Answer:
10%$29,175$2,046$6,499.50Step-by-step explanation:
a) The %tax comes from the "Rate" column on the line "up to $9525". It is 10%.
__
b) Simply compute the difference shown:
$38,700 -$9,525 = $29,175
__
c) 22% of $9,300 is ...
0.22 × $9,300 = $2,046
__
d) The total from the three previous calculations is ...
$952.50 +3,501.00 +2,046.00 = $6,499.50
Answer:
10%
$29,175
$2,046
$6,499.50
got it right on ttm.
Step-by-step explanation:
just believe me it works
WILL GIVE BRAINLIST On a coordinate plane, 2 quadrilaterals are shown. The first figure has points A (negative 2, 1), B (negative 4, 1), C (negative 4, 5), and D (negative 2, 4). Figure 2 has points A prime (2, 1), B prime (4, 1), C prime (4, 5), and D prime (2, 4). What is the rule for the reflection? rx-axis(x, y) → (–x, y) ry-axis(x, y) → (–x, y) rx-axis(x, y) → (x, –y) ry-axis(x, y) → (x, –y)
Answer:
B) ry-axis(x, y) → (–x, y)
Step-by-step explanation:
Got it right on edge2020 you can trust me :D
A circle has a radius of \blue{3}3start color #6495ed, 3, end color #6495ed. An arc in this circle has a central angle of 20^\circ20 ∘ 20, degrees.
Answer: The complete question is "A circle has a radius of \blue{3}3start color #6495ed, 3, end color #6495ed. An arc in this circle has a central angle of 20^\circ20 ∘ 20, degrees. What is the length of the arc?"
The length of the arc is 1.06667 units.
Step-by-step explanation:
According to the question the radius of the circle [tex]R=3 \, units[/tex] and central angle of arc is [tex]\Theta =20^{o}[/tex]
As we know that the length of the arc is given as: [tex]L=R\Theta[/tex]
Where R is radius of the circle, L is the length of the arc and [tex]\Theta[/tex] is central angle in radian.
Now, [tex]\Theta =20^{o}\times \frac{\Pi }{180}=\frac{\Pi }{9} \, rad[/tex]
Therefore, length of the arc is
[tex]L=3\times \frac{\Pi }{9}=\frac{\Pi }{3} =\frac{3.14}{3}=1.0466667 \, units[/tex]
Which inequality is represented by this graph
The right answer is of option D.
[tex]x \geqslant 4[/tex]
In the given graph, X is greater than 4 and X equals to 4.
Hope it helps.....
Good luck on your assignment
Sonya has two red marbles and three yellow marbles. She chooses three marbles at random. What is the probability that she has at least one marble of each color?
Answer:
90% probability that she has at least one marble of each color
Step-by-step explanation:
A probability is the number of desired outcomes divided by the number of total outcomes.
The order in which the marbles are selected is not important. So we use the combinations formula to solve this question.
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]
What is the probability that she has at least one marble of each color?
Desired outcomes:
Two red(from a set of 2) and one yellow(from a set of 3)
Or
One red(from a set of 2) and two yellows(from a set of 3).
So
[tex]D = C_{2,2}*C_{3,1} + C_{2,1}*C_{3,2} = \frac{2!}{2!(2-2)!}*\frac{3!}{1!(3-1)!} + \frac{2!}{1!(2-1)!}*\frac{3!}{2!(3-2)!} = 3 + 6 = 9[/tex]
Total outcomes:
Three marbles, from a set of 3 + 2 = 5. So
[tex]T = C_{5,3} = \frac{5!}{3!(5-3)!} = 10[/tex]
Probability:
[tex]p = \frac{D}{T} = \frac{9}{10} = 0.9[/tex]
90% probability that she has at least one marble of each color
The length of a field is twice it's breadth. If the length is 30cm. Calculate the perimeter of the field.
Answer:
b=30/2=15
peri= 90
Step-by-step explanation:
A rectangular piece of paper has a width that is 3 inches less than its length. It is cut in half along a diagonal to create two congruent right triangles with areas of 44 square inches. Which statements are true? Check all that apply.
The area of the rectangle is 88 square inches.
The equation x(x – 3) = 44 can be used to solve for the dimensions of the triangle.
The equation x2 – 3x – 88 = 0 can be used to solve for the length of the rectangle.
The triangle has a base of 11 inches and a height of 8 inches.
The rectangle has a width of 4 inches.
Answer:
⬇⬇⬇⬇⬇⬇
⬇⬇⬇⬇⬇⬇
Step-by-step explanation:
1, 3, 4
proof below
(1) The area of the rectangle is 88 square inches
(3) The equation x² – 3x – 88 = 0 can be used to solve for the length of the rectangle.
(4) The triangle has a base of 11 inches and a height of 8 inches.
Area of the rectangle
Area of a rectangle is the sum of the area of two equal right triangle.
Area of rectangle = 2(area of right triangle)
Area of rectangle = 2(44 sq inches) = 88 sq inches
Total area of the triangle with respect to length and width of the rectangleLet the length = x
then the width becomes, x - 3
Area = x(x - 3) = 88
x² - 3x = 88
x² - 3x - 88 = 0
x = 11
width = 11 - 3 = 8
Thus, the statements that are true include;
The area of the rectangle is 88 square inchesThe equation x² – 3x – 88 = 0 can be used to solve for the length of the rectangle.The triangle has a base of 11 inches and a height of 8 inches.Learn more about area of rectangle here: https://brainly.com/question/25292087
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Please help me. I’ll mark you as brainliest if correct
Answer:
b = -18
Step-by-step explanation:
(3 + 4i) (-3-2i)
When we foil:
-9 + -6i + -12i + -8i^2
-8i^2 = +8
Combine like terms:
-1 + -18i
An amusement park is installing a new roller coaster. the park intends to charge $5 per adult and $3 per child for each ride. It hopes to earn back more than the $750,000 cost of construction in four years. with the best of weather, the park can provide 100000 adult rides and 75,000 child rides in one season.
Answer:
Cost = 750,000
Income per year = 5 x 100,000 + 75,000 x 3 = 725,000
Income for 4 years = 4 x 725,000 = 2,900,000
Profit = 2,900,000 - 750,000 = 2,150,000
Step-by-step explanation:
"Children under the age of 13 are not allowed to operate a boat." Part A: Write an inequality to show the age of children who are allowed to operate a boat. (5 points) Part B: Describe in words how you can show the solution to this inequality on a number line. (5 points)
Answer:
X ≤ 13
Step-by-step explanation:
Part A: X ≤ 13
Part B: Draw a closed circle from 13 and up on the number line.
Make the arrow look like this >.
The inequality will be x ≥ 13. The age of the person should be greater than or equal to 13.
What is inequality?Inequality is defined as an equation that does not contain an equal sign. Inequality is a term that describes a statement's relative size and can be used to compare these two claims.
“Children under the age of 13 are not allowed to operate a boat.”
Let x be the age of the person.
The inequality to show the age of children who are allowed to operate a boat will be
x ≥ 13
The age of the person should be greater than or equal to 13.
More about the inequality link is given below.
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What type of infection is controlled with antibiotics?
Answer:
Bacterial infection
Step-by-step explanation:
Antibiotics are most effective against bacterial infections.
Answer:
Bacterial infection
Antibiotics are most effective against bacterial infections
Find sin 2x, cos 2x, and tan 2x if sinx =
5
13
and x terminates in quadrant I.
ala
sin 2x
U
х
cos 2x
=
tan 2x
10
Answer:
12/13 ; 5/13; 12/5
Step-by-step explanation:
sinx =5/13 =opposite/ hypothenus
By Pythagoras rule the hypothenus side can be obtained as
√ 13^2 -5^2 = √169 -25 = √144 = 12
cos x= adjacent/ hypothenus = 12/13
Now Cos2x= Sinx
And Sin2x = Cosx
Hence ;
Sin2x=12/13
Cos2x =5/13
Tan2x= Sin 2x/ Cos 2x
= 12/13 ÷ 5/13
= 12/13 × 13/5 = 12/5
If y = x² + 2x,
find the value of y when x = 5
_____________________________
Hey!!
Solution,
X=5
Now,
y=x^2+2x
=(5)^2+2*5
=25+10
= 35
So the value of y is 35
hope it helps
Good luck on your assignment
___________________________
For the given equation y = x² + 2x, the value of y when x = 5 is, 35
What is an Equation ?An equation is a mathematical term, which indicates that the value of two algebraic expressions are equal. There are various parts of an equation which are, coefficients, variables, constants, terms, operators, expressions, and equal to sign.
For example, 3x+2y=0.
Types of equation
1. Linear Equation
2. Quadratic Equation
3. Cubic Equation
Given that,
An equation, y = x² + 2x
The value of y when x is equal to 5 = ?
after putting value of x in a equation
⇒ y = 5² + 2 × 5
⇒ y = 25 + 10
⇒ y = 35
Hence, the value of y is 35
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Fraction - Multiplication : (a) 2/9 x 1/13 (b) 12/5 x 35/21
[tex]answer \\ a. \frac{2}{117} \\ b. 4 \\ solution \\ a. \: \frac{2}{9} \times \frac{1}{13} \\ = \frac{2 \times 1}{9 \times 13} \\ = \frac{2}{117} \\ b. \: \frac{12}{5} \times \frac{35}{21} \\ = divide \: 35 \: by \: 5 \: it \: becomes \\ = 12 \times \frac{7}{21} \\ divide \: 21 \: by \: 7 \: it \: becomes \\ = 12 \times \frac{1}{3} \\ divide \: 12 \: by \: 3 \: it \: becomes \\ = 4 \times 1 \\ = 4 \\ hope \: it \: helps \\ good \: luck \: on \: your \: assignment[/tex]
Answer:
[tex](a) \frac{2}{117} [/tex]
[tex](b)4[/tex]
Step-by-step explanation:
[tex](a) \frac{2}{9} \times \frac{1}{13} \\ = \frac{2}{117} [/tex]
[tex](b) \frac{12}{5} \times \frac{35}{21} \\ = \frac{84}{21} \\ = \frac{28}{7} \\ = 4[/tex]
hope this helps
brainliest appreciated
good luck! have a nice day!
What is the general form of this equation:
The line passes through the point (-2,4) with a slope -2/3
Answer: y= -2/3 + 8/3
Step-by-step explanation:
-2/3 is the slope so you just need the y-intercept to write the equation in general form or slope intercept form
4= -2/3(-2) +b
4 = 4/3 + b
-4/3 -4/3
b= 8/3
general form is y= -2/3 + 8/3
Simple regression was employed to establish the effects of childhood exposure to lead. THe effective sample size was about 122 subjects. THe independent variable was the level of dentin lead (parts per million). Below are regressions using various dependent variables.
Calculate the t statistic for each slope, at significance level = 0.01.
Dependent Variable R2 Estimated Std. t calculated p-value Differ from 0?
Slope Error
Highest grade achieved .061 −0.027 0.009 .008 No / Yes
Reading grade equivalent .121 −0.070 0.018 .000 No / Yes
Class standing .039 −0.006 0.003 .048 No / Yes
Absence from school .071 4.8 1.7 .006 No / Yes
Grammatical reasoning .051 0.159 0.062 .012 Yes / No
Vocabulary .108 −0.124 0.032 .000 No / Yes
Hand-eye coordination .043 0.041 0.018 .020 No / Yes
Reaction time .025 11.8 6.66 .080 No / Yes
Minor antisocial behavior .025 −0.639 0.36 .082 Yes / No
B) It would be inappropriate to assume cause and effect without a better understanding of how the study was conducted.
1. No
2. Yes
Answer:
Step-by-step explanation:
Simple regression was employed to establish the effects of childhood exposure to lead. THe effective sample size was about 122 subjects. THe independent variable was the level of dentin lead (parts per million). Below are regressions using various dependent variables.
Calculate the t statistic for each slope, at significance level = 0.01.
Dependent Variable R2 Estimated Std. t calculated p-value Differ from 0?
Slope Error
Highest grade achieved .061 −0.027 0.009 .008 No / Yes
Reading grade equivalent .121 −0.070 0.018 .000 No / Yes
Class standing .039 −0.006 0.003 .048 No / Yes
Absence from school .071 4.8 1.7 .006 No / Yes
Grammatical reasoning .051 0.159 0.062 .012 Yes / No
Vocabulary .108 −0.124 0.032 .000 No / Yes
Hand-eye coordination .043 0.041 0.018 .020 No / Yes
Reaction time .025 11.8 6.66 .080 No / Yes
Minor antisocial behavior .025 −0.639 0.36 .082 Yes / No
B) It would be inappropriate to assume cause and effect without a better understanding of how the study was conducted.
1. No
2. Yes
solution[tex]t=\frac{\text {estimated slope}}{\text {std error}}[/tex]
a)
Estimated Slope Std error t - calculated
-0.027 0.009 -3
-0.070 0.018 -3.89
-0.006 0.003 -2
4.8 1.7 2.82
0.159 0.062 2.56
-0.124 0.032 -3.87
0.041 0.018 2.28
11.8 6.66 1.77
-0.639 0.36 -1.78
b) Yes, It would be inappropriate to assume cause and effect without a better understanding of how the study was conducted.
A random sample of 1141 men and 1212 women aged 25-64 y (response rate 76%) completed a questionnaire and underwent a short examination in a clinic. Intake of beer, wine and spirits during a typical week, frequency of drinking, and a number of other factors were measured by a questionnaire. The present analyses are based on 891 men and 1098 women who were either nondrinkers or 'exclusive' beer drinkers (they did not drink any wine or spirits in a typical week). 500 men are beer drinkers and 325 men from this group have the obesity. 80 non-drinkers men are obese.
Required:
a. What type of study desing?
b. Which parameters can be calculated?
c. Determine it and explain the results.
Answer:
(a) A cross sectional study (b) The parameter can be computed as follows: Non-drinkers who agree exposed to obesity, Drinkers who are exposed or vulnerable to obesity (c) A postie relationship is established from the experiment between drinkers who are exposed to obesity and non drinkers who are exposed to obesity
Step-by-step explanation:
(a) The type of design is refereed to as a cross sectional study
(b) Now, because 50 men are beer drinkers out of 891 men.
Hence we can deduce form this that 500/891 gives us 0.56%.
This suggest that 0.56% men are beer drinkers out of which 325 have obesity, lets take for example 235/500 = 0.65% are exposed to obesity in which 80/ (89-500) = 80/491 = 0.16%
The non drinkers are 0.16% and are not exposed to obesity
Thus,
The parameters to be calculated is stated below:
Non-drinkers who agree exposed to obesityDrinkers who are exposed or vulnerable to obesity(c) The next step is to determine and explain the results.
In this case we can say there is a positive relationship between drinkers and non drinkers, since from the experiment 0.65% are exposed to obesity and 0.16$ non drinkers are exposed to obesity.
Which value of x is a solution to the inequality 4x-3<5x+6
Answer:x greater than -9
Step-by-step explanation:
What is five + five
we choose a sample of size 100 from a population of monthly cable bills having standard deviation $20 If we assume the population mean bill is $65, what is the probability mean of our sample is greater than $70.
Answer:
0.0062
Step-by-step explanation:
Find the standard error.
σ = 20 / √100
σ = 2
Find the z-score.
z = (x − μ) / σ
z = (70 − 65) / 2
z = 2.5
Find the probability.
P(Z > 2.5) = 1 − 0.9938
P(Z > 2.5) = 0.0062
What is the equation of the line that is parallel to the given
line and passes through the point (-4,-6 )?
x= -6
x=-4
y=-6
y=-4
Answer:
The line on the graph is y = 4, where no matter what the value of x is, the value of y will always be 4. Therefore, any line parallel to this one will be y = ?. If it passes through (-4, -6), that means that the equation is y = -6.
Answer:
С)))) Y= -6
Step-by-step explanation:
just did on edg. :D
From an urn containing 3 white and 2 black balls, two balls are drawn one after the other without replacement. What is the probability that the first ball drawn is white and the second black?
Answer:
There is a 3/5 chance of the first ball being white, and a 3/10 chance the second one is black.
Step-by-step explanation:
There are 5 balls, of which 3 are white, so you have a 3/5 chance of the first one being white. Then you have 2 white and 2 black balls. There is a 2/4 chance of picking a black ball. Multiply 3/5 and 2/4 to get 6/20, or 3/10 for choosing a white ball then a black ball.
A: What are the solutions to the quadratic equation x2+9=0? B: What is the factored form of the quadratic expression x2+9? Select one answer for question A, and select one answer for question B. B: (x+3)(x−3) B: (x+3i)(x−3i) B: (x−3i)(x−3i) B: (x+3)(x+3) A: x=3 or x=−3 A: x=3i or x=−3i A: x=3 A: x=−3i
Answer:
A. The solutions are [tex]x=3i,\:x=-3i[/tex].
B. The factored form of the quadratic expression [tex]x^2+9=(x-3i)(x+3i)[/tex]
Step-by-step explanation:
A. To find the solutions to the quadratic equation [tex]x^2+9=0[/tex] you must:
[tex]\mathrm{Subtract\:}9\mathrm{\:from\:both\:sides}\\\\x^2+9-9=0-9\\\\\mathrm{Simplify}\\\\x^2=-9\\\\\mathrm{For\:}x^2=f\left(a\right)\mathrm{\:the\:solutions\:are\:}x=\sqrt{f\left(a\right)},\:\:-\sqrt{f\left(a\right)}\\\\x=\sqrt{-9},\:x=-\sqrt{-9}[/tex]
[tex]x=\sqrt{-9} = \sqrt{-1}\sqrt{9}=\sqrt{9}i=3i\\\\x=-\sqrt{-9}=-\sqrt{-1}\sqrt{9}=-\sqrt{9}i=-3i[/tex]
The solutions are:
[tex]x=3i,\:x=-3i[/tex]
B. Two expressions are equivalent to each other if they represent the same value no matter which values we choose for the variables.
To factor [tex]x^2+9[/tex]:
First, multiply the constant in the polynomial by [tex]i^2[/tex] where [tex]i^2[/tex] is equal to -1.
[tex]x^2+9i^2[/tex]
Since both terms are perfect squares, factor using the difference of squares formula
[tex]a^2-i^2=(a+i)(a-i)[/tex]
[tex]x^2+9=x^2+9i^2=\left(-3i+x\right)\left(3i+x\right)[/tex]
(a) There are $n$ chairs in a row. Find the number of ways of choosing $k$ of these chairs, so that no two chosen chairs are adjacent.
(b) There are 10 chairs in a circle, labelled from 1 to 10. Find the number of ways of choosing 3 of these chairs, so that no two chosen chairs are adjacent.
(c) There are $n$ chairs in a circle, labelled from 1 to $n.$ Find the number of ways of choosing $k$ of these chairs, so that no two chosen chairs are adjacent.
Answer:
(A) P (n,k) = n!/(n-k)! divided by 2
(B) C (n,3) = n!/(12)(n-3)!
(C) C (n,k) = n!/(n-k)!(k!)
Step-by-step explanation:
Permutation deals with order or arrangement or position of objects. Where this does not matter, we use the Combination formula.
We divide by 2 in all cases, because no 2 chosen chairs should be adjacent.
For (B), n=10
C (n,3) = n!/(n-3)!(3!) divided by 2
3! = 3×2×1 = 6
The expression divided by 2 means it will be multiplied by 1/2
Hence 6×2 = 12
And we arrive at
C (n,3) =n!/(12)(n-3)!
What’s the correct answer for this question?
Answer:
B
Step-by-step explanation:
The triangular prism must have a larger base than the cylinder
Question
Find the equation of a line perpendicular to y
4x that contains the point (-3,-4).
Answer:
y=-1/4x -1
Step-by-step explanation:
y-y1 = -1/4(x1-x)
y-(-4) = -1/4(x-(-3)
y+4 = -1/4x +3
y=-1/4x-1
Suppose that a population of people has an average weight of 160 lbs, and standard deviation of 50 lbs, and that weight is normally distributed. A researcher samples 100 people, and measures their weight. Find the probability that the researcher observes an average weight of the 100 people to be between 150 and 170. [Round your answer to four decimal places]
Answer:
0.9544 = 95.44% probability that the researcher observes an average weight of the 100 people to be between 150 and 170.
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal probability distribution
Problems of normally distributed samples are solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore 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 pvalue, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
In this question, we have that:
[tex]\mu = 160, \sigma = 50, n = 100, s = \frac{50}{\sqrt{100}} = 5[/tex]
Find the probability that the researcher observes an average weight of the 100 people to be between 150 and 170.
This is the pvalue of Z when X = 170 subtracted by the pvalue of Z when X = 150. So
X = 170
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{170 - 160}{5}[/tex]
[tex]Z = 2[/tex]
[tex]Z = 2[/tex] has a pvalue of 0.9772
X = 150
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{150 - 160}{5}[/tex]
[tex]Z = -2[/tex]
[tex]Z = -2[/tex] has a pvalue of 0.0228
0.9772 - 0.0228 = 0.9544
0.9544 = 95.44% probability that the researcher observes an average weight of the 100 people to be between 150 and 170.
express 0.8342 as a fraction A: 8342/10 B: 8342/1000 C: 8342/10000
Answer:
[tex]\frac{8342}{10000} \\ [/tex]
Answer C is correct
Step-by-step explanation:
[tex]0.8342 = \frac{8342}{10000} [/tex]
To check whether this correct or wrong.
[tex]0.8342 \times 10000 = 8342[/tex]
hope this helps
brainliest appreciated
good luck! have a nice day!
The decimal 0.8342 expressed as a fraction is (c) 8342/10000
How to express the decimal 0.8342 as a fraction.From the question, we have the following parameters that can be used in our computation
The decimal 0.8342
Express the decimal 0.8342 as a fraction
So, we have the following representation
Fraction = 8342/10000
When the fraction is simplified, we have
Fraction = 8342/10000
Hence, the decimal 0.8342 as a fraction is (c) 8342/10000
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A glucose solution is administered intravenously into the bloodstream at a constant rate r. As the gulcose is added, it is converted into other substances and removed from the bloodstream at a rate that is proportional to the concentration at the time. Thus a model for the concentration C=C(t) of the glucose solution in the bloodstream is
dC/dt=r-kC
Where r an dk are positive constants.
1. Suppose that the concentration at time t=0 is C0. Determine the concentration at any time t by solving the differential equation.
2. Assuming that C0
Answer:
[tex]C(t) =\dfrac{ r}{k} - \left (\dfrac{r-kC_{0}}{k} \right )e^{ -kt}[/tex]
[tex]C(t) =\dfrac{ r}{k}- e^{ -kt}[/tex] ,thus, the function is said to be an increasing function.
Step-by-step explanation:
Given that:
[tex]\dfrac{dC}{dt}= r-kC[/tex]
[tex]\dfrac{dC}{r-kC}= dt[/tex]
Taking integration on both sides ;
[tex]\int\limits\dfrac{dC}{r-kC}= \int\limits \ dt[/tex]
[tex]- \dfrac{1}{k}In (r-kC)= t +D[/tex]
[tex]In(r-kC) = -kt - kD \\ \\ r- kC = e^{-kt - kD} \\ \\ r- kC = e^{-kt} e^{ - kD} \\ \\r- kC = Ae^{-kt} \\ \\ kC = r - Ae^{-kt} \\ \\ C = \dfrac{r}{k} - \dfrac{A}{k}e ^{-kt} \\ \\[/tex]
[tex]C(t) =\frac{ r}{k} - \frac{A}{k}e^{ -kt}[/tex]
here;
A is an integration constant
In order to determine A, we have [tex]C(0) = C0[/tex]
[tex]C(0) =\frac{ r}{k} - \frac{A}{k}e^{0}[/tex]
[tex]C_0 =\frac{r}{k}- \frac{A}{k}[/tex]
[tex]C_{0} =\frac{ r-A}{k}[/tex]
[tex]kC_{0} =r-A[/tex]
[tex]A =r-kC_{0}[/tex]
Thus:
[tex]C(t) =\dfrac{ r}{k} - \left (\dfrac{r-kC_{0}}{k} \right )e^{ -kt}[/tex]
2. Assuming that C0 < r/k, find lim t→[infinity] C(t) and interpret your answer
[tex]C_{0} < \lim_{t \to \infty }C(t) \\ \\C_0 < \dfrac{r}{k} \\ \\kC_0 <r[/tex]
The equation for C(t) can be rewritten as :
[tex]C(t) =\dfrac{ r}{k} - \left (\dfrac{r-kC_{0}}{k} \right )e^{ -kt}C(t) =\dfrac{ r}{k} - \left (+ve \right )e^{ -kt} \\ \\C(t) =\dfrac{ r}{k}- e^{ -kt}[/tex]
Thus; the function is said to be an increasing function.
I need help please help me is it 30?
Answer:
i think is 30$
Step-by-step explanation:
Answer:
B. $15.00
Step-by-step explanation:
Think about it this way:
3 = 1.50
6 = 3.00
8 = 4.00
12 = 6.00
If you divide each of the first numbers by the second, you'll get 2.
This means that every doughnut costs $0.50.
From there you just multiply .5 by 30
30
x .5
15
30 Donuts would cost 15 dollars.
Ok so the above is a little bit more of a complicated way to do it, but it'll be more efficient for a similar, but more difficult problem. The general goal of these problems is to find out what 1 of the item would cost. In this case it's $0.50, but you need to find that out in all of these problems.
brainliest is appreciated.
Tony rode his bicycle 3 7/10 miles to school. What is this distance written as a decimal?
Answer:
7/10=0.7
3+0.7=3.7
3.7
Hope this helps
Step-by-step explanation: