Answer: a. 0.4 × 0.15 = 0.060
Step-by-step explanation: Probability of the complement of an event is the one that is not part of the event.
For P(A):
P(A') = 1 - 0.6
P(A') = 0.4
For P(B):
P(B') = 1 - 0.85
P(B') = 0.15
To determine probability of A' and B':
P(A' and B') = P(A')*P(B')
P(A' and B') = 0.4*0.15
P(A' and B') = 0.06
Probability of the complement of the event is 0.060
Sugar, flour, and oats are stored in three drawers. The first drawer is labeled "oats", the second is labeled, "flour", the third is labeled "oats or flour". The label of each drawer does not correspond to what is stored inside of it. In which drawers is what stored?
Answer:
first = flour, second = oats, third = sugar
Step-by-step explanation:
Since the labels are "wrong", we know that the third drawer doesn't have oats or flour, therefore it has sugar. Since the first doesn't have oats, it must have flour and that makes the second drawer oats.
Answer:
first drawer has flour, second has oats, third is sugar
Step-by-step explanation:
on the first drawer, it is labelled oats, so it cannot be oats. on the second it cannot be flour, and on the third it cannot be oats or flour, which means it HAS to be sugar leaving oats and flour to be in either the first, or second.
i know it may sound a little confusing but please let me know if you dont understand
Find the particular solution to a differential equation whose general solution and initial condition are given. (C is the constant of integration.) x(t)
1. Which word best describes how you feel when working on a math assessment? ( point)
bored
excited
anxious
confident
Answer:
math is really a difficult subject for me. sometimes i feel confident when i get my answers correct, but sometimes i feel bored when i dnt get my answer. Sometimes i feel anxious , sometimes i feel excited to solve the problems.
Learn more:
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if given the diameter how can you find the radius
Answer:
Divide the diameter by 2.
Step-by-step explanation:
The radius of any circle is always the end to the center.
The diameter is a point of the circle to the opposite side.
This means that the diameter is twice the size of the radius, so to find the radius from the diameter, divide the diameter by 2.
Hope this helped!
Answer:
Divide the diameter by 2. d/2=r
Step-by-step explanation:
If a diameter has been given instead of a radius, you can find the radius by dividing the diameter by 2, for example.
If the diameter was 10, the radius would 10/2=5.
Hey! i've been working on these questions but I have no idea how to solve this one, could anybody help me? Thanks in advance!
Answer:
1) [tex]\boxed{p(x) = x^3-x^2+x-1}[/tex]
2) [tex]\boxed{p(x) = x^2+x-2}[/tex]
3) [tex]\boxed{p(x) =- 2x^2+2x+4}[/tex]
4) [tex]\boxed{p(x) = 2x^2+x-4}[/tex]
Step-by-step explanation:
Part (1)
[tex]p(x) = x^3-x^2+x-1[/tex]
As we have to determine it by ourselves, this is the polynomial having a degree of 3. p(x) with a degree of 3 means that the highest degree/exponent of x should be 3.
Part (2)
[tex]p(x) = x^2+x-2[/tex]
This can be the polynomial having the factor x-1 because if we put:
x - 1 = 0 => x = 1 in the above polynomial, it gives us a result of zero which shows us that (x-1) "is" a factor of the polynomial.
Part (3)
[tex]p(x) = -2x^2+2x+4[/tex]
This can be the polynomial for which p(0) = 4 and p(-1) = 0
Let's check:
[tex]p(0) =- 2(0)^2+2(0)+4\\p(0) = 0 + 0+4\\p(0) = 4[/tex]
[tex]p(-1)= -2(-1)^2+2(-1)+4\\p(-1) = -2(1)-2+4\\p(-1) = -2-2+4\\p(-1) = 0[/tex]
So, this is the required polynomial determined by "myself".
Part (4):
[tex]p(x) = 2x^2+x-4[/tex]
This is the polynomial having a remainder 6 when divided by (x-2)
Let's check:
Let x - 2 = 0 => x = 2
Putting in the above polynomial
[tex]p(x) = 2(2)^2+(2)-4\\Given \ that \ Remainder = 6\\6 = 2(4) +2-4\\6 = 8+2-4\\6 = 10-4\\6 = 6[/tex]
So, Proved that it has a remainder of 6 when divided by (x-2)
Zanna rounded these numbers.
7,494 7,540
7,452
First, she rounded them to the tens place. Then, she rounded them to
the hundreds place. Finally, she rounded them to the thousands place.
At which place were the rounded numbers all the same? What was the
rounded number?
Answer:
hundredths place, 7,500.
Step-by-step explanation:
They would be the same when they are all rounded all of the numbers to the the hundredths place. And that number would be 7,500.
When rounding its 5 or higher round up, if its 4 or lower round down.
HELP ME!
A standard I.Q. test produces normally distributed results with a mean of 104 and a standard deviation of 16 for 52,000 students in grade 12 in the state. Approximately how many of these students would have I.Q.s above 140?
Answer: approx 1196 students.
Step-by-step explanation:
As known for normal distribution 95.4% of all results are situating at +-2*s distance from the mean. (s is the standard deviation)
2s=16*2=32 . The mean +2s= 104+32=136 = approx 140.
95.4% from 52000 = 49608 students. The residual amont ( which is out of the border mean+-2s)= 52000-49608=2392
Because of the normal distribution simmetry the number of the students which has IQ 140 and more is twice less than 2392.
N=2392:2=1196
An investigator claims, with 95 percent confidence, that the interval between 10 and 16 miles includes the mean commute distance for all California commuters. To have 95 percent confidence signifies that
Answer:
Hello the options to your question is missing below are the options
A) if sample means were obtained for a long series of samples, approximately 95 percent of all sample means would be between 10 and 16 miles
B.the unknown population mean is definitely between 10 and 16 miles
C.if these intervals were constructed for a long series of samples, approximately 95 percent would include the unknown mean commute distance for all Californians
D.the unknown population mean is between 10 and 16 miles with probability .95
Answer : if these intervals were constructed for a long series of samples, approximately 95 percent would include the unknown mean commute distance for all Californians ( c )
Step-by-step explanation:
95% confidence
interval = 10 to 16 miles
To have 95% confidence signifies that if these intervals were constructed for a long series of samples, approximately 95 percent would include the unknown mean commute distance for all Californians
confidence interval covers a range of samples/values in the interval and the higher the % of the confidence interval the more precise the interval is,
This year Alex’s age is 1/6 of his dads. Four years later, Alex’s age is 1/4 of his dads. How old is Alex and his dad this year?
Answer:
This year:
dads: 36 years
Alex: 6 years
Step-by-step explanation:
a = d/6
a+4 = (d+4)/4
a = Alex´s actual age
d = actual age of the dad
d/6 + 4 = (d+4)/4
4{(d/6) + 4} = d+4
4*d/6 + 4*4 = d+4
4d/6 + 16 = d + 4
4d/6 = d + 4 - 16
4d = (d-12)*6
4d = 6*d +6*-12
4d = 6d - 72
4d - 6d = -72
-2d = -72
d = -72/-2
d = 36
a = d/6
a = 36/6
a = 6
probe:
a+4 = (d+4)/4
6 + 4 = (36+4)/4
10 = 40/4
If A = {2,4,6,8,10) and B = [4,8,10), then which of the following statements is false?
A n B = B
B C B
A C B
A C B because all elements of A are not found in B
33 points
1. A sandwich vendor offers a choice of hamburger, chicken, or fish on
either a plain or sesame seed bun. How many different types of
sandwiches are there to choose from?
*
4
6
12
3
Answer:
6 sandwiches to choose from because
3×2 = 6
A box contains 40 identical discs which are either red or white if probably picking a red disc is 1/4. Calculate the number of;
1. White disc.
2. red disc that should be added such that the probability of picking a red disc will be 1/4
If X = 12 units, Y = 4 units, and h = 10 units, then what is the area of the trapezoid shown above?
Answer:
52 units^2
Step-by-step explanation:
It's unclear what the leg lengths and the width are. I must assume that the lengths are 12 units and 14 units and that the width of the trapezoid is 4 units. You were given an illustration for this problem and should have shared it or described the trapezoid in words. Please do this if the answer given below does not agree with any of your answer choices.
If the lengths are 12 units and 14 units and that the width of the trapezoid is 4 units, then the area is
12 units + 14 units
A = ---------------------------- * 4 units = 52 units^2
2
Find the probability of winning a lottery with the following rule. Select the winning numbers from 1, 2, . . . ,34 . (In any order. No repeats.)
Complete Question
Find the probability of winning a lottery with the following rule. Select the six winning numbers from 1, 2, . . . ,34 . (In any order. No repeats.)
Answer:
The probability is [tex]P(winning ) = 7.435 *10^{-7}[/tex]
Step-by-step explanation:
From the question we are told that
The total winning numbers n = 34
The total number to select is r = 6
The total outcome of lottery is mathematically represented as
[tex]t_{outcome}) = \left n } \atop {}} \right. C_r[/tex]
[tex]t_{outcome}) = \frac{n! }{(n-r )! r!}[/tex]
substituting values
[tex]t_{outcome}) = \frac{ 34 ! }{(34 - 6 )! 6!}[/tex]
[tex]t_{outcome}) = \frac{ 34 ! }{28 ! 6!}[/tex]
[tex]t_{outcome}) =1344904[/tex]
The number of desired outcome is
[tex]t_{desired} = 1[/tex]
this is because the desired outcome is choosing the six winning number
The probability of winning a lottery is mathematically represented as
[tex]P(winning ) = \frac{t_{desired}}{t_{outcome}}[/tex]
substituting values
[tex]P(winning ) = \frac{1}{1344904 }[/tex]
[tex]P(winning ) = 7.435 *10^{-7}[/tex]
How do you evaluate this?
[tex]_6C_3=\dfrac{6!}{3!3!}=\dfrac{4\cdot5\cdot6}{2\cdot3}=20[/tex]
How do you write 30,8608
Answer:
it should be 308,608. the comma is after every three in this scenario.
Step-by-step explanation:
What is the opposite of the opposite of negative 52?
Answer:
-52
Step-by-step explanation:
Think of it this way. Opposite means to take the negation. So we are taking the negation of the negation of negative 52. This means mathematically:
- ( - ( -52 ) ) == -52
Cheers.
Match the base to the corresponding height.
Base (b)
Height (h)
b
h
h
b
The base 1 is matched with height 2, base 2 is matched with height 3 and base 3 is matched with height 1. The base to the corresponding height is matched in the attached figure.
What is a triangle?Triangle is the closed shaped polygon which has 3 sides and 3 interior angles. The height of the triangle is the dimension of the elevation from the opposite peak to the length of the base.
Thus, the base 1 is matched with height 2, base 2 is matched with height 3 and base 3 is matched with height 1. The base to the corresponding height is matched in the attached figure.
In the given figure, three triangles is shown with base and height. Here,
The base 1 is matched with height 2, as the height shown in figure 2 is the dimension of the elevation from the opposite peak to the length of the base 1.Similarly, base 2 is matched with height 3.Base 3 is matched with height 1.
Thus, the base 1 is matched with height 2, base 2 is matched with height 3 and base 3 is matched with height 1. The base to the corresponding height is matched in the attached figure.
Learn more about the base and height of the triangle here;
https://brainly.com/question/26043588
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Let REPEAT TM = { | M is a TM, and for all s ∈ L(M), s = uv where u = v }. Show that REPEATTM is undecidable. Do not use Rice’s Theorem.
Answer:
Step-by-step explanation:
Let REPEAT [tex]_{TM[/tex]= { | M is a TM, and for all s ∈ L(M), s = uv where u = v }
To prove that REPEAT [tex]_{TM[/tex] is undecidable.
Let REPEAT [tex]_{TM[/tex] {| M is a TM that does not accept M}
Then, we form a TM u for L by applying TM v as a subroutine.
Assume Repeat is decidable
Let M be the algorithm that TM which decides the REPEATU = on input "s" simulate the M
Accept; if M ever enters the accept state
Reject; if M ever enters the reject state
U does not decide the REPEAT as it may loop over s
so REPEAT is undecidable
Karim has two investments, one in Company A, and another in Company B. Karim purchased 3,000 shares in company A at $2.65 per share. Since purchasing the shares, the price per share increased to $2.95 per share, after which point Karim decided to sell, realizing a profit. At the same time, Karim purchased 2,000 shares in Company B at $1.55 per share. Since purchasing the shares, the share price fell to $1.30 per share, after which Karim decided to sell the shares, suffering a loss. Karim is required to pay tax at a rate of 28% on the combined profit from both investments. Calculate how much tax Karim must pay.
Answer:
A:$2478
B:$728
Total:$3206
Step-by-step explanation:
2.95x3000=8850
1.30x2000=2600
8850x0.28=2478
2600x0.28=728
2478+728=3206
An economist is interested in studying the spending habits of consumers in a particular region. The population standard deviation is known to be $1,000. A random sample of 50 individuals resulted in an average expense of $15,000. What is the width of the 99% confidence interval for the mean of expense? a. 364.28 b. 728.55 c. 329.00 d. 657.99
Answer:
The width is [tex]w = \$ 729.7[/tex]
Step-by-step explanation:
From the question we are told that
The population standard deviation is [tex]\sigma = \% 1,000[/tex]
The sample size is [tex]n = 50[/tex]
The sample mean is [tex]\= x = \$ 15,000[/tex]
Given that the confidence level is 99% then the level of significance is mathematically represented as
[tex]\alpha = 100 - 99[/tex]
=> [tex]\alpha = 1\%[/tex]
=> [tex]\alpha = 0.01[/tex]
Next we obtain the critical value of [tex]\frac{\alpha }{2}[/tex] from the normal distribution table, the value is
[tex]Z_{\frac{\alpha }{2} } = Z_{\frac{0.01 }{2} } = 2.58[/tex]
Generally margin of error is mathematically represented as
[tex]E = Z_{\frac{\alpha }{2} * \frac{\sigma }{\sqrt{n} }[/tex]
substituting values
[tex]E = 2.58 * \frac{1000 }{\sqrt{50} }[/tex]
[tex]E = 2.58 * \frac{1000 }{\sqrt{50} }[/tex]
[tex]E = 364.9[/tex]
The width of the 99% confidence interval is mathematically evaluated as
[tex]w = 2 * E[/tex]
substituting values
[tex]w = 2 * 364.9[/tex]
[tex]w = \$ 729.7[/tex]
PLZ HELPPPPPP. 25 POINTS.
A store sells books for $12 each. In the proportional relationship between x, the number of books purchased, and y, the cost per books in dollars" to "y, the total cost of the books in dollars, the constant of proportionality is 12. Which equation shows the relationship between x and y?
A. y=12/x
B. y=12x
C. y=12+x
D. y=12−x
Answer:
b
Step-by-step explanation:
because its right dummy
The graphs below have the same shape. Complete the equation of the blue
graph. Enter exponents using the caret (; for example, enter x2 as x^2.
This is equivalent to x^2+8x+13
======================================================
Explanation:
The vertex of f is at (0,0). The vertex of g is at (-4, -3). The vertex has moved 4 units to the left and 3 units down.
To shift to the left, we replace x with x+4. So we have f(x) = x^2 turn into f(x+4) = (x+4)^2 so far.
Then we subtract off 3 to move everything 3 units down. We have
g(x) = (x+4)^2-3
---------------------
Optionally we can expand things out like so
g(x) = (x+4)^2-3
g(x) = (x+4)(x+4)-3
g(x) = x(x+4)+4(x+4)-3
g(x) = x^2+4x+4x+16-3
g(x) = x^2+8x+13
Showing that (x+4)^2-3 is equivalent to x^2+8x+13
Lauren is a college sophomore majoring in business. This semester Lauren is taking courses in accounting, economics, management information systems, public speaking, and statistics. The sizes of these classes are, respectively, 375, 35, 45, 25, and 60.Required:Find the mean and the median of the class sizes. What is a better measure of Lauren's "typical class size"—the mean or the median?
Answer:
Mean = 108
Median = 45
The better measure of Lauren's "typical class size" is the Mean
Step-by-step explanation:
1. Calculating mean and median.
The mean is an important measure of central tendency, and it is the average of the measurement of a given set of data. It is calculated as follows:
[tex]Mean\ (\overline {X}) &= \frac{\sum X}{N}[/tex]
where X = individual data sets
N = total number of data
[tex]Mean= \frac{375\; +\ 35\ +\ 45\ +\ 25\ +\ 60}{5} \\=\frac{540}{5} \\= 108[/tex]
The Median divides the measurements into two equal parts, and in order to calculate the median, the distribution has to first be arranged in ascending or descending order. Arranging this series in descending order:
375, 60, 45, 35, 25
The formula for calculating median is given by:
[tex]M_{d} = \frac{N\ +\ 1}{2} th\ data\\\\=\frac{5\ +\ 1}{2}th\ data\\\\=\frac{6}{2} th\ data\\= 3rd\ data\\M_{d} = 45[/tex]
from the list or arranged data in descending order (375, 60, 45, 35, 25), the third data is 45.
Therefore, Median = 45
2. The better measure of typical class size is Mean because the mean depends on all the values of the data sets, whereas the median does not. When there are extreme values (outliers) the effect on the median is very small, whereas it is effectively captured by the mean.
2/3a - 1/6 =1/3 please help me
Answer:
[tex]a = \frac{3}{4}[/tex]
Step-by-step explanation:
Let's convert everything to sixths to make it easier to work with.
[tex]\frac{4}{6}a - \frac{1}{6} = \frac{2}{6}[/tex]
Add 1/6 to both sides:
[tex]\frac{4}{6}a = \frac{3}{6}[/tex].
Dividing both sides by 4/6:
[tex]a = \frac{3}{6} \div \frac{4}{6}\\\\a = \frac{3}{6} \cdot \frac{6}{4}\\\\a = \frac{18}{24}\\\\a = \frac{3}{4}[/tex]
Hope this helped!
please help !! Solve –2.5x ≤ 25
Answer:
x ≥-10
Step-by-step explanation:
–2.5x ≤ 25
Divide each side by -2.5, remembering to flip the inequality
–2.5x/-2.5 ≥ 25 /-2.5
x ≥-10
Answer:
[tex]x\leq -10[/tex]
Step-by-step explanation:
[tex]-2.5x\leq 25[/tex]-----> Multiply by -1:
[tex]2.5x\geq -25[/tex]-----> Divide by 2.5:
[tex]x\geq -10[/tex]
Hope this helps!
A sandman earns a commission of 26%. One week he had sales of $24400. Find the commission for the week.
Answer:
6344
Step-by-step explanation:
Find 26% of 24400
24400 * 26%
24400 * .26
6344
I need help please help meee I don’t understand
Answer:
204
Step-by-step explanation:
To simplify the shape, you can do multiple things. I've opted to shave down both prongs to take it from a 'T' shape to a rectangular prism.
For height of the prongs, take 4 from 6.
6 - 4 = 2
Divide by 2 as there are 2 prongs.
2 / 2 = 1
Remember L * W * H
6 * 3 * 1 = 18
Remember that there are two prongs!
3 + 4 = 7
6 * 7 * 4 = 168
168 + 2(18) = 204
22 tons is equivalent to ______ kilograms.
Answer:
20000 kg
Step-by-step explanation:
Recall that 1 kg = 2.2 lb approximately. Then:
22 tons 1 kg 2000 lb
------------ * ------------ * -------------- = 20000 kg
1 2.2 lb 1 ton
Find the polynomial for the area.
The area is
Answer: ¹/₂( x² - 10y² + 10xy - xy )
Step-by-step explanation:
From the diagram area of the triangle = ¹/₂ ˣ base ˣ height
where the base = x + 10y and the height = x - y
Therefore putting these into the formula above
Area = ¹/₂ [( x + 10y )( x -y )]
= ¹/₂( x² - xy + 10xy - 10y²)units²
= ¹/₂( x² - 10y² + 10xy - xy )
