Answer:
{-14, 16}
Step-by-step explanation:
The coefficients of this quadratic are a = 1, b = -2 and c = -224.
Thus, the discriminant is b^2 - 4ac, or (-2)^2 - 4(1)(-224), or 900, whose square root is 30.
Thus, the roots (solutions) are
-(-2) ± 30
x = ----------------- = {-14, 16}
2
around 2.232 to the nearest hundredth
[tex]2.232\approx2.32[/tex]
Suppose that 80% of all registered California voters favor banning the release of information from exit polls in presidential elections until after the polls in California close. A random sample of 25 registered California voters is selected.
Required:
a. Calculate the mean and standard deviation of the number of voters who favor the ban.
b. What is the probability that exactly 20 voters favor the ban?
Answer:
a. Mean = 20
Sd = 4
b. Probability of X = 20 = 0.1960
Step-by-step explanation:
we have
n = 25
p = 80% = 0.8
mean = np
= 0.8 * 25
= 20
standard deviation = √np(1-p)
= √25*0.8(1-0.8)
=√4
= 2
probability that exactly 20 favours ban
it follows a binomial distribution
= 25C20 × 0.8²⁰ × 0.2⁵
= 53130 × 0.01153 × 0.00032
= 0.1960
Probability of X = 20 = 0.1960
There are 2229 students in a school district. Among a sample of 452 students from this school district, 163 have mathematics scores below grade level. Based on this sample, estimate the number of students in this school district with mathematics scores below grade level.
a. 804
b. 844
c. 884
d. 0.36
Answer:
A. 804Step-by-step explanation:
Given the total number of students in the school to be 2229 students. If among a sample of 452 students from this school district, 163 have mathematics scores below grade level, then we can determine the number of students in this school district with mathematics scores below grade level based on the sample scores using ratio.
Let the number of students in this school district with mathematics scores below grade level be x. The ratio of the students with math score below grade level to total population will be x:2229
Also, the ratio of the sample students with math score below grade level to sample population will be 163:452
On equating both ratios, we will have;
x:2229 = 163:452
[tex]\dfrac{x}{2229} = \dfrac{163}{452}\\ \\cross\ multiplying;\\\\\\452*x = 2229*163\\\\x = \dfrac{2229*163}{452}\\ \\x = \frac{363,327}{452}\\ \\x = 803.8\\\\x \approx 804[/tex]
Hence the estimate of the number of students in this school district with mathematics scores below grade level based on the sample is 804
The Airline Passenger Association studied the relationship between the number of passengers on a particular flight and the cost of the flight. It seems logical that more passengers on the flight will result in more weight and more luggage, which in turn will result in higher fuel costs. For a sample of 21 flights, the correlation between the number of passengers and total fuel cost was 0.668.
(1)
State the decision rule for 0.10 significance level: H0: Ï â‰¤ 0; H1: Ï > 0 (Round your answer to 3 decimal places.)
Reject H0 if t >
(2)
Compute the value of the test statistic. (Round your answer to 3 decimal places.)
Value of the test statistic
Answer:
Decision Rule: To reject the null hypothesis if t > 1.328
t = 3.913
Step-by-step explanation:
The summary of the given statistics include:
sample size n = 21
the correlation between the number of passengers and total fuel cost r = 0.668
(1) We are tasked to state the decision rule for 0.10 significance level
The degree of freedom df = n - 1
degree of freedom df = 21 - 1
degree of freedom df = 19
The null and the alternative hypothesis can be computed as:
[tex]H_o : \rho < 0\\ \\ Ha : \rho > 0[/tex]
The critical value for [tex]t_{\alpha, df}[/tex] is [tex]t_{010, 19}[/tex] = 1.328
Decision Rule: To reject the null hypothesis if t > 1.328
The test statistics can be computed as follows by using the formula for t-test for Pearson Correlation:
[tex]t = r*\sqrt{ \dfrac{(n-2)}{(1-r^2)}[/tex]
[tex]t = 0.668*\sqrt{ \dfrac{(21-2)}{(1-0.668^2)}[/tex]
[tex]t = 0.668*\sqrt{ \dfrac{(19)}{(1-0.446224)}[/tex]
[tex]t = 0.668*\sqrt{ \dfrac{(19)}{(0.553776)}[/tex]
[tex]t = 0.668*5.858[/tex]
t = 3.913144
t = 3.913 to 3 decimal places
A box contains 40 tiles, and all identical
shape and size, numbered 1 through 40. If a
person picks out a single tile from the box
without looking, what is the probability the
number on the tile will be a prime number?
Answer:
32.5%
Step-by-step explanation:
Hey there!
To find the probability we first need to find the amount of prime numbers in the 1-40 set.
Prime - 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37
That’s 13 prime numbers.
Fraction - 13/40
Simplified is just 13/40.
13 / 40 = .325
Percent - 32.5%
Hope this helps :)
Consider the following functions. f={(−1,1),(1,−2),(−5,−1),(5,3)} and g={(0,2),(−3,−4),(1,−2)} Step 1 of 4: Find (f+g)(1).
Answer:
-4
Step-by-step explanation:
(f+g)(1) = f(1) +g(1)
In each case, you need to locate the ordered pair with 1 as the first element.
(1, f(1)) = (1, -2) . . . . f(1) = -2
(1, g(1)) = (1, -2) . . . . g(1) = -2
f(1) +g(1) = (-2) +(-2) = -4
(f+g)(1) = -4
what is the diameter of a circular swimming pool with a radius of 9 feet? enter only the number
Answer:
The answer is 18 feet
Step-by-step explanation:
To find the diameter of a circle given it's radius we use the formula
diameter = radius × 2
From the question
radius = 8
So the diameter is
diameter = 9 × 2 = 18 feetHope this helps you
Answer:
18
Step-by-step explanation:
Hey there!
Well radius is half the diameter so,
D = r*2
Plug in 9
D = 9*2
D = 18
Hope this helps :)
What is the slope of the line that passes through (2, 12) and (4, 20)?On the graph of the equation 3x + 2y = 18, what is the value of the y-intercept?
Answer: The slope of the line that passes through (2, 12) and (4, 20) is 4.
The value of the y-intercept is 9.
Step-by-step explanation:
Slope of line passing through (a,b) and (c,d) = [tex]\dfrac{d-b}{c-a}[/tex]
Then, the slope of the line that passes through (2, 12) and (4, 20) = [tex]\dfrac{20-12}{4-2}[/tex]
[tex]=\dfrac{8}{2}=4[/tex]
So, the slope of the line that passes through (2, 12) and (4, 20) is 4.
To find the y-intercept of 3x + 2y = 18, first write in slope intercept form y=mx+c ( where c= y-intercept ).
[tex]2y=-3x+18\\\\\Rightarrow\ y=-\dfrac{3}{2}x+9[/tex]
By comparison, c= 9
Hence, the value of the y-intercept is 9.
Factor by grouping cd-9d-4c+36
Answer:
(d-4)(c-9)
Step-by-step explanation:
cd-9d-4c+36
d(c-9)-4(c-9)
pull out the (c-9),
(d-4)(c-9)
Based on the dot plots shown in the images, which of the following is a true statement? A. Set B has the greater mode. B. Set A has more items than set B. C. Set A is more symmetric than set B. D. Set B has the greater range.
Working together, it takes two computers 10 minutes to send out a company's email. If it takes the slower computer 50 minutes to do the job on its own, how long will it take the faster computer to do the job on its own? don't round
Answer:
12.5 minutes
Step-by-step explanation:
When working together,It takes two computers 10 minutes to send out an email
It takes the slower computer 50 minutes to send out an email
Let x represent the time taken by the faster computer to do the job in its own
Therefore, the time required by the faster computer can be calculated as follows
1/x + 1/50= 1/10
Collect the like terms
1/x= 1/10-1/50
1/x= 4/50
Cross multiply both sides
4 × x = 50×1
4x=50
Divide both sides by the coefficient of x which is 4
4x/4=50/4
x= 12.5
Hence the time taken by the faster computer to finish the job on its own is 12.5 minutes
A potato chip company makes potato chips in two flavors, Regular and Salt & Vinegar. Riley is a production manager for the company who is trying to ensure that each bag contains about the same number of chips, regardless of flavor. He collects two random samples of 10 bags of chips of each flavor and counts the number of chips in each bag. Assume that the population variances of the number of chips per bag for both flavors are equal and that the number of chips per bag for both flavors are normally distributed. Let the Regular chips be the first sample, and let the Salt & Vinegar chips be the second sample. Riley conducts a two-mean hypothesis test at the 0.05 level of significance, to test if there is evidence that both flavors have the same number of chips in each bag. (a) H0:μ1=μ2; Ha:μ1≠μ2, which is a two-tailed test. (b) t≈1.44 , p-value is approximately 0.167 (c) Which of the following are appropriate conclusions for this hypothesis test?
A. There is insufficient evidence at the 0.05 level of significance to conclude that Regular and Salt & Vinegar chips have different amounts of chips per bag.B. There is sufficient evidence at the 0.05 level of significance to conclude that Regular and Salt & Vinegar chips have different amounts of chips per bag.C. Reject H0.D. Fail to reject H0.
Answer:
A. There is insufficient evidence at the 0.05 level of significance to conclude that Regular and Salt & Vinegar chips have different amounts of chips per bag.
D. Fail to reject H0.
Step-by-step explanation:
From the summary of the given test statistics.
The null and the alternative hypothesis are:
[tex]H_0:\mu_1=\mu_2 \\ \\ Ha:\mu_1 \neq \mu_2[/tex]
This test is also a two tailed test.
Similarly, the t value for the test statistics = 1.44
The p- value - 0.167
The level of significance ∝ = 0.05
The objective we are meant to achieve here is to determine which of the following from the given options are appropriate conclusions for this hypothesis test.
From what we have above:
Decision Rule: We fail to reject the null hypothesis since the p-value is greater than the level of significance at 0.05
CONCLUSION: Therefore, we can conclude that there is insufficient evidence at the 0.05 level of significance to conclude that Regular and Salt & Vinegar chips have different amounts of chips per bag as we fail to reject H0.
Which of the following statements is false?
a. A feasible solution satisfies all constraints.
b. In a linear programming problem, the objective function and the constraints must be linear functions of the decision variables.
c. It is possible to have exactly two optimal solutions to a linear programming problem.
d. An optimal solution to a linear programming problem can be found at an extreme point of the feasible region for the problem.
Answer:
d. An optimal solution to linear programming problem can be found at an extreme point of the feasible region for the problem.
Step-by-step explanation:
A feasible solution satisfies all the constraints of the problem in linear programming. The constraints are the restrictions on decision variable. They limit the value of decision variable in linear programming. Optimal solutions occur when there is feasible problem in the programming.
Factor.
x2 + 11x
x2 + 11x
x(x + 11)
11(x + 11)
0(x2 + 11x)
Answer:
x(x + 11)
Step-by-step explanation:
x^2 + 11x when factored gives a result of x(x + 11)
Answer:
x(x+11)
Step-by-step explanation:
We are given the expression:
[tex]x^2+11x[/tex]
This can be factored using the Greatest Common Factor (GCF).
The GCF of x^2 and 11x is x.
Factor out an x.
[tex]x(x+11)[/tex]
x^2+11x factored is: x(x+11).
the temp fell 3 degrees every hour for 5 hours what's the change in temperature
Answer:
-15
Step-by-step explanation:
If it fell 3 deg every hour for 5 hours so the equation is 3*5 plus a - sign because it dropped degrees
An octagonal pyramid ... how many faces does it have, how many vertices and how many edges? A triangular prism ... how many faces does it have, how many vertices and how many edges? a triangular pyramid ... how many faces does it have, how many vertices and how many edges?
1: 8 faces and 9 with the base 9 vertices and 16 edges
2: 3 faces and 5 with the bases 6 vertices and 9 edges
3: 3 faces and 4 with the base 4 vertices and 6 edges
Hope this can help you.
1: 8 faces and 9 with the base 9 vertices and 16 edges
2: 3 faces and 5 with the bases 6 vertices and 9 edges
3: 3 faces and 4 with the base 4 vertices and 6 edges
Varia is studying abroad in Europe. She is required pay $3,500 (in US dollars) per year to the university; however, she must pay in euros. How many euros can Varia expect to pay per month to the university?
Answer: 247.92 euros
Step-by-step explanation:
Given: Varia is required pay $3,500 (in US dollars) per year to the university.
So, [tex]$3500\div 12 \approx\$291.67[/tex]
i.e. She will pay $ 291.67 per month.
Recent currency value: 1 US dollar = 0.85 euro
∴ $291.67 = ( 0.85 ×291.67) euros
= 247.92 euros [Round to the nearest cent]
∴ She can expect 247.92 euros to pay per month to the university.
Let x represent the number of times a student visits a gym in a one month period. Assume that the probability distribution of X is as follows:
x 0 1 2 3
p(x) 0.37 0.29 0.22 0.12
Find the mean, of this distribution. Report your answer to two decimal places.
Answer:
1.86
Step-by-step explanation:
Given the following :
X : - - - - 0 - - - - 1 - - - - 2 - - - - - 3 - - - - 4
P(x) - 0.37 - - 0.28 - - 0.22 - - 0.22 - - 0.12
The mean of the distribution can be calculated by evaluated by determining the expected value of the distribution given that the data above is a discrete random variable. The mean value can be deduced multiplying each possible outcome by the probability of it's occurrence.
Summation of [P(x) * X] :
(0.37 * 0) + (0.28 * 1) + (0.22 * 2) + (0.22 * 3) + (0.12 * 4)
= 0 + 0.28 + 0.44 + 0.66 + 0.48
= 1.86
Aaron wants to mulch his garden. His garden is x^2+18x+81 ft^2 One bag of mulch covers x^2-81 ft^2 . Divide the expressions and simplify to find how many bags of mulch Aaron needs to mulch his garden.
Answer:
Step-by-step explanation:
Given
Garden: [tex]x^2+18x+81[/tex]
One Bag: [tex]x^2 - 81[/tex]
Requires
Determine the number of bags to cover the whole garden
This is calculated as thus;
[tex]Bags = \frac{x^2+18x+81}{x^2 - 81}[/tex]
Expand the numerator
[tex]Bags = \frac{x^2+9x+9x+81}{x^2 - 81}[/tex]
[tex]Bags = \frac{x(x+9)+9(x+9)}{x^2 - 81}[/tex]
[tex]Bags = \frac{(x+9)(x+9)}{x^2 - 81}[/tex]
Express 81 as 9²
[tex]Bags = \frac{(x+9)(x+9)}{x^2 - 9\²}[/tex]
Evaluate as difference of two squares
[tex]Bags = \frac{(x+9)(x+9)}{(x - 9)(x+9)}[/tex]
[tex]Bags = \frac{(x+9)}{(x - 9)}[/tex]
Hence, the number of bags is [tex]Bags = \frac{(x+9)}{(x - 9)}[/tex]
there are 5 discs, 6 jump ropes, 3 balls, and 12 pieces of sidewalk chalk in a bin. If two items are drawn at random without replacement, what is the probability that both items removed are not jump ropes?
Answer: 0.584
Step-by-step explanation:
We have:
5 discs
6 jump ropes
3 balls
12 pieces of sidewalk.
5 + 6 + 3 + 12 = 26
If all of them have exactly the same probability of being removed, then:
in the first selection, we do not want to remove a jump rope, so we can remove one disc, one ball or one piece of sidewalk.
The total number of those objects is:
5 + 3 + 12 = 20.
Then the probability of removing one of those objects is:
P1 = 20/26 = 0.769
Now in the second selection, we have the same situation, but now we have 25 objects in total, and because in the previous selection we removed one ball, or one disc, or one piece of sidewalk, the total number of these things now is 19.
So the probability of removing another object of that set is:
P2 = 19/25 = 0.76
The joint probability is equal to the product of the individual probabilities, so we have:
P = P1*P2 = 0.769*0.76 = 0.584
Using the power series methods solve the 1st order Lane-Emden Equation:
xy = 2y + xy = 0
You may only use a power series solution to find both linearly independent functions. This means you may not use Abel’s theorem, variation of parameters or reduction of order.
Answer:
Step-by-step explanation:
xy = 2y + xy = 0
Hence, 2y + xy = 0 ---------(1)
Differentiating equation (1) n times by Leibnitz theorem, gives:
2y(n) + xy(n) + ny(n - 1) = 0
Let x = 0: 2y(n) + ny(n - 1) = 0
2y(n) = -ny(n - 1)
∴ y(n) = -ny(n - 1)/2 for n ≥ 1
For n = 1: y = 0
For n = 2: y(1) = -y
For n = 3: -3y(2)/2
For n = 4: -2y(3)
Which statement best describes a sequence? a.All sequences have a common difference. b.A sequence is always infinite. c.A sequence is an ordered list. d.A sequence is always arithmetic or geometric.
Answer:
C
Step-by-step explanation:
A sequence is defined as a list of numbers or objects in a special order.
They may be arithmetic or geometric or neither.
For example
0, 1, 4, 9, 16, 25, ..... ← is the sequence of square numbers.
Note it is neither arithmetic or geometric.
Which solution value satisfies the inequality equation x – 5 ≤ 14?
Answer:
Any value that has x less than or equal to 19 is a solution
Step-by-step explanation:
x – 5 ≤ 14
Add 5 to each side
x – 5+5 ≤ 14+5
x ≤ 19
Any value that has x less than or equal to 19 is a solution
Answer:
[tex]\boxed{x\leq 19}[/tex]
Step-by-step explanation:
[tex]x-5\leq 14[/tex]
[tex]\sf Add \ 5 \ on \ both \ sides.[/tex]
[tex]x-5+5 \leq 14+5[/tex]
[tex]x\leq 19[/tex]
The mean temperature for the first 4 days in January was 8°C. The mean temperature for the first 5 days in January was 7°C. What was the temperature on the 5th day? SOMEONE HELP FIRST ANSWER BRAINLIEST THIS TIME I PROMISE LOL
Answer:
The temperature of the 5th day was 3°C
Step-by-step explanation:
Mean temperature of the first 4 days = 8°C
Note that:
Mean = Sum of temperatures ÷ number of days
∴ 8 = sum of temperature ÷ 4
[tex]= 8 = \frac{sum\ of\ temperatures}{4}[/tex]
[tex]= sum\ of\ temperatures\ = 8\ \times\ 4 = 32[/tex]
Therefore the sum of the first 4 days = 32
Let the temperature of the next day (the fifth day) be m
Hence,
sum of the temperatures of first 5 days = 32 + m - - - - (1)
Next, the sum of the first 5 days can be calculated from the given average of the first 5 days as follows:
Mean temperature of the first 5 days = 7
[tex]Mean = \frac{sum\ of\ temperatures}{number \ of\ days}\\\\7 = \frac{sum\ of\ temperatures}{5} \\sum\ of\ temperatures\ = \ 7\ \times\ 5\ = 35\\sum\ of\ temperature\ of\ the\ first\ 5\ days\ =\ 35 - - - - - (2)[/tex]
Now, you will notice that equation (1) = equation (2)
∴ 32 + m = 35
m = 35 - 32 = 3
therefore, the temperature of the 5th day was 3°C
How to find which ratio is largest
At an airport, 76% of recent flights have arrived on time. A sample of 11 flights is studied. Find the probability that no more than 4 of them were on time.
Answer:
The probability is [tex]P( X \le 4 ) = 0.0054[/tex]
Step-by-step explanation:
From the question we are told that
The percentage that are on time is p = 0.76
The sample size is n = 11
Generally the percentage that are not on time is
[tex]q = 1- p[/tex]
[tex]q = 1- 0.76[/tex]
[tex]q = 0.24[/tex]
The probability that no more than 4 of them were on time is mathematically represented as
[tex]P( X \le 4 ) = P(1 ) + P(2) + P(3) + P(4)[/tex]
=> [tex]P( X \le 4 ) = \left n } \atop {}} \right.C_1 p^{1} q^{n- 1} + \left n } \atop {}} \right.C_2p^{2} q^{n- 2} + \left n } \atop {}} \right.C_3 p^{3} q^{n- 3} + \left n } \atop {}} \right.C_4 p^{4} q^{n- 4}[/tex]
[tex]P( X \le 4 ) = \left 11 } \atop {}} \right.C_1 p^{1} q^{11- 1} + \left 11 } \atop {}} \right.C_2p^{2} q^{11- 2} + \left 11 } \atop {}} \right.C_3 p^{3} q^{11- 3} + \left 11 } \atop {}} \right.C_4 p^{4} q^{11- 4}[/tex]
[tex]P( X \le 4 ) = \left 11 } \atop {}} \right.C_1 p^{1} q^{10} + \left 11 } \atop {}} \right.C_2p^{2} q^{9} + \left 11 } \atop {}} \right.C_3 p^{3} q^{8} + \left 11 } \atop {}} \right.C_4 p^{4} q^{7}[/tex]
[tex]= \frac{11! }{ 10! 1!} (0.76)^{1} (0.24)^{10} + \frac{11!}{9! 2!} (0.76)^2 (0.24)^{9} + \frac{11!}{8! 3!} (0.76)^{3} (0.24)^{8} + \frac{11!}{7!4!} (0.76)^{4} (0.24)^{7}[/tex]
[tex]P( X \le 4 ) = 0.0054[/tex]
The graph of g(x) = x – 8 is a transformation of the graph of f(x) = x. Which of
the following describes the transformation?
(A) translation 8 units down
(B) translation 8 units up
(C) translation 8 units right
(D) translation 8 units left
What is the volume of a cube with side lengths that measure 8 cm?
Answer: 512 cm³
Explanation: Since the length, width, and height of a cube are all equal,
we can find the volume of a cube by multiplying side × side × side.
So we can find the volume of a cube using the formula v = s³.
In the cube in this problem, we have a side length of 8 cm.
So plugging into the formula, we have (8 cm)³
or (8 cm)(8 cm)(8 cm), which is 512 cm³.
So the volume of the cube is 512 cm³.
Answer:512[tex]cm^{3}[/tex]
Step-by-step explanation:
All sides are equal. Hence, volume =[tex]l^{3} = 8^{3} =512cm^{3}[/tex]
These girts stasts jogging from the same point around
acircular track and they complete one round in 24
Seconds 36 seconds and 48 seconds respectively,
After.
how much time will they meet atone point?
Answer:
2hrs 24mins
Step-by-step explanation:
Very simple the time they will meet again at the point will be the LCM of their various time taken to complete a cycle.
Ans LCM(24, 36, 48) = 144 mins
= 2hrs 24mins
Answer:
The answer is 2 hours and 24 minutes
Step-by-step explanation:
Hope you get this right:)
The double number line shows how many meters a dragonfly can fly in 1 second.
Answer: It's B
Step-by-step explanation:
The table that represents the double number line is (b)
How to determine the table of the number line?On the double number line, we have the following points
x: 0 1
y: 0 25
This means that as x increases by 1, y increases by 25.
So, we have:
x: 0 1 2 3 4
y: 0 25 50 75 100
The above is represented by the second table
Hence, the table that represents the double number line is (b)
Read more about number lines at:
https://brainly.com/question/4727909
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