Answer:
Step-by-step explanation:
Hello,
Factor x^2 + 64.
[tex]\boxed{x^2+64=x^2+8^2=x^2-8^2i^2=(x-8i)(x+8i)}[/tex]
Factor 16x^2 + 49.
[tex]\boxed{16x^2+49=(4x)^2-(7i)^2=(4x-7i)(4x+7i)}[/tex]
Find the product of (x + 9i)^2.
[tex]\boxed{(x+9i)^2=x^2+18xi+(9i)^2=x^2+18xi-81=x^2-81+18xi}[/tex]
Find the product of (x − 2i)^2.
[tex]\boxed{(x-2i)^2=x^2-4xi-4=x^2-4-4xi}[/tex]
Find the product of (x + (3+5i))^2.
[tex]\boxed{(x + (3+5i))^2=x^2+(3+5i)^2+2x(3+5i)=x^2+9-25+30i+6x+10xi}\\\boxed{=x^2+6x-16+(30+10x)i}[/tex]
Hope this helps.
Do not hesitate if you need further explanation.
Thank you
Consider the function g(x) = x^12. Describe the range of the function.
Answer:
0 ≤ g(x) < ∞
Step-by-step explanation:
The range is all non-negative numbers.
___
g(x) is an even-degree polynomial with a positive leading coefficient, so it opens upward. There is no added constant, so its minimum value is zero. The function can take on all values zero or greater.
range: [0, ∞)
A tourist can bicycle 28 miles in the same time as he can walk 8 miles. If he can ride 10 mph faster than he can walk, how much time (in hr) should he allow to walk a 25-mile trail? (Hint: How fast can he walk?) ________ hr. (enter a fraction)
Answer:
The answer is [tex]\frac{25}{4}[/tex]
Step-by-step explanation:
Velocity formula:
[tex]v = \frac{d}{t}[/tex]
In which v is the velocity, d is the distance, and t is the time.
A tourist can bicycle 28 miles in the same time as he can walk 8 miles. He can ride 10 mph faster than he can walk:
This means that:
[tex]v = \frac{8}{t}[/tex]
And
[tex]v + 10 = \frac{28}{t}[/tex]
[tex](v + 10)t = 28[/tex]
From the first equation:
[tex]vt = 8[/tex]
So
[tex]vt + 10 = 28[/tex]
[tex]8 + 10t = 28[/tex]
[tex]10t = 20[/tex]
[tex]t = \frac{20}{10}[/tex]
[tex]t = 2[/tex]
He walks 8 miles in two hours, so:
[tex]v = \frac{8}{2} = 4[/tex]
4 miles per hour.
How much time (in hr) should he allow to walk a 25-mile trail?
This is t when [tex]d = 25[/tex]. So
[tex]v = \frac{d}{t}[/tex]
[tex]4 = \frac{25}{t}[/tex]
[tex]4t = 25[/tex]
[tex]t = \frac{25}{4}[/tex]
The answer is [tex]\frac{25}{4}[/tex]
Let mZA = 40°. If zB is a complement of ZA, and ZC is a supplement of ZB, find these measures.
mZB =
mZC =
Angle b= 50
Angle c= 130
Complementary angles are two angles that add to equal 90
Supplementary angles are two angles that add to equal 180
To find the measurement of angle b, subtract 40 from 90 (50)
To find the measurement of angle c, subtract 50 from 180 (130)
The measures of complementary and supplementary angles are given by m∠B = 50° and m∠C = 130°
What are Supplementary and Complementary Angles?Supplementary angles are two angles that add up to 180 degrees. In other words, if angle A and angle B are supplementary, then:
A + B = 180°
Complementary angles are two angles that add up to 90 degrees. In other words, if angle A and angle B are complementary, then:
A + B = 90°
Given data ,
If m∠A = 40°, then its complement ∠B = 90° - m∠A = 90° - 40° = 50°.
Since ∠C is a supplement of ∠B, we know that m∠C + m∠B = 180°.
Therefore, we can solve for m∠C by rearranging this equation to get:
m∠C = 180° - m∠B
Substituting the value we found for m∠B, we get:
m∠C = 180° - 50° = 130°
Hence , the angles are mZB = 50° and mZC = 130°.
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Please only answer if you are 100% sure about the answer.
Answer:
Choice C.
Step-by-step explanation:
Your choice is correct
2 stands for a starting point which is 2 feet from the home
As the ant moves, over time, the distance increases according to the function
Please answer this correctly
Answer:
75%
Step-by-step explanation:
The numbers that are not 5 are 6, 7, and 8.
3 numbers are not 5 out of 4 total numbers on the spinner.
3/4 = 0.75
= 75%
Answer:
75%
Step-by-step explanation:
Total no.s = 4
Divided in parts = 25%
P(not 5) = 75%
You are reading the draft of a scientific paper that your co-worker has written. In the paper, he draws a sample from a population and computes the following two confidence intervals for : A 95% confidence interval of (90.21,100.37) A 99% confidence interval of (93.61.98.53) How do you know your co-worker made a mistake? He computed more than one confidence interval using the same sample data. Your co-worker did not round to 3 decimal places in his confidence interval upper and lower bounds The 99% confidence interval should be wider than the 95% confidence interval He is not a statistic, so it doesn't make any sense to compute confidence intervals for it. There is nothing wrong with his statements.
Answer:
The correct option is (C).
Step-by-step explanation:
The general form of a confidence interval is:
[tex]CI=SS\pm CV\cdot SE[/tex]
Here,
SS = Sample statistic
CV = critical value
SE = standard error
The width of the confidence interval is:
[tex]\text{Width}=2\cdot CV\cdot SE[/tex]
The width of the confidence interval is dependent upon the critical value and hence dependent upon the confidence level.
As the confidence level increases the critical value increases hence in turn increasing the width of the interval.
And as the confidence level decreases the critical value decreases hence in turn decreasing the width of the interval.
In this case the 95% confidence interval is, (90.21,100.37).
And the 99% confidence interval is, (93.61.98.53).
It is clear by looking at the two intervals that the 95% confidence interval is wider than the 99%. Thus, this clearly indicates that the co-worker made a mistake.
The correct option is (C).
Use the place value chart to write 9.807.
Answer:
9 ones, 8 tenths, 0 hundredths, 7 thousandths
Step-by-step explanation:
Answer:
9 thousands
8 hundreds
0 tens
7 ones
Step-by-step explanation:
Hope it helped!
Researchers fed mice a specific amount of Dieldrin, a poisonous pesticide, and studied their nervous systems to find out why Dieldrin causes seizures. The absolute refractory period, time required for nerves to recover after a stimulus, was measured and varies Normally. The measurements, in milliseconds, for six mice were 2.2, 2.4, 2.5, 2.5, 2.6, and 2.7. (10 points) Part A: Find the mean refractory period and the standard error of the mean. (2 points) Part B: Calculate a 98% confidence interval for the mean absolute refractory period for all mice when subjected to the same treatment. (4 points) Part C: Suppose the mean absolute refractory period for unpoisoned mice is known to be 2.3 milliseconds. Dieldrin poisoning should slow nerve recovery and therefore increase this period. Do the data give good evidence to support this theory? What can you conclude from a hypothesis test? Justify your response with statistical reasoning. (4 points)
Answer:
Step-by-step explanation:
Part A
Mean = (2.2 + 2.4 + 2.5 + 2.5 + 2.6 + 2.7)/6 = 2.48
Standard deviation = √(summation(x - mean)²/n
n = 6
Summation(x - mean)² = (2.2 - 2.48)^2 + (2.4 - 2.48)^2 + (2.5 - 2.48)^2 + (2.5 - 2.48)^2 + (2.6 - 2.48)^2 + (2.7 - 2.48)^2 = 0.1484
Standard deviation = √(0.1484/6
s = 0.16
Standard error = s/√n = 0.16/√6 = 0.065
Part B
Confidence interval is written as sample mean ± margin of error
Margin of error = z × s/√n
Since sample size is small and population standard deviation is unknown, z for 98% confidence level would be the t score from the student t distribution table. Degree of freedom = n - 1 = 6 - 1 = 5
Therefore, z = 3.365
Margin of error = 3.365 × 0.16/√6 = 0.22
Confidence interval is 2.48 ± 0.22
Part C
We would set up the hypothesis test. This is a test of a single population mean since we are dealing with mean
For the null hypothesis,
H0: µ = 2.3
For the alternative hypothesis,
H1: µ > 2.3
This is a right tailed test
Since the number of samples is small and no population standard deviation is given, the distribution is a student's t.
Since n = 6
Degrees of freedom, df = n - 1 = 6 - 1 = 5
t = (x - µ)/(s/√n)
Where
x = sample mean = 2.48
µ = population mean = 2.3
s = samples standard deviation = 0.16
t = (2.48 - 2.3)/(0.16/√6) = 2.76
We would determine the p value using the t test calculator. It becomes
p = 0.02
Assuming significance level, alpha = 0.05.
Since alpha, 0.05 > than the p value, 0.02, then we would reject the null hypothesis. Therefore, At a 5% level of significance, the sample data showed significant evidence that the mean absolute refractory period for all mice when subjected to the same treatment increased.
- (3/4) times (- 3/8) times ___= -3/4
Answer:
x = -8/3
Step-by-step explanation:
Step 1: Write equation
-3/4(-3/8)(x) = -3/4
Step 2: Multiply
9/32(x) = -3/4
Step 3: Divide
x = -3/4/(9/32)
x = -3/4(32/9)
x = -8/3
Answer:
-8/3
Step-by-step explanation:
-(3/4) x (-3/8)= 9/32
9/32 times (-8/3) = -3/4
Answer: -8/3
Suppose that you spin the double wheel pictured to the right. Assuming that the wheels are independent and each outcome is equally likely, determine the probability that you get red on both wheels.
A spinner consists of two concentric unequal circular wheels with the smaller one placed on the larger. The smaller wheel is divided into 8 equal sectors. The number of sectors for each color is as follows, where the label is listed first and the number of sectors is listed second: red, 3; blue, 2; yellow, 1; grey, 2. The larger wheel is divided into 12 equal sectors. The number of sectors for each color is as follows, where the label is listed first and the number of sectors is listed second: red, 4; blue, 2; yellow, 2; grey, 2; green, 2.
B=blue
G=green
Y=yellow
R=red
g=grey
The probability is:_________
Answer:
0.125
Step-by-step explanation:
Smaller Wheel
Total Number of Equal Sectors = 8
The number of Red sectors =3
The probability of obtaining red on the smaller wheel [tex]=\dfrac38[/tex]
Larger Wheel
Total Number of Equal Sectors = 12
The number of Red sectors =4
The probability of obtaining red on the larger wheel [tex]=\dfrac{4}{12}[/tex]
Assuming that the wheels are independent and each outcome is equally likely, the probability that we get red on both wheels
[tex]=\dfrac38 \times \dfrac{4}{12}\\\\=\dfrac18\\\\=0.125[/tex]
The probability is: 0.125
Decide whether the Experiment is a Binomial Experiment. If it is not, explain why:
You observe the gender of the next 850 babies born at a local hospital. The random variable represents the number of boys.
You draw a marble 350 times from a bag with three colors of marbles. The random variable represents the color of marble that is drawn.
Testing a cough suppressant using 820 people to determine if it is effective. The random variable represents the number of people who find the cough suppressant to be effective.
Answer:
Experiment 1 and 3 are clear binomial experiments.
Experiment 2 needs tweaking to be a binomial experiment.
Check Explanation.
Step-by-step explanation:
A binomial experiment is one in which
1) The probability of success doesn't change with every run or number of trials.
2) It usually consists of a fixed number of runs/trials with only two possible outcomes, a success or a failure.
3) The outcome of each trial/run of a binomial experiment is independent of one another.
Checking each of the experiments one at a time
- You observe the gender of the next 850 babies born at a local hospital. The random variable represents the number of boys.
For this experiment,
1) The probability of success doesn't change with every run or number of trials as it is a 50% chance that each child examined is a boy.
2) It consists of a fixed number of runs (850) with only two possible outcomes, success (if it's a boy) and failure (if it's a girl).
3) The probability of each trial being a boy is independent from all the other trials.
Hence, this experiment is a binomial experiment.
- You draw a marble 350 times from a bag with three colors of marbles. The random variable represents the color of marble that is drawn.
For this experiment,
1) If the marbles aren't being replaced after each draw, the probability of success, that is, picking a particular marble colour changes from trial to trial.
2) Although, it consist of a fixed number of runs/trials, there are more than two possible outcomes with 3 types of colours. Unless the experiment focuses on one colour and treats the other two colours as 'others', this condition too isn't satisfied.
3) Without replacement, the probability of success (picking a particular marble colour) in one trial isn't independent of the other trials.
This is not a binomial experiment as it doesn't satisfy all the required conditions to be one.
- Testing a cough suppressant using 820 people to determine if it is effective. The random variable represents the number of people who find the cough suppressant to be effective.
1) The probability of success doesn't change with every run or number of trials as it is the same chance that each person finds the cough suppressant to be effective.
2) It consists of a fixed number of runs (820) with only two possible outcomes, success (cough suppressant is effective) and failure (cough suppressant isn't effective).
3) The probability of each trial being a person that finds the cough suppressant to be effective, is independent from all the other trials.
Hence, this experiment is a binomial experiment.
Hope this Helps!!!
Find the Prime factors of 1729. Arrange the factors in ascending order. Find a relation between
consecutive prime factors
Answer:
prime factors in ascending order of 1729 is 7 , 13 , 19
relation between consecutive prime factors is 6
Step-by-step explanation:
given data
number = 1729
solution
we get here factors of 1729
1729 = 7 × 13 × 19
so that required prime factors in ascending order of 1729 is 7 , 13 , 19
and
now we get relation between these prime factors is the difference between consecutive prime factors is
13 - 7 = 6
19 - 13 = 6
so relation between consecutive prime factors is 6
Step-by-step explanation:
Prime factors of the number 1729 are 7,13,19
i.e. 1729 =7×13×19
The factors in ascending order are 7,13,19.
Clearly we can see that each consecutive prime factors have difference of 6.
13-7=6
19-13=6
I NEED HELP PLEASE, THANKS! Use Cramer's Rule to find the solution of the system of linear equations, if a unique solution exists. –5x + 2y – 2z = 26 3x + 5y + z = –22 –3x – 5y – 2z = 21 A. (–1, –7, 2) B. (–6, –1, 1) C. (–1, 3, 1) D. no unique solution
Answer:
Option B
Step-by-step explanation:
We are given the following system of equations -
[tex]\begin{bmatrix}-5x+2y-2z=26\\ 3x+5y+z=-22\\ -3x-5y-2z=21\end{bmatrix}[/tex]
Now by Cramer's Rule, we would first write down the matrix of the coefficients , replacing each column with the answer column -
[tex]\begin{bmatrix}-5&2&-2\\ 3&5&1\\ -3&-5&-2\end{bmatrix}[/tex] ,
[tex]\begin{bmatrix}26\\ -22\\ 21\end{bmatrix}[/tex]
Replace each column of the coefficients shown at the top, with the answer column at the bottom respectively -
[tex]\begin{bmatrix}-5&2&26\\ 3&5&-22\\ -3&-5&21\end{bmatrix}[/tex]
Now solve through Cramer's Rule -
x = Dx / D = - 6,
y = Dy / D = - 1,
z = Dz / D = 1
Solution = ( - 6, - 1, 1 ) = Option B
-5 x + 2 y - 2 z = 263 x + 5 y + z = -22 - 3 x - 5 y - 2 z = 21
Answer is x=-6,\:z=1,\:y=-1
Annual starting salaries for college graduates with degrees in business administration are generally expected to be between $43,000 and $61,600. Assume that a 95% confidence interval estimate of the population mean annual starting salary is desired.
Required:
a. What is the planning value for the population standard deviation (to the nearest whole number)?
b. How large a sample should be taken if the desired margin of error is as shown below (to the nearest whole number)?
1. $500?
2. $200?
3. $100?
Answer:
a. 4650
b.
1. 332
2. 2076
3. 8306
Step-by-step explanation:
a. The planning value for population standard deviation is,
s = (maximum - minimum) / 4
s = (61600 - 43000) / 4
s = 4650
that is, it would be 4650, the planning value for population standard deviation
b. we have to:
n = (z * s / E) ^ 2
z for confidence level 95% is 1.96, E = 500; 200; 100
replacing:
1.
n = (1.96 * 4650/500) ^ 2
n = 332.2 = 332
2.
n = (1.96 * 4650/200) ^ 2
n = 2076.6 = 2076
3.
n = (1.96 * 4650/100) ^ 2
n = 8306.4 = 8306
Find two positive numbers whose product is 16 and whose sum is a minimum. (If both values are the same number, enter it into both blanks.) (smaller number) (larger number)
Answer:
4 and 4
Step-by-step explanation:
We have 2 numbers that will be X and Y
X * Y = 16 => Y = 16 / X
We must minimize the sum, therefore:
S = X + Y
S = X + 16 / X
we derive and equal 0 and we are left with:
dS / dA = 1 - 16 / (X ^ 2) = 0
1 = 16 / X ^ 2
X ^ 2 = 16
X = 4
in the case of Y:
Y = 16/4 = 4
Therefore the numbers are 4 and 4.
The two positive numbers are 4 and 4
Let the two numbers be x and y
If the product of both numbers is 16, hence;
xy = 16 ........................... 1
If the sum will be at the minimum, hence x + y = minimum
From equation1, x = 16/ y
Substitute into the second equation to have;
16/y + y = A(y)
A(y) = 16/y + y
For the expression to be at a minimum, hence dA/dy = 0
dA/dy = -16/y² + 1
0 = -16/y² + 1
0 - 1 = -16/y²
-y² = -16
y = √16
y = 4
Recall that xy = 16
4x= 16
x = 4
Hence the two positive numbers are 4 and 4
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I paid twice as much by not waiting for a sale and not ordering on line. Which ofthe following statements is also true?
(a) I paid 200% more than I could have online and on sale.
(b) I paid 100% of what I could have online and on sale.
(c) I paid 200% of what I could have online and on sale.
(d) I paid 3 times what I could have online and on sale.
Answer:
Option (c).
Step-by-step explanation:
It is given that, I paid twice as much by not waiting for a sale and not ordering online.
Let the cost of items ordering online be x.
So, now i am paying twice of x = 2x
Now, we have find 2x is what percent of x.
[tex]Percent =\dfrac{2x}{x}\times 100=200\%[/tex]
It means, I paid 200% of what I could have online and on sale.
Therefore, the correct option is (c).
A glass vase has a circular rim with a diameter of 5in. How many inches of ribbon are needed to go once around the rim? Use 3.14
Answer:
31.4 inches
Step-by-step explanation:
The circumference of a circle has the formula 2πr.
2 × π × 5
= 10 × 3.14
= 31.4
31.4 inches of ribbon is needed to go once around the rim.
Answer:
15.7 inches of ribbon.
Step-by-step explanation:
This question is basically asking for the circumference of the glass vase's rim. We can calculate that by multiplying the diameter by π, which in this case, is 3.14.
The diameter is 5 inches, so all you need to do is 5 * 3.14 = 15.7 inches of ribbon.
Hope this helps!
There are two boxes containing only black and orange pens.
Box A has 4 black pens and 16 orange pens.
Box B has 2 black pens and 3 orange pens.
A pen is randomly chosen from each box. List these events from least likely to most likely.
Event 1: choosing a black pen from Box A.
Event 2: choosing a black or orange pen from Box A.
Event 3: choosing a white pen from Box B.
Event 4: choosing a black pen from Box B.
Answer:
Event 3 -> Event 1 -> Event 4 -> Event 2
Step-by-step explanation:
The probability of choosing a certain pen is the number of that pen in the box over the total number of pens in the box.
So we have that:
Event 1: We have 4 black pen and 20 total pens, so P = 4 / 20 = 1 / 5
Event 2: All pens are black or orange so the probability is 1.
Event 3: We don't have white pens, so the probability is 0.
Event 4: We have 2 black pen and 5 total pens, so P = 2 / 5
Listing from least likely to most likely, we have:
Event 3 -> Event 1 -> Event 4 -> Event 2
Please answer this correctly
Answer:
80%
Step-by-step explanation:
The probability of getting a four is 1/5
The probability of getting a odd is3/5
So u add them and it gives u 4/5 which in decimal is .8 which in percent is 80%
Hope this helps
Please answer this correctly
Answer:
1/5
Step-by-step explanation:
The number 5 or greater than 4 is 5.
1 number out of 5 total parts.
= 1/5
P(5 or greater than 4) = 1/5
y
X
Find the slope of the line that passes through the points
(2, -5) and (7, 1).
y
-5
6
2
7
1
Step 1: Choose (X1,Y1).
4
2.
-4
-2
2
4
6
8
Answer:
slope = [tex]\frac{6}{5}[/tex]
Step-by-step explanation:
Calculate the slope m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (2, - 5) and (x₂, y₂ ) = (7, 1)
m = [tex]\frac{1+5}{7-2}[/tex] = [tex]\frac{6}{5}[/tex]
The required slope of the line passes through the points (2, -5) and (7, 1) is m = 6/5
What is the slope of the line?The slope of the line is a tangent angle made by line with horizontal. i.e. m =tanx where x in degrees.
here,
The slope of a line passing through two points (x1, y1) and (x2, y2) is given by the formula:
m = (y2 - y1) / (x2 - x1)
Let's apply this formula to the given points:
m = (1 - (-5)) / (7 - 2)
m = 6 / 5
Thus, the required slope of the line passes through the points (2, -5) and (7, 1).
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What is 75miles/hr in feet/second?(1mile = 5280feet)
Answer:
110 feet/sec
Step-by-step explanation:
75 miles x 5280 feet
= 396000
396000/60 min
=6600
6600/60 secs
=110 feet/second
Ujalakhan01! Please help me! ASAP ONLY UJALAKHAN01. What's (x-1)(x-1)?
Answer:
x^2-2x+1
Step-by-step explanation:
We can solve this by using FOIL
First, Outside, Inside, Last
Multiply the x with the x to get x^2
Then x times -1 for the outside numbers to get -x
Then -1 times x for the inside numbers to get -x
And finally -1 and -1 for the last numbers to get 1
Add the two -x to get -2x.
Put it all together
x^2-2x+1
Answer:
[tex]x^2-2x+1[/tex]
Step-by-step explanation:
=> (x-1)(x-1)
USING FOIL
=> [tex]x^2-x-x+1[/tex]
=> [tex]x^2-2x+1[/tex]
GO DEEPER
In the last six months, Sonia's family used 456, 398,655, 508,
1,186, and 625 minutes on their cell phone plan. In an effort to spend less
time on the phone each month, Sonia's family wants to try and keep the
mean cell phone usage at 600 minutes or less. Over the last 6 months,
by how many minutes did the mean number of minutes exceed their goal?
Answer:
46
Step-by-step explanation:
Given that triangle DAE ~ triangle BAC, what is the length of side AE?
Answer:
12
Step-by-step explanation:
For polygons that are similar to each other, the ratio of their corresponding sides are usually equal to each other, as they are proportional.
Therefore, given that ∆DAE is similar to ∆BAC, AD = 6, AB = 6+4 = 10, AE = x, AC = x + 8, therefore:
AD/AB = AE/AC
6/10 = x/(x+8)
Cross multiply
6*(x+8) = x*10
6x + 48 = 10x
Subtract 6x from both sides
48 = 10x - 6x
48 = 4x
Divide both sides by 4
48/4 = x
x = 12
Length of side AE = 12
A hiker starting at point P on a straight road wants to reach a forest cabin that is 2 km from a point Q, 3 km down the road from P . She can walk 8 km/hr along the road but only 3 km/hr through the forest. She wants to minimize the time required to reach the cabin. How far down the road should she walk before setting off through the forest straight for the cabin?
Answer:
2.19 km
Step-by-step explanation:
If x is the distance she walks down the road before turning, then the total time is:
t = x/8 + √((3 − x)² + 2²) / 3
t = x/8 + √(9 − 6x + x² + 4) / 3
24t = 3x + 8√(13 − 6x + x²)
24t = 3x + 8(13 − 6x + x²)^½
Take derivative of both sides with respect to x.
24 dt/dx = 3 + 4(13 − 6x + x²)^-½ (-6 + 2x)
When t is a minimum, dt/dx = 0.
0 = 3 + 4(13 − 6x + x²)^-½ (-6 + 2x)
-3 = 4(13 − 6x + x²)^-½ (-6 + 2x)
3 / (6 − 2x) = 4(13 − 6x + x²)^-½
3 / (24 − 8x) = (13 − 6x + x²)^-½
(24 − 8x) / 3 = (13 − 6x + x²)^½
(24 − 8x)² / 9 = 13 − 6x + x²
576 − 384x + 64x² = 117 − 54x + 9x²
459 − 330x + 55x² = 0
Solve with quadratic formula.
x = [ 330 ± √((-330)² − 4(55)(459)) ] / 2(55)
x = (330 ± √7920) / 110
x = 2.19 or 3.81
Since 0 < x < 3, x = 2.19.
Select the correct answer. Vector u has its initial point at (-7, 2) and its terminal point at (11, -5). Vector v has a direction opposite that of vector u, and its magnitude is three times the magnitude of u. What is the component form of vector v? A. v = B. v = C. v = D. v =
Answer:
Step-by-step explanation:
vector u=<(11-(-7),(-5-2)>=<18,-7>
as direction is opposite to u
so vector v=-3(18,-7)=(-54,21)
A fruit company delivers its fruit in two types of boxes: large and small. A delivery of eight large boxes and four small boxes has a total weight of two hundred and one kilograms. A delivery of three large boxes and two small boxes has a total weight of eighty two kilograms. How much does each type of box weigh?
Answer:
Weight of Large Box = 18.5 kg
Weight of Large Box = 13.25 kg
Step-by-step explanation:
Given:
There are two types of boxes i.e. Large and Small
Let the weight of Large boxes = L kg
Let the weight of Small boxes = S kg
As per given statement:
A delivery of eight large boxes and four small boxes has a total weight of two hundred and one kilograms.Writing equation for above:
[tex]8L + 4S = 201[/tex] ....... (1)
A delivery of three large boxes and two small boxes has a total weight of eighty two kilograms.Writing equation for above:
[tex]3L + 2S = 82 ....... (2)[/tex]
Now, by solving the equations (1) and (2), we can get the values of L and S.
Multiplying equation (2) with 2 and subtracting from equation (1):
[tex]8L + 4S = 201[/tex]
-
[tex]2 \times (3L + 2S) = 82 \times 2[/tex]
[tex]8L + 4S = 201[/tex]
-
[tex]6L + 4S = 164[/tex]
--------------------
[tex]2L = 37[/tex]
L = 18.5 Kg
Putting value of L in equation (1):
[tex]8 \times 18.5 + 4S = 201\\\Rightarrow 148 + 4S = 201\\\Rightarrow 4S = 201 - 148\\\Rightarrow 4S = 53\\\Rightarrow S = 13.25\ kg[/tex]
So, the answer is:
Weight of Large Box = 18.5 kg
Weight of Large Box = 13.25 kg
Determine whether the pair of equations represent parallel lines, perpendicular lines, or neither.
12x + 4y = 16
24x + 8y = 36
Answer:
Parallel
Step-by-step explanation:
Parallel lines have the same slope but different y-intercepts. If you multiply the top equation by 2, you get:
2(12x + 4y = 16)
24x + 8y = 32
This shows that both lines have the same slope, but then you find the y-intercepts, they are different:
1st equation y-int = 4
2nd equation y-int = 9/2 or 4.5
According to the New York Stock Exchange, the mean portfolio value for U.S. senior citizens who are shareholders is $183,000. Assume portfolio values are normally distributed. Suppose a simple random sample of 51 senior citizen shareholders in a certain region of the United States is found to have a mean portfolio value of $198,000, with a standard deviation of $65,000.
a. From these sample results, and using the 0.05 level of significance comment on whether the mean portfolio value for all senior citizen shareholders in this region might not be the same as the mean value reported for their counterparts across the nation, by using the critical value method. Establish the null and alternative hypotheses.
b. What is your conclusion about the null hypothesis?
Answer:
The test statistic value t = 1.64 < 2.0086 at 0.05 level of significance
Null hypothesis is accepted
The mean portfolio value for all senior citizen shareholders in this region might not be the same as the mean value reported for their counterparts across the nation
Step-by-step explanation:
Step(i):-
Given mean of the population (μ) = $183,000
Given mean of the sample (x⁻) = $198,000
Given standard deviation of the sample (S) = $65,000.
Mean of the sample size 'n' = 51
level of significance α = 0.05
Step(ii):-
Null hypothesis : H₀ : There is no significance difference between the means
Alternative Hypothesis :H₁: There is significance difference between the means
Test statistic
[tex]t = \frac{x^{-}-mean }{\frac{S.D}{\sqrt{n} } }[/tex]
[tex]t = \frac{198,000- 183,000 }{\frac{ 65,000}{\sqrt{51} } }[/tex]
t = 1.64
Step(iii)
Degrees of freedom ν = n-1 = 51-1 =50
t₀.₀₅ = 2.0086
The calculated value t = 1.64 < 2.0086 at 0.05 level of significance
Null hypothesis is accepted
Final answer:-
There is no significance difference between the means
The mean portfolio value for all senior citizen shareholders in this region might not be the same as the mean value reported for their counterparts across the nation