[tex]\bf \textit{volume of a cone}\\\\ V=\cfrac{\pi r^2 h}{3}~~ \begin{cases} r=radius\\ h=height\\[-0.5em] \hrulefill\\ V=457.17\\ h = 15 \end{cases}\implies 457.17=\cfrac{\pi r^2(15)}{3}\implies 457.17=5\pi r^2 \\\\\\ \cfrac{457.17}{5\pi }=r^2\implies \sqrt{\cfrac{457.17}{5\pi }}=r\implies 5.39 \approx r~\hfill \boxed{\stackrel{diameter = 2r}{2(5.39) = 10.78}}[/tex]
In a country where prices are rising quickly, bread that now costs $1.39 will cost 2.4 times as much next year. How much will the bread cost next year? (Round your answer to the nearest cent.)
Answer:
$3.34
Step-by-step explanation:
$1.39 x 2.4 = $3.336
Answer:
next year the cost of bread will rise to $3.34
If y varies directly with x when y=16 and x=2.1, what is the value of x when y=4
Rounded to the nearest tenth
Answer: 0.53
Step-by-step explanation:
From variation ,
y ∞ x ------------------------------------------------1
y = kx , where k is called the constants of proportionality and must be calculated first before proceeding.
substitute for the values in equation 2 ,below
y = kx -----------------------------------------------2
16 = k2.1
k = 16/2.1
Now to find the value of x, make x the subject of the formula in equation 2
x = y/k
= 4/ 16/2.1
= 4 ÷ 16/2.1
= 4 x 2.1/16
= 2.1/4
= 0.525
≅ 0.53
Idk this is supper hard
Answer:
The equation of the line is: y = x + 4
Step-by-step explanation:
When we are given two points passing through a line, we can find the equation of the line by using two - point form.
Two - point form: [tex]$ \frac{\textbf{y - y}_\textbf{1}}{\textbf{y}_{\textbf{2}} \textbf{-} \textbf{y}_{\textbf{1}}} = \frac{{\textbf{x - x}_\textbf{1}}}{\textbf{x}_{\textbf{2}} \textbf{-} \textbf{x}_{\textbf{1}} }$[/tex]
where [tex]$ (x_1, y_1) \hspace{3mm} \& \hspace{3mm} (x_2, y_2) $[/tex] are the points passing through the line.
Here, let us take two points (can be any two):
[tex]$(x _1, y_1) = (1, 5) $[/tex] and
[tex]$ (x_2, y_2) = (5, 9) $[/tex]
Therefore, we have:
[tex]$ \frac{y - 5}{9 - 5} = \frac{x - 1}{5 - 1} $[/tex]
[tex]$ \iff \frac{y - 5}{4} = \frac{x - 1}{4} $[/tex]
[tex]$ \iff y - 5 = x - 1 $[/tex]
[tex]$ \implies y = x - 1 + 5 $[/tex]
[tex]$ \implies y = \textbf{x + 4} $[/tex] which is the required answer.
Help ASAP
SOLVE EACH EQUATION
7) 7(3 - 5k) - 4 = -263
8) 6(-5 - 5n) = 90
9) -6(8 + 2b) = -120
10) -168 = 7(8p - 8)
Answer:
7)k=-7.02
8)n=-4
9)b=-14
10)-2=p
A square is cut out of a circle whose diameter is approximately 14 feet. What is the approximate area (shaded region) of the remaining portion of the circle in square feet?
A.25 feet
B.40 feet
C.50 feet
D.80 feet
Answer:)
C. 50 feet^2
Step-by-step explanation:
Area of circle
A = Pi r^2 (radius is 7)
A= 153.86
Area of square
A = a^2
A= 10^2
A=100
From circle area substract square area
153.86 - 100 = 53.86
1). 21 is what percent of 168. 4) what number is 62 percent of 50
2). What is 4 percent of 150. 5) 15 percent of 15 is what
3) 1 percent of 500 is what number 6) 40 percent of 25 is what number
1) 21 is 12.50% of 168.
2) 4% of 150 is 6.
3) 1% of 500 is 5.
4) 62% of 50 is 31.
5) 15% of 15 is 2.25
6) 40 percent of 25 is 10.
Step-by-step explanation:
1). 21 is what percent of 168.
Let,
x be the percent.
Therefore,
x% of 168 = 21
[tex]\frac{x}{100}*168=21[/tex]
[tex]1.68x=21[/tex]
Dividing both sides by 1.68
[tex]\frac{1.68x}{1.68}=\frac{21}{1.68}\\x=12.50[/tex]
21 is 12.50% of 168.
2). What is 4 percent of 150.
4% of 150 = [tex]\frac{4}{100}*150[/tex]
4% of 150 = [tex]\frac{600}{100} = 6[/tex]
4% of 150 is 6.
3) 1 percent of 500 is what number
1% of 500 = [tex]\frac{1}{100}*500[/tex]
1% of 500 is 5.
4) what number is 62 percent of 50
62% of 50 = [tex]\frac{62}{100}*50[/tex]
62% of 50 = [tex]0.62*50=31[/tex]
62% of 50 is 31.
5) 15 percent of 15 is what
15% of 15 = [tex]\frac{15}{100}*15[/tex]
15% of 15 = [tex]\frac{225}{100}=2.25[/tex]
15% of 15 is 2.25
6) 40 percent of 25 is what number
40% of 25 = [tex]\frac{40}{100}*25[/tex]
40% of 25 = [tex]\frac{1000}{100}=10[/tex]
40 percent of 25 is 10.
Keywords: percentage
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What are fractions greater than 1/2 but less than one
We know that 1/2 as a decimal is 0.5. Any decimal/fraction between 0.5 and 1 will be correct. For Example, 0.75 is greater than 0.5 but less then 1. 0.75 as a fraction is 3/4.
Best of Luck!
2 Points
Solve the equation 3x + 5y = 16 for y,
Answer:
y=16-3x/5
Step-by-step explanation:
I'm adding a pic of my solution. i hope you find it helpful.
The solution to the equation 3x + 5y = 16 for y is y = (16 - 3x) / 5. This is achieved by isolating y on one side of the equation.
Explanation:To solve the equation 3x + 5y = 16 for y, you first need to isolate y on one side of the equation. This can be done in the following steps:
Subtract 3x from both sides of the equation, which gives you 5y = 16 - 3x.Next, divide every term of the equation by 5 to solve for y, which gives you y = (16 - 3x)/5.So, the solution for y in terms of x is y = (16 - 3x)/5.
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please fill in the blanks for me i really need help strugaliing the formula is ..... y=mx+b
The complete function is: [tex]y = x+55[/tex]
Step-by-step explanation:
the given table represents a linear function
The linear function is represented by:
[tex]y = mx+b[/tex]
Here
m is the slope of function and b is the y-intercept
In this case, m will be calculated as:
[tex]m= \frac{Change\ in\ y}{Change\ in\ x}\\= \frac{61-60}{6-5}\\= 1[/tex]
Hence the slope is 1.
Putting in the equation
[tex]y = x+ b[/tex]
To find the value of b, we will put any pair of x and y in the equation
[tex]61 = 5 + b\\b = 60-5\\b = 55[/tex]
Hence,
The final equation for linear function is:
[tex]y = x + 55[/tex]
Keywords: Linear function, equation
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Sacha spent
of his time in study hall on science homework and
of his time on math homework. Which expression
can be used to determine how much more of the time in study hall Sacha spent on math than on science?
O 0.58 -0.28
O 0.058 -0.028
0.625 - 0.25
0.625 -0.025
Final answer:
The expression to determine how much more time Sacha spent on math than on science is y - x.
Explanation:
To determine how much more time Sacha spent on math than on science, we need to find the difference between the time spent on math and science. Let's say Sacha spent x amount of time on science and y amount of time on math. The expression that represents the difference between the time spent on math and science is y - x.
Therefore, the correct expression to determine how much more time Sacha spent on math than on science is y - x.
Simplify 12x to the power of 7 y to the power of 3 divided by 6x to the power of 3 y
Answer:
2x⁴y²
Step-by-step explanation:
The question gives us the expression;
12x⁷y³ ÷ 6x³y
We are supposed to simplify the expression;
First we could divide the digits;
12 ÷ 6 = 2
Then we divide the like terms;
x⁷ ÷ x³
This means;
[tex]=\frac{x*x*x*x*x*x*x }{x*x*x}[/tex]
[tex]= x*x*x*x[/tex]
[tex]=x^4[/tex]
y³ ÷ y
That is;
[tex]=\frac{y*y*y}{y}[/tex]
[tex]=y*y[/tex]
[tex]=y^2[/tex]
Therefore, the simplified expression will be 2x⁴y²
Estimate, then find the difference and write in simplest form 4 1/2-3 4/5
Answer:
7/10
Step-by-step explanation:
4 1/2=9/2
3 4/5=19/5
--------------
9/2-19/5=45/10-38/10=7/10
Brainliest!!!!!! Plz help !!!!
Using data for population in the District of Columbia, write an exponential model of the form a ∙ bx to estimate this population in the years after 2005.
A.) a ∙ bx = (550,521)(0.993)x
B.) a ∙ bx = (550,521)(0.990)x
C.) a ∙ bx = (550,521)(0.992)x
D.) a ∙ bx = (550,521)(0.991)x
Answer:
Its C Hope dis helps!!!
Step-by-step explanation:
Without the actual data, we cannot definitively decide the correct exponential model for the population of the District of Columbia. The options provided all share the same initial quantity, with different growth factors. To pick one, we would need data on the annual population growth or decline.
Explanation:The question is asking us to choose an exponential model of the form a ∙ bx that best represents the population of the District of Columbia for years after 2005. As we are not provided actual data on the population growth or decline, we can't definitively choose between the options. In this kind of model, a is the initial quantity (population in the year 2005), and b is the growth factor per the time period (in this case: annually). In all options provided we have the same initial quantity '550,521'. The difference is in the growth factors .993, .990, .992, and .991. Without the actual data, we cannot definitively pick one. However, if the population is declining each year, you'd expect the growth factor to be less than 1. In case if it's growing you'd expect it to be more than 1.
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The sum of two numbers is 30 and their difference is 12 find the two numbers
Answer:
The two numbers are 21 and 9.
Step-by-step explanation:
x+y=30
x-y=12
-------------
2x=42
x=42/2
x=21
21+y=30
y=30-21=9
Write -2x = 5y + 9 in general form Ax + By + C = 0.
О — 2х = 5у +9
О 2x — Бу — 9 = 0
О 2х + 5у + 9 = 0
О 2x — Бу + 9 = 0
The football team had its photo taken there are 3 rows of 8 players each the fourth row has 6 players how many players are in the team photo?
Answer:
30 players.
Step-by-step explanation:
3 rows of 8 = 3 x 8 = 24. Plus an additional 6 players in the fourth row. 24 + 6 = 30.
The team photo consists of 30 players: 24 in the three full rows, each with 8 players, and 6 more players in the fourth row.
To find the total number of players in the team photo, you can simply add the number of players in each row together. In this case, there are three rows of 8 players each and a fourth row with 6 players.
First, calculate the total number of players in the three full rows, where each row has 8 players:
3 rows x 8 players/row = 24 players
Now, add the players from the fourth row:
24 players (from the full rows) + 6 players (from the fourth row) = 30 players
So, there are 30 players in the team photo.
In summary, the team photo includes 30 players, with 24 players in the three full rows of 8 each and an additional 6 players in the fourth row.
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6x-5y=15. X=y+3. X= ?y=?
Answer:
x=0
y=-3
6x-5y=15
x=y+3
Replace x with y+3
6(y+3)-5y=15
Distribute
6y+18-5y=15
y= -3
x=0
The solution to the system of equations is x = 0 and y = -3.
To solve the system of equations:
1. 6x - 5y = 15
2. x = y + 3
We can substitute equation 2 into equation 1 to find the value of x, and then use that value to find the value of y.
Substituting equation 2 into equation 1:
[tex]\[6(y + 3) - 5y = 15\]\[6y + 18 - 5y = 15\]\[y + 18 = 15\]\[y = 15 - 18\]\[y = -3\]\\[/tex]
Now that we have found y, we can substitute this value back into equation 2 to find x:
[tex]\[x = (-3) + 3\]\[x = 0\][/tex]
So, the solution to the system of equations is x = 0 and y = -3.
Complete Question:
Solve the system of equations 6x-5y=15
x=y+3
x=
Y=
5x=7y, X+7Y=21 how do u solve this by elemination
Answer:
The values are [tex]x=\frac{7}{2}[/tex] and [tex]y=\frac{5}{2}[/tex]
The solution is ([tex]\frac{7}{2}[/tex],[tex]\frac{5}{2}[/tex])
Step-by-step explanation:
Given equations are [tex]5x=7y\hfill (1)[/tex] and
[tex]x+7y=21\hfill (2)[/tex]
To solve the given equations by elimination method:
Equation (1) can be written as [tex]5x-7y=0\hfill (3)[/tex] and
Now multiply the equation (2) into 5 we get
[tex]5x+35y=105\hfill (4)[/tex]
Subtracting equations (3) and (4) we get
[tex]5x-7y=0[/tex]
[tex]5x+35y=105[/tex]
_________________
-42y=-105
[tex]y=\frac{105}{42}[/tex]
Therefore [tex]y=\frac{5}{2}[/tex]
Substitute the value [tex]y=\frac{5}{2}[/tex] in equation (1) we get
[tex]5x=7\times \frac{5}{2}[/tex]
[tex]5x=\frac{35}{2}[/tex]
[tex]x=\frac{35}{2\times 5}[/tex]
[tex]x=\frac{7}{2}[/tex]
Therefore [tex]x=\frac{7}{2}[/tex] and [tex]y=\frac{5}{2}[/tex]
The solution is ([tex]\frac{7}{2}[/tex],[tex]\frac{5}{2}[/tex])
19 is 25 less than the product of 9 and a number numerical expression
19 = 9x - 25 is the numerical expression for 19 is 25 less than the product of 9 and a number
Solution:
Given statement:
19 is 25 less than the product of 9 and a number
We have to write the numerical expression for given statement
Let the number be "x"
From given information,
19 is 25 less than the product of 9 and a number
"product" means multiplication
And "less than" means subtracted or reduced by
Therefore,
Product of 9 and a number is translated as [tex]9 \times x[/tex]
Therefore, given statement is written numerically as:
19 = 25 less than the product of 9 and a number
[tex]19 = (9 \times x) - 25[/tex]
[tex]19=9x-25[/tex]
Thus the expression is found
What is the percent of 47.382
Answer: 0.47382
Step-by-step explanation:
The percent of 47.382 is dividing the figure by 100%
47.382/100= 0.47382
The picture below illustrates a special type of conic section called
hyperbola. Which of the following offers the best description of hows
hyperbola is formed?
Answer:
A
Step-by-step explanation:
The picture below illustrates a hyperbola.
The intersecting plane does not pass through the vertex of a right circular cone (the vertex of the cone is the point where two nappes meet).
As you can see from the diagram, the plane intersects both nappes of a right circular cone.
Hence, correct option is option A: The plane does not pass through the vertex and intersects both nappes of a right circular cone.
What is the x-intercept of
x + 9y = 1
Mr. Kellen had an advertising budget of $50,000 to spend on advertisements for his company.
• He advertised in 7 different magazines.
• The least expensive advertisement cost $4,200.
• The most expensive advertisement cost $5,100.
Which value is a reasonable estimate of the amount of money remaining in the budget after Mr. Kellen paid for the 7 advertisements
Final answer:
To estimate the remaining advertisement budget, calculate the total possible maximum expense and subtract it from the initial budget, resulting in an approximate remaining amount of $14,300.
Explanation:
Mr. Kellen's starting budget for advertisements was $50,000. If I assume that each of the 7 advertisements costs about the maximum amount which is $5,100, the estimated total cost would be 7 times $5,100, which equals $35,700. So, a reasonable estimate of the amount of money remaining after paying for the advertisements is $50,000 - $35,700 = $14,300.
Which is the best estimate of the difference between 6 7/8 and 2 1/8
Answer: 19 /4 or 4 3/4
Step-by-step explanation:
Turn 67/8 into a improper fraction, which is 55/8
Next, also convert 21/8 into an improper fraction, which is 17/8
Next, subtract 17/8 from 55/8 and you should get 38/8
Last, simplify 38/8 to do so divide 38/8 by 4/4 and you should get 19/4 and if you want it's optional to turn it into a mixed number.
The estimate of the difference between the two fractions is: 4 3/4 = 4.75 ≈ 5.
What is the Difference between Fractions?To find the difference of two fractions means that subtract one from the other.
Thus:
Difference between 6 7/8 and 2 1/8 = 6 7/8 - 2 1/8
Change the mixed fraction to improper fractions
55/8 - 17/8
= (55 - 170/8
= 38/8 = 19/4
= 4 3/4 = 4.75 ≈ 5.
Therefore, the estimate of the difference between the two fractions is: 4 3/4 = 4.75 ≈ 5.
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Write -3/4 as either a terminating or repeating decimal
Answer:
Step-by-step explanation:
-3/4 = -0.75 (its terminating)
Answer:
Step-by-step explanation:
-3/4 = -0.75. It is terminating decimal
What is the true solution to the equation below
Answer:
C I think
Step-by-step explanation:
yeyeye
Answer:
[tex]x_{1}[/tex] = 1, [tex]x_{2}[/tex] = 4, so your answer is C
Step-by-step explanation:
Diana brought 8 3/5 yards of blue velvet material for a dress and coat. She used 3 4/5 yards on the coat. How much is left for the dress?
Answer:
4 4/5 yards are left
Step-by-step explanation:
7 8/5-3 4/5
Please help ASAP URGENT Will mark Brianlest
The scatter plot shows the relationship between the average number of nightly customers and the number of months since a restaurant opened. The equation represents the linear model for this data.
y = 5x + 120
What does the number 5 in the equation mean in this context?
A. The restaurant has been open for 5 months.
B. There were 5 customers per month after the restaurant was open 120 months.
C. For every 5 months the restaurant has been open, there are 120 more customers per night.
D. The average number of customers per night increased by 5 each month.
E. There were 5 customers per night when the restaurant opened.
Answer:
A
Step-by-step explanation:
i used the process of elimination and got rid of answers that didnt make sense but based on the info given i could tell that x was 5 months because of where the point of 5 is on the graph
Answer:
It is D.
D. The average number of customers per night increased by 5 each month.
Step-by-step explanation:
The line is going up at +5 for every month. This means 5 customers are being added every month
At a cement plant, sand is stored in a container called a hopper. The shape of the container is an inverted cone. The height is 18 feet and the radius is 12 feet. If the hopper is full and sand is emptied at the rate of 4 ft3/min, how fast is the level of sand dropping when the sand level is 6 feet high? V = 1/3r2h
Answer:
[tex]v=\frac{0,25}{\pi } ft/min[/tex]
Step-by-step explanation:
There is a relation with the initial and final dimensions of the hopper according to the sand level when its high is 6 feet as follows:
[tex]\frac{h_{1} }{h_{2} }=\frac{r_{1} }{r_2}\\{r_2}=\frac{12ft*6ft}{18ft}\\ r_2=4ft[/tex]
Where the calculated [tex]r_{2}[/tex] is given with the 6 feet hgh.
Then we have the sand flow formula which is:
[tex]Q=A*v[/tex]
Where A represents the area of the transversal section and v the velocity that we need to know, the area is:
[tex]A=\pi r^{2}\\ A=\pi *4^{2}\\ A=16\pi ft^{2}[/tex]
And finally the sand is dropping when the level is 6 feet high with the velocity (v) :
[tex]v=\frac{Q}{A} \\v=\frac{4}{16\pi }[/tex]
[tex]v=\frac{0.25}{\pi } ft/min[/tex]
The sand level in the hopper is dropping at a rate of approximately 0.08 feet per minute when the sand level is 6 feet high. This is calculated using related rates and the volume formula for a cone. The relationship between radius and height, derivative calculations, and the given sand emptying rate are essential for this solution.
To determine how fast the level of sand is dropping in the hopper, we need to use related rates. The volume V of the sand in the inverted cone is given by the formula:
V = (1/3)πr2h
In this case, the radius r and height h of the sand level are proportional because the shape is a cone. We can express the radius r in terms of the height h using similar triangles. Given the overall height is 18 feet and the radius is 12 feet, we have:
r = (12/18)h or r = (2/3)h
Substituting r into the volume formula:
V = (1/3)π[(2/3)h]2h = (4/27)πh3
We need the rate of change of the height (dh/dt) when h = 6 feet. Given dV/dt = -4 ft³/min (negative because the volume is decreasing), we use the chain rule for differentiation:
dV/dt = (dV/dh)(dh/dt)
First, find dV/dh:
dV/dh = d/dh [(4/27)πh3] = (4/27)π × 3h2 = (4/9)πh2
Using dV/dt = -4 ft³/min:
-4 = (4/9)π(h2)(dh/dt)
When h = 6 feet:
-4 = (4/9)π(62)(dh/dt)
-4 = (4/9)π(36)(dh/dt) = 16π(dh/dt)
Therefore:
dh/dt = -4/16π = -1/4π
dh/dt = -0.08 feet/min
So, the level of sand is dropping at a rate of approximately 0.08 feet per minute when the sand level is 6 feet high.
Find midpoint (-6, 3) (4,-3)
Step-by-step explanation:
Given points are (-6,3) and (4,-3)
[tex]x_1=-6 ,[/tex] [tex]y_1=3[/tex] , [tex]x_2= 4[/tex] and [tex]y_2 = -3[/tex]
Coordinate of mid point [tex](\frac{x_1+x_2}{2} ,\frac{y_1+y_2}{2} )[/tex]
[tex]=(\frac{-6+4}{2} ,\frac{3+(-3)}{2})[/tex]
=(1,0)