Answer:
approximately $23,655.91 (rounded to the nearest hundredths place)
Step-by-step explanation:
[tex]22,000=0.93x\\x=23,655.91[/tex]
The sum of the first n terms of a geometric series is 364? The sum of their reciprocals 364/243. If the first term is 1, find n and common ratio
If the geometric series has first term [tex]a[/tex] and common ratio [tex]r[/tex], then its [tex]N[/tex]-th partial sum is
[tex]\displaystyle S_N = \sum_{n=1}^N ar^{n-1} = a + ar + ar^2 + \cdots + ar^{N-1}[/tex]
Multiply both sides by [tex]r[/tex], then subtract [tex]rS_N[/tex] from [tex]S_N[/tex] to eliminate all the middle terms and solve for [tex]S_N[/tex] :
[tex]rS_N = ar + ar^2 + ar^3 + \cdots + ar^N[/tex]
[tex]\implies (1 - r) S_N = a - ar^N[/tex]
[tex]\implies S_N = \dfrac{a(1-r^N)}{1-r}[/tex]
The [tex]N[/tex]-th partial sum for the series of reciprocal terms (denoted by [tex]S'_N[/tex]) can be computed similarly:
[tex]\displaystyle S'_N = \sum_{n=1}^N \frac1{ar^{N-1}} = \frac1a + \frac1{ar} + \frac1{ar^2} + \cdots + \frac1{ar^{N-1}}[/tex]
[tex]\dfrac{S'_N}r = \dfrac1{ar} + \dfrac1{ar^2} + \dfrac1{ar^3} + \cdots + \dfrac1{ar^N}[/tex]
[tex]\implies \left(1 - \dfrac1r\right) S'_N = \dfrac1a - \dfrac1{ar^N}[/tex]
[tex]\implies S'_N = \dfrac{1 - \frac1{r^N}}{a\left(1 - \frac1r\right)} = \dfrac{r^N - 1}{a(r^N - r^{N-1})} = \dfrac{1 - r^N}{a r^{N-1} (1 - r)}[/tex]
We're given that [tex]a=1[/tex], and the sum of the first [tex]n[/tex] terms of the series is
[tex]S_n = \dfrac{1-r^n}{1-r} = 364[/tex]
and the sum of their reciprocals is
[tex]S'_n = \dfrac{1 - r^n}{r^{n-1}(1 - r)} = \dfrac{364}{243}[/tex]
By substitution,
[tex]\dfrac{1 - r^n}{r^{n-1}(1-r)} = \dfrac{364}{r^{n-1}} = \dfrac{364}{243} \implies r^{n-1} = 243[/tex]
Manipulating the [tex]S_n[/tex] equation gives
[tex]\dfrac{1 - r^n}{1-r} = 364 \implies r (364 - r^{n-1}) = 363[/tex]
so that substituting again yields
[tex]r (364 - 243) = 363 \implies 121r = 363 \implies \boxed{r=3}[/tex]
and it follows that
[tex]r^{n-1} = 243 \implies 3^{n-1} = 3^5 \implies n-1 = 5 \implies \boxed{n=6}[/tex]
A polynomial function has a root of -6 with multiplicity 3 and a root of 2 with multiplicity 4. If the function has a negative
leading coefficient and is of odd degree, which could be the graph of the function?
Answer:
Using the formula multiplicity, we find that the equation of the function will be [tex]f(x)=-(x+6)^{3} (x-2)^{4}[/tex]. The graph is in the attachment.
Step-by-step explanation:
Concept: Given that for -6, multiplicity is 3 and for 2 multiplicity is 4.
So, the equation of multiplicity is represented as:
[tex]f(x)=a(x-root)^{mutliplicity}[/tex]
This gives the following function
[tex]f(x)=a(x+6)^{3} (x-2)^{4}[/tex]
The equation has a negative leading coefficient.
This means that, the value of a is less than 0 i.e. a < 0
Assume any value of a (say a = -1), the equation becomes
[tex]f(x)=-(x+6)^{3} (x-2)^{4}[/tex]
The graph is in the attachment.
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Answer:
C
Step-by-step explanation:
trust bro
Shashi has a rectangular garden. The length of the garden is 4 feet less than twice the width. The area of the garden is 448 square feet. What is the length of the garden?
Answer:
28 feet
Step-by-step explanation:
Area of a rectangle is :
A = L × W
We are given A and a expression for L, so let's substitute :
448 = (2W-4) × W
Now we expand the left side :
2W²-4w = 448
Subtract 448 from both sides :
2W²-4W-448 = 0
Divide everything by 2 :
W²-2W-224 = 0
Now we factorise :
Find 2 numbers that multiply to give -224 and add to give -2 :
-16 and 14
Rewrite -2W with -16W and +14W :
W² - 16W + 14W -224 = 0
W(W-16) +14(W-16) = 0
(W+14)(W-16) = 0
W = -14 , W = 16
Only take positive value since this is lengths :
W = 16
Now we substitute W into the expression to find L :
L = (2W -4)
L = 2(16) - 4
L = 32 - 4
L = 28
Units will be feet since it is a length
Hope this helped and have a good day
Solve based off of the screenshot provided below.
Answer:
48 cm²
Explanation:
The figure can be cut into 1 rectangle and 1 triangle.
Area of the figure:
⇒ area of rectangle + area of triangle
⇒ Length × Width + 1/2 × Base × Height
⇒ 6 × 4 + 1/2 × 6 × 8
⇒ 24 + 24
⇒ 48
Therefore, area of figure is 48 cm².
Answer:
48 cm squared
Step-by-step explanation:
The given figure is composed of a rectangle (L=6 cm and W = 4 cm) and a right angled triangle { Base = (12- 4) = 8 cm, height = 6 cm. }
Area of the two figures is to be calculated separately and then added to get the required result.
Area of the rectangle = l × w
= 6 × 4
= 24 cm²
Area of the right triangle = ½ × base × height
= ½ × 8 × 6
= 24 cm²
Hence, area of the given figure = 24 + 24
= 48 cm squared.
If it is now 1:15, what time will it be in 1 1/2 hours' time?
Answer:
2:45
Step-by-step explanation:
1 1/2 hour is 1 hour and 30 minutes.
If we add 30 minutes to 1:15, we get 1:45
if we add 1 hour to 1:45, we get 2:45, which is our answer.
what is the length of the squares side?
Answer:
side ≈ 4.24= [tex]\frac{6}{\sqrt{2} }[/tex]
Step-by-step explanation:
sides a = b
[tex]6^{2} =a^{2} +a^{2}[/tex]
[tex]6^{2} =2a^{2}[/tex]
[tex]a^{2}= \frac{6^{2} }{2} =\frac{36}{2} =18[/tex]
[tex]a=\sqrt{18} =4.24=\sqrt{(9)(2)} =\frac{6}{\sqrt{2} }[/tex]
Hope this helps
The graph of a rational function f is shown below.
Assume that all asymptotes and intercepts are shown and that the graph has no "holes".
Use the graph to complete the following.
We have y+2 = 0 and x - 2 = 0. The provided function has an x and y-intercept of -2 and +2, respectively. There is no vertical asymptote. Two is the horizontal asymptote.
What is a graph?A diagram depicting the relationship between two or more variables, each measured along with one of a pair of axes at right angles.
The y-intercept of a function is determined by the intersection of its graph with the y-axis. The value of y on the y-axis at which the considered function crosses it is called the y-intercept.
Assume the following equation: y = f (x)
We have x =0- 2 and y+2 = 0,The x and y intercept of the given function is -2 and +2.
The vertical asymptote is none. The horizontal asymptote is 2.
Hence,we have y+2 = 0 and x - 2 = 0. The provided function has an x and y-intercept of -2 and +2, respectively. There is no vertical asymptote. Two is the horizontal asymptote.
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WHAT DOES THIS MEAN???
"If you take Nia out for mexican food, have an air freshener on standby."
Answer: Beans cause Nia to Fart!
Step-by-step explanation:
Mexican food usually contains beans, which beans are a known catalyst of flatulence. Beans induce farts and Nia does so! Farts usually stink, so an air freshener is needed.
Hi people! Can you help me figure this out? I'll mark brainliest!
D. 12.5
The equation to find the average rate of change is
[tex] \frac{y2 - y1 }{x2 - x1} [/tex]
To find the average rate of change between points (0,20) and (8,120) you need to plug it into the equation so it'll be
[tex] \frac{120 - 20}{8 - 0} [/tex]
this simplifies to
[tex] \frac{100}{8} [/tex]
which is 12.5
convert 0.390 as a fraction
Answer:
390/1000
This is the answer and hope it helps
A standard number cube with the numbers 1 through 6 is rolled. Find the probability of rolling a number greater than 2
Determine if an exponential would be an appropriate model for the data shown in each scatter plot. Select one that applies.
Answer:
Graph 1: No, a linear model would be more appropriate.Graph 2: YesGraph 3: No, a quadratic model would be more appropriate.Let f(x) = -5x^6√x + -7/x³√x. What would f’(x) be? If anyone could show me step-by-step, I would greatly appreciate it! I’ve worked out this problem 4 times already and I can’t seem to get the right answer.
Answer:
[tex]f^{\prime}\left(x\right)\ =\ -\frac{65}{2}x^{\frac{11}{2}}\ +\frac{49}{2}x^{-\frac{9}{2}}[/tex]
or
[tex]f^{\prime}\left(x\right)\ =\ -32.5x^{5.5}\ +\ 24.5x^{-4.5}[/tex]
Step-by-step explanation:
Rather than solving this question in a more complex method by directly using the product rule and quotient rule, it can first be considered to perform some algebraic manipulation (index laws) to simplify the expression before taking the derivative.
[tex]\begin{large}\begin{array}{l}f\left(x\right)\ =\ -5x^6\ \sqrt{x}\ +\ \frac{-7}{x^3\ \sqrt{x}}\\\\f\left(x\right)\ =\ -5x^6\cdot x^{\frac{1}{2}}\ +\ \frac{-7}{x^3\cdot x^{\frac{1}{2}}}\\\\f\left(x\right)\ =\ -5x^{6\ +\ \frac{1}{2}}\ +\ \frac{-7}{x^{3\ +\ \frac{1}{2}}}\\\\f\left(x\right)\ =\ -5x^{\frac{13}{2}}\ +\ \frac{-7}{x^{\frac{7}{2}}}\\\\f\left(x\right)\ =\ -5x^{\frac{13}{2}}\ -7x^{-\frac{7}{2}}\end{array}[/tex]
Now, the derivative of the function can be calculated simply by only using the power rule, which yields
[tex]\begin{large}\begin{array}{l}f\left(x\right)\ =\ -5x^{\frac{13}{2}}\ -7x^{-\frac{7}{2}}\\\\f^{\prime}\left(x\right)\ =\ \left(-5\right)\left(\frac{13}{2}\right)\left(x^{\frac{13}{2}\ -\ 1}\right)\ -\ \left(7\right)\left(-\frac{7}{2}\right)\left(x^{-\frac{7}{2}\ -\ 1}\right)\\\\f^{\prime}\left(x\right)\ =\ -\frac{65}{2}x^{\frac{11}{2}}\ +\frac{49}{2}x^{-\frac{9}{2}}\\\\f^{\prime}\left(x\right)\ =\ -32.5x^{5.5}\ +\ 24.5x^{-4.5}\end{array}\\\end{large}[/tex]
Write the equation using function notation f(x). then find f(0)
2x^2 - 3y = 6
[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]
[tex]\qquad \tt \rightarrow \: f(0) = -2[/tex]
____________________________________
[tex] \large \tt Solution \: : [/tex]
[tex]\qquad \tt \rightarrow \: 2 {x}^{2} - 3y = 6[/tex]
[tex]\qquad \tt \rightarrow \: 3y + 6 = 2 {x}^{2} [/tex]
[tex]\qquad \tt \rightarrow \: 3y = 2 {x}^{2} - 6[/tex]
[tex]\qquad \tt \rightarrow \: y = \cfrac{2 {x}^{2} - 6 }{3} [/tex]
[tex]\qquad \tt \rightarrow \: y = \cfrac{2 {}^{} }{3} {x}^{2} - 2[/tex]
[ here, y can be replaced with f(x) because y is a function of x ]
[tex]\qquad \tt \rightarrow \: f(x) = \cfrac{2 {}^{} }{3} {x}^{2} - 2[/tex]
[tex] \large\textsf{Find f(0):} [/tex]
[tex]\qquad \tt \rightarrow \: f(0) = \cfrac{2 {}^{} }{3} {(0)}^{2} - 2[/tex]
[tex]\qquad \tt \rightarrow \: f(0) = 0 - 2[/tex]
[tex]\qquad \tt \rightarrow \: f(0) = - 2[/tex]
Answered by : ❝ AǫᴜᴀWɪᴢ ❞
Please help! thank youuuu
Use polynomial long division to divide. Determine whether the divisor evenly divides into the dividend.
(8x-5)/(2x+1)
Answer:
The solution is 4 - 9/(2x + 1)
No, the divisor does not evenly divide into the dividend
Step-by-step explanation:
Please see the attached image
Placement Assessment
A certain drug is made from only two ingredients: compound A and compound B. There are 7 milliliters of compound A used for every 4 milliliters of compound
B. If a chemist wants to make 946 milliliters of the drug, how many milliliters of compound A are needed?
milliliters of compound A
X
Time Remaining: 22:11:23 I Question 17
?
Libbi
Est
Answer:
[tex]7 469.8.56[/tex]
nossa nem sei como é bom saber se fala com a mãe e o pai do mundo e vc não tem mais nada pra comer e não tem como fazer a gente vai ficar muito tempo sem fazer a mãe dela não e vc como tá o trabalho rede de nada em casa e é só pra mim né não é fácil de fazer a mãe dela e a mãe dele tá bem né não é fácil de fazer o que vc quer que Deus quiser vai dar pra mim né e não tem como fazer d id da x não vou poder é o que eu te abençoe e ilumine e ilumine todos os dias entre?01029)
What key features do the functions f(x) = 4-x and g of x equals negative one times the square root of the x minus 4 end root have in common? Both f(x) and g(x) include domain values of [–4, ∞) and range values of (–∞, ∞), and both functions have an x-intercept in common. Both f(x) and g(x) include domain values of [4, ∞), and both functions decrease over the interval (4, ∞). Both f(x) and g(x) include domain values of [4, ∞) and range values of [0, ∞), and both functions have a y-intercept in common. Both f(x) and g(x) include domain values of [–4, ∞) and range values of (–∞, ∞), and both functions are negative for the entire domain.
The statement about both functions that is true is:
Both f(x) and g(x) include domain values of [4, ∞), and both functions decrease over the interval (4, ∞). What is the domain and range for the function of y = f(x)?The domain of a function is the set of values of input for which the function is valid.
The range is the dependent variable of a set of values for which the function is defined.
Given that:
f(x) = 4 - x
The slope (m) of the function = -1x-intercept = (4,0)y-intercept = (0,4)Domain = [4,∞)For function g(x) = -1 ×[tex]\mathbf{\sqrt{x-4}}[/tex]
The domain = x ≥ 4 and the solution set is [4,∞)The range g(x) = ≤ 0 and the solution set is [-∞, 0)The function g(x) does not have a y-intercept.Therefore, from the given options, the statement about both functions that is true is:
Both f(x) and g(x) include domain values of [4, ∞), and both functions decrease over the interval (4, ∞).Learn more about the domain of a function here:
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Answer:
Both f(x) and g(x) include domain values of [4, ∞), and both functions decrease over the interval (4, ∞).
Step-by-step explanation:
I got it right on the test.
Multiply (Make sure to show work on a separate sheet of paper)
Please use the equation writer that is on top. Look for this sign √ and click on it. That will allow you to write an exponent.
(2x−4)(x−6)
Answer:
[tex]2x^{2}[/tex] - 16x + 14
Step-by-step explanation:
(2x - 4)(x - 6)
= (2x + −4)(x + −6)
= (2x)(x) + (2x)(−6) + (−4)(x) + (−4)(−6)
= [tex]2x^{2}[/tex] − 12x − 4x + 24
= [tex]2x^{2}[/tex] - 16x + 14
Evaluate:
10
Σ¹0 4(1)n-1 = [?]
Round to the nearest hundredth.
Enter
Answer:
Step-by-step explanation:
we are essentially calculating:
4(1/4)^0 + 4(1/4)^1 + 4(1/4)^2 + ... + 4(1/4)^9
Formula: [tex]\frac{a(1-r^n)}{1-r}[/tex]
4(1-(1/4)^10)/ (1-1/4) approximates to 5.33
As part of a weight loss plan, Levi’s average Calories consumed per day, denoted by c, subject to a maximum of 15 calories, is measured to calculate the amount of weight he will lose. If he is losing weight consistently, what is the domain of the function?
a. c < 0
b. c > 0
c. 0 ≤ c ≤ 15
d. 0 < c ≤ 15
Using it's concept, it is found that the domain of the function is given as follows:
d. 0 < c ≤ 15
What is the domain of a function?The domain is the set that contains all possible input values for the function.
He is losing weight consistently, hence c > 0, and the maximum amount is of 15 calories, hence c ≤ 15 and the domain is given by:
d. 0 < c ≤ 15
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Express 5.5° as a fraction. .
Answer:
11/200
Step-by-step explanation:
Convert the percentage to a fraction by placing the expression over
100
Percentage means 'out of 100
5.5
100
Convert the decimal number to a fraction by shifting the decimal point in both the numerator and denominator. Since there is
1
number to the right of the decimal point, move the decimal point
1
place to the right.
55
1000
Cancel the common factor of
55
and
1000
11/200
if the third place value of a number is 64 , What base is the number in ?
A) 2
B) 4
C) 8
D) 16
Answer:
B
Step-by-step explanation:
4, 16, 64 should be the correct order
21% of hospital patients stay for less than 1 day. If 1,134 patients in January stay less than 1 day what total of number of patients did the hospital treat in January?
find the missing values in this sequence; -6;...;3...;15.
Answer:
Maybe 9 and 12 ?
Step-by-step explanation:
-6 + 9 = 3
then 3 + 9 = 12
then 12 + 3 = 15
each term is the sum of the two that are before it
y=2x+40 and y=4x+20 when will these be equal
Answer:
When x = 10, they will both be y = 60
(10, 60)
Step-by-step explanation:
2(10) + 40 = 60
4(10) + 20 = 60
Answer:
x = 10
Step-by-step explanation:
2 (10) +40 = 60
4(10) +20 = 60
Somebody help me solve;
(1)A fair die is being rolled.
a) Find the probability that at least 5 rolls are needed to obtain the first
one.
b) Find the probability that it will take fewer than seven rolls to obtain the
second one if the first one occurs on the third roll.
(04.01, 04.02 HC)
Eric plays basketball and volleyball for a total of 95 minutes every day. He plays basketball for 25 minutes longer than he plays volleyball.
Part A: Write a pair of linear equations to show the relationship between the number of minutes Eric plays basketball (x) and the number of minutes he plays volleyball (y) every day. (5 points)
Part B: How much time does Eric spend playing volleyball every day? Show your work. (3 points)
Part C: Is it possible for Eric to have spent 35 minutes playing basketball if he plays for a total of exactly 95 minutes and plays basketball for 25 minutes longer than he plays volleyball? Explain your reasoning. (2 points)
Eric spend 60 minutes for basketball and 35 minutes for volleyball.
What is Linear Equation?An equation that has the highest degree of 1 is known as a linear equation. This means that no variable in a linear equation has an exponent more than 1. The graph of a linear equation always forms a straight line.
Here, let Eric plays basketball for x minutes.
and volleyball for y minutes.
Total time spend on playing basketball and volleyball everyday = 95 minutes.
Duration of Basketball 25 minutes more than volleyball
Now, according to question,
x + y = 95 ..........(i)
x - 25 = y ...........(ii)
On solving equation (i) and (ii), we get
x + x - 25 = 95
2x = 95 + 25
2x = 120
x = 120 / 2
x = 60
put value of x in equation (ii), we get
60 - 25 = y
y = 35
Yes, it is possible and clearly described in above calculation.
Thus, Eric spend 60 minutes for basketball and 35 minutes for volleyball.
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Please answer both questions I will give u brainliest if ur right
first one b 315, second d
Step-by-step explanation:
18*=3*+315
7*+4*=a*
A clock was reading the time accurately on Friday at noon. On Monday at 6pm the clock was running late by 468 seconds. On average, how many seconds did the clock skip every 30 minutes?
The clock was skipping 3 seconds every 30 minutes from Friday noon to Monday 6 pm.
The clock was still accurate by Friday noon. The clock was late by 468 seconds by Monday, 6 pm.
To solve the problem, we must:
Know how many 30-minutes have passed during the time period.
1 day = 24 hours
1 hour = 60 minutes = 2 × (30 minutes)
1 day = 24 hours × 2 × (30 minutes)
1 day = 48 × (30 minutes)
Thus, there are 48, 30-minutes in a day. On Friday, however, we start counting at noon, which is half of the day. Moreover, on Monday, the mark is only up to 6 pm, which is three-fourths of the day.
Friday = 48 × [tex]\frac{1}{2}[/tex] = 24
Saturday = 48
Sunday = 48
Monday = 48 × [tex]\frac{3}{4}[/tex] = 36
TOTAL = 24 + 48 + 48 + 36 = 156
Therefore, the total number of 30-minutes that have passed is 156. There were 156, 30-minutes that passed during the time period.
Divide the number of total seconds late by the number of 30-minutes passed.
That is, the number of total seconds late= 468 seconds ÷ 156
= 3 seconds
Therefore, the clock was skipping 3 seconds every 30 minutes from Friday noon to Monday 6 pm.
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Which values are part of the solution set? Check all that apply. x = 3 x = –5 x = negative one-half x = –4.5 x = –4
The values that are part of the solution are x = -5 and x = -4.5
Number linesNumber lines are lines that are used to represent the solution to inequalities.
From the given number line with he solution x > -4, this shows that all the solutions must be values that are greater than -4.
The values that are part of the solution are x = -5 and x = -4.5
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