Answer:
y (t) = 19 + 76*e^(-(1/51)*t)
Step-by-step explanation:
We have the following differential equation model:
dy / dt = - (1/51) * (y -19)
The initial conditions are: y (0) = 95 and y '(70) = 1
We solve the differential equation, separating variables:
1 / (and -19) * dy = - (1/51) * dt
we integrate on both sides:
ln (y -19) = - (1/51) * t + C
e ^ ln (y -19) = e ^ (- (1/51) * t + C)
y - 19 = C1 * e ^ (- (1/51) * t)
y = 19 + C1 * e ^ (- (1/51) * t)
replacing, and (0) = 95
95 = 19 + C1 * e ^ (- (1/51) * 0)
95 = 19 + C1 * e ^ 0
95 = 19 + C1
C1 = 95 - 19 = 76
Therefore the equation would be:
y (t) = 19 + 76 * e ^ (- (1/51) * t)
A city council has requested a household survey be conducted in a suburban area of their city. The area is broken into many distinct and unique neighborhoods, some including large homes, some with only apartments, and others a diverse mixture of housing structures. Identify the sampling methods described below, and comment on whether or not you think they would be effective in this setting.
(a) Randomly sample 50 households from the city.
(b) Divide the city into neighborhoods, and sample 20 households from each neighborhood.
(c) Divide the city into neighborhoods, randomly sample 10 neighborhoods, and sample all house-holds from those neighborhoods.
(d) Divide the city into neighborhoods, randomly sample 10 neighborhoods, and then randomly sample 20 households from those neighborhoods.
(e) Sample the 200 households closest to the city council oces.
Answer:
Option D
Step-by-step explanation:
I think the most effective sample to this setting would be to
Divide the city into neighborhoods. Randomly sample 10 neighborhoods. And then randomly sample 20 households from those neighborhoods.
The city is first divided into the various distinct and unique neighbourhoods, then randomly sample 10 neighborhood such that this sample is a representation of the many distinct and unique neighborhoods, which include some with large homes, some with only apartments, and others a diverse mixture of housing structures.
Then from each neighborhood, take a random sample of 20 households.
This way, your sample are a representation of the population.
Phil has $20,000, part of which he invests at 8% interest and the rest at 6%. If the total income from the two investments was $1460, how much did he invest at 6%?
Answer: 7000
Step-by-step explanation:
Let the amount invested in 8% account be P1 and the amount invested in 6% account be P2
. If the total amount invested is $20,000 then:
P1+P2=20,000. (Eq. 1)
The interest earned in one year from the 8% account is:
I1=0.08P1
and the interest earned in one year from the 6% account is:
I2=0.06P2
If the total interest earned is $1460, then:
I1+I2=1460
0.08P1+0.06P2=1460
(Eq. 2) From Eq. 1 :
P1=20000−P2
Substituting this into Eq. 2:
0.08 (20000−P2) + 0.06P2 = 1460
1600 − 0.08P2 + 0.06P2 = 1460
0.02P2 = 140
P2 = 140 / 0.02
P2 = 7000
Hence, he invested $7000 at the rate of 6%.
The circle shown below has AB and BC as its tangents:
AB and BC are two tangents to a circle which intersect outside the circle at a point B.
If the measure of arc AC is 120°, what is the measure of angle ABC? (1 point)
Answer:
120
Step-by-step explanation:
we know if the arc measures 120, we know that its 1/3 of the circle, so ABC will also be 120
Rogelio paints watercolors. He got a $100 gift card to the art supply store and wants to use it to buy 12 inch by 16 inch canvases. Each canvas costs $10.99. What is the maximum number of canvases he can buy with his gift card
Answer:
9 canvases
Step-by-step explanation:
To find the number of canvases Rogelio can buy, we just need to divide the value of the gift card by the value of each canvas. Then, if the result is decimal, we round down, because if we round up we will not have enough money to buy them all.
So we have that:
Number of canvases = 100 / 10.99
Number of canvases = 9.099
Rounding down, we can buy 9 canvases
What are the like terms in the algebraic expression? Negative a squared b + 6 a b minus 8 + 5 a squared b minus 6 a minus b Negative a squared b and negative 6 a Negative a squared b and 5 a squared b 6 a b and 5 a squared b 6 a b and negative 6 a
Answer:
The like terms are: [tex]a^{2}b,\ ab,\ \teaxt{and}\ a[/tex]
Step-by-step explanation:
The expression is:
[tex]-a^{2}b+6ab-8+5a^{2}b-6a-b-a^{2}b-6a-a^{2}b+5a^{2}b+6ab+5a^{2}b+6ab-6a[/tex]
Collect the like terms as follows:
[tex]-a^{2}b+6ab-8+5a^{2}b-6a-b-a^{2}b-6a-a^{2}b+5a^{2}b+6ab+5a^{2}b+6ab-6a[/tex]
[tex]=(-a^{2}b+5a^{2}b-a^{2}b-a^{2}b+5a^{2}b+5a^{2}b)+(6ab+6ab+6ab)-(6a-6a-6a)-b-8[/tex]
[tex]=12a^{2}b+18ab+18a-b-8[/tex]
Thus, the final expression is [tex]12a^{2}b+18ab+18a-b-8[/tex]
The like terms are: [tex]a^{2}b,\ ab,\ \teaxt{and}\ a[/tex].
Answer:
The CORRECT answer is B
Step-by-step explanation:
A box contains 99 green marbles and 1212 white marbles. If the first marble chosen was a green marble, what is the probability of choosing, without replacement, a white marble? Express your answer as a fraction or a decimal number rounded to four decimal places.
Answer:
0.9252Step-by-step explanation:
Adding the two together 1212 + (99 - 1)
1310
1212/1310 = 606/655
Decimal: 0.9252
I'm always happy to help :)
Which of the following number lines represents the solution to x-5>-2
Answer:
see below
Step-by-step explanation:
x-5 > -2
Add 5 to each side
x-5+5 > -2+5
x > 3
open circle at 3 line going to the right
Answer:
x>3
Step-by-step explanation:
x-5>-2
x>3
In a genetics experiment on peas, one sample of offspring contained 450 green peas and 371 yellow peas. Based on those results, estimate the probability of getting an offspring pea that is green. Is the result reasonably close to the value of three fourths that was expected?
Answer:
P(G) = 0.55
the probability of getting an offspring pea that is green. Is 0.55.
Is the result reasonably close to the value of three fourths that was expected?
No
Expected P(G)= three fourths = 3/4 = 0.75
Estimated P(G) = 0.55
Estimated P(G) is not reasonably close to 0.75
Step-by-step explanation:
Given;
Number of green peas offspring
G = 450
Number of yellow peas offspring
Y = 371
Total number of peas offspring
T = 450+371 = 821
the probability of getting an offspring pea that is green is;
P(G) = Number of green peas offspring/Total number of peas offspring
P(G) = G/T
Substituting the values;
P(G) = 450/821
P(G) = 0.548112058465
P(G) = 0.55
the probability of getting an offspring pea that is green. Is 0.55.
Is the result reasonably close to the value of three fourths that was expected?
No
Expected P(G)= three fourths = 3/4 = 0.75
Estimated P(G) = 0.55
Estimated P(G) is not reasonably close to 0.75
Write the expression 3*3*3*3*3 in exponential notation
Answer:
3^5
Step-by-step explanation:
becuase 3*3*3*3*3
Answer: 3^5 (3 to the power of 5)
Step-by-step explanation:
3 is multiplied by itself 5 times
To shorten the expression, exponential notation is used and it becomes 3^5, which essentially means three multiplied by itself 5 times
ex. 4^3 equals 4x4x4
Two cards will be dealt off the top of a well-shuffled deck. You have a choice:
i. To win $1 if the first is a king.
ii. To win $1 if the first is a king and the second is a queen.
Which option is better? Or are they equivalent? Explain briefly.
Answer:
i. is the better option.
Step-by-step explanation:
The probability first is a King = 4/52 = 1/13.
The probability second is a Queen = 4/51.
The probability first is a King and second is a Queen = 1/13 *4/51 = 4/663.
So there is a much betert chance to bet just that the first one is a King
Timmy received $50 for his birthday following the birthday party his parents promised him 5$ each week for completing his chores. Assuming Timmy completes all chores uses a linear equation to determine the number of dollars Timmy will have in 7 weeks
Answer:
$85
Step-by-step explanation:
Let y represent Timmy's money after x weeks. If we assume that the only money Timmy has is what is mentioned in the problem statement, then ...
y = 50 +5x . . . . . $50 initially plus $5 for each week
After 7 weeks, x = 7, so Timmy's fortune will be ...
y = 50 +5(7) = 50 +35
y = 85
Timmy will have $85 in 7 weeks.
What is the range of the following data set? 7.7, 8.4, 9, 8, 6.9
Answer:
The range is 2.1
Step-by-step explanation:
7.7, 8.4, 9, 8, 6.9
Put the numbers in order from smallest to largest
6.9,7.7, 8,8.4, 9
The range is the largest number minus the smallest number
9 - 6.9
2.1
What is the perimeter of this tile?
in.
in 2
3 in.
3 in.
Answer:
Perpendicular lines are lines that intersect at a right (90 degrees) angle.
Step-by-step explanation:
Answer: 12
Step-by-step explanation: each side is 3, and there are 4 sides so 3*4=12
Jose can assemble 12 car parts in 40 minutes. How many minutes
would be needed to assemble 9 parts7
Answer:
12/40=0.3
0.3 car parts per minute
9 / 0.3 = 30 minutes
30 minutes for 9 parts
Hope this helps
Step-by-step explanation:
Jose required 30 minutes to assemble 9 parts.
Jose assemble 12 car parts in 40 minutes. Time consumed by jose to assemble 9 parts to be calculated.
In mathematics it deals with numbers of operations according to the statements.
Here,
40 minute = 12 parts
40/12 = 1 part
Time to assemble 9 parts: = 40/12 x 9
= 10/3 x 9
= 30
Thus, Jose required 30 minutes to assemble 9 parts.
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Let f be the function that determines the area of a circle (in square cm) that has a radius of r cm. That is, f ( r ) represents the area of a circle (in square cm) that has a radius of r cm.Use function notation to complete the following tasks
a. Represent the area (in square cm) of a circle whose radius is 4 cm.
b. Represent how much the area (in square cm) of a circle increases by when its radius increases from 10.9 to 10.91 cm.
Answer:
(a)f(4) square cm.
(b)f(10.91)-f(10.9) Square centimeter.
Step-by-step explanation:
f(r)=the area of a circle (in square cm) that has a radius of r cm.
(a)Area (in square cm) of a circle whose radius is 4 cm.
Since r=4cm
Area of the circle = f(4) square cm.
(b) When the radius of the increases from 10.9 to 10.91 cm.
Area of the circle with a radius of 10.91 = f(10.91) square cm.Area of the circle with a radius of 10.9 = f(10.9) square cm.Change in the Area = f(10.91)-f(10.9) Square centimeter.
Three kinds of tickets were sold for a concert. Child tickets are $6, adult tickets are $12, and student tickets are $8. A total of 204 tickets were sold, bringing in a total of $2,008. If 4 more adult tickets were sold than the total number of student and child tickets combined, how many student tickets were sold? Type in your numerical answer only; do not type any words or letters with your answer.
Answer:
The number of children's tickets sold =12The number of adult's tickets sold =100The number of student's tickets sold =92Step-by-step explanation:
Let the number of children's tickets sold =c
Let the number of adult's tickets sold =a
Let the number of student's tickets sold =s
A total of 204 tickets were sold, therefore: c+a+s=204
Child tickets are $6, adult tickets are $12, and student tickets are $8.
Total revenue =$2,008
Therefore:
6c+12a+8s-2008
We are also told that 4 more adult tickets were sold than the total number of student and child tickets combined.
c+s=a+4
We then solve the resulting system of equation.
c+a+s=2046c+12a+8s=2008c+s=a+4Substituting c+s=a+4 into the first equation
c+a+s=204
a+4+a=204
2a=204-4
2a=200
a=100
Substitute a=100 into the second and third equation
6c+12(100)+8s=2008
6c+8s=2008-1200
6c+8s=808
From the third equation
c+s=100+4
c=104-s
Substitute c=104-s into 6c+8s=808
6(104-s)+8s=808
624-6s+8s=808
2s=808-624
2s=184
s=92
Since c=104-s
c=104-92
c=12
Therefore:
The number of children's tickets sold =12The number of adult's tickets sold =100The number of student's tickets sold =92Given a = 4 and b= -2, evaluate -Ib-al.
-2
-6
6
A lottery is conducted using three urns. Each urn contains chips numbered from 0 to 9. One chip is selected at random from each urn. The total number of sample points in the sample space is:_______ a) 30 b) 100 c) 729 d) 1,000"
Answer: Option d.
Step-by-step explanation:
Ok, we have 3 urns.
Each urn can give a number between 0 and 9, so each urn has 10 options.
And as the urns are different, the outcome in the first urn does not affect the outcomes in the others, and the same happens for the outcome in the second urn, so the events are independent.
The total number of combinations is equal to the product of the number of options for each event (here each urn is one event)
then the number of combinations is:
C = 10*10*10 = 10^3 = 1000
Then the correct option is d.
The mean age of 5 people in a room is 40 years. A person enters the room. The mean age is now 36. What is the age of the person who entered the room?
Answer:
[tex]\boxed{\sf \ \ \ age = 16 \ \ \ }[/tex]
Step-by-step explanation:
Hello,
as the mean age of 5 people is 40
it means that the sum of the 5 ages is 40*5=200
now a person enters the room, let's note x his age
the new mean is
[tex]\dfrac{200+x}{6}=36[/tex]
[tex]<=>200+x=6*36=216\\<=> x = 216-200=16\\[/tex]
So the age of the new person is 16
hope this helps
En el triángulo rectángulo ABC, recto en “B”, SI Tg C = 3/5, hallar el valor “cosec A”
Answer: Cosec(A) = 3.64
Step-by-step explanation:
Ok, tenemos un triangulo rectángulo.
Sabemos que B = 90° y que
tg(C) = 3.5
entonces:
Atg(Tg(C)) = C = Atg(3.5) = 74.05°.
Nosotros también sabemos que la suma de todos los ángulos interiores de un triangulo es igual que 180°
entonces:
A + B + C = 180°
A + 90° + 74.05° = 180°
A = 180° - 90° - 74.05° = 15.95°
Entonces Cosec(A) = Cosec(15.95°) = 1/sin(15.95°) = 3.64
Please answer this correctly
Answer:
I want to say 9 but im preety sure it's 6
Step-by-step explanation:
you have 54 times to pick it
you have 9 marbles,
54 divided by 9= 6
answer is 6
hope this helped:))))
have a grate dayy
Answer:
1
this is because I see only one marble present which is orange
Which expression are equivalent to 4m-2+(-8m)
Answer:
combine 4m -8m to get -4m
[tex] - 4m - 2[/tex]
Answer:
− 4m-2
Step-by-step explanation:
A cylinder has radius R = 3.7 and height H = 5.6 both measured in inches. What is the volume of this cylinder measured in cm3? (Hint: The volume of a cylinder is given by V=\pi R^2HV = π R 2 H.)
Answer:
The volume is [tex]3946.17cm^3[/tex]Step-by-step explanation:
We need to convert the radius and the height to cm first
1 cm = 0.393701 in
r (cm)= 3.7 in
[tex]h(cm)= \frac{3.7}{0.393701}= 9.398 cm[/tex]
1 cm = 0.393701 in
h (cm)= 5.6 in
[tex]h(cm)= \frac{5.6}{0.393701}= 14.22 cm[/tex]
The formula the volume of cylinder is
[tex]volume= \pi r^2h\\\\volume= 3.142*9.398^2*14.22\\volume=3946.17cm^3[/tex]
Write an equation in slope-intercept form for the line that passes through (4,5) and parallel to the to the line described by y=5x+10
Answer:
[tex]y = 5x-15[/tex]
Step-by-step explanation:
Parallel ⇒ So the slopes will definitely be equal
So,
Slope = m = 5
Now,
Point = (x,y) = (4,5)
So, x = 4, y = 5
Putting these in the slope intercept form to get b
[tex]y = mx +b \\[/tex]
5 = (5)(4) + b
5 = 20 + b
b = -20+5
b = -15
So, Putting m and b in the slope intercept form to get the required equation,
[tex]y = 5x-15[/tex]
1(3√2)2=2n what is n? this might be hard to do but I need help asap!! ty
Answer:
[tex]n=3\sqrt{2}[/tex]
Step-by-step explanation:
[tex]2n=1\times \left(3\sqrt{2}\right)\times \:2[/tex]
[tex]2n=2 \times 3\sqrt{2}[/tex]
[tex]2n=6\sqrt{2}[/tex]
[tex]\frac{2n}{2}=\frac{6\sqrt{2}}{2}[/tex]
[tex]n=3\sqrt{2}[/tex]
Answer:
n = 3√2
Step-by-step explanation:
=> [tex]1(3\sqrt{2} )2 = 2n\\6\sqrt{2} = 2n\\[/tex]
Dividing both sides by 2, we'll get
=> [tex]\frac{6\sqrt{2} }{2} = \frac{2n}{2}[/tex]
So,
=> n = [tex]3\sqrt{2}[/tex]
What is the solution to the linear function? 2/3x - 1/2 = 1/3 + 5/6x
Answer:
x = -5
Step-by-step explanation:
You are often told to start a problem like this by clearing fractions. Multiply the equation by the least common denominator of the fractions. Here, that value is 6.
4x -3 = 2 +5x . . . . multiply the equation by 6
-5 = x . . . . . . . . . . . add -2-4x to both sides
The solution is x = -5.
_____
If you're comfortable with arithmetic using fractions, you can "cut to the chase." Subtract 2/3x+1/3 from both sides:
(2/3x -1/2) -(2/3x +1/3) = (1/3 +5/6x) -(2/3x +1/3)
-1/2 -1/3 = 5/6x -2/3x . . . . simplify a little
-5/6 = 1/6x . . . . . . . . . . . . .simplify more
-5 = x . . . . . . multiply by 6
solve 3x+2/2=13
really need help fast ;-;
Answer:
3x+2=26
3x=24
x=8
Step-by-step explanation:
Answer:
The answer is 8.
Step-by-step explanation:
you need to undo.
to get the 2 out of the bottom you need to multiply both sides of the equation by 2.
now you have 3x+2= 13(2)
3x+2=26.
Now you need to subtract 2 from both sides to get rid of the 2.
Now you have 3x=26-2
3x=24.
The final step in solving for x is to divide both sides by 3.
Now you have x=24/3
which give you your final answer of x=8
Hope this helps!
The heights of 10 year old children has a normal probability distribution with mean of 54.6 inches and standard deviation of 5.7 inches. What is the approximate probability that a randomly selected 10-year old child will be more than 51.75 inches tall? Group of answer choices 0.69 0.31 0.62 0.67 0.93
Answer:
a) 0.69
The probability that a randomly selected 10-year old child will be more than 51.75 inches tall
P(X>51.75 ) = 0.6915
Step-by-step explanation:
Step(i):-
Given mean of the Population = 54.6 inches
Given standard deviation of the Population = 5.7 inches
Let 'X' be the random variable of normal distribution
Let 'X' = 51.75 inches
[tex]Z = \frac{x-mean}{S.D} = \frac{51.75-54.6}{5.7} = -0.5[/tex]
Step(ii):-
The probability that a randomly selected 10-year old child will be more than 51.75 inches tall
P(X>51.75 ) = P(Z>-0.5)
= 1 - P( Z < -0.5)
= 1 - (0.5 - A(-0.5))
= 1 -0.5 + A(-0.5)
= 0.5 + A(0.5) (∵A(-0.5)= A(0.5)
= 0.5 +0.1915
= 0.6915
Conclusion:-
The probability that a randomly selected 10-year old child will be more than 51.75 inches tall
P(X>51.75 ) = 0.6915
The figure is made up of a cylinder and a sphere which has been cut in half. The radius of each half sphere is 6 mm. What is the volume of the composite figure? Use 3.14 for Pi. Round to the nearest hundredth. A cylinder and 2 half spheres. All have a radius of 6 millimeters. The cylinder has a height of 12 millimeters. Recall the formulas V = B h and V = four-thirds pi r cubed 527.52 cubic millimeters 1,431.84 cubic millimeters 2,034.72 cubic millimeters 2,260.80 cubic millimeters
Answer:
The Last One
Step-by-step explanation:
I used a special calculator plus, I did this already lol. Trust me <3
The required volume of the composite figure is 2260.80 cubic millimeters.
What is volume?Volume is defined as the mass of the object per unit density while for geometry it is calculated as profile area multiplied by the length at which that profile is extruded.
here,
The volume of the composite figure is given as
Volume = Volume of cylinder + Volume of a sphere
= πr²h + 4/3πr³
= π [6²*12 + 4/3*6³ ]
= 2260.80 cubic millimeters.
Thus, the required volume of the composite figure is 2260.80 cubic millimeters.
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This is algebra solving linear equations
P+7/20=19/20
Answer:
P = [tex]\frac{19}{7}[/tex] or the decimal answer is 2.71
Step-by-step explanation: