Answer:
[tex]a_7=\dfrac{4}{729}[/tex]
Step-by-step explanation:
General form of geometric progression: [tex]a_n=ar^{n-1}[/tex]
(where [tex]a[/tex] is the initial term and [tex]r[/tex] is the common ratio)
Given:
[tex]a=4[/tex][tex]r=\dfrac13[/tex][tex]\implies a_n=4\left(\dfrac13\right)^{n-1}[/tex]
Therefore, when n = 7:
[tex]\implies a_7=4\left(\dfrac13\right)^{7-1}[/tex]
[tex]\implies a_7=4\left(\dfrac13\right)^{6}[/tex]
[tex]\implies a_7=4\left(\dfrac{1^6}{3^6}\right)[/tex]
[tex]\implies a_7=4\left(\dfrac{1}{729}\right)[/tex]
[tex]\implies a_7=\dfrac{4}{729}[/tex]
A student wants to create a 2:1 scale drawing of the classroom. Is this an appropriate scale to use? Why or why not?
Answer:
I don’t know figure it out
Step-by-step explanation:
Which of the following numbers is farthest from the number 2 on the number line
3 -3 6 -6 10
Answer:
-6 is the correct answer
Step-by-step explanation:
permutation:
A college has 7 good badminton players.In how many ways can a team of 5 players be selected??
Formula for permutation is:
[tex] \boxed{ \tt^{n} C_{r} = \frac{n!}{r!(n - r)!} }[/tex]
Calculation,Plug in the values:
Required number of ways = ²C7
n = 7r = 5[tex] \sf \frac{7!}{5!(7 - 5)!} [/tex]
[tex] \sf \frac{7 \times 6 \times \cancel{5!}}{ \cancel{5! }\times 2!} [/tex]
[tex] \sf \frac{7 \times 6 }{ 2!} [/tex]
[tex] \sf \frac{42 }{ 2!} [/tex]
[tex] \sf \frac{42 }{ 2} = 21[/tex]
Thus, The players can be selected in 21 different ways!!~
Here one player cannot be repeated so repeating is not allowed.
Hence we use combination heren=7r=5Total ways
[tex]\\ \rm\hookrightarrow ^nC_r=\dfrac{n!}{r!(n-r)!}[/tex]
Put values[tex]\\ \rm\hookrightarrow ^7C_5[/tex]
[tex]\\ \rm\hookrightarrow \dfrac{7!}{5!(7-5)!}[/tex]
[tex]\\ \rm\hookrightarrow \dfrac{7!}{5!2!}[/tex]
[tex]\\ \rm\hookrightarrow \dfrac{7\times 6\times 5!}{5!(2)}[/tex]
[tex]\\ \rm\hookrightarrow \dfrac{7(6)}{2}[/tex]
[tex]\\ \rm\hookrightarrow \dfrac{42}{2}[/tex]
[tex]\\ \rm\hookrightarrow 21ways[/tex]
i need the steps to the perimeter and area the radius is 5 ft
Jeremy received a basket containing 8 red and 4 green apples.
When he randomly selects and eats two apples from the basket, these are
events.
The probability that both of the apples Jeremy eats are green is
.
Answer:
It is more probable that he pick two red apples than green. Because their are more red apples thank green so the chances of him picking green apples are very slim.
Have a nice day/night!
This is an example of probability without replacement and can simply be done using the formula.
The probability that both apples he ate will be green is 1/12
Probability without replacementThis is done when we pick a value from a data set and does not replace it and hence affects the value of the original data set.
Data;
Red = 8Green = 4Jeremy ate two apples from the basket and the probability this is green would be
[tex]8 + 4 = 12\\[/tex]
The number of green apples are = 4
[tex]\frac{4}{12} * \frac{3}{12} = \frac{12}{144} = \frac{1}{12}[/tex]
The probability that both apples he ate will be green is 1/12
Learn more on probability without replacement here;
https://brainly.com/question/11405286
#SPJ2
Can you help me please understand this question
Answer:
D
Step-by-step explanation:
ey/n + k = t
To get y on its own, the first thing we need to do is subtract k from both sides to get ey/n = t - k. Next, we can multiply both sides by n to get ey = n(t - k). Finally, we can divide by e to get y = n(t - k)/e
Hope this helps!
38. Find the value of x in isosceles trapezoid ABCD.
Given: AC = 3x - 16 and BD = 10x-86
Answer:
10
Step-by-step explanation:
Diagonals of a isosceles trapezoid are congruent
3x - 16 = 10x - 86 Subtract 3x from both sides and add 86 to both sides
70 = 7x Divide
x = 10
a.
A student writes an explicit formula to represent the value of the
computer after n years below. What is the student's error? Explain. (2 points)
an= $1,500 (-15)n-1
Using exponential function concepts, it is found that the student error is in the subtraction of the day rate, as he forgot to subtract from 100% = 1.
What is an exponential function?A decaying exponential function is modeled by:
[tex]A(t) = A(0)(1 - r)^t[/tex]
In which:
A(0) is the initial value.r is the decay rate, as a decimal.In this problem, the initial value of the computer is of A(0) = 1500, while it decays at a rate of 15% a year, hence r = 0.15 and the equation is:
[tex]A(t) = A(0)(1 - r)^t[/tex]
[tex]A(t) = 1500(0.85)^t[/tex]
Or equivalently, as a sequence:
[tex]a_n = 1500(0.85)^{n-1}[/tex]
Hence, it is found that the student error is in the subtraction of the day rate, as he forgot to subtract from 100% = 1.
More can be learned about exponential function concepts at https://brainly.com/question/25537936
Please help solve the graph
Answer:
Put a point on (4, -4)
Count 1 down from the purple point, then go four points to the right.
Step-by-step explanation:
y=[tex]-\frac{1}{4}[/tex]x-3
the -1/4 is what tells you how much to move the point from the given one. In this case, it is one down (-1), and four to the right (4).
Write an equation that relates the angles in a triangle.
The measure of angle A is 45 degrees. The measure of angle B is b degrees. The measure of angle C is 3b degrees.
Step-by-step explanation:
please mark me as brainlist please
A state university locks in costs for a student once a student starts attending the university. The total cost is $22,500. A student has the following help in covering the costs of school.
An academic scholarship of $10,000.
Other scholarships and grants of $4,400.
Parents pay $1,800.
What is the amount that the student will need to save every month in order to pay off the remaining costs in 10 months?
a. $525
b.$630
c.$1,200
d. $1,440
Answer:B $630 Per Month So B
Step-by-step explanation: $22,500-$10,000=$12,500-$4,400=$8,100-$1,800=$6,300/10Months=$630
Answer:
$690
Step-by-step explanation:
If the student will need to save every month in order to pay off the remaining costs in 10 months, the amount she will need to save per month is $690
Amount and interest
Given the following information from the question
The total cost of fee = $23,500
Amount got as help;
An academic scholarship of $8,200.
Other scholarships and grants of $7.400.
Grandparents pay $1,000
Amount she had = 8200 + 7400 + 1000
Amount she had = $16600
Amount remaining = 23500 - 16600
Amount remaining = $6900
If the student will need to save every month in order to pay off the remaining costs in 10 months, the amount she will need to save per month is $690
https://brainly.com/question/22112075
Question 1
Which best describes the error in solving the equation?
Both sides of the equation should have been multiplied by 28.
Both sides of the equation should have been multiplied by 28.
Both sides of the equation should have been divided by 28.
Both sides of the equation should have been divided by 28.
Both sides of the equation should have been multiplied by 4.
Both sides of the equation should have been multiplied by 4.
From both sides of the equation, 4 should have been subtracted.
From both sides of the equation, 4 should have been , subtracted.
Question 2
Find the correct solution.
The correct solution is x=
.
Answer:
x=112
Step-by-step explanation:
What is the slope of the line that contains these points?
The average number of words in a romance novel is 64,436 and the standard deviation is 17,071. Assume the distribution is normal. Let X be the number of words in a randomly selected romance novel. Round all answers to 4 decimal places where possible.
a. What is the distribution of X? X ~ N(
64436
Correct,
17071
Correct)
b. Find the proportion of all novels that are between 72,972 and 90,043 words.
c. The 75th percentile for novels is
words. (Round to the nearest word)
d. The middle 60% of romance novels have from
words to
words. (Round to the nearest word)
b. You're looking for the probability
Pr [72,972 ≤ X ≤ 90,043]
Transform X to Z ∼ Normal(0, 1) using the rule
X = µ + σ Z
with µ = 64,436 and σ = 17,071. Then the probability is
Pr [(72,972 - µ)/σ ≤ (X - µ)/σ ≤ (90,043 - µ)/σ]
≈ Pr [0.5000 ≤ Z ≤ 1.5000]
You probably have a z-score table available, so you can look up the probabilities to be about
Pr [Z ≤ 0.5000] ≈ 0.6915
Pr [Z ≤ 1.5000] ≈ 0.9332
and then
Pr [0.5000 ≤ Z ≤ 1.5000] ≈ 0.9332 - 0.6915 = 0.2417
c. The 75th percentile word count that separates the lower 75% of the distribution from the upper 25%. In other words, its the count x such that
Pr [X ≤ x] = 0.75
Transforming to Z and looking up the z-score for 0.75, we have
Pr [(X - µ)/σ ≤ (x - µ)/σ] ≈ Pr [Z ≤ 0.6745]
so that
(x - µ)/σ ≈ 0.6745
x ≈ µ + 0.6745σ
x ≈ 75,950
d. Because the normal distribution is symmetric, the middle 60% of novels have word counts between µ - k and µ + k, where k is a constant such that
Pr [µ - k ≤ X ≤ µ + k] = 0.6
Also due to symmetry, we have
Pr [µ - k ≤ X ≤ µ + k] = 2 Pr [µ ≤ X ≤ µ + k]
⇒ Pr [µ ≤ X ≤ µ + k] = 0.3
Transform X to Z :
Pr [(µ - µ)/σ ≤ (X - µ)/σ ≤ (µ + k - µ)/σ] = 0.3
⇒ Pr [0 ≤ Z ≤ k/σ] = 0.3
⇒ Pr [Z ≤ k/σ] - Pr [Z ≤ 0] = 0.3
⇒ Pr [Z ≤ k/σ] - 0.5 = 0.3
⇒ Pr [Z ≤ k/σ] = 0.8
Consult a z-score table:
Pr [Z ≤ k/σ] ≈ Pr [Z ≤ 0.8416]
⇒ k/σ ≈ 0.8416
⇒ k ≈ 14,367
Then the middle 60% of novels have between µ - k = 50,069 and µ + k = 78,803 words.
Find the value of K when K = 5n^2 + w. when n = 4 and w = -6.
Answer:
[tex]\bold{K = 5n {}^{2} + w} [/tex]
Given ,
value of n = 4
value of w = - 6
Then ,
[tex]\bold{K = 5(4) {}^{2} + ( - 6)} \\\bold{ K = 5(16) - 6} \\\bold{ K = 80 - 6} \\ \fbox\pink{K = 74}[/tex]
hope helpful~
Answer:
Value of k is 74Step-by-step explanation:
Here we have been provided with the values of n and w that is 4 and -6 respectively.
Equation that we have,
k = 5n² + wSubstituting the values of n and w in the equation,
[tex] \implies \: \sf{k \: = \: 5(4) {}^{2} \: + \: ( - 6)}[/tex]
[tex]\implies \: \sf{k \: = \: 5(4 \times 4) \: + \: ( - 6)}[/tex]
[tex] \implies \: \sf{k \: = \: 5 \: (16) \: + \: ( - 6)}[/tex]
Multiplying 16 by 5,
[tex]\implies \: \sf{k \: = \: 5 \: \times 16 \: + \: ( - 6)}[/tex]
[tex]\implies \: \sf{k \: = \: 80 \: + \: ( - 6)}[/tex]
[tex]\implies \: \sf{k \: = \: 80 \: - \:6)}[/tex]
Subtracting 6 from 80,
[tex]\implies \: \red{\bf{k \: = \: 74}}[/tex]
Therefore, value of k is 74..!!
Let f(x) = 22 + 3.0 +2
What is the average rate of change of f(x) from 3 to 6?
Someone Please Help i need this awnser
Answer:
a1 = 8
a2 = 6
a3 = 4
a4 = 2
a5 = 0
So it would be: 8, 6, 4, 2, 0,...
Step-by-step explanation:
Just plug the term number into the equation.
an = -2n + 10
First term:
a1 = -2(1) + 10 = 8
Second term:
a2 = -2(2) + 10 = 6
Third term:
a3 = -2(3) + 10 = 4
and so on...
Hope this helped! :)
the average cost of 3 books 3:2:5 is $50. How much does each book cost?
Step-by-step explanation:
We have to find what one share is
we have 3 shares + 2 shares + 5 shares
so he have a total of 10 shares
next, we divide 50 by total shares to get what one share is
50 ÷ 10 = 5
5 is one share
fins what each is
for 3
3 shares so 3 fives
3 × 5 = 15
for 2
2 shares so 2 fives
2 × 5 = 10
and for 5
can you work it out and leave in the comments i will say if it is correct
Please list all of the fractions that are greater than 7/12
Answer:
5/9, 9/12, 6/7, 6/9 are the ones I believe so far
Step-by-step explanation:
Tim bought a certain number of bags of chips that each cost $1.05. Write an expression to show the total cost.
x is the number of bags of chips
1.05x means "1.05 times x". You could write 1.05*x or omit the multiplication symbol all together.
For example, if he bought x = 100 bags then he would spend 1.05*x = 1.05*100 = 105 dollars.
In this problem, p is in dollars and x is the number of units.
Find the producer's surplus at market equilibrium for a product if its demand function is p = 121 − [tex]x^{2}[/tex] and its supply function is p = [tex]x^{2}[/tex] + 6x + 65. (Round your answer to the nearest cent.)
The market equilibrium is the point where the demand and supply functions are equal
The producer's surplus at market equilibrium for a product is #105
How to determine the producer's surplusThe functions are given as:
[tex]p = 121 - x^2[/tex]
[tex]p = x^2 + 6x + 65[/tex]
Equate both functions
[tex]x^2 + 6x + 65 = 121 - x^2[/tex]
Collect like terms
[tex]x^2 + x^2 + 6x + 65 - 121 = 0[/tex]
Evaluate the like terms
[tex]2x^2 + 6x -56 = 0[/tex]
Divide through by 2
[tex]x^2 + 3x -28 = 0[/tex]
Expand
[tex]x^2 + 7x - 4x - 28 = 0[/tex]
Factorize
[tex]x(x + 7) - 4(x +7)= 0[/tex]
Factor out x + 7
[tex](x - 4)(x +7)= 0[/tex]
Solve for x
x = 4 or x = -7
The number of units cannot be negative,
So, we have:
x = 4
Substitute 4 for x in [tex]p = 121 - x^2[/tex]
[tex]p = 121 - 4^2[/tex]
p = 105
Hence, the producer's surplus at market equilibrium for a product is #105
Read more about equilibrium at:
https://brainly.com/question/110832
answer? to this problem please
Answer:
D
Step-by-step explanation:
There is only one vertical asymptote, x = 1.
Only D has vertical asymptote, x = 1.
Help with number 10 please
Answer:
The answer is 3
Step-by-step explanation:
I did this quiz before
Please give me right answer i mark you brainliest if you answer fast , At a stationery sale, pencils were sold in packets of 4 and erasers were sold in packets of 6. The cost of a packet of pencils was the same as the cost of a packet of erasers. Mrs Tan bought 12 pencils for $6. What was the cost of a packet o erasers?
Answer:
The answer is $2
I packet has 4 pencils so 12 pencils is 3 packets
if 3 packets cost $6 1 packet costs $2 and since 1 packet of pencils is the same price as one packet of erasers 1 packet of erasers cost $2
fill in the equation please
Answer:
57753.
Step-by-step explanation:
Basta pm na Lang.
Here is a rectangle ABCD. A B 20 cm D с 30 cm The length of the rectangle is increased by 10%. The width of the rectangle is increased by 5%. Find the percentage increase in the perimeter of the rectangle.
Answer:
8%
Step-by-step explanation:
The original perimeter is 100cm
The 20cm is representative of the width
30cm is representative of the length
length is increased by 10%
30+(.10 x 30)
(1 + .10) × 30
(100% + 10%) × 30
110% × 30
110 ÷ 100 × 30
110 × 30 ÷ 100
3,300 ÷ 100
= 33
length is increased by 5%
20 + (5% × 20) =
20 + 5% × 20 =
(1 + 5%) × 20 =
(100% + 5%) × 20 =
105% × 20 =
105 ÷ 100 × 20 =
105 × 20 ÷ 100 =
2,100 ÷ 100 =
= 21
New perimeter: 108 cm
Percentage increase:
(108-100):100*100 =
(108:100-1)*100 =
108-100 = 8
= 8%
Holly attended a conference at 11:30 A.M. The conference ended at 1:05 P.M. How long does the conference last
i neeeeeeeeeeeeeeeeeeddddddddddddddd helpppp
A company sells each product they make for $90.00. They pay $2,300.00 in monthly costs, such as rent and bills, as well as $75.00 in manufacturing costs per unit. If the company sold 495 units last month, what was their total profit?
A.
$34,825.00
B.
$6,610.00
C.
$42,175.00
D.
$5,125.00
Answer:
Option D
Step-by-step explanation:
Given the following question:
Product costs: $90
Monthly bills: $2,300
Manufacturing costs: $75
How much profit did they make in one month if they sold 495 units?
In order to find the answer, we first need to multiply the cost of the product by the units sold last month, then subtract the bills/manufacturing costs.
One unit = 90 dollars
495 units sold last month
[tex]90\times495=44550[/tex]
[tex]=44550[/tex]
The company made 44,550 from the product last month.
Now apply the fees/costs:
2,300 dollars in monthly costs
75 dollars in manufacturing costs PER UNIT
[tex]44550-2300=42250[/tex]
[tex]75\times495=37125[/tex]
[tex]42250-37125=5125[/tex]
[tex]=5125[/tex]
Which means the company made a total profit of "$5,125 dollars" or option D last month.
Hope this helps.
Please help!! the problem is attached for the standard deviation
Answer:
9.24
Step-by-step explanation:
How to make 2 numbers add up to 120 but one of the numbers is 25 more than the other.
Answer:
The answer is 47.5 and 72.5
Step-by-step explanation:
Given;The sum of two numbers is equal to 120.So,
Let the number be x and the other number be (x + 25).
Now,
x + (x + 25) = 120
x + x + 25 = 120
2x + 25 = 120
2x + 25 – 25 = 120 – 25
2x = 95
2x/2 = 95/2
x = 47.5
Thus, The number be x is equal to 47.5 and other which is more 25 than other number is (47.5 + 25) = 72.5
-TheUnknownScientist 72
Answer:
The numbers are 47.5 and 72.5
Step-by-step explanation:
Let "x" represent the larger number, then the smaller number would be equivalent to:
[tex]x-25[/tex]
Larger Number + Smaller Number = 120
Therefore...
[tex]x+x-25=120[/tex]
Combine like terms:
[tex]2x-25=120[/tex]
Add 25 to both sides (note we are utilizing the Addition Property of Equality which essentially states that if you add a value to one side of the equation, you must add it to the other side as well):
[tex]2x=120+25\\2x=145[/tex]
Divide both sides by 2 (note we are now utilizing the Division Property of Equality which essentially states that if you divide a value from one side of the equation, you must divide it from the other side as well; the same as the Addition Property of Equality, but with division instead):
[tex]x=\frac{145}{2}\\x=72.5[/tex]
Therefore...
[tex]x-25=72.5-25=47.5[/tex]