Answer:
The sample size must be of 47,059,600.
Step-by-step explanation:
We have to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1 - 0.95}{2} = 0.025[/tex]
Now, we have to find z in the Z-table as such z has a p-value of [tex]1 - \alpha[/tex].
That is z with a p-value of [tex]1 - 0.025 = 0.975[/tex], so Z = 1.96.
Now, find the margin of error M as such
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.
Standard deviation:
[tex]\sigma = 3.5[/tex]
If you want the error bound E of a 95% confidence interval to be less than 0.001, how large must the sample size n be?
This is n for which M = 0.001. So
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
[tex]0.001 = 1.96\frac{3.5}{\sqrt{n}}[/tex]
[tex]0.001\sqrt{n} = 1.96*3.5[/tex]
[tex]\sqrt{n} = \frac{1.96*3.5}{0.001}[/tex]
[tex](\sqrt{n})^2 = (\frac{1.96*3.5}{0.001})^2[/tex]
[tex]n = 47059600[/tex]
The sample size must be of 47,059,600.
Let a=⟨1,−4,2⟩ and b=⟨−5,−5,−2⟩. Compute:
a+b=⟨ ,, ⟩
a−b=⟨ ,,⟩
2a=⟨ ,,⟩
3a+4b=⟨ ,, ⟩
|a|=
Answer:
a + b = ⟨-4, -9, 0⟩
a - b = ⟨6, 1, 4⟩
2a = ⟨2, -8, 4⟩
3a + 4b = ⟨-17, -32, -2⟩
|a| = √21
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightPre-Calculus
Vectors
OperationsScalars[Magnitude] ||v|| = √(x² + y² + z²)Step-by-step explanation:
Adding and subtracting vectors are follow the similar pattern of normal order of operations:
a + b = ⟨1 - 5, -4 - 5, 2 - 2⟩ = ⟨-4, -9, 0⟩
a - b = ⟨1 + 5, -4 + 5, 2 + 2⟩ = ⟨6, 1, 4⟩
Scalar multiplication multiplies each component:
2a = ⟨2(1), 2(-4), 2(2)⟩ = ⟨2, -8, 4⟩
Remember to multiply in the scalar before doing basic operations:
3a + 4b = ⟨3(1), 3(-4), 3(2)⟩ + ⟨4(-5), 4(-5), 4(-2)⟩ = ⟨3, -12, 6⟩ + ⟨-20, -20, -8⟩ = ⟨-17, -32, -2⟩
Absolute values surrounding a vector signifies magnitude of a vector. Follow the formula:
|a| = √[1² + (-4)² + 2²] = √21
If two angles are complementary, find the measure of each of angle.
Answer:
B: 30 and 60
Step-by-step explanation:
First, let's set up an equation. Since the two angles are complementary, we can write the equation like this:
2p + p = 90
Now, let's solve it!
2p + p = 90
Combine like terms:
3p = 90
Divide each side by 3 to isolate p:
3p/3 = 90/3
p = 30
Now that we know how many degrees one of our angles is, we can subtract that from 90 to get both of the complementary angles.
90 - 30 = 60
Therefore, the two angles that are complementary in this case are 30 and 60 degrees.
if 2 shirts cost 18.80, how much would 9 shirt cost.
Answer:
84.60
Step-by-step explanation:
We can write a ratio to solve
18.80 x
--------- = --------------
2 shirts 9 shirts
Using cross products
18.80 *9 = 2x
169.2 =2x
Divide each side by 2
169.2/2 =2x/2
84.60 =x
The answer to this math problem need help
Step-by-step explanation:
you know that you can copy and paste and give the answer
A boat is pulled into a dock by means of a winch 12 feet above the deck of the boat. (a) The winch pulls in rope at a rate of 4 feet per second. Determine the speed of the boat when there is 15 feet of rope out.
Answer:
the speed of the boat is 6.67 ft/s
Step-by-step explanation:
Given;
height of the winch, h = 12 ft
the rate at which the winch pulls, the rope, = 4 ft/s
This form a right triangle problem;
let the height of the right triangle = h
let the base of the triangle = b (this corresponds to the horizontal displacement of the boat)
let the hypotenuse side = c
c² = b² + h²
[tex]2c\frac{dc}{dt} = 2b\frac{db}{dt} + 2h \frac{dh}{dt}\\\\The \ height \ of \ the \ winch \ is \ not \ changing \\\\2c\frac{dc}{dt} = 2b\frac{db}{dt} + 2h (0)\\\\2c\frac{dc}{dt} = 2b\frac{db}{dt} \\\\c\frac{dc}{dt} = b\frac{db}{dt} ----(*) \\\\when;\\\\the\ hypotenuse \ c = 15 \ ft\\\\the \ the \ the \ height, h = 12 \ ft\\\\the \ base, b \ becomes ;\\\\b^2 = c^2 -h^2\\\\b^2 = 15^2 - 12^2\\\\b^2 = 81\\\\b = \sqrt{81} \\\\b = 9 \ ft\\\\\\from \ the \ equation (*) \ above;\\\\[/tex]
[tex]c\frac{dc}{dt} = b \frac{db}{dt} \\\\dc/dt = 4 \ ft/s, \ \ c = 15 \ ft, \ \ b = 9 \ ft\\\\15 (4) = 9\frac{db}{dt} \\\\60 = 9 \frac{db}{dt} \\\\\frac{db}{dt} = \frac{60}{9} = 6.67 \ ft/s[/tex]
Therefore, the speed of the boat is 6.67 ft/s
convert the following decimals to a simplified fraction. showing all work
Hello.
Answer:
1/200, 667/500
I hoped this helped
6. The perimeter of a square room is 48 m, how much square metre carpet required it cover it ?
Answer:
144
Step-by-step explanation:
Answer:
first you have to now each side length ,since it is square so all sides are equal so 48/4=12 i.e perimeter =4 so our qoustion is area so the area of square is side square
Step-by-step explanation:
so side =12 , 12square is 144 that set.
Find the area of a triangle with the given description. (Round your answer to one decimal place.)
a triangle with sides of length 14 and 28 and included angle 20°
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Answer:
67.0 square units
Step-by-step explanation:
The formula for the area is ...
Area = 1/2ab·sin(C)
Area = (1/2)(14)(28)sin(20°) ≈ 67.036 . . . . square units
The area of the triangle is about 67.0 square units.
Find the measure of the incanted angle to the nearest degree
Answer:
34⁰
Step-by-step explanation:
let unknown angle be x
cos x=19/23
cos x=0.826
x=cos inverse of 0.826
x=34.3⁰
Consider the triangle ΔXYZ . Find the angle Z given that ZY=30 , ZX=15 , and YX=21
Step-by-step explanation:
hey bro can get the diagram
Answer:
where is the diagram plz show the diagram
Step-by-step explanation:
A group of high school students were surveyed about their handedness and their favorite sport. The results are displayed below.
Which of the following statements is not true, according to the graph?
The left-handed group has a higher percentage of people who prefer baseball.
The right-handed group has a lower percentage of people who prefer basketball.
The percentage of people who prefer soccer has a lower percentage in the left-handed group.
The percentage of people who prefer football is approximately the same for the right- and left-handed groups.
Answer:
The percentage of people who prefer football is approximately the same for the right- and left-handed groups.
Step-by-step explanation:
The bar for the right-handed group representing soccer is between 10% and 20% (below 20%) while the bar for the left-handed group representing soccer is at 20%.
Percentage of left-handed group of people who prefer soccer is higher than the right-handed group who prefer soccer. Therefore, they don't have the same percentage.
Answer:
D
Step-by-step explanation:
;)
I need to know the answer ASAP
Answer:
Step-by-step explanation:
Please help! I will give you a lot of points if you do and the brainiest!
Answer:
First truth table:
~q p V ~q ~(p V ~q)
F T F
T T F
F F T
T T F
Second truth table:
~q p V ~q ~(p V ~q)
F T F
Step-by-step explanation:
The ~ operator is a negator (or NOT), such that it is the opposite of the sign.
The first column wants the negation of [tex]q[/tex], and the values of q are
T, F, T, F, for the columns starting from the top. The negation for the columns are F, T, F, T.
For the second column, The 'V' operator is the OR operator, so a single True, or T will result in a True.
For the first row, not q is F, and T OR F will result in T.
For the second row, not q is T, and T OR T will result in T.
For the third row, not q is F, and F OR F will result in F.
For the fourth row, not q is T, and F OR T will result in T.
In the last column, we must figure out not p OR not q, which we did in the last column, so all we must do is figure out the NOT of values of the last column.
The values of the last column are T, T, F, T, respectively, so the not of the columns will be F, F, T, F.
In the bottom truth table, not q, will be F because the value of q is T. The second column wants p OR not q, and we already know that not q is F, and the value of p is T. T OR F is equal to T. In the last column, the question wants the not of p OR not q, which we did in the last column, so we must figure out the not value of the last column, which is T. The not of T is F.
What is the volume of the following rectangular prism?
Answer:
44/3
Step-by-step explanation:
V=L*W*H
WH=22/3
V=2*(22/3)
(ii). nth term of: 10+4-2...
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Answer:
an = 10 -6(n -1)
Step-by-step explanation:
The series is an arithmetic series with a first term of 10, and a common difference of 4-10 = -6. The n-th term of an arithmetic series is given by ...
an = a1 +d(n -1) . . . . . for first term a1 and common difference d
__
For the parameters this series has, the n-th term is ...
an = 10 -6(n -1)
OMG!! I’m stuck on 4a) b) c)
Help please
Answer:
a) 750 cmb) 288 cmc) 2112 cmStep-by-step explanation:
Formula for getting the surface area of a rectangular prism: SA = 2 (WL + HL + HW)a) SA = 2 (WL + HL + HW) = 2(75) + 2(225) + 2(75) = 150 + 450 + 150 = 750 cm^2b) SA = 2 (WL + HL + HW)= 2(48) + 2(72) + 2(24)= 96 + 144 + 48=288 cm^2c) SA = 2 (WL + HL + HW)= 2(400) + 2(400) + 2(256)= 800 + 800 + 512= 2112 cm^2[tex]\tt{ \green{P} \orange{s} \red{y} \blue{x} \pink{c} \purple{h} \green{i} e}[/tex]
Answer:
Below in bold.
Step-by-step explanation:
(a) The surface area consists of the sum of the area of 3 sets of 2 congruent rectangles. The 2 rectangles are on opposite sides of the solid.
= 2(15*15) + 2(5*15) + 2(5&15)
= 450 + 150 + 150
= 750 unit^2.
(b). Similarly to the above:
Surface area = 2(12*6) + 2(4*12) + 2(4*6)
= 144 + 96 + 48
= 288 unit^2.
(c) Again:
Surface area = 2(25*16) + 2(25*16) + 2(16*16)
= 400 + 400 + 256
= 1056 unit^2.
The true length of recovery for patients with knee surgery is normally distributed with a mean of 123 days and a standard deviation of 1 day. What proportion of the patients will recover between 121 and 124 days?
Answer:
0.81859
Step-by-step explanation:
Given that the length of recovery days for patients with knee surgery is normally distributed with :
Mean, μ = 123 days
Standard deviation, σ = 1 day
The proportion of patients that will recover with 121 and 124 days :
We obtain the Probability of Z score :
Z = (x - μ) / σ
P(Z < (x - μ) / σ) < Z < P(Z < (x - μ) / σ)
P(Z < (121 - 123) / 1) < Z < P(Z < (124 - 123) / 1)
P(Z < - 2) < Z < P(Z < 1)
Using the normal distribution table :
P(Z < 1) - P(Z < - 2)
0.84134 - 0.02275
= 0.81859
Researchers studied symptom distress and palliative care designation among a sample of 710 hospitalized patients. Controlling for age, they used a t-test to compare average distress from nausea scores in men and women. Lower scores indicated less distress from nausea. They report men had an average score of 1.02 and woman had an average score of 1.79. Which statement is correct?
(2pts)
Select Men had significantly less distress from nausea. as your answer
Men had significantly less distress from nausea.
Select Men had half as much distress from nausea as woman but we can not determine if this is a significant difference. as your answer
Men had half as much distress from nausea as woman but we can not determine if this is a significant difference.
Select Men had less distress from nausea on average than women but we can not determine if this is a significant difference. as your answer
Men had less distress from nausea on average than women but we can not determine if this is a significant difference.
Select There is a positive correlation between distress from nausea and gender. as your answer
There is a positive correlation between distress from nausea and gender.
Answer:
A. Men had less distress from nausea on average than women but we can not determine if this is a significant difference.
Step-by-step explanation:
Working based on the information given, the mean values of each group with with men having an average score of 1.02 and women have an average of 1.79 this reveals that distressing nausea on average is higher in women than in men . However, to test if there is a significant difference would be challenging as the information given isn't enough to make proceed with the test as the standard deviations of the two groups aren't given and no accompanying sample data is given.
Find the face value of the 20-year zero-coupon bond at 4.4%, compounded semiannually, with a price of $8,375.
$45.000
$53.000
The correct face value will be Option C ($20,000). A further solution id provided below.
Given:
Time,
t = 20 years
Rate,
r = 4.4%
Price
= $8,375
Now,
The yield will be:
= [tex]\frac{4.4}{2}[/tex]
= [tex]1.1[/tex] (%)
Time will be:
= [tex]20\times 2[/tex]
= [tex]40 \ periods[/tex]
As we know the formula,
⇒ [tex]Price \ of \ bond = \frac{Face \ value}{(1+\frac{r}{2} )^{n\times 2}}[/tex]
By substituting the values, we get
[tex]8375=\frac{Face \ value}{(1+\frac{0.044}{2} )^{20\times 2}}[/tex]
[tex]8375=\frac{Face \ value}{(1.022)^{40}}[/tex]
[tex]8375=\frac{Face \ value}{2.3880083}[/tex]
The face value will be:
[tex]Face \ value = 2.3880083\times 8375[/tex]
[tex]=20,000[/tex] ($)
Learn more about face value here:
https://brainly.com/question/14862802
The number of basic trigonometric ratios is....
A.3
B.4
C.5
D.6
Answer:
There are three basic trigonometric ratios: sine , cosine , and tangent .
Step-by-step explanation:
Martha, Lee, Nancy, Paul, and Armando have all been invited to a dinner party. They arrive randomly, and each person arrives at a different time.
a. In how many ways can they arrive?
b. In how many ways can Martha arrive first and Armando last?
c. Find the probability that Martha will arrive first and Armando last.
Show your work
Answer:
a) 120
b) 6
c) 1/20
Step-by-step explanation:
a) 5! = 120
b) (5 - 2)! = 6
c) 6/120 = 1/20
Alice wants to estimate the percentage of people who plan
on voting yes for the upcoming school levy. She surveys
380 individuals and finds that 260 plan on voting yes.
Identify the values needed to calculate a confidence interval
at the 90% confidence level. Then find the confidence interval.
zo10 z0.05 zo.025 zo01 z0.005
1.282 1.645 1.960 2.326 2.576
Use the table of common z-scores above.
Answer:
"[tex]0.6450 < p < 0.723[/tex]" is the right solution.
Step-by-step explanation:
Given:
n = 380
x = 260
Point estimate,
[tex]\hat p = \frac{x}{n}[/tex]
[tex]=\frac{260}{380}[/tex]
[tex]=0.6842[/tex]
Critical value,
[tex]Zc = 1.645[/tex]
Standard error will be:
[tex]S.E = \sqrt{\frac{0.6842(1-0.6842)}{380} }[/tex]
[tex]=0.0238[/tex]
Margin of error will be:
[tex]E = Zc\times S.E[/tex]
[tex]=1.645\times 0.0238[/tex]
[tex]=0.0392[/tex]
hence,
Confidence level will be:
= [tex]\hat p \pm E[/tex]
= [tex]0.6842 \pm 0.0392[/tex]
= [tex]0.6450 < p < 0.723[/tex]
Find the length of the missing side
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Answer:
short leg: x; long leg: 12; hypotenuse: yStep-by-step explanation:
The sides of the triangle can be read from the figure:
short leg: xlong leg: 12hypotenuse: yThe ratios tell you ...
long leg = x√3 = 12
x = 12/√3 = 4√3 . . . . . divide by √3. (same as multiply by (√3)/3)
2x = 2·4√3 = 8√3
Then the missing sides are ...
short leg: 4√3long leg: 12hypotenuse: 8√3An office manager has received a report from a consultant that includes a section on equipment replacement. The report indicates that scanners have a service life that is normally distributed with a mean of 41 months and a standard deviation of 4 months. On the basis of this information, determine the proportion of scanners that can be expected to fail within plus or minus 6 months of the mean. (Enter your answer as a percentage without the percent sign; keep 2 decimal places)
Answer:
The answer is "36.14%"
Step-by-step explanation:
The complete question is given in the attached file please find it.
[tex]\mu =41\\\\\sigma= 4\\\\P(42<\bar{x}<48)= p(\bar{x}<48)-p(\bar{x}<42)\\\\Z =\frac{(42-41)}{4} = \frac{1}{4} =0.25\\\\Z =\frac{(48-41)}{4} = \frac{7}{4} = 1.75\\\\[/tex]
Using z-table to find the value.
[tex]\to P(41<\bar{x}<48) = 0.9599- 0.5987 = 0.3614\times 100= 36.14\%[/tex]
This means that between 42 and 48 months, 36.14 % of scanners could be predicted will break down.
Given $f(x) = \frac{\sqrt{2x-6}}{x-3}$, what is the smallest possible integer value for $x$ such that $f(x)$ has a real number value? Please show steps. Thank you!
(I rewrote the question without the symbols, they are the same question)
Given f(x) = {2x-6}/{x-3}, what is the smallest possible integer value for x such that f(x) has a real number value? Thank you!
===========================================================
Explanation:
The given function is
[tex]f(x) = \frac{\sqrt{2x-6}}{x-3}[/tex]
which is the same as writing f(x) = ( sqrt(2x-6) )/(x-3)
The key for now is the square root term. Specifically, the stuff underneath. This stuff is called the radicand.
Recall that the radicand cannot be negative, or else the square root stuff will result in a complex number. Eg: [tex]\sqrt{-4} = 0+2i[/tex]
The question is basically asking: what is the smallest x such that [tex]\sqrt{2x-6}[/tex] is a real number?
Well if we made 2x-6 as small as possible, ie set it equal to 0, then we can find the answer
[tex]2x-6 = 0\\\\2x = 6\\\\x = 6/2\\\\x = 3\\\\[/tex]
I set the radicand equal to 0 because that's as small as the radicand can get (otherwise, we're dipping into negative territory).
So 2x-6 set equal to 0 leads to x = 3.
This means x = 3 produces the smallest radicand (zero) and therefore, it is the smallest allowed x value for that square root term.
But wait, if we tried x = 3 in f(x), then we get...
[tex]f(x) = \frac{\sqrt{2x-6}}{x-3}\\\\f(3) = \frac{\sqrt{2*3-6}}{3-3}\\\\f(3) = \frac{\sqrt{0}}{0}\\\\[/tex]
which isn't good. We cannot have 0 in the denominator. Dividing by zero is not allowed. The result is undefined. It doesn't even lead to a complex number. So we'll need to bump x = 3 up to x = 4. You should find that x = 4 doesn't make the denominator 0.
----------------
In short, we found that x = 3 makes the square root as small as possible while staying a real number, but it causes a division by zero error with f(x) overall. So we bump up to x = 4 instead.
Write a quadratic equation with integer coefficients having the given numbers as solutions.
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Answer:
x² -22 = 0
Step-by-step explanation:
The roots are opposites, so the equation is pretty simple.
x = ±√22
x² = 22 . . . . . square both sides
x² -22 = 0 . . . . your quadratic equation in standard form
Twelve different video games showing drug use were observed. The duration times of drug use were recorded, with the times (seconds) listed below. Assume that these sample data are used with a 0.05 significance level in a test of the claim that the population mean is greater than 85 sec. If we want to construct a confidence interval to be used for testing that claim, what confidence level should be used for a confidence interval? If the confidence interval is found to be −1.8 sec<μ<213.5 sec, what should we conclude about the claim? The given confidence interval ▼ does not contain contains the value of 85 sec, so there ▼ is is not sufficient evidence to support the claim that the mean is greater than 85 sec
Answer:
95% confidence level should be used for a confidence interval.
The given confidence interval contains the value of 85 sec, so there is not sufficient evidence to support the claim that the mean is greater than 85 sec.
Step-by-step explanation:
0.05 significance level
1 - 0.05 = 0.95
0.95*100% = 95%
This means that a 95% confidence level should be used for a confidence interval.
Confidence interval is found to be −1.8 sec<μ<213.5 sec, what should we conclude about the claim?
Contains the value of 85 sec, thus there is not sufficient evidence to support the claim that the mean is greater than 85 sec.
Will mark brainliest
Plz solve on a paper or draw on the picture thx in advance
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Answer:
the red angle has no specific value
Step-by-step explanation:
There is sufficient information here to specify all of the angles except the two unknown angles in the 70° (dark blue) triangle. Those two angles must total 110°, but that measure cannot be allocated between them based on the information in the diagram.
The attachments show that all of the given angle constraints can be met while the red angle may vary considerably. It can range through the interval (0°, 110°), but cannot be either of those end values.
Question 4 of 16
If the probability of rain today is 35%, what is the probability that it will not rain
today?
A. 100%
B. 65%
C. 35%
D. 50%
Answer:
I think the answer is B. 65%
Please help! Identify which of the following is not equivalent to a1/4
Answers (images below)
no links please!
Answer: B
Step-by-step explanation:
A) [tex]a^\frac{3}{4}[/tex]÷[tex]a^\frac{1}{2}[/tex] cannot be the answer. When a to the power of x is divided by a to the power of y it is a to the power of x-y. Ex: [tex]a^x[/tex]÷[tex]a^y=a^x^-^y[/tex]
So 3/4-1/2 is 1/4 giving us [tex]a^{\frac{1}{4} }[/tex]
B is the answer because taking the square root of a is the same as [tex]a^\frac{1}{2}[/tex] which isn't the same as [tex]a^\frac{1}{4}[/tex]
C is not the answer because when a to the power of x is multiplied by a to the power of y it is a to the power of x+y. Ex: [tex]a^x[/tex]·[tex]a^y[/tex]=[tex]a^{x+y}[/tex]
1/8+1/8=1/4 so it is [tex]a^\frac{1}{4}[/tex]
D can't be the answer. [tex]a^\frac{1}{8}[/tex] squared is the same as [tex]a^\frac{1}{8}[/tex]·[tex]a^\frac{1}{8}[/tex] so the same explanation of c applies to d
