Answer:
x = 2
Step-by-step explanation:
note that 64 = [tex]2^{6}[/tex]
then
[tex]x^{6}[/tex] = [tex]2^{6}[/tex] , so x = 2
The length of the diagonal of a wooden cube is 24 cm. The cube is cut into the cylinder of the
biggest volume possible. The volume of the cylinder is:
The volume of the cylinder is [tex]384\pi \sqrt{3cm }^{2}[/tex].
What is the diagonal of the cube?The diagonal that runs through the middle of a cube is it's main diagonal; the diagonal that runs along one of its faces is not. Any cube's major diagonal can be calculated by multiplying one side's length by the square root of three.Cos-1(2/3) is the angle formed between a cube's diagonal and the diagonal of one of its faces.Body of the diagonal=24cm.
Assume the length of the side= a.
[tex]a^{2} +(a^{2} +a^{2} )=24^{2}[/tex]
[tex]a=\sqrt[8]{3} cm[/tex]
The area of the cylinder base=[tex]\pi R^{2}[/tex]
=[tex]\pi (\frac{1}{2} \sqrt[8]{3} )^{2}[/tex]
=[tex]48cm^{2}[/tex]
The high of the cylinder is[tex]\sqrt[8]{3}cm[/tex]
The volume of the cylinder:
=s*h
=[tex]48\pi *\sqrt[8]{3}[/tex]
=[tex]384\pi \sqrt{3} cm^{3}[/tex]
The volume of the cylinder is [tex]384\pi \sqrt{3cm }^{2}[/tex].
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The biggest possible volume of the cylinder will be [tex]2089.497\hspace{1mm}\text{cm}^3[/tex].
What will be the diameter and height of the cylinder obtained from a cube and what are the formulas for the diagonal of a cube and the volume of a cylinder?If a cylinder with the biggest possible volume is cut inside the cube, the height of the cylinder and the diameter of the cylinder will be equal to the side length of the cube.For example, consider the following figure in which the cylinder is cut inside of the cube and since the side length of the cube is [tex]x[/tex], the diameter and the height of the cylinder are also [tex]x[/tex]If the side length of a cube is [tex]x[/tex] unit, then its diagonal will be [tex]x\sqrt{3}[/tex] unit.The formula for the volume of a cylinder is [tex]V=\pi r^2h[/tex], where [tex]r[/tex] is the radius and [tex]h[/tex] is the height of the cylinder. If [tex]d[/tex] is the diameter, then [tex]r=\frac{d}{2}[/tex].Now, given that the diagonal of the cube is [tex]24[/tex] cm. So, if the side length of the cube is [tex]x[/tex] cm, then we must have
[tex]x\sqrt{3}=24\\\Longrightarrow x=\frac{24}{\sqrt{3}}\\\Longrightarrow x=8\sqrt{3}[/tex]
Thus, the side length of the cube is [tex]8\sqrt{3}[/tex] cm.
So, the height of the cylinder with maximum volume will be [tex]h=8\sqrt{3}[/tex] cm and the diameter will be [tex]d=8\sqrt{3}[/tex]cm i.e. the radius will be [tex]r=\frac{d}{2}=\frac{8\sqrt{3}}{2}=4\sqrt{3}[/tex] cm.
So, using the above formula for the volume of a cylinder, we get
[tex]V=\pi r^{2}h=\pi\times (4\sqrt{3})^2\times 8\sqrt{3}=2089.497\hspace{1mm}\text{cm}^3[/tex].
Therefore, the biggest possible volume of the cylinder will be [tex]2089.497\hspace{1mm}\text{cm}^3[/tex].
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what is the equation of 7.2+c=19 ?
7.2 + c = 19
c = 19 - 7.2
c = 11.8
Answer:
Your answer is 5.
Step-by-step explanation:
7.2 + c = 19
or, 14 + c = 19
or, c = 19 - 14
or, c = 5 ans.
Hope its helpful :-)
There was an earthquake in San Francisco April 18, 1906. More recently there was another earthquake in Columbia June 27, 2014. Earthquakes are measured using the associated amplitude on the Richter scale. Let a1 be the amplitude for the San Francisco earthquake and a2 be the amplitude for the Columbian earthquake.
San Francisco earthquake equations is below:
R1=log(a1/T)+B=7.8
Columbia earthquake equations is below:
R2=log(a2/T)+B=5.6
a. Use the properties of logs to determine how many more times severe was the San Francisco earthquake? The severity is equal to the ratio below: a1/a2
Solving a logarithmic equation, it is found that the San Francisco earthquake was 24.71 times more intense than the Columbian earthquake.
How to find the ratios of the intensity of earthquakes?As given in the problem, the intensities of the earthquakes are given by logarithms of base 10. Then, supposing that the intensities are R1 and R2, with R1 greater than R2, the ratio of the intensities, that is, how much intense R1 is than R2, is given as follows:
[tex]r = 10^{\frac{R_1}{R_2}}[/tex]
For this problem, the intensities are given as follows:
San Francisco: R1 = 7.8.Columbia: R2 = 5.6.Then, the ratio of the intensities is given as follows:
[tex]r = 10^{\frac{7.8}{5.6}} = 24.71[/tex]
The San Francisco earthquake was 24.71 times more intense than the Columbian earthquake.
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crunchee corporation increases the size of its granola packages from 16 ounces to 20 ounces.what is the percent of increase in the size of crunchee's granola packages
The percentage of increase in the size is 25%
According to the statement
We have to given that the
Size of the granola packages from 16 ounces to 20 ounces.
And we have to find the percentage of the size of the crunchee's granola packages.
So, For this purpose,
The formula to calculate the percentage of increase in the size is :
Percentage to increase the size = present size - past size / present size.
Now substitute the values in the given formula is
Percentage to increase the size = (20 - 16 / 16)*100
After solving it
Percentage to increase the size = (4/16) *100
Percentage to increase the size = 25%
So, The percentage of increase in the size is 25%
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Find the volume of the parallelepiped determined by the vertices (0, 1, 0), (1, 1, 1), (0, 2, 0), (3, 1, 2)
The volume of the parallelopiped is 1 cubic units.
In this question,
A parallelepiped is a three-dimensional shape with six faces, that are all in the shape of a parallelogram. It has 6 faces, 8 vertices, and 12 edges. The volume of a parallelepiped is the space occupied by the shape in a three-dimensional plane.
Let the parallelepiped be PQRS.
The vertices of parallelepiped are P(0, 1, 0), Q(1, 1, 1), R(0, 2, 0), S(3, 1, 2).
The volume of parallelopiped can be found by using following steps.
PQ = Q - P = (1,0,1)
PR = R - P = (0,1,0)
PS = S - P = (3,0,2)
Now, the volume of parallelopiped is
[tex]v=\left\begin{vmatrix}1&0&1\\0&1&0\\3&0&2\end{vmatrix}[/tex]
The determinant the matrix is
⇒ 1(2-0) - 0(0-0) + 1(0-3)
⇒ 1(2) - 0 + (-3)
⇒ 2 - 3
⇒ -1
Hence we can conclude that the volume of the parallelopiped is 1 cubic units.
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Rearrange the formula to highlight time
Step-by-step explanation:
[tex]s = 2\pi(r)(r + h)[/tex]
[tex] \frac{s}{2\pi(r)} = r + h[/tex]
[tex] \frac{s}{2\pi(r) } - r = h[/tex]
1.Name 4 other angles whose cosine is the same as cos pi/3 . Explain using mathematical language how you know this is true.
2.Is this statement true or false? Explain your answer.
All angles that have the same cosine will have the same sine.
The trigonometry illustrates that the four angles whose cosine is the same as cos pi/3 will be 7∏/3, 13∏/3, 19∏/3, and 31∏/3
How to illustrate the information?From the information, given cos (x), the value that is similar to cos x will be the sum of the angle and multiple of 360.
Therefore, for the angle cos(∏/3), the angles that are similar to this angle will be expressed as Cos(2∏n + ∏/3) where n is any positive integer.
Then the other four angles will be 7∏/3, 13∏/3, 19∏/3, and 31∏/3. Also, the statement that all angles that have the same cosine will have the same sine is false. The sine of an angle is simply equal to the cosine of the complementary angle.
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Ramiya is using the quadratic formula to solve a quadratic equation. her equation is x = startfraction negative 3 plus or minus startroot 3 squared minus 4(1)(2) endroot over 2(1) endfraction after substituting the values of a, b, and c into the formula. which is ramiya’s quadratic equation?
The quadratic equation exists [tex]$x^{2}+3 x+2=0$[/tex].
What is the formula of the quadratic equation?If a quadratic equation exists [tex]$a x^{2}+b x+c=0$[/tex], the utilizing the quadratic equation the solutions for x will be given by
[tex]$x_{1,2}=\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a}$$[/tex]
The solution for x exists
[tex]$x=\frac{-3 \pm \sqrt{3^{2}-4(1)(2)}}{2(1)}[/tex]
Comparing equations (1) and (2) we get, a = 1, b = 3 and c = 2.
Therefore, the quadratic equation exists [tex]$x^{2}+3 x+2=0$[/tex].
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Answer:
One guy said it was B. but I'm going with A.
Step-by-step explanation:
Ramiya is using the quadratic formula to solve a quadratic equation. her equation is x = startfraction negative 3 plus or minus startroot 3 squared minus 4(1)(2) endroot over 2(1) endfraction after substituting the values of a, b, and c into the formula. which is ramiya’s quadratic equation?
help with Trigonometric identities
Answer:
Option 2
Step-by-step explanation:
Since theta is in the third quadrant, the sine of theta is negative.
By the Pythagorean identity,
[tex]\sin \theta=-\frac{\sqrt{105}}{13}[/tex]
So, using the double angle formula for sine, we get that
[tex]\sin 2\theta=\frac{16\sqrt{105}}{169}[/tex]
To promote a new brand of shoes, a shoe store will run
a promotion using a jar containing 3 red balls marked
"10% off," 2 white balls marked "30% off," and
1 green ball marked "60% off." Each customer will
randomly select 1 ball from the jar to determine the
discount that the customer will receive on any single
pair of the new brand of shoes. Given that the new
brand of shoes regularly costs $60 per pair, what is the
average discount amount, in dollars, that the store can
expect to give each customer due to this promotion?
Based on the percentage discount that one gets from the promotion using a jar, the average discount amount the shoe store can expect to give each customer is $15.
How much discount will the shoe store give on average?The average discount in percentages will be:
= (3/6 x 10%) + (2/6 x 30%) + (1/6 x 60%)
= 5% + 10% + 10%
= 25%
The average discount in cash amounts is:
= 25% x 60
= $15
In conclusion, the average discount amount that the store can expect to give each customer in dollars is $15.
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Flannery used 303030 lilies and 787878 roses to create six identical flower arrangements. write an equation to describe the relationship between lll, the number of lilies, and rrr, the number of roses.
An equation to describe the relationship between l and r is, as l = r so
5l + 13r = 108.
What is an equation?An equation is a formula in mathematics that expresses the equality of two expressions by connecting them with the equals sign =. The word equation and its cognates in various languages may have somewhat different definitions; for example, in French, an équation is defined as including one or more variables, whereas in English, an equation is any well-formed formula consisting of two expressions linked by an equals sign.To find the equation which represents the relationship between l, the number of lilies, and r, the number of roses:
Let l denote the number of lilies and r denote the number of roses.Flannery employed 30 lilies and 78 roses to create six similar flower arrangements, according to the statement.Total flower count = 30 + 78 = 1086 flower arrangements are required that is l = r = 6.Number of Lilies in one arrangement = 30/6 = 5Number of Roses in one arrangement = 78/6 = 13Then, 5l + 13r = 108.Therefore, an equation to describe the relationship between l and r is, as l = r so 5l + 13r = 108.
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The correct question is given below:
Flannery used 30 lilies and 78 roses to create six identical flower arrangements. Write an equation to describe the relationship between l, the number of lilies, and r, the number of roses.
Answer:
Step-by-step explanation:
r=13/5L
What is the numerical value of mswithin when sswithin= 70, the sample size = 17 and the number of groups = 3? group of answer choices mswithin = 70
The numeric value of ms within is = 19.
What is a numeric value?A real number, regardless of its sign, has a numerical value. A definite quantity is a defined amount measurement.To find the numeric value of ms within:
Given: Swithin = 70, sample size = 17 and number of groups = 3.
So, 17 × 3 = 51
70 - 51 = 19
Therefore, the numeric value of ms within is = 19.
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can someone please help me(20 points will give brainliest!!!)
Answer:
Step-by-step explanation:
F starts at 200 and ends at 900
V starts at 0 and ends at 100
points(0,200) and (100,900)
200-900/0-100
= -700/-100
=7 which means every 7 it goes you another 100
this is all I got hope it helps
A cell phone company wants to determine the average amount of data that their smart phone customers use each month. which group would best represent a sample of the population?
The group that would best represent a sample of the study population is: C: one thousand of their customers with a current smart phone data plan.
What is a Representative Sample of a Population?A sample that best represents a population under study is a sample that is a subset of the entire population, that is, research subjects that are drawn as samples should reflect the general characteristics of the entire population without leaving out any part of the population. Also, a good sample should enable a researcher make generalization.
A sample that is a subset of a population and reflects the characteristics of the general population would not be biased.
Given the situation above, the population of the study are smart phone customers that use dat in the cell phone company. So, a sample that would better represent this general population would be customers that currently have a smart phone plan, since the average amount of data they use is what the cell pone company wants to ascertain.
Therefore, the group that would best represent a sample of the study population is: C: one thousand of their customers with a current smart phone data plan.
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9 m
Not drawn to scale
Find the volume of the triangular prism.
6 m
6m
Answer:
162 m³Step-by-step explanation:
Volume of the prism is the product of the area of the base and the height of prism.
First, we need to find the area of its triangular base:
A = bh/2 = 9*6/2 = 27 m²Now we can find the volume:
V = 27*6 = 162 m³Area of base
1/2BH1/2(9)(6)9(3)27m²Volume
Area of base×Height27(6)162m³A circle is formed using a ribbon which has a radius of 28 cm. If a square has to be formed using the same ribbon, determine the length of the side of the square formed using the ribbon.
The length of the side of the square is [tex]44 cm[/tex].
What is a Circle?A circle is made up of all points in the same plane that are equidistant from one another. Only the bordering points make up the circle.The following are a few examples of circles in daily life: the bicycle's wheel. Dinner dish. Coin.A circle is a particular type of ellipse in mathematics or geometry where the eccentricity is zero and the two foci are congruent. A circle is also the location of points evenly spaced apart from the center. The radius of a circle is measured from the center to the edge.Determine the length of the side of the square:
Radius of circle[tex]=28.[/tex]
Circumference[tex]=2\pi r[/tex]
[tex]2\pi (28)=176[/tex]
Side of the square[tex]=\frac{176}{4} =44cm.[/tex]
The length of the side of the square is [tex]44 cm[/tex].
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What is the unit rate of change of d with respect to t? (That is, a change of 1 unit in t will correspond to a change of how many units in d?
Answer:2
Step-by-step explanation:
For 17-20, Find the value of each variable.
The unknown angles are as follows;
x = 180 degrees
r = 90 degrees.
How to find the angles of each value in a circle?The angle subtended by an arc of a circle at its centre is twice the angle it subtends anywhere on the circle's circumference.
Therefore,
x = 2(90)
x = 180
Therefore, the sum of angle in a circle is 360 degrees.
Hence, the 2 angles of the arc are the same.
Therefore,
360 - 180 = 2r
2r = 180
divide both sides by 2
2r / 2 = 180 / 2
r = 90 degrees.
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Julia is casting a play with 4 main roles. Six students
have tried out. How many different combinations of 4
students can Julia cast from the 6 students?
Using the combination formula, it is found that Julia can take 15 combinations.
What is the combination formula?[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by:
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
For this problem, 4 students are taken from a set of 6, hence the number of combinations is given as follows:
[tex]C_{6,4} = \frac{6!}{4!2!} = 15[/tex]
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Calling out to anyone who knows this. Seeking assistance!
Answer: someone already answered this check the link out
Step-by-step explanation. https://brainly.com/question/11711784
The data in the table can be entered into a calculator to determine a linear equation of best fit where x represents the number of years with a company and y represents an employee’s salary in dollars.
Based on the data given, the conclusion that can be drawn from the correlation coefficient associated with the linear equation is C. There's a weak negative correlation between the variables.
How to illustrate the information?From the information given, it can be seen that the value of y is increasing with the increase in the value of x.
This implies that the correlation is positive. Also, the change in the values of y with x are scattered a lot.
Therefore, the conclusion that can be drawn from the correlation coefficient associated with the linear equation is that there's a weak negative correlation between the variables
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At what rate of interest will the sum of Rs . 5000 give an interest of Rs . 1450 in 1year ?
Answer:
I = (PTR)/100
1450=(5000*1*R)/100
1450*100=5000R
145000/50000=R
29=R
Step-by-step explanation:
We know,
[tex] S.I. = \rm\cfrac{P*R*T}{100}[/tex]
Given,
Principal P = 5000
Rate R = R(Assume)
Time T = 1
Interest = 1450
Plug:
[tex]1450 = \frac{5000 \times r \times 1}{100} [/tex]
Solve:
[tex]1450 \times 100 = 5000 \times r[/tex]
[tex]145000 \div 5000 = r[/tex]
[tex]r \: = \: 29 \%[/tex]
Rate = 29
Therefore,the rate of Interest is 29%.
PLS help
What is the area of the circle?
A. 50.24 m 2
B. 176 / 7 m 2
C. 100.48 m 2
E. 64 m 2
5. During the season, the Rangers played 25 games. They won 14 of the games.
What fraction and percent of the games did they lose? Show your work in the
space below. Remember to check your solution.
to find the fraction of losses, we need to divide the total amount of losses by the total amount of games played.
if we know that the Rangers won 14 games but they played 25, we can write an equation to find the amount of games lost.
14 + n = 25, where n equals the amount of losses.
now we isolate by moving the 14 to the other side. to do this, we must subtract 14 from both sides, leaving us with n = 11. now we know they lost 11 games.
to find the fraction of lost games, all we need to do is divide 11 by 25 without completing the division. that leaves us with 11/25.
the Rangers lost 11/25 games during the season
hope this helped!!
The area of a park is 2,976 feet squared. If the length of the park is 62 ft, what is the width of the park?
If necessary, round to the nearest whole number.
width =
ft=
Answer:
Area of park = 2976 ft²
Length of park = 62 ft
Width of park = ?
Area of park = length ×width
2976 = 62 × width
width = 2976/62
=48 ft
How do I write a comment on the data following the completion of the scatterplot
ama is four times as old as akua in ten years time, ama will be twice as old as akua find their ages
Answer:
Akua now -- x
Ama now -- 4x
Akua in 10 years ---- x+10
Ama in 10 years ---- 4x+10
4x+10 = 2(x+10)
solve for x
let Ama's age be X and Akua's age be Y
X=4Y.......
X+10=(Y+10)2......
4Y+10=2Y+20
4Y-2Y=20-10
2Y=10 divide both side by 2
2Y/2=10/2
Y=5
X=4x5
X=20
therefore Ama =20years and Akua=5years
hope it helps..
1/3 +1/6 in fraction form
[tex]\Large\texttt{Answer}[/tex]
[tex]\bf{\cfrac{1}{2}}[/tex]
[tex]\overline{\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad}[/tex]
[tex]\Large\texttt{Process}[/tex]
Do you remember that we cannot add fractions when they have unlike denominators? We can onyl add fractions as long as they have the same denominator!
So here's the big idea: fractions must have the same denominator.
If we multiply the first fraction by 2, then both fractions will have the same denominator. *
* Why 2??
- Because:
We need to find the least common multiple of 3 and 6, which is 6. Next, what should 3 be multiplied by to result in 6? That's right, 2.
Also, we can only multiply the denominator by 2 as long as we multiply the numerator by 2!
So that's why we multiply the whole fraction by 2
[tex]\bf{\cfrac{1\times2}{3\times2}+\cfrac{1}{6}}[/tex]
Watch what happens
[tex]\bf{\cfrac{2}{6}+\cfrac{1}{6}}[/tex]
Add the numerators
[tex]\bf{\cfrac{2+1}{6}}[/tex]
[tex]\bf{\cfrac{3}{6}}[/tex]
Simplifying the fractions
[tex]\bf{\cfrac{3\div3}{6\div3}}[/tex]
[tex]\bf{\cfrac{1}{2}}[/tex]
Hope that helped
Answer: 1 / 2
Step-by-step explanation:
Given information
[tex]\frac{1}{3} ~+~\frac{1}{6}[/tex]
Convert the denominator (3, 6) into the same common denominator
Least Common Multiple (LCM) of 3 and 6 = 6
[tex]=\frac{1~*~2}{3~*~2} ~+~\frac{1}{6}[/tex]
[tex]=\frac{2}{6} ~+~\frac{1}{6}[/tex]
Combine two fractions
[tex]=\frac{2~+~1}{6}[/tex]
[tex]=\frac{3}{6}[/tex]
Simplify the fraction by dividing 3 on both numerator and denominator
[tex]=\frac{3~/~3}{6~/~3}[/tex]
[tex]=\Large\boxed{\frac{1}{2} }[/tex]
Hope this helps!! :)
Please let me know if you have any questions
Select the correct responses in the table.
The relationship between two numbers is described below, where xrepresents the first number and y represents the second number.
The square of the first number is equal to the sum of the second number and 16. The difference of 4 times the second number and 1 is equal to
the first number multiplied by 7.
Select the equations that form the system that models this situation. Then, select the solution(s) of the system.
Equations
y² +16=x
x²=y+16
1-4y=7x
(2x)² =y+16
7y-1=4x
4y-1 =7x
(1,15)
(2.-12)
Solutions
(5,9)
(8,48)
(9,3)
The system that can help to model this are
x² = y + 164y - 1 = 7xHow to solve for the system of equationWe have the following equation. Remember that a good understanding of the question is what would help us to write the equation
The condition says:
The square of first number is equal to the sum of the second number and 16:
First number = x. Square of x = x²
second number = y + 16
For the second
The difference of 4 times the second number and 1 is equal to the first number multiplied by 7:
second number is y
4*y - 1= x*7
= 4y - 1 = 7x
Hence we would have the following as our equations
x² = y + 16
4y - 1 = 7x
The solution to the equation when graphed = 5, 9
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A 3 metre long piece of ribbon is cut into
two pieces in the ratio 3:2.
How long is the shorter piece?
Step-by-step explanation:
3 meters = 300 cm
anyway, the ratio tells us that the whole ribbon can be seen as the combination of 3 + 2 = 5 equally long parts.
one such part is then
3 m / 5 = 0.6 m or 60 cm
the shorter piece is 2 of these parts long :
2 × 0.6 = 1.2 m or 120 cm