O EXPONENTAL AND LOGARITHMIC FUNCTIONS
Finding the initial or final amount in a word problem on...
An initial amount of money is placed in an account at an interest rate of 2% per year, compounded continuously. After two years, there is $1269.79 in the
account. Find the initial amount placed in the account. Round your answer to the nearest cent.
Answer:
$ 1220.00
Step-by-step explanation:
1269.79 = A [tex]e^{.02 * 2}[/tex]
1269.79 /A = [tex]e^{.04}[/tex]
ln(1269.79 /A) = .04 ln(e)
ln(1269.79 /A) = .04
1269.79 /A = [tex]e^{.04}[/tex]
1269.79 /A = 1.0408
A = 1269.79 / 1.0408
$ 1220.00
Which of the following consists of discrete data?
A. Number of suitcases on a plane.
B. Amount of rainfall.
C. Hair color.
D. Tree height.
Answer:
A
Step-by-step explanation:
Number of suitcases on a plane is discrete because you can only have an integer amount. You can't have a fraction of a suitcase on a plane.
Two systems of equations are given below. For each system, choose the best description of its solution.
x - 5y = 5
-x + 5y = -5
a. The system has no solution.
b. The system has a unique solution:
(x,y) = _______
c. The system has infinitely many solutions. They must satisfy the following equation:
y = ________
Answer:
Infinitely many solutions.
They must satisfy [tex]y = \frac{1}{5}(x - 5)[/tex]
Step-by-step explanation:
Given
[tex]x - 5y = 5[/tex]
[tex]-x + 5y = -5[/tex]
Required
The best description
Add both equations
[tex]x - x - 5y + 5y = 5 - 5[/tex]
[tex]0+0 =0[/tex]
[tex]0 = 0[/tex] ---- this means that the system has infinitely many solutions.
Make y the subject in: [tex]-x + 5y = -5[/tex]
Add x to both sides
[tex]5y = x - 5[/tex]
Divide through by 5
[tex]y = \frac{1}{5}(x - 5)[/tex]
Hence, they must satisfy: [tex]y = \frac{1}{5}(x - 5)[/tex]
For what values of the variable, do the following fractions exist: y^2-1/y+y/y-3
For what values of the variable, do the following fractions exist: b+4/b^2+7
For what values of the variable, do the following fractions exist: a/a(a-1)-1
PLEASE HELP NEED ANSWER ASAPPPP!!!! WILL GIVE BRAINLIEST TO FIRST CORRECT ANSWERRRR!!!
Answer:
Remember that the division by zero is not defined, this is the criteria that we will use in this case.
1) [tex]\frac{y^2 - 1}{y} + \frac{y}{y - 3}[/tex]
So the fractions are defined such that the denominator is never zero.
For the first fraction, the denominator is zero when y = 0
and for the second fraction, the denominator is zero when y = 3
Then the fractions exist for all real values except for y = 0 or y = 3
we can write this as:
R / {0} U { 3}
(the set of all real numbers except the elements 0 and 3)
2) [tex]\frac{b + 4}{b^2 + 7}[/tex]
Let's see the values of b such that the denominator is zero:
b^2 + 7 = 0
b^2 = -7
b = √-7
This is a complex value, assuming that b can only be a real number, there is no value of b such that the denominator is zero, then the fraction is defined for every real number.
The allowed values are R, the set of all real numbers.
3) [tex]\frac{a}{a*(a - 1) - 1}[/tex]
Again, we need to find the value of a such that the denominator is zero.
a*(a - 1) - 1 = a^2 - a - 1
So we need to solve:
a^2 - a - 1 = 0
We can use the Bhaskara's formula, the two values of a are given by:
[tex]a = \frac{-(-1) \pm \sqrt{(-1)^2 + 4*1*(-1)} }{2*1} = \frac{1 \pm \sqrt{5} }{2}[/tex]
Then the two values of a that are not allowed are:
a = (1 + √5)/2
a = (1 - √5)/2
Then the allowed values of a are:
R / {(1 + √5)/2} U {(1 - √5)/2}
Help me please I need help 6
Answer:
69.6
Step-by-step explanation:
sin 55 = x / 85
0.8191520443 = x / 85
x = 69.6
Which statements below represent the situation? Select three options.
Answer:
where is the statement
Step-by-step explanation:
its incomplete po
A section of a deck is shaped like a trapezoid. For this section, the length of one base is 23 feet, and the length of the other base is 50 feet. The height is 20 feet. What is the area of this section of the deck?
The area for the section of the deck is ____ ft
Answer:
Area of a trapezoid= (big base+small base)/2 x height
A=(67+54)/2 x 18
A=60.5 x 18
A=1089
Please Help
Solve 3(x+2)-4x=8
Hello!
3(x + 2) - 4x = 8 <=>
<=> 3x + 6 - 4x = 8 <=>
<=> -x + 6 = 8 <=>
<=> -x = 8 - 6 <=>
<=> -x = 2 <=>
<=> x = -2
Good luck! :)
Mr johnson sells erasers for $3 each. He sold 96 erasers last week and he sold 204 erasers this week.
A. $300 B $600 C $100 D $900
I believe your answer is D.) $900
204 + 96 = 300
300 x 3 = 900
I hope this is correct and helps!
Identify the transformation that occurs to create the graph of h(x).
H(x)=f(x+3)
Answer: The graph moved left 3 units.
(x, y) = (x - 3, y)
Which description of the graph of the linear inequality y > 3x – 8 is correct?
Options :
A.The graph will be a dashed line with a y-intercept of negative eight and a slope of three. The graph will be shaded below the line
B.The graph will be a solid line with a y-intercept of three and a slope of negative eight. The graph will be shaded above the line.
C. The graph will be a solid line with a y-intercept of three and a slope of negative eight. The graph will be shaded below the line.
D.The graph will be a dashed line with a y-intercept of negative eight and a slope of three. The graph will be shaded above the line
Answer:
D.The graph will be a dashed line with a y-intercept of negative eight and a slope of three. The graph will be shaded above the line
Step-by-step explanation:
The equation y > 3x – 8
Interpreting as a linear relation :
y > ax + b
Where, a = slope ; b = intercept
a = 3 ; that is a slope value of 3
b = -8 ; that is an intercept value of - 8
Since the inequality is >, a dashed line is used (dashed like is used for > and <) ; since we a have a greater than sign, the graph will be shaded above the dashed line.
Answer: The answer is D on edu 2021
Step-by-step explanation:
D.The graph will be a dashed line with a y-intercept of negative eight and a slope of three. The graph will be shaded above the line
The Power in a circuit is given by the formula P=I^{2}R, where I is the Current and R is the Resistance. If the Resistance is always constant at 500, the Current is 1, and dI/dt = -0.5, then dP/dt = -500.
True or false and please show work. Thank you
True
Step-by-step explanation:
[tex]P(t) = I^2(t)R[/tex]
Taking the derivative of P(t) with respect to time,
[tex]\dfrac{dP(t)}{dt} = 2I(t)\dfrac{dI(t)}{dt}R[/tex]
[tex]\:\:\:\:\:\:\:\:= 2(1)(-0.5)(500) = -500[/tex]
Use variation of parameters to find a general solution to the differential equation given that the functions y1 and y2 are linearly independent solutions to the corresponding homogeneous equation for t > 0.
ty'' + (2t - 1)y' - 2y = 7t2 e-2t y1 = 2t - 1, y2 = e-2t
Recall that variation of parameters is used to solve second-order ODEs of the form
y''(t) + p(t) y'(t) + q(t) y(t) = f(t)
so the first thing you need to do is divide both sides of your equation by t :
y'' + (2t - 1)/t y' - 2/t y = 7t
You're looking for a solution of the form
[tex]y=y_1u_1+y_2u_2[/tex]
where
[tex]u_1(t)=\displaystyle-\int\frac{y_2(t)f(t)}{W(y_1,y_2)}\,\mathrm dt[/tex]
[tex]u_2(t)=\displaystyle\int\frac{y_1(t)f(t)}{W(y_1,y_2)}\,\mathrm dt[/tex]
and W denotes the Wronskian determinant.
Compute the Wronskian:
[tex]W(y_1,y_2) = W\left(2t-1,e^{-2t}\right) = \begin{vmatrix}2t-1&e^{-2t}\\2&-2e^{-2t}\end{vmatrix} = -4te^{-2t}[/tex]
Then
[tex]u_1=\displaystyle-\int\frac{7te^{-2t}}{-4te^{-2t}}\,\mathrm dt=\frac74\int\mathrm dt = \frac74t[/tex]
[tex]u_2=\displaystyle\int\frac{7t(2t-1)}{-4te^{-2t}}\,\mathrm dt=-\frac74\int(2t-1)e^{2t}\,\mathrm dt=-\frac74(t-1)e^{2t}[/tex]
The general solution to the ODE is
[tex]y = C_1(2t-1) + C_2e^{-2t} + \dfrac74t(2t-1) - \dfrac74(t-1)e^{2t}e^{-2t}[/tex]
which simplifies somewhat to
[tex]\boxed{y = C_1(2t-1) + C_2e^{-2t} + \dfrac74(2t^2-2t+1)}[/tex]
When randomly selecting adults, let M denote the event of randomly selecting a male and let B denote the event of randomly selecting someone with blue eyes. What does P(M|B) represent? Is P(M|B) the same as P(B|M)?
Answer:
See explanation
Step-by-step explanation:
Given
[tex]M \to[/tex] randomly selecting a male
[tex]B \to[/tex] randomly selecting someone with blue eyes
Solving (a): Interpret P(M|B)
The above implies conditional probability
The interpretation is: the probability of selecting a male provided that a person with blue eyes has been selected
Solving (b): is (a) the same as P(B|M)
No, they are not the same.
The interpretation of P(B|M) is: the probability of selecting a person with blue eyes provided that a male has been selected
please help to solve this in written format
Answer:
50 dozen total
Step-by-step explanation:
8/12 & 10/12.... average 9/12
11/12 - 9/12 =
2/12x = 100
2x = 1200
x = 600/12
50 dozen total
Which set of statements shows the correct steps to find 45 percent of 75?
A.
Write 45 percent as 9 ´ 5 percent, and write 5 percent as StartFraction 1 Over 20 EndFraction. Then, find StartFraction 1 Over 20 EndFraction of 75: 75 times StartFraction 1 Over 20 EndFraction = StartFraction 75 Over 20 EndFraction = 3.75. Multiply 3.75 by 9 to get 33.75. So, 45 percent of 75 is 33.75.
B.
Write 45 percent as 9 ´ 5 percent, and write 5 percent as One-half. Then, find One-half of 75: 75 times one-half = StartFraction 75 Over 2 EndFraction = 33.75. Multiply 33.75 by 9 to get 303.75. So, 45 percent of 75 is 303.75.
C.
Write 45 percent as StartFraction 1 Over 45 EndFraction. Then, find StartFraction 1 Over 45 EndFraction of 75: 75 times StartFraction 1 Over 45 EndFraction = StartFraction 75 Over 45 EndFraction = 1.67. So, 45 percent of 75 is 1.67.
D.
Write 45 percent as StartFraction 1 Over 4.5 EndFraction. Then, find StartFraction 1 Over 4.5 EndFraction of 75: 75 times StartFraction 1 Over 4.5 EndFraction = StartFraction 75 Over 4.5 EndFraction = 16.7. So, 45 percent of 75 is 16.7.
Pls the answer is
D
Thank you
You are welcome
Answer:
d
Step-by-step explanation:
im smart
Problem is in the picture below
Answer:
90 maybe is a correct answer
Answer:
Y=40°
Step-by-step explanation:
VUW~YXZ
VWU~YZX
YXZ+XYZ+YZX=180°
70°+XYX+70°=180°
140°+XYZ=180°
XYZ=180°-140°
XYZ=40°
What is the slope of the line that passes through (17, −13) and (17, 8)?
(also can you try to explain ive been having trouble with these types of question)
Answer:
Slope is undefined. Line parallel to y-axis.
Step-by-step explanation:
By Analytic Geometry, we can determine the slope of a line by knowing two distinct lines and using the definition of secant line:
[tex]m = \frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex] (1)
Where:
[tex](x_{1}, y_{1})[/tex] - Coordinates of the initial point.
[tex](x_{2}, y_{2})[/tex] - Coordinates of the final point.
[tex]m[/tex] - Slope.
If we know that [tex](x_{1}, y_{1}) = (17, -13)[/tex] and [tex](x_{2}, y_{2}) = (17, 8)[/tex], then the slope of the line is:
[tex]m = \frac{8-(-13)}{17-17}[/tex]
[tex]m = \frac{21}{0}[/tex]
The slope is undefined, which means that line is parallel to y-axis.
what is the value of -3^2+(4+7)(2)?
Answer:
[tex] { - 3}^{2} + (4 + 7)(2) \\ = - 9 + 22 \\ = 13[/tex]
Suppose that you are interested in determining the average height of a person in a large city. You begin by collecting the heights of a random sample of 196 people from the city. The average height of your sample is 68 inches, while the standard deviation of the heights in your sample is 7 inches. The standard error of your estimate of the average height in the city is
Answer:
The standard error of your estimate of the average height in the city is 0.5 inches.
Step-by-step explanation:
Central Limit Theorem
The Central Limit Theorem establishes 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.
You begin by collecting the heights of a random sample of 196 people from the city.
This means that [tex]n = 196[/tex]
The standard deviation of the heights in your sample is 7 inches.
This means that [tex]\sigma = 7[/tex]
The standard error of your estimate of the average height in the city is
[tex]s = \frac{\sigma}{\sqrt{n}} = \frac{7}{\sqrt{196}} = 0.5[/tex]
The standard error of your estimate of the average height in the city is 0.5 inches.
Joe bought 200 masks and each mask costs Rs.5. How much did he pay altogether?
pls write the steps how to do if you I will give 5 star
Given:
total number of masks= 200cost of 1 mask= Rs. 5so, total cost fir 200 masks=
200×5
= 1000
therefore, Joe paid Rs. 1000 altogether.
You have to find the value of k
Answer:
115
Step-by-step explanation:
if you subtract 1/2 from a number and multiply the result by 1/2 you get 1/8. What is the no.
Step-by-step explanation:
1/6
1/6- 1/2 = 1/4
1/4*1/2= 1/8
A simple random sample of students could be achieved by stopping every other student who enters the library.
a. True
b. False
What is an amount between $2 and $10?
Answer:
6
Step-by-step explanation:
Ralph bought a computer monitor with an area of 384 square inches. The length of the monitor is six times the quantity of five less than half its width.
Answer:
eh width = 103.5 inches
Step-by-step explanation:
x = width
Length = (x/2 - 5 )*6
so 384=x+3x-30
414=4x
x=414/4=103.5 inches
Choose the correct answers for (a) the total installment price, (b) the carrying charges, and (c) the number of months needed to save money at the monthly rate to buy the item for its cash price.
A bunk bed with a cash price of $1,998, at $143 per month for 15 months
Answer:
$2,145 ; $147 ; 14 months
Step-by-step explanation:
Given that :
The cash price, that is, the amount that would be paid if customer is to pay the entire amount item is worth at once = $1998
Monthly payment = $143
Period = 15 months
The total installment price ; total amount paid on a monthly pay for 15 months :
(monthly payment * period)
($143 * 15)
= $2,145
The carrying charge :
Installment pay - Cash amount
$(2,145 - 1,998)
= $147
The number of month needed to save at Monthly rate to buy item at it's cash price :
Cash price / monthly payment
$1998 / $143
= 13.97
= 14 months
Need help
Identify the domain of the function shown in the graph
Answer:
B
Step-by-step explanation:
Mac is about to sue his contractor who promised to install a water tank that holds 260 gallons of water. Mac knows that 260 gallons is the capacity of a tank that
holds 35 cubic feet. The cylindrical tank has a radius of 2 feet and height of 2 feet 6 inches. Does the evidence indicate Mac can win the case against the contractor
if it goes to court
Does the evidence indicate Mac can win the case against the contractor if it goes to court?
Please hello :)
Answer:
Yes
Step-by-step explanation:
volume of cylinder = πr²h
volume = (3.14)(2 ft)²(2.5 ft)
volume = 31.4 ft³
The volume of the cylinder that was built is 31.4 ft³. It should have been 35 ft³. The evidence helps Mac in court.
Assume that the breaking system of a train consists of two components connected in series with both of them following Weibull distributions. For the first component the shape parameter is 2.1 and the characteristic life is 100,000 breaking events. For the second component the shape parameter is 1.8 and characteristic life of 80,000. Find the reliability of the system after 2,000 breaking events:
Answer:
0.9984
Step-by-step explanation:
we have shape parameter for the first component as 2.1
characteristics life = 100000
for this component
we have
exp(-2000/100000)².¹
= e^-0.0002705
= 0.9997
for the second component
shape parameter = 1.8
characteristic life = 80000
= exp(-2000/80000)¹.⁸
= e^-0.001307
= 0.9987
the reliability oif the system after 2000 events
= 0.9987 * 0.9997
= 0.9984
