Answers
1. x - 1/4 = 3/8;
2. x = 1/4 + 3/8;
3. x = 2/8 + 3/8;
4. x = 5/8;
Hope everything is clear.
Related Questions
solve: -3(3x+1)-41>-5(-2x+4)+5x
Answers
Answer:
Step-fbccbbby-CBC step explanation:
A cylinder has a height of 16 cm and a radius of 5 cm. A cone has a height of 12 cm and a radius of 4 cm. If the cone is placed inside the cylinder as shown, what is the volume of the air space surrounding the cone inside the cylinder? (Use 3.14 as an approximation of π.)
452.16 cm3
840.54 cm3
1,055.04 cm3
1,456.96 cm3
Answers
Cylinder: height = 16 cm ; radius = 5 cm
cone: height = 12 cm ; radius = 4 cm
Volume of cylinder = 3.14 * (5cm)² * 16cm = 1,256 cm³
Volume of cone = 3.14 * (4cm)² * 12cm/3 = 200.96 cm³
Volume of air space = 1256 cm³ - 200.96 cm³ = 1,055.04 cm³
cone: height = 12 cm ; radius = 4 cm
Volume of cylinder = 3.14 * (5cm)² * 16cm = 1,256 cm³
Volume of cone = 3.14 * (4cm)² * 12cm/3 = 200.96 cm³
Volume of air space = 1256 cm³ - 200.96 cm³ = 1,055.04 cm³
Nicolas has three fewer than twice the number of songs downloaded as Sabrina does. Interpret the meaning of the expression 2x – 3. The expression 2x – 3 represents
Answers
The expression 2x-3 represent's: The number of songs downloaded by Nicholas.
The variable x represents: The number of songs downloaded by Sabrina.
A room has an area of 60 square meters and a perimeter of 32 meters what are the length and width of the room
Answers
10*6=60
10+10+6+6=32
Joanne has 2a^3 number of animals. Ronnie has 3a^3 number of animals . Odessa has a^4 number of animals . How many animals do Joanne , Ronnie, and Odessa have altogether?
Answers
2a^3 + 3a^3 + a^4
= 5a^3 + a^4
At the beginning of a basketball season, the Panthers won 30 games out of 66 games. At this rate, how many games will they win in a normal 106-game season?
Answers
in a student council election Martha and Hillary received a total of 1600 votes, Martha received 81 more votes than Hillary, how many votes did Martha receive
Answers
If we divide 1600 by 2 people, this leaves 800 votes for each girl.
800-81=719 for Hillary
800+81=881 for Martha
We take 81 votes, from those 800,and place them in martha's votes
Just to confirm: 881+719=1600 total votes
how do logarithms work
Answers
A logarithm is the power to which a number must be raised in order to get some other number. For example, the base ten logarithm of 100 is 2, because ten raised to the power of two is 100:
log 100 = 2
because
102 = 100
This is an example of a base-ten logarithm. We call it a base ten logarithm because ten is the number that is raised to a power. The base unit is the number being raised to a power. There are logarithms using different base units. If you wanted, you could use two as a base unit. For instance, the base two logarithm of eight is three, because two raised to the power of three equals eight:
log2 8 = 3
because
23 = 8
In general, you write log followed by the base number as a subscript. The most common logarithms are base 10 logarithms and natural logarithms; they have special notations. A base ten log is written
log
and a base ten logarithmic equation is usually written in the form:
log a = r
A natural logarithm is written
ln
and a natural logarithmic equation is usually written in the form:
ln a = r
So, when you see log by itself, it means base ten log. When you see ln, it means natural logarithm (we'll define natural logarithms below). In this course only base ten and natural logarithms will be used.
Final answer:
Logarithms are used in Mathematics to solve exponential equations by converting them into linear equations. They involve finding the exponent to which a base must be raised to equal a given number. Properties of logarithms, such as the product and quotient rules, help manipulate and solve logarithmic equations.
Explanation:
Logarithms are mathematical tools used to solve exponential equations and simplify complex calculations. They are the inverse function of exponential functions and help us solve for the unknown exponent in an equation.
Logarithms work by converting exponential equations into linear equations. When we take the logarithm of a number, we are finding the exponent to which a base must be raised to equal that number. For example, the logarithm (base 10) of 100 is 2, because 10 raised to the power of 2 equals 100.
The properties of logarithms allow us to manipulate them to solve equations. Some key properties include:
The logarithm of a number raised to an exponent is the product of the exponent and the logarithm of the number.The logarithm of the number resulting from the division of two numbers is the difference between the logarithms of the two numbers.What is the greatest common factor of 49 and 84? 3 4 7 9
Answers
84: 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84
The GCF is 7
how many inches are equal to 30.48 cm
Answers
A line passes through (2, −1) and (4, 5).
Which answer is the equation of the line?
Answers
subract 5 by -1 which is 6 and divide that by 4-2 which is 2 so 6 divided by 2 is 3. then subtract the y value by 6 to get 0,-7
Solve for x. 2/3x=10 Enter your answer in the box.
Answers
= 10 ÷ 2/3
Keep, change, flip!
= 10 × 3/2
= 30 / 2
= 15
So, x = 15.
2 = 10 x 3x
2 = 30x
x = 2/30
x = 1/15
Complete te pattern 3,400,000 34,000
Answers
340 and 0.034 should be your answer
hope this helps
Mr.chu is slicing 4 cantaloupes for his class.There are 24 students in class. If Me.Chu cut the cantaloupes to make an equal portion for each student , how much of a whole cantaloupe will each student get?
Answers
Each student will receive approximately 0.1667 parts of a whole cantaloupe when Mr. Chu evenly divides 4 cantaloupes among 24 students.
Explanation:The subject of this problem is how to divide a quantity fairly between multiple recipients, also known as division. If Mr. Chu is slicing 4 cantaloupes and wants to divide them equally among 24 students, we need to find how much each student would receive.
This is solved by simply dividing the total quantity of cantaloupes by the number of students. So, 4 (whole cantaloupes) divided by 24 (students) equals 0.1667.
Therefore, each student will get approximately 0.1667 of a whole cantaloupe.
Learn more about division here:https://brainly.com/question/2273245
#SPJ11
You play video games online. When you sign up with the game site, you get 400400 points. You earn 5050 more points for each hour that you play. How many hours do you have to play to get to 1,000 points?
Answers
Based upon a long period of record keeping the following represents the probability distribution of the number of times the John Jay wifi network is slow during a week. We call the random variable x.
x 0 1 2 3 4 5 6
p(x) .08 .17 .21 k .21 k .13
a. What is the value of k?
b. Calculate the expected value of x.
c. Calculate the expected value of x^2
.
d. Calculate the variance of x.
e. Calculate the standard deviation of x
f. Calculate the variance of 3x.
g. Suppose that network slowness is independent from week to week. What is the probability that if we look at 5 separate weeks, the network has no more than 4 slow times in any of those weeks?
h. Calculate the variance of the random variable x^2
Answers
[tex]\begin{tabular} {|c|c|c|c|c|c|c|c|} x&0&1&2&3&4&5&6\\[1ex] p(x)&.08&.17& .21& k& .21& k& .13 \end{tabular}[/tex]
Part A:
The total value of p(x) = 1.
Thus,
.08 + .17 + .21 + k + .21 + k + .13 = 1
0.8 + 2k = 1
2k = 1 - 0.8 = 0.2
k = 0.2 / 2 = 0.1
Therefore, the value of k is 0.1
Part B:
The expected value of x is given by
[tex]E(x)=\Sigma xp(x) \\ \\ =0(0.08)+1(0.17)+2(0.21)+3(0.1)+4(0.21)+5(0.1)+6(0.13) \\ \\ =0+0.17+0.42+0.3+0.84+0.5+0.78=3.01[/tex]
Therefore, the expected value of x is 3.01
Part C:
The expected value of [tex]x^2[/tex] is given by
[tex]E(x^2)=\Sigma x^2p(x) \\ \\ =0^2(0.08)+1^2(0.17)+2^2(0.21)+3^2(0.1)+4^2(0.21)+5^2(0.1)+6^2(0.13) \\ \\ =0(0.08)+1(0.17)+4(0.21)+9(0.1)+16(0.21)+25(0.1)+36(0.13) \\ \\ =0+0.17+0.84+0.9+3.36+2.5+4.68=12.45[/tex]
Therefore, the expected value of [tex]\bold{x^2} [/tex] is 12.45
Part D:
The variance of x is given by
[tex]Var(x)=E(x^2)-(E(x))^2 \\ \\ =12.45 - (3.01)^2=12.45-9.06 \\ \\ =3.39[/tex]
Therefore, the variance of x is 3.39.
Part E
The standard deviation of x is given by
[tex] \sqrt{Var(x)} = \sqrt{3.39} =1.84[/tex]
Therefore, the standard deviation of x is 1.84.
Part F:
The variance of ax, where a is a constant is given by
[tex]Var(aX)=a^2Var(X)[/tex]
Thus, the variance of 3x is given by
[tex]Var(3X)=3^2Var(X)=9(3.39)=30.51[/tex]
Therefore, the variance of 3x is 30.51.
Part G:
The probability that the network has no more that 4 slow times in one week is given by
[tex]P(x\leq4)=P(0)+P(1)+P(2)+P(3)+P(4) \\ \\ =0.08+0.17+0.21+0.1+0.21=0.77[/tex]
Since, the network slowness is independent from week to week, the probability that if we look at 5 separate weeks, the network has no more than 4 slow times in any of those weeks is given by
[tex](0.77)^5=0.27[/tex]
Therefore, the probability that if we look at 5 separate weeks, the network has no more than 4 slow times in any of those weeks is 0.27
Part H:
The variance of x^2 is given by
[tex]Var(x^2)=E((x^2)^2)-(E(x^2))^2=E(x^4)-(E(x^2))^2[/tex]
[tex]E(x^4)=\Sigma x^4p(x) \\ \\ =0^4(0.08)+1^4(0.17)+2^4(0.21)+3^4(0.1)+4^4(0.21)+5^4(0.1) \\ +6^4(0.13) \\ \\ =0(0.08)+1(0.17)+16(0.21)+81(0.1)+256(0.21)+625(0.1)\\+1,296(0.13) \\ \\ =0+0.17+3.36+8.1+53.76+62.5+168.48=296.37[/tex]
Thus,
[tex]Var(x^2)=296.37-(12.45)^2=296.37-155.00=141.37[/tex]
Therefore, the variance of the random variable [tex]\bold{x^2}[/tex] is 141.37
Answer:.1
Step-by-step explanation:
How would you write 1+1 in distributive property
Answers
Hope this helps
PLS HELP! 20 POINTS AND BRAINLIEST!
25 POINTS!!!!!
In the figure below, lines m and n are parallel:
Two parallel lines are shown crossed by a transversal. The angles are labeled with number 1-8. The angles on line m where the line is crossed by the transversal are 1, 2, 3, and 4 in clockwise order from top left. The angles on line n where the line is crossed by the transversal are 5, 6, 7, and 8 in clockwise order from top left.
In the diagram shown, ∠7 measures 92 degrees. What is the measure of ∠8?
8 degrees
88 degrees
92 degrees
180 degrees
Answers
7 and 8 have to equal 180 degrees
180- 92 = 88
so angle 8 is 88 degrees
Answer:
The correct option is B) 88°.
Step-by-step explanation:
Consider the provided information.
Consider the figure 1,
m∠7=92°, then by using the property of liner pair angles, we have
m∠7 + m∠8 = 180° (Liner pair angles)
⇒m∠8 + 92° = 180°
⇒m∠8 = 180 - 92
⇒m∠8 = 88°
Therefore, the measure of m∠8 is 88°.
Hence, the correct option is B) 88°.
What does n equal in: -6(n+1) = 42 . Need help quickly. Thank you!
Answers
Estimate 508-113 help me please
Answers
The florist has 63 roses and carnations. If she has 27 roses how many carnations does she have?
Answers
PQR has two known interior angles of 34°, and 80°. △RST has two known interior angles of 24°, and 90°. What can be determined about whether △PQR and △RST are similar?
Answers
Answer:
△PQR and △RST are not similar.
Step-by-step explanation:
In triangle △PQR, two known interior angles are 34° and 80°. So the measure of third angle is
[tex]180-34-80=66[/tex]
In triangle △RST, two known interior angles are 24° and 90°.
[tex]180-24-90=66[/tex]
Two triangles are similar if their corresponding angles are same and the corresponding sides are proportional.
Since the angles of △PQR and △RST are not same, therefore we can say that the △PQR and △RST are not similar.
Suppose that 21 girls and 21 boys enter a mathemat- ics competition. furthermore, suppose that each entrant solves at most six questions, and for every boy-girl pair, there is at least one question that they both solved. show that there is a question that was solved by at least three girls and at least three boys.
Answers
Individuals shall draw a table consisting of 21 boys in each column and 21 girls in each row as shown on the image below.
The table will have 21x21 = 441 boxes. Mark each box with a letter showing the problem solved by both that boy and girl. Since at least one problem was solved by a girl and a boy, therefore each box will have a letter. Each entrant solved at most six questions, so there can be at most six letters in any row or column. This means six different letters can be there in a row only if at least 11 of the boxes contain letters appearing three or more times in the row. Individuals go through each row and color all the boxes, say blue. Therefore, 11 boxes in each row must be colored blue.
The number of the boxes that must be colored blue = 21 x 11 = 231. Individuals can apply the same process to the columns and color at least 231 boxes, say green. But the total boxes are 441 only. Therefore, by Pigeonhole principle, there will be some boxes which will be both blue and green. The problem of doubly colored boxes represents a problem solved by at least three boys and three girls.
The Pigeonhole Principle is used to show that there must be a question solved by at least three girls and three boys in a math competition with 21 girls and 21 boys.
To show that there is a question solved by at least three girls and three boys, we will use the Pigeonhole Principle.
We have 21 girls and 21 boys, each solving at most six questions.Let's assume no question is solved by at least three girls and three boys.The total number of questions solved would be at most 21 x 6 = 126, which is fewer than 21 x 2 + 21 x 2 = 84, a contradiction.Therefore, there must be a question solved by at least three girls and three boys.The number of seats in the first row of a concert hall is 6. The second row has 9seats, the third row has 12 seats, and the fourth row has 15 seats. How many seats are in the eighth row?
Answers
Evaluate the expression below when x = -2. x2 − 8 x + 6
Answers
Hint: | Rewrite the right hand side of the equation.-2. x^2 - 8 x + 6 = -2 x^2 - 8 x + 6:x = -2 x^2 - 8 x + 6
Hint: | Move everything to the left hand side.Subtract -2 x^2 - 8 x + 6 from both sides:2 x^2 + 9 x - 6 = 0
Hint: | Write the quadratic equation in standard form.Divide both sides by 2:x^2 + (9 x)/2 - 3 = 0
Hint: | Solve the quadratic equation by completing the square.Add 3 to both sides:x^2 + (9 x)/2 = 3
Hint: | Take one half of the coefficient of x and square it, then add it to both sides.Add 81/16 to both sides:x^2 + (9 x)/2 + 81/16 = 129/16
Hint: | Factor the left hand side.Write the left hand side as a square:(x + 9/4)^2 = 129/16
Hint: | Eliminate the exponent on the left hand side.Take the square root of both sides:x + 9/4 = sqrt(129)/4 or x + 9/4 = -sqrt(129)/4
Hint: | Look at the first equation: Solve for x.Subtract 9/4 from both sides:x = sqrt(129)/4 - 9/4 or x + 9/4 = -sqrt(129)/4
Hint: | Look at the second equation: Solve for x.Subtract 9/4 from both sides:Answer: x = sqrt(129)/4 - 9/4 or x = -9/4 - sqrt(129)/4
What is the equation of a line that passes through the point (5, −4) and is parallel to the line whose equation is 2x + 5y = 10?
Answers
2x + 5y = 10
dropping the final 10, and
substituting the given x and y values: (5, -4).
Then:
2(5) + 5(-4) = C C = 10-20 = -10
Thus, the equation of this new, parallel line is 2x + 5y = -10.
The equation of a line that passes through the point (5, −4) and is parallel to the line whose equation is 2x + 5y = 10 is y = (-2/5)x - 2
The equation of a straight line is given by:
y = mx + b
where y, x are variables, m is the slope of the line and b is the y intercept.
The slope of the line 2x + 5y = 10 is:
2x + 5y = 10
5y = -2x + 10
y = -2/5x + 10
Hence the slope of the line 2x + 5y = 10 is -2/5
Since both lines are parallel, hence the slope of the other line is the same (-2/5). Hence the equation of the line is:
[tex]y-y_1=m(x-x_1)\\\\y-(-4)=-\frac{2}{5} (x-5)\\\\y+4=-\frac{2}{5} x+2\\\\y=-\frac{2}{5} x-2[/tex]
The equation of a line that passes through the point (5, −4) and is parallel to the line whose equation is 2x + 5y = 10 is y = (-2/5)x - 2
Find out more at: https://brainly.com/question/18880408
how do you solve the following
6/13=3/c
Answers
Find the unit rate,Kenny reads 5/8 pages in 2/3 minute.Please show your work.
Answers
Dividing a fraction can be done as multiplying by the reciprocal.
(5/8)·(3/2)=15/16pages per minute or 0.9375 pages/min.
if m angel 1 equal 42 and m angle 2 equal 27, then m angle APC equal
Answers
180-69=111
so itd be 111. ;)
The measure of angle APC equals 69°
What is the measure of angle APC?
∠1 = 42°
∠2 = 27°
Angle APC is equal to the sum of angle 1 and angle 2.
∠APC = ∠1 + ∠2
= 42° + 27°
= 69°
Hence, m ∠ APC = 69°
Complete question:
if m ∠ 1 = 42 and m ∠ 2 = 27, then m ∠ APC = ?
A bank offers a CD that pays a simple interest rate of 6.0. How much must you put in this CD now in order to have $4500 for a home-entertainment center in 6 years.