So, 40 Customers are waiting at 10 A.M.
According to statement
Number of customers arrives at coffee shop per hour = 100
Capacity of shop for per minute per customer = 0.8 minute
Capacity of shop for customers per hour = 80
Find number of customers are by
Queue growth rate = Demand - Capacity
Put the values in the formula and find the growth rate
So,
Queue growth rate= 100 - 80 = 20.
Length of queue at 10 a.m. = 2 × 20 = 40.
So, 40 Customers are waiting at 10 A.M.
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A horse 24 feet from the center of a merry-go-round makes 32 revolutions. In order to travel the same distance, how many revolutions would a horse 8 feet from the center have to make
Using proportions, the horse 8 feet from the center would have to make 96 revolutions.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three.
A horse 24 feet from the center of a merry-go-round makes 32 revolutions. If it is 8 feet and wants the same distance, how many revolutions will it need? The rule of three is:
24 feet - 32 revolutions
8 feet - x revolutions
The measures are inverse proportional, hence:
8x = 24 x 32
x = 24 x 32/8
x = 96 revolutions.
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(1/2) 400t² = 20,000
Answer:
160000
Step-by-step explanation:
if im wrong sorry
Answer:
the answer is 10
Step-by-step explanation:
. Hello !
Because firstly divide 400 by 2
200t²=20,000t²=100....divide both sides by 200t=10....is the value after squaring both sides(score for question 3: ... of 10 points) 3. the table shows the test scores and the sleep averages of several students. test score (%) 88 75 76 92 96 94 83 90 99 65 7788 82 83 94 97 7 6.5 average sleep (h) 6 7.5 8 7 6.5 8 8.5 5 7 8 9 9 9 8.5 8.5 (a) write the least squares regression equation that models the data. let x = the test score and y = average sleep. (b) use the equation to determine the approximate test score of a student who sleeps an average of 8 hours a night. show your work. answer: 1
The linear regression model obtained by fitting the data points is Y = 0.0914X1 - 0.3741.
How to illustrate the regression?x = test score
y = average sleep
Slope = 0.0914
intercept = - 0.3741
The test score of a student that sleeps 8 hours
y = 8
8 = 0.0914X1 - 0.3741
8 + 0.3741 = 0.0914X1
X = 8.3741 / 0.0914
X = 91.62
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A cylindrical container 30cm in diameter holds approximately 30 litres of oil. how far does the oil level fall after 1 litre of oil has been used
The fall in the level of oil is 1.4147 cm when the total volume of oil consumed is 1 liter.
We assume the drop in the level of water to be d cm.
Since the container is cylindrical in shape, its volume is given as:
V = πr²h, where V is the volume, r is the radius, and h is the height.
In the question, we are given that the diameter of the can is 30 cm.
Hence its radius = 30/2 = 15 cm.
The capacity of the container is given to be 30 liters or 30*1000 = 30000 cm³.
The volume of the oil used = 1 liter or 1*1000 = 1000 cm³.
Thus, substituting V = 1000, r = 15, and h = d, in the formula of the volume, V = πr²h, we get:
1000 = π(15)²(d),
or, d = 1000/(225π) = 1.4147.
Thus, the fall in the water level is 1.4147 cm.
Therefore, the fall in the level of oil is 1.4147 cm when the total volume of oil consumed is 1 liter.
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a doctor at a local hospital is interested in estimating the birth weight of infants. How large a sample must she select if she desires to be 99% confident that her estimate is within 3 ounces of the true mean
The sample size that gives 99% confidence level and estimate will be within 3 ounces is 0.7386[tex](standard deviation)^{2}[/tex].
Given confidence level 99% and margin of error is 3 ounces of true mean.
Margin of error is the difference between the actual values and the calculated value of mean.
Sample size is the number of items taken from the population as a sample for research.
We have to find the sample size.
First we have to find the z value for the corresponding p value of 0.99.
z value=2.58
Margin of error=z*σ/[tex]\sqrt{n}[/tex]
3=2.58σ/[tex]\sqrt{n}[/tex]
[tex]\sqrt{n}[/tex]=2.58/3 σ
Squaring both sides
n=[tex]2.58^{2}[/tex]σσ
Hence the sample size needed is 2.58 ([tex](standard deviation)^{2}[/tex].
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Evaluate if t=2 and x=3: 3(2x² - £)
a.) 102
b.) 30
c.) 48
d.) 12
If LM = 3x + 5, MN = 4x, and LN
=
11x7, select all that are true
a. x=3
b. x=7
c. lm = 14
d. lm = 28
e. ln = 26
f. ln =54
We have that x = 3, LM = 14 and LN = 2. options A, C and E
How to determine the value
We known that the three sides are on a straight line
LM + MN = LN
Let's substitute the values, we have
3x + 5 + 4x = 11x - 7
Collect like terms
3x + 4x - 11x = -7 -5
-4x = -12
x = -12/ -4
x = 3
LM = 3x + 5 = 3(3) + 5 = 14
LN = 11x - 7 = 11(3) -7 = 33 -7 = 26
Thus, we have that x = 3, LM = 14 and LN = 2. options A, C and E
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which factor tree for the graph the function below? Check all that apply.
f(x)= 4•5^x
The statements that are true are B, C, and F.
Which facts are true about the exponential function?
Here we have the exponential function:
[tex]f(x) = 4*5^x[/tex]
We can see that the initial value is 4, and the base is 5. Because the base is larger than 1, this is an exponential growth function.
The statements that are true are:
B: The domain of an exponential function is always the set of all real numbers.
C: Is an exponential growth, so yes, it is increasing.
F: The y-intercept is given by evaluating the function in x = 0, when you do that, you get the initial value, which is 4. So the y-intercept is (0, 4).
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Evaluate the following
a) 5 ÷ 2 (mod 6)
b) 9 ÷ 7 (mod 7)
c) 3 × 2 ÷ 5 (mod 7)
Neither 2 nor 7 have inverses mod 6 or 7, respectively, so the expressions in (a) and (b) cannot really evaluated... At least we can evaluate (c) :
[tex]5\times3 \equiv 15 \equiv 1 \pmod 7 \\\\ \implies 3\times2\div5 \equiv 3\times2\times3 \equiv18 \equiv \boxed{4 \pmod{7}}[/tex]
What is the slope of the line that passes through (0,5) and (10,0)?
Answer:
-1/2
Step-by-step explanation:
slope is change in y / change in x
change in y is -5 bc y decreases by 5
change in x is 10 bc x increases by 10
-5/10 simplifies to -1/2
Find the quotient of the complex numbers. Express your answer in trigonometric form. SEE ATTATCHED
The quotient of the complex numbers is 3[cos(240)+ isin(240)] option (D) is correct.
What is a complex number?It is defined as the number which can be written as x+iy where x is the real number or real part of the complex number and y is the imaginary part of the complex number and i is the iota which is nothing but a square root of -1.
We have two complex number is given.
The quotient of the complex numbers:
[tex]= \rm \dfrac{12\left[cos\left(320\right)+isin\left(320\right)\right]}{4\left[cos\left(80\right)+isin\left(80\right)\right]}[/tex]
= 3[cos(320-80)+ isin(320-80)]
= 3[cos(240)+ isin(240)]
Thus, the quotient of the complex numbers is 3[cos(240)+ isin(240)] option (D) is correct.
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What is the equation of a circle whose radius is 16 units and center is at (2,-5)?
Answer:
The general equation of the circle is [tex]( {x - a})^{2} + ({y - b})^{2} = {r}^{2} \\ therefore \: we \: \: have \: \\ ( {x - 2})^{2} + (y - ( - 5)) {}^{2} = ({16})^{2} \\ ({x - 2})^{2} + ( {y + 5})^{2} = 256[/tex]HOPE THIS HELPS!After grabbing some food from the cafeteria, Ray trips causing his food to go up in the air before hitting the ground. The parabolic path of his food tray can be modeled by the function ℎ() = − 0. 2 , where h is 2 + 0. 4 + 1. 6 the height in meters after t seconds. a)
What is the maximum height of the tray?
If Ray manages to catch the tray at the same height from which the tray flew out of his hands, how long is it in the air?
The maximum height of the tray is 1.8 meters and the tray is in the air for 2 seconds
The maximum height of the trayThe distorted information (i.e. the function) in the question is:
h(t) = -0.2t^2 + 0.4t + 1.6
Differentiate the function
h'(t) = -0.4t + 0.4
Set to 0
-0.4t + 0.4 = 0
Subtract 0.4 from both sides
-0.4t = -0.4
Divide by -0.4
t = 1
Substitute t = 1 in h(t) = -0.2t^2 + 0.4t + 1.6
h(1) = -0.2(1)^2 + 0.4(1) + 1.6
Evaluate
h(1) = 1.8
Hence, the maximum height of the tray is 1.8 meters
Time spent in the airIn (a), we have:
t = 1
This represents the time to reach the maximum height.
The time spent in the air is:
T = 2t
This gives
T = 2 * 1
T = 2
Hence, the tray is in the air for 2 seconds
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A commitee is consist of 6 men and 4 woman ,a sub commitee is made by randomly choosen three commitee members .what is the probability that(a)they are all woman (b) two of them are men
Answer:
a) 1/30
b) 1/6
Step-by-step explanation:
a) There are 10 people total and a group of 3 is being chosen. However, they all need to be women:
For the first person, the probability of it being a woman is 4/10
For the second person, the probability of it being a woman (with the prerequisite that the first was a woman) is 3/9
For the third (with the same requirements) is 2/8
If we multiply all of the fractions together, we get: [tex]\frac{1}{30}[/tex]
b) There are 10 people total and a group of 3 is being chosen. However, two of them need to be men, and 1 needs to be a woman:
For the first person, the probability of it being a man is 6/10
For the second person, the probability of it being a man (with the prerequisite that the first was a man as well) is 5/9
For the third person, the probability of it being a woman (because it can only be two men) is 4/8
If we multiply all the fractions together, we get: [tex]\frac{1}{6}[/tex]
Enter the first 4 terms of the sequence defined by the given rule. assume that the domain of each function is the set of whole numbers greater than 0. f(n) = (2n + 2)2 the first 4 terms of the sequence are , , , and .
The first four terms of the sequence are 8,12,16 and 20.
What is a Sequence?A sequence is an enumerated group of items in mathematics where repetitions are permitted and order is important. Similar to a set, it has members (also called elements, or terms). The length of the series is the number of elements (potentially infinite). In contrast to a set, the same items might appear more than once in a sequence at various points, and unlike a set, the order is important. A sequence can be described formally as a function from natural numbers (the positions of the sequence's elements) to the items at each of those positions. An indexed family, which is a function from an index set that may not be a set of numbers to another set of elements, can be thought of as a generalization of the idea of a sequence.Given the function is f(n) = (2n+2)2
Now, we want first four terms, therefore, putting 1, 2, 3, 4 in the sequence we get:
f(1) = (2*1+2)2 = 8
f(2) = (2*2+2)2 = 12
f(3) = (2*3+2)2 = 16
f(4) = (2*4+2)2 = 20
Hence, The first four terms of the sequence are 8,12,16 and 20.
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Area=
Help me please!! Thanks :)
Answer:
80π
Step-by-step explanation:
Circle O with radius IO:
large radius = IO = 12 = R
Circle O with diameter JK
IJ = JK = KL = 2 × IO = 24
IJ = JK = KL = 24/3 = 8
small radius = 8/2 = 4 = r
The shaded area is a semicircle of radius 12 minus a semicircle of radius 4 plus two semicircles of radius 4.
That is the same as
1 semicircle of radius 12 plus 1 semicircle of radius 4
A = πR²/2 + πr²/2
A = π(12² + 4²)/2
A = 160π/2
A = 80π
Can someone help me out in these geometry fill in the blanks? It’s urgent, gotta have answers fast
Answer:
Vertical angles are equal
Step-by-step explanation:
-
[tex]vertical \: angles \: are \: equal[/tex]
[tex]3y = 150[/tex]
The sum of two supplementary angles equals 180 degrees
Therefore 6x +150=180
Select the two expressions equal to the area of this figure in square centimeters.
Answer:
1.(6*4) + (18*6) + (6*4)
1.(6*10) + (6*6) + (6*10)
Step-by-step explanation:
there are two ways to break this shape into three rectangles:
1.Top right rectangle, Top left rectangle, Bottom long rectangle
2. Left rectangle, Middle square, Right rectangle.
I don’t understand this. Help me please!
Answer:
2
Step-by-step explanation:
So the midpoint of AB can be calculated by finding the length of AB, dividing it by 2 and then adding it to A. So the length of AB is equal to B-A or in general the difference between two values is |a-b| where the order doesn't matter, but assuming B is the right side (meaning it should be greater than A) the length should be B-A. in this case A = -5 and B = 3 so the length is 3 - (-5) = 8. The length is 8 so the midpoint is half of that which is 4, now adding 4 to the left side (A) you get -5 + 4 = -1. So the midpoint of AB lies at -1. Now the midpoint of AC can be found using the same process. 7 - (-5) = 12 => 12/2 = 6 => -5 + 6 = 1 so the midpoint of AC is at 1. Now to find how many units from the midpoint AB to AC you just subtract the midpoint of AB from AC. this gives you 1 - (-1) which is 2.
Solve x ^ 2 - 3x = - 8 using the quadratic formula.
Answer: [tex]\frac{3 +- \sqrt{23}i}{2}[/tex] If using complex numbers, or undefined if using all real numbers
Step-by-step explanation:
Moving -8 to the left side of the eq by adding both sides by 8=
x^2-3x+8=0
The quad formula:[tex]\frac{-b +- \sqrt{b^2-4ac}}{2a}[/tex]
a=1 b=-3 c=8
Inserting a b c values into formula: [tex]\frac{-(-3) +- \sqrt{(-3)^2-4(1)(8)}}{2(1)}[/tex]
Simplifying: [tex]\frac{3 +- \sqrt{9-32}}{2}[/tex]
[tex]\frac{3 +- \sqrt{-23}}{2}[/tex] Since the square root of a negative number doesn't exist in the set of real numbers, the equation is undefined.
OR
[tex]\frac{3 +- \sqrt{23}i}{2}[/tex] Using complex numbers i, to replace the negative number created by subtracting 9-32.
Which of the Following illustrates how to find the difference of
12a ^2b and —5a^2b?
Answer:
17a^2b
Step-by-step explanation:
Difference = subtracting
12a ^2b - (-5a^2b)
12a ^2b + 5a^2b
17a^2b
The data show the heights in feet of 14 roller coasters. find the mean, median, midrange, and mode for the data.
The mean of the heights of roller coaster is 27.92 feet, median is 21, mode is 16 and mid range is 35.5.
Given heights in feet of 14 roller coaster 11,12,13,14,16,21,25,26,31,40,51,55,60.
We have to calculate the mean, median, mid range and mode for the data.
Mean is the sum of numbers divided by the numbers.
Mean=∑X/n
∑X=11+12+13+14+16+21+25+26+31+40+51+55+60
=391
n=14
Mean=391/14
=27.92 feet.
Median is the central value of the data given.
Median=(n/2)th term ,when n is even, ( n/2)th term, (n+1)/2th term when n is odd.
Median=14/2th term=7th term which is 21.
Mode is the number which has higher frequency.
Mode is 16 because it comes 2 times.
Mid range is the sum of upper value and lower value of data divided by 2.
Mid range=(11+60)/2==35.5.
Hence the mean is 27.92 feet, median is 21 feet, mid range is 35.5 feet, mode is 16 feet.
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Question is incomplete as the values of height should be included as under:
11,12,13,14,16,16,21,25,26,31,40,51,55,60.
PLS HELP ITS URGENT I HAVE LIKE A COUPLE QUESTIONS LEFT IM STUCK ON THIS
Answer: 3[tex]i[/tex]
Step-by-step explanation: The reason for this is because [tex]i[/tex] =
[tex]\sqrt{-1}[/tex], and when [tex]\sqrt{-1}[/tex] is multiplied to [tex]\sqrt{9}[/tex], it becomes [tex]\sqrt{-9}[/tex]. Since [tex]\sqrt{9}[/tex] can be simplified to 3, we can just multiply [tex]i[/tex] to 3. This becomes 3[tex]i[/tex].
Hope this helped!
Answer:
3i
Step-by-step explanation:
Damien and Anna are counting fish. They have 4 tanks with 4 fish and 5 tanks with 2 fish. They are planning to fill an order for 3 fish today. Which expression shows how many fish they will have in stock after the 3 are sold. 4×4+5×2−3 3−4×4+5×2 4+4×5+2−3 4×4×5×2−3
GIVEING BRAINLYEST!
Answer:
The answer is 4×4+5×2−3.
Step-by-step explanation:
This is because, in the original amount, they had 4 tanks with 4 fish and 5 tanks with 2 fish. 4x4 is 16 and 5x2 is 10. Then you add them together to get 26. But, you have to subtract 3 because of the order of 3 fish, which equals 23. The equation 4×4+5×2−3 shows that.
Line K has a slope of -5. Line J is perpendicular to line K. What is the slope of line K?
If line J is perpendicular of line K, they should cross to make an X. If the slope of line K is -5, Line J would be 5.
In the race Math , drivers must complete laps of miles each. Dave drove the first laps at mph and the last laps at mph. What was Dave's average speed for the race, in miles per hour
The average speed in approximately 184.62 miles per hour.
We have been given that in the race Math 600, drivers must complete 200 laps of 3 miles each. Dave drove the first 150 laps at 180 mph and the last 50 laps at 200 mph.
First of all, we will find the number of miles in 150 laps and 50 laps as:
150 X 3 miles = 450 miles
50 X 3 miles = 150 miles.
Now, we will find time taken to complete each distance as:
Time = 450/180 =2.5 hr
Time = 150/200 = 0.75 hr
Average speed = 184.62
The average speed in approximately 184.62 miles per hour.
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Evaluate the expression 9 - z when z = 4.
Answer:
its 5 5+4=9
Step-by-step explanation:
succesive approximation
Consider the following equation.
x^2-3x+2= square root √x-2 + 2
Approximate the solution to the equation using three iterations of successive approximation. Use the graph below
25 POINTS PLEASEE :( THIS HAS A TIME LIMIT AND I WILL MARK BRAINLIEST
The Approximate the solution to the equation using three iterations of successive approximation is option b: 27/8.
What is the iterations about?In the equation given:
Note that:
x²-3x+2 = square root √x-2 + 2
Therefore:
x⁴-6x³+9x²= square root x-2
x² = 3.375
Convert 3.35 into fractions and will get 27/8. So, The Approximate the solution to the equation using three iterations of successive approximation is option b: 27/8.
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1. Triangle ABC has an angle of ABC = 60°, AB = 3 √3 cm and BC = 4 √3 cm. Determine the length of AC.
Answer:
see below
Step-by-step explanation:
you can use cosine law
(3 sqrt3)^2 + (4 sqrt3)^2 - 2(3 sqrt3)(4sqrt3)cos60 = AC^2
AC = sqrt39
Jeff's mother gave him money. he used an equal amount of money each day. at the end of the 7th day, he was left with 1/4 of how much he had at first. at the end of the 9th day, he was left with $10. how much did jeff receive from his mother?
Jeff received 280$ from his mother
Such questions are the simplest as it needs you to just write the conditions accordingly which then simplifies and provides you the answer.
This question can be solved using two tricks which are shown below:-
Trick 1 :
1 – 1/4 = 3/4 (used for the 1st 7 days)
1/4 – 410 (used for 8th and 9th days)
(3/4)/7 ——- (1/4 – 10)/2
(3/4) x (2/7) = 3/14 ——- (1/4 – 10)
1/4 – 3/14 = (7 – 6)/28 = 1/28 ——- 10
28/28 ——- 10 x 28 =$ 280
Trick 2 :
7 days ——- 3/4
1 day ——- 3/28
2 days ——- 6/28
6/28 ——- (1/4 – 10) = 7/28 – 410
1/28 ——- 10
28/28 ——- 10 x 28 = $280
Thus Jeff received 280$ from his mother.
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