Answer:
4:5
Step-by-step explanation:
A pair of complementary add up to 90, given that one of them is 50, we can do this: x + 50 = 90
solve it and we get x = 40
40 + 50 = 90, so 40 and 50 are the pair of complementary angles.
As for it's Ratio, we can just get the pair and have it as 40:50 but we can reduce it to 4:5
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
Learn more about the finding the area of a segment can be found here:
https://brainly.com/question/22599425
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.
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]
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.
To know more about triangle, here:
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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.
Write each word phrase as an algebrale
expression for exercises 66-69
66) ten less than a number
67) the product of x andy
The algebraic expression for ten less than n
66) ten less than a number
Let the number be n
= n - 10
67) the product of x and y
= x × y or xy
68) The algebraic expression for ten less than n
= n - 10
Must click thanks and mark brainliest
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]
five brothers of 4, 9, 11, 13 and 16 years respectively, receive an inheritance of 1,500,000, the will stipulated that that amount must be shared by the heirs so that, placed the shares in a bank, they would result in equal capitalized amounts, when each one reached 21, could raise his share. Knowing that the bank charges an interest rate of 9% per year, what is the amount of each share?
9514 1404 393
Answer:
Youngest to oldest:
160,406.86246,805.83293,230.01348,386.58451,170.72Step-by-step explanation:
At 9% interest per year, the present value of 1 at age 20 is ...
p(a) = 1.09^(a-20)
Adding the present values for the different ages, we get a total of about 2.35528984846. Dividing the inheritance by that amount gives the multiplier for each of the present value numbers. The result is the list of shares shown above. At age 20, each brother will inherit about 636,864.29.
__
Additional comment
This is the sort of question that suggests the use of a graphing calculator or spreadsheet for doing the tedious number crunching.
(We assume the bank pays 9% per year, rather than charges 9% per year.)
After how many years, to the nearest whole year, will an investment of $100,000 compounded quarterly at 4% be worth
$213,022?
Provide your answer below:
9514 1404 393
Answer:
19 years
Step-by-step explanation:
The compound interest formula tells you the future value of principal P invested at annual rate r compounded n times per year for t years is ...
A = P(1 +r/n)^(nt)
Solving for t, we get ...
t = log(A/P)/(n·log(1 +r/n))
Using the given values, we find t to be ...
t = log(2.13022)/(4·log(1 +0.04/4)) ≈ 19.000
The investment will be worth $213,022 after 19 years.
The scatterplot shows the attendance at a pool for different daily high temperatures.
A graph titled pool attendance has temperature (degrees Fahrenheit) on the x-axis, and people (hundreds) on the y-axis. Points are at (72, 0.8), (75, 0.8), (77, 1.1), (82, 1.4), (87, 1.5), (90, 2.5), (92, 2.6), (95, 2.6), (96, 2.7). An orange point is at (86, 0.4).
Complete the statements based on the information provided.
The scatterplot including only the blue data points shows
✔ a strong positive
association. Including the orange data point at (86, 0.4) would
✔ weaken
the correlation and
✔ decrease
the value of r.
Answer:
✔ a strong positive
✔ weaken
✔ decrease
ED2021
Answer:
The scatterplot including only the blue data points shows
✔ a strong positive
association. Including the orange data point at (86, 0.4) would
✔ weaken
the correlation and
✔ decrease
the value of r.
Step-by-step explanation:
Last week, you spoke with 800 customers in 40 hours."
Employee: "That is an average of __________ customers every 30 minutes."
Answer:
10 customers
Step-by-step explanation:
Hi!
Each hour has 60 minutes, so two half hour (30 minute) blocks. Thus, 1 hour = 2 half hours, so 40 hours = 80 half hours.
800 customers in 80 half hours, divide that:
800 customers / 80 half hours = 10 customers / half hour
So, your answer is 10 customers every half hour, or 10 customers every 30 minutes.
Average is [tex]10[/tex] customers per hour
Average is a single number taken as representative of a list of numbers, usually the sum of the numbers divided by how many numbers are in the list.
Total number of customers [tex]=800[/tex]
Total number of hours [tex]=40[/tex]
[tex]=40\times 60[/tex]
[tex]=2400[/tex] minutes
Average (in every [tex]30[/tex] minutes) [tex]=[/tex] Total number of customers [tex]\div[/tex] Total number of hours
[tex]=\frac{800}{2400 \div 30}[/tex]
[tex]=10[/tex] customers per hour
For more information:
https://brainly.com/question/19622178?referrer=searchResults
Select the correct answers in the table.
Rachel enjoys exercising outdoors. Today she walked 5 2/3 miles in 2 2/3 hours. What is Rachel’s unit walking rate in miles per hour and in hours per mile?
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
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
Algebra word problem plz help me
Step-by-step explanation:
here's the answer to your question
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)
write your answer as an integer or as a decimal rounded to the nearest tenth
Answer:
FH ≈ 6.0
Step-by-step explanation:
Using the sine ratio in the right triangle
sin49° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{FH}{FG}[/tex] = [tex]\frac{FH}{8}[/tex] ( multiply both sides by 8 )
8 × sin49° = FH , then
FH ≈ 6.0 ( to the nearest tenth )
Answer:
6
Step-by-step explanation:
sin = opposite/hypotenuse
opposite = sin * hypotenuse
sin (49) = 0,75471
opposite = 0,75471 * 8 = 6,037677 = 6
Find the greatest rational number r such that the ratios 8/15 ÷ r and 18/35 ÷ r are whole numbers?
The answer is "[tex]\bold{\frac{2}{105}}[/tex]", and the further calculation can be defined as follows:
When the "r" is the greatest common divisor for the two fractions.
So, we will use Euclid's algorithm:
[tex]\to \bold{(\frac{8}{15}) -(\frac{188}{35})}\\\\\to \bold{(\frac{8}{15} -\frac{188}{35})}\\\\\to \bold{(\frac{56-54}{105})}\\\\\to \bold{(\frac{2}{105})}\\\\[/tex]
this is [tex]\bold{(\frac{8}{15}) \ \ mod \ \ (\frac{18}{35})}[/tex]
we can conclude that the GCD for [tex]\bold{\frac{54}{105}}[/tex], when divided by [tex]\bold{\frac{2}{105}}[/tex], will be the remainder is 0. Rational numbers go from [tex]\bold{\frac{2}{105}}[/tex] with the latter being the highest.
So, the final answer is "[tex]\bold{\frac{2}{105}}[/tex]".
Learn more:
greatest rational number:brainly.com/question/16660879
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
factorize : ( p- q ) cube
Answer:
[tex]( {p - q}^{3} ) \\ = {p}^{2} - 3 {p}^{2} q + 3p {q}^{2} - {q}^{3} [/tex]
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
Learn more about ARITHMETIC PROGRESSION :
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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?
HELPP plz don't send a file whats the answer and explanation plz if you can
Answer:
5/0 is not a rational number
Step-by-step explanation:
you cant divide by 0
accountancy
So i have to make trial balance and im kinda confused with 'interest'. So which side did it go to? Credit or debit? It didn't state the interest as received or expense/paid. someone told me to look at the bank but hey i need more explanation T^T
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]
A well-known brokerage firm executive claimed that 60% of investors are currently confident of meeting their investment goals. An XYZ Investor Optimism Survey, conducted over a two week period, found that in a sample of 100 people, 69% of them said they are confident of meeting their goals. Test the claim that the proportion of people who are confident is larger than 60% at the 0.01 significance level.
The null and alternative hypothesis would be:________
a. H0:μ=0.6H0:μ=0.6
H1:μ≠0.6H1:μ≠0.6
b. H0:μ=0.6H0:μ=0.6
H1:μ<0.6H1:μ<0.6
c. H0:μ=0.6H0:μ=0.6
H1:μ>0.6H1:μ>0.6
d. H0:p=0.6H0:p=0.6
H1:p≠0.6H1:p≠0.6
e. H0:p=0.6H0:p=0.6
H1:p>0.6H1:p>0.6
f. H0:p=0.6H0:p=0.6
H1:p<0.6H1:p<0.6
The test is:________
a. two-tailed
b. left-tailed
c. right-tailed
The test statistic is:_______ (to 3 decimals)
The p-value is:_______ (to 4 decimals)
Based on this we:________
a. Fail to reject the null hypothesis
b. Reject the null hypothesis
We are testing a hypothesis. So, first we identify the null and the alternative hypothesis, then we find the test statistic, and with the test statistic, the p-value is found.
Null and alternative hypothesis:
Claim the the proportion is of 60%, thus, the null hypothesis is:
[tex]H_0: p = 0.6[/tex]
Test if the proportion is greater than 60%, thus, the alternative hypothesis is:
[tex]H_1: p > 0.6[/tex]
And the answer to the first question is given by option c.
Classification:
We are testing if the proportion is greater than a value, so it is a right-tailed test.
Test statistic:
[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, [tex]\sigma[/tex] is the standard deviation and n is the size of the sample.
0.6 is tested at the null hypothesis:
This means that [tex]\mu = 0.6, \sigma = \sqrt{0.4*0.6}[/tex]
Survey, conducted over a two week period, found that in a sample of 100 people, 69% of them said they are confident of meeting their goals.
This means that [tex]n = 100, X = 0.69[/tex]
Value of the test statistic:
[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
[tex]z = \frac{0.69 - 0.6}{\frac{\sqrt{0.4*0.6}}{\sqrt{100}}}[/tex]
[tex]z = 1.837[/tex]
The test statistic is z = 1.837.
p-value:
The p-value of the test is the probability of finding a sample proportion above 0.69, which is 1 subtracted by the p-value of z = 1.837.
Looking at the z-table, z = 1.837 has a p-value of 0.9669.
1 - 0.9669 = 0.0331
The p-value is 0.0331.
Decision:
The p-value of the test is 0.0331 > 0.01, and thus:
a. Fail to reject the null hypothesis
For another example of a problem of a test of hypothesis, you can take a look at:
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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
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:
Michigan and Michigan State play each other this Saturday in football. Based on data from ESPN, Michigan averages 38.1 points per game with a SD of 8.4 and average 424 yards gained per game with a SD of 72. The correlation between points scored and yards gained is 0.68. Thus:
Average points = 38.1, SD= 8.4
Average yards gained = 424, SD= 72, r = 0.68
Required:
a. Find the slope of the regression equation for predicting number of points scored based on average yards gained per game). Report your answer to 4 decimal places.
b. If Michigan gains 500 yards in the game against Michigan State, what is Michigan's predicted points scored? Round to the nearest whole number.
Answer:
200000
by 10009
Step-by-step explanation:
nbebsbsbsbbsbsbsbsbBz
Find the local linear approximation L(x) of the function f(x) = 5−x^2 at x = 2.
Use this to estimate f(2.1).
Answer:
L(x)=-4x+9
L(2.1)=0.6
Step-by-step explanation:
It's asking us to find the tangent line to curve f(x) = 5−x^2 at x = 2.
Theb use this to estimate f(2.1).
To find slope of tangent line, we must differentiate and then plug in 2 for x.
f'(x)=0-2x by constant and power rule.
f'(x)=-2x
So the slope of the tangent line is -2(2)=-4.
A point on this tangent line shared by the curve is at x=2. We can find it's corresponding y-value using f(x)=5-x^2.
f(2)=5-(2)^2
f(2)=5-4
f(2)=1
So let's rephrase the question a little.
What's the equation for a line with slope -4 and goes through point (2,1).
Point-slope form y-y1=m(x-x1) where m is slope and (x1,y1) is a point on the line.
Plug in our information: y-1=-4(x-2).
Distribute: y-1=-4x+8
Add 1 on both sides: y=-4x+9
Let's call this equation L(x), an expression to approximate value for f near x=2.
L(x)=-4x+9
Now the appropriation at x=2.1:
L(2.1)=-4(2.1)+9
L(2.1)=-8.4+9
L(2.1)=0.6
If we did plug in 2.1 into given function we get 5-(2.1)^2=0.59 . This is pretty close to our approximation above.
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]
