What are the solutions to the equation ? e^1/4x = (4x) [tex]e^1/4x =abs( 4x)[/tex](Round to the nearest hundredth). The solutions are about x = and
Answers
The solution of the equation e^(x/4) = |4x| for the x by graphical approach is 0.27 and -0.24.
What is the equation?The definition of an equation in algebra is a mathematical statement that demonstrates the equality of 2 mathematical expressions.
A formula known as an equation uses the same sign to denote the equality of two expressions.
As per the given expression,
e^(x/4) = |4x|
The function e^(x/4) is an exponential function and the plot of this function has been plotted below.
The mode function |4x| has also been plotted below.
The point of intersection is the point where both will be the same or the solution meets.
The first point of intersection is (0.267,1.0691) so x = 0.267 ≈ 0.27
The second point of intersection (-0.2357,0.9428) so x = -0.2357 ≈ -0.24
Hence " The solution of the equation e^(x/4) = |4x| for the x by graphical approach is 0.27 and -0.24.".
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Related Questions
the square root of 31 is closer to which number? 6 or 5.
Answers
Answer:
6
Explanation:
First, we find the squares of 5 and 6.
[tex]\begin{gathered} 5^2=25 \\ 31-25=6 \end{gathered}[/tex][tex]\begin{gathered} 6^2=36 \\ 36-31=5 \end{gathered}[/tex]We conclude therefore that the square root of 31 is closer to 6 since it has a smaller difference.
Which of the following could be the product of two consecutive prime numbers?
Answers
Answer:
There is no question
Step-by-step explanation:
Have a nice day
Which equation, written in the form of y = x + b, represents the table of values?
Answers
Let:
[tex]\begin{gathered} (x1,y1)=(2,7) \\ (x2,y2)=(5,10) \end{gathered}[/tex][tex]\begin{gathered} x=2,y=7 \\ 7=2m+b \\ ---------------- \\ x=5,y=10 \\ 10=5m+b \\ ---------- \\ Let\colon \\ 2m+b=7_{\text{ }}(1) \\ 5m+b=10_{\text{ }}(2) \\ (2)-(1) \\ 5m-2m+b-b=10-7 \\ 3m=3 \\ m=1 \end{gathered}[/tex]Replace m into (1):
[tex]\begin{gathered} 2(1)+b=7 \\ 2+b=7 \\ b=7-2 \\ b=5 \end{gathered}[/tex]Answer:
[tex]y=x+5[/tex]A college conducted a survey of randomly selected freshmen about their choice of major. The table shows the results of the survey. KS
Answers
ONLY F is correct;
Here, we want to select the correct inference from the data presented
f) We want to comapre the number of English freshmen and the undecided
Both have a count of 50; we can see that these values are equal and thus, we conclude that these two are equal
This makes the inference correct
g) Here, we want to compare Education freshmen to science freshmen or others
From the question, the number of education freshmen is 60
The number of science or others is (30+25) = 55
The number for education is greater and not less
This makes this option or inference incorrect
h) Here, we want to comapre Business/Education and Science/Engineering
Business OR Education is = 45 + 60 = 105
Science OR Engineering is = 35 + 40 = 75
Business/Education is greater and this makes this option or inference wrong
j) Here, we want to compare Business and English
Business is 45
English is 50
We can see that English is greater and this makes the inference/option wrong
Graph two or more functions in the same family for which the parameter being changed is the slope, m. and is less than 0.Refer to the graph of f(x) = x + 2
Answers
We have the expression:
[tex]f(x)=x+2[/tex]If the slope is changing being less than 0, that is:
One group (A) contains 75 people. Two fifths of the people in group A will be selected to win $20 fuel cards. There is another group (B) in a nearby town that will receive the same number of fuel cards, but there are 154 people in that group. What will be the ratio of no winners in group A to nonwinners in group B after the selections are made? Express your ratio as a fraction or with a colon.
Answers
group A contains 75 people
Two-fifths of the people in group A (75*2/5=30) win $20 fuel cards.
so there are 30 fuel cards and 75-30=45 non-winners in group A
group B are 154 people and the same number of fuel cards, so 30
the number of non-winners in group B is 154-30=124
So the ratio of no winners in group A to nonwinners in group B is:
45/124
what is the slope for (0,-3),(-3,2)
Answers
Given the general rule for the slope:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]We have the following in this case:
[tex]\begin{gathered} (x_1,y_1)=(0,-3) \\ (x_2,y_2)=(-3,2) \\ \Rightarrow m=\frac{2-(-3)}{-3-0}=\frac{2+3}{-3}=-\frac{5}{3} \\ m=-\frac{5}{3} \end{gathered}[/tex]therefore, the slope is m=-5/3
You buy items costing $3000 and finance the cost with a simple interest fixed installment loan at 5% simple interest per year. The finance charge is $600.a) How many years will you be paying?b) What is your monthly payment?
Answers
Given:
The principal amount is P = $3000.
The rate of interest is r = 5% = 0.05.
The interest rate is A = $600.
The objective is,
a) To find the number of years.
b) To find the monthly payment.
Explanation:
a)
The general formula for simple interest is,
[tex]A=P\times n\times r\text{ . . . . . .(1)}[/tex]To find n:
On plugging the given values in equation (1),
[tex]\begin{gathered} 600=3000\times n\times0.05 \\ n=\frac{600}{3000\times0.05} \\ n=4 \end{gathered}[/tex]b)
Since, the total amount of the item can be calculated as,
[tex]T=A+P\text{ .. . . . (2)}[/tex]On plugging the obtained values in equation (2),
[tex]\begin{gathered} T=600+3000 \\ T=3600 \end{gathered}[/tex]To find monthly payment:
Now, the monthly payment can be calculated as,
[tex]m=\frac{T}{n\times12}\text{ . . . . .(3)}[/tex]Here, m represents the monthly payment, the product of 12 is used to convert the number of years into the number of months.
On plugging the obtained values in equation (3),
[tex]\begin{gathered} m=\frac{3600}{4\times12} \\ m=75 \end{gathered}[/tex]Hence,
a) The number of years is 4 years.
b) The monthly payment is $75.
May I get help, I know I have to multiply the possibilities, but I keep getting stuck
Answers
First we obtain each probability
The land has no oil
is a 45% chance that the land has oli , then the chance that the land has not oil is 55%
55% can be represented like 0.55
then the probability to the land has no oil is 0.55
The test shows that there is no oil
Kit claims to have an 80% of idicating oil, then the percent that there is no oil is 20%
20% can be represented like 0.2
the tne probability to shows that theere is no oil is 0.2
Finally
Multiply the probabilities to find the probability that say the land has no oil and the test shows that there is no oil
[tex]0.55\times0.2=0.11[/tex]then irhg toption is B
On the desmos app can you have more standard forms or only one?
Answers
Answer: I am pretty sure you can only have one.
Step-by-step explanation:
An athlete runs at a speed of 9 miles per hour. If one lap is 349 yards, how many laps does he run in 22 minutes
Answers
An athlete run in 22 minutes is 19.232 laps
Given,
An athlete runs at a speed of 9 miles per hour.
and, If one lap is 349 yards.
To find the how many laps does he run in 22 minutes?
Now, According to the question:
Firstly, Convert the mph into yard per minute,
Remember that:
I mile = 1,760 yard
1hour = 60 minute
Convert the speed in miles/hour to yards/minute
9 [tex]\frac{miles}{hour}[/tex] = 9[tex]\frac{1760}{60}[/tex] = 264 yard/ min
We know that
The speed is equal to divide the distance by the time
Let
s → the speed
d → the distance in yards
t → the time in minutes
Using the formula :
Speed = distance/ time
Solve the distance:
d = speed x time
Speed = 264 yard/ minute
Time = 22 minute
Therefore,
Distance = 264 x 22
Distance = 5,808 yards
Divide the distance by 302 yards to find out the number of laps
= 5,808/ 302 = 19.232 laps
Hence, An athlete run in 22 minutes is 19.232 laps
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Consider the following graph. Determine the domain and range of the graph? Is the domain and range all real numbers?
Answers
ANSWER
Domain = [-10, 10]
Range = [4]
EXPLANATION
Domain of a graph is the set of all input values on x-axis; while
Range is the set of all possible output values on y-axis.
Determining the Domain from the given graph,
The set of all INPUT values on x-axis are -10, -9, -8,....0......5,6,7,8,9,10.
So the Domain = [-10, 10].
Determining the Range from the given graph,
For the set of all possible OUTPUT values on y-axis, we only have 4,
So the Range = [4]
Hence, Domain = [-10, 10] and Range = [4]
x – a is the factor of a polynomial P(x) if P(a) is equal to
Answers
we know that
If (x-a) is a factor of P(x)
then
For x=a
the value of P(a)=0
therefore
the answer is option DSimplify the expression.9n+ 18(2n-6)
Answers
The given expression is,
[tex]\begin{gathered} 9n+18(2n-6) \\ 9n+36n-108 \\ \\ 45n=108 \end{gathered}[/tex]What is the value of the expression 4x−y2y+x when x = 3 and y = 3? −31918
Answers
7 ( 1 + 3 )
Solve the sum inside the parentheses ( 1 + 3 = 4 )
7 ( 4 )
multiply
7*4 = 28
Since the sum must equal 28
7 + 21 = 28
Correct option = 7+21
Write the equation in standard form for the hyperbola with vertices (-9,0) and (9,0) and a conjugate axis of length 16
Answers
The given vertices are (-9,0) and (9,0).
Notice that they lie on the x-axis since they have 0 as their y-coordinate.
Hence, the hyperbola is a horizontal hyperbola.
Recall that the equation of a horizontal hyperbola is given as:
[tex]\frac{(x-h)^2}{a^2}-\frac{(y-k)^2}{b^2}=1[/tex]Where (h,k) is the center and a>b.
As both vertices are equidistant from the origin, the center of the hyperbola is (0,0), and the equation becomes:
[tex]\frac{x^2}{a^2}-\frac{y^2}{b^2}=1[/tex]Note that the vertices are at (-a,0) and (a,0).
Compare with the given vertices (-9,0) and (9,0). It follows that a=9.
Substitute this into the equation:
[tex]\frac{x^2}{9^2}-\frac{y^2}{b^2}=1[/tex]Recall that the length of the conjugate axis is given as 2b, it follows that:
[tex]\begin{gathered} 2b=16 \\ \Rightarrow b=\frac{16}{2}=8 \end{gathered}[/tex]Substitute b=8 into the equation:
[tex]\begin{gathered} \frac{x^2}{9^2}-\frac{y^2}{8^2}=1 \\ \Rightarrow\frac{x^2}{81}-\frac{y^2}{64}=1 \end{gathered}[/tex]The required equation in standard form is:
[tex]\frac{x^2}{81}-\frac{y^2}{64}=1[/tex]Use complete sentences to explain the process you would use to find the volume of the shipping box.(Trying to help my son with this)
Answers
Part A)
The given shipping box is a cuboid.
Recall that the longest length of the cuboid is diagonal.
The length of the longest item that fits inside the shipping box is the measure of the diagonal of the given box.
Given that measure breadth=16 inches and measure height = 12 inches.
Recall the formula for the diagonal d of the cuboid is
[tex]d=\sqrt[]{l^2+b^2+h^2}[/tex]We need to find the measure of the length of the cuboid.
Consider the base of the cuboid which is in rectangle shape.
Here breadth of the rectangle is 16 inches and diagonal of the rectangle is 24 inches.
Recall the formula for the diagonal of the rectangle is
[tex]diagonal_{}=\sqrt[]{l^2+b^2}[/tex]Substitute diagonal =24 inches and breath =16 inches, we get
[tex]24_{}=\sqrt[]{l^2+16^2}[/tex][tex]24_{}=\sqrt[]{l^2+256}[/tex]Taking square on both sides, we get
[tex]24^2_{}=l^2+256[/tex][tex]576-256=l^2[/tex][tex]320=l^2[/tex]Taking square root on both sides, we get
[tex]\sqrt[]{320}=l[/tex][tex]l=17.89\text{ inches}[/tex]Now, substitute l=17.89, b=16, and h=12 in the diagonal of the cuboid equation to find the diagonal of the cuboid.
[tex]d^{}=\sqrt[]{17.89^2+16^2+12^2}[/tex][tex]d^{}=\sqrt[]{320+256+144}=\sqrt[]{720}=26.83\text{ inches}[/tex]Hence the length of the longest item that fits inside the shipping box is 26.8 inches.
Part B)
Consider the length l=17.89 inches, b=16 inches, and height h=12 inches.
Recall the formula for the volume of the cuboid is
[tex]V=l\times w\times h[/tex]Substitute the length l=17.89 inches, b=16 inches, and height h=12 inches, we get
[tex]V=17.89\times16\times12[/tex][tex]V=3434.88inches^3[/tex]Hence the volume of the given shipping box is 3434.88 cubic inches.
I need help with my algebra
Answers
We have the next equation line:
[tex]3x-y\text{ = 5}[/tex]We need to solve the equation for y to get the equation form
[tex]-y\text{ =5-3x}[/tex]Multiply the equation by -1
[tex](-1)-y\text{ =(-1)(5-3x)}[/tex][tex]y\text{ = -5+3x}[/tex]Where the y-intercept is -5 and the slope is 3x.
To find the line parallel we need to know that the parallel lines have the same slope.
The parallel line also intercepts y at point (0,-7).
[tex]y=mx+b[/tex]Replace the slope=m = 3
and the y-intercept is -7.
So the parallel line is:
[tex]y=3x-7[/tex]6. If you start with 200 MNM's and eat 15 every minute and your friend starts with300 MnM's but eats 25 every minute. When will you have the same number asyour friend? How much longer will it take you to finish your MnM's? At 10minutes you both will have 50 left. You will finish 1 min and 20 seconds after yourfriend.
Answers
Given:
The initial number of MNMs I have, x=200.
The number of MNM's eat by me every minute, p=15.
The initial number of MNMs my friend have, y=300.
The number of MNM's eat by friend every minute, q=25.
Let n be the number of minutes after which both will have the same number of MNM. Then, the amount of MNM remaining with me after n minutes is,
[tex]x-pn[/tex]The amount of MNM remaining with my friend after n minutes is,
[tex]y-qn[/tex]Equate the above expressions and substitute the values to find the number of minutes n.
[tex]\begin{gathered} x-pn=y-qn \\ 200-15n=300-25n \\ 25n-15n=300-200 \\ 10n=100 \\ n=\frac{100}{10} \\ n=10 \end{gathered}[/tex]Therefore, I will have the same number as my friend after 10 minutes.
The number of minutes taken by me to finish 200 MNM's is,
[tex]\begin{gathered} m=\frac{x}{p} \\ =\frac{200}{15} \\ =13\frac{5}{15} \\ =13\frac{1}{3}\text{minutes} \\ =13\text{minute}+\frac{1}{3}\min utes\times\frac{60\text{ seconds}}{1\text{ minute}} \\ =13\text{ minutes +20 seconds} \end{gathered}[/tex]So, I will take 13 minutes 20 seconds to finish the MNM's.
The number of minutes taken by my friend to finish 300 MNM's is,
[tex]\begin{gathered} k=\frac{y}{q} \\ =\frac{300}{25} \\ =12\text{ minutes} \end{gathered}[/tex]So, the friend will take 12 minutes to finish the MNM's.
So, I will finish
13. A 640 kg of a radioactive substance decays to 544 kg in 13 hours. A. Find the half-life of the substance. Be sure to show your work including the formulas you used. Round to the nearest tenth of an hour. Only solutions using formulas from the 4.6 lecture notes will receive credit.B. How much of the substance is present after 3 days? Be sure to show the model you used.C. How long does it take the substance to reach 185 kg? Be sure to show your work.
Answers
EXPLANATION
The equation for half-life is given by the following formula:
[tex]H=\frac{t\cdot\ln(2)}{\ln(\frac{A_0}{A_t})}[/tex]Replacing terms:
[tex]H=\frac{t\cdot\ln(2)}{\ln(\frac{A_0}{A_t})}=\frac{13\cdot\ln(2)}{\ln(\frac{640}{544})}=\frac{9.0109}{0.1625}=55.45[/tex]The half-life time is H =55.4 hours.
B) After three days, that is, 72 hours, the amount of substance will be given by the following relationship:
[tex]A=A_o\cdot e^{-(\frac{\ln2}{H})t}=640\cdot e^{-(\frac{\ln2}{55.4})\cdot72}=640\cdot e^{-0.90084}[/tex]Multiplying terms:
[tex]A=640\cdot0.4062=259.96\text{ Kg}[/tex]There will be 259.96 Kg after 3 days.
C) In order to compute the number of days that will take to the substance to reach a concentration equal to 185 Kg, we need to apply the following formula:
[tex]t=\frac{\ln (\frac{A}{A_o})}{-\frac{\ln (2)}{t\frac{1}{2}}}[/tex]Replacing terms:
[tex]t=\frac{\ln (\frac{185}{544})}{-\frac{\ln (2)}{55.45}}=\frac{-1.0785}{-0.0125}=\frac{1.0785}{0.0125}=86.28\text{ hours}[/tex]It will take 86.28 hours to the substance to reach 185 Kg.
The expression x^(3) gives the volume of a cube, where x is the length of one side of the cube. Find the volume of a cube with a side length of 2 meters.
Answers
Answer:
8 cubic meters
Explanation:
The length of one side of the cube = x
For any cube of side length, x:
[tex]\text{Volume}=x^3[/tex]Therefore, the volume of the cube with a side length of 2 meters is:
[tex]\begin{gathered} V=2^3 \\ =8\; m^3 \end{gathered}[/tex]D(-9,4) E(-3,4) F(-3,10) G(-9,10) rotation 180 clockwise
Answers
Answer:
D = (9,-4) E = (3,-4) F= (3, -10) G=(9,-10)
Step-by-step explanation:
Simply switch the signs (- or +)
Ex: rotate (9,1) 180 degrees
Your answer would be (-9,-1)
Chain rule in calculus
Answers
In the given example:
[tex]\begin{gathered} u=4x^3-5 \\ f(u)=u^4 \\ \text{If we do a function composition then they will be the same} \\ f(x)=\big(4x^3-5\big)^4\rightarrow f(u)=u^4,\text{ note that }u=4x^3-5 \end{gathered}[/tex]Solve for each derivative of dy/du and du/dx
[tex]\begin{gathered} \frac{du}{dx}=3\cdot4x^{3-1}-0 \\ \frac{du}{dx}=12x^2 \\ \\ \frac{dy}{du}=4\cdot u^{4-1} \\ \frac{dy}{du}=4u^3,\text{ then substitute }u \\ \frac{dy}{du}=4(4x^3-5)^3 \\ \\ \text{Complete the chain rule} \\ \frac{dy}{dx}=\frac{dy}{du}\cdot\frac{du}{dx} \\ \frac{dy}{dx}=\big(4(4x^3-5)^3\big)\big(12x^2\big)\text{ or }\frac{dy}{dx}=48x^2(4x^3-5)^3 \\ \end{gathered}[/tex]Write a rule for the nth term of the geometric sequence given a_2 = 64, r = 1/4
Answers
The n-th term of a geometric sequence is given by the formula:
[tex]\begin{gathered} U_n=a_1r^{n-1} \\ r=\text{ common ration} \\ a_1=\text{ first term} \end{gathered}[/tex]Given that:
[tex]\begin{gathered} a_2=64 \\ r=\frac{1}{4} \\ n=2 \end{gathered}[/tex]Hence,
[tex]\begin{gathered} a_2=a_1(\frac{1}{4})^{2-1}=64 \\ a_1(\frac{1}{4})=64 \\ a_1=64\times4 \\ =256 \end{gathered}[/tex]Therefore, the rule for the nth term of the sequence is
[tex]\begin{gathered} U_n=a_1r^{n-1} \\ U_n=256_{}(\frac{1}{4})^{n-1} \end{gathered}[/tex]Samantha started with $25 in her account. she saves $7 per week. Australia has no money in his account, but adds $15 per week. for how many weeks will Australia have more money in his account than Samantha
Answers
In this problem we can made a function to calculate the total amount for Samantha (S) and total amound of Australia (A) fon any time:
[tex]\begin{gathered} S=25+7t \\ A=0+15t \end{gathered}[/tex]when t is the number of weeks. if we made equal the ecuation we will have the time when they would have the same amound:
[tex]\begin{gathered} S=A \\ 25+7t=15t \end{gathered}[/tex]and we solve for t
[tex]\begin{gathered} 25=15t-7t \\ 25=8t \\ \frac{25}{8}=t \\ 3.125=t \end{gathered}[/tex]This means that in the next full number Australia will have more money than Samantha, so in 4 weeks this is going to happen.
Jason predicted that 227 students would attend the school dance.
The actual number was 250. What is the percent error of Jason's prediction?
.
1. What is the difference between the predicted value and the
actual value?
2. Complete the equation:__=p • ___
3. Solve the equation for p.
(I already did number one I just need help with 2 and 3)
Answers
Question 2
[tex]23=p \cdot 250[/tex]
The difference is 23.The actual value is 250.Question 3
[tex]p=\frac{23}{250}=0.092[/tex]
Fart A Now that you have converted a terminating decimal number Into a fractlon, try converting a repeating decimal number Into a fraction. Repeating decimal numbers are more difficult to convert Into fractions. The first step is to assign the given decimal number to be equal to a varlable, x. For the decimal number 0.3, that means X = 0.3. if x = 0.3, what does 10x equal? Font Sizes
Answers
Given x = 0.3, we're asked to find 10x. All we need to do is multiply 10 by 0.3(which is the value of x);
[tex]10\text{ }\ast\text{ 0.3 = 3}[/tex]Therefore, 10x is equal to 3.
A company has 10 software engineers and 6 civil engineers. In how many ways can they be seated around a round table so that no two of the civil engineers will sit together? [ 9! × 10!/4!)]
Answers
The software engineers can be seated on a round table with no two civil engineers sitting together is 9!×10!/4!
Given, a company has 10 software engineers and 6 civil engineers.
we need to determine in how many ways can they be seated around a round table so that no two civil engineers will sit together.
10 software engineers can be arranged around a round table in :
=(10-1)!
= 9! ways .... eq(A)
Now, we must arrange the civil engineers so that no two can sit next to one another. In other words, we can place 6 civil engineers in any of the 10 *-designated roles listed below.
This can be done in ¹⁰P₆ ways ...(B)
From A and B,
required number of ways = 9!×¹⁰P₆
= 9! × 10!/4!
Hence the number of ways the engineers can be seated is 9! × 10!/4!.
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Find the domain of the graphed function.A. -4sxs 8B. X2-4C. x is all real numbers.D. -4sxs 9
Answers
The domain of a function is the set of values over the x-axis where it is defined on a coordinate plane.
From the image, notice that the given graph is defined whenever x is between -4 and 9. Therefore, the domain of the function is:
[tex]-4\le x\le9[/tex]can someone please show me if im correct because i got 12
Answers
Given the expression:
-3 + 15
Let's evaluate the expression.
Here, we have an addition operation.
To perform the operation, add -3 and 15.
Hence, we have:
-3 + 15 = 12
Therefore, the answer to the operation is 12.
ANSWER:
12