Please help me with this!!!

Answer:

  8.1 hours

Step-by-step explanation:

A model of the fraction remaining can be ...

  f = (1/2)^(t/37) . . . . t in hours

So, for the fraction remaining being 86%, we can solve for t using ...

  0.86 = 0.5^(t/37)

  log(0.86) = (t/37)log(0.5)

  t = 37·log(0.86)/log(0.5) ≈ 8.0509 ≈ 8.1 . . . hours

It takes about 8.1 hours to decay to 86% of the original concentration.

Answer:

Step-by-step explanation:

Samantha had $620 in her savings. She wanted to have at least $200 in her account after her five days in San Diego. This means that the amount that she can spend in 5 days would be her savings minus the least amount that she wants to have left. It becomes 620 - 200 = $420

If she decides to spend her spendable amount of $420 equally per day, it means that each day, she will spend 420/5 = $84

The inequality representing the amount that she can spend for each day will be

Let y = the amount that she can pend each day. Then, it will be

y lesser than or equal to 84

Answer:

Option 4 - 0.8508

Step-by-step explanation:

Given : A multiple choice test consists of 60 questions. Each question has 4 possible answers of which one is correct. If all answers are random guesses.

To find : Estimate the probability of getting at least 20% correct ?

Solution :

20% correct out of 60,

i.e. [tex]20\%\times 60=\frac{20}{100}\times 60=12[/tex]

Minimum of 12 correct out of 60 i.e. x=12

Each question has 4 possible answers of which one is correct.

i.e. probability of answering question correctly is [tex]p=\frac{1}{4}=0.25[/tex]

Total question n=60.

Using a binomial distribution,

[tex]P(X\geq 12)=1-P(X\leq 11)[/tex]

[tex]P(X\geq 12)=1-[P(X=0)+P(X=1)+P(X=0)+P(X=1)+P(X=2)+P(X=3)+P(X=4)+P(X=5)+P(X=6)+P(X=7)+P(X=8)+P(X=9)+P(X=10)+P(X=11)][/tex]

[tex]P(X\geq 12)=1- [^{60}C_0(0.25)^0(1-0.25)+^{60-0}+^{60}C_1(0.25)^1(1-0.25)^{60-1}+^{60-1}+^{60}C_2(0.25)^2(1-0.25)^{60-2}+^{60}C_3(0.25)^3(1-0.25)^{60-3}+^{60}C_4(0.25)^4(1-0.25)^{60-4}+^{60}C_5(0.25)^5(1-0.25)^{60-5}+^{60}C_6(0.25)^6(1-0.25)^{60-6}+^{60}C_7(0.25)^7(1-0.25)^{60-7}+^{60}C_8(0.25)^8(1-0.25)^{60-8}+^{60}C_9(0.25)^9(1-0.25)^{60-9}+^{60}C_{10}(0.25)^{10}(1-0.25)^{60-10}+^{60}C_{11}(0.25)^{11}(1-0.25)^{60-11}][/tex]

[tex]P(X\geq 12)\approx 0.8508 [/tex]

Therefore, option 4 is correct.

Answer:

  4/5

Step-by-step explanation:

This is a long-winded way to ask you the sum of the three fractions:

  1/10 + 1/5 + 1/2

  = 1/10 + 2/10 + 5/10 = (1 +2 +5)/10 = 8/10

  = 4/5

Janine spends 4/5 hour doing morning activities.

Answer:

Step-by-step explanation:

1:22

Answer:

Step-by-step explanation:

so

b buys a paperback for 5.5, while after natalie purchases 35.35 for membership- her books are 2.50

blake paid 5.5

nat paid 37.85

lets see how many books blake has to pay to reach 37.85 shall we?

5.5*22=121

2.5*35=87.5

35.35+87.5=122.85

i dont think its possible

To solve -3x + 3 < 6 and find the value of x, subtract 3 from both sides and divide by -3. The solution is x > -1.

To solve the inequality -3x + 3 < 6, we want to isolate the variable x. First, subtract 3 from both sides to get -3x < 3. Then, divide both sides by -3 (remember to flip the inequality sign when dividing by a negative) to obtain x > -1. Therefore, the solution is x > -1.

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The 11 kilometer road will be 1.1 cm long on the map

Step-by-step explanation:

Scale is used on maps to show large locations or roads as small representatives of the larger objects.

The scale factor is usually in proportion to the original length or dimensions.

Given that

1 cm = 10 km

Then, we will divide the number of kilometers by 10 to find the length of road on map

11 km on map = [tex]\frac{11}{10}[/tex]

Hence,

The 11 kilometer road will be 1.1 cm long on the map

Keywords: Maps, Scales

Learn more about maps at:

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To minimize the paper used for a poster with a specific print area and margin size, we derive a formula for total paper area, take its derivative with respect to the print width, solve for the width, and then find the matching height.

To find the dimensions of the page that will minimize the amount of paper used for a rectangular poster that contains 81 square inches of print with 5-inch margins on all sides, we need to set up a function to minimize. Let the width of the print area be x inches, and the height be y inches. Therefore, the total dimensions of the poster will be (x + 10) inches wide and (y + 10) inches high due to the margins on each side.

The area of print is given, so x*y = 81. We will minimize the total area of the page, A = (x+10)(y+10). Substituting the value of y from the print area equation, y =[tex]\frac{81}{x}[/tex], we get A(x) = (x+10)([tex]\frac{81}{x}[/tex]+10).

Now, to find the dimensions that minimize the paper used, we will take the derivative of A(x) with respect to x, set it to zero, and solve for x. From there, we can find the corresponding value of y to get the dimensions that will use the least amount of paper while still fitting the print area and margins.

Answer:

  1.  9 < s < 17

  2.  5 < MN < 19

  3.  AD > BD

Step-by-step explanation:

1. The triangle inequality tells you the sum of any two sides of a triangle must exceed the length of the other side. (Some versions say, "must be not less than ..." rather than "must exceed.") In practice, this means two things:

Here, we can use the latter fact to write the desired inequality. The difference of the given sides is 13 -4 = 9; their sum is 13 +4 = 17. The third side must lie between 9 and 17. If that side length is designated "s", then ...

  9 < s < 17

(If you don't mind a "triangle" that looks like a line segment, you can use ≤ instead of <.)

__

2. Same as (1) using different numbers.

  12 -7 < MN < 12 +7

  5 < MN < 19

__

3. Side CD is congruent to itself, and side CA is shown congruent to side CB. This means the requirements of the Hinge Theorem are met. That theorem tells you the longer side is opposite the greater angle:

  AD > BD

Answer:

D is correct

Step-by-step explanation:

2x/(x-2) - (x+5)/(x+3)

2x(x+3)/(x-2)(x+3) - (x+5)(x-2)/(x+3)(x-2)

2x^2+6x/(x-2)(x+3)-(x^2+3x-10)(x+3)(x-2)

(x^2+3x+10)/(x+3)(x-2)

Answer:

x^2+3x+10/(x-2)(x+3)

Step-by-step explanation:

Just took the test

Answer:

A) [tex]E(w)=450+0.10w[/tex]

B) $1200

Step-by-step explanation:

Let w represent employee's weekly sales and [tex]E(w)[/tex] be total weekly earnings.

We have been given that a phone store employee earns a salary of $450 per week plus 10% commission on her weekly sales.

A) The total weekly earnings of employee would be weekly salary plus 10% of weekly sales.

10% of weekly sales, w, would be [tex]\frac{10}{100}*w=0.10w[/tex]

[tex]E(w)=450+0.10w[/tex]

Therefore, the function [tex]E(w)=450+0.10w[/tex] models the employee's weekly earnings.

B) To find the weekly sales in the week, when employee earned $570, we will substitute [tex]E(w)=570[/tex] in our formula and solve for w as:

[tex]570=450+0.10w[/tex]

[tex]570-450=450-450+0.10w[/tex]

[tex]120=0.10w[/tex]

[tex]0.10w=120[/tex]

[tex]\frac{0.10w}{0.10}=\frac{120}{0.10}[/tex]

[tex]x=1200[/tex]

Therefore, the amount of employee's weekly sales was $1200.

Answer:

Step-by-step explanation:

Assuming the same number of bowling and mini golf games are played, let x represent the total number of games played, either bowling or mini golf. let y represent the total cost of bowling. Let z represent the total cost of golfing

Bowling cost $2 to rent a club plus $5 per game. It means that the cost, y for x bowling games will be

y = 2 + 5x

Mini golf cost $5 to rent a club, plus $4 per game. It means that the cost, y for x mini golf games will be

z = 5 + 4x

For the total cost to be the same, we will equate both equations(y = zl

2 + 5x = 5 + 4x

5x - 4x = 5 - 2

x = 3

There would be 3 games before total cost would be the same

To find a line parallel to another, determine the slope of the original line, which is 2 in this case, and then use the point-slope form with a given point and the same slope to find the equation, resulting in y = 2x + 9.

To find an equation of the line that is parallel to another, we must first determine the slope of the given line. The line passing through the points (-3, -4) and (1, 4) has a slope calculated by the formula ∆y/∆x = (4 - (-4))/(1 - (-3)) = 8/4 = 2.

Since parallel lines have the same slope, our new line will also have a slope of 2. We can use the point-slope form of a line's equation, which is y - y1 = m(x - x1), where m is the slope and (x1, y1) is a point on the line. Substituting our known point (-1, 7) and the slope 2, we get y - 7 = 2(x - (-1)). Simplified, the equation of our parallel line is y = 2x + 9.

In 6 months, they will have same amount of money.

Step-by-step explanation:

Let,

x be the number of months

Given,

Joe's savings = $200

Per month deposit = $50

J(x)=200+50x   Eqn 1

Kathy savings = $50

Per month deposit = $75

K(x)=50+75x   Eqn 2

For same amount;

J(x)=K(x)

[tex]200+50x=50+75x\\50x-75x=50-200\\-25x=-150[/tex]

Dividing both sides by -25;

[tex]\frac{-25x}{-25}=\frac{-150}{-25}\\x=6[/tex]

In 6 months, they will have same amount of money.

Keywords: functions, division

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Answer:

It takes less time sending 5 letters the traditional way with a probability of 36.7%.

Step-by-step explanation:

First we must take into account that:

- The traditional method is distributed X ~ Poisson(L = 1)

- The new method is distributed X ~ Poisson(L = 5)

[tex]P(X=x)=\frac{L^{x}e^{-L}}{x!}[/tex]

Where L is the intensity in which the events happen in a time unit and x is the number of events.

To solve the problem we must calculate the probability of events  (to send 5 letters) in a unit of time for both methods, so:

- For the traditional method:

[tex]P(X=5)=\frac{1^{5}e^{-1}}{1!}\\\\P(X=5) = 0.367[/tex]

- For the new method:

[tex]P(X=5)=\frac{5^{5}e^{-5}}{5!}\\\\P(X=5) = 0.175[/tex]

According to this calculations we have a higher probability of sending 5 letters with the traditional method in a unit of time, that is 36.7%. Whereas sending 5 letters with the new method is less probable in a unit of time. In other words, we have more events per unit of time with the traditional method.

Answer:

Mean : [tex]\mu=8[/tex]

Variance : [tex]\sigma^2=7.92[/tex]

Standard deviation =  [tex]\sigma=2.81[/tex]

Step-by-step explanation:

We know that , in Binary Distribution having parameters p (probability of getting success in each trial) and n (Total number trials) , the mean and variance is given by:-

Mean : [tex]\mu=np[/tex]

Variance : [tex]\sigma^2=np(1-p)[/tex]

We are given that ,

Total social security recipients  : n=800

The probability of social security recipients are too young to vote : p=1%= 0.01

Here success is getting social security recipients are too young to vote .

Then, the mean, variance and standard deviation of the number of recipients who are too young to vote will be :-

Mean : [tex]\mu=800\times0.01=8[/tex]

Variance : [tex]\sigma^2=800\times 0.01(1-0.01)=8\times0.99=7.92[/tex]

Standard deviation =  [tex]\sigma=\sqrt{\sigma^2}=\sqrt{7.92}=2.81424945589\approx2.81[/tex]

Hence, the mean, variance and standard deviation of the number of recipients who are too young to vote :

Mean : [tex]\mu=8[/tex]

Variance : [tex]\sigma^2=7.92[/tex]

Standard deviation =  [tex]\sigma=2.81[/tex]

In a sample of 800 social security recipients, with 1% being too young to vote, the mean is 8, the variance is 7.92, and the standard deviation is approximately 2.81.

The study indicates that 1% of social security recipients are too young to vote. When sampling 800 social security recipients, we treat the number of recipients too young to vote as a binomial random variable (since each recipient is either too young or not, with a fixed probability of being too young).

To find the mean of the binomial distribution, we use the formula:
Mean = n * p

Where n is the sample size (800) and p is the probability of success (0.01).

Mean = 800 * 0.01 = 8

The variance of the binomial distribution is given by the formula:
Variance = n * p * (1 - p)

Variance = 800 * 0.01 * (1 - 0.01) = 7.92

To calculate the standard deviation, we take the square root of the variance.

Standard Deviation = √(Variance) = √(7.92) = 2.81

Answer:

Question 1 = $59.85.

Question 2 = 0.45

Step-by-step explanation:

Doug did cleaning for 1 ¾ hours.

Doug did paperwork for 2 1/3 hours.

Doug did serving for 1 5/8 hours.

Total time dough spent on restaurant =1 3/4+2 1/3+1 5/8 hours.

=7/4+7/3 +13/8= 42+56+39/24=137/24=5.7 hours.

In one hour Doug earns $10.50.

Therefore, in 5.7 hour Doug earns 5.7 x 10.50=$59.85.

Hence, the total which Doug earned is $59.85.

Second question answer

5/11 as a decimal is 0.45 or rounded to the nearest tenth is 0.5

Answer:

Answer:

Question 1 = $59.85.

Question 2 = 0.45

Step-by-step explanation:

Doug did cleaning for 1 ¾ hours.

Doug did paperwork for 2 1/3 hours.

Doug did serving for 1 5/8 hours.

Total time dough spent on restaurant =1 3/4+2 1/3+1 5/8 hours.

=7/4+7/3 +13/8= 42+56+39/24=137/24=5.7 hours.

In one hour Doug earns $10.50.

Therefore, in 5.7 hour Doug earns 5.7 x 10.50=$59.85.

Hence, the total which Doug earned is $59.85.

Second question answer

5/11 as a decimal is 0.45 or rounded to the nearest tenth is 0.5

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Question 1 = $59.85.

Question 2 = 0.45

Step-by-step explanation:

Doug did cleaning for 1 ¾ hours.

Doug did paperwork for 2 1/3 hours.

Doug did serving for 1 5/8 hours.

Total time dough spent on restaurant =1 3/4+2 1/3+1 5/8 hours.

=7/4+7/3 +13/8= 42+56+39/24=137/24=5.7 hours.

In one hour Doug earns $10.50.

Therefore, in 5.7 hour Doug earns 5.7 x 10.50=$59.85.

Hence, the total which Doug earned is $59.85.

Second question answer

5/11 as a decimal is 0.45 or rounded to the nearest tenth is 0.5

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Step-by-step explanation:

Hey! How are you? My name is Maria, 19 years old. Yesterday broke up with a guy, looking for casual sex.

Write me here and I will give you my phone number - *pofsex.com*

My nickname - Lovely

The probability that a woman has none of the three risk factors, given that she does not have risk factor A, is calculated to be 0.54.

To find the probability that a woman has none of the three risk factors, given that she does not have risk factor A, we will use the given probabilities and apply the principles of probability. Let's denote the probabilities of having only the risk factors as P(A), P(B), and P(C), the probabilities of having exactly two risk factors as P(A and B), P(A and C), and P(B and C), and the probability of having all three risk factors as P(A and B and C).

Given:

P(A) = P(B) = P(C) = 0.1
P(A and B) = P(A and C) = P(B and C) = 0.12
P(A and B and C | A and B) = 1/3

We can calculate P(A and B and C) using the conditional probability:

P(A and B and C) = P(A and B) × P(A and B and C | A and B) = 0.12 × 1/3 = 0.04

To find the probability of not having A, denoted as P(A'), we can use the complement rule:

P(A') = 1 - P(A) - P(A and B) - P(A and C) - P(A and B and C) = 1 - 0.1 - 0.12 - 0.12 - 0.04 = 0.62

Since P(A') includes probabilities of women with neither of the risk factors or only with B or C, we need to subtract the probabilities of having only risk factors B and C:

P(None | A') = P(A') - P(B) - P(C) + P(B and C) = 0.62 - 0.1 - 0.1 + 0.12 = 0.54

The probability that a woman has none of the three risk factors, given that she does not have risk factor A, is thus 0.54.

Answer:

The number of books left on shelves or in circulation is 1,163 .

Step-by-step explanation:

Given as :

The total number of Books in the Library = 1219

The number of lost or stolen books = 32

The number of books sent fro repair = 24

Now, Let The number of books left on shelves or in circulation = x

So,

The total number of Books in the Library  = The number of lost or stolen books + The number of books sent fro repair  + The number of books left on shelves or in circulation

I.e 1219 = 32 + 24 + x

Or, 1219 = 56 + x

Or, x = 1219 - 56

∴    x = 1,163

Hence The number of books left on shelves or in circulation is 1,163 Answer

Answer: Number of books in circulation or left on the shelf is 1163

Step-by-step explanation:

At the end of the year, 32 books were reported to be lost or stolen and 24 books were sent out for repair. This means that the number of books not in circulation is the sum of the number books that was lost or reportedly stolen and the number of books that were sent out for repair.

Therefore,

Number of books not in circulation = 32+24 = 56

The Library originally had 1219 books.

The number of books left on the shelves or in circulation will be total number of books initially - number of books not in circulation. This becomes

1219 - 56 = 1163 books

Answer:

Step-by-step explanation:

v*2+(v-14)*2=400

2v+2v-28=400

4v=400+28

4v=428

v=107 km/h

speed of slowest car=107-14=93 km/h

Answer:

25%.

Step-by-step explanation:

Let E be the event that the dart lands inside the triangle.

We have been given that a rectangular board has an area of 648 square centimeters. The triangular part of the board has an area of 162 square centimeters.

We know that probability of an event represents the chance that an event will happen.

[tex]\text{Probability}=\frac{\text{Favorable no. of events}}{\text{Total number of possible outcomes}}[/tex]

[tex]\text{Probability that dart lands inside the triangle}=\frac{\text{Area of triangle}}{\text{Area of rectangle}}[/tex]

[tex]\text{Probability that dart lands inside the triangle}=\frac{162}{648}[/tex]

[tex]\text{Probability that dart lands inside the triangle}=0.25[/tex]

Convert into percentage:

[tex]0.25\times 100\%=25\%[/tex]

Therefore, the probability that dart lands inside the triangle is 25%.

Answer:

25%

Step-by-step explanation:

Answer: 70676

Step-by-step explanation:

First we draw a diagram representing the problem, which can be found in the picture uploaded,

Point a is the point of the plane, you can see where the angle of depression is imputed in the diagram, point C is the point where the gateway arch is, and drawing a vertical line to the ground from the point of the plane, point Blank is where that vertical line touches the ground

So we can tell the the angle of depression from the plane to the arch is the same as the angel of elevation from the arch to the plane

And we are to look for the distance between B and C which is labeled x in the diagram

So looking at the right angle triangle made from this question, we can see we have the opposite length which the angle of elevation from the arch is looking at, and we are looking for the adjacent length, so we use SOH, CAH, TOA, to solve

Choosing TOA which means

Tan(angle) = (opposite length)/(adjacent length)

Tan 23 = 30000/x

Multiplying both sides by x

xtan23 = 30000

Dividing both sides by tan23

x = 30000/tan23

x = 70675.57

Approximately 70676

Answer:

  $9486.68

Step-by-step explanation:

The future value of a annuity formula can be used:

  FV = P((1+r)^n -1)/r

  750000 = P(1.06^30 -1)/0.06

  P = 750000(.06)/(1.06^30 -1) = 9486.68

Adam has to contribute $9,486.68 each year to reach his goal.

Adam can calculate how much he needs to contribute to his IRA each year using the future value of an annuity formula. By substituting the known values into the rearranged formula, he can find the required annual payment.

To find out how much Adam needs to contribute each year, we can use the formula for the future value of an annuity. The future value (FV) of an annuity formula is:

FV=P*[((1+r)^n -1)/r]

Where:

In this question, we want to find P, so we rearrange the formula as follows:

P = FV / [((1+r)^n -1)/r]

Substituting the given values:

P= $750,000 / [((1+0.06)^30 -1)/0.06]

By calculating the above expression, we will get the amount Adam needs to contribute annually to reach his goal.

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Answer:

40h+125=1205

Step-by-step explanation:

He is paid $40 for an unknown amount of hours which in this case would be considered as (h) plus a 125 service charge. Overall, he was paid $1205

Answer:  A

Step-by-step explanation:

The sum to infinity of a geometric series is

S (∞ ) = \frac{a}{1-r} ( - 1 < r < 1 )

where a is the first term 8 and r is the common ratio, hence

S(∞ ) = {8}{1-\{1}{2} } = {8}{1}{2} } = 16

Answer:

Step-by-step explanation:

32 i think

Answer: -12.286 in/sec

Step-by-step explanation:

Differentiate A=s^2 to get d(A)/d(t) = 2s * d(s)/d(t).

Plug in -43 for d(A)/d(t) since it is the rate of change for area. Plug in 7 for s since it is the value of the side length. -43 = 2(7) * d(s)/d(T).

d(s)/d(T) equals -3.0714286

Differentiate P=4s to get d(P)/d(t) = 4 * d(s)/d(t)

Plug in -3.0714286 to d(P)/d(t) = 4 * d(s)/d(t).

d(P)/d(s)= -12.286 in/sec

Final answer:

To find the rate of change of the perimeter when the square's side length is 7 inches and its area decreases at a rate of 43 square inches/sec, we calculate ds/dt and then use it to find dP/dt. The perimeter is decreasing at a rate of approximately -12.284 inches/sec.

Explanation:

The question involves finding the rate at which the perimeter of a square changes given that the area of the square is decreasing at a rate of 43 square inches per second. To solve this problem, let's denote the side length of the square as s and the area as A, so A = s². The perimeter of the square, P, is given by P = 4s.

Given that the area is decreasing at a rate of -43 square inches per second, we represent this rate of change as dA/dt = -43 inches^2/sec. We also know that at the instant when s = 7 inches, we want to find dP/dt, the rate at which the perimeter is changing.

First, we find the rate of change of the side length, ds/dt, given by differentiating A = s² with respect to time (t), giving 2s(ds/dt) = dA/dt. Substituting the given values, we get 2*7(ds/dt) = -43, solving for ds/dt gives us -43/14 = -3.071 inches/sec.

Finally, since the perimeter's rate of change, dP/dt, is 4(ds/dt), we substitute the value we found for ds/dt, resulting in dP/dt = 4*(-3.071), which equals -12.284 inches/sec. Hence, the perimeter of the square is decreasing at a rate of approximately -12.284 inches per second.

Answer:

t=4 seconds to reach the cannon floor

Step-by-step explanation:

ax^2+bx+c=0

0=-16t^2+255

-255=-16t^2

t^2=15.9375

t= 3.99

round it up...

t=4 seconds to reach the cannon floor

hope this helps!!! :)

Answer:

5 (strawberries / hours)

Step-by-step explanation:

calculation fro morning

strawberries / minutes  x   minutes / hours =   strawberries / hours

 so after adding the value in above equation

3/4* 60/1  = 45 strawberries / hours

 calculation in the afternoon

strawberries / minutes  x   minutes / hours =   strawberries / hours

 2/3 x 60/1  =  40 strawberries / hours

 so now by calculating difference between morning and afternoon packing rates,  you can easily calculate

 45-40 = 5 (strawberries / hours)

Answer:

$1300

Step-by-step explanation:

The extruder yields a revenue of $200per hour

Y denotes the number of breakdown per day.

The daily revenue generated is given as

R = 1600 - 50Y^2

We have an average of 2 breakdown per day

Lamda = 2

Represent lamda as β

E(Y) = β

E(Y(Y-1)) = β^2

E(Y^2) = E[Y(Y-1)] + E(Y)

= β^2 + β

E(R) = E(1600 - 50Y^2)

= 1600 - 50E(Y^2)

= 1600 - 50(β^2 +β)

Recall that β = lamda = 2

= 1600 - 50(2^2 + 2)

= 1600 - 50(4+2)

= 1600 - 50(6)

= 1600 - 300

= 1300

$1300

The expected daily revenue of the extruder is $1300