According to the Vertical Angle Theorem, two opposing vertical angles that are created when two lines cross one other are always equal to one another.
The opposing angles created by the junction of two lines are known as vertical angles or vertically opposed angles. A pair of angles that are vertically opposed to one another are always equal. Moreover, a vertical angle and the angle to which it is next are supplementary angles, meaning their sum is 180 degrees.
WH ⊥ VZ at y ,
Y is the midpoint of WX
Now since only one line can pass through W and Y ,
X must lie WH
Either W-Y-X-H of W-Y-H-X.
In any case W, Y, X and H are collinear.
Since, WH ⊥ VZ ⇒ WX ⊥ VZ at Y.
m∠VYW = m∠VYX = 90°
∠VYW ≅ ∠VYX = 90°.
Next,
Y is midpoint of WX
WY = XY
WY ≅ XY
Finally, VZ bisects ∠WYX
m∠WVY = m∠XVY
∠WVY ≅ ∠XVY
Using 1, 2, 3
ΔVWY ≅ ΔVXY by Right Hypotenuse side Congruency,
Alternatively ,
using 2, 3 and
VY ≅ VY
ΔVWY ≅ ΔVXY (by SSS congruence )
Using equations,
ΔVWY ≅ ΔVXY
by SAS congruence,
ΔVEY = ΔVXY by ASA Congruence
ΔVNY ≅ ΔVXY by AAS congruence
ΔVWY ≅ ΔVXY by AAS congruence.
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please help 20 points 10 ft 20 ft 15 ft Find the area. A = [?] ft² Round to the nearest hundredth. Remember: A = πr² Use 3.14 for π. Enter
Answer:
about 307.08 square feet
Step-by-step explanation:
[tex] \frac{1}{2} (20)(15) + \frac{1}{2} \pi( {10}^{2} ) = 307.08[/tex]
there are 75 people at the city swim park today. everyone in the park was wearing swim suits or sunglasses, some people had both. how many people had swim suits on but not sunglasses, if you know 63 people have swim suits on and 43 have sunglasses?
If you know 63 people have swim suits on and 43 have sunglasses, 32 people have swim suits on but not sunglasses.
To find out how many people have swim suits on but not sunglasses, we can use the principle of inclusion-exclusion.
We know that there are 75 people in the park, and 63 of them have swim suits on. We also know that 43 people have sunglasses. However, some people have both swim suits and sunglasses. Let's denote the number of people who have both by x. Then we can use the formula:
total = swim suits + sunglasses - both
Substituting in the given values, we get:
75 = 63 + 43 - x
Simplifying, we get:
x = 31
Therefore, 31 people have both swim suits and sunglasses, and the number of people who have swim suits on but not sunglasses is:
63 - 31 = 32
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Please help with these 2 problems asap !! 15 points
Answer:
11. 17
12. -16
Step-by-step explanation:
how many 8-letter words can be made from the letters wasteful if repetition of letters is not allowed?
There are 6720 8-letter words that can be formed from the letters of the word "wasteful" if repetition is not allowed.
To form an 8-letter word from the letters of the word "wasteful" without repetition, we must choose 8 letters from the 7 distinct letters "w", "a", "s", "t", "e", "f", "u" available.
Let's use the permutation formula to find the number of ways we can do this.
Permutation = (Number of objects)! / ((Number of objects) - r)!Permutation = 7! / (7 - 8)!Permutation = 7! / (-1)!But (-1)! is undefined, so there are no 8-letter words that can be formed from the letters of the word "wasteful" without repetition.
If repetition was allowed, then the number of 8-letter words that could be formed = 7^8 = 5764801.
Hence, the number of 8-letter words that can be formed from the letters of the word "wasteful" if repetition is not allowed is 6720.
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the number 5/3 can be best described as a(n) ___.
Answer: Proper fraction
Step-by-step explanation:
A proper fraction is a fraction that has its numerator value less than the denominator.
For example, ⅔, 6/7, 8/9, etc. are proper fractions.
how can the union and intersection of n sets that all are subsets of the universal set u be found using bit strings?
The union and intersection of n sets that are all subsets of the universal set u can be found using bit strings.
Bit strings are a way of representing sets as strings of binary digits. To represent a set, each element is assigned a digit of 0 or 1. A 1 indicates that the element is in the set, while a 0 indicates that the element is not in the set.
The union of the sets is found by combining the bit strings and setting any digit that is 1 in any of the sets to a 1. The intersection is found by comparing the bit strings and setting any digit that is 1 in all of the sets to a 1.
By using bit strings, we can quickly and accurately find the union and intersection of n sets that are all subsets of the universal set u.
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Brody is driving on a long road trip. He currently has 9 gallons of gas in his car. Each hour that he drives, his car uses up 2 gallons of gas. How much gas would be in the tank after driving for 2 hours? How much gas would be left after tt hours?
Answer: 5 Gallons of gas
Step-by-step explanation: Start with 9, and subtract that by how much he lost within those two hours (2t = 2(2) = 4, 9 - 4 = 5)
After driving for 2 hours, Brody would have 5 gallons of gas left in the tank. The formula to find gas left after tt hours is gas left = 9 - 2tt.
Explanation:To find out how much gas would be in Brody's tank after driving for 2 hours, we need to subtract the amount of gas used in 2 hours from the initial amount of gas in the tank. Each hour, Brody's car uses up 2 gallons of gas, so in 2 hours it would use up 2 x 2 = 4 gallons. Therefore, after driving for 2 hours, Brody would have 9 - 4 = 5 gallons of gas left in the tank.
To find out how much gas would be left after tt hours, we can use the formula: gas left = initial gas - gas used in tt hours. In this case, initial gas is 9 gallons, and gas used in tt hours is 2 x tt gallons. So the formula becomes: gas left = 9 - 2tt.
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Let c be a positive number. A differential equation of the form
dy/dt = ky^1+c
where k is a positive constant, is called a doomsday equation because the exponent in the expression ky^1+c is larger than the exponent 1 for natural growth.
(a) Determine the solution that satisfies that initial condition y(0) = yo
y = yo/(1-cyo^c kt)^1/c
(b) Show that there is a finite time t = T (doomsday) such that lim t → T - y(t) = [infinity]
y(t) → [infinity] as 1 - cyo^c kt → 0, that is, as t → 1/cyo^c kt. Define T = 1/cyo^c kt then lim t → T - y(t) = [infinity]
(c) An especially prolific breed of rabbits has the growth term ky^1.01. If 6 such rabbits breed initially and the warren has 42 rabbits after three months, then when is doomsday? ( Round your answer to two decimal places.)
_____ months
A differential equation of the form dy/dt = ky, where y(t) is a function of time t, k is a constant, and c is a positive number.
This type of equation is known as a first-order linear differential equation and is commonly used to model exponential growth or decay processes, such as population growth, radioactive decay, or compound interest.
The general solution to this equation is y(t) = ce^(kt), where c represents the initial condition at time t = 0.
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can someone help me on this
Figure1 shows pair of corresponding angles
Figure 2 and 6 shows pair of alternate exterior angles
Figure 5 shows pair of alternate interior angle
Figure3 shows pair of consecutive exterior angles
Figure 4 shows pair of consecutive interior angles
Define Alternate Exterior AnglesA set of angles on the outside of each of the two lines but on the opposing sides of the transversal are known as alternate exterior angles.
Define Alternate Interior AnglesWhen a transversal intersects two parallel lines, the angles created within are equal to the alternative pairings of those pairs.
Define Corresponding Anglesthe angles created when two parallel lines cross any other line, whether they are corresponding or matching corners with the transversal.
In the given figures
Figure1 is showing pair of the corresponding angles
Figure 2 and 6 showing pair of the alternate exterior angles
Figure 5 is showing pair of the alternate interior angle
Figure3 is showing pair of the consecutive exterior angles
Figure 4 is showing pair of the consecutive interior angles.
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I NEED HELP ON THIS ASAP!
Answer:
16 represents the hours available to sew gloves.
2 represents the cost of producing gloves for a small pair.
Step-by-step explanation:
the probability that a dessert sold at a certain cafe contains chocolate is 86%. the probability that a dessert containing chocolate also contains nuts is 30%. find the probability that a dessert chosen at random contains nuts given that it contains chocolate. round to the nearest tenth of a percent.
The probability that a dessert chosen at random contains nuts given that it contains chocolate is 34.9%.
The likelihood of any event A happening when another event B related to A has already happened is known as conditional probability. This implies that the likelihood of event A relies on event B.
The conditional probability symbol is P(A|B). Conditional probability P(A|B) is crucial for any exam that is part of a competition. The concept of conditional probability P(A|B), formula, and examples with solutions are all covered in this article. The Bayes theorem predicts the likelihood that an event connected to any condition would occur. For the situation of conditional probability, this theorem is taken into account.
Let A : a certain cafe contains chocolates
B: a dessert contains Nuts
P(A) = 86% = 0.86
P(AB) = 30% = 0.3
[tex]P(B|A) =\frac{P(AB)}{P(A)}[/tex]
= 0.3/0.86
= 34.9 %
So the answer is 34.9%
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a bag is filled with 200 silver coins and 123 gold coins. what is the theoretical probability of not pulling out a silver coin?
The theoretical probability of not picking the silver coin will be 0.38 .
Given,
200 silver coins and 123 gold coins are filled in a bag .
Now,
Total number of coins in a bag = gold + silver coins
Total number of coins in a bag = 200 + 123
Total number of coins in a bag = 323
Further ,
Probability of taking silver coin = 200/323
Probability of taking silver coin = 0.619.
probability of taking gold coin = 123/323
probability of taking gold coin = 0.38
Hence the probability of not selecting silver coin is 0.38 .
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Factor 64v+8w. ASAPPP PLSS
Answer:49 = 7×7; 64 = 8×8; Difference Square is the answer. where a =7u; b = 8v. Hope that you carry out the rest Bianca,.. Jung Tran
Step-by-step explanation:
Grace plans on going to the amusement park this Friday. It costs $10.00 to enter the park, and then $2.50 for every ride that Grace goes on. What will be the total cost if Grace goes on 7 rides?
Answer: 27.50
Step-by-step explanation: 2.50 X 7 =17.50 + 10 = 27.50
If the function, g(x), has the ordered pairs (-4, 15), (-2, 3), and (0, -1), fill in the ordered pairs that know exist on the graph of g−1(x)
Answer:
(15, - 4 ) , (3, - 2 ) , (- 1, 0 )
Step-by-step explanation:
given a point (x, y ) on a function f(x) , then the corresponding point on the inverse function is (y, x )
given the points on g(x) , then the corresponding points on [tex]g^{-1}[/tex] (x) are
(- 4, 15 ) → (15, - 4 )
(- 2, 3 ) → (3, - 2 )
(0, - 1 ) → (- 1, 0 )
volume of a sphere = ³, where r is the radius. The radius of a spherical planet is 6052 km, and its mass is 4.87 × 1027g. Calculate the density of the planet in kilograms per cubic metre (kg/m³). Give your answer in standard form to 3 s.f.
Answer:
5240 kg/m³
Step-by-step explanation:
You want the average density of a planet with radius 6052 km and mass 4.87×10^27 g.
Unit conversionThe mass is given in grams, and the corresponding unit in the desired answer is kilograms. There are 1000 g in 1 kg, so 4.87×10^27 g = 4.87×10^24 kg.
The radius is given in km, and the corresponding unit in the desired answer is meters. There are 1000 meters in 1 km, so 6052 km = 6052×10^3 m. (We could adjust the decimal point, but we choose to let the calculator do that.)
DensityThe units of density tell you it is computed by dividing the mass by the volume:
ρ = mass/volume
The volume of the sphere is found using the given formula, so the density is ...
ρ = (4.87×10^24 kg)/(4/3π(6052×10^3 m)^3)
ρ ≈ 5240 kg/m³
The average density of the planet is about 5240 kg/m³.
__
Additional comment
This is comparable to the average density of Earth, which is about 5520 kg/m³.
which set of numbers can make the inequality below true? 26> n + 15
Answer:
[tex]26 > n + 15[/tex]
[tex]11 > n[/tex]
[tex]n < 11[/tex]
the contingency table shows the results of a survey of students in two math classes. find p(more than 1 hour of tv | 6th period class). round to the nearest thousandth. did you watch more than one hour of tv last night?
The probability of P(more than 1 hour of TV | 6th period class) is option (D) 0.765
To find P(more than 1 hour of TV | 6th period class), we need to use conditional probability formula
P(more than 1 hour of TV | 6th period class) = P(more than 1 hour of TV and 6th period class) / P(6th period class)
The number of students who watched more than 1 hour of TV and were in the 6th period class is 13. Therefore, P(more than 1 hour of TV and 6th period class) = 13 / (13 + 10) = 13/23.
The total number of students in the 6th period class is 13 + 10 = 23. Therefore, P(6th period class) = 23 / (6 + 23) = 23/29.
Putting it all together
P(more than 1 hour of TV | 6th period class) = P(more than 1 hour of TV and 6th period class) / P(6th period class) = (13/23) / (23/29) = 0.765 (rounded to the nearest thousandth)
Therefore, the correct option is (D) 0.765
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The given question is incomplete, the complete question is:
The table shows the results of a survey of students in two math classes. Find P(more than 1 hour of TV | 6th period class). Round to the nearest thousandth. Did You Watch More Than One Hour of TV Last Night? Yes No 3rd period class 6 6th period class 13 10 A) 0.647 B) 0.565 C) 0.435 D) 0.765
Find the distance between the points (9,7) and (6,3).
Let (x1, y1) = (9,7) and (x2, y2) = (6,3)
By distance formula,
d = (x2 - x1)² + (y2 - y1)²
d = (6 - 9)² + (3 - 7)²
d = (-3)² + (-4)²
d = 9 + 16
d = 25 units
The table shows the dimensions of two fenced-in areas at the dog park. How many times greater is the area enclosed by the wood fence than the area enclosed by the metal fence
The area enclosed by the wood fence is 7 3/4 times greater than the area enclosed by the metal fence. So the correct answer is d. 7 3/4.
What is area?When measuring the area of a shape, we are determining the amount of surface the shape takes up.
To calculate the area enclosed by each fence, we must multiply the length and width of each.
The area enclosed by the wood fence is
6 1/2 x 2 1/4 = 14 7/8 square yards,
and the area enclosed by the metal fence is
2 3/4 x 2 1/2 = 6 7/8 square yards.
To determine how many times greater the area enclosed by the wood fence is than the area enclosed by the metal fence, we must divide the area of the wood fence by the area of the metal fence:
14 7/8 / 6 7/8 = 7 3/4.
This means the area enclosed by the wood fence is 7 3/4 times greater than the area enclosed by the metal fence.
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Please helpppppp! I really don't understand
Answer:
AB=8.1 and B=29.6
Step-by-step explanation:
1) To find the measure of AB, use the law of cosines
[tex]c^2=4^2+7^2-2(4)(7)cos(90)[/tex]
[tex]c^2 = 16+49 -56cos(90)\\c^2= 65\\c=8.1[/tex]
2) Use law of sines to find the measure of B
[tex]\frac{8.1}{sin(90)} =\frac{4}{sin(B)}[/tex]
B=29.6
Use the image below to answer the question
Answer:
∠ FZG = 38°
Step-by-step explanation:
∠ HZJ and ∠ FZG are vertically opposite angles and are congruent , then
∠ ZFG = ∠ HZJ = 38°
draw marbles from a bag which contains 5 red marbles, 6 blue marbles and 4 green marbles with replacement until you get a blue marble. a) binomial b) poisson c) hypergeometric d) none of these
the correct answer is: none of these, as only binomial distribution is applicable to this scenario.
a) This scenario follows the binomial distribution, as we are drawing marbles with replacement and interested in the number of successes (getting a blue marble) in a fixed number of trials.
b) The Poisson distribution is used to model the number of events occurring in a fixed time interval, given a certain rate of occurrence. It is not applicable in this scenario.
c) The hypergeometric distribution is used to model the probability of obtaining a certain number of successes in a sample without replacement, given a finite population of items that can be classified into successes and failures. In this scenario, we are drawing with replacement, so the hypergeometric distribution is not applicable.
d) Therefore, the correct answer is: none of these, as only binomial distribution is applicable to this scenario.
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pls help math scientific notation (view photo)
Just ignore this answer, its incorrect
*edited*
a normal distribution has a mean of 61 and a standard deviation of 14. what is the median? (enter an exact number as an integer, fraction, or decimal.)
The median of a normal distribution with a mean of $\mu$ and standard deviation of $\sigma$ is simply equal to the mean $\mu$. Therefore, for a normal distribution with a mean of 61 and a standard deviation of 14, the median is also 61.
This is because the normal distribution is a symmetric distribution, with the mean, median, and mode all located at the same point on the horizontal axis. The mean represents the center of the distribution and is also the balance point for the distribution, so half of the observations will be less than the mean and half will be greater than the mean.
Therefore, for a normal distribution with a given mean and standard deviation, we can use the mean as an estimate of the median. In this case, the mean is exactly equal to the median, so the median is 61.
It is worth noting that this property of normal distributions only holds for normal distributions, and not necessarily for other types of distributions. For example, in a skewed distribution, the mean and median may be quite different from each other.
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A snack stand sold hot dogs and chips at a recent game. The hot dogs cost $2. 50 and the chips cost $0. 75. After the game, they tallied 175 transactions totaling $262. 50. Represent the linear system in an augmented matrix:
1
1
175
2. 5
0. 75
262. 5
The number of hotdogs sold was
100. The number of chips sold was
The number of hot dogs is 100 while the number of snacks is 75. And it is found by using linear equation.
A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are present. The variables in the previous sentence, y and x, are referred to as a "linear equation of two variables" at times.
The linear equation to solve the question will be:-
h+s= 175 ------(1)
2.50h + 0.75s = 262.50 -----(2)
From equation (1), s= 175-h -----(3)
Put qeauation (3) into (2) :-
2.50h + 0.75 = 262.50
2.50 + 0.75 (175-h) = 262.50
2.50 + 131.25 - 0.75 = 262.50
Collect like terms :-
2.50-0.75= 262.50-131.25
1.75= 131.25
h= 131.25/1.75
h= 75
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Which statement describes the graph of this polynomial function?
f (x) = x Superscript 5 Baseline minus 6 x Superscript 4 Baseline + 9 x cubed
Answer:
The statement that describes the graph of the polynomial function f (x) = x^5 - 6x^4 + 9x^3 is that it has a local maximum at x = 0 and a local minimum at x = 2. The degree of the polynomial is 5, which means it has five zeros or x-intercepts. The leading coefficient is positive, which indicates that the graph will rise to the left and right. The function has a point of inflection at x = 1.5, where the concavity changes from up to down. Overall, the graph of this polynomial function has a typical "upside-down U" shape with local extrema and a point of inflection.
What is the value of
∠FDE given the following image?
The value of ∠FDE is 36°
Define the term angles?An angle is a geometric figure formed by two rays, or lines that extend infinitely in opposite directions, that share a common endpoint called the vertex. The measure of an angle is determined by the amount of rotation between the two rays.
Here given a right angle ∠CDE = 90°
So, we can say that,
∠CDF + ∠FDE = ∠CDE
(2x)° + (x+9)° = 90°
(3x + 9)° = 90°
Simplify it, x = 27°
So, the value of ∠FDE = (x+9)° = (27+9)° = 36°
Therefore, the value of ∠FDE is 36°
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The angle FDE is 36°. The required answer for the given question is option (A). 36°.
What is the value of <FDE?Trigonometry angles are the angles provided by the trigonometric function ratios. Trigonometry is the study of the connection between angles and triangle sides. Angle values vary from 0 to 360 degrees.
An angle is a shape in geometry made by two rays or lines that stretch indefinitely in opposite directions and have a common endpoint known as the vertex. The quantity of rotation among the two rays determines the size of an angle.
From the given figure,
∠CDF + ∠FDE = 90
Thus,
(2x)+(x+9) = 90
3x + 9 = 90
3x = 81
x = 27
Then we will have that the angle FDE is:
∠FDE = (27) + 9
∠FDE = 36
The angle of FDE is 36°
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answers on a multiple choice test have choices a, b, c, d. the instructor has chosen answers randomly according to a discrete uniform distribution. what is the probability the first 3 questions have the same answer choice?
The probability that the first three questions have the same answer choice is 1/4, since there are four answer choices and the instructor is randomly selecting the answers according to a discrete uniform distribution. This means that each answer choice has an equal probability of being chosen. Therefore, the probability of all three questions having the same answer is 1/4.
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a display of cans on a grocery shelf consists of 20 cans on the bottom, 18 cans in the next row, and so on in an arithmetic sequence, until the top row has 4 cans. how many cans, in total, are in the display?
In total, there are 126 cans in the showcase.
We will use the method for the sum of an arithmetic sequence to solve this problem. The formulation is:
S = (n/2)(a + l)
Wherein S is the sum of the sequence, n is the range of terms, a is the first term, and l is the last term.
In this example, the primary time period is 20, and the closing term is 4. The common difference among the terms is -2, given that we are subtracting 2 cans from each row. we will discover the number of terms using the formulation:
l = a + (n-1)d
Wherein d is the common distinction. solving for n, we get:
n = (l - a)/d + 1
n = (4 - 20)/(-2) + 1
n = 9
Now we can plug within the values for a, l, and n into the system for the sum:
S = (n/2)(a + l)
S = (9/2)(20 + 4)
S = 126
Thus, there are 126 cans in the display in total.
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