Answer: 75%
Step-by-step explanation:
186.75/249 =.75
.75x100
75%
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.
Evaluate 3|x|+2x-1 when x = -5.
Answer:
4
Step-by-step explanation:
To start off, we are going to input our x value into our expression.
3|-5| + 2(-5) - 1
Next, we are going to find the absolute value (always positive) of -5 and multiply 2 and -5.
3(5) - 10 -1
Now, we will multiply 3 and 5.
15 - 10 -1
Finally, we are going to combine our like terms (15, -10, and -1)
4
So! Our final answer for this expression is 4!
Hope this Helps! :)
Have any questions? Ask below in the comments and I will try my best to answer.
-SGO
Work out m and c for the line: y = 6 x
Answer:
m = 6
c = 0
General Formulas and Concepts:
Algebra I
Slope-Intercept Form: y = mx + c
m - slope c - y-interceptStep-by-step explanation:
Step 1: Define
y = 6x
↓ Compare to Slope-Intercept Form
Slope m = 6
y-intercept c = 0
Calculate the range and the standard deviation for the set of numbers.
6,5, 1, 5, 8, 5, 3, 5, 4,7
The range is
(Simplify your answer.)
Can I please get help with this problem?
Answer:
When time is short and you just want a rough estimate of the standard deviation, turn to the range rule to quickly estimate the standard deviation value. The standard deviation is approximately equal to the range of the data divided by 4. That's it, simple.
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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Which graph represents the function h(x)=x+0.5
Answer:
The correct graph of h(x) will be number 3 (c).
Step-by-step explanation:
We have the function h(x) = |x| + 0.5
On putting x=0, in the function h(x), we get,
h(0) = |0| + 0.5
h(0)=0 + 0.5
h(0)=0.5
Thus, the point (0,0.5) lie on the graph of h(x).
The graph that represents the function h(x) is graph (c)
How to determine the graph?The equation is given as:
h(x) = |x| + 0.5
The above equation is an absolute value function
An absolute value function is represented as:
h(x) = a|x + h| + k
Where:
Vertex = (h,k)
By comparing h(x) = a|x + h| + k and h(x) = |x| + 0.5, we have:
h = 0 and k = 0.5
So, the vertex is (0,0.5)
The graph that has a vertex of (0,0.5) is graph (c)
Hence, the graph that represents the function h(x) is graph (c)
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Banking fees have received much attention during the recent economic recession as bankslook for ways to recover from the crisis. A sample of 31 customers paid an average fee of $11.53 permonth on their checking accounts. Assume the population standard deviation is $1.50. Calculatethe margin of error for a 90% confidence interval for the mean banking fee.
Answer:
The margin of error for a 90% confidence interval for the mean banking fee is of $0.44.
Step-by-step explanation:
We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1 - 0.9}{2} = 0.05[/tex]
Now, we have to find z in the Z-table as such z has a p-value of [tex]1 - \alpha[/tex].
That is z with a pvalue of [tex]1 - 0.05 = 0.95[/tex], so Z = 1.645.
Now, find the margin of error M as such
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.
Sample of 31:
This means that [tex]n = 31[/tex]
Assume the population standard deviation is $1.50.
This means that [tex]\sigma = 1.5[/tex]
Calculate the margin of error for a 90% confidence interval for the mean banking fee.
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
[tex]M = 1.645\frac{1.5}{\sqrt{31}}[/tex]
[tex]M = 0.44[/tex]
The margin of error for a 90% confidence interval for the mean banking fee is of $0.44.
Find the slope of the line passing through the pair of points or state that the slope is undefined. Then indicate whether the line
through the points rises, falls, is horizontal, or is vertical
(2,9) and (-2,9)
13. 30 of the 100 iPads in an inventory are known to be cracked. What
is the probability you randomly select one that is not cracked?
Answer:
7/10 or 0.7
Step-by-step explanation:
a probability is always the ratio of possible cases over all cases.
"all cases" here is 100.
possible cases are all iPads not cracked in the inventory = 70 (because 30 are cracked, that leaves 100-30=70 not cracked).
so, the probability to select a non-cracked unit is
70/100 or simplified 7/10 (or 0.7)
Complete the table for the given rule.
Rule: y is 0.750.750, point, 75 greater than x
x y
0
3
9
Answer:
está inglês não dá para entende
a car drives at 45 km/h for 75 minutes how far does the car travel
Answer:
56.25km
Step-by-step explanation:
75min = 5/4 h
distance = speed * time = 45 * 5/4 = 56.25
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)
prove that 2^n+1>(n+2).sin(n)
Step-by-step explanation:
F(n)=|sin(n)|+|sin(n+1)|
then
F(n+π)=|sin(n+π)|+|sin(n+π+1)|=|sin(n)|+|sin(n+1)|=F(n)
and
F(π−n)=|sin(π−n)|+|sin(π−n+1)|=|sinn|+|sin(n−1)|≠F(n)
so we must prove when n∈(0,π), have
F(n)>2sin12
when n∈(0,π−1),then
F(n)=sinn+sin(n+1)=sinn(1+cos1)+sin1cosn
and n∈(π−1,π),then
F(n)=sinn−sin(n+1)
How prove it this two case have F(n)>2sin12? Thank you
and I know this well know inequality
|sinx|+|sin(x+1)|+|sin(x−1)|≥2sin1,x∈R
For each of the following equations, determine whether y is a function of x.
x= -7y^2
b. x = 1/4y
c. y^2 = 4x +9
d. y= 5x +8
9514 1404 393
Answer:
a) not a function
b) is a function
c) not a function
d) is a function
Step-by-step explanation:
If the graph passes the "vertical line test," then the relation is a function.
Choices B and D are linear equations. Their graph is a straight line, so each x-value corresponds to exactly one y-value. (Every non-vertical line passes the vertical line test.)
Choices A and C are equations of parabolas that open horizontally. It is easy to draw a vertical line that intersects the graph twice, so these relations fail the vertical line test.
__
B, D -- functions
A, C -- not functions
210
To rationalize the denominator of
3.11,You should multiply the expression by which fraction?
11
2- V10
2- 10
3- V11
3- V11
We should multiply the expression by √11/ √11 fraction.
What is the fundamental principle of multiplication?Multiplication is the mathematical operation that is used to determine the product of two or more numbers.
To rationalize this, we multiply both the denominator and denominator by the conjugate of the denominator.
The denominator is 2-√10 and its conjugate is; (2+√10).
(2√10)/(3√11) = (2√10)/(3√11)
= ((2√10)√11/(3√11) √11
= (2√110)/33
This is the rationalized expression.
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What is an explicit formula for the geometric sequence -64,16,-4,1,... where the first term should be f(1).
Answer:
[tex]a_{n} = -64(-\frac{1}{4})^{n-1}[/tex]
it seems like the first term is -64, so lets write the formula accordingly:
a_n = a1(r)^(n-1)
where 'n' is the number of terms
a1 is the first term of the sequence
'r' is the ratio
the ratio is [tex]-\frac{1}{4}[/tex] because -64 * [tex]-\frac{1}{4}[/tex] = 16 and so on...
the explicit formula is :
[tex]a_{n}[/tex] = [tex]-64(-\frac{1}{4} )^{n-1}[/tex]
12/1,000 into decimal
0.012 is the answer!
I hope this helps you out! :D
[tex]\\ \sf\longmapsto \dfrac{12}{1000}[/tex]
1000 has 3zeros hence decimal will go 3 points left[tex]\\ \sf\longmapsto 0.012[/tex]
More:-
[tex]\\ \sf\longmapsto \dfrac{1}{10}=0.1[/tex]
[tex]\\ \sf\longmapsto \dfrac{1}{100}=0.01[/tex]
Determine the critical values for the confidence interval for the population standard deviation from the given values. Round your answers to three decimal places.
n = 12 and c = 0.9.
Answer:
The answer is "[tex]\chi^2_{L} = 4.575 \ and\ \chi^2_{U}= 19.675[/tex]"
Step-by-step explanation:
[tex]n=12\\\\\ c= 0.9[/tex]
Calculating the level of significance [tex](\alpha) = 1 -c[/tex]
[tex]=1-0.9\\\\=0.1[/tex]
Calculating the degrees of freedom:
[tex]df=n-1=12-1=11[/tex]
Calculating the critical value:
Applying the Chi-Square table, the critical values for the two-tailed test with a degree of freedom (11) for the significance level of [tex]\alpha = 0.1[/tex]:
[tex]\chi^2_{L} = 4.575 \\\\\chi^2_{U}= 19.675[/tex]
Find the 97th term of the arithmetic sequence 17, 26,35,...
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Q12 A baker wants to order enough flour for 10 loaves of bread weighing 750g each. She has a recipe for a 500g loaf of bread which needs 480g of flour. How many kilograms of flour does the baker need? Show your working
Answer:
7.2kg of flour
Step-by-step explanation:
Total weight of bread = 10 x 750g
= 7500g = 7.5kg
500g of bread = 480g of flour
0.5kg of bread = 0.48kg of flour
7.5kg of bread = 7.2kg of flour
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?
Parallel Lines:
If the two lines are parallel and cut by a transversal line, what is the value of x?
Step-by-step explanation:
The corresponding angles theorem tells us that angles that correspond with each other are equal. In this case, B and C are corresponding angles.
(2x+8) = 60
2x = 60 - 8
2x = 52
x = 26
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 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
Shane plants a 6-inch tomato plant in his garden. The plant grows by about 12% per week for several months. Which function definition represents the height of the tomato plant (in inches) as a function of the number of weeks, t since the tomato plant was planted?
Answer:
[tex]f(t)=6(1.12^t)[/tex]
Step-by-step explanation:
every week the plant grows by 12%, so the ratio is 1.12. the original height of the plant is 6. f(x)=a(b^x) such that a=6, b=1.12, and x=t
Give the degree of the polynomial. -5-5x2wy4-y4x2-4w3
9514 1404 393
Answer:
7
Step-by-step explanation:
The degree of each term is the sum of the degrees of the variables in it.
Term, Degrees
-5, 0
-5x^2wy^4, x:2, w:1, y:4 -- term degree = 2+1+4 = 7
-y^4x^2, y:4, x:2 -- term degree = 4+2 = 6
-4w^3, w:3 -- term degree = 3
The highest of these is 7, so the degree of this polynomial is 7.
Solve for x.
A. 9
B. 12
C. 1
D. 7
Answer:
9
Step-by-step explanation:
use Tangent-chord formula for finding the arc knowing E
x=1/2n
4x+19=1/2n
n=8x+38
both arcs = 360
28x-2+8x+38=360
x=9
Where r is the radius of the cylinder and h is the height of the cylinder.
Find the surface area when r is 7 inches and h is 9 inches.
Sa of cylinder= 2(pi)rh + 2(pi)r squared
Answer:
703.7 in²
Step-by-step explanation:
SA = 2πrh+2πr²
= 2×π×7×9+2×π×7²
= 224π
= 703.7 in² (rounded to the nearest tenth)
Answer:
224π
in²
Step-by-step explanation:
terms are there. Divide 51 into three parts in AP so that the largest exceeds the smallest by 10.
The first three terms of the Arithmetic Progression are 12, 17 and 22.
For an ARITHMETIC PROGRESSION, AP ;
First term = a
Second term = a + d
Third term = a + 2d
Where, d = common difference ;
If third term exceeds smallest by 10 ;
Third term - first term
a + 2d - a = 10
2d = 10
d = 10/2
d = 5
Sum of the three terms :
a + (a + d) + a + 2d = 51
3a + 3d = 51
d = 5
3a + 3(5) = 51
3a + 15 = 51
3a = 51 - 15
3a = 36
a = 12
The AP would be:
First term, a = 12
Second term, a + d = 12 + 5 = 17
Third term = a + 2(d) = 12 + 10 = 22
Therefore , the first three terms of the AP are :
12, 17 and 22
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Please help me with this on the picture
9514 1404 393
Answer:
(-5, 4)
Step-by-step explanation:
The inside corner moves from (2, -2) to (-3, 2). That is 5 is subtracted from the x-coordinate, and 4 is added to the y-coordinate. (x, y) ⇒ (x -5, y +4)
The translation vector can be written horizontally as (-5, 4), or vertically as ...
[tex]\displaystyle\binom{-5}{4}[/tex]
