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Answer:

31.7

Step-by-step explanation:

Just subtract

Answer:

74 words per minute

Step-by-step explanation:

If the tiles

3478 words ———————-> 47 mins

?    Words ————————> 1 min

cross multiply

?=74

Answer:
Josh's percentage profit would be 52.5%.

Step-by-step explanation:

Total cost:

Josh buys 120 books for £4 each, so the total cost is:

Total cost = 120 books * £4/book = £480

Total revenue:

Josh sells half of the books for £5 each, which means he sells (1/2) * 120 = 60 books at £5 each. So, the revenue from this sale is:

Revenue = 60 books * £5/book = £300

Josh also sells 40% of the books for £7 each, which means he sells 0.4 * 120 = 48 books at £7 each. So, the revenue from this sale is:

Revenue = 48 books * £7/book = £336

The remaining books that Josh sells at £8 each are (1 - 0.5 - 0.4) = 0.1 or 10% of the total books. Therefore, the revenue from this sale is:

Revenue = 10% * 120 books * £8/book = £96

Total revenue = £300 + £336 + £96 = £732

Profit:

Profit = Total revenue - Total cost = £732 - £480 = £252

Percentage profit:

Percentage profit = (Profit / Total cost) * 100%

Percentage profit = (£252 / £480) * 100% ≈ 52.5%

Therefore, Josh's percentage profit is approximately 52.5%.

Y = (1/6)*e^5t  is  differential equation .

What exactly does differential equation mean?

An equation that connects one or more unknown functions and their derivatives is known as a differential equation in mathematics.  

                                     Applications typically use functions to describe physical quantities, derivatives to indicate the rates at which those quantities change, and differential equations to define a relationship between the two.

y′′−9y′+26y=e^(5t)

The characteristice equation of the differential equation is : r^2 -9r +26 =0

On solving we get the values of r=4.5 + 2.34i (z1) ,  4.5 - 2.4i(z2)--- (complex roots)

homogeneous solution is: yh = c1e^z1t + c2e^z2t

Plug  Y = Ae^5t in the ODE:

=   25Ae^5t -9*5Ae^5t +26Ae^5t =e^(5t)

25A -45A +26A =1 ;  6A = 1; A =1/6

Y = c1e^z1t + c2e^z2t  is a general solution but we wnata particular solution

So, simply Y = (1/6)*e^5t

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Answer:

f or 2 meters is the correct answer

Step-by-step explanation:

Answer:

2.8

Step-by-step explanation:

2.8*2.8=7.84. 2.8 is the closest to the length of one side of the square.

Answer:

If two row interchanges are made in succession, then the determinant of the new matrix is equal to the determinant of the original matrix. ( A )

Step-by-step explanation:

A and B been n*n matrices the true statement would be ;  If two row interchanges are made in succession, then the determinant of the new matrix is equal to the determinant of the original matrix.

Although other options can be true for some matrices but they are not always true for every kind matrices but option A is always true

The option is C) RNA is single stranded

Answer:

c

Step-by-step explanation:

The equation for the plane through P0(8,1,−4) perpendicular to the following line is x + 4y + 5z - 8 = 0

The slope of the perpendicular line should be a/b, and if one line is perpendicular to this line, the product of slopes should be -1. The equation of a line perpendicular to a given line ax + by + c = 0 is bx - ay + = 0, where is a constant.

The given parameters are

x=8−t​, y=1−2t​, z=3t​,

P0(- 9, 6, - 5).

Direction vector of line is < -1, 4, 5>,

This vector is normal vector for unknown plane.

So, equation of plane: -1(x - (-9)) + 4(y - 6) + 5(z - (-5)) = 0; - x - 9 + 4y - 24 + 5z + 25 = 0;

In conclusion the equation is given as  -x + 4y + 5z - 8 = 0

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Answer:

35

Step-by-step explanation:

1.8 * 15 = 27 total earning

27-20 = 7 profit

$ 7 profit  / $20 cost  = 0.35

0.35*100 = 35%

Answer:

0

Step-by-step explanation:

Answer: 5n+14-11n-2

Step-by-step explanation:

The 95% confidence interval for the population mean is approximately $4358.46 to $4441.54. Increasing the sample size is the best alternative to reduce the width of the confidence interval.

a) To make a 95% confidence interval for the population mean, we can use the formula:

Confidence interval = sample mean ± (critical value * standard error)

First, let's calculate the standard error, which is the standard deviation of the sample divided by the square root of the sample size:

Standard error = $900 / √(1800)

≈ $21.21

For a sample size of 1800, the critical value can be found using a t-distribution or approximated using a normal distribution. Since the sample size is large (n > 30), we can use the normal distribution approximation. The critical value for a 95% confidence level is approximately 1.96.

Now, we can calculate the confidence interval:

Confidence interval = $4400 ± (1.96 * $21.21)

Confidence interval ≈ $4400 ± $41.54

b) If the confidence interval obtained in part a is too wide and we want to reduce its width, there are several alternatives to consider:

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Answer:

Your answer is 8x+607

Step-by-step explanation:

The missing words in the sentence are "vanishing points" and "depth." "Vanishing points" are points where all receding parallel lines converge. These points can be on or off a picture plane. When they are off a picture plane, there is less "depth."

Mark is writing an essay on the primary concepts of perspective drawing. Here are the completed sentences: - Vanishing points are points where all receding parallel lines converge. - These points can be on or off a picture plane. - When they are off a picture plane, there is less control over their placement and accuracy in the drawing.

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Answer:

should be 8

Step-by-step explanation:

A garrison has provision for 30 days for certain men. if 2/3 of them do not attend the mess, then the food will last for 45 days. So, the correct option is (a).

Given that the provision for certain men in the garrison is for 30 days. Also, given that 2/3 of them do not attend the mess, then we have to find the number of days the food will last.

The food will last longer if the number of people attending the mess is less because the same amount of food will have to be shared between fewer people. Therefore, the food will last for more than 30 days.

Let the total number of men be x, then the number of men attending the mess is (1/3)x

And the number of men not attending the mess is (2/3)x.

Therefore, the food will last for (30 × x) / (2/3)x = 45 days

Hence, the answer of the question is 46 days.

Your question is incomplete but most probably your full question was:

A garrison has provision for 30 days for certain men. if 2/3 of them do not attend the mess, then the food will last for?

(a) 45 days

(b) 65 days

(c) 50 days

(d) none of above

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Answer: 165

Step-by-step explanation:

55 x 3 = 165

a) The graph of the object's velocity versus time can be seen below. The x-axis is labelled "time (s)" and the y-axis is labelled "velocity (m/s)". The important points on the graph are when the velocity is 0 (t = 0, 3, and 10 s) and the maximum velocity (t = 5 s).
b) The object's change in velocity over the first 3 seconds of its motion is 20 m/s.
c) The object is instantaneously at rest at t = 0, 3, and 10 s.
d) The object's total displacement over the first 10 seconds of its motion is 100 m.

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Answer:

a) 0

b) y = 2

Step-by-step explanation:

Try working out the slope:

m = y2-y1/x2-x1

plug in the values

m = 2-2/-8-4

m = 0

The slope is 0, meaning that it is a horizontal line

we now know that for every x value, the y value will be 2 since it is a horizontal line, meaning the equation of the line is y=2.

We can also get y=2 from the equation y=mx+b

b is the y-intercept (2), since m(slope) is zero, the equation will be reduced to y = +b or y = 2

The p-value, which measures the strength of evidence against the null hypothesis, is extremely small. This indicates that the observed percentage of uninsured patients (35 out of 140) is significantly lower than the expected percentage of 32%.

Given that 32% of emergency room visitors are uninsured, we can calculate the expected number of uninsured patients in a sample of 140 patients:

Expected number of uninsured patients = (32% / 100%) * 140 = 0.32 * 140 = 44.8

Now, let's calculate the test statistic, which is the z-score, using the formula:

z = (observed value - expected value) / standard deviation

where p is the expected percentage of uninsured patients (32% or 0.32) and n is the sample size (140).

standard deviation = √((0.32 * (1 - 0.32)) / 140) = √(0.21824 / 140) = 0.03753

Now we can calculate the z-score:

z = (35 - 44.8) / 0.03753 = -9.8 / 0.03753 = -261.4

Since the z-score is very large (far into the tail of the distribution), the p-value will be extremely small, approaching zero. However, we can't directly find the exact p-value from the z-score table or calculator because it is beyond the limit of standard tables. We can approximate it as essentially zero.

Therefore, the p-value of the test statistic is approximately zero (0.0000) when rounded to four decimal places.

Therefore, based on this data, there is strong evidence to support the claim that the percentage of uninsured patients is below the expected percentage.

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Step-by-step explanation:

the general equation of a parabola is

y = a(x – h)² + k.

(h, k) is the vertex of the parabola.

comparing it to

y = 3(x + 4)² - 2

we see that (h, k) = (-4, -2).

the student made a sign mistake. it is "- h" in the squared factor. so, "+4" indicates "-4" as "h".

but the student simply used "+4".

Answer:  A x=11

Step-by-step explanation:

We are assuming the lines are parallel so the angles would be equal from transverse line rules.

7x + 13 = 90                    >Subtract 13 from both sides

7x = 77                            >divide both sides by 7

x = 11                              

Step-by-step explanation:

a)  Given:  t1/2 = ln(0.5) / k       ( this is NATURAL ln...NOT base 10 LOG)

     then  k =   ln(0.5) / ( t1/2)      and t 1/2 is given as 1620 yrs

              k = ln(0.5) / 1620 = - 4.279  x 10^-4  

b)   New = n e^(kt)      n = 20 g   t = 5000   k (given above)

  New = 20 e^(-4.279 x 10^-4 * 5000)  = 2.23 g left

c)   1/4  =  e^(kt)

       1/4 = e^( 4.279x 10^-4  * t)    solve for t years

         t = 3240 years   <==== which makes sense    

                                             say you started with  10 g

                                               after one half life you would have 5

                                                  one more half life you would have 2.5

                                                      so two half lives and you have 1/4 as much

                                                            two half lives = 1620 x 2 = 3240 years      

Answer:

Step-by-step explanation:

(a) To find the probability that it is raining when you arrive in Oneirabad on a random day, we need to use the law of total probability.

Let A be the event that it is raining, and B be the event that it is the Wet season.

P(A) = P(A|B)P(B) + P(A|B')P(B')

Given that the Wet season lasts for 1/3 of the year, we have P(B) = 1/3. The probability that it is raining during the Wet season is 3/4, so P(A|B) = 3/4.

The Dry season lasts for 2/3 of the year, so P(B') = 2/3. The probability that it is raining during the Dry season is 1/6, so P(A|B') = 1/6.

Now we can calculate the probability that it is raining when you arrive:

P(A) = (3/4)(1/3) + (1/6)(2/3)

= 1/4 + 1/9

= 9/36 + 4/36

= 13/36

Therefore, the probability that it is raining when you arrive in Oneirabad on a random day is 13/36.

(b) Given that it is raining when you arrive, we can use Bayes' theorem to calculate the probability that your visit is during the Wet season.

Let C be the event that your visit is during the Wet season.

P(C|A) = (P(A|C)P(C)) / P(A)

We already know that P(A) = 13/36. The probability that it is raining during the Wet season is 3/4, so P(A|C) = 3/4. The Wet season lasts for 1/3 of the year, so P(C) = 1/3.

Now we can calculate the probability that your visit is during the Wet season:

P(C|A) = (3/4)(1/3) / (13/36)

= 1/4 / (13/36)

= 9/52

Therefore, given that it is raining when you arrive, the probability that your visit is during the Wet season is 9/52.

(c) Given that it is raining when you arrive, the probability that it will be raining when you return to Oneirabad in a year's time depends on the season. If you arrived during the Wet season, the probability of rain will be different from if you arrived during the Dry season.

Let D be the event that it is raining when you return.

If you arrived during the Wet season, the probability of rain when you return is the same as the probability of rain during the Wet season, which is 3/4.

If you arrived during the Dry season, the probability of rain when you return is the same as the probability of rain during the Dry season, which is 1/6.

Since the season you arrived in is independent of the weather when you return, we need to consider the probabilities based on the season you arrived.

Let C' be the event that your visit is during the Dry season.

P(D) = P(D|C)P(C) + P(D|C')P(C')

Since P(C) = 1/3 and P(C') = 2/3, we can calculate:

P(D) = (3/4)(1/3) + (1/6)(2/3)

= 1/4 + 1/9

= 9/36 + 4/36

= 13/36

Therefore, the probability that it will be raining when you return to Oneirabad in a year's time, given that it is raining when you arrive, is 13/36.

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5)  The derivative of f(x) = e^(2x-1) at x = ln 2 is f'(ln 2) = 8/e.

6)) This is the equation of the tangent to the graph of y = sin(x/2) when x = 2π/3.

To find the derivative of the function f(x) = e^(2x-1), we can use the chain rule. Let's denote g(x) = 2x - 1, and the derivative of e^x is e^x.

Using the chain rule, we have:

f'(x) = (e^(2x-1)) * g'(x)

To find g'(x), we differentiate g(x) = 2x - 1 with respect to x:

g'(x) = 2

Now, substitute the values into the derivative formula:

f'(x) = (e^(2x-1)) * 2

Next, we need to find f'(ln 2), which means we need to evaluate the derivative at x = ln 2:

f'(ln 2) = (e^(2*ln 2-1)) * 2

Recall that e^ln a = a, so we can simplify the expression further:

f'(ln 2) = (2^2 * e^(-1)) * 2

= (4 * 1/e) * 2

= 8/e

Therefore, the derivative of f(x) = e^(2x-1) at x = ln 2 is f'(ln 2) = 8/e.

Moving on to question 6:

To determine the equation of the tangent to the graph of y = sin(x/2) when x = 2π/3, we need to find the slope of the tangent line and a point on the line.

The derivative of y = sin(x/2) can be found using the chain rule and the derivative of sin(x):

dy/dx = (1/2) * cos(x/2)

Now, substitute x = 2π/3 into the derivative:

dy/dx = (1/2) * cos((2π/3)/2)

= (1/2) * cos(π/3)

= (1/2) * (1/2)

= 1/4

The slope of the tangent line is 1/4.

To find a point on the line, we substitute x = 2π/3 into the original equation:

y = sin((2π/3)/2)

= sin(π/3)

= √3/2

Therefore, when x = 2π/3, y = √3/2.

Using the point-slope form of a line, we have:

y - y₁ = m(x - x₁)

Plugging in the values:

y - (√3/2) = (1/4)(x - (2π/3))

Simplifying the equation:

y - (√3/2) = (1/4)x - π/6

y = (1/4)x + π/6 - √3/2

This is the equation of the tangent to the graph of y = sin(x/2) when x = 2π/3.

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Among the following values of r, 0.75 represents the strongest relationship. So, the correct option is D.

The value of r represents the strength of the correlation between two variables. The value of r ranges between -1 and 1, where a value of -1 represents a perfect negative correlation, 0 represents no correlation, and 1 represents a perfect positive correlation.

Therefore, among the given options, the value of 0.75 represents the strongest relationship. A value of 0.75 indicates a strong positive correlation between the two variables, meaning that as one variable increases, the other variable also tends to increase.

A correlation of this strength is often considered a strong relationship in many fields, such as psychology, economics, and engineering.

In contrast, a correlation of 0.50 indicates a moderate positive correlation, while a correlation of 0 indicates no correlation between the variables. A correlation of -1 indicates a perfect negative correlation, where the variables move in opposite directions.

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Answer:

2.2 chapters per hr

Step-by-step explanation:

5/2.3=2.17

Answer: 2 chapters

Step-by-step explanation:

You'll have to find the rate, so divide 5/1= 5 (this is how many times it's multiplied by) and divide 2 1/2 by 5

2.5 ÷ 5 = 0.5 = 1/2 of an hour

It takes you half an hour to read 1 chapter and since you need to find one hour, multiply 1x2

You can read 2 chapters in an hour

The value of the expression sec (-π) is equal to -1 if the given expression is undefined.

As given in the question,

Given expression: sec (-π)

Standard position of unit circle: -π is representing semicircle with terminal point on negative x-axis with coordinates (-1, 0)

Hypotenuse = √ (-1)² + 0²

                     = 1

Value of the expression is given by

sec α = Hypotenuse / Base (x-coordinate)

⇒sec(-π) = 1 / -1

⇒sec(-π) = -1

Therefore, the value of the expression sec (-π) is equal to -1.

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Answer:

1476:1845

Step-by-step explanation:

4+5=9

4÷9 ×3321

And

5÷9=3321

1476:1845