Answer: 144
Step-by-step explanation:
When we go from 4 to 16, we add 12. Then, to get to 36, we add 20. Then, we add 28 to get 64, and finally 36 to get 100. The pattern looks like we add by 8 more every time, so next number is 100 + (36 + 8) or 144.
The sequence of squares of even nos. so the 8th term would be the square of 16 which is 256.
What are arithmetic and geometric sequence?An arithmetic sequence is a set of numbers in which every no. next to the previous number has the same common difference
d = aₙ - aₙ₋₁ = aₙ₋₁ - aₙ ₋₂.
In a geometric sequence numbers are written in the same constant ratio(r).
It means every next number is a multiple of a common constant and the previous number.
r = aₙ/aₙ₋₁ = aₙ-₁/aₙ₋₂.
The given sequence is 4, 16, 36, 64, 100...
This is a sequence of squares of even nos.
The first term is the square of 2 and the second term is the square of 4 hence the 8th term would be the square of 16 which is 16² = 256.
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Find x and y so that the quadrilateral is a parallelogram. Answer below and show work.
Answer:
x = 2 , y = 29
Step-by-step explanation:
if the quadrilateral is to be a parallelogram , then
• opposite sides are congruent
• opposite angles are congruent
Then
2x + 9 = x + 11 ( subtract x from both sides )
x + 9 = 11 ( subtract 9 from both sides )
x = 2
and
3y + 19 = 106 ( subtract 19 from both sides )
3y = 87 ( divide both sides by 3 )
y = 29
if this rate of growth remains the same and the population is 550,000 in the year 2020, approximately how many people will there be after 15 years?
Gabriella, Leah and Juan, cut up a golden delicious apple and a granny Smith apple for a snack after school. They split the apples evenly between how many apples did each person get right your answer as a proper fraction or mixed number.
Step-by-step explanation:
What is the value?
Please put the full question
Then only I would be able to help you
Find the nth term of this sequence
15,12,9,6
Answer: an = 18 - 3n
Step-by-step explanation:
so the next term should be 3
Input(x):a number output(y):2less than 4 times x
The equation to describe the information that 2 less than 4 times x is 4x - 2.
What is an equation?An equation is the statement that illustrates that the variables given. In this case, two or more components are taken into consideration to describe the scenario.
In this case, 2 less than 4 times will be:
= (4 × x) - 2
= 4x - 2
Therefore, the equation is 4x - 2.
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help meeeeeeeeeeee pleaseee rnnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
The graph of f(x) = (3/4)ˣ is attached. The values are f(-2) = 16/9, f(-1) = 4/3, f(0) = 1, f(1) = 3/4 and f(2) = 9/16
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Given the exponential function:
f(x) = (3/4)ˣ
Hence:
f(-2) = (3/4)⁻² = 16/9
f(-1) = (3/4)⁻¹ = 4/3
f(0) = (3/4)⁰ = 1
f(1) = (3/4)¹ = 3/4
f(2) = (3/4)² = 9/16
The graph of f(x) = (3/4)ˣ is attached.
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What is the solution to this system of linear equation 3x 2y 14?.
The solutions to this system of linear equation 3x−2y=14 is ( [tex]\frac{2y + 14}{3}[/tex] , [tex]\frac{3x}{2}[/tex]-7).
Add 2y to both sides.
3x=14+2y
The equation is in standard form.
3x=2y+14
Divide both sides by 3.
[tex]\frac{3x}{3}[/tex] = [tex]\frac{2y + 14}{3}[/tex]
Dividing by 3 undoes the multiplication by 3.
x = [tex]\frac{2y + 14}{3}[/tex]
Now,
3x−2y=14
Subtract 3x from both sides.
−2y=14−3x
Divide both sides by −2.
[tex]\frac{-2y}{-2}[/tex] = [tex]\frac{14 - 3x}{-2}[/tex]
Dividing by −2 undoes the multiplication by −2.
y = [tex]\frac{14 - 3x}{-2}[/tex]
Divide 14−3x by −2.
y = [tex]\frac{3x}{2}[/tex] - 7
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Determine the inverse of the function f (x) = 3(x − 4)2 + 5.
inverse of f of x is equal to 4 minus the square root of the quantity of the quantity x minus 5 end quantity over 3 end quantity such that the domain of f (x) is x ≥ 4
inverse of f of x is equal to 4 minus the square root of the quantity of the quantity x minus 5 end quantity over 3 end quantity such that the domain of f (x) is x ≤ 4
inverse of f of x is equal to 4 minus the square root of the quantity x over 3 minus 5 end quantity such that the domain of f (x) is x ≥ 4
inverse of f of x is equal to 4 minus the square root of the quantity x over 3 minus 5 end quantity such that the domain of f (x) is x ≤ 4
Question 4(Multiple Choice Worth 2 points)
(02.06 MC)
Determine the inverse of the function f(x) = log2(3x + 4) − 5.
f inverse of x is equal to 2 to the power of x plus 3 all over 2
f inverse of x is equal to the quantity x plus 5 end quantity squared minus 4 all over 3
f inverse of x is equal to 2 to the power of the quantity x plus 5 end quantity minus 4 all over 3
f inverse of x is equal to 2 to the power of the quantity x minus 5 end quantity plus 4 all over 3
Question 5(Multiple Choice Worth 2 points)
(02.06 MC)
Given the graph of f(x), determine the range of f−1(x).
Rational function with one piece increasing from the left in quadrant 2 asymptotic to the line y equals 1 and passing through the point 2 comma 2 and asymptotic to the line x equals 3 and another piece increasing from the left in quadrant 4 asymptotic to the line x equals 3 passing through the point 4 comma 0 asymptotic to the line y equals 1.
Answer: The inverse of the function f(x) = 4(x-3)² + 2 is
The given function is:
f(x) = 4(x - 3)² + 2
To find the inverse of the function:
Make x as the subject of the formula
Replace x by and replace f(x) by x
Therefore, the inverse of the function is:
Step-by-step explanation:
Eduardo decided to invest money in an account that earns 3% compounded semi-annually. If he initially
deposited $750 into the account, how much will it be worth in 8 years? Round answer to the nearest
hundredth.
Answer:
$951.74
Step-by-step explanation:
You want the future value of $750 earning 3% per year for 8 years, compounded semi-annually.
Compound interestThe value of an account earning interest at rate r on principal P compounded n times per year for t years is ...
A = P(1 +r/n)^(nt)
For P=750, r=0.03, n=2, t=8, this is ...
A = 750(1 +0.03/2)^(2·8) = 750(1.015^16) ≈ 951.74
The account will be worth about $951.74 in 8 years.
__
Additional comment
All spreadsheets and many graphing calculators have the necessary financial functions for computing this value. Apps are available for the purpose, as well.
50POINTS
Do these pairs of values (x and y) represent two quantities that are
proportional?
xy
3 5
4 7
6 10
9 15
Answer:
D. No because not all of the pairs are simplified ratiosStep-by-step explanation:
The proportional relationship is:
y = kx, where k- constant of proportionalityLet's find the value of k for each pair and compare:
k = y/x1) x = 3, y = 5 ⇒ k = 5/32) x = 4, y = 7 ⇒ k = 7/43) x = 6, y = 10 ⇒ k = 10/6 = 5/34) x = 9, y = 15 ⇒ k = 15/9 = 5/3As we see thee of the pairs have same value of k, 5/3 and one is different 7/4.
The answer is no.
Answer choices given in the comment:
A. No because not all the pairs represent the same ratioB. Yes because the ratios 3/5 and 6/10 are equalC. Yes because as x increases y increasesD. No because not all of the pairs are simplified ratioskatie has £1200. she gives 1/3 of the money to her sister. Then katie give 1/4 of the remaining money to her brother. how much money does katie have left?
Answer:
£600
Step-by-step explanation:
Katie gives 1/3 of the money to her sister.
1/3 of 1200 is 400, because 1200 divided by 3 is 400. So she gives 400 to her sister, which means she has 1200-400= 800 left.
When she gives 1/4 of the remaining to her brother, that means that we need to figure out how much 1/4 of 800 is. 800 divided by 4 is 200. So Katie gives 200 to her brother.
800 that she has remaining minus the 200 she gives to her brother leaves her with 800-200 = 600
a pharmaceutical company receives large shipments of ibuprofen tablets and uses an acceptance sampling plan. this plan randomly selects and tests 21 tablets, then accepts the whole batch if there is at most one that doesn't meet the required specifications. what is the probability that this whole shipment will be accepted if a particular shipment of thousands of ibuprofen tablets actually has a 15% rate of defects? (report answer as a decimal value accurate to four decimal places.) p(accept shipment)
0.9660 is the probability that this whole shipment will be accepted if a particular shipment of thousands of ibuprofen tablets actually has a 15% rate of defects
What is probability ?Probability turned into added into arithmetic to are expecting the possibility of an occasion occurring. Probability essentially approach how in all likelihood it's miles that some thing will happen. This is the fundamental principle of possibility and is likewise utilized in possibility distributions to examine feasible consequences of random experiments.
CalculationIf the number of tablets in a shipment is sufficiently large, we can consider the testing procedure you describe (selecting a random sample of 29 ibuprofen tablets and counting the number of defective tablets in the sample) to be a binomial probability experiment.
Let X = (Number of defective ibuprofen tablets in a random sample of 29 tablets.) Then we may reasonably assume that X follows a binomial distribution. For each "trial" (that is, each tablet selected), there are two possible outcomes, "success" (the tablet is defective), or "failure" (the tablet is not defective). Note that the word success as used in the binomial distribution does not carry the connotation of being a "good" outcome. A "success" is simply the outcome you are interested in counting, which in this case is the number of defectives in the sample. The important parameters for a binomial distribution are n (the number of trials) and p (the probability of success on any one trial.) For this situation, we have p = .01 (since we are told 1% of the tablets in the shipment are defective) and n = 29. The general formula for the binomial distribution is
P(x) = nCx·px·(1 - p)n-x
where x is the number of successes in n trials (In this problem, x is the number of defectives in a random sample of 29 tablets.) The symbol nCx is the "number of combinations of n things taken x at a time". This is the number ways of choosing x distinct objects from a set of n objects, without regard to order. It is given by
nCx = n!/[x!·(n-x)!]
where ! is the factorial symbol.
We want to find the probability that the shipment is accepted. We are told that a shipment will be accepted if at most one tablet doesn't meet the required specifications. That is, the number of defectives must be less than or equal to one.
P(Shipment accepted) = P(X ≤ 1). (In this case, X ≤ 1 if and only if X=0 or X=1)= P(0) + P(1).
So we calculate P(0) (the probability of 0 defective tablets in the shipment), and P(1) (the probability of 1 defective.) Using the formula for the binomial distribution, we have
P(0) = 29C0·(.01)0·(1 - .01)29 - 0.
But 29C0 = 1, so
P(0) = 1·(.01)0·(.99)29 ≅ .74717
Also,
P(1) = 29C1·(.01)1·(1 - .01)29 - 1.
Calculating 29C1, we have
29C1 = 29!/[1!·(29-1)!] = 29, so
P(1) = 29·(.01)1·(99)28
P(1) ≅ .21887
Finally, then, we have
P(Shipment accepted) ≅ .74717 + .21887 ≅ .9660 (to 4 decimal places.)
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Mari cella has a bag containing 35 nickels and quarters. The total value of these coins is less than $2.50. What is the maximum number of quarters that meets these conditions?
What is the probability of selecting a king or queen from a standard deck of 52 cards
If the regular price of the pair of glasses was $72 how much did Gabriela pay wit the discount
The amount Gabriela paid with the discount is $50.4.
How to find the amount paid with the discount?Discount is a reduction in price. Discount means reducing the price or value of an object or item.
Gabriela bought a new pair of glasses at the store when they were 30% off the sale.
The regular price of the glasses is 72 dollars. The amount Gabriela paid with the discount can be calculated as follows:
discount = 30% off of the sale
discount = 30 / 100 × 72
discount = 2160/ 100
discount = 21.6 dollars
Therefore,
price paid with the discount = 72 - 21.6
price paid with the discount = 50.4 dollar
Therefore, the amount she paid with the discount is 50.4 dollars
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(9,−7) after a dilation by a scale factor of 4 centered at the origin?
The image of the coordinates after a dilation of (9, −7) by a scale factor of 4 centered at the origin include the following: (36, -28).
What is dilation?In Geometry, dilation can be defined as a type of transformation which typically changes the size of a geometric object, but not its shape. This ultimately implies that, the size of the geometric object would be increased or decreased based on the scale factor used.
Next, we would have to dilate the coordinates of the preimage (9, -7) by using a scale factor of 4 centered at the origin as follows:
Coordinate A (9, -7) → Coordinate A' (9 × 4, -7 × 4) = Coordinate A' (36, -28).
In conclusion, the coordinates of the image after a dilation are (36, -28).
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5x+6y +39 = 0
3y = 4x
Answer:
Step-by-step explanation:
Move all terms not containing xx from the center section of the inequality.
Inequality Form:
0<x<30<x<3
Interval Notation:
(0,3)
Answer:
y=-4
x=-3
Step-by-step explanation:
x=3y/4
5*(3y/4) +6y+39=0
15y/4+6y+39=0
3.75y+6y+39=0
9.75y=-39
y=-4
x=-3
make x the subject of the formular 6x+a=5(x+t)
The value of x is (5t-a) when the formula is 6x+a=5(x+t).
According to the question,
We have the following information:
6x+a=5(x+t)
Now, from this formula, we have to mark the value of x or in other words, we have to find the value of x.
Now, multiplying 5 into the bracket on the right hand side:
6x+a = 5x+5t
Subtracting 5x from both sides of the equation:
6x-5x+a = 5t
x+a = 5t
Subtracting a from both sides of the equation, we will get the final value of x in terms of t and a:
x = 5t-a
Hence, the value of x is (5t-a) when the formula is 6x+a=5(x+t).
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\frac{1}{6}f^3a=
6
1
\frac{1}{6}f^3a=
6
1
f
3
a=
\,\,D
D
Answer:
no
Step-by-step explanation:
\frac{1}{6}f^3a=
6
1
\frac{1}{6}f^3a=
6
1
f
3
a=
\,\,D
D
Triangle xyz was translated up 2 and right 3 units, creating triangle cab. Which relationship between the parts of the two triangles must be true?.
Triangle xyz was translated up 2 and right 3 units, creating triangle cab.
To find out the relationship between the parts of the two triangles must be true:
YZ ≅ AB
A translation is known as a rigid transformation. This is because it preserves congruence. Since CAB is created from XYZ, this tells us that:
X corresponds to C; Y corresponds to A; Z corresponds to B; XY corresponds to CA; YZ corresponds to AB; and XZ corresponds to CB.
Since the triangles are congruent, the corresponding pieces are congruent as well.
Out of these corresponding congruent pieces of triangles, the only one in our options is YZ ≅ AB.
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please help me this is geometry
Answer:
50
Step-by-step explanation:
Since 45-45-90 tri, x^2+x^2=100^2
So 2x^2=10000
2x=100 and x=50
Answer:
a = 70.71068 = 50√2
Step-by-step explanation:
Given c=100 and ∠β=45°,a = 70.71068 = 50√2a = √c^2 - b^2
= √1002 - 70.7106781186552
= √5000
= 70.71068 = 50√2
Thanks.
Hollie says, "when you cube root a
number, the answer is always smaller."
Show she is wrong.
When you cube root a number, the answer is always smaller. This is true.
What is a number's cube root?The cube root, denoted by, is the inverse of the cube of a number. For example, 216, or the cube root of 216, equals 6 because multiplying 6 three times yields 216. In other words, because 6³ = 216.
A number's cube root is a value that, when multiplied by itself three times, yields the original value. For example, the cube root of 27 is 3, denoted as 3³ because multiplying 3 by itself three times yields 3 x 3 x 3 = 27.
In this case, we have showed that the answer will be smaller than the original number.
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Plot 5/3 and it oppoite on the number line. Select the point on the line to plot the point
[tex]\frac{5}{3}[/tex]The point on the number line to plot the point which is opposite [tex]\frac{5}{3}[/tex] is [tex]\frac{-5}{3}[/tex]
What is a number line?A number line is a horizontal representation of a number of parts with equal intervals.
What exactly is a number line?
A number line is a horizontal line with evenly spaced numerical increments. It shows how to answer plotted the number on the line.
Which points on the number line are diametrically opposed?If two numbers are the same distance from 0 and on opposite sides of the number line, they are opposites.
For example, 4 is the inverse of -4, and -4 is the inverse of 4. They are both equal distances from zero.
Given: number is [tex]\frac{5}{3}[/tex]
The opposite of 5/3 is the additive inverse let x be the additive inverse
[tex]\frac{5}{3}[/tex] + x = 0
x = 0 - [tex]\frac{5}{3}[/tex]
x= - [tex]\frac{5}{3}[/tex]
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Someone solve this with solution than you.
15-8k+15k - 8 = 42
Answer:
k=5
Step-by-step explanation:
15-8k+15k-8=42
15+7k=50
7k=35
k=5
Please if possible, give an explanation.
Answer:
Step-by-step explanation:
put the day and the amount of money you made
if the zeroes of the quadric polynomial 2x^2-5x+k are reciprocal to each other then find the value of k
Answer:
The value of k is 1.
Step-by-step explanation:
Answer:
The value of k=1
Step-by-step explanation:
Question 4 please help it's important
A matrix is a form of writing items in rows and columns.
The matrice B is
[tex]B=\left[\begin{array}{ccc}9&-6\\12&15\\-3&-18\end{array}\right][/tex]
The value of [tex]b_{11}[/tex] = 9
The value of [tex]b_{22}[/tex] = 15
The value of [tex]b_{31}[/tex] = -3
The value of [tex]b_{32}[/tex] = -18
What is a matrix?A matrix is a form of writing items in rows and columns.
[tex]\left[\begin{array}{ccc}a_{11}&a_{12}&a_{13}\\a_{21}&a_{22}&a_{23}\\a_{31}&a_{32}&a_{33}\end{array}\right][/tex]
We have,
[tex]A=\left[\begin{array}{ccc}3&-2\\4&5\\-1&-6\end{array}\right][/tex]
B = 3A
We will multiply 3 with all the items in matrices A.
[tex]B=\left[\begin{array}{ccc}9&-6\\12&15\\-3&-18\end{array}\right][/tex]
This is in the form of
[tex]B=\left[\begin{array}{ccc}b_{11}&b_{12}\\b_{21}&b_{22}\\b_{31}&b_{32}\end{array}\right][/tex]
Now,
The value of [tex]b_{11}[/tex] = 9
The value of [tex]b_{22}[/tex] = 15
The value of [tex]b_{31}[/tex] = -3
The value of [tex]b_{32}[/tex] = -18
Thus,
The matrice B is
[tex]B=\left[\begin{array}{ccc}9&-6\\12&15\\-3&-18\end{array}\right][/tex]
This is in the form of
[tex]B=\left[\begin{array}{ccc}b_{11}&b_{12}\\b_{21}&b_{22}\\b_{31}&b_{32}\end{array}\right][/tex]
The value of [tex]b_{11}[/tex] = 9
The value of [tex]b_{22}[/tex] = 15
The value of [tex]b_{31}[/tex] = -3
The value of [tex]b_{32}[/tex] = -18
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How to solve for k=x/y?
Answer:
Step-by-step explanation:
k=x÷y
Multiply both sides of the equation by y.
ky=x
Swap sides so that all variable terms are on the left-hand side.
x=ky
Under a dilation, the point (2, 6) is moved to (6, 18). What is the scale factor of the dilation? enter your answer in the box.
Under a dilation, the point (2, 6) is moved to (6, 18). the scale factor of the dilation is 3
We know that if we transform point (x,y) by using dilation with scale factor k then the coordinate of the image will be (kx,ky).
Given: under a dilation, the point (2, 6) is moved to (6, 18)
Here (x,y)=(2,6) and (kx,ky)=(6,18)
x = 2
kx = 6
k = 6/x
k = 6/2
k = 3
Similarly taking y into account
y = 6
ky = 18
k = 18/y
k = 18/6
k = 3
Hence, Under a dilation, the point (2, 6) is moved to (6, 18). the scale factor of the dilation is 3
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find the slop of the line passing through the points (2,7) and (-1,4)
Answer:
1
Step-by-step explanation:
Change is y over the change in x
The y's are 4 and 7.
The x's are -1 and 2
[tex]\frac{4-7}{-1-2}[/tex] = [tex]\frac{-3}{-3}[/tex] = 1
