The time until recharge for a battery in a laptop computer under common conditions is normally distributed with mean of 265 minutes and a standard deviation of 50 minutes.

a) What is the probability that a battery lasts more than four hours? 0.692 (Round the answer to 3 decimal places.)

b) What are the quartiles (the 25% and 75% values) of battery life?

25% value = 231 minutes (Round the answer to the nearest integer.)

75% value = 299 minutes (Round the answer to the nearest integer.)

c) What value of life in minutes is exceeded with 95% probability?

The valid conclusion that we can have from the given premises are:∃xQ(x) and ∃x¬P(x) → ∃xQ(x).∃xQ(x) can be proved by taking ∃x¬P(x) from the premises and then by applying resolution steps with the premise

∀x(P(x) ∨ Q(x)) we get ∃xQ(x).

Q2. (4300)8 is the octal expansion of the number that succeeds (4277)8. Here's how we can find the solution: In octal, the digits are 0, 1, 2, 3, 4, 5, 6, and 7. To find the next number after (4277)8, we just add 1 to the last digit. So, the next number would be (4278)8.

However, since the last digit is 7, we have to "carry over" to the next digit. We add 1 to the 8's place, but that carries over to the next digit, and so on. So, the next number after (4277)8 is (4300)8. Q3. (E1F)16 is the hexadecimal expansion of the number that precedes (E20)16.

Here's how we can find the solution:In hexadecimal, the digits are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, and F. To find the number that precedes (E20)16, we just subtract 1 from the last digit. Since the last digit is 0, we have to "borrow" from the digit to its left. That digit is E, which is one less than F.

So, we borrow from that digit and add 1 to the last digit. Thus, the number that precedes (E20)16 is (E1F)16.

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Answer:

25 ( A)

pls mark me as BRAINLIEST

stay at home stay safe

and keep rocking

Answer:

A

Step-by-step explanation:

The first ten primes are

2,3,5,7,11,13,17,19,23,27

so the number is

2*3*5*7*11*13*17*23*27

so

2*11 is 22, so 22 divides the number

2*3 is 6, so 6 divides the number

2 is there so 2 divides the number

So the only one is 25.

Answer:

b=4.8 or 48/10

Step-by-step explanation:

So first combine like terms

-5b+6+3b=3b-18

-2b+6=3b-18 (-3b from each side)

-5b+6=-18(-6 from each side)

-5b=-24(divide by -5)

b=4.8 or 48/10

Answer:

24 /5

Step-by-step explanation:

Easy algebra work

Outliers are any observations that fall more than 1.5 IQR below Q1 or more than 1.5 IQR above Q3.

Outliers:

While observing the data in the observations some of data may fall outside the general scope of the other observations. Such observations are called outliers.

Given,

An outlier is an observation which is less than IQR or greater than Q3 times IQR.

Here we need to find in Q1 and Q3 place variations.

When we use the IQR method of identifying outliers to set up a “fence” outside of Q1 and Q3.  Any values which fall outside of the identified  fence are considered outliers.

To build this fence we take 1.5 times the IQR and then subtract this value from Q1 and add this value to Q3.

Like,

IQR = (1.5 - Q1)

IQR = (1.5 + Q3)

This gives us the minimum and maximum fence posts that we compare each observation to.

Therefore, any observations that are more than 1.5 IQR below Q1 or more than 1.5 IQR above Q3 are considered outliers.

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Answer:3

Step-by-step explanation:

$5.30+$2.50=$7.80

$18.40-$7.80=$10.60

10.60÷5.30=2

2+ the on that was added on at the start =3

Answer:

\(H_{o}\): Larger proportion of news media = democrats

Ha : Large proportion of news media \(\neq\) democrats  

Step-by-step explanation:

The correct order of the steps of a hypothesis test is given following  

1. Determine the null and alternative hypothesis.

2. Select a sample and compute the z - score for the sample mean.

3. Determine the probability at which you will conclude that the sample outcome is very unlikely.

4. Make a decision about the unknown population.

These steps are performed in the given sequence to test a hypothesis.

Answer:

Surface Area would be 200² inches.

Step-by-step explanation:

SA=2(12*9)+2(9*2)+2(12*2)

SA=2(108)+2(18)+2(24)

SA=216+36+48

SA=200² in.

Assuming that other factors are held constant, the sample means difference Increases. (option C)

The null hypothesis and the alternative hypothesis are the two types of hypotheses for a test.

Step 1: The null hypothesis is based on the assumption that there is no difference between the true mean (µ) and the compare value (\(m_{o}\)). The alternative hypothesis is based on this assumption.

Step 2: Increasing the sample mean difference would probably make it more likely that the null hypothesis will be rejected, as long as other factors stay the same.

As a result, option C is the right one.

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(Complete question)

Assuming that other factors are held constant, which approach would tend to increase the likelihood of rejecting the null hypothesis?​

a. ​Decrease the sample mean difference.

b. ​Increase the sample variance.

c. ​Increase the sample mean difference.

d. ​Decrease the sample size.

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\(2x - 6 = 8\)

Add sides 6

\(2x - 6 + 6 = 8 + 6\)

\(2x = 14\)

Divide sides by 2

\( \frac{2x}{2} = \frac{14}{2} \\ \)

\(x = 7\)

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The correct answer is (( B )) .

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1. The linear function that models his distance from Washington, D.C. as a function of time, in hours, is:

d(t) = 109.5 - 55t.

2. The time it will take him to arrive at a rest stop that is 60.2 miles from Richmond, VA is of: 0.9 hours = 54 minutes.

The slope-intercept representation of a linear function is given by the equation shown as follows:

y = mx + b

The coefficients of the function and their meaning are described as follows:

In the context of this problem, these parameters are given as follows:

Hence the function is:

d(t) = 109.5 - 55t.

The time it will take him to arrive at a rest stop that is 60.2 miles from Richmond, VA is t when d(t) = 60.2 hence:

60.2 = 109.5 - 55t.

55t = 109.5 - 60.2

t = (109.5 - 60.2)/55

t = 0.9 hours = 54 minutes.

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The random variable n is defined as the smallest integer value of k for which the sum of the first k random variables in the sequence is greater than or equal to the constant c.

We have a sequence of independent uniform [0,1] random variables, denoted as x1, x2, x3, and so on. We also have a fixed constant c, which belongs to the interval [0,1].
Now, we want to define a random variable called n using these terms. The random variable n represents the smallest integer value k, such that the sum of the first k random variables in the sequence (x1 + x2 + ... + xk) is greater than or equal to the constant c.

To illustrate this, let's break down the steps involved in finding the value of n:
1. Start with k = 1.
2. Calculate the sum of the first k random variables: (x1 + x2 + ... + xk).
3. If the sum obtained in step 2 is greater than or equal to c, then stop and assign the value of n as k.
4. If the sum obtained in step 2 is less than c, increment k by 1 and repeat steps 2 and 3.
5. Continue repeating steps 2 to 4 until we find the smallest k such that the sum is greater than or equal to c. Assign this value of k as n.

So, in summary, the random variable n is defined as the smallest integer value of k for which the sum of the first k random variables in the sequence is greater than or equal to the constant c.
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Answer:

step 3 addition: 20 + 9 = 29

step 4 subtraction: 29 - 2 = 27

solution 27

Step-by-step explanation:

since there's no more multiplication or division, you add and subtract from left to right

Answer:

steps below

Step-by-step explanation:

will solve a and d here, to solve c and d is crazy.

for this equation we have 4 roots: p (3-2i), q(3+2i), r(1+i), s(1-i)

z⁴+az³ + bz² +cz +d = (z+p)(z+q)(z+r)(z+s) = 0

                                = z⁴ + (p+q+r+s)z³ + (pq+pr+ps+qr+qs+rs)z²

                                   +(pqr+pqs+prs+qrs)z + pqrs                                    

d = pqrs = (3-2i)(3+2i)(1+i)(1-i) = (9-4(-1))(1-1(-1) = 13*2 = 26

a = p+q+r+s = (3-2i)+(3+2i)+(1+i)+(1-i) = 8

b = pq+pr+ps+qr+qs+rs  .... calculate it , if you are interested

c = pqr+pqs+prs+qrs

True. In 2016, the percentage of the ageing population (55 years or older) in state prisons surpassed the percentage of people aged 18-24 for the first time.

This trend reflects the overall growth of the ageing population within the United States and is a result of various factors such as longer life expectancy, harsher sentencing laws, and an increase in older individuals being convicted of crimes.
As the ageing population in state prisons continues to grow, it poses several challenges for the correctional system. These challenges include providing appropriate healthcare and accommodations for older inmates and addressing the specific needs of this population, such as mobility assistance and specialized medical care.
In conclusion, the shift in the age demographics of state prisons has significant implications for the management and administration of correctional facilities. It is crucial to address the unique needs of the ageing population within these institutions and adapt policies and practices accordingly to ensure the well-being and fair treatment of all inmates, regardless of their age.

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the values are: sin(t) = 3/5, cos(t) = -4/5, csc(t) = 5/3, sec(t) = -5/4, cot(t) = -4/3

Given information: tan(t) = -3/4sin(t) > 0Since tan(t) = -3/4, let's consider a right-angled triangle ABC with opposite side BC = -3 and adjacent side AC = 4. Therefore, the hypotenuse AB can be obtained using the Pythagoras theorem asAB² = AC² + BC²AB² = 4² + (-3)²AB² = 16 + 9AB² = 25AB = √25 = 5Now we can find the required trigonometric ratios using the values of the sides of the triangle. The angles A and B are such that cos(t) = AC/AB = 4/5 and sin(t) = BC/AB = -3/5. Here we have sin(t) > 0 which implies t lies in the second quadrant. Calculations :We know that: cos(t) = AC/AB = 4/5tan(t) = BC/AC = -3/4sin(t) = BC/AB = -3/5csc(t) = AB/BC = -5/3sec(t) = AB/AC = 5/4cot(t) = AC/BC = -4/3Answer:sin(t) = BC/AB = -3/5cos(t) = AC/AB = 4/5csc(t) = AB/BC = -5/3sec(t) = AB/AC = 5/4cot(t) = AC/BC = -4/3
Given that tan(t) = -3/4 and sin(t) > 0, we can determine the values of the trigonometric functions:
1. sin(t) and cos(t):
Since tan(t) = sin(t)/cos(t), we can use Pythagorean triple 3-4-5 to find sin(t) and cos(t).
sin(t) = 3/5 (positive since sin(t) > 0)
cos(t) = -4/5 (negative because tan(t) is negative)
2. csc(t), sec(t), and cot(t) are the reciprocals of sin(t), cos(t), and tan(t) respectively.
csc(t) = 5/3
sec(t) = -5/4
cot(t) = -4/3

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Answer:

a=(0,0)

Step-by-step explanation:

i actually dont know but thnks for the points BTW

The lines that represent the approximate directrices of the ellipse are x = -6.6 and x = 10.6.

The lines that represent the approximate directrices of the ellipse are x = -6.6 and x = 10.6.

Given an ellipse with center (0,0) that has the equation

\($\frac{x^2}{225}+\frac{y^2}{400}=1$\),

find the directrices.

Solution: The standard equation of an ellipse with center (0,0) is

\($\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$\)

Where 'a' is the semi-major axis and 'b' is the semi-minor axis. Comparing this equation with

\($\frac{x^2}{225}+\frac{y^2}{400}=1$\)

gives us: a=15 and b=20.

The distance between the center and each focus is given by the relation:

\($c=\sqrt{a^2-b^2}$\)

Where 'c' is the distance between the center and each focus.

Substituting the values of 'a' and 'b' gives:

\($c=\sqrt{15^2-20^2}$ = $\sqrt{-175}$ = $i\sqrt{175}$\)

The directrices are on the major axis. The distance between the center and each directrix is

\($d=\frac{a^2}{c}$\).

Substituting the value of 'a' and 'c' gives:

\(d=\frac{15^2}{i\sqrt{175}}$ $=$ $\frac{225}{i\sqrt{175}}$\)

\($= \frac{15\sqrt{7}}{7}i$\)

Therefore, the equations of the directrices are \($x=-\frac{15\sqrt{7}}{7}$\) and \($x=\frac{15\sqrt{7}}{7}$\)

Round to the nearest tenth, the answer is -6.6 and 10.6 respectively. Thus, the lines that represent the approximate directrices of the ellipse are x = -6.6 and x = 10.6.

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Answer:

Step-by-step explanation:

Answer:

9% only a guess.May not be correct..

The point A after reflection over the line y = 1 becomes A' (-3,3).

Reflection is the transformation which produces a mirror image of an object. The mirror image can be either about any line.

In our question,

The object is a triangle ∠ABC and the line is y=1.

Point A before reflection (equation 1):

A = (-3,-1)

After reflection, the point is shifted along y axis and x remains constant.

Reflection about y=1 of point A:

A ⇔ A'

( x, y) ⇔ ( x, y+4)'

Put the values of x and y using equation 1.

(-3, -1) ⇔ ( -3, -1+4)'

(-3, -1) ⇔ (-3, -1) ⇔ ( -3, -1+4)'

Hence the point A will transform to the point A' (-3, 3) after reflecting about y=1.

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The length, l, of Olive’s picture frame is 18 - 1.25d, if Olive and Ryan have picture frames with the same perimeter.

It is defined as the area occupied by the rectangle in two-dimensional planner geometry.

The area of a rectangle can be calculated using the following formula:

Rectangle area = length x width

It is defined as two-dimensional geometry in which the angle between the adjacent sides is 90 degrees. It is a type of quadrilateral.

The perimeter of the rectangle = 2(length + width)

Let a by b the dimensions for Olive's picture

Let c by d the dimensions for Ryan's picture

b = 1.25d

The perimeter of the picture = 2(9 + 9) = 36

2(a + b) = 36

a + b = 18

a = 18 - b = 18 - 1.25d

Thus, the length, l, of Olive’s picture frame is 18 - 1.25d, if Olive and Ryan have picture frames with the same perimeter.

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The circumstance that the score is located 5 points above the mean a central value, relatively close to the mean is when the population standard deviation is much greater than 5.

Standard Deviation is a measure which shows how much variation (such as spread, dispersion, spread,) from the mean exists. The standard deviation indicates a “typical” deviation from the mean. It is a popular measure of variability because it returns to the original units of measure of the data set.

Here, we have

We have to find under what circumstances is a score that is 5 points above the mean considered a central value--meaning it is relatively close to the mean.

We concluded from the above statement that when the population standard deviation is much greater than 5.

Hence, when the population standard deviation is much greater than 5 then, the score that is 5 points above the mean is considered a central value.

Therefore, the correct option is D.

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Answer:

Complex sentence

Step-by-step explanation:

It begins with a dependent clause and is followed by an independent clause.

The approximate length of ab is 12.2 feet

A right triangle's hypotenuse (the side that faces the right angle) has a square length that, according to the Pythagorean theorem, is equal to the sum of the squares of the other two sides' lengths.

It can be written as c2 = a2 + b2 where c is the hypotenuse's length and a and b are the other two sides' lengths. Pythagoras, a Greek mathematician, is credited with discovering the theorem, which bears his name.

The Pythagorean theorem, which asserts that in a right triangle, the sum of the squares of the two shorter sides is equal to the square of the longest side, can be used to estimate the length of AB (the hypotenuse).

The distances along the room's 11-foot and 13-foot sides serve as the two shorter sides in this situation, while AB serves as the hypotenuse. AB is around the following length:

√(11^2 + 13^2 + 10^2) = √(146) = 12.2 feet

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The expression after simplification is 6x - 6.

An expression in math is a statement with a minimum of two numbers or variables and at least one math operation. This math operation can be addition, subtraction, multiplication, or division.

The given expression is -4 + 2x + 4x - 2.

\(\sf 2x+4x-4-2\)

\(\sf 6x-4-2\)

\(\bold{6x-6}\)

Hence, the simplification of the expression -4 + 2x + 4x - 2 is 6x - 6.

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Answer: John grew 4 and 3/4 inches in one year.

Step-by-step explanation:

Start by subtracting  64.375 (64 and 3/8) by 59.625 (59 and 5/8).

Type your numbers into a calculator (both ways can be put into your calculator, but decimals are easier for you to type)

Get your final answer of 4.75.

Hope this helps!

The integral ∫cosx/sin^2(x-2) dx= sin(2)ln|sin(x - 2)| - sin(2)cos(x) + sin(2) + cot(x - 2) + 2cot(x - 2)cos(2). Using substitution and partial fractions, we can follow these steps:

First, let's make a substitution by setting u = x - 2. This implies du = dx, and the integral becomes ∫cos(u + 2)/sin^2(u) du.

Next, we apply partial fractions to express sin^(-2)(u) as a sum of simpler fractions. We can write sin^(-2)(u) = A/(sin(u)) + B/(sin(u))^2, where A and B are constants.

Now, we need to find the values of A and B. By finding a common denominator and comparing the numerators, we obtain 1 = A.sin(u) + B.

To determine the values of A and B, we can use a trigonometric identity: sin(u + v) = sin(u).cos(v) + cos(u).sin(v). In our case, sin(u + 2) = sin(u).cos(2) + cos(u).sin(2).

By comparing the coefficients of sin(u) and cos(u) on both sides of the equation, we have A = sin(2) and B = -cos(2).

Substituting these values back into the partial fractions expression, we get sin^(-2)(u) = sin(2)/(sin(u)) - cos(2)/(sin(u))^2.

Now we can rewrite the integral as ∫cos(u + 2)(sin(2)/(sin(u)) - cos(2)/(sin(u))^2) du.

Integrating these terms separately, we have ∫sin(2)cos(u + 2)/sin(u) du - ∫cos(2)/sin^2(u) du.

Integrating the first term is straightforward, resulting in -sin(2)ln|sin(u)| - sin(2)cos(u + 2). For the second term, it simplifies to -cot(u) - 2cot(u)cos(2).

Finally, substituting back u = x - 2 and simplifying, we get the answer: -sin(2)ln|sin(x - 2)| - sin(2)cos(x) + sin(2) + cot(x - 2) + 2cot(x - 2)cos(2).

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Answer:

a=?

a=?

a=?

Step-by-step explanation: