Answer:
Step-by-step explanation:
4a
Find X FIND Y
PlEase Help me
The X and Y angles created by lines intersection in the pictures are 18° and 54°.
Based on the picture, angle ∠MON is a right angle hence it has an 90° angle. We then know that the ∠MOA is 72°. Because angle ∠MOA lies within the angle ∠MON, hence we can write the following formula:
∠MON = ∠MOA +∠AON = 90°
∠MON = 72° + ∠AON = 90°
∠AON = 18° ... (i)
If we focus on the line CD being intersected by the line AB, hence we can conclude that the angles form by this intersection will follow these rules:
∠AOD = ∠BOC
∠AOC = ∠BOD
∠AOD + AOC = 180°
∠BOC + ∠BOD = 180°
Based on the picture, we know that:
∠BOC = x
∠AOC = ∠MOA + ∠MOC
∠AOC = 72° + y ...(ii)
∠AOD = ∠AON + ∠NOD
∠AOD = 18° +2x
∠BOC = 3x ... (iii)
Because we already know that ∠BOC = AOD, hence we could rewrite the formula into:
∠BOC = ∠AOD
3x = 18° + 2x
x = 18° ... (iv)
To find the value of y, we need to focus on angle ∠AOC. Based on the previous calculations and formulas, we know that:
∠AOC + ∠BOC = 180° ... (v)
Input equations (ii) and (iv) into (v)
∠AOC + ∠BOC = 180°
(72° + y) + 3x = 180°
72° + y + 3(18°) = 180°
126° + y = 180°
y = 54° ... (vi)
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1. Is the game fair? We are flipping a coin twice. The first player wins if we get 2 tails, and the second player wins if we get 1 head and 1 tail. 2. Is the game fair? we are tossing two dice and the first player wins if the sum on the dice is 9 and the second player wins if the sum on the dice is 5.
The classification of each game as fair or not, using probabilities, is given as follows:
1. Fair.
2. Fair.
What is a fair game?A fair game is a game in which each competitor will have the same chance of winning the game.
These changes are calculated using probabilities, which is the number of desired outcomes in the context of the experiment divided by the number of total outcomes.
The probability of two tails when two fair coins are tossed is:
p = 1/2 x 1/2 = 1/4.
The probability of one head and one tail when two fair coins are tossed is:
p = 1/2 x 1/2 = 1/4.
In game 1, the two players have the same probability of winning, hence it is a fair game.
When two dice are thrown, there are 36 possible outcomes. The number of outcomes regarding the sums are given as follows:
Sum of 9: (3, 6), (4,5), (5,4), (6,3) -> 4 outcomes -> 1/9 probability.Sum of 5: (1,4), (2,3), (3,2), (4,1) -> 4 outcomes -> 1/9 probability.Same probabilities, hence game 2 is also fair.
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Grocery Giant is having a sale on Swiss cheese, 24 slices for $7.20.
How much would it cost to buy 5 slices of cheese at the same rate?
Answer:
$1.50
Step-by-step explanation:
first, find the unit rate which is 0.3 (7.2/24)
then multiply that by 5
Use the data 2, 3, 3, 5, 5, 6. Add 2 to each of the numbers. How does this affect the mean? How does this affect the
standard deviation?
Choose the correct answer below.
OA. Both of the mean and the standard deviation will be increased.
OB. The standard deviation will be increased by 2, and the mean will remain the same.
OC. Both of the mean and the standard deviation will remain the same.
OD. The mean will be increased by 2, and the standard deviation will remain the same.
stio
stio
stio
stio
The mean will be increased by 2, and the standard deviation will remain the same (option D).
What happens to the mean and the standard deviation?The first step is to determine the initial mean and standard deviation of the data.
Mean is the average of a set of numbers.
Mean = sum of numbers / total number in the data
(2 + 3 +3 + 5 + 5 + 6) / 6
24 / 6 = 4
Standard deviation is used to determine how the values in a group differs from the mean of the values in the group. It is a measure of variation.
Standard deviation of the initial data = √[{(2 - 4)² + (3 -4)² + (3 - 4)² + (5 - 4)² + (5 - 4)² + (6 - 4)²} / 6] = 1.414
Now, determine the mean and the standard deviation of the new data
New data : (2 + 2 =4)
3 + 2 = 5
3 + 2 = 5
5 + 2 = 7
5 + 2 = 7
6 + 2 = 8
Mean = (4 + 5 + 5 + 7 + 7 + 8) / 6 = 6
Standard deviation = √[{(4 - 6)² + (5 - 6)²+ (5 - 6)² + (7 - 6)² + (7 - 6)² + (8 - 6)²} / 6] = 1.41
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an integer between 1000 and 9999, inclusive, is called balanced if the sum of its two leftmost digits equals the sum of its two rightmost digits. how many balanced integers are there?
An integer between 1000 and 9999 inclusive is called balanced if the sum of its two leftmost digits equals the sum of its two right most digit. Therefore, there are 615 balanced integers .
If the common sum of the first two and last two digits is n ,
such that 1 ≤n ≤ 9 , there are n choices for the first two digits and n +1 choices for the second two digits (since zero may not be the first digit).
This gives:
∑⁹ₙ₋₁ n(n+1) balanced numbers.
If the common sum of the first two and last two digits is n, such that:
10≤ n ≤ 18
there are 19 - n choices for both pairs.
This gives : ∑ₙ ₁₀¹⁸ ( 19 - n)²
= ∑₁⁹ n²
= 285balanced numbers.
Thus, there are in total 330 + 285 = 615 balanced numbers.
Both summations may be calculated using the formula for the sum of consecutive squares, namely:
∑₁ⁿ k² = n (n+1) (2n + 1) / 6
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PLEASE HELP (BRAINLIEST IF CORRECT) - INVERSE DERIVATIVES
Answer:
h(3)=4
Step-by-step explanation:
macie has 36 photos of kekinga, her favourite gorilla at the calgary zoo she wants to arrange the photos in groups that have equal number of rows and columns.
Answer:
6×6
Step-by-step explanation:
6×6=36 and so it would be 6 rows and 6 columns.
Solve the equation. 2 + |t + 6| = 12
Question 10 options:
[4, -11]
[4, 11]
[-16, 4]
[-4, 16]
Answer:
c) [-16, 4]
Step-by-step explanation:
Given equation,
→ 2 + |t + 6| = 12
Now the value of t will be,
→ 2 + |t + 6| = 12
→ 2 + t + 6 = 12 || → 2 -(t + 6) = 12
→ t + 8 = 12 || → -t - 4 = 12
→ t = 12 - 8 || → -t = 12 + 4
→ [ t = 4 ] || → [ t = -16 ]
Hence, value of t is 4 (or) -16.
find the unit rate of each of them!! help me asap it’s due today at 11:59 pm!!
the one with the Pepsi says
Coca-Cola - $1.29 for 1.25L
Pepsi - $2.49 for 2L and the Ib stands for pounds!!
The unit rate of the Coca-Cola is $ 1.032 and the unit rate of the Pepsi is $ 1.245.
Given, cost of Coca-Cola is
$1.29 for 1.25L
and cost of Pepsi is
$2.49 for 2L
we have to find the unit rate of each of the following,
As, the cost of Coca-Cola is
$1.29 for 1.25L
$1.29 = 1.25L
1 L = 1.29/1.25
1 L = $ 1.032
Now, the cost of Pepsi is
$2.49 for 2L
$2.49 = 2L
1 L = 2.49/2
1 L = $ 1.245
Hence, the unit rate of the Coca-Cola is $ 1.032 and the unit rate of the Pepsi is $ 1.245.
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Giovanni can read 300 words per minute. If there are approximately 350 words on a page, about how many pages can he read in 2 hours?
The number of pages Giovanni can read in 2 hours is approximately 103.
How to find the number of pages he can read in 2 hours?Giovanni can read 300 words per minute. There are approximately 350 words on a page.
The number of pages he can read in 2 hours can be calculated as follows:
Therefore,
1 hour = 60 minutes
2 hours = 120 minutes.
Therefore,
1 minute = 300 words
120 minutes = ?
cross multiply
number of words he can read in 2 hours = 120 × 300 = 36000
350 words = 1 page
36000 words = ?
cross multiply
number of pages he read in 2 hours = 36000 / 350
number of pages he read in 2 hours = 102.857142857
Therefore, he read about 103 pages in 2 hours.
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i love math
1) John noticed that the amount he was paying for his lunch was a rearrangement of the digits of the amount of money he had in his pocket, and that the money he had left over was yet another rearrangement of the same three digits! How much money did John start with?
2) A small number of cards has been lost from a complete pack. If I deal among four people, three cards remain. If I deal among three people, two remain and if I deal among five people, two cards remain. How many cards are there?
There doesn't seem to be enough information to answer problem 1.
I would ask your teacher for clarification.
=============================================
Problem 2
Answer: 47 cards--------------------------
Explanation
x = number of cards, which is some positive whole number.
Your teacher has provided these facts:
If I deal among four people, three cards remain. If I deal among three people, two cards remain.If I deal among five people, two cards remain.which I'll call "fact 1", "fact 2", "fact 3" in that order.
For now I'll focus on fact 3.
Recall that multiples of 5 either end with 0 or 5. Example: 25 is a multiple of 5, and so is 60.
Fact 3 says that we get a remainder 2 when dividing by 5. Therefore, x must be something like 25+2 = 27 or 60+2 = 62. I added 2 to each previous example mentioned earlier.
In short, the value of x must end with 2 or 7.
-------------------
Now focus on fact 1.
The multiples of 4 are {4, 8, 12, ...} all of which are even since 2 is a factor of each.
Add remainder 3 to each item to get {7, 11, 15, ...} and it should be fairly obvious that all of these items are odd.
What does this mean? It means we know 100% that x ends with 7 in the units digit. If x has 2 in the units digit, then x would be even, but it's not in the set {7, 11, 15, ...}
So this is very useful info that x ends with 7.
x could be any of these: {7, 17, 27, 37, ...}
-------------------
We've looked at facts 1 and 3 so far. The only thing left is fact 2.
List the multiples of 3 to get
{3, 6, 9, 12, 15, 18, ...}
then add on the remainder 2 giving this new updated set
{5, 8, 11, 14, 17, 20, ...}
We see that 17 is in that set which fits the criteria of "the number ends with 7". So it's possible that 17 is the answer.
But 17/4 = 4 remainder 1 which doesn't fit fact 1 (since we want remainder 3 instead).
But we can add on multiples of 3*5 = 15 to extend to this new set of
{17, 32, 47, 62, 77, ...}
then erase stuff that ends with 2 to get
{17, 47, 77, ...}
Through guess and check, 47 will work out as shown in the next section below. Therefore, 47 is the final answer.
-------------------
Check:
47/4 = 11 remainder 347/3 = 15 remainder 247/5 = 9 remainder 2We get the proper remainders mentioned earlier, so the answer has been confirmed.
-------------------
Side note: The convention for problems like this is to use the Chinese Remainder Theorem. However, I decided not to use it because I wasn't sure if your teacher has covered modulo arithmetic yet or not. If s/he has covered it, then I recommend using that method instead of what I posted above. It's a much more efficient option.
4. Kojo is given $1.20 to buy some peaches and apples. Peaches cost
20c each, apples 10c each. He is told to buy at least 6 individual
fruits, but he must not buy more apples than peaches.
Let x be the number of peaches Kojo buys.
Let y be the number of apples Kojo buys.
(a) Write down three inequalities which must be satisfied.
(b) Draw a linear programming graph and use it to list the
combinations of fruit that are open to Kojo.
Required inequalities are 0.20x=1.20, 0.10y = 1.20 and 0.20x + 0.10y = 1.20. Combination of fruits open to Kojo are (6,0), (1,10), (2,8), (3,6), (4,4), (5,2), (0,12)
Given,
Kojo is given $1.20 to buy some peaches and apples. Peaches cost 20c each, apples 10c each.
He is told to buy at least 6 individual fruits, but he must not buy more apples than peaches.
Let x be the number of peaches Kojo buys.
Let y be the number of apples Kojo buys.
(a)Since Kojo has $1.20 to buy peaches and apples; and each peach and apple costs 20c and 10c respectively.
We have the following inequalitites:
0.20x = 1.20
0.10y = 1.20
0.20x + 0.10y = 1.20
(b)Possible combinations of fruits are as follows:
x = 1.20/0.20 = 6
y = 1.20/0.10 = 12
x = 1,2,3,4,5 ; y = 10,8,6,4,2
Thus, Required inequalities are 0.20x=1.20, 0.10y = 1.20 and 0.20x + 0.10y = 1.20. Combination of fruits open to Kojo are (6,0), (1,10), (2,8), (3,6), (4,4), (5,2), (0,12)
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which equation represents a liner function? y=-4x+5; y=x^3; y=-3x^2+2;y=2x^2
Answer:
y=-4x+5;
Step-by-step explanation:
the linear functions are represented by the power of x as 1
Answer:
y=-4x+5
Step-by-step explanation:
the degree of the variable(x) in the function is 1.
Ricky has two barrels of water one contains 12 gallons of rainwater and one is being filled at the rate of 2 1/3 gallons per week the second barrel has 42 gallons of rainwater and is being used to water the crops at a rate of one and 5/6 gallon per week about how many weeks will it take before the two barrels are at the same level
Answer:
7.2 weeks
Step-by-step explanation:
12 + [tex]\frac{7}{3}[/tex] x = 42 - [tex]\frac{11}{6}[/tex]x Multiply all the way through by 6 to clear the fractions
72 + 14x = 252 -11x Add 11x to both sides
72 + 25x = 252 Subtract 72 from both sides
25x = 180 Divide both sides by 25
x = 7.2
Gabrielle is 10 years younger than Mikhail. The sum of their ages is 74. What is Mikhail's age?
Answer:
Mikhail is 42 years old
Step-by-step explanation:
[tex]A(50)=266(1/2)^{50/30}[/tex]
the answer is 83.7; rounded up to 84
i dont understand why this is the answer; can anyone explain to me what steps i have to do first? ty!! (if there's 2 people that answered, ill give brainliest to the smartest answer that helps me understand why 84's the answer)
Pls help me with this question it would be very appreciated <3
Write down all the whole numbers between 25 and 50 and have a difference of 4 between their digits
Answer:
Step-by-step explanation: I don’t know if this is what your asking for but 26, 37, 48.
help find the area im putting a lot of points up
A publisher needs to send many books to a local book retailer and will send the books in a combination of small and large boxes. Each small box can hold 25 books and each large box can hold 35 books. A total of 15 boxes were sent which can hold 455 books altogether. Determine the number of small boxes sent and the number of large boxes sent.
The number of small boxes sent is 7 and the number of large boxes sent is 8 .
In the question ,
it is given that ,
the number of books that a small box can hold = 25 books
the number of books that a large box can hold = 35 books .
let the number of small boxes be "s" ,
So , the total number of books in s boxes will be 25s .
since the total number of boxes given is 15 ,
So , the number of large boxes = 15 - s
So , the number of books in the (15-s) large boxes = 35(15-s),
also given that total books altogether = 455 ,
According to the question ,
the equation becomes
25s + 35(15-s) = 455
25s + 35*15 - 35s = 455
525 - 10s = 455
10s = 525 - 455
10s = 70
s = 70/10
s = 7 boxes
and large boxes = 15 - 7 = 8 boxes .
Therefore , The number of small boxes sent is 7 and the number of large boxes sent is 8 .
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8th grade math! (Picture attatched)
The equations that represent the left side, right side, top side and bottom side are y = 3x+2, y = 3x-10, y = 5 and y = -1 respectively
How to write the equation that represents each side of the figure?The slope-intercept form of the equation of a line is y =mx+c,
where m is the slope and c is the y-intercept
slope(m) = y2-y1 / x2-x1
Left side
The line moves from point 1 (-1, -1) to point 2 (1,5)
x1 = -1, y1 = -1 and x2 = 1, y2 = 5
Slope(m) = 5-(-1) / 1-(-1) = 6/2 = 3
Using the equation of a line for 2 points:
y-y1 = m(x-x1)
y-(-1) = 3(x-(-1))
y+1 = 3(x+1)
y+1 = 3x+3
y = 3x+2
Right side
The line moves from point 1 (3, -1) to point 2 (5,5)
Slope(m) = 5-(-1) / 5-3 = 6/2 = 3
y-(-1) = 3(x-3)
y+1 = 3x -9
y = 3x-10
Top side
y = 5
Bottom side
y = -1
Therefore, equation for the left side : y = 3x+2, equation for the right side: y = 3x-10, equation for the top side: y = 5 and equation for the bottom side: y = -1
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Find the measure of each angle indicated by the “?”. Also tell me what type of angle it is for example: alternate exterior.
Answer: ? = 50, same side interior angles
? = 84, alternate interior angles
Step-by-step explanation:
130 + x = 180
-130 = -130
x = 50
alternate interior angles are congruent
50° is the value of the missing angle.
Since u and v lines are parallel so the angle asked and the angle with the value of 130° are alternate interior angle.
Alternate interior angles have the following characteristics:
They are congruent: Alternate interior angles are equal in measure. If one angle measures x degrees, the other alternate interior angle will also measure x degrees.They are on opposite sides: Alternate interior angles are located on opposite sides of the transversal.They are inside the parallel lines: Alternate interior angles are positioned between the two parallel lines.Therefore,
x+130 = 180
x =180-130
x =50°
therefore, the missing angle is 50°.
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It takes Kade 6 hours to clean the gym. It takes Cade 7 hours to clean the same gym. How long would it take Kade and Cade if they work together? Sat up the equation to solve this problem.
Find the area of the triangle pictured above.
Round your answer to the nearest tenth
Question Help: Video
Solve the following system of equations with the substitution method:
√x + y
ly
=
4
3x
Somebody help please
The value x is 1 and y is 3.
What is Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given:
x+ y = 4
y= 3x
Now solving above equations
x+ 3x = 4
4x = 4
x= 1
and, y = 3x = 3
Hence, the value x is 1 and y is 3.
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Please I need help please
After solving the value of x is 14.048.
Given:
KM represents an angle bisector.
Let y be the length of KM.
From the figure:
[tex]12.3^{2} = 5.4^{2} +y^{2}[/tex]
151.29 - 29.16 = [tex]y^{2}[/tex]
130.13 = [tex]y^{2}[/tex]
y = 11.407
[tex]x^{2} =8.2^{2} +11.407^{2}[/tex]
= 67.24 + 130.13
= [tex]\sqrt{197.37}[/tex]
x = 14.048.
Therefore After solving the value of x is 14.048.
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When I am added to -6 The result is 18 who am I
Answer:
I think 24
Step-by-step explanation:
-6 + 24 =18
please help me with this
also, I have nothing to do... any suggestions?
Answer:
[tex]l=\frac{A}{W}\\[/tex]
Step-by-step explanation:
Sometimes we have to manipulate a variable this is often easier to do when we solve for the variable we want and input numbers into the rest of the equation
Let's say A=16 and w=8
Solving for l would me using the A=lw and inputing those values
A=lw
16=l(8)
[tex]\frac{16}{8}=\frac{8l}{8}[/tex]
[tex]l=\frac{16}{8} \\[/tex] or [tex]l=2[/tex]
If A = 16 and w = 8, we could substitute those values into the original equation(A=lw) and say that
[tex]l=\frac{A}{W}[/tex]
Sometimes we have to manipulate a variable.
This is often easier to do when we solve for the variable we want and input numbers into the rest of the equation.
I hope this explanation is helpful :)
5 1/3 divided by 2 2/3
Answer:
2
Step-by-step explanation:
first turn the fractions improper to get 16/3 divided by 8/3
then keep the first fraction the same but flip the second fraction and change divide to multiply to get 16/3 times 3/8
last multiply across to get 48/24 then simplify to get 2
2
Step-by-step explanation:
[tex] \frac{ 5\frac{1}{3} }{2 \frac{2}{3} } [/tex]
[tex] = \frac{ \frac{15 + 1}{3} }{ \frac{6 + 2}{3} } [/tex]
[tex] = \frac{ \frac{16}{3} }{ \frac{8}{3} } [/tex]
Shift denominator term i.e. 8/3 to numerator. Then, the fraction will be get reciprocal i.e. 8/3 to 3/8.
[tex] \frac{16}{3} \times \frac{3}{8} [/tex]
[tex] = { \red{ \tt{ \frac{ \cancel{48^{2}}}{ \cancel {24}_{1}}}}}[/tex]
= 2
PLEASE HELP
These box plots show the prices for two different brands of shoes.
Which statement is the most appropriate comparison of the spreads?
By using the box plots, the statement that is most appropriate comparison of the spread is option D. The interquartile range (IQR) for brand A, $10, is less than the IQR for brand B, $25.
Box plot
A box plot refers the a type of chart often used in explanatory data analysis and it visually show the distribution of numerical data and skewness through displaying the data quartiles (or percentiles) and averages.
Given,
Here we have the box plot that contains the details about the comparison of spread.
Now, we have to find the statement is the most appropriate comparison of the spreads
In the given box plots, we have identified that the
Lower quartile of A = 70
Upper quartile of A = 80
Similarly,
Lower quartile of B = 25
Upper quartile of B = 50
Then the inter quartile is calculated as,
Brand A has interquartile range = 80- 70 =10,
Where as
Brand B has interquartile range = 50 - 25 = 25.
Therefore, the option D is correct.
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Marcelo was practicing penalty shots during soccer practice. Marcelo made 10 out of 25 of the shots he attempted. If Marcelo missed 30 shots, how many total shots did he take?
Marcelo will have to take 50 shots in order to miss 30 shots because the ratio of shots to missed shots is 5:3
Proportions and RatiosA ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0. A proportion is an equation in which two ratios are set equal to each other. For example, if there is 1 boy and 3 girls you could write the ratio as: 1 : 3 (for every one boy there are 3 girls) 1 / 4 are boys and 3 / 4 are girls.
To solve this question, we can simply compare the ratio or proportion of shots to the number of missed shots.
In every 25 shots taken, he made 10 shots. This implies he lose 15 shots.
So, for every 25 shots, he lost 15 shots.
How many shots did he take to miss 30 shots.
25 shots = 15 missed shots
x shots = 30 missed shots
crossed multiply both sides and solve for x
x = (30 * 25) / 15
x = 50 shots.
Marcelo took 50 shots.
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