Answer:
270
Step-by-step explanation:
For any arithmetic sequence
nth term is given by
nth term = a + (n-1)d
where a is first term,
d is common difference
d is given by nth term - (n-1)th term
sum of n terms given by
sum = n/2(2a + (n-1)d)
________________________________________________
Given arithmetic sequence
-2,0,2,4,6,8...
first term a = -2
lets take third term as nth term and second term as (n-1)th term to find common difference d.
d = 2 - 0 = 2
using a = -2 , d = 2, n = 18
thus, sum of first 18 terms = n/2(2a + (n-1)d)
=18/2( 2*(-2) + (18-1) 2)
=9 ( -4 + 34)
=9 ( 30) = 270
Thus, sum of first 18 terms is 270.
6
Cheryl had 160 stickers more than Gareth. If Cheryl gave 185 stickers
to Gareth, Gareth would have 3 times as many stickers as Cheryl
How many stickers did Gareth have at first?
165
Answer:
260 stickers
Step-by-step explanation:
Let Gareth's stickers be x.
Hence Cheryl sticker is 160+x;
If Cheryl gave 185 stickers
to Gareth, it means:
Cheryl has at the moment;
160 + x - 185 = x - 25
At this time when Gareth receives 185 he now has:
x+ 185
Also when he receives x +185, he has 3 times Cherry's meaning:
x+185 =3(x-25)
x + 185 = 3x -75
185 + 75 = 3x-2x
260= x
x = 260.
Hence Gareth has 260 stickers
Please answer this correctly
Answer:
4
Step-by-step explanation:
Set the height of the missing bar to 4 as there are 4 quantities between 21-25.
A local cable company claims that the proportion of people who have Internet access is less than 63%. To test this claim, a random sample of 800 people is taken and its determined that 478 people have Internet access. The following is the setup for this hypothesis test: H0:p=0.63 Ha:p<0.63 Find the p-value for this hypothesis test for a proportion and round your answer to 3 decimal places.
Answer:
Step-by-step explanation:
For the null hypothesis,
H0 : p = 0.63
For the alternative hypothesis,
Ha : p < 0.63
This is a left tailed test
Considering the population proportion, probability of success, p = 0.63
q = probability of failure = 1 - p
q = 1 - 0.63 = 0.37
Considering the sample,
Sample proportion, P = x/n
Where
x = number of success = 478
n = number of samples = 800
P = 478/800 = 0.6
We would determine the test statistic which is the z score
z = (P - p)/√pq/n
z = (0.6 - 0.63)/√(0.63 × 0.37)/800 = - 1.76
From the normal distribution table, the area below the test z score in the left tail 0.039
Thus
p = 0.039
Answer:
-3.66
Step-by-step explanation:
Express loga 6 + loga 70 as a single logarithm
Answer:
logₐ(420)
Step-by-step explanation:
Answer:
The answer is
[tex] log_{a}(420) [/tex]
Step-by-step explanation:
You have to use Logarithm Law,
[tex] log_{a}(b) + log_{a}(c) ⇒ log_{a}(b \times c) [/tex]
* Take note, number b and c can only be multiplied when they have the same base, a
So for this question :
[tex] log_{a}(6) + log_{a}(70) [/tex]
[tex] = log_{a}(6 \times 70) [/tex]
[tex] = log_{a}(420) [/tex]
Help help , Please help! Brainliest if correct! What was the equation of the graph below before it was shifted to the left 1.5 units? A. G(x)=(x3)^3-(x-3) B. G(x)=(x-1.5)^3 C. G(x)=(x)^3 D.G(x)=x^3-x
Answer:
A. G(x) = (x -3)^3 -(x -3)
Step-by-step explanation:
The graph before it was shifted left will be a right-shift of the equation shown. That is accomplished by replacing x with (x-1.5). Then the right-shifted equation is ...
G(x) = ((x-1.5) -1.5)^3 -((x -1.5) -1.5)
G(x) = (x -3)^3 -(x -3) . . . . matches choice A
8. Mr. Azu invested an amount at rate of 12% per annum and invested another amount, GH¢
580.00 more than the first at 14%. If Mr. Azu had total accumulated amount of
GH¢2,358.60, how much was his total investment?
Answer:
GH¢. 18098.46
Step-by-step explanation:
Let the first investment giving 12% interest per annum be Bank A
Let the 2nd investment giving 10% per annum be bank B
Let the first amount invested be
GH¢. X and let the second amount invested be GH¢. X + 580
Thus; In bank A;
Principal amount in first = GH¢. x
rate = 12 %
time = 1 year
Formula for simple interest = PRT/100
Where P is principal, R is rate and T is time.
So, interest in his investment = 12X/100 = 0.12X
while in bank B;
principal amount = GH¢. X + 580
rate = 14%
time = 1 yr
So, interest in his investment = [(X + 580) × 14]/100
= 0.14(X + 580)
So, total accumulated interest is;
0.12X + 0.14(X + 580) = 0.12X + 0.14X + 81.2 = 0.26X + 81.2
Now, we are given accumulated interest = GH¢. 2,358.60
Thus;
2358.60 = (0.26X + 81.2)
2358.6 - 81.2 = 0.26X
X = 2277.4/0.26
X = 8759.23
So,
first amount invested = GH¢. 8759.23
Second amount invested = GH¢. 8759.23 + GH¢. 580 = GH¢. 9339.23
Total amount invested = GH¢. 8759.23 + GH¢. 9339.23 = GH¢. 18098.46
Show all work to solve the equation for x. If a solution is extraneous, be sure to identify it. Square root of the quantity x + 6 end quantity - 4 = x.
Answer:
x = 2 is the solution of the given equation
Step-by-step explanation:
Step(i):-
Given equation
[tex]\sqrt{x+6-4} = x[/tex]
squaring on both sides , we get
[tex](\sqrt{x+2})^{2} = x^{2}[/tex]
⇒ x + 2 = x²
⇒x² - x -2 =0
Step(ii):-
Given x² - x -2 =0
⇒ x² - 2x + x - 2 =0
⇒ x ( x-2) + 1(x - 2) =0
⇒ (x + 1) ( x-2) =0
⇒ x = -1 and x =2
x = 2 is the solution of the given equation
Verification:-
[tex]\sqrt{x+6-4} = x[/tex]
Put x= 2
[tex]\sqrt{2+6-4} = 2[/tex]
[tex]\sqrt{4} = 2[/tex]
2 = 2
A man is giving a dinner party. His current wine supply includes 8 bottles of zinfandel, 10 of merlot, and 12 of cabernet, all from different wineries. a) If he wants to serve 3 bottles of zinfandel and serving order is important, how many ways are there to do this? (2 points) b) If 6 bottles are randomly selected, what is the probability that this results in two bottles of each variety being chosen? (4 points) c) If 6 bottles are randomly selected, what is the probability that all of them are the same variety?
Answer:
a. 336
b. 14.01%
c. 0.2%
Step-by-step explanation:
a. We have that the number of zinfandel bottles is 8 and that the number of zinfandel served is 3, therefore:
n = 8 and r = 3
we can calculate it by means of permutation:
nPr = n! / (n-r)!
replacing:
8P3 = 8! / (8-3)!
8P3 = 336
Which means there are 336 ways.
b. First we must calculate the ways to choose 2 bottles of each variety, through combinations:
nCr = n! / (r! * (n-r)!
We know that there are 8 bottles zinfandel, 10 of merlot, and 12 of cabernet, and we must choose 2 of each, therefore it would be:
8C2 * 10C2 * 12C2
8! / (2! * (8-2)! * 10! / (2! * (10-2)! * 12! / (2! * (12-2)!
28 * 45 * 66 = 83160
Now we must calculate the total number of ways, that is, choose 6 bottles of the 30 total (8 + 10 + 12)
30C6 = 30! / (6! * (30-6)! = 593775
Thus:
83160/593775 = 0.1401
In other words, the probability is 14.01%
c. In this case, we must calculate the number of ways of 8 bottles zinfandel, 10 of merlot, and 12 of cabernet choose 6, that is to say that they are all of the same variety, therefore:
8C6 + 10C6 + 12C6
8! / (6! * (8-6)! + 10! / (6! * (10-6)! + 12! / (6! * (12-6)!
28 + 210 + 924 = 1162
And that divide it by the total amount that we calculated the previous point, 30C6 = 593775
Thus:
1162/593775 = 0.002
In other words, the probability 0.2%
The mean weight of frozen yogurt cups in an ice cream parlor is 8 oz.Suppose the weight of each cup served is normally distributed withstandard deviation 0.5 oz, independently of others.(a) What is the probability of getting a cup weighing more than 8.64oz
Answer:
10.03% probability of getting a cup weighing more than 8.64oz
Step-by-step explanation:
Problems of normally distributed samples are solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
In this question, we have that:
[tex]\mu = 8, \sigma = 0.5[/tex]
What is the probability of getting a cup weighing more than 8.64oz
This is the 1 subtracted by the pvalue of Z when X = 8.64. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{8.64 - 8}{0.5}[/tex]
[tex]Z = 1.28[/tex]
[tex]Z = 1.28[/tex] has a pvalue of 0.8997
1 - 0.8997 = 0.1003
10.03% probability of getting a cup weighing more than 8.64oz
Write the value of the digit 5 in this number:178.25
I
Step-by-step explanation:
178.25
The number 5 is in the place of one's so the value of 5 is 5
Rewrite the expression in the form z^n
[tex] \sqrt[5]{z {}^{4}z {{}^{ \frac{ - 3}{2} } } } [/tex]
Answer:
[tex]z^{0.5}[/tex]
Step-by-step explanation:
So first simplify inside:
[tex]z^4z^{-1.5}=z^{2.5}[/tex]
Now divide that by 5:
[tex]z^{0.5}[/tex]
someone plz help asap plz
Answer:
a) 6
b) 10
Step-by-step explanation:
a) The area of a rhombus is half the product of the diagonals, meaning that the area of the shaded part is 4*3/2=6 square meters.
b) To find the area of the white background, you need to find the area of the full rectangle, and then to find the area of both rhombii. The area of the black rhombus is 2*4/2=4 square meters. The area of the full rectangle is 4*5=20 units. Subtracting the areas of the two rhombii, you get an area for the white background of 20-6-4=10 square meters. Hope this helps!
Express each percent as a fraction in simplest form.
a. 85%
b. 5 72%
c. 12.55%
Answer:
(a) 17/20 b.5/18/25 c. 1.255
A box lunch costs b. A bag of chips is $2 extra. Choose the expression to show the cost of 12 lunches with chips and 10 lunches without?
Answer:
22b+24
Step-by-step explanation:
If a box lunch costs b and a bag of chips is $2 extra then we would have:
box lunch = b dollars
box lunch with bag of chips = b + 2 dollars
Now, we need to find the expression for the cost of 12 lunches with chips and 10 lunches without chips, this would be:
12 lunches with chips = 12 (b + 2)
10 lunches without chips = 10b
Let's sum up and simplify these two expressions:
[tex]12(b+2)+10b\\12b+24+10b\\22b+24[/tex]
Thus, the cost of 12 lunches with chips and 10 lunches without chips is 22b+24
Maddie is packing moving boxes. She has one 3 cubic-foot box and one 6 cubic-foot box. How many cubic feet of clothing can she fit in the two boxes?
8 9 10 12
Answer:
She can fit 9 cubic feet of clothing in the two boxes.
Step-by-step explanation:
She can fit a total of 3 cubic feet of clothing in one box, and the other she can fit a total 6 cubic feet.
3 + 6 = 9
Answer:
9 cu ft.
Step-by-step explanation:
That is the sum of the capacities of the 2 boxes
= 3 + 6
= 9 cu ft.
You have 125 g of a certain seasoning and are told that it contains 14.0 g of salt. What is the percentage of salt by mass in this seasoning? Express the percentage numerically. Do not round.
Answer:
[tex]\frac{14}{125}\times 100=11.2\%[/tex]
A standardized exam's scores are normally distributed. In a recent year, the mean test score was 1521 and the standard deviation was 314. The test scores of four students selected at random are 1920, 1290, 2220, and 1420. Find the z-scores that correspond to each value and determine whether any of the values are unusual
Answer:
A score of 1920 has a z-score of 1.27.
A score of 1290 has a z-score of -0.74.
A score of 2220 has a z-score of 2.23.
A score of 1420 has a z-score of -0.32.
The score of 2220 is more than two standard deviations from the mean, so it is unusual.
Step-by-step explanation:
When the distribution is normal, we use the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
If X is 2 or more standard deviations from the mean, it is considered unusual.
In this question, we have that:
[tex]\mu = 1521, \sigma = 314[/tex]
Score of 1920:
X = 1920. Then
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{1920 - 1521}{314}[/tex]
[tex]Z = 1.27[/tex]
A score of 1920 has a z-score of 1.27.
Score of 1290:
X = 1290. Then
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{1290 - 1521}{314}[/tex]
[tex]Z = -0.74[/tex]
A score of 1290 has a z-score of -0.74.
Score of 2220:
X = 1290. Then
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{2220 - 1521}{314}[/tex]
[tex]Z = 2.23[/tex]
A score of 2220 has a z-score of 2.23.
Since it is more than 2 standard deviations of the mean, the score of 2220 is unusual.
Score of 1420:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{1420 - 1521}{314}[/tex]
[tex]Z = -0.32[/tex]
A score of 1420 has a z-score of -0.32.
how to differentiate functions
Answer: see boxed answers below
Step-by-step explanation:
(i) multiply the exponent to the coefficient then subtract 1 from the exponent.
[tex]y=\dfrac{3}{5x^3}+3x^4+2x^2-20\\\\\\\text{rewrite it as follows}: y=\dfrac{3}{5}x^{-3}+3x^4+2x^2-20x^0\\\\\\y'=(-3)\dfrac{3}{5}x^{-3-1}+(4)3x^{4-1}+(2)2x^{2-1}-(0)20x^{0-1}\\\\\\y'=-\dfrac{9}{5}x^{-4}+12x^3+4x^1-0\\\\\\y'=\large\boxed{-\dfrac{9}{5x^{4}}+12x^3+4x}[/tex]
(ii) Use the division formula: [tex]y = \dfrac{a}{b}\rightarrow \quad y'=\dfrac{ab'-a'b}{b^2}[/tex]
[tex]a=5x^3+1\qquad \qquad a'=15x^2\\b=3x^5+4x^2\qquad \quad b'=15x^4+8x\\\\\\y'=\dfrac{(15x^2)(3x^5+4x^2)-(5x^3+1)(15x^4+8x)}{(3x^5+4x^2)^2}\\\\\\.\quad =\dfrac{45x^7+60x^4-75x^7-55x^4-8x}{(3x^5+4x^2)^2}\\\\\\.\quad =\large\boxed{\dfrac{-35x^7+5x^4-8x}{(3x^5+4x^2)^2}}[/tex]
y = -9x - 2; (4, -37)
A. Yes it satisfies the equation
B. No the ordered pair does not satisfy the equation
Answer:
B. No the ordered pair does not satisfy the equation
Step-by-step explanation:
y = -9x - 2
Substitute the point in and see if it is true
-37 = -9(4) -2
-37 = -36 -2
-37 = -38
This is not true so the point is not a solution
Find the VOLUME of this composite solid.
Answer:
(294π +448) cm³ ≈ 1371.6 cm³
Step-by-step explanation:
The half-cylinder at the right end has a radius of 7 cm, as does the one on top. Together, the total length of these half-cylinders is 8 cm + 4cm = 12 cm. That is equivalent in volume to a whole cylinder of radius 7 cm that is 6 cm long.
The cylinder volume is ...
V = πr²h = π(7 cm)²(6 cm) = 294π cm³
__
The cuboid underlying the top half-cylinder has dimensions 4 cm by 8 cm by 14 cm (twice the radius). So, its volume is ...
V = LWH = (4 cm)(8 cm)(14 cm) = 448 cm³
Then the total volume of the composite figure is ...
(294π +448) cm³ ≈ 1371.6 cm³
What is the value of x to the nearest tenth? gradpoint
Answer:
5
Step-by-step explanation:
A Biology test contains 10 multiple choice questions each with 5 choices and one correct answer. If a law school student just randomly guesses on each of the 10 questions, i.e., the probability of getting a correct answer on any given question is 0.2. Assume that all questions are answered independently. (a) What is the probability that the student answers at least 9 questions correctly
Answer:
0.0004% probability that the student answers at least 9 questions correctly
Step-by-step explanation:
For each question, there are only two possible outcomes. Either the student guesses the correct answer, or he does not. All questions are answered independently. This means that we use the binomial distribution 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.
In this question, we have that:
[tex]n = 10, p = 0.2[/tex]
What is the probability that the student answers at least 9 questions correctly
[tex]P(X \geq 9) = P(X = 9) + P(X = 10)[/tex]
In which
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 9) = C_{10,9}.(0.2)^{9}.(0.8)^{1} = 0.000004[/tex]
[tex]P(X = 10) = C_{10,10}.(0.2)^{10}.(0.8)^{0} \approx 0 [/tex]
[tex]P(X \geq 9) = P(X = 9) + P(X = 10) = 0.000004 + 0 = 0.000004[/tex]
0.0004% probability that the student answers at least 9 questions correctly
Jack buys a bag of 5 apples, each
equal in size. He eats of 1/2 of one apple.
What fraction of the bag of
apples did he eat?
Answer:
4 1/2
Step-by-step explanation:
5 apples - 1/2 apple =
4 1/2 apple
or
9/2
Find the length of Line segment A C . Use that length to find the length of Line segment C D . Triangle A B C is shown. A perpendicular bisector is drawn from point A to point C on side B D. Angle A B C is 30 degrees and angle A D C is 25 degrees. The length of A B is 10 centimeters. What is the length of Line segment C D? Round to the nearest tenth. 2.3 cm 4.0 cm 10.7 cm 18.6 cm
Answer:
10.7 CM
Step-by-step explanation:
Correct on Edge 2020
Answer:
answer is C 10.7 cm
Step-by-step explanation:
got it right on edg 2020-2021
* If you are given the measurements of two sides of a triangle,
what will be true about the triangles you make?
Answer:both sides will be equal
Step-by-step explanation:
You play a game that requires rolling a six sided die then randomly choosing a card from a deck containg 8 red cards ,6 blue cards and 8 yellow cards whats the probability that younroll a 3 on the due and choose a red card
Answer:
2/33
Step-by-step explanation:
Probability that a 3 is rolled on the die = 1/6 (equal chance of rolling any number)
Probability of choosing a red card = 8/22 (8 red cards, 22 cards in total)
8/22 = 4/11
Probability of rolling a 3 AND choosing a red card = 1/6 x 4/11
= 4/66
= 2/33
An amount was invested at r% per quarter. What value of r will ensure that accumulated amount at the end of one year is 1.5 times more than amount invested? Correct to 2 decimal places
Answer:
25.75 % interest rate
Step-by-step explanation:
Given:
Amount was invested = r% per quarter
Amount invested = P
Rate of interest = r % per quarter
Time (n) = 4 Quarters
Computation:
A = P(1 + r/100)ⁿ
According to question.
⇒ A = P + 1.5P = 2.5P
⇒ 2.5P = P(1 + r/100)⁴
⇒ 2.5 = (1 + r/100)⁴
⇒ 1 + r/100 = 1.2575
⇒ r/100 = 0.2575
⇒ r = 25.75
25.75 % interest rate
adiocarbon dating of blackened grains from the site of ancient Jericho provides a date of 1315 BC ± 13 years for the fall of the city. What is the relative amount of 14C in the old grain vs the new grain in 2007 AD? (A0 = original radioactivity; At = radioactivity in 2007 AD).
Answer:
[tex]\left(\frac{m(t)}{m_{o}} \right)_{min} \approx 0.659[/tex] and [tex]\left(\frac{m(t)}{m_{o}} \right)_{max} \approx 0.661[/tex]
Step-by-step explanation:
The equation of the isotope decay is:
[tex]\frac{m(t)}{m_{o}} = e^{-\frac{t}{\tau} }[/tex]
14-Carbon has a half-life of 5568 years, the time constant of the isotope is:
[tex]\tau = \frac{5568\,years}{\ln 2}[/tex]
[tex]\tau \approx 8032.926\,years[/tex]
The decay time is:
[tex]t = 1315\,years + 2007\,years \pm 13\,years[/tex] (There is no a year 0 in chronology).
[tex]t = 3335 \pm 13\,years[/tex]
Lastly, the relative amount is estimated by direct substitution:
[tex]\frac{m(t)}{m_{o}} = e^{-\frac{3335\,years}{8032.926\,years} }\cdot e^{\mp\frac{13\,years}{8032.926\,years} }[/tex]
[tex]\left(\frac{m(t)}{m_{o}} \right)_{min} = e^{-\frac{3335\,years}{8032.926\,years} }\cdot e^{-\frac{13\,years}{8032.926\,years} }[/tex]
[tex]\left(\frac{m(t)}{m_{o}} \right)_{min} \approx 0.659[/tex]
[tex]\left(\frac{m(t)}{m_{o}} \right)_{max} = e^{-\frac{3335\,years}{8032.926\,years} }\cdot e^{\frac{13\,years}{8032.926\,years} }[/tex]
[tex]\left(\frac{m(t)}{m_{o}} \right)_{max} \approx 0.661[/tex]
Complete this expression using the distributive property
5(4 + 8) =
O (5 + 4)(5 + 8)
O 5(4) + 8
O 5(4) + 5(8)
O (5+4) + (5 + 8)
Answer:
5(4) + 5(8)
Step-by-step explanation:
Through destributive property, 5 is multiplied by both 4 and 8
Answer:
the person above is right thank and five star them
Step-by-step explanation:
Please help me with this problem I'm lost
Answer:
24
Step-by-step explanation:
Multiple (4)(2)= 8
-3(8) =24
