A) The number of people who have started the rumor is N(0)=12
B) The number of students who are in the school are 1800
C) The number of days the rumor spreads to ½ the student body are 8 days.
D) The number of students who have heard the rumor when the rumor is spreading the fastest are 900.
The rate of change in students per day at this time is 281.
What is meant by rate of change?The rate of change is a mathematical term that describes the percentage change in value over a given time period and represents the momentum of a variable.
A) Number of people who have heard the rumor after t days is given by:
N (t) = 1800/1+149e^-0.625t
At start t=0, so from the above equation at t=0, we get
N(0)=(1800)/1+149e^0
N(0)=1800/(1+149(1))
N(0)=1800/150
N(0)=12
B) At t=∞, all of the students would have heard the rumor. So putting t↔∞ in the above equation we get,
[tex]\lim_{t \to \infty}[/tex]N(t)=[tex]\lim_{t \to \infty}[/tex] 1800/1+149e^-0.625t
=1800/(1+0)
=1800
Therefore, the number of students in the school are 1800.
C) Putting N=1800/2 in the above equation, we get
1800/2= 1800/1+149e^-0.625t
1+149e^-0.625t=2
e^-0.625t=(2-1)/149
=1/149
Taking log on both sides, we get
ln(e^-0.625t)=ln(1/149)
-0.625t=-ln(149)
t=ln(149)/0.625
t=8.006≈8
D) N'(t)=0.625N(1-(N/1800)
=0.625(N-(N²/1800)
=(0.625/1800)(1800N-N²)
=(0.625/1800)(900²-900²+1800N-N²)
=(0.625/1800)(900²-(N²-1800N+900²)
N'(t)=(0.625/1800)(900²-(N-900)²)
For N to be maximum,
N=900
Thus, rumor is spreading fastest when 900 students have heard the rumor.
And rate of change in students per day is obtained by putting N=900 in expression of N'(t) as follows:
N'(t)=(0.625×900)(1-(900/800))
N'(t)=281.25≈281
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(1 point) find how many positive integers with exactly four decimal digits, that is, positive integers between 1000 and 9999 inclusive, have distinct digits :
The number of positive integers with exactly four decimal digits that is positive integers between 1000 and 9999 is 4536.
The positive integers between 1000 and 9999 inclusive have 4 digits.
The first digit cannot be zero because otherwise, it will become a digit integer.
So, the first digit can be filled in 9 ways.
The second digit can be filled by 9 different ways.
Because the second digit cannot be the same as that of the first digit but zero can be the second digit.
The third digit can be filled by 8 different ways.
The fourth digit can be filled in 7 different ways.
Number of four decimals digits = 9 * 9 * 8 * 7
= 81 * 8 * 7
= 81 * 56
= 4536 digits.
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Sketch the curve with the given vector equation by finding the following points. (Select Update Graph to see your response plotted on the screen. Select the Submit button to grade your response.)
r(t) = 2 cos(t)i + 2 sin(t)j + k r(0 (x, y, z) = (x, y, z) = -() -C (39) (x, y, z) = (x, y, z) = (Tt) (x, y, z) = (1) (X, Y, 2) = (33) (1) (x, y, z) = (x, y, z) = r(27) (x, y, z) =
Zoe goes to a restaurant and the subtotal on the bill was xx dollars. A tax of 5% is applied to the bill. Zoe decides to leave a tip of 15% on the entire bill (including the tax). Write an expression in terms of xx that represents the total amount that Zoe paid.
The expression in terms of x that represents the total amount that Zoe paid is 1.2075x
What is an expression that represents the total amount that Zoe paid?Expression are simply used to illustrate the datathat are given. It should be noted that it's usually represented by the variables given.
From the information, Zoe goes to a restaurant and the subtotal on the bill was x dollars. A tax of 5% is applied to the bill and Zoe decides to leave a tip of 15% on the entire bill.
The expression will be:
= x + (5% × x) + (15% × 1.05x)
= x + 0.05x + 0.1575x
= 1.2075x
Therefore, the expression based on the above will be 1.2075x.
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in a proof what is the reason that justifies this statement: segment bp is congruent to segment bp.
The necessary explanation is that segment BP is congruent to segment BP, which is the common side of both triangles.
Two figures or items are congruent in geometry if they have about the same size, or if one has the same shape and size as its mirror counterpart.
As seen in the illustration, segment BP and segment BP are congruent since segment BP is the common side of both triangles BPS and BPY.
As a result, the necessary explanation seems to be that segment BP is congruent to segment BP and that segment BP is the identical side of both triangles.
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To lose weight, Kelly reduced her caloric intake from 2000 per day to 1360 per day. What is the percent of decrease in calories
Step-by-step explanation:
2000-1360=640
%change=640/2000×100
=32%
If the cos 0 = 5/13 and tan 0 = 12/5, what is sin 0?
Answer:
sin(x) = 12/13
Step-by-step explanation:
cos^(-1)(5/13) = 0.176
tan^(-1)(12/5) = 0.176
sin(0.176 radians) = 12/13
Brainliest, please!Prove that x^3+15x^2+74x+120 is always divisible by 6. Please
It is true that the polynomial is divisible by 6
How to prove the division of the polynomial?From the question, we have the following polynomial that can be used in our computation:
Polynomial = x^3+15x^2+74x+120
Divisor = 6
Rewrite the given parameters as
P(x) = x³ +15x² + 74x + 120
x = -6
Substitute x = -6 in the equation P(x) = x³ +15x² + 74x + 120
P(-6) = (-6)³ +15(-6)² + 74(-6) + 120
Evaluate
P(-6) = 0
because the result is 0, the polynomial is divisible
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Y= -4 cos 5x -10 please answer this someone
The trigonometric function, Y = -4·cos 5·x - 10 is undefined at Y = 0, but the function arranged as Y = -4·cos(5·x - 10) has an x-intercept at x = π/10 + 2
What is a trigonometric function?A trigonometric function indicates the relationship between angles and the lengths of sides of angles.
The specified function can be presented as follows;
Y = -4·co(5·x) - 10
There are two unknown variables
The number of equations is one
The number of equations is less than the number of unknowns, the equation is said therefore, to be undetermined.The function, at Y = 0, can be evaluated as follows;
Y = 0 = -4·co(5·x) - 10
cos(5·x) = 10/(-4) = -2.5
5·x = arccos(-2.5) = Undefined
However, when the function is; Y = -4·cos((5·x) - 10), we get;
At Y = 0
0 = -4·cos((5·x) - 10)
cos((5·x) - 10) = 0/(-4) = 0
5·x - 10 = arccos(0) = π/2
Therefore;
x = (π/2 + 10)/5 = π/10 + 2
(-π/2 + 10)/5
An x-intercept is at x = π/10 + 2
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approximately what does the box portion of a boxplot display? group of answer choices the upper quarter of the data the middle half of the data the lower quarter of the data the middle quarter of the data
The box portion of a boxplot display the middle half of the data.
We know that a box and whisker plot which is also known as a box plot.
It represents the five-number summary of dataset.
This five-number summary is nothing but the minimum, first quartile, median, third quartile, and maximum.
In box and whisker plot, we draw a box from the first quartile to the third quartile.
In bosplot, the left and right sides of the box are the lower and upper quartiles.
The box covers the 50% of the data is found. It covers the interquartile range.
Therefore, the box portion displays the middle half of the data.
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a rectangular block of mass m has dimensions as shown. in terms of m, a, b and c, find the rotational inertia of the block about an axis of rotation through one of the corners of the block which is perpendicular to the large faces. b. let m
The answer of the given question is A rectangular block of mass m has an inertia moment of Bh3/3.
What is moment of inertia?When a body resists having the direction of its rotation along an axis changed by the application of a torque, this resistance is referred to as having moment of inertia. There are four types of axes: internal, external, fixed, and moving. It is possible to calculate the moment of inertia (I), which is always expressed in terms of that axis, by adding the results of multiplying each particle's mass by the square of its distance from the axis within the particular body. Moment of inertia is the same as mass in linear momentum when calculating the angular momentum of a rigid body.
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a If you have 2/3 of your first 18-egg carton full, how many more eggs will fit in that
carton? What fraction card will you need to draw to fill the first carton exactly?
Answer:
6 eggs
Step-b6y-step explanation:
18 - (18× 2/3) = 6
●●●●●●/●●●●●●/○○○○○○
if f=72 when a=9 find a when f=56
Answer: just use the internet
Step-by-step explanation:
boom yo answer
how would the test statistic change for the wilcoxon rank sum test for the crickets data if the largest value in the fed group had actually been 100 hrs?
The assumptions of the two-sample t-test for comparing two population means:
1. The two samples are independent of one another.
2. The two populations have equal variance or spread.
3. The two populations are normally distributed.
The Wilcoxon test is based upon ranking the nA +nB observations of the combined sample. Each observation has a rank: the smallest has rank 1, the 2nd smallest rank 2, and so on. The wilcoxon rank-sum test statistic is the sum of the ranks for observations from one of the samples.
The Wilcoxon signed rank test is a non-paracontinuouse-level test, in contrast to the dependent samples t-test.
Wilcoxon tests have about 95% of the power of a t-test if the data really are normal, and are often far more powerful if the data is not, so just use a Wilcoxon.
The Wilcoxon test may produce misleading results if many measurements are the same value. When many values are the same, their relative ranks are the same, and this has the effect of diluting the test.
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a clinical sample of patients with anorexia nervosa is randomly assigned to receive either cognitive-behavioral or psychodynamic therapy. upon completion of treatment, all participants are exposed to three different types of everyday stressors at different times. after exposure to each stressor type, the amount of food consumed by participants is recorded. which is the correct classification of this design?
2x3 mixed factorial design is the correct classification of this design.
In the given question, we have to find which is the correct classification of this design.
Three subgroups can be identified within this clinical grouping, though there are no clear divisions between them. The first category includes instances that closely resemble anorexia nervosa or bulimia nervosa but fall short of the diagnostic criteria's cutoff point.
Cases where the characteristics of AN and BN occur in various combinations from those seen in the prototypic illnesses make up the second and largest class.
Those who suffer from binge eating disorder make up the third grouping.
So, 2x3 mixed factorial design is the correct classification of this design.
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The right question is given below:
What is the value of x?
1/4 (6x - 2) = x - 2
Answer:
Step-by-step explanation:
0
Answer:
x = 3
Step-by-step explanation:
1/4 (6x - 2) = x - 2
1.5x - 0.5 = x - 2
1.5x = x - 1.5
0.5x = 1.5
x = 3
Could you please give me brainliest for this? Thank you!
5. Find the value of x.
48
8x
Answer:
Step-by-step explanation:
try 6
Answer: 6
Step-by-step explanation: 6 x 8 = 48
Before doing laundry, an unlucky student must recover from illness. The number of days the student is ill is determined as follows. We toss a fair coin and we roll a fair 6-sided die. If the coin is heads, the student is ill for n days, where n is the outcome of the die roll. If the coin is tails, the student is ill for 2n days, where n is the outcome of the die roll. What is Ex(u)? Example: If the die roll is 5, the student delays for U = 5 days if the coin toss is heads and U = 10 days if the coin toss is tails.
The student will be out of class for 2n days if the coin comes up tails, where n is the result of the die roll, which the probability will be 25.
An unfortunate student must recover from illness before washing laundry. The following formula is used to calculate the student's illness duration. We roll a fair 6-sided die and toss a fair coin. The student is absent from class for n days if the coin comes up heads, where n is the result of the die roll.
Ex(u) = (1/2)(1/6)*5+(1/2)(1/6)10+(1/2)(1/6)15+(1/2)(1/6)20 + (1/2)(1/6)25+(1/2)(1/6)*30
Probability = 25
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One serving of a fruit punch recipe serves 16 people.
Which of the following answer choices correctly lists the ordered pairs for 1, 2, 3, and 4 servings? (number of servings, number of people served)
This is the correct answer
(1, 16), (2, 32), (3, 48), (4, 64)
Now for part 2 Plot the ordered pairs from question 1. You can only plot one point at a time. Plot serving 1 below. The image is below. Please snip and sketch the image then edit the image and draw where the points go. Thanks :)
The required list of the ordered pairs for 1, 2, 3, and 4 servings as (1, 16), (2, 32), (3, 48), (4, 64).
What is an ordered pair?An ordered pair is made up of two components isolated by a comma and put inside parentheses. (x, y) indicates an ordered pair, where 'x' is the first component and 'y' is the second component in the ordered pair.
One serving of a fruit punch recipe serves 16 people.
As per the given question, the required solution would be as:
1 x 16 = 16 ⇒ (1, 16)
2 x 16 = 16 ⇒ (2, 32)
3 x 16 = 16 ⇒ (3, 48)
4 x 16 = 16 ⇒ (4, 64)
Thus, the required list of the ordered pairs for 1, 2, 3, and 4 servings as (1, 16), (2, 32), (3, 48), (4, 64).
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7. A square pyramid has triangular faces, each with a base, of 8 inches and a height of 14 inches. The total surface area of the square pyramid is 288 in2. What is the area of the base of the square pyramid?
-3(x-4)=-9(x-1) solving linear equations
-3(x-4)=-9(x-1)
-3x+12=-9x+9
-3x+9x=9-12
6x=-3
x= -3/6
x=-1/2
What is the measure of angle A in this triangle?
Enter your answer in the box.
m∠A=
The measure of angle A in this triangle is 50°.
How to calculate the angle?It is important to note that a triangle has three sides and the total angle is 180°.
Therefore A = 2x - 10
B = 70
C = x + 30
The angles will be illustrated thus:
2x - 10 + 70 + x + 30 = 180
3x + 90 = 180
3x = 180 - 90
3x = 90
Divide
x = 90/3
x = 30
Therefore A will be:
= 2x - 10
= 2(30) - 10
= 60 - 10
= 50°
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the number 120 is increased by 50%, and the result is then decreased by 30% to give the number x. what is the value of x?
Answer:
x = 126
Step-by-step explanation:
1. 120 + 120(.50) = 180
2. 180 - 180(.30) = 126
The melting point of a solid is the temperature at which is solid melts to become a liquid. The melting point of the element bromine is about 19°F. This is about 57°F more than the melting point of mercury. Which of the following equations can you use to find the melting point of mercury? What is the melting point of mercury?
x + 57 = 19
x - 57 = 19
x + 19 = 57
x + 19 = -57
Answer: A
Step-by-step explanation: If the melting point of Bromine is 19 degrees and the melting point of mercury is 57 degrees less than that then x (which is mercury's melting point) plus 57 degrees will equal 19.
The American Community Survey (ACS), part of the United States Census Bureau, conducts a yearly census similar to the one taken every ten years, but with a smaller percentage of participants. The most recent survey estimates with confidence that the mean household income in the U.S. falls between . Find the point estimate for mean U.S. household income and the error bound for mean U.S. household income.
the error bound for the mean U.S. household income is +/- $234, while the point estimate is $63179.
A yearly census identical to the one performed every ten years is conducted by the American Community Survey (ACS), a division of the United States Census Bureau, but with a lower participation rate. Since the most recent poll has high confidence that the mean household income in the United States is between, the point estimate for that income is $63179, and the error bound is +/- $234.
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Determine the slope of the line
A. 1/3
B. -1/3
C. 3/1
D. -3/1
Answer: C
Step-by-step explanation:
The graph is going up not going down so it can't be a negative slope and we can eliminate choices B & D. We know that the slope is rising over run, and we see that the y increase by 3, and x increase by 1, so the slope is 3/1.
A daycare center has a weekly revenue of $15,000. The daycare director has created a monthly budget using the following percentages for expenses:
Percent
Employee Wages 40%
Building Rent 5%
Supplies 15%
Equipment 5%
Educational Licensing 2%
Food 13%
Utilities 10%
Maintenance 5%
Emergency/Repair 5%
Which balance sheet correctly represents the daycare's income, expenses, and balance?
A: Income
Amount
Weekly Income $15,000.00
Total Monthly Income $65,000.00
Expenses
Percent Amount
Employee Wages 40% $26,000.00
Building Rent 5% $3,250.00
Supplies 15% $9,750.00
Equipment 5% $326.29
Educational Licensing 2% $1,300.00
Food 13% $8,450.00
Utilities 10% $6,500.00
Maintenance 5% $3,250.00
Emergency/Repair 5% $3,250.00
$65,000.00
Balance
Income $65,000.00
Expenses $65,000.00
Balance $0
B; Income
Amount
Weekly Income $15,000.00
Total Monthly Income $30,000.00
Expenses
Percent Amount
Employee Wages 40% $12,000.00
Building Rent 5% $1,500.00
Supplies 15% $4,500.00
Equipment 5% $1,500.00
Educational Licensing 2% $600.00
Food 13% $3,900.00
Utilities 10% $3,000.00
Maintenance 5% $1,500.00
Emergency/Repair 5% $1,500.00
$30,000.00
Balance
Income $30,000.00
Expenses $30,000.00
Balance $0
C; Income
Amount
Weekly Income $15,000.00
Total Monthly Income $60,000.00
Expenses
Percent Amount
Employee Wages 40% $24,000.00
Building Rent 5% $3,000.00
Supplies 15% $9,000.00
Equipment 5% $3,000.00
Educational Licensing 2% $1,200.00
Food 13% $7,800.00
Utilities 10% $3,000.00
Maintenance 5% $3,000.00
Emergency/Repair 5% $1,500.00
$60,000.00
Balance
Income $60,000.00
Expenses $60,000.00
Balance $0
D; Income
Amount
Weekly Income $15,000.00
Total Monthly Income $67,500.00
Expenses
Percent Amount
Employee Wages 40% $27,000.00
Building Rent 5% $3,375.00
Supplies 15% $10,125.00
Equipment 5% $3,375.00
Educational Licensing 2% $1,350.00
Food 13% $8,775.00
Utilities 10% $6,750.00
Maintenance 5% $3,375.00
Emergency/Repair 5% $3,375.00
$67,500.00
Balance
Income $67,500.00
Expenses $67,500.00
Balance $0
The balance sheet that correctly represents the daycare's income, expenses, and balance is given as follows:
C; Income
Amount
Weekly Income $15,000.00
Total Monthly Income $60,000.00
Expenses
Percent Amount
Employee Wages 40% $24,000.00
Building Rent 5% $3,000.00
Supplies 15% $9,000.00
Equipment 5% $3,000.00
Educational Licensing 2% $1,200.00
Food 13% $7,800.00
Utilities 10% $3,000.00
Maintenance 5% $3,000.00
Emergency/Repair 5% $1,500.00
$60,000.00
Balance
Income $60,000.00
Expenses $60,000.00
Balance $0
How to obtain the balance sheet?The first step in obtaining the balance sheet is obtaining the total monthly income.
The weekly income is of $15,000, while a month is composed by four weeks, hence the monthly income is of:
4 x $15,000 = $60,000.
Then the percentages of each expenses are applied to find the values, for example, 40% of that is for employee wages, hence:
0.4 x 60,000 = $24,000.
From the percentages stated in the problem, 100% of the income is turned into expenses, hence the balance will be of zero and option C is correct.
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how to write the expression 12 and
Answer: What is the last part of the question?
Step-by-step explanation:
I can't answer the question because it is incomplete. Sorry :(
directions in attachment!
The answers are 285 and 7392.
Which number line represents the solutions to |x + 4 = 2?
Assume that a procedure yields a binomial distribution with a trial repeated n=5n=5 times. Use either the binomial probability formula (or a technology like Excel or StatDisk) to find the probability of k=1k=1 successes given the probability p=p=9/10 of success on a single trial.
(Report answer accurate to 4 decimal places.)
P(X=k)=
By using Binomial Distribution, it can be calculated that -
P(X = 1) = 0.0005
What is Binomial Distribution?
Binomial distribution is a discrete type probability distribution whose probability density function is given by
P(X = x) = [tex]{n \choose x} p^xq^{n - x}[/tex]
Where p is the probability of success and q is the probability of failure
Here, Binomial Distribution of probability is used
k = 1
p = 0.9
q = 1 - 0.9 = 0.1
n = 5
P(X = 1) = [tex]{5 \choose 1} (0.9)^1(0.1)^{5 - 1}[/tex]
= 0.00045
= 0.0005
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