Answer:
A)
Step-by-step explanation:
The theorem states that if a right triangle has two sides equal to a and b, and a hypotenuse equal to c, then a squared plus b squared equals c squared.
the square of the length of the hypotenuse of a right triangle equals the sum of the squares of the lengths of the other two sides.
hope this help please mark me
Final answer:
A) 'All of the answers are correct.' would be the best answer.
Explanation:
The correct answer to the question 'Which of these best describes the Pythagorean theorem?' is option C), which states 'The sum of the squares of the smaller sides of a right triangle equal the square of the largest side.'
However, option D) 'A-squared plus B-squared equals C-squared.' is also a correct representation of the theorem. Therefore, if all given options were correct representations of the theorem, then the best choice would be A) 'All of the answers are correct.'
The Pythagorean theorem is a fundamental principle in geometry that relates the lengths of the sides of a right triangle. Specifically, it states that the square of the length of the hypotenuse (side c) is equal to the sum of the squares of the lengths of the other two sides (sides a and b).
This relationship can be expressed with the formula a² + b² = c², where c represents the hypotenuse and a and b represent the legs of the right triangle.
If one needs to find the length of the hypotenuse, one can use the formula c = √(a² + b²).
120 students in a fifth grade class are surveyed about what kinds of pets they have. Of the 120 students,
30 have a goldfish, 40 have a mouse, and 10 have a goldfish and a mouse. Using this information, answer
each of the following questions.
Let G be the event that a randomly selected student has a goldfish and M be the event that a randomly
selected student has a mouse.
What is P(G), the probability that a student in the class has a goldfish?
What is P(M), the probability that a student in the class has a mouse?
What is P(G and M), the probability that a student in the class has a goldfish and a mouse?
What is PG or M), the probability that a student in the class has a goldfish or a mouse?
Answer: P(G) = 1/4
P(M) = 1/3
P(G and M) = 1/12
P(G or M) = 1/2
Step-by-step explanation:
Probability refers to potential. A random event's occurrence is the subject of this area of mathematics.
The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events.
The degree to which something is likely to happen is basically what probability means.
Given:
Total Students Surveyed = 120
30 have a goldfish, 40 have a mouse, and 10 have a goldfish and a mouse.
First, the the probability that a student in the class has a goldfish
P(G) = 30/ 120
= 1/4
second, the probability that a student in the class has a mouse
P(M) = 40/120
= 1/3
Third, the probability that a student in the class has a goldfish and a mouse
P(G and M) = 1/4 x 1/3
= 1/12
Fourth the probability that a student in the class has a goldfish or a mouse
P(G or M) = P(G)+ P(M) - P( G and M)
= 1/3+ 1/4 - 1/12
= 6/12
= 1/2
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A bag contains red and blue marbles, such that the probability of drawing a blue marble is 2. An experiment consists of drawing a
marble, replacing it, and drawing another marble. The two draws are independent. A random variable assigns the number of blue
marbles to each outcome.
Complete the probability distribution table on your own paper. Answer the question in the text box below.
Probability Distribution
Number of blue
Probability
What is the probability of drawing exactly one blue marble? Write a simplified fraction
Mark this and return
Save and Exit
Next
Submit
Answer:
The probability mass function of random variable X which represents the number of blue marbles draan in 2 draws with replacement.
X | P(X)
0 | 0.390625
1 | 0.46875
2 | 0.140625
b) The probability of drawing exactly one blue marble = 0.46875
Step-by-step explanation:
Complete Question
A bag contains red and blue marbles, such that the probability of drawing a blue marble is 3/8. an experiment consists of drawing a marble, replacing it, and drawing another marble. The two draws are independent. A random variable assigns the number of blue marbles to each outcome.
To write the Probabilty mass function, we have to establish that in two draws with replacement, the possible number of blue marbles that can be drawn is 0, 1 and 2.
Probability of drawing a blue marble = P(B) = (3/8)
Probability of not drawing a blue marble = P(B') = 1 - (3/8) = (5/8)
- Probability of drawing 0 blue marbles in 2 draws with replacement = P(B') × P(B') = (5/8) × (5/8) = (25/64) = 0.390625
- Probability of drawing one blue marble in 2 draws with replacement
= [P(B) × P(B')] + [P(B') × P(B)]
= (2) × (3/8) × (5/8) = (30/64) = (15/32) = 0.46875
- Probability of drawing two blue marble in 2 draws with replacement = P(B) × P(B)
= (3/8) × (3/8) = (9/64) = 0.140625
The probability mass function of random variable X which represents the number of blue marbles draan in 2 draws with replacement.
X | P(X)
0 | 0.390625
1 | 0.46875
2 | 0.140625
b) Probability of drawing one blue marble in 2 draws with replacement
= [P(B) × P(B')] + [P(B') × P(B)]
= (2) × (3/8) × (5/8) = (30/64) = (15/32) = 0.46875
Hope this Helps!!!
A month of the year is chosen at random. What is the probability that the month starts with the letter J or the letter M?
Answer:
5 Months start with"J" or "M"
January March May June July
So the probability of a randomly selected month beginning with J or M is
5 / 12
Step-by-step explanation:
Answer: C 5/12
Step-by-step explanation:
EDGE (GOT RIGHT) (:
A movie ticket cost me $5.60 after a 20% coupon. What was the original price of the ticket?
Answer:
7.00
Step-by-step explanation:
discount = original price *20%
final price = original price - discount
Substituting the equation for discount
final price = original price - original price*20%
Factoring out the original price
final price = original price (1-20%)
Changing to decimal form and putting the final price
5.60 = original price (1-.2)
5.60 = original price (.8)
Divide by each side by .8
5.6/.8 = original price (.8)/.8
7 = original price
Mr. Mole and Bugs Bunny started digging their way into the ground from different locations at the same time. They each dug at a constant rate.
The following equation gives Mr. Mole's altitude (in meters relative to the ground) as a function of time (in minutes). A = -4-0.6t
Bugs Bunny's altitude (in meters relative to the ground) as a function of time (in minutes) is given by the following table of values:
Time (Minutes) Altitude (Meters)
2 -1.6
9 -7.2
16 -12.8
Who dug faster?
A) Mr. Mole
B) Bugs Bunny
C) They both dug at the same rate
Who started at a higher altitude?
A) Mr. Mole
B) Bugs Bunny
C) They both started at the same altitude
Answer:
Bugs bunny did both
Step-by-step explanation:
B
Bugs Bunny dug faster than Mr. Mole since his digging rate is -0.8 meters per minute compared to Mr. Mole's -0.6 meters per minute. Bugs Bunny also started at a higher altitude compared to Mr. Mole. This comparison involves understanding the rates of change from given functions and data points.
To determine who dug faster between Mr. Mole and Bugs Bunny, we need to compare their digging rates.
Comparing Digging Rates
Mr. Mole's altitude function is given by A = -4 - 0.6t. The rate at which Mr. Mole digs is represented by the coefficient of t, which is -0.6 meters per minute.
To find Bugs Bunny's digging rate from the table, we need to calculate the change in altitude over the change in time:From time 2 minutes (-1.6 m) to time 9 minutes (-7.2 m):Rate = (final altitude - initial altitude) / (final time - initial time)= (-7.2 - (-1.6)) / (9 - 2) = -5.6 / 7 ≈ -0.8 meters per minuteFrom time 9 minutes (-7.2 m) to time 16 minutes (-12.8 m):Rate = (final altitude - initial altitude) / (final time - initial time)= (-12.8 - (-7.2)) / (16 - 9) = -5.6 / 7 ≈ -0.8 meters per minuteSince Bugs Bunny's rate is -0.8 meters per minute and Mr. Mole's rate is -0.6 meters per minute, **Bugs Bunny dug faster**.
Comparing Starting Altitudes
Comparing their initial altitudes:
Mr. Mole's initial altitude is -4 meters (when t = 0).
From the table, Bugs Bunny's initial data point is at time 2 minutes, altitude -1.6 meters. To find his initial altitude, we assume constant rate from this point backward:
(-1.6 meters at 2 minutes) + (0.8 meters/minute × 2 minutes) = -1.6 + 1.6 = 0 meters
Thus, Bugs Bunny started at a higher altitude.
What are two ways that mathematics are present in nature?
Answer:
These patterns recur in different contexts and can sometimes be modelled mathematically. Natural patterns include symmetries, trees, spirals, meanders, waves, foams, tessellations, cracks and stripes. Early Greek philosophers studied pattern, with Plato, Pythagoras and Empedocles attempting to explain order in nature.
Hope this Helps!
Sincerely; Victoria <3
In the below figure what is the value of ∠QPR, in degrees, if ∠SPQ is a straight line? The measure of a straight angle is 180 degrees.
Answer:
180
Step-by-step explanation:
spr is one line and qp is another in a perpendicular position
∠QPR has a measure of 61°
What is a linear pair?A linear pair of angles is formed when two lines intersect at a single point. Angles are referred to as linear if they follow the intersection of the two lines in a straight line. The sum of the angles in a pair of linear equations is always 180°.
As per the given data:
From a horizontal line, a line is drawn such that it forms 2 angles, one ∠SPR = 119 degrees and one ∠QPR.
We have to find out the value of ∠QPR.
As the line is drawn from a horizontal line, it forms a linear pair.
From the linear pair property, the sum of the angles must be equal to 180 degrees as the line is horizontal.
After using the aforementioned property:
∠SPR + ∠QPR = 180°
119 + ∠QPR = 180
∠QPR = 180 - 119
∠QPR = 61°
Hence, The measure of angle ∠QPR is 61 degrees.
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(The given question is incomplete, the complete question is given below)
what does m equal in this equation, m-7=17
Answer:
Given
m - 7 = 17
m = 17 +7
Therefore m = 24
Answer:
m=24
Step-by-step explanation:
Since m-7=17
We are to find the value of m
And this can be done by making m the subject of formula
So m-7=17
Add 7 to both sides
m=17+7
m=24
Therefore m is 24
2 Points
It's Crazy Sock Day, and you need to wear a pair of mismatched socks to
school. You have White, Red, Blue, and Green socks to choose from. Which
list shows all possible combinations of two different sock colors?
O
A. WR, RW, WB, BW, WG, GW, RB, BR, RG, GR, BG, GB
O B. WR, WB, WG, RB, RG, BG
O C. WR, RB, BG, GW
O D. WW, WR, WB, WG, RR, RB, RG, BB, BG
Answer:
B. WR, WB, WG, RB, RG, BG
Step-by-step explanation:
It's only asking for how many color combos you can get, so you multiply 4 by 3, then divide by 2, to get the 6 different combinations.
Toni is considering a 3/27 balloon mortgage with an interest rate of 5.1% to
purchase a house for $121,000. What will be her balloon payment at the end
of 3 years?
O
A. $109,715.78
O
B. $108,908.33
O
C. $108,983.14
O
D. $115,460.91
Answer:the answer is D
Step-by-step explanation:
$115,460.91
Her balloon payment at the end of 3 years is $115,460.91. The correct option is D.
What is balloon mortgage?A balloon mortgage is one of the loan with low initial payments but the borrower is needed to repay the balance in a lump sump amount.
Given is the 3/27 balloon mortgage with an interest rate of 5.1% to purchase a house for $121,000.
The rate is fixed for a period of 3 years and later converts to a new fixed rate for the left 27 years.
using the formula for balloon payment.
FV = P*(1+r)n–P*[(1+r)n–1/r]
Substitute P = $121000, r = 5.1 and n=3 years, we get the balloon payment is
FV = $115,460.91
Thus, her balloon payment at the end of 3 years is $115,460.91. The correct option is D.
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Which pair of ratios form a proportion? 97 points
5 : 10 and 10 : 15
8 : 12 and 18 : 27
9 : 15 and 24 : 30
6 : 20 and 7 : 30
Answer:
8 : 12 and 18 : 27
Step-by-step explanation:
5 : 10 and 10 : 15
Divide each by 5
1:2 and 2:3 The ratios are not the same
8 : 12 and 18 : 27
Divide the first by 4 and the second by 9
2:3 and 2:3 This is a proportion
9 : 15 and 24 : 30
Divide the first by 3 and the second by 6
3:5 and 4:5 The ratios are not the same
6 : 20 and 7 : 30
Divide the first by 2 and leave the second alone
2:10 and 7: 30 The ratios are not the same
Answer:
B. 8 : 12 and 18 : 27
Step-by-step explanation:
8 : 12
Reduces to
2 : 3
18 : 27
Reduces to
2 : 3
Same simplified ratio, hence proportional
I will give you brainliest plz help me
Answer:
There are 36 cubes
Step-by-step explanation:
Answer:
18 cm or 36 cubes
Step-by-step explanation:
hxlxb
h=3
l=3
b=4
3x3x4
36
36 divided by 2 since each cube is half
18
A school dedicated 50% of the courtyard area for students to start a garden. The students
want to know how much of the 632-square-foot space they will be able to use.
Which expression shows a way to find 50% of 632?
.632
2
.632
Answer:
A. 50% of 632
Step-by-step explanation:
The percentage refers to the whole garden (632) and the amount of this garden they will be able to use. If you need to find the exact number I suggest turning the percent into a fraction (50% is also 1/2) then multilying it by the total (632).
Answer:
317
Step-by-step explanation:
You can find the answer via the equation
632*50%
or
632/2
ABCD shown in the coordinate plane below, is dilated with the center at the origin to form quadrilateral
EFGH
What is the scale factor of the dilation?
tontit
A. 1/4
B. 1/3
C. 3
D. 4
Answer:C
Step-by-step explanation:
Find the greatest common factor of 12 w' and 8w
Answer:4w
Step-by-step explanation:
To find the greatest common factors of 12w and 8w
Using product of prime factor we get
12w=2×2×3×w
8w=2×2×2×w
Common factors
=2×2×w
=4w
Answer:
4w.
Step-by-step explanation:
12w and 4w:
The GCF of 12 and 8 = 4.
So the answer is 4w.
a coin lands on heads 200 times
the relative frequency of heads is 0.4
Answer:
The number of times coin thrown was 500.
Step-by-step explanation:
Relative\ frequency=\frac{Number\ of\ lands\ on\ heads}{Number\ of\ times\ coin\ thrown}
0.4=\frac{200}{x}
By cross multiplying we get:
0.4x=200
Dividing both sides by 0.4 we get:
x=500.
Mike purchased a round wall clock the clocks radius is 10m what is the circumference of the clock
Answer:
62.8 m
Step-by-step explanation:
The circumference of the clock is the circumference of a circle which is given by
2 Pi r
Where
Pi = 3.14
Radius r = 10m
Therefore
Circumference = 2 x 3.14 x 10
= 62.8 m
The circumference of the clock is approximately 62.8 meters.
Explanation:To find the circumference of a circle, you can use the formula C = 2πr, where C is the circumference and r is the radius of the circle. In this case, the radius of the clock is given as 10m. Substituting this value into the formula, we have C = 2π(10) = 20π. The approximate value of π is 3.14, so the circumference of the clock is approximately 20(3.14) = 62.8m.
To find the circumference (C) of a round wall clock, you can use the formula C = 2πr, where π (pi) is approximately 3.14 and r is the radius of the clock. In this case, the radius is given as 10 meters. Substituting this value into the formula, the circumference is calculated as C = 2 * 3.14 * 10 meters, which equals 62.8 meters.
Therefore, the circumference of Mike's round wall clock is approximately 62.8 meters. This value represents the total distance around the edge or perimeter of the circular clock face.
When a number is increased by 48%, the result is 92. What is the original number to the nearest tenth?
Answer:
So you are trying to find 48% of 92, correct?
Step-by-step explanation:
Answer:
44.2
Step-by-step explanation:
Take 92 and multiply it by .48
Please help!
How do I tell the difference between sss and sas?
SSS (Side-Side-Side) requires three pairs of equal sides to prove triangle congruence, while SAS (Side-Angle-Side) requires two pairs of equal sides and one pair of equal included angles.
Explanation:In mathematics, specifically in geometry, SSS (Side-Side-Side) and SAS (Side-Angle-Side) are two methods used to determine if two triangles are congruent. Congruent triangles are triangles that have the same size and shape.
SSS (Side-Side-Side)
The SSS criterion states that if all three sides of one triangle are respectively equal in length to all three sides of another triangle, then the two triangles are congruent. You do not need to know any angle measurements.
SAS (Side-Angle-Side)
The SAS criterion states that if two sides and the included angle (the angle between the two sides) of one triangle are equal to two sides and the included angle of another triangle, then the two triangles are congruent.
To distinguish between the two, remember that for SSS you're comparing three sides, and for SAS you're comparing two sides and the angle that is between them.
A gate is 3 feet tall and casts a shadow 5 feet long. At the same time, a nearby building is 27 ft tall. If this is to be a proportional relationship, what is the length of the building's shadow?
Answer:
the length of the shadow is 45 feet long
Step-by-step explanation:
6. Under what circumstances would it be better for you to work at Burger Bistro, and under what circumstances would it be better for you to work at Cheeseburger City? Please be specific in your answer.
Answer:
Burger Bistro would be better at 8+ hours. Cheeseburger City would be better at 1-7 hours.
Step-by-step explanation:
Answer:
If you were working either 8-12 hours a day it would be better to work at Burger Bistro. If you multiply 8 by $8 you will get $64 which is more pay then cheese burger city.
tyrell, katy and lucy were eating grapes. tyrell ate twice as many grape as katy, and lucy ate half as many grapes as katy. if katy ate 6 grapes, how many grapes did the three of them eat in all.
Answer:
21
Step-by-step explanation:
k=6 t=k *2=12 l=k/2 =3 6+12+3=21
Answer:
21
Step-by-step explanation:
To find out how much Tyrell ate, you multiply 6 times two (which is 12), then to find out how much Lucy ate, you have to divide 2 and 6 (Which is 3) . Now you add up how many they ate in all.. 6 (Katy) plus 12 (Tyrell) and that equals 18, then you add 3 (Lucy), which comes to a total of 21
John surveyed 25 of his classmates about their music preferences7 students said they like hip-hop, 13 students said they pop, and 8 students said they liked neither hip-hop nor pop musicJohn made a Venn diagram to find the number of students who like both hip-hop and pop music Evaluate John's work Did he use the Venn diagram accurately to arrive at a correct solution?
Answer:
The venn diagram is not included in the question, but il try to answer it in a general way.
We have a sample of 25 persons.
7 of them like hiphop.
13 of them like pop
8 of them do not like neither.
So in our Venn diagarm we will have two circles, one for the students that like pop and other for the students that like hip-hop.
in the pop circle we have 13 students, in the circle of hiphop we have 7 students, and outside both circles we have 8 stundents.
Now, if we add it all we get:
13 + 7 + 8 = 28,
But we have 25 students, this means that 3 of the students like both genres, hip hop and pop.
Then the circles of hip hop and pop must have an intersection, and in the intersection we must have 3 students.
estimate the following difference by replacing each fraction with 0, 1/2 or 1.
7/8 - 6/11
drag numbers to the boxes to complete your answer. numbers may be used more than once or not at all.
1, 1/2, 0, 1/4, 1/8, 2
The estimated difference is [tex]\( \frac{1}{2} \).[/tex]
To estimate the difference [tex]\( \frac{7}{8} - \frac{6}{11} \)[/tex] by replacing each fraction with 0, 1/2, or 1, let's break it down:
For [tex]\( \frac{7}{8} \):[/tex]
- [tex]\( \frac{7}{8} \)[/tex] is close to 1 since it's almost a whole.
For [tex]\( \frac{6}{11} \):[/tex]
- [tex]\( \frac{6}{11} \)[/tex] is close to 1/2 since it's a bit more than half.
So, we have:
[tex]\( 1 - \frac{1}{2} = \frac{1}{2} \)[/tex]
Therefore, the estimated difference is [tex]\( \frac{1}{2} \).[/tex]
How much of Earth is covered by Wilderness if we do NOT include frozen areas in the number? Is this
concerning?
Answer:
23%
Step-by-step explanation:
can someone pls solve this for me
Given:
m∠WYX = 20°
m∠XYZ = 135°
To find:
The measure of arc WXZ.
Solution:
m∠WYZ = m∠WYX + m∠XYZ
m∠WYZ = 20° + 135°
m∠WYZ = 155°
The measure of inscribed angle is half of the intercepted arc.
[tex]$\Rightarrow m \angle WYZ = \frac{1}{2} m (ar WXZ)[/tex]
[tex]$\Rightarrow 155^\circ = \frac{1}{2} m (ar WXZ)[/tex]
Multiply by 2 on both sides.
[tex]$\Rightarrow 2\times 155^\circ = 2 \times \frac{1}{2} m (ar WXZ)[/tex]
[tex]$\Rightarrow 310^\circ = m (ar WXZ)[/tex]
The measure of arc WXZ IS 310°.
can anyone answer this
Express 20 cm to 400 mm in simplest form
Answer:
Step-by-step explanation:
36/24 or 3/2
write this polynomial in standard form (x+2)(x+5)
Answer:
14
Step-by-step explanation:
Exponential functions increase rapidly how would you describe the behavior of an inverse function to that
The exponential functions have the form f(x) = bˣ where b> 0 and b≠0.
Step-by-step explanation:
Exponential function is given in the form of f(x)= bˣ
When working with the inverse of a function, the inputs (x) and outputs(y) exchange their places and the inverse will be the reflection over the identity line y= x
The example of exponential function is the growth of bacteria. If you start with 1 bacterium and it doubles every hour, you will have 2x bacteria after x hours and it is written as f(x) = 2x.
The exponential function will be bigger than the polynomial and it always have the positive number other than 1 as the base.
The instantaneous rate of change of a quantity with respect to time is proportional to the quantity by itself.