Answer:
95 times digit 9 appears in all integers from 1 to 500.
Step-by-step explanation:
No. of 9 from
1-9: 1 time
10-19: 1 time
20-29: 1 time
30-39: 1 time
40-49: 1 time
50-59: 1 time
60-69: 1 time
70-79: 1 time
80-89 : 1 time
from 90 to 99
there will be one in 91 to 98
then two 9 in 99
thus, no of 9 from 90 to 99 is 10
Thus, total 9's from 1 to 99 is 9+10 = 19
Thus there 19 9's in 1 to 99
similarly
there will be
19 9's in 100 to 199
19 9's in 200 to 299
19 9's in 300 to 399
19 9's in 400 to 499
Thus, total 9's will be
19 + 19 + 19+ 19 + 19 + 19 = 95
Thus, 95 times digit 9 appears in all integers from 1 to 500.
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Astrid is in charge of building a new fleet of ships. Each ship requires 40 tons of w
sailors. She receives a delivery of 4 tons of wood each day. The deliveries can con
afterwards the weather is too bad to allow them. Overall, she wants to build enou
least 2100 sailors.
How much wood does Astrid need to accommodate 2100 sailors?
tons
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This question is incomplete.
Complete Question
Astrid is in charge of building a new fleet of ships. Each ship requires 40 tons of wood, and accommodates 300 sailors. She receives a delivery of 4 tons of wood each day. The deliveries can continue for 100 days at most, afterwards the weather is too bad to allow them. Overall, she wants to build enough ships to accommodate at least 2100 sailors. How much wood does Astrid need to accommodate 2100 sailors?
Answer:
280 tons of wood.
Step-by-step explanation:
From the above question:
To make 1 ship = we require 40 tons of wood.
1 ship = can accommodate 300 sailors.
Step 1
If :
300 sailors = 1 ship
2100 sailors = y ships
Cross Multiply
300 × y ships = 1 ship × 2100 sailors
y ships = 2100 / 300
y ships = 7
Hence, 2100 sailors can occupy 7 ships.
Step 2
We are told in the question that:
Astrid wants to build enough ships to accommodate at least 2100 sailors. How much wood does Astrid need to accommodate 2100 sailors?
If:
1 ship = 40 tons of wood
Since 7 ships can accommodate 2100 sailors,
7 ships =
7 × 40 tons of wood = 280 tons of wood.
Therefore , Astrid needs 280 tons of wood to accommodate 2100 sailors.
Find an exact value of sin(17pi/12)
●✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎❀✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎●
Hi my lil bunny!
❧⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯☙
[tex]\frac{(17)(3.141593)}{12}[/tex]
= [tex]\frac{53.407075}{12}[/tex]
= [tex]4.45059[/tex]
❧⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯☙
●✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎❀✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎●
If this helped you, could you maybe give brainliest..?
Also Have a great day/night!
❀*May*❀
I have an answer and explanation but I can't type so search up the question you asked and you should get an answer and explanation from s0cratic.
What is the slope of the line shown below?
A.
B.
C.
-
D.
3
Answer:
D
Step-by-step explanation:
Option D is correct. Slope of the line shown in the graph is 3.
The slope of the line is the ratio of the rise to the run, or rise divided by the run.
It describes the steepness of line in the coordinate plane.
The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.
The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is
m=(y₂-y₁)/(x₂-x₁)
The line is passing through point (2, 2) and (4, 8).
Lets find the corresponding point values y₂= 8, y₁ = 2, x₂= 4 and x₁ =2.
Plug in the values in slope formula:
Slope = (8-2)/(4-2)
=6/2
=3
Hence, slope of the line shown in the graph is 3. Option D is correct.
To learn more on slope of line click:
https://brainly.com/question/16180119
#SPJ4
Point R divides PG in the ratio 1:3. If the x-coordinate of R is -1 and the x-coordinate of P is -3, what is the x-coordinate of Q
Answer:
option C . 5
Step-by-step explanation:
For two points (x1,y1) and (x2,y2) divided by a point p in ratio m:n then coordinates of that point is given by
p : (nx1+mx2)/(m+n), (ny1+my2)/(m+n),
Given
x coordinate of P (-3)
x coordinate of Q (a) since we have to find it , let it be a
x coordinate of R(-1)\
ratio = 1:3
_______________________________________
Using the above formula to find the point of division
we can get value of x coordinate for point Q
x coordinate of R = 3*-3 + 1*a/(1+3)
-1 = (-9 + a)/4
=> -4 = -9 +a
=>a = -4+9 = 5
Thus, x coordinate of Q is 5
y =
1
8
x + 3
A) Slope: 8; y-intercept: 3
B) Slope: 1
3
; y-intercept: 1
8
C) Slope: 1; y-intercept: 1
8
D) Slope: 1
8
; y-intercept: 3
Answer:
The slope is 1/8 and the y intercept is 3
Step-by-step explanation:
y = 1/8 x +3
This is in slope intercept form
y = mx+b where m is the slope and b is the y intercept
The slope is 1/8 and the y intercept is 3
Paisley is playing with a yo-yo. The following graph traces the path of the yo-yo while it is in the air, where y is the height of the yo-yo above the
ground, and x is the time, in seconds, from when the yo-yo leaves Paisley's hand Five stages of the yo-yo's path are marked on the graph.
Which of the five stages shows the slowest rate of change in the yo-yo's height above the ground?
А
В
C
D
Answer:
C
Step-by-step explanation:
From the graph we can notice that the yo-yo crosses five positions: A,B,C,D and E.
The path created by the yo-yo has a parabolic form.
● In the area C, the yoyo crosses the vertex in wich the rate of change equals 0.
●In A the parabola decreases dramatically
● In B, the parabola is decreasing but slower than A.
● In D, the parabola is increasing in a fast way
● In E, the parabola is increasing faster than D.
● In the first half of C, the parabola is decreasing slower than B and A.
● At the vertex, the parabola has a null rate of change.
● In the second half of C, the parabola is increasing but slower than D and E.
So we deduce that C has the slowest rate of change.
Answer:
The answer is C i took the test
Step-by-step explanation:
Write the equation of the line that passes through (-1,5) and has a slope of 3 in point slope form
Answer:
y-5=3(x+1)
Step-by-step explanation:
we use the point-slope formula to plug all of our values in.
[tex]y-y_{1}=m(x-x_{1})[/tex]
x = 4 7 9 I dont mind for a step by step
Answer:
[tex]\boxed{\sf x = 9}[/tex]
Step-by-step explanation:
According to chord-chord theorem:
=> [tex]x* 2 = 3 * 6[/tex]
=> [tex]2x = 18[/tex]
Dividing both sides by 2
=> x = 18/2
=> x = 9
QUESTION TWO [25 MARKS] a) Your task is to interview a representative sample of attendees for the large concert venue where you work. The new season schedule includes 200 live concerts featuring all types of musicians and musical groups. Since neither the number of attendees nor their descriptive characteristics are known in advance you decide on nonprobability sampling. Based on past seating configurations, you can calculate the number of tickets that will be available for each of the 200 concerts. Thus, collectively, you will know the number of possible attendees for each type of music From attendance research conducted at concerts held by the Glacier Symphony during the previous two years, you can obtain gender data on attendees by type of music. How would you conduct a reasonably reliable nonprobability sampling? T5 marks] (b) A recent article in Nairobi Post Weekly Edition indicated that about 80% of the
Answer:
The answer to this question depends, in part, on the kinds of questions that you want to ask them. If the purpose of the survey is to try and figure out what concert patrons are thinking, then you want to try to get a good variety of ideas. In that case, you're no so interested in having a sample of individuals that's exactly representative of the population of concert goers. You only want to get a wide variety of the ideas that are out there. This is called heterogeneity sampling. That is, in this case, we'll be trying to get a sample not of people, but of ideas. In this case, we'd use brainstorming groups, panel sessions, and other group discussion methods to get all the ideas out there.
This approach is not an appropriate one if the purpose of the questions is to determine the preferences of the population of theater goers. That's because it doesn't communicate the popularity or prevalence of ideas in the sample. If this is a problem, and it likely is, it seems more appropriate to use some sort of purposive sampling method like modal interest sampling. This approach requires determining what the typical concert goer is like . If the company determines that the typical (or modal) attender is a young single person in college, then those people are sought out and interviewed. This is the sort of polling that is used in election polls where they interview "typical voters." For different genres of music and concert, a different typical concert goer could be postulated and different surveys and interview styles determined.
Probably most appropriate to this problem, though, is quota sampling. This form of purposive sampling uses demographic and other information to determine how many of different kinds of people to interview. For instance, if it is determined that only 20% of concert goers for a particular concert were women, then only 20% of the nonprobability sample should be made up of women. As long as these quotas are met, the sample can be sufficiently random.
I recommend using a combination of quota sampling and modal instance sampling. It seems to me that the kinds of people who attend concerts are idiosyncratic in some ways. Inasmuch as we can define universal characteristics of concert goers, we should seek to include only those people in the sample, but since we have demographic data as well, we should use these proportions as quotas as we select typical concert goers. For example, suppose we determine that the vast majority of people who attend operas make over $80,000/year, then we should limit our sample to people with that income level, but if we also know that 80% of opera attenders are women, we should work to insure that not more than 20% of our sample is men.
For f(x) = 3х – 5 and g(x) = х2+ 2, find (f+ g)(x).
ОА. ? + 3х – 7
ОВ. 3х2 – 30
Ос. 3х3 – 3
OD. х2 + 3х - з
Answer:
x^2 +3x -3
Step-by-step explanation:
f(x) = 3х – 5
g(x) = х^2+ 2,
(f+g)(x) = 3х – 5 +х^2+ 2
Combine like terms
= x^2 +3x -3
Given the exponential function f(x) = 16(0.75)", classify the function as exponential growth or decay and determine the percent rate of growth or decay.
Exponential growth, 75% increase
O Exponential decay, 75% decrease
O Exponential growth, 25% increase
Exponential decay, 25% decrease
Answer:
D
Step-by-step explanation:
To determine if a function is exponential decay or growth, simply look at the rate. If the rate is less than one, it is decay. It it's greater than one, it's growth.
The rate in the given function is 0.75 or 75%. 0.75 is less than one so it's exponential decay.
To determine the percent decrease, simply subtract the rate into 1 or 100%. Thus:
[tex]1-0.75=0.25[/tex]
Therefore, it is a 0.25 or 25% decrease.
The answer is D.
Answer: D
Step-by-step explanation:
1-0.75=0.25
Therefore, it decreases Exponential decay,25 percent decrease
A shopping centre wants to examine the amount of space required for parking. Studies indicated that 50% of staff and shoppers use public transportation. A survey of 1002 was taken, and 483 responded that they used public transportation. At 5% level of significance, is it reasonable to conclude that the survey results indicate a change?
Answer:
We accept H₀ data from the survey is not enough to claim that 50% of the proportion indicated in previous studies have change
Step-by-step explanation:
To get conclusions about the survey we need to develop a hypothesis test of proportion
According to previous studies, (p₀ ) 50 % of staff and customers use public transportation, and we got from a survey 0f 1002 people 483 responded they also use then p = 483/1002 then
n sample size is 1002 and p = 0,482 (48,2 % )
Test Hypothesis
Null hypothesis H₀ p = p₀
Alternative hypothesis Hₐ p < p₀
CI = 95 % α = 5 % α = 0,05 and from z-table we find z score for that value z(c) = - 1,64
z(s) = ( p - p₀ ) / √ (p₀*q₀)/ n p₀ = q₀ = 0,5
z(s) = - 0,018* 31,65 / 0,5
z(s) = - 1,1394
To compare
z(s) and z(c) -1,1394 > 1,64
Then z(s) is inside the acceptance region. We accept H₀ , because we don´t have enough evidence to claim that the survey results indicate a change in
the original proportion
List the sides in order from the largest to the smallest. A. XY, YW, WX B. XY, WX, YW C. WX, YW, XY D. WX, XY, YW
Answer:
Option (D)
Step-by-step explanation:
By applying Sine rule in the given triangle WXY,
[tex]\frac{\text{SinW}}{\text{XY}}=\frac{\text{SinY}}{\text{XW}}=\frac{\text{SinX}}{\text{WY}}[/tex]
[tex]\frac{\text{Sin59}}{\text{XY}}=\frac{\text{Sin82}}{\text{XW}}=\frac{\text{Sin39}}{\text{WY}}[/tex]
[tex]\frac{\text{Sin59}}{\text{XY}}=\frac{\text{Sin82}}{\text{XW}}[/tex]
[tex]\frac{\text{XW}}{\text{XY}}=\frac{\text{Sin82}}{\text{Sin59}}[/tex]
= 1.1489
XW : XY ≈ 1.15 : 1
[tex]\frac{\text{Sin59}}{\text{XY}}=\frac{\text{Sin39}}{\text{WY}}[/tex]
[tex]\frac{\text{XY}}{\text{WY}}=\frac{\text{Sin59}}{\text{Sin39}}[/tex]
[tex]\frac{\text{XY}}{\text{WY}}=\frac{1.36}{1}[/tex]
[tex]\frac{\text{XY}}{\text{WY}}=\frac{\frac{1}{1}}{\frac{1}{1.36} }[/tex]
[tex]\frac{\text{XY}}{\text{WY}}=\frac{1}{0.7342}[/tex]
XY : WY = 1 : 0.7342
XW : XY : WY = 1.15 : 1 : 0.7342
Therefore, WX > XY > WY
Option (D). will be the correct option.
Suppose that you begin with 10 grams of magic crystals, and your crystals grow at a
continuous rate of 25% every day (that's why they're magic). How many grams of
crystals will you have after one week (7 days)?!
ANSWER IS BRAINLEIST
Answer:
After 7 days the crystals will be 57.57 grams.
Step-by-step explanation:
In this the continuous exponential growth formula will be used.
y = A e ^rt
Where A = original amount = 10 grams
y is the growth after 7 days
e is Euler's number= 2.719
t is the time in hours , weeks, years etc.= 7 days
r is the rate in decimals = 25% = 0.25
Putting the values in the formula:
y = A e ^rt
y = 10 e ^0.25 (7)
Calculating with the calculator
y = 10* 2.719^1.75
y= 57.57 grams.
After 7 days the crystals will be 57.57 grams.
Answer:
57.55g
Step-by-step explanation:
Use the formula f(t) = aert, where a = 10, r = 0.25, and t = 7. This gives f(7) = 10e(0.25)(7) = 10e1.75 ≈ 10(5.755) ≈ 57.55.
Which of the following is not a characteristic of the F distribution? Multiple Choice It is always right-skewed. It describes the ratio of two variances. It is a family based on two sets of degrees of freedom. It is negative when s12 is smaller than s22.
Answer:
It is negative when s12 is smaller than s22.
Step-by-step explanation:
The F distribution has the following properties.
1) It is always right-skewed. but as the degrees of freedom v1 and v2 become large F distribution approaches normal distribution.
2) It describes the ratio of two variances.
3) It is a family based on two sets of degrees of freedom.
4) It is negative when s12 is smaller than s22. This is not true sometimes as the F distribution does not depend on the population variance but on the two parameters v1 and v2.
A study claimed residents in a suburb town spend at most 1.9 hours per weekday commuting to and from their jobs. A researcher believed commute times were now different and wants to test this claim by sampling 14 adults. Sample statistics for these 14 adults are: X = 2.2 $=0.7 Can the researcher support the claim that mean commuting time is more than 1.9 hours ? Test using a =.01.
Answer:
There is no sufficient evidence to support the claim that mean commuting time is more than 1.9 hours
Step-by-step explanation:
From the question we are told that
The population mean is [tex]\mu = 1.9 \ hr[/tex]
The sample mean is [tex]\= x = 2.2[/tex]
The standard deviation is [tex]\sigma = 0.7[/tex]
The sample size is [tex]n = 14[/tex]
The level of significance is [tex]\alpha = 0.01[/tex]
The null hypothesis is [tex]H_o : \mu = 1.9 \ hr[/tex]
The alternative hypothesis is [tex]H_a : \mu > 1.9 \ hr[/tex]
Generally the test statistics is mathematically represented as
[tex]t = \frac{\= x - \mu }{ \frac{\sigma}{ \sqrt{n} } }[/tex]
[tex]t = \frac{ 2.2 - 1.9 }{ \frac{0.7 }{ \sqrt{14} } }[/tex]
[tex]t = 1.6036[/tex]
The p-value is obtained from the z-table, the value is
[tex]p-value = P(t > 1.6036) = 0.054401[/tex]
Looking at the value of [tex]p-value \ and \ \alpha[/tex] we see that [tex]p-value > \alpha[/tex]
So we fail reject the null hypothesis
Hence we can conclude that there is no sufficient evidence to support the claim that mean commuting time is more than 1.9 hours
1. What is sin(A)?
1
T
2
2. What is
tan(B)?
5
3
4
13
12
이
3. What is
cos(C)?
5
3
B
5
6
4. What is
cos(D)?
7
AddP
Answer:
Sin A=0.6
Tan B = 1.3333
Cos C= 0.9231
Cos C= 0.3846
Step-by-step explanation:
For sin A
Sin A= opposite/hypotenuse
Sin A= 3/5
Sin A=0.6
For Tan B
Tan B = opposite/adjacent
Tan B = 4/3
Tan B = 1.3333
For cos C
Cos C = adjacent/hypotenuse
Cos C= 12/13
Cos C= 0.9231
For Cos D
Cos D= adjacent/hypotenuse
Cos C = 5/13
Cos C= 0.3846
The ball bearing have volumes of 1.6cm cube and 5.4cm cube . Find the ratio of their surface area.
Answer:
4/9
Step-by-step explanation:
The scale factor for the linear dimensions of the ball bearings will be the cube root of the volume scale factor:
k = ∛(1.6/5.4) = 2/3
Then the scale factor for the areas will be the square of this scale factor:
ratio of surface area = (2/3)² = 4/9
_____
The area is the product of two linear dimensions, so its scale factor is the product of the linear dimension scale factors. That is, the scale factor for area is the square of the linear dimension scale factor.
Similarly, volume is the product of three linear dimensions, so its scale factor is the cube of the linear dimension scale factor.
Hi Maths lovers, if someone can explain me when l want to get NR doing NSR way ( going upwards) where this 3/5 b + 2/5 a or 2/5 a + 3/5 b comes from? Thanks
Answer:
see explanation
Step-by-step explanation:
SQ = SP + PQ = - b + a
Since SN : NQ = 3 : 2 then SQ = 3 + 2 = 5 parts , thus
SN = [tex]\frac{3}{5}[/tex] SQ = [tex]\frac{3}{5}[/tex] ( - b + a) = - [tex]\frac{3}{5}[/tex]b + [tex]\frac{3}{5}[/tex] a
Thus
NR = NS + SR
= - (- [tex]\frac{3}{5}[/tex] b + [tex]\frac{3}{5}[/tex] a) + a
= [tex]\frac{3}{5}[/tex] b - [tex]\frac{3}{5}[/tex] a + a
= [tex]\frac{2}{5}[/tex] a + [tex]\frac{3}{5}[/tex] b
Answer:
Yeah
Step-by-step explanation:
Very simple
It was said that
SN:NQ=3:2
→2SN = 3NQ
SN=SR-NR
SN=a - NR
NQ = NR - QR
NQ=NR - b
SQ = SN + NQ
Recall that SN=(3NQ)/2
SQ = (3NQ)/2 + NQ
SQ = (5/2)NQ
a - b = (5/2)(NR - b)
After simplification
NR = (2/5)a - (2/5)b +b
Factorize
NR = (2/5)a + (-2/5 + 1)b
NR = (2/5)a + (3/5)b
What is the rate of change from x = 0 to x = pi over 2 ? (6 points) trig graph with points at: (0, negative 4) and (pi over 2, 0) and (pi, 4) and (3 pi over 2, 0) and (2 pi, negative 4)
Answer:
Rate of Change : 8 / π
Step-by-step explanation:
To determine this rate of change, we have to first consider the points at x = 0 and x = π / 2.
When x = 0, f( x ) = - 4,
When x = π / 2, f( x ) = 0
Remember that rate of change is represented by a change in y / change in x. Therefore,
( 0 - ( - 4 ) ) / ( π / 2 - 0 ),
( 0 + 4 ) / ( π / 2 ),
4 / π / 2 = 8 / π
Therefore the rate of change from x = 0 ➡ x = π / 2 will be 8 / π.
MY
A circle with radius of 5 cm sits inside a 11 cm x 11 cm rectangle.
Col
What is the area of the shaded region?
Round your final answer to the nearest hundredth.
MY
11 cm
Pro
Pro
Теа
5 cm
11 cm
cm2
2 of 4 OOO
Help
Step-by-step explanation:
Hi, there!!!
According to the question we must find the area of shaded region, but we must find area of circle and rectangle to find area of shaded region,
So, let's simply work with it,
Firstly, finding the area of rectangle,
length = 11cm.
breadth = 11cm.
now, area= length× breadth.
or, a = 11cm× 11cm.
a= 121cm^2
Now, let's work out the area of circle.
radius= 5cm
and pi. = 3.14 {using pi value as 3.14}
now,
area of a circle = pi× r^2
or, a= 3.14×5^2
or, a = 78.5 cm^2.
Therefore, The area of a circle is 78.5cm^2.
Now lastly finding the area of shadedregion,
area of shaded region = area of rectangle - area of circle.
or, area of shaded region = 121cm^2 - 78.5cm^2
Therefore, the area of shaded region is 42.5 cm^2.
Hope it helps...
Do numbers below 0 make sense outside of the context of temperature? If you think so, give some examples to show how they make sense. If you don’t think so, give some examples to show otherwise.
Answer:
Yes, they make sense outside the context of temperature.
Step-by-step explanation:
If you are standing in a line, and mark your current position as 0 then if you take two steps ahead it can be counted as positive and if you take two steps back from your current position it can be counted as negative. The positive and negative can denote your forward and backward movement respectively.
If we denote the growth in companies revenue as positive and dip as negative then it would also make sense. A positive number would mean profit for the company while a negative sign would show loss.
Problem 1. (1 point) A steel ball weighing 128 pounds is suspended from a spring. This stretches the spring 128101 feet. The ball is started in motion from the equilibrium position with a downward velocity of 2 feet per second. The air resistance (in pounds) of the moving ball numerically equals 4 times its velocity (in feet per second) . Suppose that after t seconds the ball is y feet below its rest position. Find y in terms of t. (Note that this means that the positive direction for y is down.)
Answer:
seeed
Step-by-step] explanation:
ddd~!`
Mark has a collection of 80 coins. There are only nickels and dimes in the collection. The total value of the coins is $5.00. How many dimes does Mark have?
Answer:
number of nickel = 60
number of dimes = 20
Step-by-step explanation:
1 nickel = 5 cents
1 dimes = 10 cents
$1 = 100 cents
we will use these value to solve the questions
_______________________________
Total no of coins = 80
let the number of nickels be x
let the number of dimes be y
thus,
x+y = 80
y = 80-x equation 2
value of x nickels = 5x
value of y dimes = 10y
Total value of x nickels and y dimes = 5x+10y
The total value of the coins is $5.00
total value of the coins in cents = 5*100 = 500
thus
5x+10y = 500
using y = 80-x from equation 2
5x + 10(80 - x) = 500
5x + 800 - 10x = 500
-5x = 500 - 800 = -300
x = -300/-5 = 60
Thus,
number of nickel = 60
number of dimes = 80-60 = 20
cherry pies ratio is 240 to 3 pies.how many Cherry's to make 9 pies
Answer:
720
Step-by-step explanation:
It takes 240 cherries to make 3 pies.
9 pies are 3 times 3 pies, so it takes 3 times as many cherries.
3 * 240 cherries = 720 cherries.
[tex]\text{Find how many cherries is needed for 9 pies}\\\\\text{We know that there are 240 total cherries on 3 pies}\\\\\text{Now we need to find how many cherries will 9 pies need}\\\\\text{We simply have to multiply 240 by 3, since 3 multiplied by 3 is 9 pies}\\\text{So we would do the same with the cherries by multiplying it by 3}\\\\240\cdot3=720\\\\\boxed{\text{720 cherries}}[/tex]
Evaluate the double integral ∬Ry2x2+y2dA, where R is the region that lies between the circles x2+y2=16 and x2+y2=121, by changing to polar coordinates.
Answer:
See answer and graph below
Step-by-step explanation:
∬Ry2x2+y2dA
=∫Ry.2x.2+y.2dA
=A(2y+4Ryx)+c
=∫Ry.2x.2+y.2dA
Integral of a constant ∫pdx=px
=(2x+2.2Ryx)A
=A(2y+4Ryx)
=A(2y+4Ryx)+c
The graph of y=A(2y+4Ryx)+c assuming A=1 and c=2
The evaluation of the double integral is [tex]\mathbf{ \dfrac{105}{2}\pi }[/tex]
The double integral [tex]\mathbf{\int \int _R\ \dfrac{y^2}{x^2+y^2} \ dA}[/tex], where R is the region that lies between
the circles [tex]\mathbf{x^2 +y^2 = 16 \ and \ x^2 + y^2 = 121}[/tex].
Let consider x = rcosθ and y = rsinθ because x² + y² = r²;
Now, the double integral can be written in polar coordinates as:
[tex]\mathbf{\implies \int \int _R\ \dfrac{y^2}{x^2+y^2} \ dxdy}[/tex]
[tex]\mathbf{\implies \int \int _R\ \dfrac{r^2 \ sin^2 \theta}{r^2} \ rdrd\theta}[/tex]
[tex]\mathbf{\implies \int \int _R\ \ sin^2 \theta \ r \ drd\theta}[/tex]
Thus, the integral becomes:
[tex]\mathbf{=\int^{2 \pi}_{0} sin^2 \theta d\theta \int ^{11}_{4} rdr }[/tex]
since 2sin² = 1 - cos2θ∴
[tex]\mathbf{=\int^{2 \pi}_{0} \dfrac{1-cos 2 \theta }{2} \ \theta \ d\theta\dfrac{r}{2} \Big|^{11}_{4}dr }[/tex]
[tex]\mathbf{\implies \dfrac{1}{2} \Big[\theta - \dfrac{sin \ 2 \theta}{2}\Big]^{2 \pi}_{0} \ \times\Big[ \dfrac{11^2-4^2}{2}\Big]}[/tex]
[tex]\mathbf{\implies \dfrac{\pi}{2} \times\Big[ 121-16\Big]}[/tex]
[tex]\mathbf{\implies \dfrac{105}{2}\pi }[/tex]
Learn more about double integral here:
https://brainly.com/question/19756166
True or false? "In any sample data set, the sum of all the values is equal to the product of the mean and the sample size."
Answer:
TRUEStep-by-step explanation:
One of the method of analysing the distribution of a dataset is by finding the mean of the dataset which is part of the measure of central of tendency.
Mean of a dataset is also known as the average and it is the ratio of the sum of the individual dataset to the sample size.
Mathematically xbar = ΣXi/N where
ΣXi is the sum of the individual dataset
N is the sample size
xbar is the mean
From the formula, ΣXi = xbar * N
This means that the sum of the individual dataset (all values in the dataset) is equal to the product of the mean (xbar) and the sample size(N).
Hence the statement that In any sample data set, the sum of all the values is equal to the product of the mean and the sample size."is TRUE
solve for x: 7^2x+3 =2401 . show substitution of your solution to verify the equation. show steps. show work.
Answer:
X= 1/2
Step-by-step explanation:
7^2x+3 =2401
7^(2x+3 )=2401
7^(2x+3 )= 7^4
Taking away the base because its equal to 7
Then solving the power as an equation
2x+3= 4
2x= 4-3
2x= 1
X=1/2
Now substituting x into the equation to know if we are correct
7^(2x+3 )=2401
Where x= 1/2
7^(2*(1/2) +3)= 7^4
7^(1+3)= 7^4
7^4= 7^4
7^4= 2401
Reduce 18/24 to its lowest terms
Answer:
3/4
Step-by-step explanation:
find a common number that 18 and 24 are both divisible by. I chose 6. So when i divide 6 by 18, I got 3. Which I put on my numerator, when I divided 24 by 6 I got 4 which I put on my denominator. My end result was 3/4
Answer:
3/4
Step-by-step explanation:
18/24
=2*9=18
=2*12=24
=9/12
=3/4
Weekly wages at a certain factory are
normally distributed with a mean of
$400 and a standard deviation of $50.
Find the probability that a worker
selected at random makes between
$450 and $500.
Answer:
13.59%
Step-by-step explanation:
Calculate the z-scores.
z = (x − μ) / σ
z₁ = (450 − 400) / 50
z₁ = 1
z₂ = (500 − 400) / 50
z₂ = 2
Use a chart or calculator to find the probability.
P(1 < Z < 2)
= P(Z < 2) − P(Z < 1)
= 0.9772 − 0.8413
= 0.1359
Answer:
13.5
Step-by-step explanation:
Acellus sux
