Answer:
D. The zeros are the hot dog prices that give $0.00 profit (no profit).
Step-by-step explanation:
Given the function y=-2(x-3)² + 4
The zeros of the function are the points at which the graph of the function crosses the x axis if plotted. y is the daily profit (in hundreds of dollars) and x is the price of the hot dog. To find the zeros, we substitute x = 0 and solve.
Therefore: y=2(x-3)² + 4
0 = 2(x-3)² + 4
-2(x² - 6x + 9) + 4 = 0
-2x² + 12x - 18 + 4 = 0
2x² - 12x + 18 - 4 = 0
2x² - 12x + 14 = 0
2(x² - 6x + 7) = 0
x² - 6x + 7 = 0
Solving the quadratic equation gives:
x = 3 + √2 and x = 3 - √2
This means that the graph crosses x at 3 + √2 and 3 - √2.
The zeros of the function are 3 + √2 and 3 - √2. The zeros of the function is the point where y = 0, that is the point that the hot dog prices that give $0.00 profit (no profit).
Please answer this correctly without making mistakes
Step-by-step explanation:
Option A and B are the correct answer because it equal to 688.5 and 688.05
Answer:
it is 1377/2 and 688 1/17 thats the answer
Step-by-step explanation:
x
Find the value
of x. Show
3
10
your work.
Step-by-step explanation:
Hello, there!!!
Let ABC be a Right angled triangle,
where, AB = 3
BC= 10
and AC= x
now,
As the triangle is a Right angled triangle, taking angle C asrefrence angle. we get,
h= AC = x
p= AB = 3
b= BC= 10
now, by Pythagoras relation we get,
[tex]h = \sqrt{ {p}^{2} + {b}^{2} } [/tex]
[tex]or ,\: h = \sqrt{ {3}^{2} + {10}^{2} } [/tex]
by simplifying it we get,
h = 10.44030
Therefore, the answer is x= 10.
Hope it helps...
Identify the decimals labeled with the letters A, B, and C on the scale below. Letter A represents the decimal Letter B represents the decimal Letter C represents the decimal
[tex]10[/tex] divisions between $15.59$ and $15.6$ so each division is $\frac{15.60-15.59}{10}=0.001$
A is 5 division from $15.59$, so, A is $15.59+5\times 0.001=15.595$
similarly, C is 4 division behind $15.59$ so it is $15.590-4\times0.001=15.586$
and B is $15.601$
which operation should you perform first when evaluating the expression 3²+ 2
Answer:
You should calculate 3² first.
Step-by-step explanation:
In PEMDAS, E (which stands for exponents) comes before A (which stands for addition) so therefore you should calculate 3² first.
Explanation:
The acronym PEMDAS helps determine the order of operations
P = parenthesis
E = exponents
M = multiplication
D = division
A = addition
S = subtraction
With the expression [tex]3^2+2[/tex] we have two operations going on here: exponents and addition.
Since exponents comes before addition (E comes before A in PEMDAS), this means we evaluate [tex]3^2[/tex] first, then add later.
Lynn estimates roof jon 1500,bo estimates 2400. What's the ratio to lynn to bo
Answer:
5:8
Step-by-step explanation:
If I understand your question correctly, we have 1500/2400=15/24=5/8, so we have Lynn:Bo is 5:8, however, in the future please be more clear.
What is "estimates roof jon"? And, instead of saying "ratio to lynn to bo" say "What is the ratio of the estimates?" or whatever you're asking. If this answer is wrong, you only have yourself to blame.
HELPP PLEASEE ��2222 is the diameter of a circle. The coordinates are �(−2, −3) and �(−12, −5). At what coordinate is the center of the circle located? A. (5, 1) B. (−5, −1) C. (−4, −7) D. (−7, −4)
Answer:
(-7, -4) which is your answer D in the list of options
Step-by-step explanation:
The center of the circle should be located half way in between the given points on the plane.
Then the center ahs to be located half way for the x coordinates of both points:
half way between -12 and -2 (notice that there is a difference of 10 units between them), therefore half way would be at 5 units to the right from the furthest point, that is -12 + 5 = -7
Similarly, for the y coordinate, we see that the difference is between -5 and -3 (a difference of two units) therefore the center point will be located half way (that is one unit) up from the lowest y coordinate: -5 + 1 = -4
Then the center of the circle is located at (-7, -4)
Using fluorescent imaging techniques, researchers observed that the position of binding sites on HIV peptides is approximately Normally distributed with a mean of 2.45 microns and a standard deviation of 0.35 micron. What is the standardized score for a binding site position of 2.03 microns? (Enter your answer rounded to one decimal place.)
Answer:
The values is
Step-by-step explanation:
From the question we are told that
The population mean is [tex]\mu = 2.45[/tex]
The standard deviation is [tex]\sigma = 0.35 \ mi[/tex]
The random value is [tex]x = 2.03[/tex]
The standardized score for a binding site position of 2.03 microns is mathematically represented as
[tex]z-score = \frac{x - \mu}{ \sigma }[/tex]
=> [tex]z-score = \frac{2.03 - 2.45}{ 0.35}[/tex]
=> [tex]z-score = -1.2[/tex]
A particular salad contains 4 units of vitamin A, 5 units of vitamin B complex, and 2 mg of fat per serving. A nutritious soup contains 6 units of vitamin A, 2 units of vitamin B complex, and 3 mg of fat per serving. If a lunch consisting of these two foods is to have at least 10 units of vitamin A and at least 10 units of vitamin B complex, how many servings of each should be used to minimize the total number of milligrams of fat
Answer:
2 servings of salad and 1 serving of soup
Step-by-step explanation:
In the given scenario the aim is to minimise the fat content of the food combination.
Fat content of soup is 3mg while fat content of salad is 2 mg.
Using Soup as 0 and Salad as 2 will not give the required vitamin content
The logical step will be to keep servings of soup to the minimum.
Let's see some combinations of salad and soup. Keeping serving of soup to the minimum of 1
1. 1 serving of salad and one serving of soup will contain 10 mg of vitamin A, 7 mg of vitamin B complex, and 3 mg of fat.
This will not work because amount of vitamin B complex is not up to 10 mg
2. 2 servings of salad and 1 serving of soup. Will contain 14 mg of vitamin A, 12 mg of vitamin B, and 7 mg of fat
This is the best option as we have amount of vitamin A and vitamin B complex in adequate quantity.
Also fat is lowest in this combination because soup the food with highest fat content is at minimum amount of one serving
What is the value of this expression when x = -6 and y = — 1/2? 4(x^2+3) -2y A. -131 B. -35 C. 57 1/2 D. 157
Answer:
D
Step-by-step explanation:
[tex]4(x^2+3)-2y\\\\=4((-6)^2+3)-2(\frac{-1}{2} )\\\\=4(36+3)+1\\\\=4(39)+1\\\\=156+1\\\\=157[/tex]
The value of the expression 4(x² + 3) - 2y is 157, when x = -6 and y = -1/2.
What is an algebraic expression?An algebraic expression is consists of variables, numbers with various mathematical operations,
The given expression is,
4(x² + 3) - 2y
Substitute x = -6 and y = -1/2 to find the value of expression,
= 4 ((-6)² + 3) - 2(-1/2)
= 4 (36 + 3) + 1
= 4 x 39 + 1
= 156 + 1
= 157
The required value of the expression is 157.
To know more about Algebraic expression on:
https://brainly.com/question/19245500
#SPJ2
Jonah read 5 1/2 chapters in his book in 90 minutes how long did it take him to read one chapter
Answer:
around 16 minutes. you partition an hour and a half (all out) by what number of sections he read (5.5
Step-by-step explanation:
−(−49) = −49 true or false?
The regular hexagon ABCDEF rotates 240º counterclockwise about its center to form hexagon A′B′C′D′E′F′. Point C′ of the image coincides with point
of the preimage. Point D′ of the image coincides with point
of the preimage.
Answer:
Point C: G
Point D: F
Step-by-step explanation:
A hexagon has 6 sides.
360/6=60
Every 60°, it moves one section.
240/60=4.
So it moves 4 sections.
C would move 4 sections BACK (B, A, F, G)
D would also move 4 sections back (C, B, A, F)
Answer:
Point C is: E
point D is : F
Step-by-step explanation:
Could someone help me pls! And could you explain if possible? Thanks you
Answer:
3%
Step-by-step explanation:
1. Set up the equation
6(0.18) + 12x = 18(0.08)
2. Simplify
1.08 + 12x = 1.44
3. Solve
12x = 0.36
x = 0.03
0.03 = 3%
A la propiedad fundamental de las proporcionas, comprueba si las siguientes son o no hay elementos a) 5/7 a 15/21 b) 20/7 a 5/3 c) 16/8 a 4/2
Answer:
fucuvucybycych tcy bic ttx TV ubtx4 cub yceec inivtxr xxv kb
Step-by-step explanation:
t tcextvtcbu6gt CNN tx r.c tct yvrr TV unu9gvt e tch r,e xxv t u.un4crcuv3cinycycr xxv yctzrctvtcrzecycyvubr xiu nyfex tut uhyh
Help Quick Please. Will give brainliest.
Answer:
72[tex]\sqrt{3}[/tex] units²
Step-by-step explanation:
The area (A) of the triangle is calculated as
A = [tex]\frac{1}{2}[/tex] bh ( b is the base and h the perpendicular height )
Here b = ST = a = 12 and h = RS
To calculate RS use the tangent ratio in the right triangle and the exact value
tan60° = [tex]\sqrt{3}[/tex] , thus
tan60° = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{RS}{ST}[/tex] = [tex]\frac{RS}{12}[/tex] = [tex]\sqrt{3}[/tex] ( multiply both sides by 12 )
RS = 12[tex]\sqrt{3}[/tex]
Thus
A = [tex]\frac{1}{2}[/tex] × 12 × 12[tex]\sqrt{3}[/tex] = 6 × 12[tex]\sqrt{3}[/tex] = 72[tex]\sqrt{3}[/tex] units²
Molly’s house is located at point X. Molly wants Sophia and Cole to meet at her house because she thinks it is the same distance from Sophia’s house and Cole’s house. Which could prove that Molly’s house is the samedistance from Sophia’s and Cole’s houses?
Answer:
Cole's House
Step-by-step explanation:
Cole house is closer because molly and Sophia can go there together because there both girls
Find the center, vertices, and foci of the ellipse with equation 4x2 + 9y2 = 36. Center: (0, 0); Vertices: (-3, 0), (3, 0); Foci: Ordered pair negative square root 5 comma 0 and ordered pair square root 5 comma 0 Center: (0, 0); Vertices: (-9, 0), (9, 0); Foci: Ordered pair negative square root 65 comma 0 and ordered pair square root 65 comma 0 Center: (0, 0); Vertices: (0, -3), (0, -3); Foci: Ordered pair 0 comma negative square root 5 and ordered pair 0 comma square root 5 Center: (0, 0); Vertices: (0, -9), (0, 9); Foci: Ordered pair 0 comma negative square root 65 and ordered pair 0 comma square root 65
Answer:
Option A.
Step-by-step explanation:
The given equation of ellipse is
[tex]4x^2+9y^2=36[/tex]
Divide both sides by 36.
[tex]\dfrac{4x^2}{36}+\dfrac{9y^2}{36}=1[/tex]
[tex]\dfrac{x^2}{9}+\dfrac{y^2}{4}=1[/tex]
[tex]\dfrac{x^2}{3^2}+\dfrac{y^2}{2^2}=1[/tex] ...(1)
The standard form of an ellipse is
[tex]\dfrac{(x-h)^2}{a^2}+\dfrac{(y-k)^2}{b^2}=1[/tex] ...(2)
where, (h,k) is center, (h±a,k) are vertices and (h±c,k) are foci.
On comparing (1) and (2), we get
[tex]h=0,k=0,a=3,b=2[/tex]
Now,
Center [tex]=(h,k)=(0,0)[/tex]
Vertices [tex]=(h\pm a,k)=(0\pm 3,0)=(3,0),(-3,0)[/tex]
We know that
[tex]c=\sqrt{a^2-b^2}=\sqrt{3^2-2^2}=\sqrt{5}[/tex]
Foci [tex]=(h\pm c,k)=(0\pm \sqrt{5},0)=(\sqrt{5},0),(-\sqrt{5},0)[/tex]
Therefore, the correct option is A.
Two samples from the same population both have M = 84 and s2 = 20, but one sample has n = 10 and the other has n = 20 scores. Both samples are used to evaluate a hypothesis stating that μ = 80 and to compute Cohen’s d. How will the outcomes for the two samples compare?
Complete Question
Two samples from the same population both have M = 84 and s2 = 20, but one sample has n = 10 and the other has n = 20 scores. Both samples are used to evaluate a hypothesis stating that μ = 80 and to compute Cohen’s d. How will the outcomes for the two samples compare?
a.
The larger sample is more likely to reject the hypothesis and will produce a larger value for Cohen’s d.
b.
The larger sample is more likely to reject the hypothesis, but the two samples will have the same value for Cohen’s d.
c.
The larger sample is less likely to reject the hypothesis and will produce a larger value for Cohen’s d.
d.
The larger sample is less likely to reject the hypothesis, but the two samples will have the same value for Cohen’s d.
Answer:
The Cohen's d value is [tex]d = 0.895[/tex]
The correct option is b
Step-by-step explanation:
From the question we are told that
The sample mean of each population is [tex]M = 84[/tex]
The variance of each population is [tex]s^2 = 20[/tex]
The first sample size is [tex]n_1 = 10[/tex]
The second sample size is [tex]n_2 = 20[/tex]
The null hypothesis is [tex]H_o : \mu = 80[/tex]
Generally the standard deviation is mathematically evaluated as
[tex]s = \sqrt{20 }[/tex]
=> [tex]s = 4.47[/tex]
The first test statistics is evaluated as
[tex]t_1 = \frac{M - \mu }{ \frac{\sigma }{ \sqrt{n_1} } }[/tex]
=> [tex]t_1 = \frac{84 - 80 }{ \frac{4.47 }{ \sqrt{10} } }[/tex]
=> [tex]t_1 = 2.8298[/tex]
The second test statistics is evaluated as
[tex]t_2 = \frac{M - \mu }{ \frac{\sigma }{ \sqrt{n_2} } }[/tex]
=> [tex]t_2 = \frac{84 - 80 }{ \frac{4.47 }{ \sqrt{20} } }[/tex]
=> [tex]t_2 = 4.0[/tex]
The sample with the larger test statistics (sample size) will more likely reject the null hypothesis
Generally the Cohen's d value is mathematically evaluated as
[tex]d = \frac{M - \mu }{s }[/tex]
=> [tex]d = \frac{ 84 - 80 }{4.47 }[/tex]
=> [tex]d = 0.895[/tex]
Given that the the sample mean and sample size are the same for both sample the Cohen's d value will be the same
I
Ifm DGF = 72, what equation can you use to find mZEGF?
Answer:
see explanation
Step-by-step explanation:
∠ DGE + ∠ EGF = ∠ DGF , that is
∠ EGF = ∠ DGF - ∠ DGE
∠ EGF = 72° - ∠ DGE
The expression $16x^2-106x-105$ can be written as $(8x + a)(2x + b),$ where $a$ and $b$ are integers. What is $a + 2b$?
Answer:
-23
Step-by-step explanation:
16x² - 106x - 105
factoring X
14 x -120 = -1680
14 - 120 = -106
16x² + 14x - 120x - 105
(16x² + 14x) -(120x - 105)
factor out 2 and -15 to get the same expression (8x + 7)
2x(8x + 7) - 15(8x + 7)
(8x + 7)(2x - 15)
a = 7
b = -15
a + 2b
7 + (-15 x 2)
7 + (-30)
= -23
Suppose that the neighboring cities of Tweed and Ledee are long-term rivals. Neal, who was born and raised in Tweed, is confident that Tweed residents are more concerned about the environment than the residents of Ledee. He knows that the average electricity consumption of Tweed households last February was 854.11 kWh and decides to test if Ledee residents used more electricity that month, on average. He collects data from 65 Ledee households and calculates the average electricity consumption to be 879.28 kWh with a standard deviation of 133.29 kWh. There are no outliers in his sample data. Neal does not know the population standard deviation nor the population distribution. He uses a one-sample t-test with a significance level of α = 0.05 to test the null hypothesis, H0:µ=854.11, against the alternative hypothesis, H1:μ>854.11 , where μ is the average electricity consumption of Ledee households last February. Neal calculates a t‑statistic of 1.522 and a P-value of 0.066.
Based on these results, complete the following sentences to state the decision and conclusion of the test.
Neal's decision is to__________ the __________ (p 0.066). There is_________ evidence to _________ the claim that the average electricity consumption of ____________ is _________ , ________
Complete Question
The option to the blank space are shown on the first uploaded image
Answer:
Neal's decision is to fail to reject the null hypothesis (p 0.066). There is no sufficient evidence to prove the claim that the average electricity consumption of all Ledee household is greater than , 854.28 kWh
Step-by-step explanation:
From the question we are told that
The population mean is [tex]\mu = 854.11[/tex]
The sample size is [tex]n = 65[/tex]
The sample mean is [tex]\= x = 879.28 \ kWh[/tex]
The standard deviation is [tex]\sigma = 133.29 \ kWh[/tex]
The level of significance is [tex]\alpha = 0.05[/tex]
The null hypothesis is [tex]H_o: \mu = 854.11[/tex]
The alternative hypothesis is [tex]H_a : \mu > 854.11[/tex]
The t-statistics is [tex]t = 1.522[/tex]
The p-value is [tex]p-value = 0.066[/tex]
Now from the given data we can see that
[tex]p-value < \alpha[/tex]
Generally when this is the case , we fail to reject the null hypothesis
So
Neal's decision is to fail to reject the null hypothesis (p 0.066). There is no sufficient evidence to prove the claim that the average electricity consumption of all Ledee household is greater than , 854.28 kWh
The amounts of nicotine in a certain brand of cigarette are normally distributed with a mean of 0.966 grams and a standard deviation of 0.315 grams. Find the probability of randomly selecting a cigarette with 0.305 grams of nicotine or less.
Answer:
The probability is [tex]P(X \le 0.305 ) = 0.01795[/tex]
Step-by-step explanation:
From the question we are told that
The population mean is [tex]\mu = 0.966 \ grams[/tex]
The standard deviation is [tex]\sigma = 0.315 \ grams[/tex]
Given that the amounts of nicotine in a certain brand of cigarette are normally distributed
Then the probability of randomly selecting a cigarette with 0.305 grams of nicotine or less is mathematically represented as
[tex]P(X \le 0.305 ) = 1 - P(X > 0.305) = 1 - P(\frac{X - \mu }{\sigma } > \frac{0.305 - \mu }{\sigma } )[/tex]
Generally
[tex]\frac{X - \mu }{\sigma } = Z (The \ standardized \ value \ of X )[/tex]
So
[tex]P(X \le 0.305 ) = 1 - P(X > 0.305) = 1 - P(Z > \frac{0.305 - 0.966 }{0.315} )[/tex]
[tex]P(X \le 0.305 ) = 1 - P(X > 0.305) = 1 - P(Z >-2.0984 )[/tex]
From the z-table(reference calculator dot net ) value of [tex]P(Z >-2.0984 ) =0.98205[/tex]
So
[tex]P(X \le 0.305 ) = 1 - P(X > 0.305) = 1 - 0.98205[/tex]
=> [tex]P(X \le 0.305 ) = 1 - P(X > 0.305) = 0.01795[/tex]
=> [tex]P(X \le 0.305 ) = 0.01795[/tex]
Simplify 10 - [14 = (3 + 4) · 2]+3
Answer:
There is a typo near the equal sign.
There can be two different answers if we think that = sign as + or -.
First way: Making = as +
=> 10 - [14 + (3+4) x 2] +3
=> 10 - [14 + 7 x 2] + 3
=> 10 - [14 + 14] + 3
=> 10 - 28 + 3
=> 10 + 3 - 28
=> 13 - 28
=> -15
=> So, -15 is the answer if we consider "=" sign as "+" sign.
Second way: Making = as -
=> 10 - [14 - (3+4) x 2] + 3
=> 10 - [14 - 7 x 2] + 3
=> 10 - [14 - 14] + 3
=> 10 - 0 + 3
=> 10 + 3
=> 13
=> So, 13 is the answer if we consider "=" sign as "-" sign.
1 If a = p^1/3-p^-1/3
prove that: a^3 + 3a = p - 1/p
Hello, please consider the following.
We know that
[tex]a = p^{\frac{1}{3}}-p^{-\frac{1}{3}}\\\\=p^{\frac{1}{3}}-\dfrac{1}{p^{\frac{1}{3}}}[/tex]
And we can write that.
[tex](p-\dfrac{1}{p})^3=(p-\dfrac{1}{p})(p^2-2+\dfrac{1}{p^2})\\\\=p^3-2p+\dfrac{1}{p}-p+\dfrac{2}{p}-\dfrac{1}{p^3}\\\\=p^3-\dfrac{1}{p^3}-3(p-\dfrac{1}{p})[/tex]
It means that, by replacing p by [tex]p^{1/3}[/tex]
[tex](p^{1/3}-\dfrac{1}{p^{1/3}})^3=p-\dfrac{1}{p}-3(p^{1/3}-\dfrac{1}{p^{1/3}})\\\\\\\text{ So }\\\\a^3=p-\dfrac{1}{p}-3a\\\\<=>\boxed{ a^3+3a=p-\dfrac{1}{p} }[/tex]
Hope this helps.
Do not hesitate if you need further explanation.
Thank you
Solve this problem using the Trigonometric identities (secA+1)(SecA-1)= tan^2A
Step-by-step explanation:
( secA + 1)( sec A - 1)
Using the expansion
( a + b)( a - b) = a² - b²
Expand the expression
We have
sec²A + secA - secA - 1
That's
sec² A - 1
From trigonometric identities
sec²A - 1 = tan ²ASo we have the final answer as
tan²AAs proven
Hope this helps you
Step-by-step explanation:
Here,
LHS
= (SecA+1)(secA -1)
[tex] = {sec}^{2} A - 1[/tex]
[tex]{as{a}^{2} - {b}^{2} =(a + b)(a - b)[/tex]
Now, we have formula that:
[tex] {sec}^{2} \alpha - {tan \alpha }^{2} = 1[/tex]
[tex] {tan}^{2} \alpha = {sec }^{2} \alpha - 1[/tex]
as we got ,
[tex] = {sec}^{2} A- 1[/tex]
This is equal to:
[tex] = {tan}^{2} A[/tex]
= RHS proved.
Hope it helps....
Which is the graph of g(x) = (0.5)x + 3 – 4?
Answer:
Graph (A)
Step-by-step explanation:
Given question is incomplete; find the question in the attachment.
Given function is g(x) = [tex](0.5)^{x+3}-4[/tex]
Parent function of the given function is,
f(x) = [tex](0.5)^{x}[/tex]
When the function 'f' is shifted by 3 units left over the x-axis, translated function will be,
h(x) = f(x+3) = [tex](0.5)^{x+3}[/tex]
When h(x) is shifted 4 units down, translated function will be,
g(x) = h(x) - 4
g(x) = [tex](0.5)^{x+3}-4[/tex]
g(x) has a y-intercept as (-4).
From the given graphs, Graph A shows the y-intercept as (-4).
Therefore, Graph A will be the answer.
Answer:
The Answer A is correct
Step-by-step explanation:
I took the edg2020 test
Solve x/10 = -7 A. x = 3 B. x = -0.7 C. x = -17 D. x = -70
Answer:
x = -70
Step-by-step explanation:
x/10 = -7
Multiply each side by 10
x/10*10 = -7*10
x = -70
A 95% confidence interval for the mean number of television per American household is (1.15, 4.20). For each of the following statements about the above confidence interval, choose true or false.
a. The probability that u is between 1.15 and 4.20 is .95.
b. We are 95% confident that the true mean number of televisions per American household is between 1.15 and 4.20.
c. 95% of all samples should have x-bars between 1.15 and 4.20 televisions.
d. 95% of all American households have between 1.15 and 4.20 televisions
e. Of 100 intervals calculated the same way (95%), we expect 95 of them to capture the population mean.
f. Of 100 intervals calculated the same way (95%), we expect 100 of them to capture the sample mean.
Answer:
a. False
b. True
c. False
d. False
e.True
f. True
Step-by-step explanation:
The 95% is confidence interval its not a probability estimate. The probability will be different from the confidence interval. Confidence interval is about the population mean and is not calculated based on sample mean. Every confidence interval contains the sample mean. There is 95% confidence that the number of televisions per American household is between 1.15 to 4.20.
Evaluate 2/3 + 1/3 + 1/6 + … THIS IS CONTINUOUS. It is NOT as simple as 2/3 + 1/3 + 1/6.
[tex]a=\dfrac{2}{3}\\r=\dfrac{1}{2}[/tex]
The sum exists if [tex]|r|<1[/tex]
[tex]\left|\dfrac{1}{2}\right|<1[/tex] therefore the sum exists
[tex]\displaystyle\\\sum_{k=0}^{\infty}ar^k=\dfrac{a}{1-r}[/tex]
[tex]\dfrac{2}{3}+\dfrac{1}{3}+\dfrac{1}{6}+\ldots=\dfrac{\dfrac{2}{3}}{1-\dfrac{1}{2}}=\dfrac{\dfrac{2}{3}}{\dfrac{1}{2}}=\dfrac{2}{3}\cdot 2=\dfrac{4}{3}[/tex]
The U.S. National Whitewater Center in Charlotte uses a pump station to provide the flow of water necessary to operate the rapids. The pump station contains 7 pumps, each with a capacity to deliver 80,000 gallons per minute (gpm). The water channels and ponds in the facility contain 13 million gallons of water. If the pump station is operating 5 pumps simultaneously, assuming ideal conditions how long will it take to completely pump the volume of the system through the pump station
Answer:
t = 32,5 minutes
Step-by-step explanation:
Volume to fill = 13000000 Gal
5 pumps delivering 80000 gal/min
5 * 80000 = 400000 gal/min
If we divide the total volume by the amount of water delivered for the 5 pumps, we get the required time to fill the volume, then
t = 13000000/ 400000
t = 32,5 minutes
