First distribute through the set of parentheses.
When we distribute, we multiply the number outside
times each of the terms located inside the set.
So we have -2(x) + -2(4) or -2x - 8.
Now we have -2x - 8 + 5x + 10.
Combine like terms → your numbers and your "x" terms.
-2x + 5x is 3x and -8 + 10 is 2.
So we have 3x + 2.
3x + 2 cannot be simplified any further.
list 5 rational numbers between -4/7 and 1/2
Answer:
0, 1/10, 2/10, 3/10, 4/10, or
Step-by-step explanation:
-4/7 is about -0.57 in decimal form,
1/2 is 0.5
So we need to find 5 rational numbers between -0.58 and 0.5
A rational number is a number which can be expressed as a fraction.
0 can be expressed as 0/10
0.1 can be expressed as 1/10
0.2 can be expressed as 2/10
0.3 can be expressed as 3/10
0.4 can be expressed as 4/10
So just use those.
Find the acute angle between the diagonal of rectangle whose sides are 5cm and 7cm
Answer:
The arc tangent of angle a = (5/7)
angle a = 35.538 Degrees
Of course, we might be solving for angle b so,
angle b = 90 -35.538 Degrees = 54.462 Degrees
Step-by-step explanation:
Factor completely x3 + 9x2 + 27x+ 27
Answer:
(x + 3)^3
Step-by-step explanation:
I don't exactly know how to break this down into small steps. I can tell you that it is something like (x + a)^3
It turns out that a = 3 because all the signs in the given equation are +
Answer
(x + a) = (x + 3)^3
What is the best interpretation of V(4)=64
I assume the normal function is V(x)=y
So if we plug it in, we know that at x=4, the y value of the function is 64.
Consider the line 9x – 7y=-8.
What is the slope of a line perpendicular to this line?
What is the slope of a line parallel to this line?
Slope of a perpendicular line:
Х
?
Slope of a parallel line:
Answer:
Step-by-step explanation:
Before you can answer you have to solve the equation for y.
Y = 9/7 x+8/7
Parallel lines have the same slope so would also be 9/7
Perpendicular lines have opposite reciprocal slope so would be -7/9
Answer:
y=-9/7x-8/7
Step-by-step explanation:
9x – 7y=-8
-9x -9x
-7y=-9x-8
then divide all sides by -7
y=-9/7x-8/7
Suppose that an outbreak of cholera follows severe flooding in an isolated town of 3662 people. Initially (Day 0), 36 people are infected. Every day after, 34% of those still healthy fall ill.
How many people will be infected by the end of day 9?
Answer:
3576 infected people
Step-by-step explanation:
We have to apply the following formula, which tells us the number of healthy people:
A = p * (1 - r / 100) ^ t
where,
p = initial population,
r = rate of change per period (days)
t = number of periods (days)
Now, we know that the initial population is 3,662 but there are already a total of 36 infected, therefore:
3662 - 36 = 3626
that would be our p, now, we replace:
A = 3626 * (1 - 34/100) ^ 9
A = 86.16
Therefore, those infected would be:
3662 - 86.16 = 3575.84
This means that there are a total of 3576 infected people.
The price of a truck depreciates 15% in a year.
What will be its price in a year if the initial price is
currently 25.000$? -
Answer:
$1.66666667 (or just 1.6)
Step-by-step explanation:
$25.000 US dollars divided by 15 = $1.66666667 US dollars
Please help me thanks
Answer:
-75 and 75
Step-by-step explanation:
The two numbers chosen or plotted by them are:
-75 and 75
Step-by-step explanation:
It is given that Bernita and Derek each plot a number on a number line with the properties:
1. The two numbers they have plotted are unique or different.
2. Also there absolute value is same.
3. The sum of the absolute values of the numbers is 150.
We know that Absolute value of a positive number is a number itself and absolute value of a negative number is it's inverse.
So the two numbers that satisfy the above three properties are:
-75 and 75.
Fill in missing information to make the equality true:
(... +2a)2 = … +12ab2+4a2.
Answer:
I suppose it should be
6b² and (6b²)²
or
6b² and 36[tex]b^{4}[/tex]
Step-by-step explanation:
(a+b)² = a² + 2ab + b²
therefore
(6b²+2a)² = (6b²)² + 12ab² + 4a²
The missing information to make the equality true are 3b² and (3b²)². This can be obtained by using the algebraic identity (x+y)² =x² + 2xy + y².
Find the missing information:Let the missing information be p and p²
Then the given equation will be: (p+2a)² =p² + 12ab² + 4a²
The algebraic identities is (x+y)² =x² +2xy+y²
Comparing the given equation with the algebra formula we get
y=2a
2xy =12ab² ⇒2x(2a) = 12 ab² ⇒ x = 3b²
Therefore the given equation will be
(3b²+2a)² = (3b²)²+12ab²+4a²
Hence the missing information to make the equality true are 3b² and (3b²)².
Learn more about algebraic identities here:
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The city of Raleigh has 9,200 registered voters. There are two candidates for city council in an upcoming election: Brown and Feliz. The day before the election, a telephone poll of 200 randomly selected registered voters was conducted. 65 said they'd vote for Brown, 121 said they'd vote for Feliz, and 14 were undecided.
A. what is the population of this survey?B. What is the size of populationC. What is the size of the sampleD. Give the sample statistic for the proportion of voters surveyed who said they'd vote for Brown.E. Based on the sample, we might expect how many of th 9500 voters to vote for Brown
Answer:
A) The population of this survey is the registered voters in the city of Raleigh.
B) 9500
C) 200
D) 0.325
E) 3088
Step-by-step explanation:
A) The population of this survey is the registered voters in the city of Raleigh.
B) Population size can be defined as the total number of individuals in a population. Here the total number of individuals are the registered voters in the city. Therefore the size of the population is 9500.
c) Sample size is defined as the number of individual samples in a statistical test. Here the sample size is the 200 randomly selected registered voters. It is denoted as "n".
d) The sample statistic for the proportion of voters surveyed who said they'd vote for Brown would be:
p' = voters for brown / sample size
[tex] p' = \frac{65}{200} = 0.325 [/tex]
The sample statistic for the proportion of voters surveyed who said they'd vote for Brown is 0.325
E) The expected number of voters for Brown based on the sample:
0.325 * 9500 = 3087.5
Approximately 3088
The expected number of voters for Brown based on the sample might be 3088 voters.
what is a acute?? i dont really seem to get it
Answer:
an angle less than 90 degrees
Step-by-step explanation:
so like this angle /_
this is obtuse \_
this is right |_
What decimal part of one dollar is three quarters?
Answer:
0.75
Step-by-step explanation:
One dollar/four quarters-1.00
three quarters-0.75
two quarters-0.50
one quarter-0.25
Hope this helps
A hose can fill a swimming pool in 12 hours. Another hose needs 6 more hours to fill the pool than the two hoses combined. How long would it take the second hose to fill the pool?
Answer:
I believe it is 12, but I'm not sure.
Step-by-step explanation:
If there is 2 of the first hose, then it can fill the pool twice as fast, so thats 6 hours. (12 divided by 2 = 6).
If the second hose takes 6 hours more than that, then that would be 12 hours.(6+6=12)
Find the probability of the indicated event if P(E)equals0.25 and P(F)equals0.40. Find P(E or F) if P(E and F)equals0.05.
Answer:
[tex] P(E) =0.25, P(F) = 0.40, P(E \cap F) =0.05[/tex]
[tex] P(E \cup F)= P(E) +P(F) -P(E \cap F)[/tex]
And replacing we got:
[tex] P(E \cup F)=0.25 +0.40 -0.05 = 0.6[/tex]
Step-by-step explanation:
For this case we have the following probabilities given:
[tex] P(E) =0.25, P(F) = 0.40, P(E \cap F) =0.05[/tex]
And we want to find this probability:
[tex] P(E \cup F)[/tex]
And we can use the total probability rule given by:
[tex] P(E \cup F)= P(E) +P(F) -P(E \cap F)[/tex]
And replacing we got:
[tex] P(E \cup F)=0.25 +0.40 -0.05 = 0.6[/tex]
A classroom contains 13 students. A student committee of 3 (president, vice-president, and treasurer) must be selected. Harry Potter will serve only as president and only if either of his friends Ron Weasley or Hermione Granger serve as vice president; otherwise he leaves the group. The others (including Ron and Hermione) have no such restrictions. What is the probability that Ron or Hermione become the president of this group
Answer:
16.39%
Step-by-step explanation:
We have a total number of forms, which are as follows:
-Harry Potter will serve as President AND Ron will serve as Vice President AND anyone will serve as Treasurer:
p1 = 1P11 = 11! / (11-1)! = 11
-Harry Potter will serve as President AND Hermione will serve as Vice President AND anyone who serves as Treasurer is:
p2 = 1P11 = 11! / (11-1)! = 11
- Harry Potter will not serve as President means that no one except Harry Potter (12 remaining students) serve in three locations:
p3 = 12P3 = 12! / (12-3)! = 1320
in total it would be:
11 + 11 + 1320 = 1342
Now the favorable cases are:
- Hermione becomes the president of this group, which means that anyone except Hermione and Harry Potter (11 remaining students) serve in the remaining two places:
p1 = 11P2 = 11! / (11-2)! = 110
- Ron becoming the president of this group means that anyone except Ron and Harry Potter (remaining 8 students) serve in the remaining two places:
p2 = 11P2 = 11! / (11-2)! = 110
adding it would be: 110 + 110 = 220
now then the final probability is the favorable cases among the totals:
220/1342 = 0.1639
Which means that the probability is 16.39%
Answer:
33% probability
1/3
Step-by-step explanation:
100% Hermione though.
The distribution of grades in an introductory finance class is normally distributed, with an expected grade of 68. If the standard deviation of grades is 15, in what range would you expect 68.26 percent of the grades to fall? (Round answers to 2 decimal places, e.g. 15.25. Hint: Think in terms of what the expected highest and lowest scores would be for 68.26% of the students taking the exam.)
Answer:
The range that you would expect 68.26 percent of the grades to fall is between 53 and 83.
Step-by-step explanation:
Problems of normally distributed samples can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
In this question:
[tex]\mu = 68, \sigma = 15[/tex]
Middle 68.26% of the grades:
From the
50 - (68.26/2) = 15.87th percentile
To the
50 + (68.26/2) = 84.13rd percentile.
15.87th percentile:
X when Z has a pvalue of 0.1587. So X when Z = -1.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]-1 = \frac{X - 68}{15}[/tex]
[tex]X - 68 = -1*15[/tex]
[tex]X = 53[/tex]
84.13rd percentile:
X when Z has a pvalue of 0.8413. So X when Z = 1.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]1 = \frac{X - 68}{15}[/tex]
[tex]X - 68 = 1*15[/tex]
[tex]X = 83[/tex]
The range that you would expect 68.26 percent of the grades to fall is between 53 and 83.
5500 milliliters equal how many liters show work
Answer:
5.5 liters
Step-by-step explanation:
1 milliliter equals to 1/1000 part of a liter, which is 0.001 liter.
1 milliliter = 1 * 0.001 liter
So if you have 5500 milliliters that means it equals to 5500 times one milliliters and 1 milliliter = 1 * 0.001 liter, so for 5500 milliliters it is 5500 times as much
5500 * 0.001
5500 * 1/1000
5500 / 1000
5.5 liters
As long as you know this number 0.001 , then it is easily to calculate between liters and milliliters.
EXTRA:
To convert from amount A which is given in a certain quantity, to another quantity, you sometimes have to multiply and in other cases you need to divide by a certain factor. The factor defines the relationship between the quantities.
Suppose you have 1000 times 1 milliliter then you can find the amount in liters by multiplying that number of milliliters times 0.001.
It is easy to see that
1000 * 1/1000
1000 / 1000
= 1 liter, but that is easy, because I choose an easy number for the amount of milliliters to convert into liters. But it works exactly the same for any amount!
On her way to work, a commuter encounters four traffic signals. Assume that the distance between each of the four is sufficiently great that her probability of getting a green light at any intersection is independent of what happened at any previous intersection. The first two lights are green for forty seconds of each minute; the last two, for thirty seconds of each minute.What is the probability that the commuter has to stop at least three times?
Answer:
7 in 36 or 0.1944
Step-by-step explanation:
The probability of having to stop at least three times is the probability of getting 3 or 4 red lights.
For the first two lights, the probability of getting them red is 20 in 60 (1/3).
For the last two lights, the probability of getting them red is 30 in 60 (1/2).
The probability of all of them being red is:
[tex]P(R=4) = \frac{1}{3}*\frac{1}{3}*\frac{1}{2}*\frac{1}{2}\\P(R=4) =\frac{1}{36}=\frac{1}{36}[/tex]
The probability of three of them being red (3 red + 1 green) is:
[tex]P(R=3) = {(1-\frac{1}{3})*\frac{1}{3}*\frac{1}{2}}*\frac{1}{2}+(1-\frac{1}{3})*\frac{1}{3}*\frac{1}{2}*\frac{1}{2}+\frac{1}{3}*\frac{1}{3}*(1-\frac{1}{2})*\frac{1}{2}+\frac{1}{3}*\frac{1}{3}*(1-\frac{1}{2})*\frac{1}{2}\\P(R=3) =2*(\frac{2}{3}*\frac{1}{3}*\frac{1}{2}*\frac{1}{2})+2*(\frac{1}{3}*\frac{1}{3}*\frac{1}{2}*\frac{1}{2})\\ P(R=3) =\frac{4}{36}+\frac{2}{36}\\ P(R=3) =\frac{6}{36}[/tex]
Therefore, the probability of at least three red lights is:
[tex]P=\frac{1}{36}+\frac{6}{36}=\frac{7}{36}\\ P=0.1944[/tex]
The probability is 7 in 36 or 0.1944.
The probability that the commuter has to stop at least three times is at least 5.55%.
Since on her way to work, a commuter encounters four traffic signals, assuming that the distance between each of the four is sufficiently great that her probability of getting a green light at any intersection is independent of what happened at any previous intersection, and the first two lights are green for forty seconds of each minute; the last two, for thirty seconds of each minute, to determine what is the probability that the commuter has to stop at least three times the following calculation must be performed:
4/6 = 2/3 = 0.66666 0.5 x 0.5 x 0.333 = 0.083333 0.5 x 0.333 x 0.333 = 0.055555
Therefore, the probability that the commuter has to stop at least three times is at least 5.55%.
Learn more in https://brainly.com/question/23273737
An insurance company charges $800 annually for car insurance. The policy specifies that the company will pay $1000 for a minor accident and $5000 for a major accident. If the probability of a motorist having a minor accident during the year is 0.2 and of having a major accident is 0.05 (and these events are mutually exclusive), what is the insurance company's expected profit on the policy
Answer: the expected profit will be $755 annually.
Explanation: Expected Profit (EP) = Charges (income for the insurance company) - probability of minor accidents X amount payable for a minor accident - probability of mayor accidents X amount payable for a major accident.
800- 1000 (0.2) -5000 (0.05)= 800-20-25= 755
When we multiply a number by 3, we
sometimes/always/never v
get the same value as if we added 6
to that number.
Stuck? Watch a video or use a hint.
Report a problem
7 of 7 ..
nyone, anywhere
Imnact
Math by grace
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Answer:
? what's the question??????????????????
Solve for x.
x + 3 = Sqrt 4x+17
Answer:
Step-by-step explanation
How many fluid ounces are there in 3 pints and 4 fluid ounces?
Answer:
52 US fluid ounces
Step-by-step explanation:
6 fluid ounces
How many fluid ounces in a pint? There are 16 fluid ounces in a pint.
Answer: 52 fluid ounces
16. The population of a town is 41732. If there are 19569 male then find the
number of females in the towny
Answer:
The answer is, 22,163
Step-by-step explanation:
Take the total amount of people (41732) and subtract the amount of males (19569) to get your answer.
41732-19569=22,163
Please answer this correctly
Answer:
0
Step-by-step explanation:
Since the original: 6 is not either the largest or the smallest, it wouldn't affect the range
The only numbers that can affect the range when replaced are the greatest and the least values: 5 and 9
What is the sum of 7 3/5 and 2 4/5?
Step-by-step explanation:
[tex]7 \times \frac{3}{5} + 2 \times \frac{4}{5} \\ \frac{38}{5} + \frac{14}{5} \\ \frac{38 + 14}{5} \\ \frac{52}{5} \\ 10 \times \frac{2}{5} [/tex]
Answer:
Step-by-step explanation
7 [tex]\frac{3}{5}[/tex] + 2 [tex]\frac{4}{5}[/tex]
= 38/5 + 14/5
=52/5
An engineer wants to obtain a random sample of the output from a process manufacturing digital cameras. The process operates 16 hours per day, five days per week. She selects five cameras on Monday, Tuesday and Wednesday at random between 3pm and 4pm each day. This is an example of
Answer:
Non-Random Sample
Step-by-step explanation:
A sample in which each element has an equal chance of being selected is known as a random sample. Otherwise, a sample is said to be a non - random sample.
An engineer selects five cameras on Monday, Tuesday, and Wednesday at random between 3 pm and 4 pm each day. So, the cameras that are not in the process of production between 3 pm and 4 pm have no chances of being selected.
So, each camera does not have an equal chance of being selected.
This is an example of a non - random sample.
Suppose your marketing colleague used a known population mean and standard deviation to compute the standard error as 52.4 for samples of a particular size. You don't know the particular sample size but your colleague told you that the sample size is greater than 70. Your boss asks what the standard error would be if you quintuple (5x) the sample size. What is the standard error for the new sample size? Please round your answer to the nearest tenth.
Answer:
The new standard error is [tex]e_{new} = 23.4[/tex]
Step-by-step explanation:
From the question we are told that
The standard error is [tex]e = 52.4[/tex]
Generally the standard error is mathematically represented as
[tex]e = \frac{6}{\sqrt{n} }[/tex]
Where n is the sample size
for the original standard error we have
[tex]52.4 = \frac{6}{\sqrt{n} }[/tex]
Now sample size is quintuple
[tex]e_{new} = \frac{6}{\sqrt{5 * n} }[/tex]
[tex]but \ \ 52.4 = \frac{6}{\sqrt{n} }[/tex]
So [tex]e_{new} = \frac{52.4}{\sqrt{5} }[/tex]
[tex]e_{new} = 23.4[/tex]
Which is the vertex of x^2 + 10x = - 17?
Answer:
(-5, -8)
Step-by-step explanation:
Parabolas always have a lowest point (or a highest point, if the parabola is upside-down). This point, where the parabola changes direction, is called the "vertex". If the quadratic is written in the form y = a(x – h)2 + k, then the vertex is the point (h, k).
x^2 + 10x = - 17
x^2+10x+17=0
x^2+2*5x+25 - 8=0
(x+5)^2-8=0
h=-5, k= -8
vertex is (-5, -8)
When dots are printed from a laser printer to form letters, they must be close enough so that you do not see the individual dots of ink. To do this, the separation of the dots must be less than Raleigh's criterion of your eye at distances typical for reading Randomized Variables D 2.5 mm d-38 cm Take the pupil of the eye to be 2.5 mm in diameter and the distance from the paper to the eye as 38 cm. Find the minimum separation of two dots such that they cannot be resolved in cm. Assume a wavelength of 555 nm for visible light.
Answer:
The minimum separation is [tex]z = 1.0292 *10^{-4} \ m[/tex]
Step-by-step explanation:
From the question we are told that
The reading randomized variable are [tex]D= 2.5 \ mm[/tex] and [tex]d = 38 \ cm[/tex]
The diameter of the pupil is [tex]d = 2.5 \ mm = \frac{2.5}{1000} = 0.0025 \ m[/tex]
The distance from the paper is [tex]D = 38 \ cm = 0.38 \ m[/tex]
The wavelength is [tex]\lambda = 555 \ nm = 555 * 10 ^{-9} m[/tex]
Generally the Raleigh's equation for resolution is
[tex]\theta = 1.22 [\frac{\lambda}{D} ][/tex]
substituting values
[tex]\theta = 1.22 * \frac{555*10^{-9}}{0.0025}[/tex]
[tex]\theta = 2.7084*10^{-4} \ rad[/tex]
The minimum separation of two dots is mathematically represented as
[tex]z = \theta d[/tex]
substituting values
[tex]z = 2.7084*10^{-4} * 0.38[/tex]
[tex]z = 1.0292 *10^{-4} \ m[/tex]
Which of the following is the result of the operation below?
Answer:
The result of the operation is:
[tex]\left[\begin{array}{ccc|c}1&2&3&6\\0&-1&-2&-8\\0&2&1&5\end{array}\right][/tex]
Step-by-step explanation:
The matrix provided is:
[tex]\left[\begin{array}{ccc|c}1&2&3&6\\1&1&1&-2\\0&2&1&5\end{array}\right][/tex]
The operation to be performed is:
[tex]-R_{1}+R_{2}[/tex] → [tex]R_{2}[/tex]
The operation implies that, we need to replace the values in row 2 by the result of the expression ([tex]-R_{1}+R_{2}[/tex]).
Complete the operation as follows:
[tex]\left[\begin{array}{ccc|c}1&2&3&6\\1&1&1&-2\\0&2&1&5\end{array}\right]\rightarrow \ \left[\begin{array}{ccc|c}1&2&3&6\\(-1+1)&(-2+1)&(-3+1)&(-6-2)\\0&2&1&5\end{array}\right][/tex]
[tex]\rightarrow\ \left[\begin{array}{ccc|c}1&2&3&6\\0&-1&-2&-8\\0&2&1&5\end{array}\right][/tex]
Thus, the result of the operation is:
[tex]\left[\begin{array}{ccc|c}1&2&3&6\\0&-1&-2&-8\\0&2&1&5\end{array}\right][/tex]
Answer:
A
Step-by-step explanation:
edge 2021
