Answer:
The 5-hour decay factor for the number of mg of caffeine in Ben's body is of 0.1469.
Step-by-step explanation:
After consuming the energy drink, the amount of caffeine in Ben's body decreases exponentially.
This means that the amount of caffeine after t hours is given by:
[tex]A(t) = A(0)e^{-kt}[/tex]
In which A(0) is the initial amount and k is the decay rate, as a decimal.
The 10-hour decay factor for the number of mg of caffeine in Ben's body is 0.2722.
1 - 0.2722 = 0.7278, thus, [tex]A(10) = 0.7278A(0)[/tex]. We use this to find k.
[tex]A(t) = A(0)e^{-kt}[/tex]
[tex]0.7278A(0) = A(0)e^{-10k}[/tex]
[tex]e^{-10k} = 0.7278[/tex]
[tex]\ln{e^{-10k}} = \ln{0.7278}[/tex]
[tex]-10k = \ln{0.7278}[/tex]
[tex]k = -\frac{\ln{0.7278}}{10}[/tex]
[tex]k = 0.03177289938 [/tex]
Then
[tex]A(t) = A(0)e^{-0.03177289938t}[/tex]
What is the 5-hour growth/decay factor for the number of mg of caffeine in Ben's body?
We have to find find A(5), as a function of A(0). So
[tex]A(5) = A(0)e^{-0.03177289938*5}[/tex]
[tex]A(5) = 0.8531[/tex]
The decay factor is:
1 - 0.8531 = 0.1469
The 5-hour decay factor for the number of mg of caffeine in Ben's body is of 0.1469.
Instructions: State what additional information is required in order
to know that the triangles in the image below are congruent for the
reason given
Reasory. SAS Postulate
Answer:
HJ = FG
Step-by-step explanation:
SAS means side - (included) angle - side.
we have one angle confirmed (at H and at G).
we have actually one side confirmed (HG), because the graphic shows that this side is shared between the triangles. so, implicitly it is not only congruent but really identical.
so, we need the confirmation of the second side enclosing the confirmed angle.
A box plot is shown
O
2
4
6
8
10
12
Determine the five-statistical summary of the data. Drag the correct number to each variable in the summary.
14
16
18
20
22 24 26
28
30
Minimum:
Maximum:
Median:
First Quartile:
Third Quartile:
1
2
3
4
11
5
12
6
ما تا ته
13
14
8
21
15
22
16
10
23
17
24
18
25
19
26
20
27
28
29
30
Please answer fast
Answer:
Minimum = 8
Maximum = 28
Median = 22
First Quartile = 12
Third Quartile = 26
Step-by-step explanation:
✔️Minimum value = the value at the beginning of the whisker from your left = 8
✔️Maximum value = the value at the end of the whisker to your right = 28
✔️Median = the value at the vertical line that divides the box into two = 22
✔️First Quartile = the value at the beginning of the edge of the box = 12
✔️Third Quartile = the value at end of the edge of the box = 26
Pls help
Q.2 Choose the correct alternative for each question.
1. 400 is successor of ______.
A. 399 B.401 C. 398 D. 402
(1 Marks each)
2. The product of a non-zero whole number and its predecessor is always_________.
A. an odd number B. an even numberC. 0 D. a prime number
KHALSA LITTLE FLOWER SCHOOL | GRADE 6 | Mathematics 1
3. The predecessor of 1 million is ___________.
A. 99999 B. 1000001 C. 2000000 D. 999999
4. Whole numbers are closed under ________.
A. addition and subtraction B. addition and multiplication C. addition and division D. subtraction and division
5. The only whole number which does not have a predecessor is ________. A.2 B.0 C.3 D.1
6. ________ million make 1 crore.
A. 100 B. 10 C. 1000 D. 10,000
7. 3856 is rounded off to the nearest tens as ______.
A. 3850 B. 3860 C. 3800 D. 3000 8. In Roman numerals, the symbol ______ can be repeated.
A. D B. V C. X D. L
9. The Roman numeral for 91 is _______.
A. IXLL B. CXI C. IXC D. XCI
10. The Roman numeral LV stands for _______.
A. 65 B. 45 C. 55 D. 105
Answer:
Step-by-step explanation:
1-399
2 C
3-A 99999
4a
5b
7 b
8 C
9D
10c
A newspaper advertisement offers a $9,000 car for nothing down and for 36 easy monthly payments of $317.50 what is the simple interest rate?
Answer:
27%
Step-by-step explanation:
Let x = simple interest rate
$9000 / 36 = $250 per month
$250x = 317.5
Divide both sides by 250
250x/250 = 317.5/250
x = 1.27
Let's check
250 x 1.27 = 317.5
If you were to multiply by .27 then it would just go down
250 x .27 = 67.5
áp dụng quy tắc khai phương 1 tích hãy tính
Answer:
Please write out in english
Step-by-step explanation:
I cannot help unless you can translate.
The vertex form of the equation of a parabola is y =
standard form of the equation?
Y=1/2(x - 4)^2 +13. What is the
O A. y-2x2-8x+29
O B. y=zx2 - 4x +21
O C. y=1* -8x+21
O D. y - 4x2 - 4x +29
Answer:
Step-by-step explanation:
y = ½(x-4)² + 13
y = ½(x² - 8x + 16) + 13
y = ½x² - 4x + 21
what represent the relationship between the total mass of a crate
9514 1404 393
Answer:
(a) M = 0.25n +100
Step-by-step explanation:
The distance between the dots on the graph is a rise of 1 grid square and a run of 2 grid squares. If we extend the sequence of dots to the left, we expect to place one at (0, 100). That is, the y-intercept of this function is 100 (eliminates choices C and D).
The rise of 1 grid square represents 25 kg, and the run of 2 grid squares represents 100 CDs. Then the slope of the function (rate of change) is ...
slope = rise/run = 25/100 kg/CD = 0.25
Then the equation describing the points on the graph will be ...
M = 0.25n +100
Use: Ck = k! (n-k)!
n!
n k
to solve the combination.
How many ways can you
choose steak, fish, or chicken if you
can only choose two meats?
Answer:
3 ways.
Step-by-step explanation:
Combinations formula:
[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
In this question:
2 meats from a set of 3(steak, fish or chicken). So
[tex]C_{3,2} = \frac{3!}{2!1!} = 3[/tex]
3 ways.
A farm orders x horse shoes for its horses. The farm does not order extras and all the horses will get new horse shoes. Apply the k-to-1 rule to determine the number of horses on the farm. Express your answer as a function of x. You should not need the ceiling or floor functions.
Answer:
Here,
x/4
Then the
k-to-1 rule.
Suppose there is a k-to-1 correspondence from a finite set A to a finite set B. Then |B| = |A|/k.
Find the sum of -3x^2-4x+3 2x^2+3
Given that ƒ(x) = 3^x, identify the function g(x) shown in the figure. A) g(x) = −3^-x
B) g(x) = −(1∕3)^x
C) g(x) = 3^−x
D) g(x) = −3^x
Answer:
Option (D)
Step-by-step explanation:
From the graph attached,
Function 'f' is the reflected across x-axis to get the graph function 'g'.
Therefore, by definition of reflection across x-axis,
g(x) = -f(x)
g(x) = [tex]-3^x[/tex]
Option (D) will be the answer.
What is the distance between the points (7, 8) and (-8, 0) on a coordinate grid?
Answer:
17 units
Step-by-step explanation:
Use the distance formula, [tex]d = \sqrt{(x_2 - x_1)^2 + (y_2-y_1)^2}[/tex]
Plug in the points and simplify:
[tex]d = \sqrt{(x_2 - x_1)^2 + (y_2-y_1)^2}[/tex]
[tex]d = \sqrt{(-8 - 7)^2 + (0-8)^2}[/tex]
[tex]d = \sqrt{(-15)^2 + (-8)^2}[/tex]
[tex]d = \sqrt{225 + 64[/tex]
[tex]d = \sqrt{289[/tex]
[tex]d = 17[/tex]
So, the distance between the points is 17 units
Suppose the variable x is represented by a standard normal distribution. What is the probability of x > 0.3 ? Please specify your answer in decimal terms and round your answer to the nearest hundredth (e.g., enter 12 percent as 0.12).
Answer: 0.38
Step-by-step explanation:
Since the variable x is represented by a standard normal distribution, the probability of x > 0.3 will be calculated thus:
P(x > 0.3)
Then, we will use a standard normal table
P(z > 0.3)
= 1 - p(z < 0.3)
= 1 - 0.62
= 0.38
Therefore, p(x > 0.3) = 0.38
The probability of x > 0.3 is 0.38.
A small boat can travel at 28 per hour how many hours will it take to go across the bay that is 56 miles wide
Answer:
2 hours
Remember that time = distance/rate
The distance you need to cover is 56 miles, while you go 28 miles per hour. Using these, we get this:
time=56/28
time=2
So it will take two hours to go across a 56 mile wide bay at 28 mph.
Step-by-step explanation:
What three consecutive integers equal -87?
Answer:
What three consecutive integers have a sum of 87? Which means that the first number is 28, the second number is 28 + 1 and the third number is 28 + 2. Therefore, three consecutive integers that add up to 87 are 28, 29, and 30. We know our answer is correct because 28 + 29 + 30 equals 87 as displayed above.
Step-by-step explanation:
Consecutive integers are as simple as 1, 2, 3!
Integers are consecutive if one follows another. How do we "jump" from one integer to the next? We add 1, right? 7, 8 and 9 are three consecutive integers. Add one to 7 to get 8 and add one more to get 9.
Now lets think about this in algebraic terms. Lets name these consecutive integers , x, y and z.
The problem tells us that their sum is -87. (Recall, "sum" is just a fancy word for the answer when we add.)
x+y+z = -87
Here is the trick! We need to rewrite this equation so that we have only one variable. Easy!
y is one more that x, so y= x+1
And z is one more than y, so z= y+1. But y is also equal to (x+1)! So z=y+1=(x+1)+1=x+2
Now we have a problem that we can solve! x+(x+1)+(x+2)=-87.
Combining term.: 3x+3=-87
Subtract 3 from both sides of the equation: 3x=84
Divide each side of the equation by 3: x=28
We have solved for x, but we are not done! We need to find y and z. I know you can do this. Remember y is one more than x and z is one more than y.
Check your work! Make sure these three consecutive numbers do in fact add up to -87.
It takes 12 people 15 hours to complete and certain job.how many hours would it take 18 people, working at the same rate to complete 2/5 of the same job?
Answer:
9 hours
Step-by-step explanation:
12 people take 15 hours to complete one job. First let's ask how long it would take 18 people working at the same rate to complete the same job? We can use proportions to answer this
[tex]\frac{12 people}{15 hours} = \frac{18 people}{x hours}\\x = \frac{18\times15}{12} = 22.5[/tex]
Now we know that one job takes 18 people 22.5 hours, so 2/5 of the job would take
[tex]\frac{18\times15}{12} \times \frac{2}{5} = 9[/tex]
Find the 5 data points needed for a box plot of the given data set: { 8, 19, 11, 20, 2, 14, 17, 9, 15}
Give the answers in order from least to greatest.
Data Point 1:
Data Point 2:
Data Point 3:
Data Point 4:
Data Point 5:
Answers:
Data Point 1: 2 Data Point 2: 8.5 Data Point 3: 14 Data Point 4: 18 Data Point 5: 20The boxplot is shown below.
=========================================
Explanation:
What your teacher wants is the five number summary.
This consists of:
MinQ1MedianQ3MaxGiven in that exact order.
The given data set is { 8, 19, 11, 20, 2, 14, 17, 9, 15}
This sorts to {2, 8, 9, 11, 14, 15, 17, 19, 20}
From this sorted set, we see that 2 is the smallest item. So this is the min value. This is data point 1.
The max is the largest item, which in this case is 20, so this value goes in the box for data point 5.
---------------------
Count out the number of values in the sorted set. You should count out n = 9 items.
Because n is odd, this means the median is in slot n/2 = 9/2 = 4.5 = 5
The value in the 5th slot is 14 which is the median (data point 3).
-----------------------
Once you determine the median, break the sorted set up like so
L = {2, 8, 9, 11}
U = {15, 17, 19, 20}
L is the lower set of values smaller than the median
U is the upper set of values larger than the median
The median itself is not part of set L and not part of set U either. It's ignored entirely from this point on.
From here, we find the middle values of L and U
You should find that the middle value of L is (8+9)/2 = 17/2 = 8.5 which is the value of Q1 (data point 2)
And also, the middle value of set U is (17+19)/2 = 36/2 = 18 which is the value of Q3 (data point 4)
-----------------------
To wrap everything up, we have this five number summary
Min = 2Q1 = 8.5Median = 14Q3 = 18Max = 20These will determine the features of the boxplot as shown below.
In this case, there are no outliers.
find the form of the general solution of y^(4)(x) - n^2y''(x)=g(x)
The differential equation
[tex]y^{(4)}-n^2y'' = g(x)[/tex]
has characteristic equation
r ⁴ - n ² r ² = r ² (r ² - n ²) = r ² (r - n) (r + n) = 0
with roots r = 0 (multiplicity 2), r = -1, and r = 1, so the characteristic solution is
[tex]y_c=C_1+C_2x+C_3e^{-nx}+C_4e^{nx}[/tex]
For the non-homogeneous equation, reduce the order by substituting u(x) = y''(x), so that u''(x) is the 4th derivative of y, and
[tex]u''-n^2u = g(x)[/tex]
Solve for u by using the method of variation of parameters. Note that the characteristic equation now only admits the two exponential solutions found earlier; I denote them by u₁ and u₂. Now we look for a particular solution of the form
[tex]u_p = u_1z_1 + u_2z_2[/tex]
where
[tex]\displaystyle z_1(x) = -\int\frac{u_2(x)g(x)}{W(u_1(x),u_2(x))}\,\mathrm dx[/tex]
[tex]\displaystyle z_2(x) = \int\frac{u_1(x)g(x)}{W(u_1(x),u_2(x))}\,\mathrm dx[/tex]
where W (u₁, u₂) is the Wronskian of u₁ and u₂. We have
[tex]W(u_1(x),u_2(x)) = \begin{vmatrix}e^{-nx}&e^{nx}\\-ne^{-nx}&ne^{nx}\end{vmatrix} = 2n[/tex]
and so
[tex]\displaystyle z_1(x) = -\frac1{2n}\int e^{nx}g(x)\,\mathrm dx[/tex]
[tex]\displaystyle z_2(x) = \frac1{2n}\int e^{-nx}g(x)\,\mathrm dx[/tex]
So we have
[tex]\displaystyle u_p = -\frac1{2n}e^{-nx}\int_0^x e^{n\xi}g(\xi)\,\mathrm d\xi + \frac1{2n}e^{nx}\int_0^xe^{-n\xi}g(\xi)\,\mathrm d\xi[/tex]
and hence
[tex]u(x)=C_1e^{-nx}+C_2e^{nx}+u_p(x)[/tex]
Finally, integrate both sides twice to solve for y :
[tex]\displaystyle y(x)=C_1+C_2x+C_3e^{-nx}+C_4e^{nx}+\int_0^x\int_0^\omega u_p(\xi)\,\mathrm d\xi\,\mathrm d\omega[/tex]
The total amount of time university students in the United States spend sleeping grooming, eating and drinking, and traveling is about Average weekday time use for full-time college and university students in the US Sleeping 36.2% Leisure and sports 17.19% 3.3% 4.2% Grooming 13.8% 5.8% Eating and drinking Educational activities 10.0% 9.696 Traveling Other Work and related activities
Answer:
yes
Step-by-step explanation:
The total amount of time university students in the United States spend sleeping, eating and drinking, and doing leisure and sports is about: Average weekday time used for full-time college and university students in the US Sleeping 36.2% Leisure and sports 17.1% 3.3% Grooming 4.2% Eating and drinking 13.8% 5.8% Educational activities 9.6% Traveling 10.0% Other Work and related activities A A 1/3 of their total time 3/5 of their total time C) 1/2 of their total time 3/4 of their total time
How many hours of sleep does a typical college student get on a weekday?"Our data was consistent with what researchers have found in academic studies — that students are in bed, on average, seven to eight hours per weeknight," says Brian Wilt, Jawbone's head of data science and analytics.
How much time does the average college student spend sleeping?On average, college students get a whopping six hours of sleep a night according to a study by the University of Georgia. Lack of sleep can take a toll on your mental health, cause a reduction in cognitive performance and affect your memory capacity!
Learn more about the average college student spend sleeping at
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HELP!!!!!!!!!
What is | 12 − 2i |?
Answer:
Answer is 2√37
Step-by-step explanation:
since a+bi = sqrt(144+4) = sqrt(148) = 2sqrt37
For an ordered pair left parenthesis x comma y right parenthesis in a relation, the x element represents the
Answer:
the x éléments représente the domain
x represents the value on the x-axis and the coordinate is also known as abscissa.
What is coordinate geometry?Coordinate geometry is the study of geometry using the points in space. Using this, it is possible to find the distance between the points, the dividing line is m:n ratio, finding the mid-point of the line, etc.
For an ordered pair left parenthesis x comma y right parenthesis in a relation that is (x, y).
Here x represents the value on the x-axis and the coordinate is also known as abscissa.
More about the coordinate geometry link is given below.
https://brainly.com/question/1601567
The faces of all prisms are _____________.
triangles
circles
parallelograms
trapezoids
There is 60% chance of making $12,000, 10% chance of breaking even and 30% chance of losing $6,200. What is the expected value of the purchase?
Answer:
$5,340
Step-by-step explanation:
Given :
Making a probability distribution :
X : ___12000 ____0 _____-6200
P(X) __ 0.6 _____ 0.1 _____ 0.3
Tge expected value of the purchase si equal to the expected value or average, E(X) :
E(X) = ΣX*p(X)
E(X) = (12000 * 0.6) + (0 * 0.1) + (-6200 * 0.3)
E(X) = 7200 + 0 - 1860
E(X) = $5,340
What is the measure of the angle in red?
70°
Answer:
See pic below.
Answer: C. 380°
Step-by-step explanation:
Heather has $45.71 in her savings account. She bought six packs of markers to donate to her school. Write an expression for how much money she has in her bank account after the donation
Answer:
45.71 - 6x = y
Step-by-step explanation:
x is the cost of the packs of markers
y is how much money she has left in her bank account
A washer and a dryer cost $858 combined. The washer costs $92 less than the dryer. What is the cost of the dryer?
Answer:
383
Step-by-step explanation:
Let dryer be d.
(d + 92) + d = 858
2d + 92 = 858
-92 = -92
---------------------
2d = 766
---- ------
2 2
d = 383
The dryer is $383
Hope this helped.
Answer:
$475
Step-by-step explanation:
The dryer costs x.
Since the washer costs $92 less than the dryer, then the dryer costs x - 92.
Combined, they cost $858.
x + x - 92 = 858
2x - 92 = 858
2x = 950
x = 475
Answer: $475
14. The area of 10 square plots is 160 ares. Find the length in metres of the side of each plot (3mks)
Answer:
Step-by-step explanation:
1 are = 100 m²
Assuming the ten squares are congruent, the area of each square is 160/10 = 16 are
16 are × 100 m²/are = 1600 m²
each side is √1600 = 40 m
The length of side of plot is 40 meters.
What is area?The total space occupied by a flat (2-D) surface or shape of an object is known as area.
Draw a square on a piece of paper with a pencil. It has two dimensions. The term "area" refers to the area that the shape occupies on the paper.
Now picture your square as being comprised of smaller unit squares. The number of unit squares required to cover a 2-D shape's total surface area is used to calculate its area.
Given the area of 10 square plot is 160 are,
here 1 are = 100 m²
area of 10 square plot = 160 x 100 = 16,000 m²
area of 1 square plot = 16000/10 = 1600 m²
area of square is "a²"
where a is side of square
area = a² = 1600 m²
a = √1600
a = 40 m
Hence the length of side of each plot is 40 meters.
Learn more about area;
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What is the are of the polygon below!help please!
Answer:
Area= 525
Step-by-step explanation:
14x9=126
3x7=21
14x27=378
126+21+378=525
What is the next fraction in each of the following patterns? a. 1⁄40, 4⁄40, 9⁄40, 16⁄40, 25⁄40 . . .? b. 3⁄101, 4⁄101, 7⁄101, 11⁄101, 18⁄101, 29⁄101 . . .? c. 5⁄1, 10⁄2, 9⁄2, 18⁄4, 17⁄8, 34⁄32, 33⁄256 . . .?
Answer:
a.
[tex] \frac{36}{40} [/tex]
The scores of students on a standardized test are normally distributed with a mean of 300 and a standarddeviation of 40.
(a) What proportion of scores lie between 220 and 380 points?
(b) What is the probability that a randomly chosen student scores is below 260?
(c) What percent of scores are above 326.8 points?
Answer:
a) 0.9544 = 95.44% of scores lie between 220 and 380 points.
b) 0.1587 = 15.87% probability that a randomly chosen student scores is below 260.
c) 25.14% of scores are above 326.8 points.
Step-by-step explanation:
Normal Probability Distribution
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score 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 p-value, we get the probability that the value of the measure is greater than X.
Mean of 300 and a standard deviation of 40.
This means that [tex]\mu = 300, \sigma = 40[/tex]
(a) What proportion of scores lie between 220 and 380 points?
This is the p-value of Z when X = 380 subtracted by the p-value of Z when X = 220.
X = 380
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{380 - 300}{40}[/tex]
[tex]Z = 2[/tex]
[tex]Z = 2[/tex] has a p-value of 0.9772.
X = 220
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{220 - 300}{40}[/tex]
[tex]Z = -2[/tex]
[tex]Z = -2[/tex] has a p-value of 0.0228.
0.9772 - 0.0228 = 0.9544
0.9544 = 95.44% of scores lie between 220 and 380 points.
(b) What is the probability that a randomly chosen student scores is below 260?
This is the p-value of Z when X = 260. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{260 - 300}{40}[/tex]
[tex]Z = -1[/tex]
[tex]Z = -1[/tex] has a p-value of 0.1587.
0.1587 = 15.87% probability that a randomly chosen student scores is below 260.
(c) What percent of scores are above 326.8 points?
The proportion is 1 subtracted by the p-value of Z when X = 326.8. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{326.8 - 300}{40}[/tex]
[tex]Z = 0.67[/tex]
[tex]Z = 0.67[/tex] has a p-value of 0.7486.
1 - 0.7486 = 0.2514
0.2514*100% = 25.14%
25.14% of scores are above 326.8 points.
