Which of the following best describes the volume of a cylinder?
A.
the circumference of the circular base multiplied by the height of the cylinder
B.
the area of the circular base multiplied by the height of the cylinder
C.
the sum of the areas of the two circular bases multiplied by the height of the cylinder
D.
the area of the lateral face multiplied by the radius of the circular base
The correct option that describes the volume of a cylinder is B: the area of the circular base multiplied by the height of the cylinder, represented by the formula \(V = \pi r^2 h\).
The volume of a cylinder is best described by option B, which states it is the area of the circular base multiplied by the height of the cylinder. The area of the base, which is a circle, is calculated using the formula \\(\pi r^2\), where \(r\) represents the radius of the circle. To find the volume, this area is then multiplied by the height \(h\) of the cylinder, giving the formula for the volume \(V = \pi r^2 h\).
PLEEEAAASE HEEEELP
what is the cube root of -729a^9 b^6
-9a3b2
-9a2b3
*Will give brainliest. $1,500 is invested into an account with an interest rate of 6.75%. How many years will it take for the account to reach $7,300? Round to the nearest hundredth
Using the compound interest formula, it will take approximately 24.53 years for an initial investment of $1,500 to grow to $7,300 at an annual interest rate of 6.75%. This is calculated by solving for t in the rearranged compound interest formula.
To determine how many years it will take for your $1,500 investment to reach $7,300 with an interest rate of 6.75% compounded annually, we use the formula for compound interest:
[tex]A = P(1 + r/n)^{(nt)[/tex]
Where:
A is the amount of money accumulated after n years, including interest.P is the principal amount (the initial amount of money, $1,500).r is the annual interest rate (decimal, so 6.75% becomes 0.0675).n is the number of times that interest is compounded per year (since it's annual, n = 1).t is the number of years.We rearrange the formula to solve for t:
t = (log(A/P) / log(1 + r/n)) / n
Plug in the known values:
t = (log(7300/1500) / log(1 + 0.0675)) / 1
Calculate the logarithms:
t ≈ (log(4.8667) / log(1.0675))
t ≈ (0.6887 / 0.0281)
t ≈ 24.53
It will take approximately 24.53 years for the investment to grow to $7,300.
Which of the following expressions is this one equivalent to?
(3x^3+15x^2+17x+3)/x+5
A. x^3-2x+5+(7/x+5)
B. 3x-17+(88/x+5)
C. 3x^2+17-(82/x+5)
D. 3x^2-5x-8-(37/x+5)
...?
Answer:
option (c) is correct,
[tex]3x^2+17-\frac{82}{x+5}[/tex] is the equivalent fraction to the given expression [tex]\frac{3x^3+15x^2+17x+3}{x+5}[/tex]
Step-by-step explanation:
Given expression , [tex]\frac{3x^3+15x^2+17x+3}{x+5}[/tex]
We have to choose an equivalent fraction from the given options.
Consider expression (c) ,
[tex]3x^2+17-\frac{82}{x+5}[/tex]
Taking LCM , Multiply [tex]3x^2+17[/tex] by (x+5) , we get,
[tex]\frac{3x^2(x+5)+17(x+5)-82}{x+5}[/tex]
On solving , we get,
[tex]\frac{3x^3+15x^2+17x+85-82}{x+5}[/tex]
On simplifying, we get,
[tex]\frac{3x^3+15x^2+17x+3}{x+5}[/tex]
Which is equal to the given expression.
Thus, option (c) is correct,
[tex]3x^2+17-\frac{82}{x+5}[/tex] is the equivalent fraction to the given expression [tex]\frac{3x^3+15x^2+17x+3}{x+5}[/tex]
Harriet is comparing the costs of calling cards. To use card A, the cost is $1.00 to connect and then $0.04 per minute. To use card B, it costs $0.65 to connect and then $0.06 per minute. For what number of minutes does it cost the same amount to use each card for a single call?
Answer: There are 17.5 minutes for which it costs the same amount to use each card for a single call.
Step-by-step explanation:
Let the number of minutes be x
To use card A, the cost is $1.00 to connect and then $0.04 per minute.
So, our expression becomes,
[tex]1+0.04x[/tex]
To use card B, the cost is $0.65 to connect and then $0.06 per minute.
So, our expression becomes,
[tex]0.65+0.06x[/tex]
According to question, if it cost the same amount to use each card for a single call, then it will be
[tex]1+0.04x=0.65+0.06x\\\\1-0.65=0.06x-0.04x\\\\0.35=0.02x\\\\\frac{0.35}{0.02}=x\\\\17.5=x[/tex]
Hence, there are 17.5 minutes for which it costs the same amount to use each card for a single call.
289 + 456 x 789 / 489 - 746 + 2457 x 3453 / 3646 =
Solve for x. x - 8 = -10 x = 2 x = -2 x = 18 x = -18
Answer:
x = -2
Step-by-step explanation:
1. Determine which ratio forms a proportion with 9/5 by finding a common multiplier.
a. 54/30 b. 45/50 c. 45/40 d. 90/20 2. Determine which ratio forms a proportion with 15/8 by using cross products.
a. 25/16 b. 30/12 c. 60/32 d. 75/32 3. Solve 3/27 = w/54 a. 2 b. 6 c. 9 d. 18 4. In a survey, 3 out of 10 people names blue as their favorite color. 1 out of 5 named red. If 1,200 people were included in the survey, how many named blue or red as their favorite color?
a. 700 people b. 800 people c. 600 people d. 400 people 5.Solve the proportion using cross products. Round to the nearest hundredth if necessary.
12 miles/27 hours = 4 miles/ h hours a. 28 b. 12 c. 9 d. 18 6. LA is about 385 miles from San F. How far apart would the cities be on the map with a scale of 1 inch = 15 miles. If necessary, round to the nearest hundredth.
a. 26.33 in. b. 25.67 in. c. 24.33 in. d. 27.50 in
Final answer:
To find the ratio that forms a proportion with 9/5, we can find a common multiplier for each option and check if the resulting ratios are equal to 9/5.
Explanation:
If we want to determine which ratio forms a proportion with 9/5, we can find a common multiplier. We can multiply both the numerator and denominator of each ratio by the same number and check if the resulting ratios are equal to 9/5.
Let's check each option:
a. 54/30: multiplying by 6 gives us 54/30 = 9/5, so this ratio forms a proportion with 9/5.b. 45/50: multiplying by 10 gives us 450/500 = 9/10, so this ratio does not form a proportion with 9/5.c. 45/40: multiplying by 8 gives us 360/320 = 9/8, so this ratio does not form a proportion with 9/5.d. 90/20: multiplying by 2 gives us 180/40 = 9/2, so this ratio does not form a proportion with 9/5.Therefore, the ratio 54/30 (option a) forms a proportion with 9/5.
Which of the following options best describes an algebraic fraction?
Select All That Apply.
1.) Common denominators
2.) a variable in the numerator
3.) a variable in the denominator
4.) a variable with an exponent.
I already know 4 for sure is one...
Answer:
Option 1,2 and 3.
Step-by-step explanation:
An algebraic expression is such a mathematical representation of variables
Algebra is relation with variables a,y,z and so on
So, Option 2 is correct that is it will contain variable in numerator.
Similarly, Option 3 is correct that is it will contain variable in denominator.
Option 4 is incorrect because if it contains variable with an exponent then it will not be algebraic it will become exponent function.
Option 1 is correct because it may have common denominator an algebraic fraction will have common denominator.
What does this mean:
(25ab^3)^1/3 divided by (ab)^-1/2
Please help! I'm really confused.
Angle A = 8x - 2, angle B = 2x - 8, and angle C = 94 - 4x. List the sides of triangle ABC in order from shortest to longest.
Options: (all are line segments)
o AC, AB, BC
o AC, BC, AB
o AB, AC, BC
o AC, BC, AB
Answer:
First option is correct.
Step-by-step explanation:
In triangle ABC, [tex]\angle A=8x-2[/tex], [tex]\angle B=2x-8[/tex] and [tex]\angle C=94-4x[/tex].
According to angle sum property of a triangle, the sum of interior angles of a triangle is 180 degree.
[tex]\angle A+\angle B+\angle C=180^{\circ}[/tex]
[tex]8x-2+2x-8+94-4x=180[/tex]
[tex]6x+84=180[/tex]
[tex]6x=96[/tex]
Divide both sides by 6.
[tex]x=16[/tex]
Therefore the value of x is 16. The measure of angles are
[tex]\angle A=8(16)-2=126[/tex]
[tex]\angle B=2(16)-8=24[/tex]
[tex]\angle C=94-4(16)=30[/tex]
The opposite angle of shortest side is always smallest interior angle. Similarly the opposite angle of longest side is always largest interior angle.
[tex]\angle B<\angle C<\angle A[/tex]
[tex]AC<AB<BC[/tex]
Therefore option 1 is correct.
defined as a set of points equidistant from a given point
Answer:
C) circle
Step-by-step explanation:
y+4=-2(x-1) slope intercept form
The given equation in slope-intercept form is y = -2x - 2.
What is Slope?Slope of a line is defined as the change in the value of y-coordinate with respect to the x-coordinate value. It is usually denoted by 'm'.
It can also be defined as the tangent of the angle that the given line is making with the X-axis.
That is m = tan θ, where θ is the angle that line is making with the X-axis.
The equation of a line in slope-intercept form is given by,
y = mx + c
Here, c is called the y-intercept, the value of which is the value of the y-coordinate when the line touches the Y-axis.
Now,
y + 4 = -2 (x - 1)
y + 4 = -2x + 2
y = -2x + 2 - 4
y = -2x - 2
The equation of the line in slope-intercept form is y = -2x - 2.
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Match the definition with the terms.
1. a portion of a large group
2. choosing a sample so that every member has an equal chance of being chosen
3. choosing a sample from people who are under 15 years old
4. using the responses of a small group to make conclusions about the large group.
random sample
sample
biased sample
estimating from a sample
When you sign up for a movie service, you get three free months of movies. Then you are charged $15 per month to rent movies. If you pay $90, how many months of use do you get?
Answer:
9 months!!
Step-by-step explanation:
At the city museum child admission is $5.70 and the adult admission is $9.60 on Thursday,186 ticket were sold for a total sales of $1399.50. How many child tickets were sold that day?
1) Is it possible to have a function f defined on [ 2 , 4 ] and meets the given conditions?
f is continuous on [ 2 , 4 ), minimum value f(4)=2, and no maximum value.
2) Is it possible to have a function f defined on [ 4 , 5 ] and meets the given conditions?
f is continuous on [ 4 , 5 ], takes on no rational values.
3) Is it possible to have a function f defined on [ 2 , 5 ] and meets the given conditions?
f is continuous on [ 2 ,5 ] and the range of f is an unbounded interval.
The possibility statements are:
PossiblePossibleNot possibleStatement 1
The function is defined on [2.4]
The above means that, the minimum is 2, and the maximum is 4
However, since the function is continuous at [2,4), the close bracket ")" means that the function extends indefinitely i.e. no maximum.
Hence, this statement is possible
Statement 2
The function is defined on [4.5]
The above means that, the minimum is 4, and the maximum is 5
However, since the function is continuous at [4,5], the close brackets "[" and "]" mean that the function have finite values
Hence, this statement is possible
Statement 3
The function is defined on [2,5]
The above means that, the minimum is 2, and the maximum is 5
However, since the function is continuous at [2,5], the close brackets "[" and "]" mean that the function have finite values and it has bounded intervals
Hence, this statement is not possible
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What are the sine, cosine, and tangent of Θ = 3 pi over 4 radians?
sin Θ = square root 2 over 2; cos Θ = negative square root 2 over 2; tan Θ = -1
sin Θ = negative square root 2 over 2; cos Θ = square root 2 over 2; tan Θ = 1
sin Θ = square root 2 over 2; cos Θ = negative square root 2 over 2; tan Θ = 1
sin Θ = negative square root 2 over 2; cos Θ = square root 2 over 2; tan Θ = -1
Describe the angle formed by the hands of a clock at 3:00 in the term of degrees and radians ...?
Answer:
90 degree and [tex]\frac{pi}{180}[/tex] radians.
Step-by-step explanation:
Given : Angle formed by the hands of a clock at 3:00
To find : Write in term of degrees and radians ...
Solution : We have given that a clock show the time 3 :00
We know that at 3 : 00 clock show hour hand at 3 and minute hand at 12.
Angle formed by the minute hand at 12 and hour hand at 3 is 90 degree.
90 degree = [tex]\frac{pi}{180}[/tex] radian.
Therefore, 90 degree and [tex]\frac{pi}{180}[/tex]radians.
Which of the following expressions is a polynomial?
A. f(x)=4/x-11x^2
B. 4x^3-13x^2+5x
C. 5x^3+7x^4-1/2x
D. -3x^4+8x^2-2√x+1
...?
The answer is c.
F(x)=5x^3+7x^4-1/2x
What is the sum of 58 76?
"The sum of 58 and 76 is 134.
To find the sum of two numbers, one simply needs to add them together. In this case, the numbers are 58 and 76.
The addition can be performed as follows:
[tex]\[ 58 + 76 = 134 \][/tex]
Thus, the correct answer to the question ""What is the sum of 58 and 76?"" is 134."
The value of a van depreciates at the rate of 20% per year. Gary buys a new van for £27500. After n years the value of the van is £11264. Find the value of n.
Answer:
n = 3years
Step-by-step explanation:
If Gary buys a van £27500 and sell the van at a value of the £11264 after n years, depreciation will give us;
£27500-£11264 = £16236
If the van depreciates by 20% each year, yearly depreciation will be;
20% of £27500 = £5500
To get the total number of years n it takes the van to depreciate to £11264 will give total depreciation amount/yearly depreciation amount which gives;
£16236/£5500 = 2.9years
This means that the van has depreciate from £27500 to £11264 after 3years
5/7 x 21/25 what is the answer to this???!!?!?!!!?
The formula D = rt gives the distance traveled in time T at rate R. A bicyclist rides at a constant rate of 15 miles per hour. How many miles will she travel in 3.5 hours?
A. 52.5
B. 4.3
C. 23.3
D. 18.5
aidan makes 12 bracelets on Monday. He makes 8 more bracelets each day from tuesday through thursday. how many bracelets does adian make on friday
Aidan makes 8 bracelets each day from Tuesday to Thursday, resulting in 24 bracelets for those three days. Adding this to the 12 he made on Monday gives us 36 bracelets up to Thursday. Aidan continues the same pattern on Friday, making 8 more bracelets, totaling 44 bracelets.
Explanation:To determine how many bracelets Aidan makes on Friday, we need to calculate the total number he makes from Tuesday through Thursday and then add it to the number of bracelets he already made on Monday. He starts with 12 bracelets on Monday and makes 8 more each day from Tuesday to Thursday. Calculating the bracelets made from Tuesday through Thursday involves multiplication of the daily bracelet count by the number of days.
Aidan makes 8 bracelets each day for three days, which is calculated as follows:
8 bracelets/day × 3 days = 24 braceletsWe then add this to the initial 12 bracelets made on Monday:
12 bracelets + 24 bracelets = 36 bracelets in total from Monday to ThursdaySince the pattern of bracelet making doesn’t specify any change on Friday, we assume Aidan continues to make 8 bracelets on Friday as well. So, he makes 8 bracelets on Friday.
The total number of bracelets Aidan makes up to Friday is the sum of bracelets made from Monday through Thursday plus the bracelets made on Friday:
36 bracelets (Monday - Thursday) + 8 bracelets (Friday) = 44 bracelets totalFinal answer:
Aidan makes 44 bracelets on Friday.
Explanation:
To find out how many bracelets Aidan makes on Friday, we need to calculate the total number of bracelets he makes from Monday through Thursday. On Monday, Aidan makes 12 bracelets. From Tuesday through Thursday, he makes 8 more bracelets each day. So the number of bracelets he makes on Tuesday is 12 + 8, on Wednesday is 12 + 8 + 8, and on Thursday is 12 + 8 + 8 + 8.
Now, to calculate the number of bracelets he makes on Friday, we need to add 8 to the total number of bracelets he made on Thursday. So the total number of bracelets he makes on Friday is 12 + 8 + 8 + 8 + 8.
Therefore, Aidan makes 12 + 8 + 8 + 8 + 8 = 44 bracelets on Friday.
Explain how you would know log3100 is between 4 and 5 without the use of a calculator.
...?
I have three numbers. The biggest one is twice the middle one, and the biggest one plus the middle one is four times the smallest one. The smallest one plus the middle one is two less than the biggest one. What are the numbers? ...?
Let
x------> the biggest number
y------> the middle number
z------> the smallest number
we know that
[tex]x=2y[/tex] -------> equation [tex]1[/tex]
[tex]x+y=4z[/tex] -------> equation [tex]2[/tex]
[tex]z+y=x-2[/tex] -------> equation [tex]3[/tex]
substitute equation [tex]1[/tex] in equation [tex]2[/tex] and equation [tex]3[/tex]
[tex][2y]+y=4z[/tex] ------> [tex]3y=4z[/tex] ------> equation [tex]4[/tex]
[tex]z+y=[2y]-2[/tex] ----> [tex]z+2=y[/tex] ------> equation [tex]5[/tex]
using a graph tool-----> to resolve the system of equations
see the attached figure
the solution is the point [tex](6,8)[/tex]
[tex]z=6\\y=8[/tex]
Find the value of x
[tex]x=2y[/tex]
[tex]x=2*8=16[/tex]
therefore
the answer is
the biggest number is [tex]16[/tex]
the the middle number is [tex]8[/tex]
the smallest number is [tex]6[/tex]
Why Are Mr. and Mrs. Number so Happy?
Mr. and Mrs. Number are so happy because they are both prime numbers, which are natural numbers greater than 1 that have no positive divisors other than 1 and themselves.
For example:
Mr. Number could be 2, as it is divisible only by 1 and 2.
Mrs. Number could be 3, as it is divisible only by 1 and 3.
Prime numbers have unique properties and are considered special in mathematics. They play a fundamental role in number theory and various mathematical algorithms. Additionally, prime numbers are essential in cryptography, ensuring secure communication and data encryption.
So, Mr. and Mrs. Number are happy because they share the special quality of being prime numbers, making them quite unique and valuable in the mathematics.
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32/50 in simplest form