Answer:
The sample needed is [tex]n =150[/tex]
Step-by-step explanation:
From the question we are told that
The margin of error is [tex]E = 0.08[/tex]
The confidence level is [tex]C = 95 \% = 0.95[/tex]
Given that the confidence level is 95% the level of significance is mathematically represented as
[tex]\alpha = 1 - 0.95[/tex]
[tex]\alpha = 0.05[/tex]
Next we obtain the critical value of [tex]\frac{\alpha }{2}[/tex] from the z-table , the value is [tex]Z_{\frac{\alpha }{2} } = 1.96[/tex]
The reason we are obtaining critical value of [tex]\frac{\alpha }{2}[/tex] instead of [tex]\alpha[/tex] is because
[tex]\alpha[/tex] represents the area under the normal curve where the confidence level interval ( [tex]1-\alpha[/tex] ) did not cover which include both the left and right tail while
[tex]\frac{\alpha }{2}[/tex] is just the area of one tail which what we required to calculate the margin of error
The sample size is mathematically represented as
[tex]n = [\frac{Z_{\frac{\alpha }{2} }}{E} ]^2 * \r p[1-\r p][/tex]
Here [tex]\r p[/tex] is sample proportion of people that supported her and we will assume this to be 50% = 0.5
So
[tex]n = [\frac{1.96}{ 0.08} ]^2 * [0.5 (1- 0.5)][/tex]
[tex]n =150[/tex]
Gena wants to estimate the quotient of –21.87 divided by 4.79. Which expression shows the best expression to estimate the quotient using front-end estimation? Negative 21 divided by 4 Negative 21 divided by 5 Negative 20 divided by 4 Negative 20 divided by 5
Answer:
-21/5 = -4.2
Step-by-step explanation:
-21.87 / 4.79 = -4.5657.....
So, the quotients is -4
Now, Let's see who's quotient is equal to think one:
-21/4 = -5.25
-21/5 = -4.2
-40/4 = -5
-20/5 = 4
Answer:
-21/5 = -4.2
Step-by-step explanation:
VW=40in. The radius of the circle is 25 inches. Find the length of CT.
Answer:
The answer is B. 40 inches.
Step-by-step explanation:
The question starts by telling you that line VW is equal to 40 in. If you look at the picture you can see it is divided into 2 equal parts of 20 in each. If you look at line CT, you can see that there are the same marks meaning that those segments are also 20 in. That means that line CT and line VW are equal and that line CT is equal to 40 in.
Find the critical point of the given function and then determine whether it is a local maximum, local minimum, or saddle point.
Answer:
critical point of the given function f(x,y) = x²+y²+2xy is from line y = -x is the critical point of the function f(x0,y0) = 0
and it local minimum.
Step-by-step explanation:
Let the given function be;
f(x,y) = x²+y²+2xy
From above function, we can locate relative minima, maxima and the saddle point
f(x,y) = x²+y²+2xy = (x+y)²
df/dx = 2x+2y = 0 ---- (1)
df/dy =2y+2x = 0 ---- (2)
From eqn 1 and 2 above,
The arbitrary point (x0,y0) from line y = -x is the critical point of the function f(x0,y0) = 0
Then, from f(x,y) >= 0 for arbitrary (x,y) € R^n, the arbitrary point from the line x = -y is local minima of the function f.
PLEASE HELP!! Write the proportion. 120 feet is to 150 feet as 8 feet is to 10 feet. (18 points!!)
Answer:
4 : 5
Step-by-step explanation:
you can divide 120 and 150 by 30 and 8 and 10 by 2.
120/30 = 4
150/30 = 5
8/2 = 4
10/2=5
Answer: 4:5
Step-by-step explanation:
what is the 20th term of the arithmetic sequence a(n)=-5+(n-1)3
Answer:
52
Step-by-step explanation:
a(n)=-5+(n-1)3
a(20)=-5+(20-1)3
a(20)=52
The 20th term of the arithmetic sequence is 52.
What is Arithmetic sequence?An arithmetic sequence is a list of numbers with a definite pattern. If you take any number in the sequence then subtract it by the previous one, and the result is always the same or constant then it is an arithmetic sequence.
For example,
In an arithmetic sequence, the difference between consecutive terms is always the same. For example, the sequence 3, 5, 7, 9 ... is arithmetic because the difference between consecutive terms is always two.
The nth term of an arithmetic sequence is given by an = a + (n – 1)d.
Given:
a(n)=-5+(n-1)3
First term,
a(1)= -5 + 0
a(1)= -5
second, a(2)= -5 + 1*3
a(2)= -2
Third, a(3)= -5+6
a(3)= 1
d= 3
So, the 20th term
a(20)= -5+ (20-1)3
a(20)= -5 + 57
a(20)= 52
Hence, the 20th term is 52.
Learn more about Arithmetic Sequence here:
https://brainly.com/question/10396151
#SPJ2
The function y = sin^?1(3x + 1) is a composition, and so we must use the Chain Rule, given below, to find the derivative. d dx [f(g(x))] = f '(g(x))g'(x) For the given function sin^?1(3x + 1), the "inside" function is 3x + 1 and the "outside" function is f(x) = arcsin(x).
Recall that the derivative of y = sin?1(x) is y' =__________?
Answer:
dy/dx = 3/√1-(3x+1)²
Step-by-step exxplanation:
Given the inverse function y = sin^-1(3x+1), to find the derivative of the expression, we will use the chain rule as shown;
Let u = 3x+1 ...1
y = sin⁻¹u ...2
From equation 1, du/dx = 3
from equation 2;
Taking the sin of both sides;
siny = sin(sin⁻¹u)
siny = u
u = siny
du/dy = cosy
dy/du = 1/cosy
from trig identity, cos y = √1-sin²y
dy/du = 1/√1-sin²y
Ssince u = siny
dy/du = 1/√1-u²
According to chain rule, dy/dx = dy/dy*du/dx
dy/dx = 1/√1-u² * 3
dy/dx = 3/√1-u²
Substituting u = 3x+1 into the final equation, we will have;
dy/dx = 3/√1-(3x+1)²
solve this for me plzzz
Answer: a- steve
Step-by-step explanation:
Answer:
B Emma is correct
Step-by-step explanation:
72 students choose to attend one of three after school activities: football, tennis or running. There are 25 boys. 27 students choose football, of which 17 are girls. 18 students choose tennis. 24 girls choose running. A student is selected at random. What is the probability this student chose running? Give your answer in its simplest form.
Answer:
3/8
Step-by-step explanation:
There are 72 students. 27 students choose football, and 18 choose tennis, which means 27 choose running.
So the probability that a student chooses running is 27/72, which reduces to 3/8.
Which of the following functions best describes this graph ?
Answer:
answer D
Step-by-step explanation:
Lets have a look to the graph and to the each of given functions.
As we can see in graph it intersects X in points (-3;0) and (-6;0) that means the function has the roots x1=-3 and x2=-6
Function A has the roots x1=+3 and x2=+6 => doesn' t fit
Function B has only 1 root x=2 , so can be factorized y=(x-2)^2 => doesn' t fit
Function C has 2 roots x1=4 and x2=-5 => doesn' t fit
Function D can be factotized as y=(x+6)*(x+3) so has 2 roots x1=-6 x2=-3 => exactly what we need!!!
We can also notice that the coefficient near x² is equal to 1 and is positive.
That means the legs of the graph directed up,- this is exactly like in our graph. It gives us extra argument why we choose D.
what is 99/00+44(55)99
Answer:
undefined! one cannot divide by 0
Step-by-step explanation:
Answer:
undefined!
Step-by-step explanation:
Assume that y varies directly with
x, then solve.
If y=6 when x=2/3 find x when y=12.
Х=? (It’s a fraction)
Answer:
x = 4/3
Step-by-step explanation:
Direct variation:
y = kx
We use the given x-y point to find k.
6 = k * 2/3
k = 6 * 3/2
k = 9
The equation is
y = 9x
For y = 12,
12 = 9x
x = 12/9
x = 4/3
A firm just paid an annual dividend of $1.40 and increases that dividend by 2 percent each year. How do you find the price if the firm's stock at year 4 if the discount rate is 13 percent?
Answer:
14.05
Step-by-step explanation:
We have the following:
Current Dividend = D0 = $ 1.40
g = growth rate = 2%
r = discount rate = 13%
Dividend in Year 5
= D5 = D0 * (1 + g) ^ 5
= $ 1.40 * (1 + 2%) ^ 5
= $ 1.40 * (1.02) ^ 5
Firm Stock Price at the end of year 4 = Dividend in Year 5 / (r - g)
= $ 1.40 * (1.02) ^ 5 / (13% -2%)
= $ 1.40 * (1.02) ^ 5 / (0.13 - 0.02)
Therefore, firm stock at the end of year 4 is
P4 = $ 1.40 * (1.02) ^ 5 / (0.13 - 0.02) = 14.05
Please help. I’ll mark you as brainliest if correct!
Answer:
Step-by-step explanation:
children=c
adults=a
c+a=359
a=359-c
2.75c+6a=1621
2.75 c+6(359-c)=1621
2.75 c+2154-6c=1621
-3.25 c=1621-2154
-3.25 c=-533
[tex]-\frac{325}{100} c=-533\\-\frac{13}{4} c=-533\\c=-533 \times \frac{-4}{13} =41 \times 4=164 \\children=164\\adults=359-164=195[/tex]
Please do either 40 or 39
Answer:
y = 1.8
Step-by-step explanation:
Question 39).
Let the operation which defines the relation between a and b is O.
Relation between a and b has been given as,
a O b = [tex]\frac{(a+b)}{(a-b)}[/tex]
Following the same operation, relation between 3 and y will be,
3 O y = [tex]\frac{3+y}{3-y}[/tex]
Since 3 O y = 4,
[tex]\frac{3+y}{3-y}=4[/tex]
3 + y = 12 - 4y
3 + y + 4y = 12 - 4y + 4y
3 + 5y = 12
3 + 5y - 3 = 12 - 3
5y = 9
[tex]\frac{5y}{5}=\frac{9}{5}[/tex]
y = 1.8
Therefore, y = 1.8 will be the answer.
Use the graph to solve the given system of equations, then enter your solution below. {x−3y=−3x+y=5
Answer:
Step-by-step explanation:
Given the system of equation x−3y=−3 and x+y=5, we can solve for x and y by solving the equation simultaneously using the substitution method.
x−3y=−3_____________ 1
x+y=5 ______________2
From equation 2; x = 5- y ________ 3
Substitute equation 3 into equation 1
Since x - 3y = -3
(5-y)-3y = -3
5-y-3y = -3
5-4y = -3
Subtract 5 from both sides of the equation
5-4y-5 = -3-5
-4y = -8
Divide both sides by -4
-4y/-4 = -8/-4
y = 2
Substitute y = 2 into equation 2 to get the value of y;
From equation 2, x+y = 5
x+2 = 5
Subtract 2 from both sides of the equation
x+2-2 = 5-2
x = 3
Hence the value of x and y from the graph will be 3 and 2 respectively.
I really need help on this question
Answer:
d. 38
Step-by-step explanation:
AB = AD - BD = 54 - 36 = 18
AC = AB + BC = 18 + 20 = 38
Safegate Foods, Inc., is redesigning the checkout lanes in its supermarkets throughout the country and is considering two designs. Tests on customer checkout times conducted at two stores where the two new systems have been installed result in the following summary of the data.
System System B
n1=120 n2=100
x1=4.1 minutes x2=3.4 minutes
σ1=2.2minutes σ2= 1.5 minutes
Test at the 0.05 level of significance to determinewhether the population mean checkout times of the two newsystems differ. Which system is preferred?
Answer:
We conclude that the population means checkout times of the two new systems differ.
Step-by-step explanation:
We are given the result in the following summary of the data;
System System B
n1=120 n2=100
x1=4.1 min x2=3.4 min
σ1=2.2 min σ2= 1.5 min
Let [tex]\mu_1[/tex] = population mean checkout time of the first new system
[tex]\mu_2[/tex] = population mean checkout time of the second new system
So, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu_1=\mu_2[/tex] {means that the population mean checkout times of the two new systems are equal}
Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu_1\neq \mu_2[/tex] {means that the population mean checkout times of the two new systems differ}
The test statistics that will be used here is Two-sample z-test statistics because we know about population standard deviations;
T.S. = [tex]\frac{(\bar X_1-\bar X_2)-(\mu_1-\mu_2)}{\sqrt{\frac{\sigma_1^{2} }{n_1} + \frac{\sigma_2^{2} }{n_2}} }[/tex] ~ N(0,1)
where, [tex]\bar X_1[/tex] = sample mean checkout time of the first new systems = 4.1 min
[tex]\bar X_2[/tex] = sample mean checkout time of the second new systems = 3.4 min
[tex]\sigma_1[/tex] = population standard deviation of the first new systems = 2.2 min
[tex]\sigma_2[/tex] = population standard deviation of the second new systems = 1.5 min
[tex]n_1[/tex] = sample of the first new systems = 120
[tex]n_2[/tex] = sample of the second new systems = 100
So, the test statistics = [tex]\frac{(4.1-3.4)-(0)}{\sqrt{\frac{2.2^{2} }{120} + \frac{1.5^{2} }{100}} }[/tex]
= 2.792
The value of z-test statistics is 2.792.
Now, at 0.05 level of significance, the z table gives a critical value of -1.96 and 1.96 for the two-tailed test.
Since the value of our test statistics does not lie within the range of critical values of z, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region.
Therefore, we conclude that the population mean checkout times of the two new systems differ.
-2x(x+3)-(x+1)(x-2)=
Answer:
-3x^2 -5x +2
Step-by-step explanation:
-2x(x+3)-(x+1)(x-2)=
Distribute
-2x^2 -6x -(x+1)(x-2)
Foil
-2x^2 -6x -(x^2 -2x +x -2)
Combine like terms
-2x^2 -6x -(x^2 -x -2)
Distribute the minus sign
-2x^2 -6x -x^2 +x +2
Combine like terms
-2x^2 -x^2 -6x +x +2
-3x^2 -5x +2
Answer:
[tex]\huge\boxed{-2x(x+3)-(x+1)(x-2)=-3x^2-5x+2}[/tex]
Step-by-step explanation:
[tex]-2x(x+3)-(x+1)(x-2)[/tex]
Use the distributive property: a(b + c) = ab + ac
and FOIL: (a + b)(c + d) = ac + ad + bc + bd
[tex]=(-2x)(x)+(-2x)(3)-\bigg[(x)(x)+(x)(-2)+(1)(x)+(1)(-2)\bigg]\\\\=-2x^2-6x-\bigg(x^2-2x+x-2\bigg)=-2x^2-6x-x^2-(-2x)-x-(-2)\\\\=-2x^2-6x-x^2+2x-x+2[/tex]
Combine like terms:
[tex]=(-2x^2-x^2)+(-6x+2x-x)+2=-3x^2+(-5x)+2\\\\=-3x^2-5x+2[/tex]
a sample of bacteria is growing at an hourly rate of 14% according to the exponential growth function.the sa
Answer:
pleasse elaborate more
Step-by-step explanation:
Imagine working in a freelance developer earning 80 USD per hour how many weeks you will have to take a 12 hour flight on a weekday you can either book a flight for ticket for 11 AM for 900 USD or 11 PM flight or 11 USD there is no Internet boards if you take the day off like you will lose a day of work what would you do
Answer:
pay the 11 AM ticket
Step-by-step explanation:
Note that the flight last for 12 hours, and assuming the freelance developer can still work (have access to the internet) on the airplane throughout the flight, he stand to earn $960 ($80*12), which will still cover the cost of the flight with a profit of $60 ($960-900).
However, if he decides to pay the $11 flight ticket and there is no Internet on boards; there by losing a day of work, he stand to have lost working time which would earn with $900.
Therefore, the best choice is to pay the 11 AM ticket.
42.
You were given the four numbers below and were asked to find the sum
of the first two numbers, the difference between the last two numbers,
the quotient when the sum is divided by the difference and the product
when the quotient is multiplied by 8. What is the final answer?
6458 2994
7013
6945
Answer:
1112
Step-by-step explanation:
6458 + 2994 = 9452
7013 - 6945 = 68
9452/68 = 139
139 * 8 = 1112
helpppppppppppppppppppppp i will give star thanks bralienst
Answer:
90/x=70/100 that's my answer
[tex]90 \x = 70 \100[/tex]
Answer:
90/x = 70/100
Step-by-step explanation:
Is means equals and of means multiply
90 = 70% *x
Changing to decimal form
90 = .70x
Changing to fraction form
90 = 70/100 *x
Divide each side by x
90/x = 70/100
Determine the domain of the function. f as a function of x is equal to the square root of two minus x.
x ≤ 2
All real numbers
x > 2
All real numbers except 2
Answer:
A. x <= 2
Step-by-step explanation:
The domain of a real function should be all real numbers. In
f(x) = sqrt(2-x)
we need 2-x to be non-negative, therefore
2-x >= 0
which implies
x <= 2
Answer:
[tex]\Huge \boxed{{x\leq 2}}[/tex]
Step-by-step explanation:
The function is given,
[tex]f(x)=\sqrt{2-x}[/tex]
The domain of a function are all possible values of x.
There are restrictions for the value of x.
2 - x cannot be equal to a negative number, because the square root of a negative number is undefined. 2 - x has to equal to 0 or be greater than 0.
[tex]2-x\geq 0[/tex]
[tex]-x\geq -2[/tex]
[tex]x\leq 2[/tex]
The domain of the function is x ≤ 2.
Factories A, B and C produce computers. Factory A produces 4 times as manycomputers as factory C, and factory B produces 7 times as many computers asfactory C. The probability that a computer produced by factory A is defective is0.04, the probability that a computer produced by factory B is defective is 0.02,and the probability that a computer produced by factory C is defective is 0.03. Acomputer is selected at random and found to be defective. What is the probabilityit came from factory A?
Answer:
The probability is [tex]P(A') = 0.485[/tex]
Step-by-step explanation:
Let assume that the number of computer produced by factory C is k = 1
So From the question we are told that
The number produced by factory A is 4k = 4
The number produced by factory B is 7k = 7
The probability of defective computers from A is [tex]P(A) = 0.04[/tex]
The probability of defective computers from B is [tex]P(B) = 0.02[/tex]
The probability of defective computers from C is [tex]P(C) = 0.03[/tex]
Now the probability of factory A producing a defective computer out of the 4 computers produced is
[tex]P(a) = 4 * P(A)[/tex]
substituting values
[tex]P(a) = 4 * 0.04[/tex]
[tex]P(a) = 0.16[/tex]
The probability of factory B producing a defective computer out of the 7 computers produced is
[tex]P(b) = 7 * P(B)[/tex]
substituting values
[tex]P(b) = 7 * 0.02[/tex]
[tex]P(b) = 0.14[/tex]
The probability of factory C producing a defective computer out of the 1 computer produced is
[tex]P(c) = 1 * P(C)[/tex]
substituting values
[tex]P(c) = 1 * 0.03[/tex]
[tex]P(b) = 0.03[/tex]
So the probability that the a computer produced from the three factory will be defective is
[tex]P(t) = P(a) + P(b) + P(c)[/tex]
substituting values
[tex]P(t) = 0.16 + 0.14 + 0.03[/tex]
[tex]P(t) = 0.33[/tex]
Now the probability that the defective computer is produced from factory A is
[tex]P(A') = \frac{P(a)}{P(t)}[/tex]
[tex]P(A') = \frac{ 0.16}{0.33}[/tex]
[tex]P(A') = 0.485[/tex]
Which expression is equivalent to 2m^2 - m^2(7-m)+6m^2?
Answer:
[tex]m^3+m^2[/tex]
Step-by-step explanation:
=> [tex]2m^2-m^2(7-m)+6m^2[/tex]
Collecting like terms and expanding the brackets
=> [tex]2m^2+6m^2-7m^2+m^3[/tex]
=> [tex]8m^2-7m^2+m^3[/tex]
=> [tex]m^2+m^3[/tex]
=> [tex]m^3+m^2[/tex]
Translate and solve: 3x less than two times the sum of 2X and one is equal to the sum of 2 and 5
Answer:
The answer is x = 5Step-by-step explanation:
The statement
3x less than two times the sum of 2X and one is written as
2( 2x + 1) - 3x
the sum of 2 and 5 is written as
2 + 5
Equate the two statements
We have
2( 2x + 1) - 3x = 2+5
Expand
4x + 2 - 3x = 7
Simplify
4x - 3x = 7 - 2
We have the final answer as
x = 5Hope this helps you
A dress regularly sells for $137. The sale price is $102.75. Find the discount & the percent of the discount
Answer:
Discount : $34.25 off. Percent of the discount : 25%
Step-by-step explanation:
137 - 102.75 = 34.25.
34.25/137 x 100 = 25%
Which equation is the inverse of y = 16x2 + 1? y = plus-or-minus StartRoot StartFraction x Over 16 EndFraction minus 1 EndRoot y = StartFraction plus-or-minus StartRoot x minus 1 EndRoot Over 16 EndFraction y = StartFraction plus-or-minus StartRoot x EndRoot Over 4 EndFraction minus one-fourth y = StartFraction plus-or-minus StartRoot x minus 1 EndRoot Over 4 EndFraction
Answer:
The inverse is ±sqrt((x-1))/ 4
Step-by-step explanation:
y = 16x^2 + 1
To find the inverse, exchange x and y
x = 16 y^2 +1
Then solve for y
Subtract 1
x-1 = 16 y^2
Divide by 16
(x-1)/16 = y^2
Take the square root of each side
±sqrt((x-1)/16) = sqrt(y^2)
±sqrt((x-1))/ sqrt(16) = y
±sqrt((x-1))/ 4 = y
The inverse is ±sqrt((x-1))/ 4
Answer:
D
Step-by-step explanation:
Find the mean and standard deviation for each binomial random variable:
Answer: a) Mean = [tex]=37.80[/tex]
Standard deviation=[tex]=1.9442[/tex]
b) Mean = [tex]56.00[/tex]
Standard deviation=[tex]4.0988[/tex]
c) Mean = [tex]=24[/tex]
Standard deviation=[tex]2.4495[/tex]
Step-by-step explanation:
To compute Mean and standard deviation , we use following formula:
Mean = [tex]n\pi[/tex]
Standard deviation=[tex]\sqrt{n\pi(1-\pi)}[/tex]
a. [tex]n=42,\ \pi=0.90[/tex]
Mean = [tex]42\times0.90=37.80[/tex]
Standard deviation=[tex]\sqrt{42(0.90)(0.10)}=\sqrt{3.78}\approx1.9442[/tex]
b. [tex]n=80,\ \pi=0.70[/tex]
Mean = [tex]80\times0.70=56.00[/tex]
Standard deviation=[tex]\sqrt{80(0.70)(0.30)}=\sqrt{16.8}\approx4.0988[/tex]
c. [tex]n=32,\ \pi=0.75[/tex]
Mean = [tex]32\times0.75=24[/tex]
Standard deviation=[tex]\sqrt{32(0.75)(0.25)}=\sqrt{6}\approx2.4495[/tex]
A bag of marbles contains 4 green marbles, 3 blue marbles, 2 red marbles, and 5 yellow marbles. How many total possible outcomes are there when choosing a marble from the bag?
Answer:
its 14/C
Step-by-step explanation:
i got i right on edg U^U
Answer:
16
Step-by-step explanation:
i did edge test yea dont be imma fake :***