Answer:
4 tokens.
Step-by-step explanation:
The expected value of a given event is calculated as:
EV = (x₁*p₁ + x₂*p2 + ... + xₙ*pₙ)
Where xₙ is the n-th outcome, and pₙ is its probability.
In this case, our experiment is:
You draw two times.
We have 30 cards with no prize
We have 10 cards with a prize.
A total of 40 cards.
As we draw two times (and the first time we draw a card we put it back in the deck) we can consider the events as independent, so we can find the expected value per draw.
Now we can define:
x₁ = drawing a blank card = 0 tokens
The probability will be equal to the quotient between the number of blank cards and the total number of cards
p₁ = 30/40 = 3/4
x₂ = drawing a prized card = 8 tokens.
The probability will be equal to the quotient between the number of prized cards and the total number of cards:
p₂ = 10/40 = 1/4
Then the expected value per draw is:
EV = ( (3/4)*0 tokens + (1/4)* 8 tokens) = 2 tokens.
And we have two draws, then the expected value of two draws is two times the expected value per draw, this means that the expected value in our case is:
expected value = 2*(2 tokens) = 4 tokens.
The correct option is the first one, counting from the top.
Perform the following mathematical operation, and report the answer to the appropriate number of significant figures.
1204.2 + 4.72613 = [?]
The value of 1204.2 + 4.72613 is 1208.92613.
What is meaning of significant figures of a number?
Significant figures are the number of digits that add to the correctness of a value, frequently a measurement. The first non-zero digit is where we start counting significant figures. Determine how many significant digits there are given a range of numbers.
Given number is 1204.2 and 4.72613.
If add zeros after the last digit of the decimal number, then the number will remains same.
The rewrite form of 1204.2 is 1204.20000.
Before combining two decimal integers, make sure they both have the same number of digits after the decimal point. If they don't, move a number's right by a number of zeros until they do.
Then, place the decimal points vertically and write one number on top of the other. Bring the decimal point directly below the decimal point and add as you would with full numbers.
The sum of 1204.20000 and 4.72613
1204.20000
+4.72613
__________
1208.92613
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6 people equally share 1/2 a pan of mac and cheese write a division expression to represent the situation
Answer:
6/1.5
Step-by-step explanation:
You said equally, so you need to make sure that each person gets an even share. To do this, you can do people/things. Hence why the answer is 6/1.5!
[tex]\int\limits^2_076e^4 {x} \, dx[/tex]
This graph best represents the motion of an object that
a
is increasing its' acceleration.
b
first increases acceleration then remains constant.
c
shows no motion.
d
was at rest and is accelerating uniformly.
The motion of the object on the graph, can best be represented as an object that d. was at rest and is accelerating uniformly.
What is the acceleration ?The object on the graph is accelerating such that the acceleration is stable and uniform. This is why the speed - time line is a straight and diagonal line to show that the speed is proportional to time.
We know that the object started from rest because at the point where time was 0, the object was not accelerating and so was not moving. As time moves on, the object increases speed, thereby accelerating.
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Patty needs 3/4 cup of bananas to make a loaf of banana bread.
Patty has 1 1/3 cups of bananas.
Does Patty have enough bananas to make 2 loaves of banana bread?
Answer:
She Does NOT
Step-by-step explanation:
3/4 is .75 1 1/3 is 1.33 3/4*2= 1.5 which is more than 1.33
I've been unable to figure this out. Anyone able to assist on which is the correct answer?
The domain and range of the given function are {-2, 0, 1, 2, 3} and {-3, 0, 2, 3, 4} respectively
Domain and Range of a FunctionThe domain of a function is the set of values that we are allowed to plug into our function. This set is the x values in a function such as f(x). The range of a function is the set of values that the function assumes. This set is the values that the function shoots out after we plug an x value in.
The domain of a function can be said as all possible values of x and the range of a function is all possible values of y.
The given function is
f(x) = {(0, -3), (2, 0), (3, 2), (1, 4), (-2, 3)
The domain of the function can be given as;
Domain : {-2, 0, 1, 2, 3}
Range : {-3, 0, 2, 3, 4}
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A man standing on the deck of a ship, h m above the sea level, observes that the angles of elevation and depression of the top and the bottom of a cliff are A and B respectively. Find the height of the cliff in terms of A, B and h
give me the correct ans with clear explainnation and I will give u the BRAINLIEST!
The height of the cliff in terms of A, B and h are 40 meters.
What is a right-angled triangle?A triangle is said to be right-angled if one of its inner angles is 90 degrees, or if any one of its angles is a right angle.
A man standing on the deck of a ship.
Let C be the position of man.
And the angles of elevation and depression of the top and the bottom of a cliff are A and B respectively 60° and 30°.
That means, ∠DCH = 60° and ∠BCD = 30°.
The diagram is given in the attached image.
HD = x And BD = 10 meters.
In right-triangle ΔCDH,
we have,
tan60° = HD / CD
√3 = x / CD
CD = x/√3
In right-triangle ΔCDB,
we have,
tan30° = BD/CD
CD = 10√3
So, the distance of the ship from the cliff is 10√3 meters.
Comparing, the both values of CD,
10√3 = x/√3
x = 10√3 × √3
x = 10 × 3
x = 30 meters.
Now, the total height of cliff = BD + DH
= 10 + 30
= 40 meters.
Therefore, the height of the cliff is 40 meters.
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a rectangle in the first and second quadrants of the coordinate plane has its base along the x-axis and two vertices on the parabola defined by y
The area of rectangle with has its vertices defined on parabola is 32 square units.
What is rectangle?An example of a quadrilateral with equal and parallel opposite sides is a rectangle. It is a polygon with four sides and four angles that are each 90 degrees. A rectangle is a shape with only two dimensions.
What are other terms to describe rectangle?Square, figure, oblong, parallelogram, plane a.re terms to describe rectangle
Equation of Parabola is y = 12 - x^2 is an even function.
Therefore, its rectangle form also is even at the origin.
We know area of rectangle = length × width
Here,
length = 2x, width = y
Area, A = 2x(12 - x2)
⇒ A = 24x - 2x^3
Take derivative of A with respect to x
⇒ A' = 24 - 6x^2
The area is largest when A' = 0
⇒ 24 - 6x^2 = 0
⇒ x^2 = 4
⇒ x = 2
Put the value of x in y = 12 - x^2
⇒ y = 12 - 4
⇒ y = 8
Area = 2(2)(8) = 32
Therefore, the largest area of a rectangle is 32 square units.
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Hypothesis 1 H0: Receiving a 20 percent off coupon does not increase the number of customers visiting the Lotions and Potions soap store. Ha: Receiving a 20 percent off coupon increases customers visiting the Lotions and Potions soap store. Data Customers on file who visited the store during coupon promo: 32 percent Customers on file who visit the store during a typical week: 30 percent Sample size: 4,500 Questions Did you use a z-test or t-test? Why? What is the P value? Do you accept or reject the alternative hypothesis? Should Lotions and Potions continue to offer this promotion in order to increase visits? Why or why not?
The data Customers on file who visited the store during coupon promo is 32% .
a) We use Z-test for testing hypothesis in this case because it is single proportion.
b) The P-value is 0.0017.
c) As P value < α = 0.05 , So we reject the null hypothesis.
d) Yes, Lotions and Potions continue to offer this promotion in order to increase visits because null hypothesis is rejected that alternative hypothesis is true which gives the same results.
The Null and Alternative hypothesis related to 20 percent off coupon does not increase the number of customers or increase the number of customers.
Sample size ,n = 4,500
Significance level, 0.05
a) We use z-test, because this is single proportion hypothesis test.
Below are the null and alternative Hypothesis,
Null Hypothesis, H₀ : p = 0.3
Alternative Hypothesis, Hₐ : p > 0.3
b) Test statistic,
z = (p-cap - p)/sqrt(p×(1-p)/n)
z = (0.32 - 0.3)/sqrt(0.3× (1-0.3)/4500)
z = 2.93
Using the Z-table, the P value at significance level 0.05 and z = 2.93 is 0.0017
As we see P-value < α = 0.05, so, reject the null hypothesis.
Yes, Lotions and Potions should continue to offer this promotion in order to increase visits.
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if all possible samples of size n are drawn from an infinite population with a mean of 36 and a standard deviation of 22, then the standard error of the sample mean equals 2 for samples of size:
Thus , it is False. As there is confidence level is not given, then cant calculate the sample size.
The standard deviation is what?The standard deviation in statistics is a measure of how widely spread a set of values can be or how much they can vary. A low standard deviation denotes that values are typically close to the mean of the collection, whereas a high standard deviation indicates that values are dispersed across a greater range.
Here,
The standard error of the sample mean is equal to 2 for samples of size n if all conceivable samples of that size are taken from a population with an infinite mean and standard deviation.
In the above statement confidence level is not given.
Thus , it is False. As there is confidence level is not given, then cant calculate the sample size.
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Use the scale to help you solve the equation and find the value of x. Enter the
value of x below.
x + 3 = 9
X=_____
Answer:
x=6
Step-by-step explanation:
9-3=6 or 6+3=9
NO LINKS!!
A deposit pf $6000 is made in a college savings fund that pays 5.0% interest, compounded continuously. The balance will be given to a student after the money has earned interest for 40 years. How much (in dollars) will the student receive? (Round your answer to the nearest cent.)
Answer:
$44,334.34
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{8.5 cm}\underline{Continuous Compounding Formula}\\\\$ A=Pe^{rt}$\\\\where:\\\\ \phantom{ww}$\bullet$ $A =$ final amount \\\phantom{ww}$\bullet$ $P =$ principal amount \\\phantom{ww}$\bullet$ $e =$ Euler's number (constant) \\\phantom{ww}$\bullet$ $r =$ annual interest rate (in decimal form) \\\phantom{ww}$\bullet$ $t =$ time (in years) \\\end{minipage}}[/tex]
Given:
P = $6000r = 5.0% = 0.05t = 40 yearsSubstitute the given values into the continuous compounding formula and solve for A:
[tex]\implies A=6000e^{0.05 \times40}[/tex]
[tex]\implies A=6000e^2[/tex]
[tex]\implies A=6000(7.3890560...)[/tex]
[tex]\implies A=44334.33659...[/tex]
Therefore, the balance of the account after 40 years will be $44,334.34 (nearest cent).
Clare would like to buy a video game that costs at least $130. She has saved $48 so far and plans on saving $5 of her allowance each week. Write an inequality to find out the number of weeks it will take until she has enough money to buy the game.
Answer:
5x+48=130
Step-by-step explanation:
5 is the money she gets each week. X is the number of weeks. X can be found easily but for the sake of this question, It's unknown. so 5x and then add the 48 she's already saved you get 5x+48=130 or 5x+48 is greater than or equal to 130.
I NEED HELP FAST
A colony of bacteria grows according to the law of inhibited growth. If there were 200 bacteria at noon, and 550 at 2 pm. Determine when the colony will reach a population of 2000.
logistic model:[tex]y(t)=\frac{c}{1+ae^-bt}[/tex]
I feel like I'm not given enough information. I'll assume that the limit is 10000
The colony will reach a population of 2000 in time -
t = - {log(2000 - c) - log(a) + log(c)}/b.
What is a mathematical function, equation and expression? function : In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function.expression : A mathematical expression is made up of terms (constants and variables) separated by mathematical operators.equation : A mathematical equation is used to equate two expressions.Given is that a colony of bacteria grows according to the law of inhibited growth. If there were 200 bacteria at noon, and 550 at 2 pm.
The logistic model is given as -
y(t) = {c/(1 + a[tex]e^{-bt}[/tex])}
For y(t) = 2000
2000 = {c/(1 + a[tex]e^{-bt}[/tex])}
(2000/c) = 1/(1 + a[tex]e^{-bt}[/tex])
(1 + a[tex]e^{-bt}[/tex]) = (2000/c)
a[tex]e^{-bt}[/tex] = (2000/c) - 1
a[tex]e^{-bt}[/tex] = (2000 - c)/c
[tex]e^{-bt}[/tex] = (2000 - c)/(ac)
(-bt)log{e} = log {(2000 - c)/(ac)}
- bt = log(2000 - c) - log(ac)
- bt = log(2000 - c) - log(a) + log(c)
t = - {log(2000 - c) - log(a) + log(c)}/b
Therefore, the colony will reach a population of 2000 in time -
t = - {log(2000 - c) - log(a) + log(c)}/b.
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What is the common ratio of the geometric sequence below?
625, 125, 25, 5, 1,
The common ratio is 1/5. By dividing each word by the term before it, we may find the geometric progression's common difference.
How to find common ratio ?The common ratio in geometric progression is the ratio of any term in the sequence to divided by the first term.
The Formula to calculate the common ratio in geometric progression, a, ar, ar2, ar3, ar4, ar5… is,
Common ratio = ar/ a = ar2/ ar = ……. = an/ an-1
As stated in the definition, we can compute the common difference of a geometric progression by dividing any term by its preceding term.
Given, the geometric sequence is 625, 125, 25, 5, 1,....
We have to find the common ratio of the given geometric sequence.
In geometric sequence, a, b, c, d, … the common ratio r is given by
r = b/a = c/b = d/c.
So, r = 125/625 = 25/125 = 5/25 = 1/5;
r = 1/5
Therefore, the common ratio is r = 1/5.
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Answer:
B. 25/125
Step-by-step explanation:
What is the slope of (0,0) and (4,12)
[tex] \Large{\boxed{\sf Slope = 3}} [/tex]
[tex] \\ [/tex]
Explanation:The slope of a line passing through two points, also known as its gradient, is calculated using the slope formula.
[tex] \\ [/tex]
[tex] \Large{\left[ \begin{array}{c c c} \underline{\tt Slope \ formula \text{:}} \\~ \\ \tt m = \dfrac{rise}{run} = \dfrac{\Delta y}{\Delta x} = \dfrac{y_2 - y_1}{x_2 - x_1}\end{array} \right] } [/tex]
Where m is the slope of the line.
[tex] \\ [/tex]
First, let's identify our values:
[tex] \sf (\underbrace{\sf 0}_{x_1} \ , \ \overbrace{\sf 0}^{y_1} ) \ \ and \ \ (\underbrace{\sf 4}_{x_2} \ , \ \overbrace{\sf 12}^{y_2} ) [/tex]
[tex] \\ [/tex]
Now, substitute these values into the formula:
[tex] \sf \rightarrow m = \dfrac{12 - 0}{4 - 0} \\ \\ \sf \rightarrow m = \dfrac{12}{4} \\ \\ \\ \rightarrow \boxed{\boxed{\sf m = 3}} [/tex]
[tex] \\ [/tex]
[tex] \hrulefill [/tex]
[tex] \\ [/tex]
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Answer:
slope = 3
How to Solve:
The question is asking us to find the slope, given two points.
These points are (0,0) and (4,12).
We will use the slope formula:
[tex]\boldsymbol{m=\dfrac{y_2-y_1}{x_2-x_1}}[/tex]
Where:
m = slope(x₁,y₁) and (x₂,y₂) are points that the line passes throughPlug in the data:
[tex]\boldsymbol{m=\dfrac{12-0}{4-0}}[/tex]
[tex]\boldsymbol{m=\dfrac{12}{4}}[/tex]
Simplify the fraction to its lowest terms:
[tex]\boldsymbol{m=3}[/tex]
Therefore, the slope is 3.
Graph y +1 = 1/3 (x-3)
The graph of the linear equation, y + 1 = 1/3(x - 3), is given in the attachment below.
How to Graph a Linear Equation?A linear equation is an equation of the form "y = mx + b," where x and y are variables, and m is the slope and b is the y-intercept.
To graph a linear equation, of y + 1 = 1/3(x - 3), you can use the following steps:
Rewrite the equation in slope-intercept form to determine its slope (m) and the y-intercept (b).
y + 1 = 1/3(x - 3)
y + 1 = 1/3x - 1
y = 1/3x - 1 - 1
y = 1/3x - 2
The slope (m) of the line would be 1/3, which is the rise over the run of the line.
The y-intercept (b) of the line would be -2, which means the line will intercept the y-axis at -2.
The graph of y + 1 = 1/3(x - 3) is shown in the image below.
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Task: Gym Membership
Instructions
Function c is defined by the equation c(n) = 50 + 4n. It gives the monthly cost, in dollars, of visiting a gym as a function of the number of visits, n.
Complete each of the 2 activities for this Task.
Activity 1 of 2
Find the value of c(7).
Activity 2 of 2
Explain what the value of c(7) you found means in this situation.
The value of c(7) = 78 and 78 represents the monthly cost of visiting the gym 7 times.
Finding p(a) from p(x)
To find p(a) for a given polynomial p(x) we need to substitute x = a in the given polynomial i.e in place of x.
Here we have
Function c is defined by the equation c(n) = 50 + 4n.
It gives the monthly cost, in dollars, of visiting a gym as a function of the number of visits n.
Activity 1 of 2
Find the value of c(7).
=> c(7) = 50 + 4(7)
=> c(7) = 50 + 28
=> c(7) = 78
Activity 2 of 2
Explain what the value of c(7) you found means in this situation.
In c(n) = 50 + 4n, n represents the number of visits in a month and 50+4n will represent the monthly cost in dollars
If we apply the above statement to c(7) = 78
then 7 represents the number of visits and 78 represents the monthly cost of visiting the gym 7 times
Therefore,
The value of c(7) = 78 and 78 represents the monthly cost of visiting the gym 7 times.
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he equations of two lines are given. determine whether the lines are parallel, perpendicular, or neither. y
By definition, perpendicular strains are strains intersecting at a proper attitude. The letters T and L are examples of perpendicular strains. By definition, parallel strains are strains at the equal aircraft that in no way intersect.
The letters N and Z include pairs of parallel linetwo non-vertical strains which are withinside the equal aircraft has the equal slope, then they may be stated to be parallel. Two parallel strains might not ever intersect. If non-vertical strains withinside the equal aircraft intersect at a proper attitude then they may be stated to be perpendicular.
We can decide from their equations whether or not strains are parallel with the aid of using evaluating their slopes. If the slopes are the equal and the y-intercepts are different, the strains are parallel. If the slopes are different, the strains aren't parallel. Unlike parallel strains, perpendicular strains do intersect.
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Suppose the COMBINED area is known to be 0.10416, assume there is equal area on each side. Determine the corresponding Z-scores.
A) z=±1.62 B) z=±1.58 C) z=±1.72 D) z=±1.66 E) z=±1.69 F) z=±1.49 G) None of These
The solution is once more 1.28 since a combined area of 0.10416 to the right implies that it must also have an area of 0.90 to the left.
Since each normally distributed random variable has a slightly different distribution shape, standardizing the variable to give it a mean of 0 and a standard deviation of 1 is the only method to determine regions using a table. How do we go about doing that? Employ the z-score!
Z = ( x - μ)/σ
If a mean and standard deviation are present for the random variable X,
Then a random variable with a mean of 0 and a standard deviation of 1 is produced by converting X using the z-score!
With that in mind, all that remains is to understand how to find areas under the standard normal curve, which can then be applied to any random variable with a normal distribution.
Since an area of 0.10416 to the right means that it must have an area of 0.90 to the left, the answer is once again 1.28.
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Find the slope of the line y=5x+12.
Write your answer as an integer or as a simplified proper or improper fraction.
Answer:
5
Step-by-step explanation:
The slope or gradient of the line
using this formula as our guide line
y = mx +b
where m = slope
x = x– intercept
b = y– intercept
so
y = 5x + 12
the slope will be 5
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I need help with these 2 questions.
A) Write and solve a proportion to determine the height of the cell phone tower. Please show your work.
B) What is the height of the tower in meters?
Part (A)
Because the right triangles are similar, we can form two ratios P/Q and R/S that are equal to one another.
P/Q = R/S
where,
P = height of the personQ = horizontal distance person is from the left-most cornerR = height of the towerS = horizontal distance the tower is from the left-most cornerIn this case,
P = 1.8 metersQ = 6 metersR = unknown, we'll use variable hS = 60 metersTherefore, we go from this
P/Q = R/S
to this
(1.8)/6 = h/60
Other equations can be set up. This means there are other possible final answers. The key is to have things be consistent. The equation I've set up has the vertical components as the numerators, while the horizontal components are the denominators.
--------------
Answer: (1.8)/6 = h/60====================================================
Part (B)
Let's cross multiply and solve for h.
(1.8)/6 = h/60
1.8*60 = 6h
108 = 6h
6h = 108
h = 108/6
h = 18
--------------
Answer: 18 metersAnswer:
A). [tex]\frac{1.8}{6} = \frac{height}{60}[/tex]
B). 18 meters tall
Step-by-step explanation:
We see TWO right triangles in this problem:
the one with the man and the 6m and the one with the phone tower and the 60mThese triangles are proportional so we can make a ratio out of them
the height of the man over the side of the triangle (6m)
and the height of the tower over the length of its triangle (60m)
Set these equal to each other to complete part A
[tex]\frac{1.8}{6} = \frac{height}{60}[/tex]
And by using cross multiplication (which is what you do for ratios), solve for h!
For a quick example of cross multiplication, I've attached a picture.
Now let's do it!
1.8 × 60 = 6 × h
108 = 6h
108/6 = h
h = 18
The height of the cell phone tower is 18 meters.
Which of the following shows 12 more than a number, written as an algebraic expression?
A. 12-n
B.12+n
C.n-12
D.12n
write an integral that expresses the increase in the perimeter p(s) of a square when its side length s increases from 2 units to 5 units
The integral to express the increase in the perimeter p(s) of a square when its side length s increases from 2 units to 5 units is:
p(s) = 4s
Integral = ∫2s5s ds
= ∫2s5s dx
= [s2/2]2s5s
= (25/2) - (4/2)
= 20/2
= 10
Therefore, the increase in the perimeter of the square when its side length s increases from 2 units to 5 units is 10 units.
To calculate this increase, we used the formula for the perimeter of a square, which is 4s, and the integral from 2s to 5s, which gives us the area under the graph and the difference between the two side lengths. We then solved for the integral and multiplied it by 4 to get the increase in the perimeter.
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A pilot flies in a straight path for 130 minutes. She then makes a course correction, heading 10° to the right of her original course, and flies 145minutes in the new direction. If she maintains a constant speed of 600 miles per hour, how far is she from her starting position? Round your answer to the nearest mile. Enter deg after any degree value.
By using properties of triangle, it can be calculated that-
The pilot is 2740 miles from her starting position.
What is a triangle?
A triangle is a three sided two dimensional figure. A triangle has three sides and three interior angles.
Here,
The diagram has been attached
Time = 130 minutes = 2 hrs 10 minutes = [tex]2 + \frac{10}{60}[/tex] hours = [tex]\frac{13}{6}[/tex] hours
Speed = 600 miles per hour
Distance = [tex]\frac{13}{6} \times 600[/tex] = 1300 miles
Now,
Time = 145 minutes = 2 hrs 25 minutes = [tex]2 + \frac{25}{60}[/tex] hours = [tex]\frac{29}{12}[/tex] hours
Distance = [tex]\frac{29}{12}\times 600[/tex] = 1450 miles
Angle = [tex]10^{\circ}[/tex]
[tex]c^2 = 1300^2 + 1450^2 - 2\times 1300\times 1450\times cos(180-10)\\c^2 = 1690000 + 2102500 - (-3712725.2)\\c^2= 7505225.2\\c= \sqrt{7505225.2}\\c = 2740[/tex]
The pilot is 2740 miles from her starting position.
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How to find the missing side Using Pythagoras Theorem?
Let K=[tex]20^{20}[/tex].Suppose that [tex]\frac{20^{k} }{k^{20} } =20^{n}[/tex].find the largest power of 20 that divides n?
Answer:
20^2 = 400, the 2nd power of 20
Step-by-step explanation:
Given that k=20^20 and 20^k/k^20 = 20^n, you want the largest power of 20 that divides n.
LogarithmsTaking the base-20 logarithm of both equations, we have ...
[tex]\log_{20}{k}=\log_{20}{20^{20}}\ \Longrightarrow\ \log_{20}{k}=20\\\\\log_{20}{\dfrac{20^k}{k^{20}}}=\log_{20}{20^n}\ \Longrightarrow\ k-20\log_{20}{k}=n[/tex]
Substituting for k and log(k), we get ...
[tex]20^{20} -20\cdot20=n\\\\20^2(20^{18}-1)=n[/tex]
This shows us the largest power of 20 that is a factor of n is 20².
The concentration C(t) of a certain drug in the bloodstream after t minutes is given by the formula C(t)=0.05(1−e^−0.2t). What is the concentration after 12 minutes? Round to three decimal places.
Thus after 12 minutes concentration of drug is 0.045.
The concentration C(t) of a certain drug in the bloodstream after t minutes is given by the formula [tex]c(t) = 0.05(1-e^{-0.2t} )[/tex]
Drug concentration is amongst the most important determinants of clinical response to a drug.
Drug concentration will be seen to increase in biological samples drawn from the systemic circulation when the amount of drug absorbed exceeds the amount of drug that is distributed into the extravascular tissues and the drug that is metabolized and/or excreted during this period.
Thus after 12 minutes concentration of the drug is = C(5).
Now
C(5) = [tex]0.05(1-e^{-0.2t} )[/tex]
= [tex]0.05(1-e^{-2.4} )[/tex]
= 0.05(1-0.0907)
= 0.05×0.9093
= 0.045
The drug concentration is 0.045.
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find the equation of the tangent to the circle 4x²+4y²=25 what are parallel to the line 3x+5y+7=0
Answer:
Step-by-step explanation:
To find the equation of the tangent to the circle 4x^2 + 4y^2 = 25 that is parallel to the line 3x + 5y + 7 = 0, we can use the following steps:
Rewrite the equation of the circle in standard form: (x - a)^2 + (y - b)^2 = r^2, where (a, b) is the center of the circle and r is the radius.
In this case, the equation of the circle is already in standard form, so we can skip this step.
Find the slope of the line 3x + 5y + 7 = 0. The slope is -3/5.
Find the slope of the tangent to the circle. The slope of the tangent will be equal to the slope of the line, which is -3/5.
Substitute the slope of the tangent and the coordinates of a point on the circle into the point-slope form of the equation of a line: y - y1 = m(x - x1), where (x1, y1) is a point on the circle and m is the slope.
In this case, we can substitute the coordinates of the center of the circle (which is (0, 0)) and the slope of the tangent (-3/5) into the point-slope form to get:
y - 0 = (-3/5)(x - 0)
Simplify to get the equation of the tangent: y = -3/5x.
Therefore, the equation of the tangent to the circle 4x^2 + 4y^2 = 25 that is parallel to the line 3x + 5y + 7 = 0 is y = -3/5x.
Help please fast!! picture attached below 27 point
What is the mean number of points scored by these players?
A. 7
B. 8
C. 9
D. 10
Option (b) is correct as mean of top five scorers on soccer team is 8 from given bar graph.
What is mean in statistics?In statistics, in addition to the mode and median, the mean is one of the measures of central tendency. Simply put, the mean is the average of the values in the given set. It indicates that values in a particular data set are distributed equally. The three most frequently employed measures of central tendency are the mean, median, and mode. The total values provided in a datasheet must be added, and the sum must be divided by the total number of values in order to determine the mean. When all of the values are organized in ascending order, the Median is the median value of the given data. While the number in the list that is repeated a maximum of times is the mode.
Mean = (Sum of values)/(Total observations)
Using above formula, we get
Calculating mean for given bar graph,
[tex]=\frac{4+6+10+9+11}{5}\\=\frac{40}{5}\\=8[/tex]
So, mean score of five players comes out to be 8.
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