Answer:
C) SQRT(65)
Step-by-step explanation:
the magnitude of 1-8i is given by the following:
sqrt(a^2+b^2)
sqrt(1^2+8^2)
=sqrt(1+64)
=sqrt(65)
It is to be noted that the magnitude of |1 − 8i| is √(65) (Option C)
What is the computation of the above?To find the magnitude (or absolute value) of a complex number, we use the formula |a + bi| = √(a² + b²). In this case, the complex number is 1 - 8i.
Using the formula, we have -
|1 - 8i| = √(1² + (-8)²)
= √(1 + 64)
= √65
Hence, the magnitude of 1 - 8i is √65.
So the correct answer is C) √65.
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How can you simplify this expression?
Answer:
add the exponents
Step-by-step explanation:
(1/4)^3 evaluate simplify
Answer:
[tex]\frac{1}{64}[/tex]
Step-by-step explanation:
This is an Exponent. It is when a number is being multiplied as many times as the Exponent on top.
[tex]\left(\frac{1}{4}\right)^3[/tex] The ³ is the exponent,
[tex]\frac{1}{4} \times\frac{1}{4} \times\frac{1}{4}[/tex] is the expansion, and
Multiply on top: 1 × 1 × 1 = 1
Multiply the bottom: 4 × 4 = 16. 16 × 4 = 64
Hence, [tex]\frac{1}{64}[/tex] is the product or simplified form.
Another way:
[tex]\underline{\mathrm{Exponent\:rule\:}}\left(\frac{a}{b}\right)^c=\frac{a^c}{b^c}[/tex]
[tex]\left(\frac{1}{4}\right)^3[/tex]
[tex]=\frac{1^3}{4^3}[/tex]
[tex]1^3=1[/tex]
[tex]=\frac{1}{4^3}[/tex]
[tex]4^3=64[/tex]
[tex]=\frac{1}{64}[/tex]
A programmer plans to develop a new software system. In planning for the operating system that he will use, he needs to estimate the percentage of computers that use a new operating system. How many computers must be surveyed in order to be % confident that his estimate is in error by no more than percentage point Complete parts (a) through (c) below.
A) Assume nothing is known about the percentage of computers with new operating systems
n =
round up to the nearest integer
b) Assume that the recent survey suggest that about 96% of computers use a operating system.
n =
round up to the nearest integer
C) Does the additional survey information from part (b) have much of an effect on the sample size that is required?
A.
Yes, using the additional survey information from part (b) dramatically reduces the sample size.
B.
No, using the additional survey information from part (b) does not change the sample size.
C.
Yes, using the additional survey information from part (b) dramatically increases the sample size.
D.
No, using the additional survey information from part (b) only slightly increases the sample size.
Using the z-distribution, we have that:
a) A sample of 601 is needed.
b) A sample of 93 is needed.
c) A. Yes, using the additional survey information from part (b) dramatically reduces the sample size.
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]\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]\frac{1+\alpha}{2}[/tex].
The margin of error is:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
95% confidence level, hence[tex]\alpha = 0.95[/tex], z is the value of Z that has a p-value of [tex]\frac{1+0.95}{2} = 0.975[/tex], so [tex]z = 1.96[/tex].
For this problem, we consider that we want it to be within 4%.
Item a:
The sample size is n for which M = 0.04.There is no estimate, hence [tex]\pi = 0.5[/tex][tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
[tex]0.04 = 1.96\sqrt{\frac{0.5(0.5)}{n}}[/tex]
[tex]0.04\sqrt{n} = 1.96\sqrt{0.5(0.5)}[/tex]
[tex]\sqrt{n} = \frac{1.96\sqrt{0.5(0.5)}}{0.04}[/tex]
[tex](\sqrt{n})^2 = \left(\frac{1.96\sqrt{0.5(0.5)}}{0.04}\right)^2[/tex]
[tex]n = 600.25[/tex]
Rounding up:
A sample of 601 is needed.
Item b:
The estimate is [tex]\pi = 0.96[/tex], hence:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
[tex]0.04 = 1.96\sqrt{\frac{0.96(0.04)}{n}}[/tex]
[tex]0.04\sqrt{n} = 1.96\sqrt{0.96(0.04)}[/tex]
[tex]\sqrt{n} = \frac{1.96\sqrt{0.96(0.04)}}{0.04}[/tex]
[tex](\sqrt{n})^2 = \left(\frac{1.96\sqrt{0.96(0.04)}}{0.04}\right)^2[/tex]
[tex]n = 92.2[/tex]
Rounding up:
A sample of 93 is needed.
Item c:
The closer the estimate is to [tex]\pi = 0.5[/tex], the larger the sample size needed, hence, the correct option is A.
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What’s 12.71 divided 6.2?
Answer:
2.05
Step-by-step explanation:
12.71/6.2=2.05
The value of the expression 12.71 ÷ 6.2 using the division property will be 2.05.
What is Algebra?Algebra is the study of algebraic expressions, while logic is the manipulation of those concepts.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This rule is used to answer the problem correctly and precisely.
The numbers are given below.
12.71 and 6.2
Then the division of the decimal numbers 12.71 and 6.2 will be given by putting a divide sign between them. Then we have
⇒ 12.71 ÷ 6.2
⇒ 12.71 / 6.2
⇒ 2.05
The worth of the articulation 12.71 ÷ 6.2 utilizing the division property will be 2.05.
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What is the sum of the coefficients in the expression below?
22°y2 + 5x+ y2 - 6xy' +7
Answer:
485y to the power 2 + 5x to the power 2 - 6xy to the power 3 + 7
Step-by-step explanation:
I hope this helps. Also, there's this free app called Quick Math. If you need the steps, you should check there first, and maybe you should try that for other math problems as well.
Good luck and have a great rest of your day.
Pleaseeeeeeeeeee help me
Answer:
[tex]\huge\boxed{6x-7y=21}[/tex]
Step-by-step explanation:
The slope-intercept form of an equation of a line:
[tex]y=mx+b[/tex]
[tex]m[/tex] - slope
[tex]b[/tex] - y-intercept (0, b)
We have:
[tex]y=\dfrac{2}{3}x-3\to m=\dfrac{2}{3};\ b=-3[/tex]
From answers:
[tex]6x-7y=21\qquad|-6x\\\\-7y=-6x+21\qquad|:(-7)\\\\y=\dfrac{6}{7}x-3\to m=\dfrac{6}{7};\ \boxed{b=-3}[/tex]
[tex]-\dfrac{2}{3}x+3y=6\qquad|+\dfrac{2}{3}x\\\\3y=\dfrac{2}{3}x+6\qquad|:3\\\\y=\dfrac{2}{9}x+2\to m=\dfrac{2}{9};\ b=2[/tex]
[tex]\dfrac{2}{3}x+3y=-3\qquad|-\dfrac{2}{3}x\\\\3y=-\dfrac{2}{3}x-3\qquad|:3\\\\y=-\dfrac{2}{9}x-1\to m=-\dfrac{2}{9};\ b=-1[/tex]
[tex]x+4y=12\qquad|-x\\\\4y=-x+12\qquad|:4\\\\y=-\dfrac{1}{4}x+3\to m=-\dfrac{1}{4};\ b=3[/tex]
Answer:
6x-7y=21
Step-by-step explanation: :)
The mean hourly wage for employees in goods-producing industries was $24.57, April 12, 2012 (Bureau of Labor Statistics). Suppose a sample of 30 employees from the manufacturing industry is taken, in April 2012, to see if the mean hourly wage differs from the reported mean of $24.57 for the goods-producing industries.
a. State the null and alternative hypotheses we should use to test whether the population mean hourly wage in the manufacturing industry differs from the population mean hourly wage in the goods-producing industries.
b. Suppose a sample of 30 employees from the manufacturing industry showed a sam- ple mean of $23.89 per hour. Assume a population standard deviation of $2.40 per hour and compute the p-value.
c. With a = .05 as the level of significance, what is your conclusion?
d. Repeat the preceding hypothesis test using the critical value approach.
Step-by-step explanation:
a. The null hypothesis is generally an exact value and the alternative hypothesis is the one we are trying to show. We are trying to show that the population mean is different from $24.57, so the hypotheses are as follows:
Null: The population mean hourly wage in the manufacturing industry is the same as the population mean hourly wage in the goods-producing industries
Alternative: The population mean hourly wage in the manufacturing industry differs from the population mean hourly wage in the goods-producing industries
b.
Because we know the population standard deviation, we can use a z test
Plugging in the values:
Expected population mean: 24.57
Sample average: 23.89
Sample size: 30
Population standard deviation: 2.4, we get 0.1207 as our p-value.
c. Using a = 0.05, our p-value is greater than that, so we can not conclude the alternative hypothesis (The population mean hourly wage in the manufacturing industry differs from the population mean hourly wage in the goods-producing industries)
d. Using a critical value calculator, we can find that for a two-tailed approach, the critical value would be 1.96. This would mean that the z score would have to be greater than 1.96 or less than -1.96 for the results to be significant. The population mean we would plug in here is 24.57, while the raw score would be 23.89 and the standard deviation would be 2.4. The z score we get is -0.283, which is not in the values specified (>1.96 or <-1.95) so we cannot conclude the alternative hypothesis
Desde los extremos A y B de un tendedero de 240 cm de largo partes dos hormigas simultáneamente. La hormiga que sale de A avanza a 10 cm/s, y la que se mueve desde el extremo B lleva una carga, por lo que se desplaza a 6 cm/s. ¿A qué distancia del punto A se encontrarán y en cuánto tiempo? Traza una recta que represente el desplazamiento de cada una de las hormigas.
Ambas hormigas se encontraran a 15 segundos, y a 150 centímetros del punto A.
Dado que desde los extremos A y B de un tendedero de 240 cm de largo partes dos hormigas simultáneamente, y la hormiga que sale de A avanza a 10 cm/s, y la que se mueve desde el extremo B lleva una carga, por lo que se desplaza a 6 cm/s, para determinar a qué distancia del punto A se encontrarán y en cuánto tiempo se debe realizar el siguiente cálculo:
10 x 15 = 1506 x 15 = 90150 + 90 = 240Por lo tanto, ambas hormigas se encontraran a 15 segundos, y a 150 centímetros del punto A.
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6. Kendrick bought 4 bags of bagels. Every bag had a dozen bagels. How many bagels did Kendrick buy?
Answer:
Kendrick bought 48 bagels.
Step-by-step explanation:
For this question, you would simply have to multiply 4 by 12.
Dozen means 12.
4x12=48
48 bagels.
The probability of the test showing negative given the person does not have the disease?
If Y varies directly as x and y= 49 when x= 40, find y if x =34
Answer:
y = 41.65
Step-by-step explanation:
Given y varies directly as x then the equation relating them is
y = kx ← k is the constant of variation
To find k use the condition y = 49 when x = 40
49 = 40k ( divide both sides by 40 )
[tex]\frac{49}{40}[/tex] = k = 1.225
y = 1.225x ← equation of variation
When x = 34 , then
y = 1.225 × 34 = 41.65
The average playing time of compact discs in a large collection is 35 minutes, and the standard deviation is 5 minutes.
a. What value is 1 standard deviation above the mean? 1 standard deviation below the mean? What values are 2 standard deviations away from the mean?
b. Without assuming anything about the distribution of times, at least what percentage of the times is between 25 and 45 minutes?
c. Without assuming anything about the distribution of times, what can be said about the percentage of times that are either less than 20 minutes or greater than 50 minutes?
d. Assuming that the distribution of times is approximately normal, about what percentage of times are between 25 and 45 minutes? less than 20 minutes or greater than 50 minutes? less than 20 minutes?
68% are within 30 minutes to 40 minutes, 95% are within 25 minutes to 45 minutes and 99.7% are within 20 minutes to 50 minutes
The three sigma rule states that 68% are within one standard deviation of the mean, 95% are within two standard deviation from the mean and 99.7% are within three standard deviation from the mean.
Given that μ = 35, σ = 5
68% are within one standard deviation = μ ± σ = 35 ± 5 = (30, 40)
95% are within two standard deviation = μ ± 2σ = 35 ± 2*5 = (25, 45)
99.7% are within three standard deviation = μ ± 3σ = 35 ± 3*5 = (20, 50)
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Which of the following numbers can be expressed as a decimal that terminates? 3/2,2/3,3/4,5/7
Answer:
Step-by-step explanation:
An example of one fraction that does NOT terminate is 2/3.
2/3 = 0.666666666666666 .... That's the easy way to tackle the problem. Pick out the ones that don't terminate.
5/7 is the other one. It does not terminate either. It has 6 digits in a block that keeps on repeating itself forever.
5/7 = .571428 571428 which goes on forever.
So the two that do terminate are
3/2 which = 1.5
3/4 which = 0.75
Mrs. Nisbet had 97 books in her classroom library. She received a grant to expand her classroom library. After spending the money, she had 213 books. What is the percent increase? *
Answer: 219
Step-by-step explanation:
What’s the Question? Selena ran farther than
Manny.
If Selena ran x miles and manny ran y miles, who ran more miles
x=any number
y=any number smaller than x
22. PLEASE HELP PLEASSSSSSEEEEEEEEEEEEEEE
15 points
Answer:
Step-by-step explanation:
2
Windstrong has an elevation of -28.7 feet, and Kennington has an elevation of 28.7 feet. Which of the following is true?
A.
Windstrong's elevation < Kennington's elevation
B.
Windstrong's elevation = Kennington's elevation
C.
Windstrong's elevation > Kennington's elevation
Answer:
b
Step-by-step explanation:
pls help wiht this question ill give you 69 points whoever awnsers
Answer:
what's thequestion?
Step-by-step explanation:
what equation is equivalent to 7-2x=5
Answer:
x = 1New equation: 7 - 2 = 5Step-by-step explanation:
7 - 2x = 5=> 7 - 5 = 2x=> 2 = 2x=> x = 1Conclusion:
Since:
x = 1Our new equation will be 7 - 2 = 5
Hoped this helped.
Hey there!
7 - 2x = 5
-2x + 7 = 5
SUBTRACT 7 to BOTH SIDES
-2x + 7 - 7 = 5 - 7
CANCEL out: 7 - 7 because that gives you 0
KEEP: 5 - 7 because it helps solve for the x-value
NEW EQUATION: -2x = 5 - 7
SIMPLIFY IT!
-2x = -2
DIVIDE -2 to BOTH SIDES
-2x/-2 = -2/-2
CANCEL out: -2/-2 (on the LEFT SIDE) because that gives you 1
KEEP: -2/-2 (on the RIGHT SIDE) because it helps you solve for the x-value
NEW EQUATION: x = -2/-2
SIMPLIFY IT!
x = 1
Therefore, your answer should be: x = 1
Checking to make sure it is correct!
-2x + 7 = 5
-2(1) + 7 = 5
-2 + 7 = 5
So, this makes this statement TRUE
Good luck on your assignment and enjoy your day!
~Amphitrite1040:)
6. Is the inequality 5 - x2 < 4
true for x= 1?
Answer:
no
Step-by-step explanation:
since x=1 5-2<4 so then 3<4 so no Im not sure
Answer:
No
Step-by-step explanation:
5-x² when x=1 is 4.
1²=1
5-1=4
4 is not less than 4 so it can't be true.
Please answer I need step by step explanation
Answer:
10 cm
Simplified explanation/tl;dr: the small triangle is two thirds the size of the big triangle, so the missing side on the small triangle is two thirds the size of the same side on the big triangle
Long explanation/step by step:
It looks scary, but don't worry; for questions like this just find the ratio then multiply it by the similar side to find the missing side.
This is what I mean: 8/12 simplified is 2/3 (4 is the common factor and 8/4 = 2 and 12/4 = 3). That's your fraction to multiply by.
I chose 8 and 12 because look how the triangles are the same shape just different sizes, that means they're similar. the similar sides are just the same side on both triangles. (for this one, BC and GH are similar). to find how much smaller it is in fraction form, you just take two of the same sides and divide the small one by the big one. (big number becomes top, small becomes bottom)
now just multiply 15 by 2/3 by using fraction multiplication. 15/1 x 2/3 = 30/3. Simplify that to 10/1 (3 is the common factor and 30/3 = 10 and 3/3 = 1). 10/1 = 10.
i need help with this question
Answer:
check online for more information
Find the perimeter and area of this polygon. (Geometry)
Answer:
rectangle= 22*9 = 198ft
triangle=11*10 = 110 ft
110+ 198 = 308 polygon
can someone gimme the answer please
Answer:
g(x) = 1/4 f(x)
Step-by-step explanation:
(x,y) -> (x , 1/4 y) .. vertical compression
Find the next three terms in the arithmetic sequence.
6, 12,18, 24,...
In developing an interval estimate of the population mean, if the population standard deviation is unknown _____.
Answer:
the sample standard deviation and t distribution can be used
Step-by-step explanation:
MARKING AS BRAINLIEST!! Starr if given functions are inverse)!
Answer: They are inverses of each other
==========================================================
Explanation:
We'll need to compute h(f(x)) and f(h(x)) to see if we get x each time.
[tex]h(x) = 9x-4\\\\h(f(x)) = 9(f(x))-4\\\\h(f(x)) = 9\left(\frac{x+4}{9}\right)-4\\\\h(f(x)) = x+4-4\\\\h(f(x)) = x\\\\[/tex]
and,
[tex]f(x) = \frac{x+4}{9}\\\\f(h(x)) = \frac{h(x)+4}{9}\\\\f(h(x)) = \frac{9x-4+4}{9}\\\\f(h(x)) = \frac{9x}{9}\\\\f(h(x)) = x\\\\[/tex]
Both composite functions lead to x each time.
The equations h(f(x)) = x and f(h(x)) = x being true means each function is the inverse of the other.
The perimeter of a rectangle is 2020 units.
The length of the rectangle is the distance from (-2,6)(−2,6) to (5,6)(5,6).
What is the width, in units, of the rectangle?
Answer:
8.4
Step-by-step explanation:
edge
5. Which of the following linear expressions is a factor of the cubic polynomial x^3 + 9x² +16x-12?
(1) x+6
(3) r-3
(2) x-1
(4) x+2
Answer:
(1) x+6
Step-by-step explanation:
Possible rational zeroes include ±1, ±2, ±3, ±4, ±6, ±12
Check each answer choice with synthetic division:
1 | 1 9 16 -12
__1_10_26
1 10 26 | 14
-2 | 1 9 16 -12
__-2_-14_-4
1 7 2 | -16
-6 | 1 9 16 -12
__-6_-18_12
1 3 -2 | 0
Therefore, x+6 is a factor of the polynomial
Answer:
(1) x+6
Step-by-step explanation:
Less than and equal to is closed or open
Answer:
less than is
<
Step-by-step explanation:
equal to is =
mark me as brainliest pls
