Answer:
196 in/cm/m²
Step-by-step explanation:
Given that the scale factor is a : b , then the area factor is a² : b² Here the scale factor is 1 : 7 , thus area scale factor is 1² : 7² = 1 : 49 That is the area of the dilated square is 49 times the original square. area of dilated square = 4 × 49 = 196 in/cm/m²
Maite has money in an interest-bearing account. The table shows how much money is in the account at the end of each year.
N
Year Amount
1 $1,000.00
$1,030.00
3 $1,060.90
4 $1,092.73
5 $1,125.51
This situation represents
sequence.
The common
is
At the end of the seventh year, Maite will have $
in the account
Determining how much money will be in the account of Maite at the end of each year, we use an exponential growth factor, since this is a geometric sequence.
1. This situation represents a geometric sequence.
A geometric sequence increases by a common exponential growth factor.
2. The common exponential factor is 1.03 (which gives a growth rate of 3% annually). See how this factor is determined below.
3. At the end of the seventh year, Maite will have $1,194.05 in the account. See the calculation below.
Data and Calculations:
Year Amount
1 $1,000.00
2 $1,030.00
3 $1,060.90
4 $1,092.73
5 $1,125.51
6 $1,159.27 ($1,125.51 * 1.03)
7 $1,194.05 ($1,159.27 * 1.03)
The common exponential factor = 1.03 (1 + 0.03)
To obtain the common exponential factor, subtract Year 2 account balance from Year 1 account balance. Divide the result by Year 1 account balance. This operation can also be carried out with Year 2 and Year 3 balances or Year 4 and Year 5 balances.
To determine how much money will be in the account of Maite at the end of Year 6, using Year 5 as a base = (Year 5 account balance * Exponential Factor)
= $1,159.27 ($1,125.51 * 1.03)
To determine Year 7 account balance, we use Year 6 above as the base
= $1.194.05 ($1,159.27 * 1.03)
Learn more about geometric sequence and exponential growth here: https://brainly.com/question/7154553
Answer:
This situation represents a geometric sequence.
The common ratio is 1.03
At the end of the seventh year, Maite will have $1,194.06 in the account.
Step-by-step explanation:
Plato
At a Noodles & Company restaurant, the probability that a customer will order a nonalcoholic beverage is .50. Find the probability that in a sample of 14 customers, at least 7 will order a nonalcoholic beverage
For each customer, there are only two possible outcomes. Either they will order an alcoholic beverage, or they will not. The probability of a customer ordering an alcoholic beverage is independent of any other customer, which means that the binomial probability distribution is used to solve this question..
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
At a Noodles & Company restaurant, the probability that a customer will order a nonalcoholic beverage is .50
This means that [tex]p = 0.5[/tex]
Sample of 14 customers
This means that [tex]n = 14[/tex]
Probability that at least 7 will order a nonalcoholic beverage
This is:
[tex]P(X \geq 7) = 1 - P(X < 7)[/tex]
In which
[tex]P(X < 7) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) + P(X = 6)[/tex]
Then
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{14,0}.(0.5)^{0}.(0.5)^{14} = 0.0001[/tex]
[tex]P(X = 1) = C_{14,1}.(0.5)^{1}.(0.5)^{13} = 0.0009[/tex]
[tex]P(X = 2) = C_{14,2}.(0.5)^{2}.(0.5)^{12} = 0.0056[/tex]
[tex]P(X = 3) = C_{14,3}.(0.5)^{3}.(0.5)^{11} = 0.0222[/tex]
[tex]P(X = 4) = C_{14,4}.(0.5)^{4}.(0.5)^{10} = 0.0611[/tex]
[tex]P(X = 5) = C_{14,5}.(0.5)^{5}.(0.5)^{9} = 0.1222[/tex]
[tex]P(X = 6) = C_{14,6}.(0.5)^{6}.(0.5)^{8} = 0.1833[/tex]
So
[tex]P(X < 7) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) + P(X = 6) = 0.0001 + 0.0009 + 0.0056 + 0.0222 + 0.0611 + 0.1222 + 0.1833 = 0.3954[/tex]
[tex]P(X \geq 7) = 1 - P(X < 7) = 1 - 0.3954 = 0.6046[/tex]
0.6046 = 60.46% probability that at least 7 will order a nonalcoholic beverage.
For more on the binomial distribution, you can check https://brainly.com/question/15557838
(2X²+3X-1)+(X²-2X+3)
Answer:
3x^2+x+2
Step-by-step explanation:
Let's simplify step-by-step.
2x2+3x−1+x2−2x+3
=2x2+3x+−1+x2+−2x+3
Combine Like Terms:
=2x2+3x+−1+x2+−2x+3
=(2x2+x2)+(3x+−2x)+(−1+3)
Choose the number that belongs to the set described
Answer:
Natural numbers,integers, rational numbers, irrational numbers.
The measure of one of the small angles of a right triangle is 45 less than twice the measure of the other small angle. Find the measure of both angles.
Answer:
Step-by-step explanation:
A right triangle has one right angle and two acute angles.
A and B are the acute angles.
A+B = 90°
One acute angle is 45 less than twice the other acute angle.
A = 2B-45°
(2B-45°) + B = 90°
3B = 135°
B = 45°
A = 45°
what are the coordinates of A,B and C
Answer:
Please display full question . your question is incomplete ..
Answer:
Step-by-step explanation:
Please display a picture
Thomas' dog
had 10 puppies. 2
were yellow, 5. were
mixed and the rest
were black. What
decimal represents black dogs out of the total.
black dogs out of
the total?
Answer
0.3
Step-by-step explanation:
A hot air ballon is hovering 94 meters above the ground and begins to assend at a rate of 8 meters per second Let y be the height of the balloon in meters seconds after it begins to assend. Write an equation in slope-intercept form that models the height of the balloon. And how high is the ballon after 25 seconds?
Hi
let's call X amount of second going and Y the height reach by the ballon.
so Y=8X+94
f(x) = 8X+94
If you want to know how high will the ballon be in 25 seconds, remplace X by 25 and do the math. Have fun .
what is equivalent to (160 times243)1/5th
9514 1404 393
Answer:
480
Step-by-step explanation:
The expression evaluates to ...
160·243^(1/5) = 160·(3^5)^(1/5) = 160·3 = 480
Consider the following theorem. Theorem If f is integrable on [a, b], then b a f(x) dx = lim n→[infinity] n i = 1 f(xi)Δx where Δx = b − a n and xi = a + iΔx. Use the given theorem to evaluate the definite integral. 9 (x2 − 4x + 6) dx 1
Split up the interval [1, 9] into n subintervals of equal length (9 - 1)/n = 8/n :
[1, 1 + 8/n], [1 + 8/n, 1 + 16/n], [1 + 16/n, 1 + 24/n], …, [1 + 8 (n - 1)/n, 9]
It should be clear that the left endpoint of each subinterval make up an arithmetic sequence, so that the i-th subinterval has left endpoint
1 + 8/n (i - 1)
Then we approximate the definite integral by the sum of the areas of n rectangles with length 8/n and height [tex]f(x_i)[/tex] :
[tex]\displaystyle \int_1^9 (x^2-4x+6) \,\mathrm dx \approx \sum_{i=1}^n \frac8n\left(\left(1+\frac8n(i-1)\right)^2-4\left(1+\frac8n(i-1)\right)+6\right)[/tex]
Take the limit as n approaches infinity and the approximation becomes exact. So we have
[tex]\displaystyle \int_1^9 (x^2-4x+6) \,\mathrm dx = \lim_{n\to\infty} \sum_{i=1}^n \frac8n\left(\left(1+\frac8n(i-1)\right)^2-4\left(1+\frac8n(i-1)\right)+6\right) \\\\ = \lim_{n\to\infty} \frac8n \sum_{i=1}^n \left(1+\frac{16}n(i-1)+\frac{64}{n^2}(i-1)^2-4-\frac{32}n(i-1)+6\right) \\\\= \lim_{n\to\infty} \frac8{n^3} \sum_{i=1}^n \left(64(i-1)^2-16n(i-1)+3n^2\right) \\\\= \lim_{n\to\infty} \frac8{n^3} \sum_{i=0}^{n-1} \left(64i^2-16ni+3n^2\right) \\\\= \lim_{n\to\infty} \frac8{n^3} \left(64\sum_{i=0}^{n-1}i^2 - 16n\sum_{i=0}^{n-1}i + 3n^2\sum{i=0}^{n-1}1\right) \\\\= \lim_{n\to\infty} \frac8{n^3} \left(\frac{64(2n-1)n(n-1)}{6} - \frac{16n^2(n-1)}{2} + 3n^3\right) \\\\= \lim_{n\to\infty} \frac8{n^3} \left(\frac{49n^3}3-24n^2+\frac{32n}3\right) \\\\= \lim_{n\to\infty} \frac{8\left(49n^2-72n+32\right)}{3n^2} = \boxed{\frac{392}3}[/tex]
(PLEASE HELP ITS THE LAST QUESTION)
Find the measure of angle L.
A) 21.6°
B) 43.8°
C) 33.4°
D) 21.9°
Answer:
A
Step-by-step explanation:
lemme meh knw if it was helpful..
Enter a value that would not make relation a function (-4,0),(?,8),(9,0),(-5,2)
Answer:
Step-by-step explanation:
? = -4, 9, or -5
The solution is, b.) y = 2(x+9) ( x - 4) and, c.) y = - 2(x+9) ( x - 4), these function's graph has a zeros at (4,0) and (-9,0).
What are zeros of quadratic function?The zero of the function is where the y-value is zero. The zero of a function is any replacement for the variable that will produce an answer of zero. Graphically, the real zero of a function is where the graph of the function crosses the x‐axis; that is, the real zero of a function is the x‐intercept(s) of the graph of the function.
here, we have,
from the given the information , we get,
If one zero is x= 4, then one factor of the expression would be (x - 4).
Similarly if another zero is x=-9, then another factor of the expression would be (x+9)
We have two answers with these two factors and both are possible. So, the answers are b and c.
Hence, The solution is, b.) y = 2(x+9) ( x - 4) and, c.) y = - 2(x+9) ( x - 4), these function's graph has a zeros at (4,0) and (-9,0).
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complete question:
Which function's graph has a zeros at (4,0) and (-9,0)?
I am 10% older than my wife,my wife is x% younger than i am find x
You = her*1.1
her = you/1.1 = you*0.9090...
her = you - you*(1 - 0.9090...) = you - you*0.0909...
--> 9.09% younger
x = 9.09
HOPE SO IT HELPS YOU
The required value of x is 0.909.
What is percentage?A percentage is a value that indicates 100th part of any quantity.
A percentage can be converted into a fraction or a decimal by dividing it by 100.
Given that,
The husband is 10% older than wife.
And, the wife is x% younger than husband.
Suppose the age of husband is h and of wife be w.
The following equations can be written for the given case,
(h - w)/w × 100 = 10 (1)
And, (h - w)/h × 100 = x (2)
Divide both equations to get,
h/w = 10/x
Equation (1) can be written as,
h/w - 1 = 10
=> 10/x - 1 = 10
=> 10/x = 11
=> x = 10/11
=> x = 0.909
Hence the value of x for the given case is 0.909.
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Show that the points A(2, 2), B(5,7), C(-5, 13), and D(-8, 8) are the vertices of a rectangle.
A. AB = CD = 18; BC = DA = 4
B. AB = CD = 34: BC = DA = V136
C. AC = BD = 170
D. AB = CD = 34: BC = DA = V136; AC = BD = v170
Please select the best answer from the choices provided
Answer:
Step-by-step explanation:
Using V as a substitute for √ is misleading. Better to write “square root of x”.
AC = BD = √170
The employee engagement score for a team was 4.89 this month. The score has been improving at a rate of 12% per month. What was the score 4 months ago?
The engagement score in 4 months would be 7.69
We are to determine the future value of engagement score in 4 months
The formula for calculating future value:
FV = P (1 + r)^n
FV = Future value
P = Present value = 4.89
R = rate of increase = 12%
N = number of months = 4
4.89 ( 1.12)^4 = 7.69
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the lengths of the sides of a triangle are in as ratio 3:4:5., find the lengths of the sides of this triangle if its perimeter is 96 cm
Answer:
24,32,40
Step-by-step explanation:
side 1: side2: side3: total
3 4 5 3+4+5=12
The total is the perimeter = 96
96/12 = 8
Multiply each term by 8
side 1: side2: side3: total
3*8 4*8 5*8 12*8
24 32 40 96
Let the sides of the triangle ABC be 3x , 4x and 5x.
Where x is a multiple.Perimeter of triangle = 3x + 4x + 5x
[tex] \bf \rightarrow \: 96 \: = \: 12x[/tex]
[tex]\bf \rightarrow \: \frac{96}{12} \: = \: x \\ [/tex]
[tex]\bf \rightarrow \: \cancel\frac{96}{12} \: ^{8} \: = \: x \\ [/tex]
[tex]\bf \rightarrow \: x \: = \: 8[/tex]
Required sides are :[tex] \bf \implies \: 3x \: = \: 3 \: \times \: 8 \: = 24[/tex]
[tex]\bf \implies \: 4x \: = \: 4 \: \times \: 8 \: = 32[/tex]
[tex]\bf \implies \: 5x \: = \: 5 \: \times \: 8 \: = 40[/tex]
Hence , the sides of the triangle are 24 , 32 and 40.
please help me I need help
Answer:
This is so hard for me. I can't understand. I am in grade 9 now.
The perimeter of a square is 14 cm. Find the area
Step-by-step explanation:
A = 12.25cm2
P perimeter 14cm
Answer:
A=12.25cm²
P=14
Pass The following Journal Entry .
1. Salaries remaining unpaid Rs.15000 and rent due to landlord Rs.2000
Please This is Accountancy questions Don't spaim
good lesson udayy...........
Step-by-step explanation:
1.→ Salaries A/c Dr. 15,000 To O/s Salaries A/c 15,000→ Rent A/c Dr. 2,000To O/s Rent A/c 2,0001st (´-ω-｀)))。。
Convert the degree measurement to radians. Express answer as multiple of π: - 60°
A. π/3
B. −π/4
C. −π/5
D. −π/3
Answer:
-pi/3
Step-by-step explanation:
To convert from degree to radians, multiply by pi/180
-60 * pi/180 = -60/180 *pi = -pi/3
Answer:
D. -pi/3
Step-by-step explanation:
degree to radians formula: x=degree, x*pi/180
x=-60
-60*pi/180=-pi/3
Giải phương trình vi phân cấp 2
Answer:
bajskalakbskajalabsnsja
SOMEONE PLEASEEEEEEEEEE HELP!!!!!!!!1
Answer: Angle LMN = 45
Step-by-step explanation:
The line MN will be parallel to the side Line JK
And LJ will be transversal
Therefore
Angle LMN = LJK (Corresponding angles)
ATQ
⇒3 + 6x = 101 - 8x
⇒6x + 8x = 101 -3
⇒14x = 98
⇒x = 98/14
⇒x = 7
Angle LMN = 3 + 6x
= 3 + 6(7)
= 3 + 42
= 45
Therefore Angle LMN will be 45°
Must click thanks and mark brainliest
Simplify the following expression. 12a + 2a
Answer:
[tex]14a[/tex]
Step-by-step explanation:
Combining like-terms gives us [tex]12a+2a=14a[/tex]
Hope this helped!
Answer:
14a
Step-by-step explanation:
what decimal is equivalent to 0.85
Answer: 17/20
Step-by-step explanation:
0.85 = 85/100 = 17/20
The number 0.85 can be written using the fraction 85/100 which is equal to 17/20 when reduced to lowest terms.
Can anyone please help me with this ?
Answer:
6.7
Step-by-step explanation:
The formula for volume is V=lwh.
320=(6)(8)x
Solve.
320=48x
Divide both sides by 48.
6.6666666=x
Round to the nearest tenth.
x=6.7
I hope this helps!
pls ❤ and give brainliest pls
Answer:
6.7 =x
Step-by-step explanation:
The volume is given by
V = l*w*h
320 = 8*6*x
320 =48x
Divide each side by 48
320/48 = 48x/48
6.6666666 = x
Rounding to the nearest tenth
6.7 =x
5. Two unbiased dice are rolled. Calculate the probability that the sum of the two dice is:
ws
(a) 4
(b) 7
(c) Less than 7
Simplify: 41a-2b + 3c) + 11a
Step-by-step explanation:
41a+11a-2b+3c
52a-2b+3c
Step-by-step explanation:
(41a-2b+3c) +11a
open the bracket
41a-2b+3c+11a
collect like terms
41a+11a-2b+3c
52a-5bc
so final answer is 52a-5bc
because they are not like terms they are unlike terms
Simplify 4^-4.
please help I have 10 minutes
Answer:
1/256
Step-by-step explanation:
[tex]4^{-4}[/tex]
[tex](1/4)^{4}[/tex]
=> 1/256
Louise has a hard time keeping her workspace clean at her job. She tries, but it just ends up getting messy again. Which of the following is a likely outcome of her consistent messiness? a) She will have fewer safety issues. b) She will feel more productive. c) Customers will think she is very busy. d) She will have a hard time focusing.
(-72)(-15)= explain
