Answer:
a) [tex]E(\bar x) = \mu_{1} = 22[/tex] inches
The sampling distribution of the sample means annual rainfall for California is 1.278.
b)
[tex]E(\bar x) = \mu_{2} = 42[/tex] inches
The sampling distribution of the sample means annual rainfall for New York is 1.0435.
c)
Here, The standard error of New York is smaller because the sample size is larger than for California.
Step-by-step explanation:
California:
[tex]\mu_{1} = 22[/tex] inches.
[tex]\sigma_{1}[/tex] = 7 inches.
[tex]n_{1}[/tex] = 30 years.
New York:
[tex]\mu_{2} = 42[/tex] inches.
[tex]\sigma_{2}[/tex] = 7 inches.
[tex]n_{2}[/tex] = 45 years.
a)
[tex]E(\bar x) = \mu_{1} = 22[/tex] inches
[tex]\sigma^{p} _{\bar x} = \frac{\sigma_{1} }{\sqrt n_{1} } \\\\\\\sigma^{p} _{\bar x} = \frac{7}{\sqrt 30} \\\\\sigma^{p} _{\bar x} = 1.278[/tex]
b)
[tex]E(\bar x) = \mu_{2} = 42[/tex] inches
[tex]\sigma _{\bar x} = \frac{\sigma_{2} }{\sqrt n_{2} } \\\\\\\sigma_{\bar x} = \frac{7}{\sqrt45} \\\\\sigma _{\bar x} = 1.0435[/tex]
c)
Here, The standard error of New York is smaller because the sample size is larger than for California.
Complete the table for the given rule.
Rule: y is 0.75 greater than x
x y
0
3
9
The complete table is
x y
0 0.75
3 3.75
9 9.75
What is equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
What is substitution?Substitution means putting numbers in place of letters to calculate the value of an expression or equation.
According to the given question.
We have values of x.
Also, one rule that y is 0.75 greater than x.
So, we have a equation for finding the value of y i.e.
[tex]y = x + 0.75..(i)[/tex]
For finding the value of y
At x = 0, substitute x = 0 in equation (i)
[tex]y = 0 + 0.75\\\implies y = 0.75[/tex]
At x = 3, substitute x = 3 in equation (i)
[tex]y = 3+0.75\\\implies y = 3.75[/tex]
At x = 9, substitute x = 9 in equation (i)
[tex]y = 9+0.75\\\implies y = 9.75[/tex]
Hence, the complete table is
x y
0 0.75
3 3.75
9 9.75
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Triangle ABL is an isosceles triangle in circle A with a radius of 11, PL = 16, and ∠PAL = 93°. Find the area of the circle enclosed by line PL and arc PL. Show all work and round your answer to two decimal places.
The area bounded by a chord and arc it intercepts is known as a segment of a circle segment of a circle
The area of the circle enclosed by line PL and arc PL is approximately 37.62 square units
The reason the above value is correct is as follows:
The given parameters in the question are;
The radius of the circle, r = 11
The length of the chord PL = 16
The measure of angle ∠PAL = 93°
Required:
The area of part of the circle enclosed by chord PL and arc PL
Solution:
The shaded area of the given circle is the minor segment of the circle enclosed by line PL and arc PL
The area of a segment of a circle is given by the following formula;
Area of segment = Area of the sector - Area of the triangle
Area of segment = Area of minor sector APL - Area of triangle APL
Area of minor sector APL:
Area of a sector = (θ/360)×π·r²
Where;
r = The radius of the circle
θ = The angle of the sector of the circle
Plugging in the the values of r and θ, we get;
Area of the minor sector APL = (93°/360°) × π × 11² ≈ 98.2 square units
Area of Triangle APL:
Area of a triangle = (1/2) × Base length × Height
Therefore;
The area of ΔAPL = (1/2) × 16 × 11 × cos(93°/2) ≈ 60.58 square units
Required shaded area enclosed by line PL and arc PL:
Therefore, the area of shaded segment enclosed by line PL and arc PL is found as follows;
Area of the required segment PL ≈ (98.2 - 60.58) square units = 37.62 square units
The area of the circle enclosed by line PL and arc PL ≈ 37.62 square units
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The area of the circle enclosed by line segment PL and circle arc PL is 37.80 square units.
The calculation of the area between line segment PL and circle arc PL is described below:
1) Calculation of the area of the circle arc.
2) Calculation of the area of the triangle.
3) Subtracting the area found in 2) from the area found in 1).
Step 1:
The area of a circle arc is determined by the following formula:
[tex]A_{ca} = \frac{\alpha\cdot \pi\cdot r^{2}}{360}[/tex] (1)
Where:
[tex]A_{ca}[/tex] - Area of the circle arc.
[tex]\alpha[/tex] - Arc angle, in sexagesimal degrees.
[tex]r[/tex] - Radius.
If we know that [tex]\alpha = 93^{\circ}[/tex] and [tex]r = 11[/tex], then the area of the circle arc is:
[tex]A_{ca} = \frac{93\cdot \pi\cdot 11^{2}}{360}[/tex]
[tex]A_{ca} \approx 98.201[/tex]
Step 2:
The area of the triangle is determined by Heron's formula:
[tex]A_{t} = \sqrt{s\cdot (s-l)\cdot (s-r)^{2}}[/tex] (2)
[tex]s = \frac{l + 2\cdot r}{2}[/tex]
Where:
[tex]A_{t}[/tex] - Area of the triangle.
[tex]r[/tex] - Radius.
[tex]l[/tex] - Length of the line segment PL.
If we know that [tex]l = 16[/tex] and [tex]r = 11[/tex], then the area of the triangle is:
[tex]s = \frac{16+2\cdot (11)}{2}[/tex]
[tex]s = 19[/tex]
[tex]A_{t} = \sqrt{19\cdot (19-16)\cdot (19-11)^{2}}[/tex]
[tex]A_{t} \approx 60.399[/tex]
Step 3:
And the area between the line segment PL and the circle arc PL is:
[tex]A_{s} = A_{ca}-A_{t}[/tex]
[tex]A_{s} = 98.201 - 60.399[/tex]
[tex]A_{s} = 37.802[/tex]
The area of the circle enclosed by line segment PL and circle arc PL is 37.80 square units.
90units needed 8 units per case what's the #of cases & # of additional units
Answer:
# of cases: 11
Additional units: 2
Step-by-step explanation:
If each case can hold 8 units, and we want to find the total # number of cases, we have to divide the # of units (8) for one case by the total # units (90).
As you can see, after dividing by 8, we have a total of 11 cases and a remainder of 2 units. The remainder will be the # of additional units because we cannot have another case filled with 8 units.
The polygons in each pair are similar. Find the missing side length.
Let missing side be x
If both polygons are similar
[tex]\\ \sf\longmapsto \dfrac{3}{4}=\dfrac{18}{x}[/tex]
[tex]\\ \sf\longmapsto 3x=4(18)[/tex]
[tex]\\ \sf\longmapsto 3x=72[/tex]
[tex]\\ \sf\longmapsto x=\dfrac{72}{3}[/tex]
[tex]\\ \sf\longmapsto x=24[/tex]
Round 5,821 to the nearest thousands place:
Answer:
6000 hope this helps
if the question is 5,422 then the round figure is 5000
but the question is 5,821 its above 5500 will be 6000
kabura bought a piece of cloth 3 metres long. The material shrunk by 1% after washing. What was the new length of the cloth
Answer:
2.97m
Step-by-step explanation:
1% of 3m =1/100×3=0.03
0.03m of cloth was shrunk,
So, New lenght : 3-0.03=2.97m
please helpppp i need it by tonight its very important
Answer:
m<1=145
m<2=35
m<3=35
Step-by-step explanation:
measure one is supplementary(the angles add to 180) to measure four.
so we do 180-35=145
measure 2 is congruent to measure four because they are corresponding angles
so measure 2=35
and measure 3 is also congruent to measure 4 because the are corresponding angles
so m<3=35
Factors and rewrite the expression 25x-15
Answer:
5(5x-3)
Step-by-step explanation:
The common factor in this expression is 5 so divide 5 to all the values
25/5=5
-15/5= -3
Put these values into parenthesis and leave the 5 on the left side and out of the parenthesis
5(5x-3)
Answer:
5(5x - 3)
Step-by-step explanation:
The greatest common factor here is 5. Divide each term by 5 and simplify.
25x/5 = 5x
15/5 = 3
Therefore, the answer is 5(5x - 3).
Please help explanation if possible
Answer:
18.84 feet. let me know if you have ay other questions.
Step-by-step explanation:
The way to find the formula for circumference is kinda complicated so it is best to ust memorize the formula, which is 2πr. or 2 times pi times the radius.
Your problem gives you the formula, but instead of 2 and r in it you have d, which is the diameter.
The diameter of the circle is 2 times the radius, so that's why it is replaced.
the radius is the distance from the center fo the circle to one edge, and the diameter is the distance through the circle passing through its center. so it's the center to one end plus the center to another end. or r+r which is also 2r.
So d = 2r, so in this problem d =6 feet.
So now the formula πd = 3.14*6 feet = 18.84 feet
A car insurance company has determined that6% of all drivers were involved in a car accident last year. If14drivers are randomly selected, what is the probability of getting at most 3 who were involved in a car accidentlast year
Answer:
[tex]P(x \le 3) = 0.9920[/tex]
Step-by-step explanation:
Given
[tex]p = 6\%[/tex] --- proportion of drivers that had accident
[tex]n = 14[/tex] -- selected drivers
Required
[tex]P(x \le 3)[/tex]
The question is an illustration of binomial probability, and it is calculated using:
[tex]P(x ) = ^nC_x * p^x * (1 - p)^{n-x}[/tex]
So, we have:
[tex]P(x \le 3) = P(x = 0) +P(x = 1) +P(x = 2) +P(x = 3)[/tex]
[tex]P(x=0 ) = ^{14}C_0 * (6\%)^0 * (1 - 6\%)^{14-0} = 0.42052319017[/tex]
[tex]P(x=1 ) = ^{14}C_1 * (6\%)^1 * (1 - 6\%)^{14-1} = 0.37578668057[/tex]
[tex]P(x=2 ) = ^{14}C_2 * (6\%)^2 * (1 - 6\%)^{14-2} = 0.15591149513[/tex]
[tex]P(x=3 ) = ^{14}C_3 * (6\%)^3 * (1 - 6\%)^{14-3} = 0.03980719024[/tex]
So, we have:
[tex]P(x \le 3) = 0.42052319017+0.37578668057+0.15591149513+0.03980719024[/tex]
[tex]P(x \le 3) = 0.99202855611[/tex]
[tex]P(x \le 3) = 0.9920[/tex] -- approximated
factorize : ( p- q ) cube
Answer:
[tex]( {p - q}^{3} ) \\ = {p}^{2} - 3 {p}^{2} q + 3p {q}^{2} - {q}^{3} [/tex]
HELPPPPP ASP PLZZZZZ
Answer:
[tex](f-g)(x)[/tex]
[tex]f(x)-g(x)[/tex]
[tex]x^{2} -6x-27-x+9[/tex]
[tex]x^{2} -7x-18[/tex]
----------------------
[tex](f*g)(x)[/tex]
[tex]=f(x)g(x)[/tex]
[tex](x^{2} -6x-27)(x-9)[/tex]
[tex]=x^{3} -15x^{2}+27x+243[/tex]
----------------------
[tex]\frac{f}{g} (x)[/tex]
[tex]\frac{x^{2} -6x-27}{x-9}[/tex]
[tex]\frac{(x-9)(x+3)}{x-9}[/tex]
[tex]x+3[/tex]
-----------------------
[tex](f+g)(x)[/tex]
[tex]f(x)+g(x)[/tex]
[tex]=x^{2} -6x-27+x-9[/tex]
[tex]=x^{2} -5x-36[/tex]
------------------------
OAmalOHopeO
------------------------
look at the image below
Answer:
201.1 km²
Step-by-step explanation:
Surface area of a sphere= 4πr², where r = radius
so,
4πr²
= 4×π×4²
= 64π
= 201.1 km² (rounded to the nearest tenth)
Which two shapes make up the digital camera below?
Rectangular prism and cylinder make up a camera.
What is rectangular prism and cylinder?A cube is a rectangular prism with all of its sides being the same length, a triangular prism has a triangle as its base, and a rectangular prism has a rectangle as its foundation. Another form of right prism that has a circle as its basis is a cylinder.
A rectangular prism includes a total of 6 faces, 12 sides, and eight vertices. Like a cuboid, it contains three dimensions- the base width, the height, and the length. The top and base of the rectangular prism exist rectangular. The pairs of opposite faces of a rectangular prism exist as identical or congruent.
A cylinder contains traditionally been a three-dimensional solid, one of the most essential curvilinear geometric shapes. Geometrically, it includes been regarded as a prism with a circle as its base.
Hence, Rectangular prism and cylinder make up a camera.
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A factory used 99.19 kilograms of tomatoes to make 7 batches of pasta sauce. What quantity of tomatoes did the factory put in each batch?
Answer:
14.17 kilograms
Step-by-step explanation:
Find what quantity of tomatoes was in each batch by dividing the total amount of tomatoes by the number of batches:
99.19/7
= 14.17
So, the factory put 14.17 kilograms of tomatoes in each batch.
Your parents deposit 2 50-dollar bills at the bank.
How much money did they deposit?
Answer: $100
Step-by-step explanation:
Considering 50 + 50 = 100
This means that the amount of money is $100
A popular beach erodes 4 inches per year on average.
An eroding beach.
A. How many years will it take for the coastline to erode one foot?
Answer:
3 years
Step-by-step explanation:
4 inches per year on average
1 foot = 12 inches
12 divided by 4 equals 3
therefore it is 3 years
Im new to this app!
And im looking for help!!
Please help ASAP!!!
Please!!!!
y=x²-10x-7
a>0 so we will be looking for minimum
x=-b/2a=10/2=5
y=25-50-7=-32
Answer: (5;32)
Shawn has 4 times as many candies as Jason, who has a third as many candies as
lan. If Shawn has 64 candies, how many candies does Ian have?
Start with the number 2380.
Divide by 10,
The 8 will end up in the _____ place.
The 8 will end up in the "ones place".
How can we interpret the division?When 'a' is divided by 'b', then the result we get from the division is the part of 'a' that each one of 'b' items will get. Division can be interpreted as equally dividing the number that is being divided into total x parts, where x is the number of parts the given number is divided.
We need to find the 8 will end up in which place
A negative divided by a negative is positive, then;
2380/ 10 = 238
Therefore, The 8 will end up in the _ ones_ place.
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Give example to verify if the given statement is true or false
1) if two numbers are co-primes , at least one of them should be prime number.
Answer:
no
Step-by-step explanation:
if two numbers are co-prime that is not necessary that one of them must be a prime number
Starting with a fresh bar of soap, you weigh the bar each day after you take a shower. Then you find the regression line for predicting weight from number of days elapsed. The slope of this line will be:__________.
Answer:
The slope will be negative
Step-by-step explanation:
The slope of the regression line tells us about the relationship or behavior of the dependent and independent variables. In the scenario above, where the weight is being compared with the number of days elapsed. What is expected of the weight and quantity of a bar soap each time it is used for a shower is that it will decrease in weight. Therefore, as the number of days increases, and hence, number of showers rise, the weight of soap will decrease. Hence, we'll obtain a negative slope, one in which the increase in a variable leads to decrease in the other.
please help me with both questions
Answer:
(b) 829 seconds
(c) 13.8 minutes
Step-by-step explanation:
(b) 2.48×10⁸/2.99×10⁵ = 829 seconds
(c) 829/60 = 13.8 minutes
Paul can install a 300-square-foot hardwood floor in 18 hours. Matt can install the same floor in 22 hours. How long would it take Paul and Matt to install the floor working together?
4 hours
9.9 hours
13.2 hours
30 hours
Answer:
9.9 hours
Step-by-step explanation:
The formula to determine the time together is
1/a+1/b = 1/c where a and b are the times alone and c is the time together
1/18 + 1/22 = 1/c
The least common multiply of the denominators is 198c
198c(1/18 + 1/22 = 1/c)
11c+ 9c = 198
20c = 198
Divide by 20
20c/20 =198/20
c =9.9
Answer:
B - 9.9 hrs
Step-by-step explanation:
took the test.
Which graph matches the exponential function f(x) = (3)x?
PLSS HELPPPP WILL GIVE BRAINLESSS A 22-foot ladder is resting against the side of a building. The bottom of the ladder is 3 feet from the building. Find the measure of the angle the ladder makes with the ground. Round your answer to the nearest tenth of a degree.
Answer:
The answer is 82.2
Step-by-step explanation
hope this helps
According to this diagram, what is tan 62°?
62°
17
18
280
90°
15
O A.
8
17
OB.끝
O c. 1
8
15
D.
15
8
O
E.
17
15
F.
15
17
Answer:
15/8
Step-by-step explanation:
tan(62)=P/B
tan(62)=15/8
The segments shown below could form a triangle.
A
C
7
9
12
B
А
a
A. True
B. False
Answer:
TRUE
Step-by-step explanation:
I SEEN SOME ONE ELSE WIT 5 STARS SAY SO(:
The given segment can form triangle. Therefore, the given statement is true.
What is triangle?A polygon has three edges as well as three vertices is called a triangle. It's one of the fundamental geometric shapes. In Euclidean geometry, each and every three points that are not collinear produce a distinct triangle and a distinct plane. In other words, every triangle was contained in a plane, and there is only single plane that encompasses that triangle.
All triangles are enclosed in a single plane if all of geometry is the Euclidean plane, however this is no longer true in higher-dimensional Euclidean spaces. Unless when otherwise specified, this article discusses triangles within Euclidean geometry, namely the Euclidean plane. The given segment can form triangle.
Therefore, the given statement is true.
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2(4×+2)=10
[tex]6 \times + 4 = 10 \\ \\ 6 \times = 10 - 4 \\ \\ 6 \times = 6 \\ \\ [/tex]
that is the answer
Answer:
x = 3/4
Step-by-step explanation:
2(4x + 2) = 10 Remove the brackets
8x + 4 = 10 Subtract 4 from both sides
8x = 6 Divide by 8
x = 6/8
x = 3/4
Check
2(4*3/4 + 2) =?10
2( 3 + 2) = 10
2*5 = 10
10 = 10
Convert 0.450 to a proper fraction
Answer:
9/20
Step-by-step explanation:
450/1000
this is not the answer, because it is not simplified
so here we have to find common factor and simplifying
________________________________________________
450/1000 is simplified to 9/20, and it can no longer be simplified.
