Answer:
dA/dt = k1(M-A) - k2(A)
Step-by-step explanation:
If M denote the total amount of the subject and A is the amount memorized, the amount that is left to be memorized is (M-A)
Then, we can write the sentence "the rate at which a subject is memorized is assumed to be proportional to the amount that is left to be memorized" as:
Rate Memorized = k1(M-A)
Where k1 is the constant of proportionality for the rate at which material is memorized.
At the same way, we can write the sentence: "the rate at which material is forgotten is proportional to the amount memorized" as:
Rate forgotten = k2(A)
Where k2 is the constant of proportionality for the rate at which material is forgotten.
Finally, the differential equation for the amount A(t) is equal to:
dA/dt = Rate Memorized - Rate Forgotten
dA/dt = k1(M-A) - k2(A)
Please help! Correct answer only, please! Determine the value of the following if it is possible. If it is not possible, explain. A. B. C. D.
Answer: C
Step-by-step explanation:
Multiply the number outside of the matrix to EVERY value inside that matrix.
Addition and subtraction of matrices is very simple - just add (or subtract) the values of each matrix that have the same designation.
[tex]X\left[\begin{array}{cc}a&b\\c&d\end{array}\right] +Y\left[\begin{array}{cc}e&f\\g&h\end{array}\right]=\left[\begin{array}{cc}X(a)+Y(e)&X(b)+Y(f)\\X(c)+Y(g)&X(d)+Y(h)\end{array}\right]\\\\\\\\\\-3\left[\begin{array}{cc}2&7\\8&-6\end{array}\right] +2\left[\begin{array}{cc}0&1\\4&-2\end{array}\right]\\\\\\=\left[\begin{array}{cc}-3(2)+2(0)&-3(7)+2(1)\\-3(8)+2(4)&-3(-6)+2(-2)\end{array}\right] \\\\\\=\left[\begin{array}{cc}-6&-19\\-16&14\end{array}\right][/tex]
True or False - the following scenario depicts an independent relationship between variables (tree growth and air quality): 20% of trees growing in a particular region are not growing to their expected height. In a particular neighborhood in that region, the Air Quality Index is labeled as "Unhealthy for Sensitive Groups" or worse 30% of the time. 10% of the trees in the region grow in this neighborhood. If you randomly measured the growth of a tree in that neighborhood, then the probability that that tree is not growing to its expected height is 33.33%.
For the polynomial below, what is the coefficient of the term with the power of 3?
A.0
B.1
C.6
D.5
Answer:
Option B
Step-by-step explanation:
x^3
Coefficient = 1
Option B
Answer:
B = 1
Step-by-step explanation:
this is becus we don't write 1 as a coefficient it's there but in an invisible form
anyone who make the one visible is considered an amateur
I need HELP! is the missing value 25?
Answer: choice3) 25
Step-by-step explanation:
The constant ratio of y/x is 2.5
so if the x value is 10 the y value would be 25(10*2.5).
The graph of a linear function is a _______
The graph of a linear function is a straight line.
Robin read somewhere that adding salt to water while heating it will raise the temperature of
the water causing it to boil faster. To test this claim, she filled 30 identical pots with one quart
of water. She randomly selected 15 of the pots and added 1 teaspoon of salt. She then placed
each pot on identical burners set to the highest setting. She measured the water temperature
In each pot after 5 minutes.
Is Robin's research method an example of an observational study experiment, or
simulation?
b
If Robin does find that there is a difference between the water temperatures in the pots
with salt compared to those without can she conclude that the salt caused the
difference in temperature?
Answer:
a. An experiment
b. No
Step-by-step explanation:
a. Robin's research method can be concluded to be an experiment because she has a testable group (pots of water with salt) and a control group (pots of water without salt).
2. Based on this alone, she cannot conclude that the salt caused the
difference in temperature because she has not set some appropriate conditions which are to be met for this test.
(3х^2y^3)^3 =
3x^5y^6
9х^6y^9
27x^5y^6
27x^6y^9
Answer:
27x^6y^9
Step-by-step explanation:
The outside exponent multiplies all of the inside exponents. The applicable rules of exponents are ...
(ab)^c = (a^c)(b^c)
(a^b)^c = a^(bc)
__
(3x^2y^3) = (3^3)(x^(2·3))(y^(3·3)) = 27x^6y^9
how do you find the zero(s) of a polynomial function
Answer:
by using the quadratic formula
Step-by-step explanation:
negative b plus or minus the square root of b squared minus 4ac, then all divided by 2a
A restaurant serves hot chocolate that has a mean temperature of 175 degrees with a standard deviation of 6.2 degrees. Find the probability that a randomly selected cup of hot chocolate would have a temperature of less than 164 degrees. Would this outcome warrant a replacement cup (meaning that it would be unusual)?Group of answer choices
Answer:
3.8% , unusual
Step-by-step explanation:
We have that the mean is 175 degrees (m) and the standard deviation is 6.2 degrees (sd), so we are asked:
P (x <164)
P ((x - m) / sd <(164 -175) /6.2)
P (z <- 1.77)
If we look in the normal distribution table we have to:
P (x <164) = 0.0384
That is, the probability is 3.8%
Unusual is when the probability is less than 5%, that is to say in this case if it can be said that an unusual data.
Brian flips a fair coin 3 times. What is the probability of getting exactly 2 tails?
Answer:
3/8
Step-by-step explanation:
The possible outcomes
TTT TTH THT THH HHH HHT HTH HTT = 8 outcomes
There are TTH THT HTT 3 with exactly two tails
P ( exactly 2 tails) = 3/8
Answer:
[tex]\frac{3}{8}[/tex]
Step-by-step explanation:
The outcomes you are looking for are either HTT, THT, or TTH.
The possibility to toss tails or heads is 0.5. Thus the possibility to throw T and then H and then H is:
[tex]\frac{1}{2} \times \frac{1}{2} \times \frac{1}{2} = \frac{1}{8}[/tex]
We have three ways of getting 2 tails, the possibility of throwing exactly two tails in three tosses is:
[tex]\frac{1}{8} + \frac{1}{8} + \frac{1}{8} = \frac{3}{8}[/tex]
0.375 is the probability of getting exactly 2 tails in 3 tosses.
{0 tails}={HHH}
{1 tails}={TTH, THT, HTT}
{2 tails}={HTT, TTH, THT}
{3 tails}={TTT}
There are 3 cases with getting two tails out of 8 possible outcomes.
Sean wants to buy a personal insurance policy that will pay monthly benefits to his son after Sean dies. He pays $500
monthly over the next 10 years to the insurer.
What type of insurance should he buy?
A annuity
B premium
C dividends
D liability
Answer:
B.
Step-by-step explanation:
Premium insurance is an insurance amount paid to the insurer periodically. In this type of insurance, the insurer is required to provide coverage. This insurance policy covers healthcare, life, auto, home, etc. In this insurance, one is required to pay a certain amount of money on monthly, quarterly, or annually basis.
In the given scenario, Sean should buy premium insurance as it covers life and healthcare insurance as well. He can pay $500 on monthly basis to the insurance company. And after Sean's death, his son can claim the amount.
So, the correct answer is option B.
Answer:
A. annuity
Step-by-step explanation:
I know it is a little late for this answer, but I thought I would add it for anyone else who is struggling :) I know it is annuity because I literally just took the test and got it right.
In an aquarium, there are 4 large fish and 16 small fish. Half of the small fish are blue. One fish is selected at random. Find the probability that it is a small, blue fish. Write your answer as a fraction in simplest form.
Answer:
2/5
Step-by-step explanation:
There are 20 fish, 8 of which are small and blue. Therefore, the probability of randomly selecting a small blue fish is 8/20 = 2/5.
Solve the system of equations. \begin{aligned} & -9x+4y = 6 \\\\ & 9x+5y=-33 \end{aligned} −9x+4y=6 9x+5y=−33
Answer:
x = -2
y = -3
Step-by-step explanation:
We can use either substitution or elimination for this problem. I will use elimination to solve this problem:
Step 1: Eliminate x by adding the 2 equations together
9y = -27
y = -3
Step 2: Plug in y into one of the original equations to get x
-9x + 4(-3) = 6
-9x -12 = 6
-9x = 18
x = 2
And we have our final answers!
The height of a stream of water from the nozzle of a fire hose is modeled by h(x) =-0.03x2+ 2x + 38 where h(x) is the height in feet, of the stream of water x feet from the fire truck. 1. What is the maximum height the water from this nozzle can reach? What is the maximum distance from the firetruck a firefighter can stand and still reach the fire?
Answer:
height: 71.33 feetreach: 82.10 feetStep-by-step explanation:
The equation can be rewritten to vertex form:
h(x) = -0.03(x² - 200/3x) +38
h(x) = -0.03(x² -200/3x +(100/3)²) +38 +.03(100/3)²
h(x) = -0.03(x -33 1/3)² +71 1/3
The vertex is (33 1/3, 71 1/3), so the maximum height the water will reach is 71 1/3 feet.
__
When h(x) = 0, the water reaches as far as it possibly can.
0 = -0.03(x -33 1/3)² +71 1/3
(-71 1/3)/(-0.03) = (x -33 1/3)² . . . subtract 71 1/3; divide by -0.03
√(2377.78) = x -33.33 . . . . . . . . positive square root
82.10 ≈ x
The maximum distance the water will reach is 82.10 feet.
Complete the following subtraction exercises.
10 – 2 =
14 – 6 =
15 – 9 =
17 – 8 =
13 – 5 =
11 – 8 =
20 – 8 =
16 – 7 =
12 – 9 =
21 – 9 =
11 – 6 =
5 – 5 =
4 – 0 =
16 – 8 =
10 – 5 =
18 – 7 =
13 – 8 =
12 – 4 =
Answer:
Below
Step-by-step explanation:
8,8,6,9,8,3,12,9,3,12,5,0,4,8,5,11,5,8. Answers are in order from the first to the last
-3
n is an integer.
Write down the possible values of n.
I
Answer:
since n is an integer you substitute n with all the integers. But since that is too much you should use infinity.
n=[-∞,+∞] where -∞ is a negative infinity which stands for negative numbers and +∞ is a positive infinity where it stands for positive numbers.
an integer contains negative and positive numbers so above is the answer.
Step-by-step explanation:
Need help ASAP please
Answer:
r = l / π/180× θ
11.6 cm
Step-by-step explanation:
l = π/180 × r × θ
r = l / π/180× θ
r = 12.5 / π/180× 62
r = 11.55156845
a boat operator in a boat can travel 15m/sec in still water he tries to cross a river which is flowing at 5 m/sec south. A) what is the resultant velocity of the boat? B) The takes exactly 55 seconds to cross the river in the resulting velocity, how many meters did the boat travel?
Answer:
a) 15.8 ms-1
b)869 m
Step-by-step explanation:
We have to obtain the resultant velocity by the Pythagorean theory;
R^2= V1^2 + V2^2
Where
R= resultant velocity of the boat
V1= velocity of the boat
V2= velocity of the flowing river
Thus;
R= √V1^2 + V2^2
R= √15^2 + 5^2
R= √225 + 25
R= √250
R= 15.8 ms-1
B) from
v= s/t
Where
v= velocity (resultant velocity in this case)
s= distance
t= time (55 secs)
s= vt
s= 15.8×55
s= 869 m
which table has the largest area, square tables with a side length of 36 inches, rectangular table 20 inches wide and 73 inches long, round tables with a diameter of 42 inches
Answer:
rectangular table
Step-by-step explanation:
You want to know the largest area of tables that are ...
36 inches square20 inches by 73 inches42 inches in diameterArea FormulasThe formulas for the areas of the various shapes are ...
square: A = s²rectangle: A = LWcircle: A = πr² . . . . . . where r is half the diameterSquareThe area of the square table is ...
A = (36 in)² = 1296 in²
RectangleThe area of the rectangular table is ...
A = (20 in)(73 in) = 1460 in²
CircleThe area of the round table is ...
A = π(21 in)² ≈ 1385 in²
The rectangular table has the largest area.
__
Additional comment
You can eliminate the square table right away by realizing the rectangular table is more than twice as long, and more than half as wide. If the rectangle were 18 in by 72 in, it would have the same area as the square.
Find the equation for the plane through the points Upper P0 (-2 ,2 ,-5),Q0 (1,2,-1), and Upper R0 (-1,-5,4 ).
The equation of plane is:________
Answer:
28x - 23y - 21z = 3
Step-by-step explanation:
First, we need to find two vectors in the plane as:
vector PQ = Q - P = (1, 2, -1) - (-2, 2, -5) = (3, 0, 4)
vector PR = R - P = (-1, -5, 4) - (-2 ,2 ,-5) = (1, -7, 9)
Then, we need to find a normal vector to the plane as:
PQ x RQ = ((0*9)-(4*-7), -(3*(9)-(4*1), (3*-7)-(0*1))
PQ x RQ = (28, -23, -21)
Finally, the equation of a plane is:
A(x-x0) + B(y-y0) + C(z-z0) = 0
Where (A,B,C) is a normal vector to the plane and (x0, y0, z0) is a point in the plane. So, replacing (A,B,C) by (28, -23, -21) and (x0, y0, z0) by P0(-2,2,-5), we can write the equation of the plane as:
28(x+2) - 23(y-2) - 21(z+5) = 0
Solving, we get:
28x + 56 - 23y + 46 - 21z - 105 = 0
28x - 23y - 21z - 3 = 0
28x - 23y - 21z = 3
To examine the effect of high-dose green tea extract on weight loss, researchers conducted a randomized, double-blind trial on a random sample of 115 women with obesity from Taiwan. Some of these women were randomly assigned to the main treatment group taking a high-dose green tea extract ("EGCG") daily for 12 weeks. The published abstract of this 2015 study reports that, "Significant weight loss, from 76.8 ± 11.3 kg to 75.7 ± 11.5 kg (p = 0.025), was observed in the treatment group after 12 weeks of high-dose EGCG treatment."
Which of the following inference procedures would be used to reach the quoted conclusion?
a. Z procedure for a proportion
b. Chi-square for two-way tables
c. Chi-square for goodness of fit
d. Two sample t procedure for two means
e. One sample or matched-pairs t procedure for a mean
f. ANOVA for several means
Answer:
d. Two sample t procedure for two means.
Step-by-step explanation:
The study have a treatment group, which is the group of women that are taking the high dose of green tea extract, and a control group, in order to compare. They are assigned randomly to each group.
Then, the difference fo the two sample means is calculated and a t-test is performed in order to conclude if the two populations means are significantly different.
Apparently they are significantly different, as this is the conclusion with a P-value of 0.025.
find the slope of the line that passes through the points (5,1) and (-4,1)
Answer:
B. 0
Step-by-step explanation:
To find slope, use [tex]m = \frac{y2 - y1}{x2 - x1}[/tex] to find m in y = mx + b. Your m is always your slope.
Simplify the expression. (-3 + 6i)(-3 + 5i)
Answer:
11i-6
Step-by-step explanation:
Answer:
11i-6
Step-by-step explanation:
(-3+6i)(-3+5i)
combine like terms (-3)+(-3)=-6
6i+5i=11i
Stephanie spent $110 on 1.7 pounds of coffee. she wants to know how much each pound costs. how would she find out how much each pound costs? write equation and explain how you got that answer.
$64.71 rounded, explanation attached
EASY question will rate brainliest no explanation neccesary
Answer: choice A
Step-by-step explanation:
the shaded parts add up to 4wholes and 1/4
or 17/4=4 1/4
The Fan Cost Index (FCI) represents the cost of four average-price tickets, refreshments, and souvenirs to a sporting event. The FCIs for an independent golf league and an independent arena football league totaled $124.41. The arena football FCI was $7.79 more than that of golf. What were the FCIs for these sports?
Answer:
Golf league FCI = $58.31
Arena football league FCI = $66.10
Step-by-step explanation:
Let G be the fan cost index for the golf league and F be the fan cost index for the football league. The following system of equations can be modeled from the given information:
[tex]F+G = 124.41\\F=G+7.79[/tex]
Solving this linear system (substituting the second equation into the first one):
[tex]7.79+G+G = 124.41\\G= \$58.31\\F = 58.31+7.79\\F=\$66.10[/tex]
Golf league FCI = $58.31
Arena football league FCI = $66.10
The beginning balance on a monthly bank statement for ignatius checking account was $124.82, and the ending balance was $659.27. What can be said about Ignatius transactions for the month
Answer:
He had 534.45 more in credits that debits
Step-by-step explanation:
Ignatius hd $534.45 more in credits than in debits. Since Ignatius had an initial balance of $124.82 at the beginning of the month and ended the month with $659.27 he was up money versus what he had in his account at the beginning of the month. During the month Ignatius made money that was credited to his account so that he ended it with a higher balance.
15 less than three times the width 3
its the answer 3w-15?
Answer:
Yes, the answer is 3w-15
Step-by-step explanation:
-15 (fifteen less than)
3w (three times the width)
The angles of a triangle are such that one angle is 100 degrees more than the smallest angle, while the third angle is 2 times as large as the smallest angle. Find the measure of all three angles.
Answer:
20, 40, 120
Step-by-step explanation:
Smallest angle = x
Second angle = x + 100
Third angle = 2x
4x + 100 = 180
4x = 80
x = 20
20, 120, 40
Use the given data to construct a box plot and identify the 5-number summary. Eleven different second-year medical students at Bellevue Hospital measured the blood pressure of the same person. The systolic readings (mmHg) are listed below.
{ 130, 135, 140, 120, 130, 130, 144, 143, 140, 130, 150 }
Answer:
[tex] Min =120, Max= 150[/tex]
The first quartile can be calculated with this data:
130, 135, 140, 120, 130, 130
And the middle value is:
[tex] Q_1 = \frac{140+120}{2}=130[/tex]
The median is the value in the 6th position from the dataset ordered and we got:
[tex] Median= 135[/tex]
The third quartile can be calculated with this data:
135 140 140 143 144 150
And the middle value is:
[tex] Q_3 = \frac{140+143}{2}=141.5[/tex]
The five number summary for this case:
Min. 1st Qu. Median Mean 3rd Qu. Max.
120.0 130.0 135.0 135.6 141.5 150.0
The boxplot is on the figure attached
Step-by-step explanation:
We have the following data given:
130, 135, 140, 120, 130, 130, 144, 143, 140, 130, 150
If we sort the values on increasing order we got:
120 130 130 130 130 135 140 140 143 144 150
The minimum and maximum are:
[tex] Min =120, Max= 150[/tex]
The first quartile can be calculated with this data:
130, 135, 140, 120, 130, 130
And the middle value is:
[tex] Q_1 = \frac{140+120}{2}=130[/tex]
The median is the value in the 6th position from the dataset ordered and we got:
[tex] Median= 135[/tex]
The third quartile can be calculated with this data:
135 140 140 143 144 150
And the middle value is:
[tex] Q_3 = \frac{140+143}{2}=141.5[/tex]
The five number summary for this case:
Min. 1st Qu. Median Mean 3rd Qu. Max.
120.0 130.0 135.0 135.6 141.5 150.0
The boxplot is on the figure attached