Answer:
The 95% confidence interval for the proportion of respondents who say the Internet has strengthened their relationship with family and friends is:
[tex]0.72 \pm 1.96\sqrt{\frac{0.72*0.28}{n}}[/tex]
In which n is the sample size of the survey.
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the z-score that has a p-value of [tex]1 - \frac{\alpha}{2}[/tex].
The sample survey showed that 72% of Internet users said the Internet has generally strengthened their relationship with family and friends.
This means that [tex]\pi = 0.72[/tex]
95% confidence level
So [tex]\alpha = 0.05[/tex], z is the value of Z that has a p-value of [tex]1 - \frac{0.05}{2} = 0.975[/tex], so [tex]Z = 1.96[/tex].
Confidence interval:
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
[tex]0.72 \pm 1.96\sqrt{\frac{0.72*0.28}{n}}[/tex]
The 95% confidence interval for the proportion of respondents who say the Internet has strengthened their relationship with family and friends is:
[tex]0.72 \pm 1.96\sqrt{\frac{0.72*0.28}{n}}[/tex]
In which n is the sample size of the survey.
find the HCF of 54 and 81 by prime factorization method. pls send the photo
3║54, 81
3║18, 27
3║9, 9
3║3, 3
3║1, 1
HCF = 27
Must click thanks and mark brainliest
Answer:
Hello,
Step-by-step explanation:
[tex]\begin{array}{c||c}\begin{array}{c|c}54&2\\27&3\\9&3\\3&3\\1\\\end{array}&\begin{array}{c|c}81&3\\27&3\\9&3\\3&3\\1\\\end{array}\end{array}\\\\54=2^1*3^3\\ 81=3^4\\\\\boxed{HCF(54,81)=3^3=27}\\[/tex]
Which transformations are needed to change the parent sine function to y = one-fourth sine (4 (x + StartFraction pi Over 6 EndFraction))? vertical stretch of One-fourth, horizontal stretch to a period of 2p, phase shift of StartFraction pi Over 6 EndFraction units to the left vertical compression of One-fourth, horizontal compression to a period of StartFraction pi Over 2 EndFraction, phase shift of StartFraction pi Over 6 EndFraction units to the left vertical stretch of 4, horizontal stretch to a period of 8p, phase shift of StartFraction pi Over 6 EndFraction units to the right vertical compression of 4, horizontal compression to a period of StartFraction pi Over 4 EndFraction, phase shift of StartFraction pi Over 6 EndFraction units to the right
Answer: Option B is correct
Step-by-step explanation: edge 2021
Answer:
b
Step-by-step explanation:
simplify
7(a²)³ x 8a⁵ / 4a⁷ and explain
Answer: 14a^4
Step-by-step explanation:
What is the missing digit?
820,107
– 65□,084
167,023
Cuánto es 324 por 171
Answer:
la respuesta es 55,404
I hope this helped
If you order 6 pizzas, you will get 60 slices of pizza. How many slices are there in one pizza?
Answer:
10
Step-by-step explanation:
because 60/6 is ten
hope this helped
Answer:
10 because 60/6 =10 this is the answer
please help this is due soon
A.) Evaluate f(1)
B.) given: f(x) =1, find x
Answer:
f(1) = -2
f(x) =1 when x=0 or x=-2
Step-by-step explanation:
f(1) is the y value when x=1
f(1) = -2
f(x) = 1 means find the x value when y=1
when y =1, x =0 and -2
hi hi hi please help ♀️
Answer:
Cooper read the least because
Step-by-step explanation:
1/5 is less than
Answer: Cooper read more
Step-by-step explanation:
Using the Factor Theorem, which of the polynomial functions has the zeros 2, radical 3 , and negative radical 3 ? f (x) = x3 – 2x2 – 3x + 6 f (x)= x3 – 2x2 + 3x + 6 f (x) = x3 + 2x2 – 3x + 6 f (x) = x3 + 2x2 – 3x – 6
Answer:
A
[tex]f(x) = x^3 - 2x^2 -3x + 6[/tex]
Step-by-step explanation:
According to the Factor Theorem, if (x - k) is a factor of a polynomial P(x), then P(k) must equal zero.
We are given that a polynomial function has the zeros 2, √3, and -√3. So, we can let k = 2, √3, -√3.
So, according to the Factor Theorem, P(2), P(√3) and P(-√3) must equal 0.
Testing each choice, we can see that only A is true:
[tex]\displaystyle f(x) = x^3 - 2x^2 - 3x + 6[/tex]
Testing all three values yields that:
[tex]\displaystyle \begin{aligned} f(2) &= (2)^3 - 2(2)^2 -3(2) + 6 \\ &= (8) - (8) -(6) + (6) \\ &= 0\stackrel{\checkmark}{=}0 \\ \displaystyle f(\sqrt{3}) &= (\sqrt{3})^3 - 2(\sqrt{3})^2 - 3(\sqrt{3}) + 6 \\ &=(3\sqrt{3}) -(6)-(3\sqrt{3}) + 6 \\ &= 0\stackrel{\checkmark}{=}0 \\ f(-\sqrt{3}) &= (-\sqrt{3})^3 - 2(-\sqrt{3})^2 - 3(-\sqrt{3}) + 6 \\ &=(-3\sqrt{3}) -(6)+(3\sqrt{3}) + 6 \\ &= 0\stackrel{\checkmark}{=}0 \end{aligned}[/tex]
Hence, our answer is A.
The range is the set of________
A) First Coordinates
B) Ordered Pairs
C) Second coordinates
Answer:
The range is the set of first coordinates
7th grade math!!! Please help!! will mark brainlist
The answer is the first choice. If every 2 cm. is 4 cm., that means that the dimensions' values are doubled. Then, you can just double the dimensions. Preferably, in my opinion, this is the easier way to go. By your preference, though, you can do it the longer way as well.
There are 4 2s in the number 8.
There are 3 2s in the number 6.
If each of the 2s are 4s,
So, therefore,
Transforming the 2s to 4s,
4x4=16 cm.
3x4=12 cm.
So, this means that the final answer is the first choice. I hoped that this helped answer your question. Enjoy your day, and take care!
Answer:
`Length=16 feet, width=12 feet
Image result for how to use scale model step by step'
Divide the real life dimension of either length or width by that of the model. So the real life object had a length of 32m, and the model had a length of 8, then do 8(4). This is equal to 32, then divide by 2.
Hope this helps love <3
multiply 631.6 by 0.8
Answer: multiply 631.6 by 0.8 = 505.28
Identify the triangle, ABC, which has a 72∘ angle and a 36∘ angle.
Answer:
isosceles acute
Step-by-step explanation:
sum of angles in a triangle = 180
to find third angle, subtract 72 & 36 from 180 and you get 72
72, 36, and 72 are all less than 90 so it will be an acute triangle
It will also be isosceles bc there are 2 angles of the same measure
identify the roots of the equation and the multiplicities of the roots 8(x - 2)³ = 0
Answer:
The root of the equation is 2 with multiplicity 3
Step-by-step explanation:
8(x-2)^3=0
(x-2)^3=0
The root of the equation is 2 with multiplicity 3
Lee is in customer service. How can she best support her internal customer, Dan? O al Prioritize other tasks and customers O b) Ask him a lot of personal questions O c) Give him her full attention when he's speaking O d) Check with him before completing basic tasks
Solve the system of equations.
3x + 4y + 3z = 5
2x + 2y + 3z = 5
5x+ 6y+7z = 7
a. (x = 13, y=-6, z = -2)
b. (x = 15, y = -8, z = -4)
c. (x = 16, y = -9, z = -1)
d. (x = 14, y = -7, z = 3)
Answer:
x = 14
y = -7
z = -3
but this is none of the provided answer options !
Step-by-step explanation:
it's really easy by principle. it's just some work to do.
we try to find equations to express one variable in terms of the others.
but one thing there is : your teacher made a mistake.
the right solution is x = 14, y = -7, z = -3
your teacher made a typo at d.
but the right answer should be d.
just to give you an idea how this can be done (and also to prove that there is a mistake by the teacher):
we can directly try to transform one expression into one that describes x by y and z.
and then another to describe e.g. z by y. and then solve the third one just for y. and then we get the other 2 by these other expressions.
or we can e.g. add or subtract one equation to/from another. this is one of these cases, because we can find really simple expressions that way :
we do
5x + 6y + 7z = 7
- (3x + 4y + 3z = 5)
- (2x + 2y + 3z = 5)
---------------------------
0x + 0y + z = -3
=> z = -3
3x + 4y - 3×3 = 5
3x = -4y + 14
x = (-4y + 14)/3
2×(-4y + 14)/3 + 2y - 9 = 5
(-8y + 28)/3 + 2y = 14
-8y + 28 + 6y = 42
-2y = 14
y = -7
x = (-4×-7 + 14)/3 = (28+14)/3 = 42/3 = 14
Find an equation of the circle whose diameter has endpoints (-6, -1) and (-2,3).
Step-by-step explanation:
Let find the distance of the diameter. using distance formula.
[tex](3 + 1) {}^{2} + ( - 2 + 6) {}^{2} = \sqrt{8} [/tex]
The diameter is sqr root of 8 units.
A circle equation is
[tex] {x}^{2} + {y}^{2} = {r}^{2} [/tex]
where r is the radius. The radius is half the diameter so
[tex]r = \frac{ \sqrt{8} }{2} = \frac{ \sqrt{8} }{ \sqrt{4} } = \sqrt{2} [/tex]
[tex] {r}^{2} = { \sqrt{2} }^{2} = 2[/tex]
So our radius is 2.
Now we need to find the midpoint or Center of the diameter.
[tex] \frac{ - 6 - 2}{2} = - 4[/tex]
[tex] \frac{3 - 1}{2} = 1[/tex]
So the center of the circle is (-4,1). So our equation of the Circle us
[tex](x + 4) {}^{2} + (y - 1) {}^{2} = ( \sqrt{2} ) {}^{2} [/tex]
9x-5
14x+24
A
Determine the value of x.
1) x= -5.8
2) x= -7
3) x= 7
4) x= 32.2
Answer:
the answer to the question
is x=-5.8
Example 2.20
Solution
After 7% discount, Faizal get RM1,930 from a bank. He then promised to pay the bank RM2,000
after x days. Determine the value of x.
Kaspersk
Th
The period of days (value of x) for which Faizal promised to pay the bank RM 2,000 after getting 7% discounted present value of RM 1,930 is 180 days.
The value of x is the period of days (number of days) that the loan from the bank will last before Faizal, who received RM 1,930 discounted at 7%, would repay the bank the principal and interest of RM 2,000.
This implies that Faizal is paying an interest of RM 70 (RM 2,000 - RM 1,930), since he borrowed RM 1,930 and will repay RM 2,000.
Data and Calculations:
Present value of loan received = RM 1,930
Discount rate per year = 7%
Future value of the loan to be repaid to the bank = RM 2,000
Interest expense for one year based on 7% = RM 140 (RM 2,000 x 7%)
Interest expense for 180 days or 6 months = RM 70 (RM 2,000 - RM 1,930) or (RM 2,000 x 7%) x 180/360
Interest expense that equals RM 70 will be half of a year or 180 days (RM 140 * 180/360)
Thus, the period of days (x) that will lapse for Faizal to repay the bank is 180 days or half of a year (6 months).
Learn more about time period of a loan here: https://brainly.com/question/19118285
Which of the following quadratic equations is written in general form?
The 3rd one
Step-by-step explanation:
Reason being that it has no factors, meaning it cannot be simplified any further, but quadratic method can be used to attain factors.
hope it makes sense :)
Solve each system by graphing.
9514 1404 393
Answer:
no solution
Step-by-step explanation:
These lines have the same slope and different y-intercepts, so graph as parallel lines. As such, they will have no point of intersection, so there is NO SOLUTION to this system of inconsistent equations.
.. Find the L.C.M. of (a - 5)(a – 4) and (a + 4)(a – 5)
A-5 A-5 AND A-4 A-5
A-10 AND A-1
Hope it helps you
Three brothers enter a race with 8 friends. The racers draw lots to determine their
starting positions. What is the probability that the older brother, Mike, will start in lane 1, with
his other brothers, Stan and Steve beside him in lanes 2 and 3 in that order?
The function f(t) = t2 + 6t − 20 represents a parabola.
Part A: Rewrite the function in vertex form by completing the square. Show your work.
Part B: Determine the vertex and indicate whether it is a maximum or a minimum on the graph. How do you know?
Part C: Determine the axis of symmetry for f(t).
Answer:
Step-by-step explanation:
Note that the equation should be
f(t) = t^2 + 6t - 20
A. Completing the square
coefficient of the t term: 6
divide it in half: 3
square it: 3²
add 3² to complete the square and subtract 3² to keep the equation balanced:
f(t) = (t² + 6t + 3²) - 3² - 20
f(t) = (t+3)² - 29. This is the equation in vertex form.
:::::
B. Vertex (-3, -29)
The leading coefficient of the equation is +1. Since the leading coefficient is positive, the parabola opens upwards. Therefore, the vertex is a minimum.
:::::
The axis of symmetry is the vertical line passing through the vertex: x = -3
Find the final amount in each of these retirement accounts, in which the rate
of return on the account and the regular contribution change over time,
(a) $400 per month invested at 4%, compounded monthly, for 10 years, then
$600 per month invested at 6%, compounded monthly, for 10 years
(b) $1,000 per quarter invested at 4.42%, compounded quarterly, for 10 years,
then $1,500 per quarter invested at 7.4%, compounded quarterly, for 15
years
Answer:
Compound Interest: The future value (FV) of an investment of present value (PV) dollars earning interest at an annual rate of r compounded m times per year for a period of t years is:
FV = PV(1 + r/m)mt
or
FV = PV(1 + i)n
where i = r/m is the interest per compounding period and n = mt is the number of compounding periods.
One may solve for the present value PV to obtain:
PV = FV/(1 + r/m)mt
Numerical Example: For 4-year investment of $20,000 earning 8.5% per year, with interest re-invested each month, the future value is
FV = PV(1 + r/m)mt = 20,000(1 + 0.085/12)(12)(4) = $28,065.30
Notice that the interest earned is $28,065.30 - $20,000 = $8,065.30 -- considerably more than the corresponding simple interest.
Effective Interest Rate: If money is invested at an annual rate r, compounded m times per year, the effective interest rate is:
reff = (1 + r/m)m - 1.
This is the interest rate that would give the same yield if compounded only once per year. In this context r is also called the nominal rate, and is often denoted as rnom.
Numerical Example: A CD paying 9.8% compounded monthly has a nominal rate of rnom = 0.098, and an effective rate of:
r eff =(1 + rnom /m)m = (1 + 0.098/12)12 - 1 = 0.1025.
Thus, we get an effective interest rate of 10.25%, since the compounding makes the CD paying 9.8% compounded monthly really pay 10.25% interest over the course of the year.
Mortgage Payments Components: Let where P = principal, r = interest rate per period, n = number of periods, k = number of payments, R = monthly payment, and D = debt balance after K payments, then
R = P × r / [1 - (1 + r)-n]
and
D = P × (1 + r)k - R × [(1 + r)k - 1)/r]
Accelerating Mortgage Payments Components: Suppose one decides to pay more than the monthly payment, the question is how many months will it take until the mortgage is paid off? The answer is, the rounded-up, where:
n = log[x / (x – P × r)] / log (1 + r)
where Log is the logarithm in any base, say 10, or e.
Future Value (FV) of an Annuity Components: Ler where R = payment, r = rate of interest, and n = number of payments, then
FV = [ R(1 + r)n - 1 ] / r
Future Value for an Increasing Annuity: It is an increasing annuity is an investment that is earning interest, and into which regular payments of a fixed amount are made. Suppose one makes a payment of R at the end of each compounding period into an investment with a present value of PV, paying interest at an annual rate of r compounded m times per year, then the future value after t years will be
FV = PV(1 + i)n + [ R ( (1 + i)n - 1 ) ] / i
where i = r/m is the interest paid each period and n = m × t is the total number of periods.
Numerical Example: You deposit $100 per month into an account that now contains $5,000 and earns 5% interest per year compounded monthly. After 10 years, the amount of money in the account is:
FV = PV(1 + i)n + [ R(1 + i)n - 1 ] / i =
5,000(1+0.05/12)120 + [100(1+0.05/12)120 - 1 ] / (0.05/12)
-8=8(-3+a) plz help me and show work simply
Answer:
[tex] - 8 = 8( - 3 + a) \\ - 8 = - 24 + 8a \\ 8a = 16 \\ a = 2[/tex]
Answer:
2
Step-by-step explanation:
-8 = 8a - 24
16 = 8a
a =2
I hope this helps! :)40 points if answered
ZA and B are supplementary angles. If m A = (82 + 6)° and m
B = (72 +24), then find the measure of ZB.
Answer:
94
Step-by-step explanation:
Supplementary angles add to 180
8x+6 + 7x+24 = 180
Combine like terms
15x+30=180
Subtract 30 from each side
15x+30-30 = 180-30
15x= 150
Divide by 15
15x/15 = 150/15
x = 10
We want to find angle B
B = 7x+24 = 7*10+24 = 70+24 = 94
Answer:
Supplementary angles are angles that add up to 180 degrees (in other words, make up a straight line when you put them together).
So we can write: (8x+6) + (7x+24) = 180
Combine like terms: 15x+30 = 180
Subtract: 15x = 150
Divide: x = 10
If x = 10, and the measure of angle B can be written as 7x+24, then the measure of angle b is 7(10)+24, or 94.
Let me know if this helps!
What is the conjugate of 3+6i?
A -3 - 6i
B 3 - 6i
C 3 + 6i
D 9i
Answer:
B
Step-by-step explanation:
A conjugate is a term that has the same real part of its original but opposite terms of the second sign
Look at
[tex]3 + 6i[/tex]
The real part is 3 so B and C are the only possible answer.
The conjugate has the opposite sign of the second sign so the answer is
B
[tex]3 - 6i[/tex]
If the product of three identical numbers is 1000, find one of the number?
Answer:
10
Step-by-step explanation:
Three identical numbers whose product is 1000
10 * 10 * 10
