Answers
The sum of angles ∠D and ∠F in quadrilateral DEFG, inscribed in circle P, is equal to 180∘.
To prove that m∠D + m∠F = 180∘, we can use the property of angles inscribed in a circle.
In a circle, an inscribed angle is equal to half the measure of its intercepted arc. Therefore, if we can show that arc DE + arc FG = 360∘, we can conclude that m∠D + m∠F = 180∘.
Let's start the proof:
1. Quadrilateral DEFG is inscribed in circle P. This means that all the vertices of the quadrilateral lie on the circumference of the circle.
2. Let's consider arc DE and arc FG. These arcs are intercepted by angles ∠D and ∠F, respectively.
3. By the property of angles inscribed in a circle, we know that the measure of an inscribed angle is equal to half the measure of its intercepted arc.
4. Therefore, m∠D = 1/2(arc DE) and m∠F = 1/2(arc FG).
5. We want to prove that m∠D + m∠F = 180∘. This is equivalent to showing that 1/2(arc DE) + 1/2(arc FG) = 180∘.
6. Combining the fractions, we have 1/2(arc DE + arc FG) = 180∘.
7. Now, we need to show that arc DE + arc FG = 360∘.
8. Since quadrilateral DEFG is inscribed in circle P, the sum of the measures of all the arcs intercepted by the sides of the quadrilateral is equal to 360∘.
9. This means that arc DE + arc EF + arc FG + arc GD = 360∘.
10. However, we can observe that arc EF and arc GD are opposite sides of the same chord, so they have equal measures. Therefore, arc EF = arc GD.
11. Substituting arc GD with arc EF in the equation from step 9, we have arc DE + arc EF + arc FG + arc EF = 360∘.
12. Simplifying the equation, we get 2(arc DE + arc EF + arc FG) = 360∘.
13. Dividing both sides by 2, we have arc DE + arc EF + arc FG = 180∘.
14. Comparing this result with step 7, we can conclude that arc DE + arc FG = 180∘.
15. Finally, going back to our initial goal, we can now substitute arc DE + arc FG with 180∘ in the equation from step 6: 1/2(180∘) = 180∘.
16. Simplifying, we have 90∘ = 180∘, which is a true statement.
17. Therefore, we have proven that m∠D + m∠F = 180∘.
Thus, we have successfully proved that the sum of angles ∠D and ∠F in quadrilateral DEFG, inscribed in circle P, is equal to 180∘.
For more questions on quadrilateral .
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Related Questions
A survey of 340 randomly chosen US adults found that 60% of the 150 men and 50% of the 190 women ran a five-kilometer race during the past month. Do these data provide statistical evidence at the α = 0.05 level that women are less likely than men to run a five-kilometer race? Be sure to state the parameter, check conditions, perform calculations, and make conclusion(s). (10 points)
Answers
Answer:
The p-value is less than the significance level, so we will reject the null hypothesis, and conclude that at 5% significance level, the proportion for women that ran 5 km is more than the proportion of male that ran the 5 km. Thus, women are more likely to run the 5 km race.
Step-by-step explanation:
We are given;
Number of males selected; n₁ = 150
Number of females selected; n₂ = 190
Proportion of the males; p₁ = 0.6
Proportion of females; p₂ = 0.5
Let's define the hypotheses;
Null hypothesis; H0: p₁ ≥ p₂
Alternative hypothesis; Ha: p₁ < p₂
Now, the z score formula for this is;
z = (p₁ - p₂)/√(p^(1 - p^))(1/n₁ + 1/n₂))
Where;
p^ = (p₁ + p₂)/2
p^ = (0.6 + 0.5)/2
p^ = 0.55
Thus;
z = (0.6 - 0.5)/√(0.55(1 - 0.55))((1/150) + (1/190))
z = 0.1/0.0543
z = 1.84
From online p-value from z-score calculator attached, using z = 1.84, significance level = 0.05, one tailed hypothesis, we have;
P-value = 0.033
The p-value is less than the significance level, so we will reject the null hypothesis, and conclude that at 5% significance level, the proportion for women that ran 5 km is more than the proportion of male that ran the 5 km. Thus, women are more likely to run the 5 km race.
Although if we check at 0.01 significance level, we will not have the same answer as the p-value will be greater.
can someone pleaseee help me i’ll give you brainliest
Answers
Answer:
a
Step-by-step explanation:
when reflected by x-axis, the x stays the same but the y turns negative.
What are the roots of the equation?
x2 + x - 6 = 0
Answers
Your answer:
x = 2, -3
I need help Asap please
Answers
9514 1404 393
Answer:
c
Step-by-step explanation:
Choice A lists most of them, but choice C lists them all.
__
Vertical angles are on opposite sides of the intersection of crossing lines. They share a vertex, and have sides that are opposite rays.
Can someone tell me how to do this and give me the answer please
Answers
Answer:
C. 94 Supplementary angles
Step-by-step explanation:
Obtain the truth value of
(i)
If 5 + 6 = 11, then 11 – 6 = 5.
(ii)
If 5 + 8 = 12, then 12 + 8 = 20.
(iii)
If 6 + 9 = 14, then 14 – 7 = 8
(iv)
If 7 + 8 = 15, then 8 – 7 = 2
Answers
I need help ! We are doing log lines
Answers
Answer:
exponent
Step-by-step explanation:
To get log2(4)=2
so 2 to the power of 2 is 4
4 is the number between brackets in log
another example
log2(8)=3
2 to the power of 3 is 8
Geometry please help!!!!!
Answers
Mark rows a boat 8 miles an hour in calm water. When the rate of a river's current is 3 mph, it takes Mark 2 hours longer to row a given distance upstream than to travel the same distance downstream. How long will it take him to row downstream? How many miles will he row in total? Time: Distance:
Answers
Answer:
utprirtdufyfohxhcf2667566596 y _&÷&8€5697= 34 minutos y el no te
Ben ran 2/3 of a mile and walked 5/12 of a mile. How much farther did Ben run than walk?
Answers
Answer:
1.016 of a mile.
Step-by-step explanation:
What is 5 3/4 -1 5/12= ?
Answers
Answer:
4.33333333333 or 4 and 1/3
Step-by-step explanation:
Answer:
4 1/3
Step-by-step explanation:
1) Convert 5 3/4 to improper fraction.
2) Simplify 5x4 to 20.
3) Simplify 20+3 to 23.
4) Convert 1 5/12 to an improper fraction.
5) Simplify 1x12 to 12.
6) Simplify 12+5 to 17.
7) Find the least common denominator of 23/4 & 17/12.
8) Make the denominators the same.
9) Join the denominators.
10) Simplify 52/12 ( 4 1/3 )
Hope this helped!
.
What would you multiply by to find 80% of an amount
Answers
Answer:
× [tex]\frac{80}{100}[/tex]
Step-by-step explanation:
For example-
80% of 400 (working in the attachment)
HOPE IT HELPS
Am I correct? I put
Answers
Answer:
yes
Step-by-step explanation:
(2/5)^3=
anybody help???
Answers
Answer:
8/ 125
Step-by-step explanation:
8/ 125
Answer:
8/125
Step-by-step explanation:
I think. you can use the app photo math
Try Again
The price of an item has been reduced by 70%. The original price was $49.
Use the ALEKS calculator to find the price of the item now.
s
Answers
Answer:
$34.30
Step-by-step explanation:
Use the equation:
F=P(r)
F=final price
P=principal (starting) amount
r=rate, normally a percent and has to be converted to a decimal
**Since this problem asks us to go down, there is no 1+r. That's when it gives us the final price and asks us to find the original.
Plug in the values: F = 49(.7)
F=$34.30 (don't forget the $ sign)
PLEASE HELPPP!!!
FIRST ONE TO ANSWER GETS BRAINLIEST Use the expression shown below.
1 x x x x
1 x 1
Part A
Enter a number in the box to show an equivalent expression using an exponent.
(1)
LOOK AT THE PHOTO I PUT
Answers
Answer:
[tex]1/4x^{5}[/tex]
Step-by-step explanation:
A car rental company is interested in the amount of time its vehicles are out of operation for repair work. A random sample of 21 cars showed that, over the past year, the numbers of days that each of these cars had been inoperative were as follows: 15, 11, 19, 24, 6, 18, 20, 15, 18, 12, 14, 19, 5, 21, 12, 11, 8, 10, 7, 2, 14 Assuming that the population is normally distributed, construct a 95% confidence interval for the mean number of days that vehicles in the company's fleet are out of operation.
Answers
Answer:
(10.891; 15.869)
Step-by-step explanation:
Given the data::
15, 11, 19, 24, 6, 18, 20, 15, 18, 12, 14, 19, 5, 21, 12, 11, 8, 10, 7, 2, 14
The confidence interval is obtained using the relation :
Mean ± margin of error
Margin of Error = Zcritical * s/sqrt(n)
Using a calculator, the mean value of the data and standard deviation above is :
Mean = Σx / n ; n = sample size
Mean, xbar = 281 / 21
Mean = 13.38
Standard deviation , s = sqrt[Σ(X - xbar)²/ n-1]
Standard deviation, s = 5.82
Margin of Error = Zcritical * s/sqrt(n)
Zcritical at 95% confidence level = 1.96
Margin of Error = 1.96 * 5.82/sqrt(21) = 2.489
Confidence interval :
Mean ± margin of error
13.38 ± 2.489
Lower boundary = (13.38 - 2.489) = 10.891
Upper boundary = (13.38 + 2.489) = 15.869
(10.891; 15.869)
Cylinder A has radius r and height h as shown in the diagram. Cylinder B has radius 2r and height 2h. How many times greater is the surface area of Cylinder B than the surface area of Cylinder A?
I will ONLY give you a brainliest of you answer this questions CORRECTLY!
Answers
Answer:
Therefore, Cylinder B's surface area is four times greater than Cylinder A's surface area.
Step-by-step explanation:
Surface area of a cylinder = 2πrh+2πr² = 2π(rh+r²)
Cylinder A = 2π(rh+r²)
Cylinder B = 2π((2r)(2h)+(2r)²) = 2π(4rh+4r²)=2π(4(rh+r²))
To find how many times greater Cylinder B's surface area is than Cylinder A's surface area, divide:
[tex]\frac{Cylinder B}{Cylinder A}[/tex]
=2π(4(rh+r²))/2π(rh+r²)
(divide top and bottom by 2π)
=4(rh+r²)/(rh+r²)
(divide top and bottom by (rh+r²))
=4
Therefore, Cylinder B's surface area is four times greater than Cylinder A's surface area.
Stephanie is going to paint the walls and ceiling of her bedroom. Her room is 18 feet long, 17 feet wide and 9 feet high.
What is the square footage (area) of the walls and ceiling that Stephanie will be painting?
The square footage Stephanie will be painting is ________ square feet. (Enter the number only)
How many gallons of paint does Stephanie have to purchase if each gallon of paint covers 250 square feet?
Stephanie will have to buy _____ gallons of paint. (Remember, you can only purchase a WHOLE number of gallons;Enter the number only)
If each gallon cost $23.75, how much will Stephanie spend on paint?
Stephanie will spend $________ on paint. (Enter the number only)
Answers
Answer:
55
Step-by-step explanation:
54v–42w.
Write your answer as a product with a whole number greater than 1
Answers
9514 1404 393
Answer:
6(9v -7w)
Step-by-step explanation:
The greatest common factor of the two terms is 6. Any factor of 6 can be brought outside parentheses:
54v -42w = 2(27v -21w) = 3(18v -14w) = 6(9v -7w)
The hypotenuse of a right triangle is 12.4 ft. One of the other two sides is 5.8 ft How
long is the third side?
Answers
a^2 + b^2 = c^2
Hypothenuse = 12.4
Let’s assume a = 5.8
Plug into the equation
5.8^2 + b^2 = 12.4^2
33.64 + b^2 = 153.76
b^2 = 120.12
b = square root of 120.12
10.9599270071 (calculator used)
Solution: around 11 ft
The radius of a circle is 4 centimeters. What is the circle's area?
Answers
The formula to find area of a circle is A = π r².
The radius is 4, so we can plug that in.
A=π4²
4 squared is 16.
A=π(16)
We can use 3.14 for pi.
A=3.14*16
A=50.24
So the area of this circle is 50.24 cm²
---
hope it helps
Find the radius of the circle given the area of the sector is 153.9 and the angle measure
is 90 degrees.
Answers
Answer:
14
Step-by-step explanation:
area of sector = 153.9
or, (1/2) r²∅ = 153.9
or, r²∅ = 153.9 ×2
or, r²∅ = 307.8
or, r²× π/2 = 307.8
or, r² = 615.6/π
or, r² = 196
or, r=√196
r = 14
Select the correct answer.
Which statement is true?
A.
The mean lies to the right of the median for a positively skewed distribution.
B.
The mean lies to the left of the median for a positively skewed distribution.
C.
The mean lies to the left of the median for a symmetric distribution.
D.
A distribution skewed to the right is said to be negatively skewed.
E.
A distribution skewed to the left is said to be positively skewed.
Answers
Answer:
The correct answer would be The mean lies to the left od the median for a positively skewed distribution
Step-by-step explanation:
Answer: The mean lies to the left odd the median for a positively skewed distribution
Jaime has 50 rock songs, 35 dance songs and 15 rap songs on his play list. If his music player randomly selects a song, what is the probability that it is a rock song?
Answers
40 POINTS !! 40 POINTS !!
PLEASE HELP , DONT SKIP !
NO LINKS OR FILES.
Answers
Answer:
??????
Step-by-step explanation:
Answer:
wow this is not 40 points there u get no help
Step-by-step explanation:
PLEASE HURRY THIS IS DUE IN 20MIN
The Green River Freeway has a minimum and a maximum speed limit. Tony drove for 4 hours at the minimum speed limit and 7 hours at the maximum limit, a distance of 710 miles. Rae drove 4 hours at the minimum speed limit and 6 hours at the maximum limit, a distance of 640 miles SOLVE USING elimination
Answers
This is not my answer I found it from another brainly
From the beginning we know we are dealing with two different rates. Distance is equal to (Speed X Time). We have two different speeds though. We will call the min speed = x and the max speed = y. With those two ideas in place we can make two equations for both Tony and Rae.
Tony:
2x+3.5y=355
Rae:
2x+3y=320
Now you can solve the equations by subtracting Rae's equation from Tony's
.5y=35 solve for y and you get 70
Now plug that y value back into either equation and you can solve for x. I'll use Rae's distance:
2x+3(70)=320
x=55
What is sin ?
What is a cos?
Answers
Answer:
Cos: adjacent / hypotenuse
In a right angled triangle, the cosine of an angle is: The length of the adjacent side divided by the length of the hypotenuse. The abbreviation is cos. cos(θ) = adjacent / hypotenuse. Well Done!
Sin: In mathematics, the sine is a trigonometric function of an angle. The sine of an acute angle is defined in the context of a right triangle: for the specified angle, it is the ratio of the length of the side that is opposite that angle, to the length of the longest side of the triangle.
hope this helps out, if not, i'm sorry
Step-by-step explanation:
Answer:
Sin=O/H
Cos=A/H
Step-by-step explanation:
Sin in full is some, a trigonometric ratio calculated by dividing the opposite over the hypotenuse.
Cos is in full cosine , also a trigonometric ratio calculated by dividing the adjacent over the hypotenuse.
Where does the graph of cosine begin?
Answers
9514 1404 393
Answer:
wherever you want it to
Step-by-step explanation:
The cosine function is defined for all real numbers. A graph of it can exist on any interval from -∞ to +∞. Since you make the graph, and it is impossible for you to graph x = -∞, the left side of the graph (where it "begins") will be the point you decide to use to start graphing.
which of these object does not represent a plane
a .top of a box b .blackboard c. cover of the book the d. star in the sky
Answers
Answer:
D. star in the sky
Step-by-step explanation:
To be honest, none of them represent the plane but I think that's a better answer. OwO