For more questions on critical value
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Find the midpoint between A and C.
A. (1, 1)
B. (5, -7)
C. (-5, 7)
D. (0.5, 0.5)
Answer:
D. [tex]\displaystyle (0,5, 0,5)[/tex]
Step-by-step explanation:
C(3, −3) and A(−2, 4)
Just by looking at the graph, we can CLEARLY see that answer choice D is EXACTLY halfway in between the two given endpoints.
I am joyous to assist you anytime.