Simplify. 1/3(1−1/4)^2 please
Answers
Answer:
3/16
Step-by-step explanation:
1/3(1-1/4)^2
1/3(3/4)^2
1/3(9/16)
3/16
Answer:
\(\huge \boxed{\frac{3 }{16}}\)
\(\rule[225]{225}{2}\)
Step-by-step explanation:
\(\displaystyle \frac{1}{3} (1-\frac{1}{4} )^2\)
Solving for brackets:
\(\displaystyle \frac{1}{3} (\frac{4}{4} -\frac{1}{4} )^2\)
\(\displaystyle \frac{1}{3} (\frac{3}{4} )^2\)
Squaring the fraction:
\(\displaystyle \frac{1}{3} (\frac{3^2 }{4^2 } )\)
\(\displaystyle \frac{1}{3} (\frac{9 }{16} )\)
Multiplying the fractions:
\(\displaystyle \frac{1 \times 9 }{3 \times 16}\)
\(\displaystyle \frac{9 }{48}\)
Simplifying the fraction:
\(\displaystyle \frac{3 }{16}\)
\(\rule[225]{225}{2}\)
Related Questions
The 10 letters a to k leaving out stand for the digits 0 - 9 but not necessarily in that order. find which letter stands to each digit if the following sums holds:
A x B = B ----------------------F x H =CJ
B x C = AC ------------------ H x J = KJ
C x D = BC -------------------- J x K = E
D x E = CH -------------------- K x G = G
E x F = DK --------------------A x G = G
Extension
Find the missing numbers for the sum:
Answers
A variable holds a place in a quantity or expression and can be defined based on specific application
Part A;
A = 1, B = 3, C = 5, D = 7, E = 8, F = 9, G = 0, H = 6, J = 4, K = 2
Part B;
193, 99, 1 9 107, 99, 920, 891, 2 97, 297
The reason the above values are correct is as follows:
The given parameters are;
The letters representing the 10 numbers 0 to 9 are;
A, B, C, D, E, F, G, H, J and K
A × B = The number B...(1)
B × C = The number AC...(2)
C × D = The number BC...(3)
D × E = The number CH...(4)
E × F = The number DK...(5)
F × H = The number CJ...(6)
H × J = The number KJ...(7)
J × K = The number E...(8)
K × G = The number G...(9)
A × G = The number G...(10)
From equation (1), and (2), we have that either A = 1, or B = 1
If B = 1, then B × C = C ≠ AC
Therefore, A = 1
B × C = 1C, therefore, 1C is either 12, 14, 15, 16, or 18
From K × G = G, we have that G = 0
From the multiplication tables, we have;
4 × 6 = 24
9 × 6 = 54
Comparing with equation (6) and (7) gives;
F × H = CJ...(6)
H × J = KJ...(7)
Let J = 4, and H = 6, therefore from J × K = E, to get a unit number, K ≤ 2
∴ K = 2, which gives;
E = 8,
From the above multiplication, C = 5, and F = 9
From which we have; B = 3
C × D = BC gives;
5 × D = 35. therefore. D = 7
Therefore, we have;
A = 1, B = 3, C = 5, D = 7, E = 8, F = 9, G = 0, H = 6, , J = 4, K = 2
Part B
From the long division, we have that the first digit of the dividend is 1 and the first digit of the quotient is also 1, given that the 2 digit divisor number when multiplied by the first digit of quotient number gives a two digit number and that the 2 digit divisor can only divide 19X number once, we have that the possible values of 2 digit number will be larger than 95 which can be 96, 97, 98, or 99
Given that the first digit of the second to the last row is 2, we have that the last number of the quotient is 3, which gives;
9* × 1*3 = 19***
Given that the second digit of the dividend is a '9', we have that, the middle digit of the quotient is also a 9 otherwise we get a lesser value. Which gives;
9* × 193 = 19***
By checking, we also get the that the second digit of the divisor must also be a 9, to give;
99 × 193 = 19,107
We verify as follows;
193
19107 ÷ 99
\({}\) 99
\({}\)920
891
\({}\)297
\({}\) 297
Therefore, the numbers are;
193, 99, 1 9 107, 99, 920, 891, 2 97, 297
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Look at the problem: (3x - 5)(x + 4)
Explain how to use the FOIL method to multiply the binomials.
Answers
Answer: 3x^2 + 7x - 20
Step-by-step explanation:
The foil method means:
First (multiply the first numbers in each binomial)
Outside (Multiply the first number in the first binomial and second number in the second binomial)
Inside (Multiply the second number in the first binomial with the first number in the second binomial)
Last (Multiply the second number in both binomials)
Therefore the equation can be simplified into: (3x * x) + (3x * 4) + (-5 * x) + (-5 * 4)
After simplifying further you get: 3x^2 + 12x - 5x - 20
You can now combine the 12x and -5x into 7x
if minnie has 7 apples and mickey takes 100 how much did minnie lose?
Answers
Explanation
if minnie has 7 apples
\(\text{minnie}\rightarrow\text{ 7 apples}\)and and mickey takes 100,then:
Mickey can not take 100 aples, because Minnie only has 7
then, the other options is that minnies
Which of the following is a statistical question that can result in numerical data?
What is the name of your favorite pizza store?
How many hours this week did you spend on homework?
How many times did you go swimming this year?
How many pink erasers do the students in your class have?
Answers
A statistical question that can result in numerical data is How many times did you go swimming this year? So, the correct option is A).
The statistical question that can result in numerical data is "How many hours this week did you spend on homework?" and "How many times did you go swimming this year?".
These questions involve counting or measuring quantities, which can be represented using numerical data. The other two questions do not involve numerical data and therefore cannot be considered statistical questions that result in numerical data. So, the correct answer is B).
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Answer:
How many pink erasers do the students in your class have?
Suppose 1000 people enter a chess tournament. The champion is determined in such a way that a player is eliminated after one loss and games are played until only one entrant has not lost. (Assume there are no ties.)
Required information:
The given tournament can be modeled as a full binary tree with the winner of the entire tournament as the root. Which of the following is true for the binary tree?
A. Each internal vertex represents the winner of the game played by its two siblings, and there are 1000 leaves, one for each contestant.
B. Each internal vertex represents the winner of the game played by its parents, and there are 2000 leaves, two for each contestant.
C. Each internal vertex represents the winner of the game played by its parents, and there are 1000 leaves, one for each contestant.
D. Each internal vertex represents the winner of the game played by its two children, and there are 1000 leaves, one for each contestant.
E. Each internal vertex represents the winner of the game played by its two children, and there are 2000 leaves, two for each contestant.
Answers
Answer:
Each internal vertex represents the winner of the game played by its parents, and there are 1000 leaves, one for each contestant.
Step-by-step explanation:
There are many ways to illustrate the rooted tree model to calculate the number of games that must be played until only one player is left who has not lost.
We could go about this manually. Though this would be somewhat tedious, I have done it and attached it to this answer. Note that when the number of players is odd, an extra game has to be played to ensure that all entrants at that round of the tournament have played at least one game at that round. Note that there is no limit on the number of games a player can play; the only condition is that a player is eliminated once the player loses.
The sum of the figures in the third column is 999.
We could also use the formula for rooted trees to calculate the number of games that would be played.
\(i=\frac{l - 1}{m - 1}\)
where i is the number of "internal nodes," which represents the number of games played for an "m-ary" tree, which is the number of players involved in each game and l is known as "the number of leaves," in this case, the number of players.
The number of players is 1000 and each game involves 2 players. Therefore, the number of games played, i, is given by
\(i=\frac{l - 1}{m - 1} \\\\ i=\frac{1000 - 1}{2 - 1} \\\\= \frac{999}{1} \\\\=999\)
Answer: C. Each internal vertex represents the winner of the game played by its parents, and there are 1000 leaves, one for each contestant.
Step-by-step explanation: A tree is a connected undirected graph with no simple circuits. When its elements has at most 2 children, it is a Binary Tree.
The tree is formed by nodes. The topmost node is called Root and except for it, every node is connected by a direct line from exactly one other node. This type of node is called Parent.
Parent can be direct connect to a number of other nodes, which are Children and can also be internal nodes.
NOdes with no children are Leaves or external nodes.
In the Binary Tree described by the question, the number of participants is 1000, so there will be 1000 leaves. Each internal vertex repsents the winner of a game played by its parents, i.e., each is a Child, a internal node.
The right answer is alternative C.
A packing box is 6 feet deep. One side of the box is 1.7 times longer than the other. The volume of the box is 24ft3. What are the dimensions of the box?
Answers
24/6=4
1.7x^2=4
X=1.534
1.7x=2.6078
please it is timed will give 30 points
Answers
Answer:
36 units squared
Step-by-step explanation:
Since this is kind of a weird shape, we can split it into two smaller shapes, a triangle, and a rectangle.
The rectangle is 6 units wide, and 4 units long. Multiply the length and width to get 24 units squared.
The triangle has a base of 6 and a height of 4, so multiply the base and height, then divide by 2. 6 times 4 is 24 and that divided by 2 is 12.
Finally add the two areas together. 24+12=36 units squared.
Answer:
36
Step-by-step explanation:
Since the two triangles on the bottom are the same, we can flip one of them over onto the other, and they will make a square. Then the top rectangle is 24, and the bottom new square would be 12 and 24 plus 12 is 36
Can someone help me?
Answers
Answer:
QR is 1.2 due to both triangle are similar
Answer:
the answer should be 0.96 units
Step-by-step explanation:
1.6/2.0=.8
.8x1.2= .96
Given the matrix:
a= 2 5
4 -8
The sum of the elements in row 1 is:
The sum of the elements in column 2 is:
Answers
Answer:
The answer is as follows
1) 7
2) 3
3) 4
Answer:
7
-3
4
Step-by-step explanation:
1. Find the value of x for which is parallel to m. The figure is not to scale. 60 150 90 30 30° Y 60° ро
Answers
The value of x for which the two lines are parallel is given as follows:
x = 60º.
What are consecutive interior angles?We have two parallel lines that are cut by a transversal, and the two angles are between the parallel lines and on the same side of the transversal, meaning that they are consecutive interior angles.
Consecutive interior angles are supplementary, meaning that the sum of their measures is of 180º, hence the value of x can be found as follows:
x + 2x = 180
3x = 180º
x = 180º/3
x = 60º.
Missing InformationThe figure is given by the image presented at the end of the answer.
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Marcus is reading a 80-page book. He read the first 20 pages in 30 minutes. If Marcus continues to read a the same rate, how long will it take him to finish the book? Set up the table to represent the information from the problem. Pages Minutes 20 30 You got it! How long will it take Marcus to read his book? Pages Minutes 20 30 80
Answers
Using division, we can find that Marcus will take 2 hours or 120 minutes to read the book.
Define division?Repetitive subtraction is the process of division. It is the multiplication operation's opposite. It is described as the process of creating equitable groups. By dividing numbers, we divide a larger number down into smaller ones such that the larger number obtained will be equal to the multiplication of the smaller numbers.
Marcus is reading a book with 80 pages.
He reads first 20 pages in 30 mins.
So, to read 1 page time taken
= 30/20
= 3/2
= 1.5 mins
Now to read 80 pages, time taken will be:
80 × 1.5
= 120 mins.
Therefore, Marcus will take 2 hours or 120 minutes to read the book.
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Please answer this correctly
Answers
Answer:
20-39 => 2
40-59 => 1
60-79 => 1
80-99 => 6
100-119 => 5
Answer: 2, 1, 1, 6, 5
Step-by-step explanation:
20-39
2 | 3
3 | 9
40-59
5 | 0
60-79
7 | 5
80-99
8 | 1 2 4
9 | 3 9 9
100-119
10 | 1 1 5 6
11 | 1
Point a is at (2,-8) and point c is at (-4,7). Find the coordinates of point b on ac such that the ratio of ab to bc is 2:1
Answers
Answer:(-2,2)
Step-by-step explanation:
Convert 125 to base three
Answers
The exponent form of the given number is 5³.
What is the exponent?Exponent is defined as the method of expressing large numbers in terms of powers. That means, exponent refers to how many times a number multiplied by itself.
The given number is 125.
Here, 125 can be written as 5×5×5
= 5³
Here, the base is 5 and power is 3.
Therefore, the exponent form of the given number is 5³.
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In a class of 36 students, 27 download rap music onto their mobile phones.
What percentage of the students listen to rap music?
Answers
Approximately 75% of the students in the class listen to rap music.
Percentage is a way of expressing a proportion or a fraction of a whole quantity in terms of 100. It is denoted by the symbol "%". The term "percent" comes from the Latin word "per centum," which means "per hundred."
To calculate the percentage of students who listen to rap music, you can use the following formula:
Percentage = (Number of students who listen to rap music / Total number of students) * 100
In this case:
Number of students who listen to rap music = 27
Total number of students = 36
Percentage = (27 / 36) * 100 ≈ 75%
So, approximately 75% of the students in the class listen to rap music.
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Select the correct answer from each drop-down menu.
The area of the shaded square is
square inches. The length of the unshaded rectangle is
inches.
The estimated value of the length of the shaded square is
inches. The estimated value of the area of the unshaded rectangle is
square inches.
Answers
The completed statement with regards to the area of the square and the rectangle are;
The estimated value of the length of the shaded square is 5·√5 inches. The estimated value of the area of the unshaded rectangle is 175 square inches.
What is the area of a square?The area of a square is the product of the side lengths which are congruent, therefore;
Area of a square = Side length, s × Side length, s = s²
The possible figure in the question includes;
A shaded square that is 125 square inches
An adjacent unshaded rectangle, that share a side with the square that has a side length of 7·√5 inches
Please find attached the possible drawing of the figure in the question, (not drawn to scale) obtained from a similar question posted online, created with MS Word.
Therefore;
The side length of the square = √(125) inches = 5·√5 inches
The estimated value of the side length of the square is; 5·√5 inches
The area of a rectangle = Length × Width
The length of the rectangle = 7·√5 inches
The width of the rectangle = 5·√5 inches
Therefore;
The area of the unshaded rectangle, therefore is; 5·√5 × 7·√5 = 175
The estimated area of the unshaded rectangle is 175 square inches
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anyone can solve this?
\( \sqrt[4] {a}^{3 \:} to \: power\)
Answers
The value of the expression \(\sqrt[4]{a}^3\) when evaluated is \(a^\frac34\)
How to evaluate the expressionFrom the question, we have the following parameters that can be used in our computation:
\(\sqrt[4]{a}^3\)
Consider an expression expressed as xⁿ
The expression can be expanded as
xⁿ = x * x * x .... in n places
Using the above as a guide, we have the following:
\(\sqrt[4]{a}^3 = \sqrt[4]{a} * \sqrt[4]{a} * \sqrt[4]{a}\)
Apply the exponent rule of indices
\(\sqrt[4]{a}^3 = a^\frac14 * a^\frac14 * a^\frac14\)
Apply the power rule of indices
\(\sqrt[4]{a}^3 = a^\frac34\)
Hence, the expression \(\sqrt[4]{a}^3\) when evaluated is \(a^\frac34\)
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As Venus revolves around the sun, it travels at a rate of approximately 22 miles per second. Convert this rate to kilometers per second. At this
rate, how many kilometers will Venus travel in 10 seconds? In your computations, assume that 1 mile is equal to 1.6 kilometers. Do not
round
your answers.
Answers
Answer:
13.75 m/sec
Step-by-step explanation:
Since the 'per second' part stays the same, simply multiply 22 kilometers by the reciprocal of 1.6:
\(22(\frac{1}{1.6})\)
then simplify the fraction:
\(= 22(\frac{10}{16})\)
\(= 22(\frac{5}{8})\)
and solve to get
\(= 13 \frac{3}{4}\) miles per second as the answer.
or optionally:
13.75 m/sec
Proving Triangles Congruent: ASA AAS
Answers
The congruence theorem required for each figure are
1. AAS
2. ASA
3. ASA
4. ASA
5. ASA
6. ASA
What is ASA congruence theorem?ASA (Angle-Side-Angle) congruence theorem states that if two triangles have two angles and the included side in common, then they are congruent.
That is to say, if two angles and the included side of one triangle are congruent to the corresponding two angles and included side of another triangle, then the two triangles are congruent.
AAS (Angle-Angle-Side) congruence theorem states that if two angles and a non-included side of one triangle are congruent to the corresponding angles and non-included side of another triangle, then the two triangles are congruent.
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PLEASE HELP IM SO LOST
Answers
Answer: f(x) has an axis of symmetry at x = 4 and h(x) has an axis of symmetry at x = -2
Step-by-step explanation:
You can easily find the axis of symmetry by investigating around which line the functions are symmetrical about
for instance, in h(x), the graph is symmetrical on either side of x = -2, meaning that the line x = -2 cuts the parabola in 'half'
in f(x), this is a little harder to think about, but if you know how the graph will be shifted on the x-axis you can figure it out! In this case (x-4)^2 means that the graph will be shifted on the x-axis 4 units to the right (or from the origin to +4 on the X axis)
as such the line x = 4 will cut the function f(x) in 'half'
A biologist wants to know the width w of a river in order to properly set instruments for studying the pollutants in the water. From point A, the biologist walks upstream 100 feet and sights to point C. From this sighting, it is determined that θ = 59° (see figure). How wide is the river? Verify your result numerically. (Round your answer to one decimal place.)
Answers
Answer:
download omni calculator it will help
Solve the equation 3x-6=3(x-2)
Answers
Answer:
0=0
Step-by-step explanation:
both sides are true for the equation
Answer:
your question is wrong
because the x end up cancelling each other
Question 6 of 10
How many dimensions does a point have?
A. Zero
B. Three
C. Two
D. One
Answers
question is attached and i accidentally selected one so ignore that hahah
Answers
Answer:
Explanation:
Given:
Focus above the ground = 40 ft
Recall the below equation of a parabola;
\(\begin{gathered} (x-h)^2=4a(y-k)^ \\ \end{gathered}\)Given that the focus is 40 ft above the ground, then h = 0, so we'll have;
\(\begin{gathered} (x-0)^2=4a(y-k) \\ y=\frac{x^2}{4a+k} \end{gathered}\)Note that the focus point is (h, a + k) where a + k =
how do i do this
the possible answers are
30, 40, 50, 60
Answers
The figure in the question is a kite and the value of the angle 4 is equal to 40°
Interior angles of a kiteA kite has 4 interior angles and the sum of these interior angles is 360°. In these angles, it has one pair of opposite angles that are obtuse angles and are equa
Let us represent the angle 3 with x, so that;
angle 1 = 2x,
angle 2 = x + 20
angle 1 + angle 4 = one of the pair of opposite angles
angle 1 + angle 3 + 90° = 180° {sum of interior angles of a triangle}
2x + x + 90°= 180°
3x = 180° - 90° {subtract 90° from both sides}
x = 90°/3 {divide through by 3}
x = 30°
so;
angle 1= 60°
angle 2 = 50°
sum of interior angles of kite (quadrilateral) = 360°
2(angle 3) + 2(angle 2) + 2(angle 1 + angle 4) = 360°
60° + 100° + 2(60° + angle 4) = 360°
60° + 100° + 120° + 2(angle 4) = 360° {open bracket}
280° + 2(angle 4) = 360°
2(angle 4) = 360° - 280° {subtract 280° from both sides}
2(angle 4) = 80°
angle 4 = 80°/2 {divide through by 2}
angle 4 = 40°
Therefore, the angle 4 of the kite is equal to the value of 40°.
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The brewsters are saving for their daughters college days. The would like to be able to withdraw $800
Answers
Answer:
Very nice
Step-by-step explanation:
is there a question? or more information on it?
A baseball league finds that the speeds of pitches are normally distributed,
with a mean of 89 mph and a standard deviation of 2.4 mph. One pitch is
thrown at a speed of 83.2 mph. What is the z-score of this pitch? Round your
answer to two decimal places.
A. -2.42
B. -2.72
C. 2.42
D. 2.72
Answers
someone help me plz!!
Answers
Answer: x=15
Step-by-step explanation:
Since these are supplementary angles, we know that if we add them together we would get 180 deg. so....
(7x-10)+ (6x-5)=180
Kay so now we can combine like terms.
13x-15=180
Now we can add 15 to both sides.
13x=195
Finally Divide 13 on both sides.
X would then now equal 15.
3.26d+9.75d−2.65 what does this equal
Answers
Answer:
13.01d - 2.65
Step-by-step explanation:
3.26d + 9.75d − 2.65
combine like terms
3.26d + 9.75d = 13.01d
nothing further can be done, recombine
13.01d - 2.65
2) A 25 foot ladder leans against a house. The base of the ladder is 7 feet
away from the house. What is h, the height of the house? #2 pleasee
Answers
Step by step
Using Pythagorean theorem, we can find the height of the right triangle
We know a= 7, we know c= 25, we need to find b
a^2 + b^2 = c^2
7^2 + b^2 = 25^2
49 + b^2 = 625
Subtract 49 from both sides to solve b
49 - 49 + b^2 = 625 - 49
b^2 = 576
Take square root of both sides
√ b^2 = √ 576
b = 24 ft
Now according to the drawing, the ladder did not go to the top of the house, we need to add 11 ft to 24 ft = 35 ft total height