Answer:
90
Step-by-step explanation:
Add up all the numbers in the data set and divide that number by the amount of numbers in the data set
85 + 97 + 84 + 88 + 95 + 100 + 81 = 630
630/7 = 90
Find the area of the following region.
The region common to the circles r=-2sin(theta) and r=1
The area of the region common to both circles is -6.67 square units
How to find the area common to both circles?Since r = -2sinθ and r = 1, we find their points of intersection.
So, r = r
-2sinθ = 1
sinθ = -1/2
θ = sin⁻¹(-1/2)
θ = 7π/6
So, the circles intersect at (1, 7π/6)
To find the area of the region common to both circles, we integrate from r = 0 to r = 1 and θ = 0 to θ = 7π/6
[tex]A = \int\limits^1 _0 \int\limits^\frac{7\pi }{6} _0( {r - r}) \, dr \,d\alpha \\A = \int\limits^1 _0 \int\limits^\frac{7\pi }{6} _0( {-2sin\alpha - 1}) \, dr \,d\alpha \\A = -\int\limits^1 _0 \int\limits^\frac{7\pi }{6} _0 {2sin\alpha \, dr \,d\alpha - \int\limits^1 _0 \int\limits^\frac{7\pi }{6} _01} \, dr \,d\alpha \\A = 2[cos\alpha]_{0} ^{\frac{7\pi }{6} } [r]_{0} ^{1} r - [r]_{0} ^{1}} [\alpha ]_{0} ^{\frac{7\pi }{6}}} \\[/tex]
[tex]A = 2[cos{\frac{7\pi }{6} - cos0] [1 - 0] - ([1 - 0][\frac{7\pi }{6} - 0]\\[/tex]
A = 2(-¹/₂ - 1) - (1 × 7π/6)
A = 2(-3/2) - 7π/6
A = -3 - 7π/6
A = (-18 - 7π)/6
A = (-18 - 21.99)/6
A = -39.99/6
A = -6.67 square units
So, the area of the region common to both circles is -6.67 square units
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The number of goldfish in a tank is 22, and the volume of the tank is 56 cubic feet. What is the density of the tank?.
Answer:
0.39??
Step-by-step explanation:
if x=p+2 and y=p-3, show that x+y+1=2p and x-y-5=0
If [tex]x=p+2[/tex] and [tex]y=p-3[/tex], then
[tex]x+y = (p+2) + (p-3) = 2p - 1 \implies x+y+1=2p[/tex]
and
[tex]x-y = (p+2)-(p-3) = 5 \implies x-y-5=0[/tex]
as required.
a bag has 6 green, 4 red, 5 yellow and 15 blue marbles what is the possibility that the marble is red or blue
Answer: 19/30 or about 63%
Step-by-step explanation: Add all your marble up so 6+4+5+15 to get the total amount of options or marbles in this case. Now find out how many red and blue marbles you have so 4+15 or 19 now you can divide the red and blue marbles by the total amount of marbles to get your percentage of pulling a red or blue marble from the bag.
Part 1 of 3
the accompanying data are 45 commute times to work in minutes for workers of age 16 or older in chicago. construct a frequency distribution. use a
the data amounts appear to have a normal distribution? examine the data and identify anything appearing to be unique.
click the icon to view the commute times.
construct the frequency distribution.
commute time
(minutes)
frequency
(type whole numbers.)
The frequency distribution has been illustrated based on the information given.
What is frequency distribution?It should be noted that frequency distribution is the representation that displays the number of observations that are in a given interval.
From the data distribution, the frequency distribution will be:
Class. Frequency
0 - 14. 5
15 - 29. 15
30 - 44. 13
45 - 59. 6
60 - 74. 5
75 - 89. 1
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A = 1/ 7 - 4√3
B = 1/ 7+ 4√3
Find....
A) a² + b²
B) a³ + b³
The value of a2+b2 = 0.05
The value of a3+b3 = 41.73
Concept: (a+b)2 = a2+b2+2ab
(a-b)2 = a2+b2-2ab
(a+b)3 = a3+b3+3a2b+3ab2
(a-b)3 = a3-b3-3a2b+3ab2
(I) a²+b²=(1/7-4✓3)²+(1/7+4✓3)²
⇒ ( 1/49 - 48) +(1/49 + 48)=(1-2352/49) + (1+2353/49)
⇒ -47.97 +48.02= 0.05
(ii) a³+b³=(1/7-4✓3)³+(1/7+4✓3)³
⇒(-6.78)³ +(7.07)³
⇒-311.66 +353.39= 41.73
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Based on the details in this excerpt, which word best describes the garage?
Answer:The end of immigration quotas in the 1960s led to
a significant decrease in safe places for refugee immigrants.
a significant increase in discrimination against immigrants.
a significant increase in the number of Asian immigrants.
a significant decrease in the number of Asian immigrants.
Step-by-step explanation:
Find the value of x
Answer:
3
Step-by-step explanation:
11(3)+2 = 6
also,
33-29 =
and
29 - 23 = 6
I take a guss, but I think its 3
Which measurement statement is correct?
Answer:
there are 2 cups in a pint is correct.
Step-by-step explanation:
I WILL GIVE BRAINIEST
Line AB and Line CD bisect each other at point E. If AE = 3x - 10y + 123, BE = -2x - 7y + 122, CE = 9x + 10y - 171, and DE = 3x + 20y - 249, what are the values of x and y?
The values of x and y are 7 and 12 respectively
Solving simultaneous equationsFrom the question, we are to determine the values of x and y
From the given information,
Line AB and Line CD bisect each other at point E
Then, we can conclude that
AE = BE
and
CE = DE
From the given information,
AE = 3x - 10y + 123
BE = -2x - 7y + 122
CE = 9x + 10y - 171
DE = 3x + 20y - 249
Then, we can write that
3x - 10y + 123 = -2x - 7y + 122
Simplifying
3x +2x -10y + 7y = 122 -123
5x -3y = -1 ----------- (1)
Also,
9x + 10y - 171 = 3x + 20y - 249
Simplifying
9x -3x +10y -20y = -249 + 171
6x -10y = -78 --------- (2)
Now, solve equations (1) and (2) simultaneously
5x -3y = -1 ----------- (1)
6x -10y = -78 --------- (2)
Multiply equation (1) by 10 and equation (2) by 3
10 × ( 5x -3y = -1
3 × ( 6x -10y = -78
50x -30y = -10 ----------- (3)
18x -30y = -234--------- (4)
Then, subtracting equation (4) from equation (3), we get
50x -18x -30y-(-30y) = -10-(-234)
32x -30y + 30y = -10 + 234
32x = 224
∴ x = 224/32
x = 7
Put the value of x into equation (1), to find y
5x -3y = -1
5(7) -3y = -1
35 -3y = -1
35 + 1 = 3y
36 = 3y
∴ y = 36/3
y = 12
Hence, the values of x and y are 7 and 12 respectively
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What is the equation of the line that passes through (-3, 4) and (3, -2)?
y = - x - 1
y = x + 7
y = x - 1
y = - x + 1
Answer:
y = -x +1
Step-by-step explanation:
p1 (-3,4)
p2 ( 3, -2)
line equation y = mx + b
The slope m equals
[tex] \frac{y2 - 21}{x2 - x1} [/tex]
[tex] \frac{ - 2 - 4}{3 - - 3} = \frac{ - 6}{6} = - 1[/tex]
y = - x + b
from any point
-2 = -3 + b
b = 1
line equation = y = -x +1
simplify the ratio 42:63
Answer: 2:3
Step-by-step explanation:
common factor of 42 and 63: 21
42/21= 2
63/21= 3
find the common factor to find the ratio!
therefore the ratio is 2:3
A charity bingo game costs $2 per round and has a $13 entry fee for an adult. It costs $3 per round and a $10 entry fee for a child. For how many rounds of bingo are the costs the same for an adult and a child?.
The number of rounds of bingo when the two costs would be the same is 3.
When would the two costs be the same?The equation that represents the total cost for adults is : 13 +2r
The equation that represents the total cost for children: 10 + 3r
where r is the number of rounds
When the two costs are the same, the two above equations would be equal: 13 + 2r = 10 + 3r
13 - 10 = 3r - 2r
r = 3
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All the square numbers between 20 and 50
it is 3 numbers all together and they are 25, 36 and 49.
A shop sells the same type of nails in 3
different sized packets.
Calculate the price per 10 nails for each
size of pack.
Write down which sized packet is the
best value for money in the comment
box.
Answer:
52, 53, 54, pack 1.
Step-by-step explanation:
1)
1.56 = 30
10 = 1.56 / 3
10 = 52 pence
2)
2.12 = 40
10 = 2.12 / 4
10 = 53 pence
3)
3.78 = 70
10 = 3.78 / 7
10 = 54 pence
The cheapest one is the small pack
The function f(x) = –x2 – 4x + 5 is shown on the graph. On a coordinate plane, a parabola opens down. It goes through (negative 5, 0), has a vertex at (negative 2, 9), and goes through (1, 0). Which statement about the function is true? The domain of the function is all real numbers less than or equal to −2. The domain of the function is all real numbers less than or equal to 9. The range of the function is all real numbers less than or equal to −2. The range of the function is all real numbers less than or equal to 9.
The true statement about the function f(x) = -x² - 4x + 5 is that:
The range of the function is all real numbers less than or equal to 9.What is the domain and range for the function of y = f(x)?The domain of a function is the set of given values of input for which the function is valid and true.
The range is the dependent variable of a given set of values for which the function is defined.
The domain of the function: f(x) = -x² - 4x + 5 are all real number from -∞ to +∞For a parabola ax² + bx + c with the vertex [tex]\mathbf{(x_v,y_v)}[/tex]
If a < 0, then the range is f(x) ≤ [tex]\mathbf{y_v}[/tex]If a > 0, then the range f(x) ≥ [tex]\mathbf{y_v}[/tex]Here; a = -1,The vertex for an up-down facing parabola for a function y = ax² + bx + c is:
[tex]\mathbf{x_v = -\dfrac{b}{2a}}[/tex]
Thus,
vertex [tex]\mathbf{(x_v,y_v)}[/tex] = (-2, 9)Range: f(x) ≤ 9
Therefore, we can conclude that the range of the function is all real numbers less than or equal to 9.
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i need help i don’t know how to solve these!
Its actually pretty simple, all you do is graph both inequalities and wherever both of the shaded areas overlap is where all of the solutions will be. Hope this helps
The graph below represents which system of inequalities
Y≤-2×+3
Y≤x+3
y≥-2x+3
2 ≥x+3
Y ≤3x+2
Y ≤-x+2
Y >2x+3
Y >x+3
Answer:
a
Step-by-step explanation:
9x-7=-52
Show all work and justify each step
Answer:
x = -5
Step-by-step explanation:
9x - 7 = -52
we want to single out x,
add 7 to both sides to be one step closer to getting x alone
9x - 7 + 7 = -52 + 7
9x = -45
divided both sides by 9 to get x alone
9x / 9 = -45 / 9
x = -5
Let me know if you need any clarification!
[tex] 9x - 7 = - 52[/tex]
Firstly rearrange the variable on the left side of the equation...
[tex]9x = - 52 + 7[/tex]
Calculate the sum or differences
[tex]9x = - 45[/tex]
[tex]x = - \frac{45}{9} \\ [/tex]
[tex]x = - 5[/tex]
:)
..
B varies inversely with c. when b is 2, c is 8. find the value of c when b is 5.
Answer:
3.2
The value of C when B is 5 is 3.2
Step-by-step explanation:
What is the measure of the central angle of a circle with radius 60 cm the intercepts a 15 pi centimeters arc
The measure of the central angle of a circle is 45⁰
What is Angle?A figure which is formed by two rays or lines that shares a common endpoint is called an angle.
Here,
Theta (angle) θ = arc length / radius
θ = 15 π / 60 cm
θ = 0.79 radians
Convert to degrees
θ = 0.79 radians = 0.79 X 180/ π
= 0.79 X 180/ 3.14
= 45⁰
Thus, the measure of the central angle of a circle is 45⁰.
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please help me solve this HCF
Answer:
(x+y)
Step-by-step explanation:
[tex] {x}^{2} - {y}^{2} = (x + y)(x - y)[/tex]
Thus, the HCF is (x+y).
Answer:
(x + y)
Step-by-step explanation:
Factorizing both terms :
x² - y² = (x + y)(x - y)(x + y)² = (x + y)(x + y)The HCF of the terms is (x + y).
5) A restaurant menu has 6 starters, 10 mains and 6 desserts.
A customer can choose from the following meals
a starter and a main,
a main and a dessert,
a starter, a main and a dessert.
Show that there are 480 different ways of choosing a meal at this restaurant.
Answer: 360
Step-by-step explanation: 6 times 6 times 10 = 360
Question 4 of 10
Which pairs of angles in the figure below are vertical angles?
Check all that apply.
Answer:
B and D
Step-by-step explanation:
A is not a intersecting angles they are like doodles, B makes intersecting lines, C doesnt intersect properly its only like a Y with and extra angle and D is absolutely perfect. So, thats why its B and D
There are 20 teachers and 705 students in Corey's school.
What is the ratio of teachers to students?
A. 725:20
B. 705:20
C. 20:725
D. 20:795
Answer:
all the options are incorrect
Given - 20 teachers
- 705 students
To find - ratio of teachers to students
20/705
20 : 705 .
Fill in the table.
x y
-4 5
-2 3
0 1
2 -1
4 -3
This is a linear function which means that the domain and range are:
Domain:
Range:
*Reminder: another way to write negative infinity to positive infinity is
"all real numbers"
The domain of the linear function is a real number, and the range of the linear function is also a real number.
What are domain and range?The domain means all the possible values of x and the range means all the possible values of y.
The table is given below.
x y
-4 5
-2 3
0 1
2 -1
4 -3
Then the linear function will be
y – 1 = [(5 – 1) / (- 4 – 0)] (x – 0)
y – 1 = -x
x + y = 1
Then the domain of the linear function is a real number and the range of the linear function is also a real number.
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What are the solutions to the following system of equations?
y = x² + 7x - 5
2x - y = -9
Answer:
x= -7, y= -5 and
x= 2, y= 13
This may also be written as (-7, -5) and (2, 13).
Step-by-step explanation:
Start by labelling the two given equations:
y= x² +7x -5 -----(1)
2x -y= -9 -----(2)
Let's solve by substitution!
Making y the subject of formula in equation (2):
From (2): y= 2x +9 -----(3)
Substitute (3) into (1):
2x +9= x² +7x -5
x² +7x -5 -2x -9= 0
x² +5x -14= 0
Factorise:
(x +7)(x -2)= 0
x +7= 0 or x -2= 0
x= -7 or x= 2
Find the respective values of y.
Substitute into (1):
y= (-7)² +7(-7) -5 or y= (2)² +7(2) -5
y= 49 -49 -5 or y= 4 +14 -5
y= -5 or y= 13
Thus, the solutions are (-7, -5) and (2, 13).
Choose the simplified form of the fifth term of the
expansion.
O-60x²y³
O -30x²y³
O 30x²y³
O 60x²y³
The Correct Question is ......
Question :
Choose the simplified form of the fifth term of ⁶C₄ (2x)² (-y²)⁴
Answer: D. 60x²y⁸ is the simplified form of the fifth term of the
expansion ⁶C₄ (2x)² (-y²)⁴.
What is an Expression?An expression is a sentence with a minimum of two numbers or variables and at least one math operation.
This math operation can be addition, subtraction, multiplication, or division.
According to the Given Expression,
⁶C₄ (2x)² (-y²)⁴
The value of the combination can be written as,
[tex]= [\frac{6!}{4!(6-4)!} ] (2x)^{2} (-y^{2})^{4}[/tex]
= 15 (4x²) (-y²)⁴
The value of y can be written as,
= 15 (4x²) y⁸
= 60 x²y⁸
Therefore,
The value of the expression ⁶C₄ (2x)² (-y²)⁴ is 60x²y⁸.
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A cylinder has a diameter of 14 cm and height of 20cm . find the curved surface area
Answer:
879.6452 cm
Step-by-step explanation:
The curved surface area of a cylinder is calculated using the formula, curved surface area of cylinder = 2πrh, where 'r' is the radius and 'h' is the height of the cylinder.
diameter = 2r
14=2(r)
7=r
2(π)(7)(20) cm
2(3.14159)(7)(20)
879.6452
What is the formula for the margin of error?
Answer:
[tex]ME =\frac{z*s}{\sqrt{n}}[/tex]
Step-by-step explanation:
In a random survey sample, a margin of error is a statistical measurement that takes into account the discrepancy between actual and anticipated findings
To find margin of error, you need
Get the population standard deviation (σ) and sample size (n)n = sample size
Take the square root of your sample size and divide it into your population standard deviationσ = population standard deviation Multiply the result by the z-score consistent with your desired confidence interval according to the following table:z = z-score
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