The Volume of the Cylinder B is gotten as; 720 cm³
What is the Volume of the Cylinder?We are given 2 similar cylinders with;
ratio of heights = a : b
Thus;
ratio of areas = a² : b²
We are given that;
Height of A is 5cm.
Height of B is 10cm.
Thus;
Ratio of heights = 5 : 10 = 1 : 2
Therefore;
ratio of areas = 1² : 2² = 1 : 4
The cross sectional area of B is 4 times the cross sectional area of A. Thus;
Cross sectional area of B = 4 × 18 = 72 cm²
Volume of cylinder = cross section area × height
Volume of cylinder B = 72 × 10 = 720 cm³
The complete question is;
A and B are two cylinders that are mathematically similar.
The area of the cross-section of cylinder A is 18cm².
Height of A is 5cm.
Height of B is 10cm.
Work out the volume of cylinder B
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Using the image, find the midpoint of the line segment. Reduce all fractions and enter using a forward slash (i.e. "/").
14) Adelina is comparing prices for two brands of health and energy bars at the local grocery store.
She wants to get the best price for each bar. Feel Great energy bars are $18 for 12 bars. Super
Power bars cost $21.75 for 15 bars.
a) Write an equation to find the price for each bar of the Feel Great brand.
b) Write an equation to find the price of each bar for the Super Power brand.
c) Which bar should Adelina buy? Explain your reasoning.
The bar which Adelina should buy is super power brand because it cost less than feel great energy bar at $1.45 per bar
Unit priceFeel great energy bars = Total cost / number of bars
= $18 / 12
= $1.5 per bar
Super power brand = Total cost / number of bars
= $21.75 / 15
= $1.45 per bar
Therefore, the bar which Adelina should buy is super power brand because it cost less than feel great energy bar at $1.45 per bar
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What is the sum of the geometric sequence -3, 18, -108,
if there are 8 terms?
Step-by-step explanation:
using gp formula
tn=ar^n-1
which our a which is the first term is = -3
our r which is t2/t1=-6
t8=(-3)(-6)^8-1
=(-3)(-6)^7
=(-3)(-279936)
=839808
Determine the most probable next term in each list of numbers.
Answer:
23. 216
24. 56
25. 52
for 26, 27 i'll try to calculate the answer, sorry
5- Calculate the radius of a circle whose area is equal to the sum of the areas of 3 circles of radii 2cm, 3cm and 4cm
respectively.
the radius of the new circle =5cm
5cm is your answer love
Polynomial functions can model situations that change directions multiple times. what is a situation in which a polynomial model might make sense and why?
A polynomial function exists a function that contains only non-negative integer powers or only positive integer exponents of a variable in an equation like the quadratic equation, cubic equation, etc.
What are the two types of functions?The variety of function kinds can model circumstances in the real world. Properties or key components of functions create more or less suitable models, relating to the circumstances.
Linear: These relationships maintain constant rates of change. The distance traveled by a car moving at a constant speed over time exists linear.
Exponential: Connections that show a percent change exist exponential. The growth of a financial investment accumulating interest over time exists exponential.
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What is the next number in the arithmetic sequence below??
I think it's D but I'm not sure.
20 POINTS
The following are the ages of 15 music teachers in a school district. 24, 26, 27, 29, 29, 32, 37, 40, 40, 41, 45, 52, 56, 56, 58. Notice that the ages are ordered from least to greatest. Make a box-and-whisker plot for the data.
The box and whisker plot is plotted with minimum value 24, maximum value 58, first quartile 29, third quartile 52 and median 40.
Given that, the ages of 15 music teachers in a school district are 24, 26, 27, 29, 29, 32, 37, 40, 40, 41, 45, 52, 56, 56, 58.
A box and whisker plot also called a box plot displays the five-number summary of a set of data. The five-number summary is the minimum, first quartile, median, third quartile, and maximum. In a box plot, we draw a box from the first quartile to the third quartile. A vertical line goes through the box at the median.
Minimum value = 24
Maximum value = 58
First quartile = 29
Third quartile = 52
Median = 40
Therefore, the box and whisker plot is plotted with minimum value 24, maximum value 58, first quartile 29, third quartile 52 and median 40.
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What is the range of the following set?
28, 45, 12, 34, 36, 45, 19, 20
A. 33
B. 57
C. 45
D. 8
Answer: A. 33
Step-by-step explanation:
PLEASE HELP!!! This table shows the profit for a company (in millions of dollars) in different years. The quadratic regression equation that models these data is y=-0.34x^2+4.43x +3.46. Using the quadratic regression equation, what was the predicted profit in year 4?
Answer:
15740000 million dollars in profit in year 4
Step-by-step explanation:
Now since you didn't provide the table, im going to have to assume the years are going to be the X while the Y is going to be profit.
Using the equation you provided y=-0.34x^2+4.43x +3.46, we can simply put 4 as our x value (since x represents years) and we would get 15.74. Now you have to remember to convert it into millions to show the profit so 15.74 times 1,000,000 would be 15740000 million dollars
Suppose that a, b, c, d are positive real numbers such that a/b < c/d . What can you say about the fraction (a+c)/(b+d) ? Is it always, sometimes, or never between the fractions a/b and c/d ? Provide evidence of your claim. (If always or never, give an algebraic proof, otherwise, give two quadruples values of a, b, c, d in which one quadruple has (a+c)/(b+d) between a/b and c/d and the other does not.)
Answer: (a−c)(b−c)>0
Step-by-step explanation:
ab>1 and ac<01. a>0 if c<0 and also b>02. a<0 if c>0 and also b<0
how i did it:
At the vert first, write the inequality as an equation.
Solve the provided equation for one or more values.
Now, display all the values obtained in the number line.
Use open circles to show the excluded values on the number line.
Find the interim.
At the moment, take any random value from the interval and substitute it in the inequality equation to check whether the values reassure the inequality equation.
Intervals that reassure the inequality equation are the solutions of the given inequality equation.
Evaluate f(-3) for f(x) = 2^x
a. 1/8
b. -8
c. 8
d. -6
Answer:
A
Step-by-step explanation:
f(-3) = 2^-3
to get rid of a negative in an exponent, move the whole thing to the denominator.
1/(2^3)
2^3 = 2×2×2
1/(2×2×2)
1/8
Measure of angle TRV?
Answer:
130 degrees
Step-by-step explanation:
We know (x-10)+(2x+10) is 180 degrees.
So first we need to find x. (x-10)+(2x+10)=3x
3x=180
x=60
Angle TRV is 2x+10.
If we input 60 in the place of x, it is 2(60)+10=120+10=130.
The answer is 130 degrees.
40 cm³ of water is poured into an empty measuring cylinder. A stone of mass 129g is put into the cylinder. If the density of the mixture of the stone is 8.6g/cm³, find the new reading of the cylinder.
Step-by-step explanation:
I assume the measuring cylinder measures the cm³ of its normally liquid content.
because for anything else we would need more information about the dimensions of the cylinder.
and so, originally the cylinder shows 40 cm³.
after dropping the stone in, how many cm³ of water is the cylinder then showing ?
let's first mention some facts we are going to use :
water weighs 1 kg (1000 g) per liter.
and 1 liter fits exactly into a cube of
10 cm × 10 cm × 10 cm = 1000 cm³
so, 1 cm³ water weighs exactly 1 g and has therefore a density of 1 g / cm³.
the stone has a density of 8.6 g / cm³, is therefore heavier than water and sinks (and replaces water correspondingly).
how many cm³ does the stone have (and replaces water) ?
well, it has 129 g, and 8.6 g of the stone fill a cm³.
so, it has
129 / 8.6 = 15 cm³
therefore, as these 15 cm³ of stone replace 15 cm³ of water, this is the same as putting 40 + 15 = 55 cm³ of water into the measuring cylinder.
and the cylinder reads now 55 cm³.
FYI : but there is still only 40 cm³ of water in there.
this is actually used to calculate the density of objects (by first weighing and then dropping them into the water to see how much water they replace).
Answer: 55 cm³.
Step-by-step explanation:
[tex]\displaystyle\\m_{stone}=129\ g\ \ \ \ \ \rho_{stone}=8,6\ \frac{g}{cm^3} \ \ \ \ \ V_{water}=40\ cm^3\ \ \ \ \ V=?.\\ \boxed {\rho=\frac{m}{V} }\\V=\frac{m}{\rho} \\V=V_{water}+V_{stone}\\V_{stone}=\frac{m_{stone}}{\rho_{stone}} \\V_{stone}=\frac{129}{8,6}\\V_{stone }=15\ cm^3.\\V=40+15\\V=55\ cm^3.[/tex]
Which of the following is true with respect to the following functions:
The option that is true with regard to the following functions is Option B. "The domain g(x) and h(x) include all real number while the domain of i(x) and h(x) are restricted"
What is the explanation for the above?Lets examine f(x) = 3x + 14Note that this function is indicative of a straight-line. See the attached graph for function 1. Note that it doesn't have any end points. That is, it is Asymptote.
Let us examine h(x) = 3ˣ + 1This represents an exponential graph. Just like the function above it doesn't have any end point. It however has an asymptote:
y = 0
Let us look at F'(x) = Log₃ (x = 1).
This is indicative of logarithm graph. It doesn't have any end but has an asymptote x == 0
Let us take a look at g(x) = X⁴ + 3x² - 14Notice that in the mid point there is an end point given as (0, -14). Thus, it is correct to state that the function in Option B is the only one that exhibits end behavior and as such is restricted.
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Find u special 4 A. 22‾√ 2 2 B. 4 C. 2 D. 2‾√
The value of u in the special triangle is 2√3
How to solve for u in the special triangle?The complete question is added as an attachment
From the attached figure, the value of u can be calculated using the following sine trigonometry ratio
sin(x) = Opposite/Hypotenuse
Where
x = 30
Opposite = u
Hypotenuse = 4√3
Substitute the known values in the above equation
sin(30) = u/4√3
Multiply both sides of the equation by 4√3
u = 4√3 * sin(30)
Evaluate the trigonometry expression sin(30)
u = 4√3 * 1/2
Evaluate the product
u = 2√3
Hence, the value of u in the special triangle is 2√3
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Solve the initial value problem.
ds 36t(91²-7)³, s(1)=1
dt
The solution is s =
Integrate both sides.
[tex]\displaystyle \int \frac{ds}{dt} \, dt = \int 36t (9t^2 - 7)^3 \, dt[/tex]
On the right side, substitute [tex]u=9t^2-7[/tex] and [tex]du=18t\,dt[/tex], so that
[tex]\displaystyle \int 36t (9t^2 - 7)^3 \, dt = 2 \int u^3 \, du = \frac12 u^4 + C = \frac12 (9t^2 - 7)^4 + C[/tex]
Use the initial value to solve for [tex]C[/tex].
[tex]s(1) = 1 \implies 1 = \dfrac12 (9 - 7)^4 + C \implies 1 = 8 + C \implies C=-7[/tex]
Then the particular solution is
[tex]s(t) = \boxed{\dfrac12 (9t^2 - 7)^4 - 7}[/tex]
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.
Answer:
See below
Step-by-step explanation:
Out of 25 games, they won 14
Fraction won = won / total = 14 / 25
Percent won = won /total * 100 % = 14/25 * 100 = .56 * 100 % = 56 %
To find the number of games lost
25-14 = 11
Fraction won = won / total = 11 / 25
Percent won = won /total * 100 % = 11/25 * 100 = .44 * 100 % = 44 %
To check your work, the percent total should be 100
56+44 = 100
What tow numbers have a product of 52 and,when the larger number is divided by the smaller number, a quotient 4?
The numbers are 14.42 and 3.6055.
What is a dividend?It is the whole which is to be divided into different equal parts. For example, if 10 divided by 2 is 5, then 10 is the dividend here, which is divided into two equal parts whereas 2 is the divisor, the quotient is 5 and the remainder is 0.
We can write the system of equations
x*y=52 .......(1)
[tex]\frac{x}{y}[/tex]=4 ........(2)
We can use substitution to solve
From equation (2) we get,
x = 4y .......(3)
now substitute in equation (1)
4y*y = 52
[tex]4y^{2} = 52[/tex]
[tex]y^{2} = \frac{52}{4}[/tex]
[tex]y = \sqrt{13}[/tex]
y = 3.605
We can solve for x = ?
from equation (3)
x = 4y
x = 4*3.605
x = 14.42
Hence, The numbers are 14.42 and 3.6055.
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Please help!! 100 points
The graph shows a system of inequalities.
Which point is a solution to the system
(-1,6)
(0,22)
(2,9)
(8,2)
Answer: (2,9)
Step-by-step explanation:
The point lies in the region that is shaded by both inequalities.
3m
2. What is the volume of this object?
1m
2 m
6 m
4 m
3 m
Answer:
60m3
Step-by-step explanation:
my son got the right anser
Answer:
60m^3
Step-by-step explanation:
The formula for volume of a rectangular prism is height*width*depth
We can see two distinct shapes here
First, we find the volume for the bigger shape
We can see the measurements that pertain to it...
Width is 6m, depth is 3m, and height is also 3m
Multiply those three, you get 54m^3
Now the smaller shape...
1m in width, 2m in height, and 3m in depth
Multiply those, get 6m^3
Add the two shapes together, 54+6=60m^3
‼️‼️‼️‼️HELP‼️‼️‼️‼️‼️
A certain item is available at 7 stores. Three stores sell it for $20, two stores sell it for $15, one store sells it for $13, and one sells it for $16. What is the average (arithmetic mean) of the median price and the mode price?
The average median and mode price is $18. Option C is correct.
Given that certain item is available at 7 stores, three stores sell them for $20, two stores sell them for $15, one store sells them for $13, and one sells them for $16.
The mean is the average of the given numbers and is calculated by dividing the sum of the given numbers by the total number of numbers.
Firstly, we will find the median of the given items by arranging the given numbers in ascending order, we get
13,15,15,16,20,20,20
To find the median use the formula (n+1)/2, where n is the number of values in your dataset.
(7+1)/2=8/2=4
In the ascending order numbers 4th term is 16.
So, median is 16
Mode is the highest repeating term in the set or numbers.
So, here mode is 20
Now, we will calculate the average of median and mode, we get
Average=(median +mode)/2
Average=(16+20)/2
Average=18
Hence, the average (arithmetic mean) of the median price and the mode price where certain item is available at 7 stores, three stores sell it for $20, two stores sell it for $15, one store sells it for $13, and one sells it for $16 is $18.
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What is the slope of the line that passes through
the points (2,
-4) and (5, 2)? Write your
answer in simplest form.
Answer:
2
Step-by-step explanation:
slope : ( The amount y increases , when x is increased by 1 )
slope : { y2 - y1 / x2 - x1 }
slope : y2 = 2
y1 = -4
x2 = 5
x1 = 2
You must minus the values in the formula to find the slope line that passes through the points:
slope : { y2 - y1 / x2 - x1 }
slope : (2) - (-4) / (5) - (2)
=> 2 + 3 / 3
=> 6/3
=> 2
Text explanation:
Difference between both y-coordinates. = 6
Difference between both x-coordinates. = 3
Divide the difference between y and x. =
y/x =2
Which means the slope of the line that passes through the points (2,-4) and (5,2) is 2.
Hope this helps! Sorry it took so long! ⸜(｡˃ ᵕ ˂ )⸝ xx
The slope of the line that passes through the points (2, -4) and (5, 2) is 2.
What is Slope?A slope is also known as the gradient of a line is a number that helps to know both the direction and the steepness of the line.
slope = (y₂-y₁)/(x₂-x₁)
The slope of the line that passes through the points (2, -4) and (5, 2) can be calculated as shown below,
Slope = (y₂-y₁)/(x₂-x₁) = [2 - (-4)] / (5 - 2)= 6/3 = 2
Hence, the slope of the line that passes through the points (2, -4) and (5, 2) is 2.
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pls look at pic before help out confused
Answer:
Option 4
Step-by-step explanation:
By the Pythagorean identity, and the fact we are in the first quadrant,
[tex]\cos \theta=\frac{4}{5}[/tex]
Using the double angle formula for cosine,
[tex]\cos 2\theta=2\cos^{2} \theta-1=2\left(\frac{4}{5} \right)^2 -1=\frac{7}{25}[/tex]
Nick wrote the function p(x) = 17 + 42x – 7x2 in vertex form. His work is below.
p(x) = –7x2 + 42x + 17
p(x) = –7(x2 – 6x) + 17
(StartFraction negative 6 Over 2 EndFraction) squared = 9; p(x) = –7(x2 – 6x + 9) + 17
p(x) = –7(x – 3)2 + 17
When Nick checked his work it did not match the standard form function. Analyze Nick’s work. What was his mistake?
In step 1, he did not put the function in standard form correctly.
In step 2, he should have also factored –7 from the constant term, 17.
In step 3, he did not subtract –7(9) to keep the function equivalent.
In step 4, he did not write the perfect square trinomial correctly as a binomial squared.
Answer:
step 3
Step-by-step explanation:
he should have subtracted 9 to the outside.
whatever you do to the inside you must do to the opposite to the outside
so your final form must be -7(x-3)^2 + 8
if a skip rope is a meter long and its a cm less how much is it pls answer
Answer:
99cm
Step-by-step explanation:
A meter is equal to 100cm
The rope is a metre (m) long but a centimetre (cm) less.
100cm - 1cm = 99cm
3(x - 5) = 2(x - 5) + x
Solve for x please helppp
Answer: No solution
Distribute the parenthesis
3x-15=2x-10+x
Combine like terms
3x-15=3x-10
This answer has no solution for x.
Divide. Write the quotient in lowest terms.
4 2/3 / 7
The quotient in lowest term exists 2/3.
What is an improper fraction?An improper fraction exists as a fraction whose numerator exists equivalent to, larger than, or of equivalent or higher degree than the denominator.
Given the quotient: [tex]$4\frac{2}{3} \div 7[/tex]
Write [tex]$\frac{2}{3}[/tex] in improper fraction
[tex]$4\frac{2}{3}= \frac{14}{3}[/tex]
Dividing throughout by 7 on both sides of the equation, we get
[tex]$4\frac{2}{3} \div 7 = \frac{14}{3}\div 7[/tex]
Change the division sign to multiplication by taking the reciprocal of 7
[tex]$\frac{14}{3}\div 7 = \frac{14}{3} \times \frac{1}{7}[/tex]
Simplifying the above equation, we get
[tex]$\frac{14}{3}\div 7 = \frac{2}{3}[/tex]
Therefore, the quotient in lowest term exists 2/3.
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Slope=
Help me please thanks
Answer:
0
Step-by-step explanation:
In cartesian graphs, the slope or a gradient of a fully horizontal line will always be 0.
where should i place the points!! help please