well, keeping in mind that a year has 365 years, so let's see
[tex]\stackrel{Oct}{10}~~ + ~~\stackrel{Nov}{30}~~ + ~~\stackrel{Dec}{31}~~ + ~~\stackrel{Jan}{31}~~ + ~~\stackrel{Feb}{21}\implies 123~days[/tex]
so the 3600 were borrowed for only 123 days of a year, that'd be 123/365 of a year, thus
[tex]~~~~~~ \textit{Simple Interest Earned Amount} \\\\ A=P(1+rt)\qquad \begin{cases} A=\textit{accumulated amount}\dotfill & \$3694.63\\ P=\textit{original amount deposited}\dotfill & \$3600\\ r=rate\to r\%\to \frac{r}{100}\\ t=years\dotfill &\frac{123}{365} \end{cases}[/tex]
[tex]3694.63=3600[1+(\frac{r}{100})(\frac{123}{365})]\implies \cfrac{3694.63}{3600}=1+\cfrac{123r}{36500} \\\\\\ \cfrac{3694.63}{3600}-1=\cfrac{123r}{36500}\implies \left( \cfrac{36500}{123} \right)\left( \cfrac{3694.63}{3600}-1 \right)=r\implies \stackrel{\%}{7.8}\approx r[/tex]
7.8% is the simple interest rate was charged if Robin repaid $3,694.63.
What is simple InterestSimple interest is based on the principal amount of a loan or the first deposit in a savings account.
A=P(1+rt)
A is final amount, P is principle amount, r is rate of interest and t is time.
We know that in a year we have 365 days.
But the time here is from oct 21 to feb 21, which has 123 days.
so the 3600 were borrowed for only 123 days of a year, that'd be 123/365 of a year, thus
Apply these values in formula
A=P(1+rt)
3694.63=3600(1+r/100(123/365))
3694.63=3600(1+123r/36500)
3694.63/3600=1+123r/36500
3694.63/3600-1=123r/36500
(3694.63-3600)/3600=123r/36500
94.63/3600=123r/36500
Apply cross multiplication
3453995=442800r
7.80=r
Hence 7.8% is the simple interest rate was charged if Robin repaid $3,694.63.
To learn more on simple interest click:
https://brainly.com/question/25845758
#SPJ2
Find the surface area of the figure. Round to the nearest hundredth of a unit. Let a = 1.9,b = 0.1, and c = 2
Answer:
I believe its 20.8, but I may be wrong
Step-by-step explanation:
The residual plot for a data set is shown below...
Based on the residual plot, which statement best explains whether the regression line is a good model for the data set and why?
A. The regression line is not a good model because there is no pattern in the residuals.
B. The regression line is a good model because the residuals are randomly distributed.
C. The regression line is not a good model because only one point in the residual plot is on the x-axis.
D. The regression line is a good model because there is one point in the residual plot on the x-axis.
Based on the residual plot given, the statement that describes if the model is good is B. The regression line is a good model because the residuals are randomly distributed.
Why is the residual line a good model?For a model to be considered ideal or good, the residuals from the model should be randomly distributed in an equal manner around the regression line.
The residual plot shows that the residuals are randomly distributed which means that the regression line is a good model.
Find out more on residuals at https://brainly.com/question/1447173.
#SPJ1
Once a delay or disability is diagnosed, the best thing to do is to continue to be a family’s knowledgeable and reliable partner in child care.Once a delay or disability is diagnosed, the best thing to do is to continue to be a family’s knowledgeable and reliable partner in child care.
Once you detect that there is a delay or disability, then you should continue to be the reliable partner in child care to the family so this is True.
What should be done when a delay in child development is seen?The observation and screening process can lead to a child care partner discovering a delay or disability.
When this happens, you should report to your supervisor to check if the child is eligible for federal and state programs related to their condition. Whatever the case, you should remain accessible to the family as their partner in child care.
Find out more on child development delays at https://brainly.com/question/5082527
#SPJ1
The half-life of iron-52 is approximately 8.3 hours.How much of a 13 gram sample of iron-52 would remain after 8 hours? Round to three decimal places.
6.665 grams of the 13 grams remain after 8 hours.
How much of a 13 gram sample of iron-52 would remain after 8 hours?The decay equation for the 13 grams of iron-52 is:
[tex]N(t) = 13g*e^{(-ln(2)/8.3h)*t}}[/tex]
Where N is the amount of iron-52, and t is the time in years.
Where we used the fact that the half-life is exactly 8.3 hours.
Now, the amount that is left is given by N(8h), so we just need to replace the variable t by by 8 hours, so we get:
[tex]N(8h) = 13g*e^{(-ln(2)/8.3h)*8h}} = 6.665g[/tex]
So 6.665 grams of the 13 grams remain after 8 hours.
If you want to learn more about half-life:
https://brainly.com/question/11152793
#SPJ1
Find the area of the kite. 9 2 3
Answer:
33 units²
Refer to the attached page
I've shown the complete calculation over there.
Answer: 33
Step-by-step explanation:
one easy way to do it is by finding the area of the 4 triangles.
because the top two and the bottom two are the same that helps a lot. The first triangle is 9 times three and then cut your answer in half. Do the same thing for the other 9 times three triangle you will end up with 27. for the top two you would multiply 3 times two to get 6 cut 6 in half to get 3. do the same or the other triangle and now you just have to add.
3 plus 3 plus 13.5 plus 13.5
to get 33
need heeeelp please
The given expression is factored as [tex]4v^{7} x^{3} (7y^{6} -3v^{2} x^{6} )[/tex]
Given expression: [tex]28v^{7}x^{3}y^{6}-12v^{9} x^{9}[/tex]
In order to factorize the given expression, take out the common terms and then simplify further.
[tex]28v^{7}x^{3}y^{6}-12v^{9} x^{9}=4v^{7} x^{3} (7y^{6} -3v^{2} x^{6} )[/tex]
In mathematics, a factor is a divisor of a given integer that divides it exactly, leaving no leftover.
A number can have either positive or negative factors.
A number has a finite number of factors.
A number's factor will never be more than or equal to the provided number.
Every number contains at least two factors, 1 and the actual number, with the exception of 0 and 1.
Finding a number's factors involves using the division and multiplication operations.
Learn more about factors here:
https://brainly.com/question/25829061
#SPJ1
Whole page of geometry stuff for 50 points only do 2,3 and 4 ( serious answers only or 1 star and report )
See below for the distance between the points and the lines
How to determine the distance between the lines and the points?Question 2
The line and the points are given as:
x = y
P = (4, -2)
Rewrite the equation as:
y = x
The slope of the above equation is
m = 1
The slope of a line perpendicular to it is
m = -1
A linear equation is represented as:
y = mx + b
Substitute m = -1
y = -x + b
Substitute (4, -2) in y = -x + b
-2 = -4 + b
Solve for b
b = 2
Substitute b = 2 in y = -x + b
y = -x + 2
So, we have:
x = y and y = -x + 2
Substitute x for y
x = -x + 2
Solve for x
x = 1
Substitute x = 1 in y = x
y = 1
So, we have the following points
(1, 1) and (4, -2)
The distance between the above points is
d = √(x2 - x1)² + (y2 - y1)²
So, we have:
d = √(1 - 4)² + (1 + 2)²
Evaluate
d = 3√2
Hence, the distance between x = y and P = (4, -2) is 3√2 units
Question 3
The line and the points are given as:
y = 2x + 1
Q = (2, 10)
The slope of the above equation is
m = 2
The slope of a line perpendicular to it is
m = -1/2
A linear equation is represented as:
y = mx + b
Substitute m = -1/2
y = -1/2x + b
Substitute (2, 10) in y = -1/2x + b
10 = -1/2 * 2 + b
Solve for b
b = 11
Substitute b = 11 in y = -1/2x + b
y = -1/2x + 11
So, we have:
y = 2x + 1 and y = -1/2x + 11
Substitute 2x + 1 for y
2x + 1 = -1/2x + 11
Solve for x
x = 4
Substitute x = 4 in y = 2x + 1
y = 9
So, we have the following points
(4, 9) and (2, 10)
The distance between the above points is
d = √(x2 - x1)² + (y2 - y1)²
So, we have:
d = √(4 - 2)² + (9 - 10)²
Evaluate
d = √5
Hence, the distance between the line and the point is √5 units
Question 4
The line and the points are given as:
y = -x + 3
R = (-5, 0)
The slope of the above equation is
m = -1
The slope of a line perpendicular to it is
m = 1
A linear equation is represented as:
y = mx + b
Substitute m = 1
y = x + b
Substitute (-5, 0) in y = x + b
0 = 5 + b
Solve for b
b = -5
Substitute b = 5 in y = x + b
y = x + 5
So, we have:
y = x + 5 and y = -x + 3
Substitute x + 5 for y
x + 5 = -x + 3
Solve for x
x = -1
Substitute x = -1 in y = x + 3
y = 2
So, we have the following points
(-1, 2) and (-5, 0)
The distance between the above points is
d = √(x2 - x1)² + (y2 - y1)²
So, we have:
d = √(-1 + 5)² + (2 - 0)²
Evaluate
d = 2√5
Hence, the distance between the line and the point is 2√5 units
Read more about distance at:
https://brainly.com/question/7243416
#SPJ1
Please help me with the first question!
[tex] \qquad \qquad \bf \huge\star \: \: \large{ \underline{Answer} } \huge \: \: \star[/tex]
[tex]\qquad❖ \: \sf \: \angle C = 63 \degree[/tex]
[tex]\textsf{ \underline{\underline{Steps to solve the problem} }:}[/tex]
[tex]\qquad❖ \: \sf \:x + 4x + 12 + x=180°[/tex]
( Angle EBA= Angle DBC, and the three angles sum upto 180° due to linear pair property )
[tex]\qquad❖ \: \sf \:6x + 12 = 180[/tex]
[tex]\qquad❖ \: \sf \:6x = 180 - 12[/tex]
[tex]\qquad❖ \: \sf \:6x = 168[/tex]
[tex]\qquad❖ \: \sf \:x = 28 \degree[/tex]
Next,
[tex]\qquad❖ \: \sf \: \angle C + \angle D + x = 180°[/tex]
[tex]\qquad❖ \: \sf \: \angle C +3x + 5 + x = 180°[/tex]
[tex]\qquad❖ \: \sf \: \angle C +4x = 180 - 5[/tex]
[tex]\qquad❖ \: \sf \: \angle C +4(28) = 175[/tex]
( x = 28° )
[tex]\qquad❖ \: \sf \: \angle C +112 = 175[/tex]
[tex]\qquad❖ \: \sf \: \angle C = 175 - 112[/tex]
[tex]\qquad❖ \: \sf \: \angle C = 63 \degree[/tex]
[tex] \qquad \large \sf {Conclusion} : [/tex]
[tex]\qquad❖ \: \sf \: \angle C = 63 \degree[/tex]
Fraction how do you make 0.475 a simple fraction
Answer: 19/40
Step-by-step explanation:
First Write 0.475 as 0.4751Multiply both numerator and denominator by 10 for every number after the decimal point0.475 × 10001 × 1000 = 4751000. Reducing the fraction gives The answer
express 350 as a product of prime factors
Answer:
2^1 × 5^2 × 7^1 = 350
Step-by-step explanation:
2, 5, 7 are prime
first step is to divide the number 350 with the prime factor 2
continue dividing the number 175 by the next smallest prime factor
stop until you can't divide anymore
https://www.cuemath.com/numbers/factors-of-350/
Find g(x), where g(x) is the translation 2 units left and 13 units up of f(x)=–7x+7.
Answer:
[tex]g(x)=-7x+6[/tex]
Step-by-step explanation:
Translations
For a > 0
[tex]f(x+a) \implies f(x) \: \textsf{translated}\:a\:\textsf{units left}[/tex]
[tex]f(x-a) \implies f(x) \: \textsf{translated}\:a\:\textsf{units right}[/tex]
[tex]f(x)+a \implies f(x) \: \textsf{translated}\:a\:\textsf{units up}[/tex]
[tex]f(x)-a \implies f(x) \: \textsf{translated}\:a\:\textsf{units down}[/tex]
Parent function:
[tex]f(x)=-7x+7[/tex]
Translation of 2 units left:
[tex]\implies f(x+2)=-7(x+2)+7[/tex]
Translation of 13 units up:
[tex]\implies f(x+2)+13=-7(x+2)+7+13[/tex]
Simplifying:
[tex]\implies g(x)=-7(x+2)+7+13[/tex]
[tex]\implies g(x)=-7x-14+7+13[/tex]
[tex]\implies g(x)=-7x+6[/tex]
Learn more about graph transformations here:
https://brainly.com/question/28041916
https://brainly.com/question/27930491
Describe in detail how you would create a number line with the following points: 1, 3.25, the opposite of 2, and – (–4fraction of one-half). Please be sure to describe on which tick marks each point is plotted and how many tick marks are between each integer. It may help for you to draw this number line by hand on a sheet of paper first.
The detail Description on how to create a number line with the above points is given below:
What is the Description?Note that we were given the following: points 4, 1, 25, and opposite of 2. The step to take to First draw on Number Line.
Since Numbers with a negative sign are known to be less than zero ( Right of zero is shown by ‘+’ sign and to the left of zero is shown by ‘–’ sign while the + sign numbers can be depicted as simply numbers)
Then:
Draw a line and select some points that is known to have an equal distance and then select and mark a point as zero on that line. The Points to the right of zero will be called positive integers and they are those marked as 1, 2, 3, etc., and also, the points to the left of zero are said to be negative integers and are known to be marked – 1, – 2, – 3, etc.Then take the line to 4 unit on right sides from Zero to depict the point 4.Then Go 3 units to the Left from zero to depict the opposite of 3Then Divide number line between 1 and 2 in four equal parts and then take to 1 part right of point 1.Lastly, divide the number line that is between 0 & -1 into two Equal parts and then take 1 part left of 0.Therefore, The detail Description on how to create a number line with the above points given above is correct:
Learn more about integer from
https://brainly.com/question/17695139
#SPJ1
If F(x) = 3x² - 8x + C and F(1) = -6, what is the value of C?
Answer:
The value of C will be -1.
Step-by-step explanation:
Greetings !
[tex]f(1) = - 6 \\ thus \: substitute \: in \: the \: equation \: \\ f(x) = 3x {}^{2} - 8x + c \\ - 6 = 3(1) {}^{2} - 8(1) + c \\ - 6 = 3 - 8 + c \\ - 6 = - 5 + c \\ - 1 = c \\ c = - 1 \\ therefore \: f(x) = 3x {}^{2} - 8x - 1 \\ f(1) = 3(1) {}^{2} - 8(1) - 1 \\ f(1) = 3 - 8 - 1 \\ f(1) =3 - 9 \\ f(1) = - 6[/tex]
1. What is the chance of landing on a number divisible by 2?
6
1
2
4
3
The chance or probability of landing on a number divisible by 2 is 1/2.
The likelihood of an event occurring is defined by probability. By simply dividing the favorable number of possibilities by the entire number of possible outcomes, the probability of an occurrence can be determined using the probability formula. Because the favorable number of outcomes can never exceed the entire number of outcomes, the chance of an event occurring might range from 0 to 1.
According to the question,
Total number of outcomes = 6
Favorable number of outcomes = 3
Thus, the required Probability = 3/6 =1/2
Learn more about probability here:
https://brainly.com/question/24756209
#SPJ1
By selling a TV for Rs 6900, a shopkeeper loses 8%. Find his cost price. What must be the price so as to make a profit of 12%?
Answer:
The selling price must be ₹8400 to make a profit of 12%======================
GivenSelling price of a TV is ₹6900,With this price the loss is 8%.To find SP to make a profit of 12%SolutionFind the cost, x:
x - 8% of x = 6900x - 0.08x = 69000.92x = 6900x = 6900/0.92x = 7500Find the price to get 12% profit:
7500 + 12% = 7500*1.12 = 8400ASAP help me with this question.
(6
In a city of 56,000 people, there are 21,000 people under 25 years of age. What percent of the population is under 25 years of age?
Answer:
37.5
Step-by-step explanation:
So whenever you want to find "x" percent of a number, you just do: [tex]\frac{x}{100} * n = \text{x\% of n}[/tex]. You're essentially converting the percentage to it's decimal value by dividing by 100.
Given this information, we're solving for x, instead of x% of n. In this case n = 56,000, and x% of 56,000 is 21,000
[tex]\frac{x}{100} * 56000 = 2100[/tex]
Divide both sides by 56,000
[tex]\frac{x}{100} = \frac{21,000}{56,000}[/tex]
Multiply both sides by 100
[tex]x = 100(\frac{21,000}{56,000})[/tex]
Simplify:
[tex]x = 37.5\%[/tex]
This can be generally thought of as:
[tex]x=100(\frac{part}{whole})[/tex]
where part = partial amount, or how much is after finding what x% is of the whole amount, but in this case we know what it is, we just don't know what the "x" percent is.
the drawing plan for a new CrossFit studio shows a rectangle that is 19.5 inches by 15 inches, as shown below. The scale in the plan is 3in.:8ft. Find the length and width of the actual studio.
Answer:
Length = 52 ft
Width = 40 ft
Step-by-step explanation:
Given information:
length = 19.5 inwidth = 15 inscale = 3 in : 8 ftScale
[tex]\implies \sf 3 \: in : 8 \: ft[/tex]
[tex]\implies \sf 1 \: in : \dfrac{8}{3} \: ft[/tex]
To find the length and width of the studio in feet, multiply the length and width in inches by 8/3:
[tex]\sf Length = 19.5 \times \dfrac{8}{3}=52\:ft[/tex]
[tex]\sf Width = 15 \times \dfrac{8}{3}=40\:ft[/tex]
Therefore, the length of the actual studio is 52 ft and the width of the actual studio is 40 ft.
Scale is 3in:8ft
So
1in=8/3ftLength
19.5(8/3)ft52ftWidth
15(8/3)40ftA triangle with a base of 16 cm and a height of 9 cm.
Answer: 288
Step-by-step explanation:
(16x9)x2
The width of a rectangle is 9 less than twice its length. If the area of the rectangle is 96
cm ^2 , what is the length of the diagonal?
Thee diagonal of the rectangle is 13.86 cm long.
What is the length of the diagonal of rectangle?We are given that;
Width of a rectangle is 9 less than twice its length. Thus, if length is L, then;
W = 2L - 9
Area formula for a rectangle is;
A = Length * Width
We are given area of rectangle = 96 cm²
Thus;
L(2L - 9) = 96
2L² - 9L = 96
2L² - 9L - 96 = 0
Using online quadratic equation calculator gives;
L = 9.53 cm
Thus;
W = 2(9.53) - 9
W = 19.06 - 9
W = 10.06 cm
The diagonal of the triangle will be gotten from Pythagoras theorem;
D = √(9.53² + 10.06²)
D = √192.0245
D = 13.86 cm
Thus, we conclude that the diagonal of the rectangle is 13.86 cm long.
Read more about Rectangle Diagonal at; https://brainly.com/question/7071655
#SPJ1
Use the formula to find the standard error of the distribution of differences in sample means, x¯1-x¯2. Samples of size 100 from Population 1 with mean 90 and standard deviation 11 and samples of size 85 from Population 2 with mean 71 and standard deviation 15 Round your answer for the standard error to two decimal places. standard error = Enter your answer in accordance to the question statement
Using the Central Limit Theorem, the standard error of the distribution of differences in sample means is of 1.97.
What is the standard error for each sample?According to the Central Limit Theorem, it is given by the standard deviation of the sample divided by the square root of the sample size, hence:
s1 = 11/sqrt(100) = 1.1.s2 = 15/sqrt(85) = 1.63.What is the square root of the distribution of differences?It is given by the square root of the sum of the standard errors of each sample squared, hence:
s = sqrt(1.1² + 1.63²) = 1.97.
More can be learned about the Central Limit Theorem at https://brainly.com/question/16695444
#SPJ1
Which statement is true about the voting results?
Answer:
11% more people voted for Candidate B than Candidate A
Step-by-step explanation:
15+6=21
9+23=32
32-21=11
Suppose you average 82 on your first 7 test. What must you score on the eighth test to raise your average to 84?
so hmmm on average on the last 7 test, you get 82, so hmmm we could say that on each of the 7 tests you got 82, so you got 82, 7 times.
now, let's say in the 8th test, you get a grade of "g", now, if we were to get an average of all 8 tests, that means the average will simply be (82*7) + "g", and we know that's 84, so
[tex]\cfrac{(\stackrel{\textit{sum of all first seven tests}}{82+82+82+82+82+82+82})~~ + ~~g}{8}~~ = ~~84\implies \cfrac{(82\cdot 7)~~ + ~~g}{8}~~ = ~~84 \\\\\\ \cfrac{574+g}{8}=84\implies 574+g=672\implies g=672-574\implies g=98[/tex]
You must score 98 on the eighth test to raise your average to 84.
Average = Sum of all scores / Number of scores
The average score is given as 82, so the sum of the first 7 test scores would be 82 multiplied by 7.
The average to 84, we need to find the sum of all 8 test scores. Let's represent the score we need on the eighth test as "x."
Average = Sum of all scores / Number of scores
Using this equation, we can write:
84 = (Sum of the first 7 test scores + x) / 8
Multiply both sides of the equation by 8:
8 * 84 = Sum of the first 7 test scores + x
672 = Sum of the first 7 test scores + x
Subtract:
672 - Sum of the first 7 test scores = x
Substitute the sum of the first 7 test scores (82 * 7) into the equation:
x = 672 - (82 * 7)
x = 672 - 574
x = 98
Therefore, you must score 98 on the eighth test to raise your average to 84.
Learn more about averages here;
https://brainly.com/question/27851466
#SPJ3
PLEASE HELP I will give 50 points! PLEASE ANSWER CORRECTLY
In a school, 10% of the students have green eyes. Find the experimental probability that in a group of 4 students, at least one of them has green eyes. The problem has been simulated by generating random numbers. The digits 0-9 were used. Let the number "9" represent the 10% of students with green eyes. A sample of 20 random numbers is shown. 7918 7910 2546 1390 6075 2386 0793 7359 3048 1230 2816 6147 5978 5621 9732 9436 3806 5971 6173 1430 Experimental Probability = [?]% =
Answer: 45%
Step-by-step explanation:
Given:
A sample of 20 random numbers.The number "9" represents the 10% of students having green eyes.Find:
The experimental probability that in a group of 4 students, at least one of them has green eyes.The number of groups which contains 9 is 9 and the total number of groups are 20.
So,
P = 9 / 20 = 0.45 = 45%
Therefore, the experimental probability is 45%
Which shows all of the zeros of function shown on the graph
Answer: C
Step-by-step explanation:
The zeros of a graph are where the graph intersects the x-axis.
question in pictures
The derivatives of the functions are listed below:
(a) [tex]f'(x) = -7\cdot x^{-\frac{9}{2} }- 2\cdot x + 4 - \frac{1}{5} - 5\cdot x^{-2}[/tex]
(b) [tex]f'(x) = \frac{1}{3}\cdot (x + 3)^{-\frac{2}{3} }\cdot (x+ 5)^{\frac{1}{3} } + \frac{1}{3} \cdot (x + 5)^{-\frac{2}{3} } \cdot (x + 3)^{\frac{1}{3} }[/tex]
(c) f'(x) = [(cos x + sin x) · (x² - 1) - (sin x - cos x) · (2 · x)] / (x² - 1)²
(d) f'(x) = (5ˣ · ㏑ 5) · ㏒₅ x + 5ˣ · [1 / (x · ㏑ 5)]
(e) f'(x) = 45 · (x⁻⁵ + √3)⁻⁸ · x⁻⁶
(f) [tex]f'(x) = (\ln x + 1)\cdot [7^{x\cdot \ln x \cdot \ln 7}+7\cdot (x\cdot \ln x)^{6}][/tex]
(g) [tex]f'(x) = -2\cdot \arccos x \cdot \left(\frac{1}{\sqrt{1 - x^{2}}} \right) - \left(\frac{1}{1 + x} \right) \cdot \left(\frac{1}{2} \cdot x^{-\frac{1}{2} }\right)[/tex]
(h) f'(x) = cot x + cos (㏑ x) · (1 / x)
How to find the first derivative of a group of functions
In this question we must obtain the first derivatives of each expression by applying differentiation rules:
(a) [tex]f(x) = 2 \cdot x^{-\frac{7}{2} } - x^{2} + 4 \cdot x - \frac{x}{5} + \frac{5}{x} - \sqrt[11]{2022}[/tex]
[tex]f(x) = 2 \cdot x^{-\frac{7}{2} } - x^{2} + 4 \cdot x - \frac{x}{5} + \frac{5}{x} - \sqrt[11]{2022}[/tex] Given[tex]f(x) = 2 \cdot x^{-\frac{7}{2} } - x^{2} + 4\cdot x - \frac{x}{5} + 5 \cdot x^{-1} - \sqrt[11]{2022}[/tex] Definition of power[tex]f'(x) = -7\cdot x^{-\frac{9}{2} }- 2\cdot x + 4 - \frac{1}{5} - 5\cdot x^{-2}[/tex] Derivative of constant and power functions / Derivative of an addition of functions / Result(b) [tex]f(x) = \sqrt[3]{x + 3} \cdot \sqrt[3]{x + 5}[/tex]
[tex]f(x) = \sqrt[3]{x + 3} \cdot \sqrt[3]{x + 5}[/tex] Given[tex]f(x) = (x + 3)^{\frac{1}{3} }\cdot (x + 5)^{\frac{1}{3} }[/tex] Definition of power[tex]f'(x) = \frac{1}{3}\cdot (x + 3)^{-\frac{2}{3} }\cdot (x+ 5)^{\frac{1}{3} } + \frac{1}{3} \cdot (x + 5)^{-\frac{2}{3} } \cdot (x + 3)^{\frac{1}{3} }[/tex] Derivative of a product of functions / Derivative of power function / Rule of chain / Result(c) f(x) = (sin x - cos x) / (x² - 1)
f(x) = (sin x - cos x) / (x² - 1) Givenf'(x) = [(cos x + sin x) · (x² - 1) - (sin x - cos x) · (2 · x)] / (x² - 1)² Derivative of cosine / Derivative of sine / Derivative of power function / Derivative of a constant / Derivative of a division of functions / Result(d) f(x) = 5ˣ · ㏒₅ x
f(x) = 5ˣ · ㏒₅ x Givenf'(x) = (5ˣ · ㏑ 5) · ㏒₅ x + 5ˣ · [1 / (x · ㏑ 5)] Derivative of an exponential function / Derivative of a logarithmic function / Derivative of a product of functions / Result(e) f(x) = (x⁻⁵ + √3)⁻⁹
f(x) = (x⁻⁵ + √3)⁻⁹ Givenf'(x) = - 9 · (x⁻⁵ + √3)⁻⁸ · (- 5) · x⁻⁶ Rule of chain / Derivative of sum of functions / Derivative of power function / Derivative of constant functionf'(x) = 45 · (x⁻⁵ + √3)⁻⁸ · x⁻⁶ Associative and commutative properties / Definition of multiplication / Result(f) [tex]f(x) = 7^{x\cdot \ln x} + (x \cdot \ln x)^{7}[/tex]
[tex]f(x) = 7^{x\cdot \ln x} + (x \cdot \ln x)^{7}[/tex] Given[tex]f'(x) = 7^{x\cdot\ln x} \cdot \ln 7 \cdot (\ln x + 1) + 7\cdot (x\cdot \ln x)^{6}\cdot (\ln x + 1)[/tex] Rule of chain / Derivative of sum of functions / Derivative of multiplication of functions / Derivative of logarithmic functions / Derivative of potential functions [tex]f'(x) = (\ln x + 1)\cdot [7^{x\cdot \ln x \cdot \ln 7}+7\cdot (x\cdot \ln x)^{6}][/tex] Distributive property / Result(g) [tex]f(x) = \arccos^{2} x - \arctan (\sqrt{x})[/tex]
[tex]f(x) = \arccos^{2} x - \arctan (\sqrt{x})[/tex] Given[tex]f'(x) = -2\cdot \arccos x \cdot \left(\frac{1}{\sqrt{1 - x^{2}}} \right) - \left(\frac{1}{1 + x} \right) \cdot \left(\frac{1}{2} \cdot x^{-\frac{1}{2} }\right)[/tex] Derivative of the subtraction of functions / Derivative of arccosine / Derivative of arctangent / Rule of chain / Derivative of power functions / Result(h) f(x) = ㏑ (sin x) + sin (㏑ x)
f(x) = ㏑ (sin x) + sin (㏑ x) Givenf'(x) = (1 / sin x) · cos x + cos (㏑ x) · (1 / x) Rule of chain / Derivative of sine / Derivative of natural logarithm /Derivative of addition of functions f'(x) = cot x + cos (㏑ x) · (1 / x) cot x = cos x / sin x / ResultTo learn more on derivatives: https://brainly.com/question/23847661
#SPJ1
A certain insecticide kills 60% of all insects in laboratory experiments. A sample of 7 insects is exposed to the insecticide in a particular experiment. What is the probability that exactly 4 insects will survive? Round your answer to four decimal places.
Step-by-step explanation:
the probability of 1 tested insect is killed is 60% or 0.6.
the probability that it is not killed is then 1-0.6 = 0.4.
when we test 7 insects and exactly 4 survive is the event that
3 insects are killed, 4 insects survive.
the probability for one such case is
0.6×0.6×0.6 × 0.4×0.4×0.4×0.4
how many such cases do we have ?
as many as ways we can select 4 insects out of the given 7.
these are 7 over 4 combinations :
7! / (4! × (7-4)!) = 7! / (4! × 3!) = 7×6×5/(3×2) = 7×5 = 35
so, the probability that exactly 4 out of 7 tested insects survive is
35 × 0.6³ × 0.4⁴ = 0.193536 ≈ 0.1935
How many three-digit positive integers have three different digits and at least one prime digit?
The number of three-digit positive integers that have three different digits and at least one prime digit are 7960.
What are prime numbers?The definition of a prime number is a natural number larger than 1 that is not the sum of two lesser natural numbers. A composite number is any natural number that is more than 1 but not a prime.
The only two components in prime numbers are 1 and the number itself.
Any whole number greater than one is a prime number.
It has exactly two factors—1 and the actual number.
There is just one 2-digit even prime number.
Every pair of prime numbers is always a co-prime.
The product of prime numbers can be used to represent any number.
Three-digit positive integers that have three different digits and at least one prime digit = 3!*4!*10*9 = 7960
To learn more about prime numbers here:
brainly.com/question/145452
#SPJ1
Below, the two-way table is given for a class
of students.
Sophomore
Freshmen
4
3
6
4
Juniors Seniors Total
2
6
Male
Female
Total
If a male student is selected at random, what is the
probability the student is a freshman.
2
3
P (Freshman | Male) = [?]%
Round to the nearest whole percent.
Enter
Answer:
2/7 = 29% (nearest percent)
Step-by-step explanation:
Calculate the totals and add them to the table:
[tex]\begin{array}{| c | c | c | c | c | c |}\cline{1-6} & \sf Freshman & \sf Sophmore & \sf Juniors & \sf Seniors & \sf Total \\\cline{1-6} \sf Male & 4 & 6 & 2 & 2 & 14\\\cline{1-6} \sf Female & 3 & 4 & 6 & 3 & 16\\\cline{1-6} \sf Total & 7 & 10 & 8 & 5 & 30\\\cline{1-6}\end{array}[/tex]
Probability Formula
[tex]\sf Probability\:of\:an\:event\:occurring = \dfrac{Number\:of\:ways\:it\:can\:occur}{Total\:number\:of\:possible\:outcomes}[/tex]
Let P(A) = probability that the student is a freshman
Let P(B) = probability that the student is male
Use the given table to calculate the probability that the student is male:
[tex]\sf \implies P(B)=\dfrac{14}{30}[/tex]
And the probability that the student is a freshman and male:
[tex]\implies \sf P(A \cap B)=\dfrac{4}{30}[/tex]
To find the probability that the student owns a credit card given that the they are a freshman, use the conditional probability formula:
Conditional Probability Formula
The probability of A given B is:
[tex]\sf P(A|B)=\dfrac{P(A \cap B)}{P(B)}[/tex]
Substitute the found values into the formula:
[tex]\implies \sf P(Freshman|Male)=\dfrac{\dfrac{4}{30}}{\dfrac{14}{30}}=\dfrac{4}{14}=\dfrac{2}{7}=0.28571...=29\%[/tex]
Therefore, the probability that the student is a freshman given they are male is 29% (nearest percent).
Learn more about conditional probability here:
https://brainly.com/question/28028208
https://brainly.com/question/23957743
DJ Larissa is making a playlist for a friend; she is trying to decide what 10 songs to play and in what order they should be played .
Step 2. If she has her choices narrowed down to 7 blues, 3 hip-hop, 5 reggae, and 7 rock songs, and she wants to play no more 4 blues songs, how many different playlist or possible? Express your answer in scientific notation rounding to the hundredths place
The total number of ways are formed is 4.43 x 10^10 by rounding to the hundredths place.
According to the statement
we have given that the some numbers of the songs which are added by the larrisa in her playlist.
And we have to tell the ways which are formed with the help of the combination and permutations.
So, For this purpose we know that the
The first condition we have given that the
"play no more than 4 blues songs" - indicates playlist can contain 0, 1, 2, 3, or 4 blues songs. You need to analyze five different cases and add them up together in the end. From 7 blues songs, you can either "pick" 0, 1, 2, 3, or 4. Since order matters, it's a permutation, not a combination.
Afterwards, it gets tricky. Consider the first case, where we have 0 blues songs. This means that there are 10 spaces for the remaining (3+5+7 = 15) songs, which means that they can be arranged in (7P0 ∙ 15P10) ways.
For the next case, where we have 1 blues songs, it means that there are 9 spaces for the remaining 15 songs, which means that they can be arranged in (7P1 ∙ 15P9) ways. Continue doing this for the cases of 2, 3, and 4 blues songs and add up all the cases together.
And from this way we get the all combinations which are formed.
So, For this purpose
n = (7P0 ∙ 15P10) + (7P1 ∙ 15P9) + (7P2 ∙ 15P8) + (7P3 ∙ 15P7) + (7P4 ∙ 15P6) = 4.43459016×1010,
which rounded to the hundredths place, is 4.43 x 10^10 possible playlists.
So, The total number of ways are formed is 4.43 x 10^10 by rounding to the hundredths place.
Learn more about the combination and permutations here
https://brainly.com/question/3901018
#SPJ1
Answer:
Step-by-step explanation: