Solution :
Here the subintervals of equal length will be :
[tex][6:00, 6:30], [6:30, 7:00], [7:00, 7:30], [7:30, 8:00], [8:00, 8:30], [8:30, 9:00][/tex]
So thee mid points are
[tex]x_1 = 6:15, \ x_2=6:45, \ x_3=7:15, \ x_4=7:45, \ x_5, 8:15, \ x_6 = 8:45[/tex]
The length of each sub-interval is = [tex]\frac{9-6}{6} = \frac{3}{6} = 0.5[/tex]
So, total amount of rainfall will be :
[tex]$=0.5 \sum^6_{i=1} f(x_i)$[/tex]
[tex]$=0.5\left( f(x_1)+f(x_2)+....+ f(x_6)\right)$[/tex]
= 0.5 (2.8 + 3.5 + 4.2 + 5.6 + 3.3 + 0.4)
= 0.5 (19.8)
= 9.9
The total amount of rainfall that falls between 6:00 a.m. and 9:00 a.m. using a midpoint sum with 6 equal subintervals is 9.9.
Given that,
The rate of rainfall (mm per hour) over time.
Rate of rainfall;
6;00 6;15 6;30 6;45 7;00 7;15 7;30 7;45 8;00 8;15 8;30 8;45 9;00
Time
2.0 2.8 3.0 3.5 3.8 4.2 4.8 5.6 4.0 3.3 1.8 0.4 1.2
We have to determine,
0.4 9:00 am 1.2.
The total amount of rainfall that falls between 6:00 a.m. and 9:00 a.m. using a midpoint sum with 6 equal subintervals is?
According to the question,
Rate of rainfall;
6;00 6;15 6;30 6;45 7;00 7;15 7;30 7;45 8;00 8;15 8;30 8;45 9;00
Time
2.0 2.8 3.0 3.5 3.8 4.2 4.8 5.6 4.0 3.3 1.8 0.4 1.2
Here, the midpoints sum with 6 equal subintervals are,
[tex]\rm x_1 = 6;15, \ x _2 = 6;45, \ x_3 = 7;15, \ x_4 = 7;45, x_5 = 8;15 , \ x_6 = 8;45[/tex]
Then, the length of each subinterval is,
[tex]= \dfrac{9-6}{6}\\\\= \dfrac{3}{6}\\\\= \dfrac{1}{2}[/tex]
The total amount of rainfall that falls between 6;00 to 9;00 am using the midpoint subinterval is,
[tex]\rm = \dfrac{1}{2} \sum^{6}_{i=0} f(x_i)\\\\= \dfrac{1}{2} \sum^{6}_{i=0} f(x_1)+ f(x_2) + f(x_3) + f(x_4) +f(x_5)+f(x_6)\\\\= \dfrac{1}{2} (2.8+ 3.5+4.2+ 5.6+3.3+0.4}\\\\= \dfrac{1}{2} \times 19.8\\\\= 9.9[/tex]
Hence, The total amount of rainfall that falls between 6:00 a.m. and 9:00 a.m. using a midpoint sum with 6 equal subintervals is 9.9.
For more details refer to the link given below.
https://brainly.com/question/795909
Solve y = x + 6 for x.
Ox = y + 6
Ox= -y + 6
O x = y - 6
Ox= -y-6
Answer:
x = y - 6
Step-by-step explanation:
y = x + 6 (Given)
y - 6 = x (Subtracted 6 on both sides)
here is the picture!
someone please answer ASAP!!
i need to know if my math is right
Answer:
good luck
Step-by-step explanation:
you will get answers after some time
Answer:
base 48
width 8 and length 6
pls brainliest. should work and you get points back
Classify the quadrilateral.
Answer: B
Step-by-step explanation: If a quadrilateral is a parallelogram, then opposite sides are congruent and parallel, so this must be a parallelogram.
PLS HELP ASAP! Find the Surface Area of the given figure.
THANK YOU!
Answer:
158 m^2
Step-by-step explanation:
l = 5 m, w = 3 m, h = 8 m
S.A. = [tex]2(lw+wh+lh)[/tex]
S.A. = 2{(5)(3) + (3)(8) + (5)(8)}
S.A. = 2(15 + 24 + 40)
S.A. = 2(79)
S.A. = 158 m^2
Hope this help!!!
Have a nice day!!!
Someone please help with this ASAP!!! I will give brainliest
Answer:
12m
7m
2520 m³
Step-by-step explanation:
Answer:
h=7m
top width=12m
v=l*w*h
=28*12*10=3360
volume of the top=3*20*12
720
v of the shape is= 3360-720
=2649
what Will You nota miss about remote learning
Answer:
using brainly
Step-by-step explanation:
Answer:
waking up everyday and listening to them fuss about calling home even though im already home
Maya read 40 pages in 60 minutes
Calculate 18t -t +6q-6
Answer:
17t+6q-6
Step-by-step explanation:
18t -t +6q-6
Combine like terms
17t+6q-6
Answer:
17t+6q-6
Step-by-step explanation:
18t-t =17t
others don't change as they are not the factors of the same character
Which of the following triangles have three sides of different length?
A. acute
B. scalene
C.equilateral
D. right
Answer:
C
Step-by-step explanation:
correct me if iam wrong
Question attached please answer brainliest to best answer
Answer:
B
Step-by-step explanation:
Have a nice day :)
HELPPP!!! PLEASEEEEEEE
Answer:
Step-by-step explanation:
37
What is the probability that a randomly selected
purchase has less than two tickets?
Answer:
The answers for your question is 0.17
can someone please please answer this
Answer:
720 degrees
Step-by-step explanation:
sum of interior angles of any polygon is given by the equation
[tex]sum \: = (n - 2) \times 180[/tex]
where n is the number of sides of the polygon. in the question the polygon has 6 sides. hence n = 6 and
[tex]sum \: = (6 - 2) \times 180 \\ = 4 \times 180 \\ = 720 \: degrees[/tex]
15. Mr Muthu bought some apples and oranges. The price of the fruits were as shown below. Fruit Price Apples 60¢ each Oranges 80€ aach The ratio of the number of apples bought to the number of oranges bought was 3:4. He spent $75 on the apples and oranges. How many apples did he buy?
Answer:
40
Step-by-step explanation:
you mutiply then take away the 2 last digits
Answer:
Step-by-step explanation:
0.6*3t+0.8*4t=75
so t=15
apple=3t=45
orange=4t=60
Additional Activities
Directions: Use a non-standard unit of the same material and
size. Which unit will give the greater number for the volume of the
container using ping-pong balls and monggo seeds? Visualize the
volume of each box, explain your answer. Write your answers on a
sheet of paper
.
2.
1.
Ping-Pong balls
Monggo seeds
Answer:Ping Pong Balls
Step-by-step explanation:
Jeffery has two pets that he feeds daily. His dog eats 3/4 cup of food. His cat, on the other hand, eats 1/2 of what his dog eats. How much food does his cat eat?
Answer:
3/8 cup
Step-by-step explanation:
Dog : 3/4 cup
Cat: 1/2 (Dog) = 1/2 (3/4 cup) = 3/8 cup
Hope this helps!!!
Have a great day!!!
Sam puts $10,000 in an account earning 4% interest, compounded monthly. If he adds 5100 to the account each month, how much
will the account be worth in 10 years?
A. $26,489.23
B. $29,633.31
C. $32,722.56
D. $34,693.81
12. The heights of 53 students at Park School are shown in the histogram below.
Height of Students
18
Number of Students
NA ON
44 46 48 50 52 54 56 58 60
Height (inches)
Based on the data in the histogram, which statement is true?
A There are 12 students between 46 and 50 inches in height.
B. Exactly 18% of the students are between 52 and 54 inches in height.
C. More students are between 54 and 60 inches than between 46 and 50 inches in height.
Fewer students are between 44 and 52 inches than between 52 and 60 inches in height.
D
Answer:
Fewer students are between 44 and 52 inches than between 52 and 60 inches in height.
Step-by-step explanation:
Given
See attachment for histogram
Required
Select the true statement
Option A: Class 46-50 = 12 students
From the histogram, we have:'
[tex]Class\ 46 - 48 = 8; Class\ 48 - 50 = 3[/tex]
So:
[tex]Class\ 46 - 48 = Class\ 46 - 48 + Class\ 48 - 50[/tex]
[tex]Class\ 46 - 48 = 8+ 3[/tex]
[tex]Class\ 46 - 48 = 11[/tex]
(a) is false
Option B: %Class 52-54 = 18%
From the histogram, we have:'
[tex]Class\ 52-54 = 18[/tex]
and
[tex]Total = 53[/tex]
So, the percentage is:
[tex]\% Class\ 52-54 = \frac{Class\ 52-54}{Total}[/tex]
[tex]\% Class\ 52-54 = \frac{18}{53}[/tex]
[tex]\% Class\ 52-54 = 0.3396[/tex]
Express as percentage:
[tex]\% Class\ 52-54 = 33.96\%[/tex]
(b) is false
Option C: Class 54-60 > Class 46 - 50 students
From the histogram, we have:'
[tex]Class\ 54-60 =Class\ 54-56 + Class\ 56-58 + Class\ 58-60[/tex]
[tex]Class\ 54-60 = 4 + 4+3[/tex]
[tex]Class\ 54-60 = 11[/tex]
In (a), we have:
[tex]Class\ 46 - 48 = 11[/tex]
By comparison:
[tex]Class\ 54-60 =Class\ 46 - 48 = 11[/tex]
(c) is false
Option D: Class 44-52 < Class 52 - 60 students
From the histogram, we have:'
[tex]Class\ 44-52 =Class\ 44-56 + Class\ 46-48 + Class\ 48-50 +Class\ 50-52[/tex]
[tex]Class\ 44-52 = 4+8+3+9[/tex]
[tex]Class\ 44-52 = 24[/tex]
[tex]Class\ 52-60 =Class\ 52 - 54 + Class\ 54-56 + Class\ 56-58 + Class\ 58-60[/tex]
[tex]Class\ 52-60 = 18+ 4 + 4+3[/tex]
[tex]Class\ 52-60 = 29[/tex]
By comparison:
[tex]24 < 29[/tex]
i.e.
[tex]Class\ 44 - 55 < Class\ 52 - 60[/tex]
(d) is true
What is the least common multiple (LQM) of 8 and 12?
Answer:
24
Step-by-step explanation:
The LCM of 8 and 12 is 24. Find least common multiple (LCM) of: 16 & 24 4 & 6 24 & 36 40 & 60 56 & 84 16 & 12 8 & 24 24 & 12 8 & 36 40 & 12 8 & 60 56 & 12 8 & 84
A past study claims that adults in America spend an average of 17 hours a week on leisure activities. A researcher wanted to test this claim. She took a sample of 10 adults and asked them about the time they spent per week on leisure activities. Their responses (in hours) are as follows:13242137152518224032Assume that the times spent on leisure activities by all adults are normally distributed. At the 5% significance level, can you conclude that the claim of this earlier study is true
Answer:
The claim is false.
Step-by-step explanation:
Given the data :
13 24 21 37 15 25 18 22 40 32
The sample mean and standard deviation can ben calculated for the given sample.
Using calculator :
Sample mean, xbar = 24.7
Sample standard deviation, s = 9.04
Sample size, n = 10
The hypothesis :
H0 : μ = 17
H1 : μ ≠ 17
The test statistic :
(xbar - μ) ÷ (s/√(n))
(24.7 - 17) ÷ (9.04/√(10))
7.7 / 2.8586990
Test statistic = 2.694
We can obtain the Pvalue, at α = 0.05 ; df = n-1 = 9
Pvalue = 0.0246
Since Pvalue < α ; we reject the null ; Hence, there is significant evidence to conclude that an adult American does not spend average of 17 hours in leisure
length of rope measures 8 3/4 km. If a piece of rope measuring 2 1/2 km was cut off, what length of rope remained? *
Answer:
6 1/4 simplified 25/4 decimal 6.25
Step-by-step explanation:
if the rope is 8 3/4 and you took away a piece that is equal to 2 1/2 which means you subtract them from each other to get your final answer of 6 1/4
i need help plz
i will mark you brainlest
Answer:
[tex] \frac{7}{4} - \frac{3}{4} = \frac{4}{4} [/tex]
Step-by-step explanation:
To find the number midway between 3/2 and 4/2, add them up and divide by 2
we have, 3/2 + 4/2 = 7/2
7/2 ÷ 2 = 7/4
Repeat the same for the number midway between 1/2 and 2/2 to get 3/4
The answer then is, 7/4 - 3/4 = 4/4
write down all the factors of each number
a. 10
b. 25
c. 36
d. 50
e. 100
Answer:
Below
Step-by-step explanation:
The factors of 10 are 1, 2, 5, 10.
The factors of 25 are 1, 5, and 25.
Factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, and 36
Factors of 50: 1, 2, 5, 10, 25, 50.
Factors of 100: 1, 2, 4, 5, 10, 20, 25, 50, and 100.
Which of the following is a characteristic of a plane
Answer:
I think you meant to add a list of answers but didn't so here's the characteristics of a plane: Flat, two dimensional, extends infinitely, and is assembled about multiple points and lines.
Step-by-step explanation:
Answer:
If you are taking the FLVS test it is "Two endpoints"
Step-by-step explanation:
Just took the test
hope it helps :)
Adam is 9 years old and Billy is 11 years old. What will be the ratio of Adams’ age to Billy’s age in exactly one year’s time? Give your answer in its simplest form. *
Answer:
10 / 12
simplified:
5/6
since 5 is a prime number, we can't simplify this ratio any further
help me pleaseeeeeeeeeeeeeeeeeee
Answer:
answer a and d
Step-by-step explanation:
one thing i could say it would not be C because if it were symetric, i already see 2 lines that are not symetrical in anyway
sure the graph could extend to infinity and negative infinity and if you see the right arrow, it is pointing down-wards, so if it goes bellow 0, point (0,0) would not be your expected number to see as the minimum
and between -1 and 1, yes, we can already see that the line from -1 and 1 is exponentially increasing
HELPPPPPP don't troll ima report
Answer:
The x-coordinates for which the gradient of the curve is 5 is at x = -1/2 and x = 1/2.
Step-by-step explanation:
We have the function:
[tex]\displaystyle y=\frac{x^2 -1}{x}[/tex]
And we want to find the x-coordinates for which the gradient (or slope) at the point is 5.
The gradients of a curve at a point is given by its derivative. Find the derivative:
[tex]\displaystyle \frac{dy}{dx}=\frac{d}{dx}\left[\frac{x^2-1}{x}\right][/tex]
Use the quotient rule:
[tex]\displaystyle \frac{dy}{dx}=\frac{(x^2-1)'(x)-(x^2-1)(x)'}{(x)^2}[/tex]
Simplify:
[tex]\displaystyle \frac{dy}{dx}=\frac{(2x)(x)-(x^2-1)(1)}{x^2}[/tex]
Simplify:
[tex]\displaystyle \frac{dy}{dx}=\frac{x^2+1}{x^2}[/tex]
Since the gradient is 5, substitute 5 for dy/dx and solve for x:
[tex]\displaystyle 5=\frac{x^2+1}{x^2}[/tex]Multiply both sides by x² (x ≠ 0):
[tex]5x^2=x^2+1[/tex]
Subtract x² from boths sides:
[tex]4x^2=1[/tex]
Solve for x:
[tex]\displaystyle x=\pm\sqrt{\frac{1}{4}}=\frac{1}{2}\text{ or } -\frac{1}{2}[/tex]
So, the x-coordinates for which the gradient of the curve is 5 is at x = -1/2 and x = 1/2.
12.) The FAA has to periodically revise their rules regarding weight estimates that vary by
season. Airlines currently use an estimate for the weight of an adult male passenger of 190 lbs.
in the summer that assumes
he carries sixteen pounds of baggage and has five pounds of
clothing. According to your textbook, assume that men (not clothed nor carrying baggage) have
weights that are normally distributed with a mean of 188.6 lbs. and a standard deviation of 38.9
lbs.
a.) If one adult male is randomly selected and is assumed to be also carrying 21 lbs. due to
clothing and baggage, find the probability that the total weight is greater than 190 lbs.
b.) What total weight would separate the lower 20% of men carrying 21 lbs. of clothing and
baggage from the top 80%?
Answer:
a) 0.4856 = 48.56% probability that the total weight is greater than 190 lbs.
b) A total weight of 155.9 lbs.
Step-by-step explanation:
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Mean of 188.6 lbs. and a standard deviation of 38.9 lbs.
This means that [tex]\mu = 188.6, \sigma = 38.9[/etx]
21 lbs of baggage are taken into consideration in this estimate.
a.) If one adult male is randomly selected and is assumed to be also carrying 21 lbs. due to clothing and baggage, find the probability that the total weight is greater than 190 lbs.
This is 1 subtracted by the the p-value of Z = 190. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{190 - 188.6}{38.9}[/tex]
[tex]Z = 0.036[/tex]
[tex]Z = 0.036[/tex] has a p-value of 0.5144.
1 - 0.5144 = 0.4856.
0.4856 = 48.56% probability that the total weight is greater than 190 lbs.
b.) What total weight would separate the lower 20% of men carrying 21 lbs. of clothing and baggage from the top 80%?
This is the 20th percentile, which is X when Z has a p-value of 0.2, so X when Z = -0.84.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]-0.84 = \frac{X - 188.6}{38.9}[/tex]
[tex]X - 188.6 = -0.84*38.9[/tex]
[tex]X = 155.9[/tex]
A total weight of 155.9 lbs.
write the equation of a circle with a center at (-1, -4) that passes through the point (-1,-1)
Answer:
Equation of the circle :
[tex](x+ 1)^2 + (y+4)^2 = 9[/tex]
Step-by-step explanation:
Equation of a circle with centre (a, b) and radius ,r :
[tex](x - a)^2 + (y-b)^2 = r^2[/tex] ------(1)
Here a = -1, b = -4
find radius:
Since the circle passes through (-1, -1) , the radius is the distance between the centre and the point.
[tex]distance, r = \sqrt{(-1 -(-1))^2 +(-4 -(-1))^2 }[/tex]
[tex]= \sqrt{9} = 3[/tex]
Substitute the values in (1) :
[tex](x - (-1))^2 + (y-(-4))^2 = 3^2\\\\(x+ 1)^2 + (y+4)^2 = 9[/tex]
HELP ME PLS I SUCK AT MATH I NEED ANSWER ASAP