Answer:
$638641.33
Step-by-step explanation:
Adam earns $45,000 in his first year.
His salary increases by 3% each successive year. Therefore, his salary the next year is 103% of his previous year.
This is a geometric sequence where the:
First Term, a= $45,000Common ratio, r =103%=1.03(a)
Sum of geometric series[tex]=\dfrac{a(r^n-1)}{r-1}[/tex]
Substituting the given values, Adam's total earnings over n years
[tex]=\dfrac{45000(1.03^n-1)}{1.03-1}\\\\$Adam's Total Earnings=\dfrac{45000(1.03^n-1)}{0,03}[/tex]
(b)When n=12 years
[tex]\text{Adam's Total Earnings for the first 12 years=}\dfrac{45000(1.03^{12}-1)}{0.03}\\=\$638641.33$ (correct to the nearest cent)[/tex]
A research institute poll asked respondents if they felt vulnerable to identity theft. In the poll, n = 1083 and x=550 who said “yes “ Use a 99% confidence level
A. Find the best point estimate of the population p.
Step-by-step explanation:
p = x / n
p = 550 / 1083
p = 0.5078
Please help. Only if you know how to do this . I’ll mark you as brainliest if correct.
[tex]answer \\ g(x) = |x - 2| + 1 \\ here \: f(x) = |x| \\ if \: we \: want \: to \: shift \: this \: function \: 2 \: \\ unit \: right \: then \: make \: transformation \\ \: of \: x \: by \: (x - 2) \\ and \: if \: we \: want \: to \: make \: function \: \\ goes \: up \: with \: 1 \: unit \: then \: transformation \\ is \: f(x) \: by \: f(x) + 1 \\ now \\ g(x) = |x - 2| + 1 \\ hope \: it \: helps[/tex]
The amount of calories consumed by customers at the Chinese buffet is normally distributed with mean 2617 and standard deviation 586. One randomly selected customer is observed to see how many calories X that customer consumes. Round all answers to 4 decimal places where possible.
a. What is the distribution of X? X N,(_____ , ____)
b. Find the probability that the customer consumes less than 2409 calories. ______
c. What proportion of the customers consume over 2764 calories? __________
d, The Piggy award will given out to the 1% of customers who consume the most calories. What is the fewest number of calories a person must consume to receive the Piggy award? __________ calories. (Round to the nearest calorie)
Answer:
a) N(2617, 586)
b) 0.3613 = 36.13% probability that the customer consumes less than 2409 calories.
c) 0.4013 = 40.13% of the customers consume over 2764 calories
d) 3981 calories.
Step-by-step explanation:
Problems of normally distributed samples can be 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 = 2617, \sigma = 586[/tex]
a. What is the distribution of X?
Here we first place the mean, then the standard deviation.
N(2617, 586)
b. Find the probability that the customer consumes less than 2409 calories.
This is the pvalue of Z when X = 2409. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{2409 - 2617}{586}[/tex]
[tex]Z = -0.355[/tex]
[tex]Z = -0.355[/tex] has a pvalue of 0.3613
0.3613 = 36.13% probability that the customer consumes less than 2409 calories.
c. What proportion of the customers consume over 2764 calories?
This is 1 subtracted by the pvalue of Z when X = 2764. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{2764 - 2617}{586}[/tex]
[tex]Z = 0.25[/tex]
[tex]Z = 0.25[/tex] has a pvalue of 0.5987
1 - 0.5987 = 0.4013
0.4013 = 40.13% of the customers consume over 2764 calories
d. The Piggy award will given out to the 1% of customers who consume the most calories. What is the fewest number of calories a person must consume to receive the Piggy award?
Top 1%, so the 100-1 = 99th percentile.
The 99th percentile is the value of X when Z has a pvalue of 0.99. So it is X when Z = 2.327. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]2.327 = \frac{X - 2617}{586}[/tex]
[tex]X - 2617 = 2.327*586[/tex]
[tex]X = 3980.6[/tex]
Rounding to the nearest calorie, 3981 calories.
Which expression is equivalent to the given expression? (3m-4)^3(3m^5)
Answer: D.
Step-by-step explanation:
You want to cube each term in the parentheses. When you take an exponent to an exponent, you just multiply them. You get (27m^-12). In order to get rid of that negative exponent, you should put a one over the m term and make -12, +12:
[tex](\frac{27}{m^12} )(3m^5)[/tex]
Multiply the numerators to get:
[tex]81m^5[/tex]
You now have:
[tex]\frac{81m^5}{m^12}[/tex]
When you divide exponents, you subtract them. 5 - 12 = -7
You have m^-7 which is the same as 1/m^7. Finally, mulitply that by the 81 we left out to get the answer of D.
The expression equivalent to the given expression (3m⁻⁴)³(3m⁵) is 81/m⁷. So, option D is correct.
What is exponentiation?Exponentiation is a mathematical operation that involves two numbers, the base b, and the exponent or power n, and is pronounced as "b raised to the power of n." It is written as bⁿ and is pronounced as "b raised to the power of n."
When n is a positive integer, bⁿ = b × b × b ×...× b
and b⁻ⁿ = 1/bⁿ
If n = 0, then b⁰ = 1.
How to solve this problem?Here, (3m⁻⁴)³(3m⁵) = (3³)(m⁻⁴)³(3m⁵) = (27m⁻¹²)(3m⁵) = 81m⁵⁻¹² = 81/m⁷
Therefore, the expression equivalent to the given expression (3m⁻⁴)³(3m⁵) is 81/m⁷. So, option D is correct.
Learn more about exponentiation here -
https://brainly.com/question/14513824
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If a graph of y=-9x+ 3 were changed to a graph of y=-9x + 1, how would the
y-intercept change?
Answer:
y-intercept decreased by 3-1= 2 points
Step-by-step explanation:
y=-9x+ 3 ⇒ y-intercept= 3
y=-9x + 1 ⇒ y-intercept= 1
y-intercept decreased by 3-1= 2 points = the line shifted down by 2 points
Answer:
Hello!
Answer: y-intercept decreased by 2 points because 3-1=2
I hope I was of help. If not, please let me know! Thanks!
Step-by-step explanation:
en un parque hay una zona de columpios y una pista de patinaje que ocupa en total 5 quintos del espacio .si los columpios ocupan 2 septimos del parque . que fraccion del parque ocupa la pista de patinaje
Answer:
The rink occupies 69% of the whole park, approximately, which is equivalent to 280/408.Step-by-step explanation:
To solve this problem, we need to find the number which express the whole park.
Notice that the park is divided in two sections, one occupies 5/8 of the total, and the other occupies 2/7 of the total. So, the sum would be
[tex]\frac{5}{8}+\frac{2}{7}=\frac{35+16}{56} =\frac{51}{56}[/tex]
Now we have the total space there, we need to divide 5/8 by 51/56, so
[tex]\frac{5}{8} \div \frac{51}{56}=\frac{5}{8} \times \frac{56}{51}=\frac{280}{408} \approx 0.69[/tex]
Therefore, the rink occupies 69% of the whole park, approximately, which is equivalent to 280/408.
Classify the following triangle check all that apply. 98,41,41
Answer:
B. Isosceles triangle
Answer: obtuse and isosceles <3
Step-by-step explanation:
I need help! Someone help me please
Answer:
4. 27
Step-by-step explanation:
11-10=1 which is <=16
15-10=5 which is <=16
26-10=16 which is <=16
27-10=17 which isn't <=16
Therefore 27 doesn't satisfy the inequality
Answer:
4. 27
Step-by-step explanation:
w - 10 ≤ 16
w≤16 + 10
w ≤ 26
11 ≤ 26
15≤26
26≤26
26≤ 27 False
which is pattern 12,24,36,48
Answer:
multiples of 12
Step-by-step explanation: when looking at the GCF, the answer is 12
Prove that : sin^4(2x)=3/8-1/2cos4x+1/8cos8x
Someone plzz help!!!
When estimating the minimum sample size for proportion, it is indicated to keep a 50/50 split between the probabilities of success (p) and failure (q), even if we know from previous studies where the split has been in the past.
a.True
b. False .
c. That's a tricky
Answer:
b) False
Explanation:
It is not needed to keep 50/50 split.
Ryan remembers numbers using images that look somewhat like each number: 0 is a ball, 1 is a stick, 2 is a hanger, 3 is a comb, 4 is a kite, etc. Ryan remembered a 4-digit phone extension with this story: A person uses a hanger to pop a ball, then flies two kites. What number is Ryan likely remembering? (1) 2044 or (2) 2042 (3) 2004 or (4) 2204
Answer:
2044
Step-by-step explanation:
just follow the story
a person uses a
hanger (2)
to pop a
ball (0)
then flies
two kites (44)
Answer:
1). 2044
Step-by-step explanation:
The story includes: a hanger, a ball, and two kites (in that order)
From the information given, a hanger is 2, a ball is 0, and a kite is 4.
So it would be 2044.
what is the range of the exponential function shown below? f(x)=9*2^x
Answer:
(0, ∞)
Step-by-step explanation:
An exponential function has a horizontal asymptote at y=0. Its vertical extent is toward infinity.
The range is ...
0 < f(x) < ∞
ASAP! GIVING BRAINLIEST! Please read the question THEN answer CORRECTLY! NO guessing. I say no guessing because people usually guess on my questions.
Answer:
a
Step-by-step explanation:
because as absolute value gets smaller the line gets steeper
r
A 12cmx2cm rectangle sits inside a circle with a radius of 8cm. What isnthe area of the shaded region of the circle
Answer:
The answer would 177.06 centimeters
A sample of 500 nursing applications included 60
from men. Find the 90% confielence interval
for the
true proportion of men who applied to the nursing
program.
Answer:
90% confidence interval for the true proportion of men who applied to the nursing program.
(0.09674 ,0.14326)
Step-by-step explanation:
Explanation:-
Given sample size 'n' = 500
sample proportion
[tex]p = \frac{x}{n} = \frac{60}{500} = 0.12[/tex]
Level of significance ∝= 0.90 or 0.10
90% confidence interval for the true proportion of men who applied to the nursing program.
[tex](p - Z_{\frac{0.10}{2} } \sqrt{\frac{p(1-p)}{n} } , p + Z_{\frac{0.10}{2} } \sqrt{\frac{p(1-p)}{n} })[/tex]
[tex](p - Z_{0.05 } \sqrt{\frac{p(1-p)}{n} } , p + Z_{0.05 } \sqrt{\frac{p(1-p)}{n} })[/tex]
[tex](0.12 - 1.645 \sqrt{\frac{0.12(1-0.12)}{500} } , 0.12 + 1.645 \sqrt{\frac{0.12(1-0.12)}{500} })[/tex]
On calculation , we get
( 0.12 - 0.02326 , 0.12 + 0.02326)
(0.09674 ,0.14326)
Final answer:-
90% confidence interval for the true proportion of men who applied to the nursing program.
(0.09674 ,0.14326)
Two positive, consecutive, odd integers have a product of 143.
Complete the equation to represent finding x, the greater integer.
x(x –
) = 143
What is the greater integer?
Step-by-step explanation:
x and x+2 are the numbers
x(x+2)=143
x²+2x-143=0
x²+13x-11x-143=0
x(x+13)- 11(x+13)=0
(x+13). (x-11)=0
x+13=0. x=-13
x-11=0. x=11
Suppose cattle in a large herd have a mean weight of 3181lbs and a standard deviation of 119lbs. What is the probability that the mean weight of the sample of cows would differ from the population mean by greater than 11lbs if 49 cows are sampled at random from the herd
Answer:
51.56% probability that the mean weight of the sample of cows would differ from the population mean by greater than 11lbs if 49 cows are sampled at random from the herd
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal probability distribution
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.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
In this question, we have that:
[tex]\mu = 3181, \sigma = 119, n = 49, s = \frac{119}{\sqrt{49}} = 17[/tex]
What is the probability that the mean weight of the sample of cows would differ from the population mean by greater than 11lbs if 49 cows are sampled at random from the herd
Lower than 3181 - 11 = 3170 lbs or greater than 3181 + 11 = 3192 lbs. Since the normal distribution is symmetric, these probabilities are equal. So i will find one of them, and multiply by 2.
Probability of mean weight lower than 3170 lbs:
This is 1 subtracted by the pvalue of Z when X = 3170. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{3170 - 3181}{17}[/tex]
[tex]Z = -0.65[/tex]
[tex]Z = -0.65[/tex] has a pvalue of 0.2578
2*0.2578 = 0.5156
51.56% probability that the mean weight of the sample of cows would differ from the population mean by greater than 11lbs if 49 cows are sampled at random from the herd
12
? Select three options.
Which phrases can be represented by the algebraic expression
W
12 divided by a number
the quotient of 12 and a number
a number divided by 12
a number divided into 12
the product of 12 and a number
Answer:
Step-by-step explanation: its 24
1,2,5
Step-by-step explanation:
Chen spent 7 hours at school on Friday he spent 30 minutes at lunch 50 minutes at a school assembly and the rest in class how much time did Chen spend in class
Answer:
5 hours and 40 minutes would be class
Step-by-step explanation:
We know that the total time is 7 hours, which in minutes would be:
7 * 60 = 420
420 minutes would be class, now, we subtract the other times that are not to be in class and it would be:
420 - 30 - 50 = 340
So we could say that in class it takes 340 minutes, and if we spend hours it would be:
340/60 = 5.67 hours or also 5 hours and 40 minutes would be class.
What are the solutions of the equation 9x^4 – 2x^2 – 7 = 0? Use u substitution to solve
Answer:
[tex]x=1\\x=-1[/tex]
Step-by-step explanation:
[tex]9x^{4} -2x^{2} -7=0\\y=x^{2} \\9y^{2} -2y-7=0\\y=\frac{2\pm\sqrt{(-2)^{2} -4*9(-7)} }{2*9} =\frac{2\pm\sqrt{4+252} }{18} =\frac{2\pm\sqrt{256} }{18}[/tex]
[tex]\sqrt{256} =16[/tex]
[tex]y=\frac{2+16}{18} =\frac{18}{18} =1 \\or \\y=\frac{2-16}{18} =-\frac{14}{18} =-\frac{7}{9}[/tex]
[tex]x^{2} = 1 \\or \\x^{2} =-\frac{7}{9}[/tex]
[tex]x=\pm 1[/tex]
[tex]x^{2} =-\frac{7}{9}[/tex] has no solution since fot all [tex]x[/tex] on the real line, [tex]x^{2} \geq 0[/tex] and [tex]-\frac{7}{9} < 0.[/tex]
algebra parabola question see picture above
Answer:
see below
Step-by-step explanation:
(-1, -9) is a vertex or minimum.
(-4, 0) is an x-intercept / zero of the function / solution
(2, 0) is also an x-intercept / zero of the function / solution
The parabola has a minimum.
The luxury Swiss Chalet hotel general manager (GM) reported to her owner that the hotel's Occupancy Index for the calendar year 2019 was 1.25. Based upon only this information alone, what MUST be correct?
Answer:
the Swiss Chalet had higher occupancy than its competitive set in 2019
Step-by-step explanation:
Two people took turns tossing a fair die until one of them tossed a 6. PersonA tossed first, B second, A third, and so on. Given that person B threw the first 6, whatis the probability that B obtained the first 6 on her second toss (that is, on the fourth tossoverall)?
Answer: 0.0965
Step-by-step explanation:
This would happen if:
First toss: Here we must have any number that is not 6.
the options are 1, 2, 3, 4, 5 so the probablity is p1 = 5/6
The same happens for the second toss, p2 = 5/6
and for the third one: p3 = 5/6
for the fourth toss, person B must roll a 6, so the probability here is p4 = 1/6
Now, the joint probability is equal to the product of the probabilities for each toss, this is:
P = p1*p2*p3*p4 = (5/6)^3*(1/6) = 0.0965
The chess clubs of two schools consist of, respectively, 8 and 9 players. Four members from each club are randomly chosen to participate in a contest between the two schools. The chosen players from one team are then randomly paired with those from the other team, and each pairing plays a game of chess. Suppose that Rebecca and her sister Elise are on the chess clubs at different schools. What is the probability that
Answer:
A)1/18
B)1/6
C)13/18
Step-by-step explanation:
THIS IS THE COMPLETE QUESTION BELOW,
The chess clubs of two schools consist of, respectively, 8 and 9 players. Four members from each club are randomly chosen to participate in a contest between the two schools. The chosen players from one team are then randomly paired with those from the other team, and each pairing plays a game of chess. Suppose that Rebecca and her sister Elise are on the chess clubs at different schools. What is the probability that (a) Rebecca and Elise will be paired? (b) Rebecca and Elise will be chosen to represent their schools but will not play each other? (c) either Rebecca or Elise will be chosen to represent her school?
CHECK THE ATTACHMENT'S FOR STEP BY STEP EXPLANATION
In a car dealership there are 5 models that get displayed in a line in the front of the parking lot for prime viewing. The dealership sells 15 different models. In how many ways can the 5 models be displayed
Answer:
360360
Step-by-step explanation:
We have the following information:
Number of ways of choosing 5 car models from 15 different models = 15C5
Number of arranging above 5 models = 5!
Therefore, the total number of displayong 5 models would be:
15C5 * 5!
nCr = n! / (r! * (n-r)!)
we replace:
15! / (5! * (15-5)!) * 5! = 15! / 10! = 360360
So there are a total of 360 360 ways to display the 5 car models.
Answer: 360,360
Step-by-step explanation:
Exactly one pair of opposite sides is parallel
Answer:
Yeah btw is this a question?
(2)/(5) and (1)/(x)common denominator =10 find the value of x
Answer:
[tex]x=5/48[/tex]
Step-by-step explanation:
[tex]2/5 + 1/x =10[/tex]
[tex]1/x=10-2/5[/tex]
[tex]1/x=48/5[/tex]
[tex]48x=5[/tex]
[tex]x=5/48[/tex]
Answer:
[tex]x = \frac{5}{48} [/tex]
Step-by-step explanation:
[tex]\frac{2}{5} + \frac{1}{x} = 10 \\ \frac{1}{x} = 10 - \frac{2}{5} \\ \frac{1}{x} = \frac{50 - 2}{5} \\ \frac{1}{ x } = \frac{48}{5} \\
use \: \: \: \: cross \: \: \: multiply
\\ 5 = 48x \\ \frac{5}{48} = \frac{48x}{48} \\ x = \frac{5}{48} \\ [/tex]
hope this helps
brainliest appreciated
good luck! have a nice day!
Suppose a population of rodents satisfies the differential equation dP 2 kP dt = . Initially there are P (0 2 ) = rodents, and their number is increasing at the rate of 1 dP dt = rodent per month when there are P = 10 rodents. How long will it take for this population to grow to
Answer:
Suppose a population of rodents satisfies the differential equation dP 2 kP dt = . Initially there are P (0 2 ) = rodents, and their number is increasing at the rate of 1 dP dt = rodent per month when there are P = 10 rodents.
How long will it take for this population to grow to a hundred rodents? To a thousand rodents?
Step-by-step explanation:
Use the initial condition when dp/dt = 1, p = 10 to get k;
[tex]\frac{dp}{dt} =kp^2\\\\1=k(10)^2\\\\k=\frac{1}{100}[/tex]
Seperate the differential equation and solve for the constant C.
[tex]\frac{dp}{p^2}=kdt\\\\-\frac{1}{p}=kt+C\\\\\frac{1}{p}=-kt+C\\\\p=-\frac{1}{kt+C} \\\\2=-\frac{1}{0+C}\\\\-\frac{1}{2}=C\\\\p(t)=-\frac{1}{\frac{t}{100}-\frac{1}{2} }\\\\p(t)=-\frac{1}{\frac{2t-100}{200} }\\\\-\frac{200}{2t-100}[/tex]
You have 100 rodents when:
[tex]100=-\frac{200}{2t-100} \\\\2t-100=-\frac{200}{100} \\\\2t=98\\\\t=49\ months[/tex]
You have 1000 rodents when:
[tex]1000=-\frac{200}{2t-100} \\\\2t-100=-\frac{200}{1000} \\\\2t=99.8\\\\t=49.9\ months[/tex]
3. (03.06)
Choose the point-slope form of the equation below that represents the line that passes through the points (-6, 4) and (2,0). (2 points)
Answer:
work is shown and pictured
