Answer:
[tex]f(g(2)) = 2[/tex]
Step-by-step explanation:
Given
[tex]x \to f(x)[/tex]
[tex]-6 \to 1[/tex]
[tex]-3 \to 2[/tex]
[tex]g(x) = f^{-1}(x)[/tex] --- inverse
Required
[tex]f(g(2))[/tex]
For two functions f(x) and g(x) where f(x) and g(x)are inverse;
[tex]f(g(x)) = x[/tex]
So, by comparison:
[tex]f(g(2)) = 2[/tex]
1. In the spring of 2017, the Consumer Reports National Research Center conducted a survey of 1007 adults to learn about their major health-care concerns. The survey results showed that 574 of the respondents lack confidence they will be able to afford health insurance in the future. Develop a 90% confidence interval for the population proportion of adults who lack confidence they will be able to afford health insurance in the future.
Answer:
The correct answer is "1668". A further solution is provided below.
Step-by-step explanation:
According to the question,
Estimated proportion,
[tex]\hat{p} = \frac{574}{1007}[/tex]
[tex]=0.57[/tex]
Margin of error,
E = 0.02
Level of confidence,
= 90%
= 0.90
Critical value,
[tex]Z_{0.10}=1.65[/tex]
Now,
⇒ [tex]0.02=1.65\times \sqrt{\frac{0.57\times 0.43}{n} }[/tex]
[tex]0.0004=2.7225\times \frac{0.2451}{n}[/tex]
[tex]n=\frac{2.7225\times 0.2451}{0.0004}[/tex]
[tex]=1668.21[/tex]
or,
[tex]n \simeq 1668[/tex]
una fuerza constante F de magnitud igual a 3lb se aplica al bloque que se muestra en la figura. F tiene la misma dirección que el vector a= 3i + 4j. determine el trabajo realizado en la dirección de movimiento si el bloque se mueve de P1 (3, 1) a P2 (9, 3). Suponga que la distancia se mide en pies.
Identify the domain of the table of values shown
Answer:
{-6,0,2,4}
Step-by-step explanation:
On weekend nights, a large urban hospital has an average of 4.8 emergency arrivals per hour. Let X be the number of arrivals per hour on a weekend night at this hospital. Assume that successive arrivals are random and independent. What is the probability P(X < 3)?
Answer:
P(X < 3) = 0.14254
Step-by-step explanation:
We have only the mean, which means that the Poisson distribution is used to solve this question.
Poisson distribution:
In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:
[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]
In which
x is the number of sucesses
e = 2.71828 is the Euler number
[tex]\mu[/tex] is the mean in the given interval.
On weekend nights, a large urban hospital has an average of 4.8 emergency arrivals per hour.
This means that [tex]\mu = 4.8[/tex]
What is the probability P(X < 3)?
[tex]P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2)[/tex]
So
[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]
[tex]P(X = 0) = \frac{e^{-4.8}*4.8^{0}}{(0)!} = 0.00823[/tex]
[tex]P(X = 1) = \frac{e^{-4.8}*4.8^{1}}{(1)!} = 0.03950[/tex]
[tex]P(X = 2) = \frac{e^{-4.8}*4.8^{2}}{(2)!} = 0.09481[/tex]
So
[tex]P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2) = 0.00823 + 0.03950 + 0.09481 = 0.14254[/tex]
P(X < 3) = 0.14254
Which operation will solve the following word problem? Andrea's class has 20 students and half of the students are studying math, half of these are studying word problems. How many are studying word problems?
Addition
Subtraction
Division
Multiplication
divide .2÷20 =10 10 students are Studing word problems
Find the Taylor series for f(x) centered at the given value of a. (Assume that f has a power series expansion. Do not show that Rn(x)→0 . f(x)=lnx, a=
Answer:
Here we just want to find the Taylor series for f(x) = ln(x), centered at the value of a (which we do not know).
Remember that the general Taylor expansion is:
[tex]f(x) = f(a) + f'(a)*(x - a) + \frac{1}{2!}*f''(a)(x -a)^2 + ...[/tex]
for our function we have:
f'(x) = 1/x
f''(x) = -1/x^2
f'''(x) = (1/2)*(1/x^3)
this is enough, now just let's write the series:
[tex]f(x) = ln(a) + \frac{1}{a} *(x - a) - \frac{1}{2!} *\frac{1}{a^2} *(x - a)^2 + \frac{1}{3!} *\frac{1}{2*a^3} *(x - a)^3 + ....[/tex]
This is the Taylor series to 3rd degree, you just need to change the value of a for the required value.
Please help!! Picture included!
Answer: the answer is c
Step-by-step explanation:brainlist [tex]\left[\begin{array}{ccc}1&2&3\\4&5&6\\7&8&9\end{array}\right][/tex]
The solution of this equation has an error. Which of the following steps has the error? 18 − (3x + 5) = 8
Step 1: 18 − 3x + 5 = 8
Step 2: -3x + 23 = 8
Step 3: -3x = -15
Step 4: x = 5
Step 1 Step 2 Step 3 Step 4. ?
Answer:
Step 1
Because the number in front of the bracket is 1 and it is also affected by the negative sign(-),5 is supposed to be negative not positive because (negative by positive is negative)
And since the first step has an error in it,the remaining steps would also be wrong.
Tom's graduation picnic costs $4 for every attendee. At most how many attendees can there be if Tom budgets a total of $36 for his graduation picnic?
HELP FAST PLEASEEEEEE
Which of the tables represents a function?
Table AInput
Output
3
1
3
4
2
3
Table BInput
Output
2
7
5
6
2
9
Table CInput
Output
1
5
7
2
7
3
Table DInput
Output
3
4
1
5
8
5
Select one:
a. Table A
b. Table B
c. Table C
d. Table D
Answer:
d.......................
Find the value of x pls help
9514 1404 393
Answer:
x = 36°
Step-by-step explanation:
The exterior angle is equal to the sum of the remote interior angles. A linear pair is supplementary. So, you can find x either of two ways:
2x = x + (180 -4x) ⇒ 5x = 180 ⇒ x = 36
Or ..
4x = x + (180 -2x) ⇒ 5x = 180 ⇒ x = 36
The value of x is 36°.
need help now!!! Please and thanks
Answer:
the answer of r is 8 i hope it will help
A statistics professor plans classes so carefully that the lengths of her classes are uniformly distributed between 47.0 and 57.0 minutes. Find the probability that a given class period runs between 51.25 and 51.5 minutes.
Answer:
0.025 = 2.5% probability that a given class period runs between 51.25 and 51.5 minutes.
Step-by-step explanation:
Uniform probability distribution:
An uniform distribution has two bounds, a and b.
The probability of finding a value between c and d is:
[tex]P(c \leq X \leq d) = \frac{d - c}{b - a}[/tex]
Uniformly distributed between 47.0 and 57.0 minutes.
This means that [tex]a = 47, b = 57[/tex]
Find the probability that a given class period runs between 51.25 and 51.5 minutes.
[tex]P(c \leq X \leq d) = \frac{51.5 - 51.25}{57 - 47} = 0.025[/tex]
0.025 = 2.5% probability that a given class period runs between 51.25 and 51.5 minutes.
The following data were collected from a simple random sample from an infinite population.
13 15 14 16 12
The point estimate of the population standard deviation is _____.
Answer:
15
Step-by-step explanation:
There are 92 students enrolled in an French course and 248 students enrolled in a Spanish course. Construct a ratio comparing students enrolled in a French course to students enrolled in a Spanish course. Write your answer as a decimal, rounded to the thousandths place.
Answer:
0.371
Step-by-step explanation:
The ratio comparing students enrolled in a French course to students enrolled in a Spanish course rounded to the thousandths place is 0.371.
What is the ratio?A ratio indicates how many times one number contains another. If a and b are to objects then ratio of a to the b is given as a : b.
Now it is given that,
Students enrolled in a French course = 92
Students enrolled in a Spanish course = 248
So, Ratio comparing students enrolled in a French course to students enrolled in a Spanish = Students enrolled in a French course / Students enrolled in a Spanish course
⇒ Ratio comparing students enrolled in a French course to students enrolled in a Spanish = 92/248
⇒ Ratio comparing students enrolled in a French course to students enrolled in a Spanish = 0.370967
To rounded to the thousandths place, the digit at the thousandth place is 0 and right to it is 9 which is greater than 5 so round up the place value at thousandths place.
⇒ Ratio comparing students enrolled in a French course to students enrolled in a Spanish = 0.371
Thus, the ratio comparing students enrolled in a French course to students enrolled in a Spanish course rounded to the thousandths place is 0.371.
To learn more about ratio:
https://brainly.com/question/1504221
#SPJ2
(3x^3)^2 write without exponent
Answer:
9*x*x*x*x*x*x.
Step-by-step explanation:
(3x^3)^2
= 3^2 * x^(3*2)
= 3^2 * x^6
= 9*x*x*x*x*x*x
The function c(r)=2r+12.5 represents the cost c, in dollars, of riding r rides
at a carnival. How much does it cost to get into the carnival? *
1 point
A.$2
B. $12.50
C. $14.50
D.r
Gloria received a 4 percent raise and is now making $24,960 a year, what was her salary before the raise?
She gets a 4% raise so her new pay is 100% + 4% of her previous pay.
104% = 1.04 as a decimal.
Divide her new pay by 1.04:
24,960 / 1.04 = 24,000
Her previous pay was $24,000
A rectangular vegetable garden will have a width that is 3 feet less than the length, and an area of 54square feet. If x represents the length, then the length can be found by solving the equation: x(x-3)=54 What is the length, x, of the garden? The length is blank feet.
Answer: 9 feet
Step-by-step explanation:
From the information given, we have already been given the equation which is x(x-3)=54. Therefore we will find the value of x which will be:
x(x-3)=54
x² - 3x - 54
x² - 9x + 6x - 54
x(x - 9) + 6(x - 9)
Therefore,
(x - 9) = 0
x = 0 + 9
x = 9
The length is 9 feet
The width will be:
x - 3 = 9 - 3 = 6 feet
What is the value of x
Answer:
[tex]6x+3+69=180[/tex]
[tex]6x=180-72[/tex]
[tex]6x=108[/tex]
[tex]x=18[/tex]
--------------------------
hope it helps..
have a great day!!
I need help with this problem.
Answer:
-4
Step-by-step explanation:
2t=-1-7
t=-8/2
t=-4
i am not sure also
1 point
Use log10 3-0.4771; log10 5 0.699010810 7 0.8451; log10 11 1.0414 to approximate the value of each expression-
log10 14710910 (147)
Answer:
[tex]\log_{10}(147) = 2.1673[/tex]
Step-by-step explanation:
Given
[tex]\log_{10} 3 = 0.4771[/tex]
[tex]\log_{10} 5 = 0.6990[/tex]
[tex]\log_{10} 7= 0.8451[/tex]
[tex]\log_{10} 11 = 1.0414[/tex]
Required
Evaluate [tex]\log_{10}(147)[/tex]
Expand
[tex]\log_{10}(147) = \log_{10}(49 * 3)[/tex]
Further expand
[tex]\log_{10}(147) = \log_{10}(7 * 7 * 3)[/tex]
Apply product rule of logarithm
[tex]\log_{10}(147) = \log_{10}(7) + \log_{10}(7) + \log_{10}(3)[/tex]
Substitute values for log(7) and log(3)
[tex]\log_{10}(147) = 0.8451 + 0.8451 + 0.4771[/tex]
[tex]\log_{10}(147) = 2.1673[/tex]
2/9 divided by 5/6
help pleaseee
Hey there!
[tex]\mathsf{\dfrac{2}{9}\div\dfrac{5}{6}}[/tex]
[tex]\mathsf{= \dfrac{2\times6}{9\times5}}[/tex]
[tex]\mathsf{2\times 6 = \bf 12}[/tex]
[tex]\mathsf{9\times5 = \bf 45}[/tex]
[tex]\boxed{\mathsf{=\bf \dfrac{12}{45}}}[/tex]
[tex]\large\textsf{BOTH NUMBERS has the Greatest Common Factor (GCF) of 3}[/tex]
[tex]\mathsf{= \dfrac{12\div3}{45\div3}}[/tex]
[tex]\mathsf{12\div3=\bf 4}[/tex]
[tex]\mathsf{45\div3=\bf 15}[/tex]
[tex]\boxed{\mathsf{=\bf \dfrac{4}{15}}}[/tex]
[tex]\boxed{\boxed{\large\textsf{Answer: }\mathsf{\bf \dfrac{4}{15}}}}\huge\checkmark[/tex]
[tex]\large\textsf{Good luck on your assignment and enjoy your day!}\\\\\\~\frak{Amphitrite1040:)}}[/tex]
In order to win a prize, Heather randomly draws two balls from a basket of 40. There are 25 blue balls, and the rest are green balls. Of the blue balls, 12% are winning balls. Of the green balls, 20% are winning balls. Calculate the expected number of winning balls that Heather draws.
Answer:
The expected number of winning balls that Heather draws is 0.3.
Step-by-step explanation:
The balls are chosen without replacement, which means that the hypergeometric distribution is used to solve this question.
Hypergeometric distribution:
The probability of x successes is given by the following formula:
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]
In which:
x is the number of successes.
N is the size of the population.
n is the size of the sample.
k is the total number of desired outcomes.
Combinations formula:
[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]
Expected value of the hypergeometric distribution:
The expected value is given by:
[tex]E(X) = \frac{nk}{N}[/tex]
Expected number of blue and green balls:
40 balls, which means that [tex]N = 40[/tex]
2 are chosen, which means that [tex]n = 2[/tex]
25 are blue, which means that [tex]k = 25[/tex]
So
[tex]E(X) = \frac{nk}{N} = \frac{25(2)}{40} = 1.25[/tex]
1.25 balls are expected to be blue and 2 - 1.25 = 0.75 green.
Of the blue balls, 12% are winning.
Of the green balls, 20% are winning.
Calculate the expected number of winning balls that Heather draws.
[tex]E_w = 1.25*0.12 + 0.75*0.2 = 0.3[/tex]
The expected number of winning balls that Heather draws is 0.3.
The explicit rule for a sequence and one of the specific terms is given. Find the position of the given term.
f(n) = 3.75n − 27.5; 25
Step 1 out of 2:
You know that the value of f(n) is 25. Substitute 25 for f(n) in f(n) = 3.75n − 27.5.
25 = 3.75n − 27.5
= 3.75n
Answer:
14
Step-by-step explanation:
Given :
f(n) = 3.75n − 27.5
f(n) = 25
Put f(n) = 25 in the equation :
25 = 3.75n - 27.5
25 + 27.5 = 3.75n
52.5 = 3.75n
52.5 / 3 75 = n
14 = n
The position of the term is 14
A rectangle is drawn so the width is 6 inches longer than the height. If the rectangle's diagonal measurement is 27 inches, find the height.
Give your answer rounded to 1 decimal place.
Answer:
height = 3
Step-by-step explanation:
x(x+6) = 27
x^2 + 6x - 27 = 0
(x+9)(x-3) = 0
x = 3
John's age 4 years ago, if he will be y years old in 5 years
9514 1404 393
Answer:
y -9
Step-by-step explanation:
From 4 years ago until 5 years from now, John will age 9 years. That is, his age 4 years ago is 9 years less than it will be in 5 years.
John's age 4 years ago is y-9 years.
convert 1.5% to decimal and a fraction. Show and explain your method
Answer:
0.015 and 3/200.
Step-by-step explanation:
1.5% is equal to 0.015. Percents are always equal to their decimal counterparts; basically, the number over 100. Dividing 1.5 by 100 will yield us 0.015.
0.015 is going to be equal to 15/1000, or 3/200. Since we did 1.5/100, we need to multiply both sides of the fraction by 10 so there are no decimal points. Therefore, this is 15/1000. If we divide both sides of this fraction by 5, then we get 3/200, which is the most simplified form.
There are 4 routes from Danbury to Hartford and 6 routes from Hartford to Springfield. You need to drive from Danbury to Springfield for an important meeting. You don’t know it, but there are traffic jams on 2 of the 4 routes and on 3 of the 6 routes. Answer the following:
a. You will miss your meeting if you hit a traffic jam on both sections of the journey. What is the probability of this happening?
b. You will be late for your meeting if you hit a traffic jam on at least one, but not both sections of the trip. What is the probability of this?
c. What is the probability that you will hit no traffic jam?
Answer:
a. P) = 0.25
b. P) = 0.25
c. P) = 0.5
Step-by-step explanation:
a) 1/4 as 1/2 x 1/2 = 1/4 = 0.25 This becomes reduced as we are multiplying one complete probability journey by another complete probability journey.
b) see above as 1/2 x 1/4 and 1/4 x 1/2 = 2.5 = 1/4 = 0.25
or we can Set to 1 and 1 - 3/4 = 1/4. = 0.25.
c) 1/2 as half of the journeys have traffic jams so its 1 - 1/2 = 1/2 = 0.5
is this right? PLEASE HELP ILL MARK
Answer:
yeah u r correct...hope it helps ..stay safe healthy and happy.