What is the decimal equivalent of the rational number -1/8
Answer:
-0.125
Step-by-step explanation:
To find the decimal version of the fraction, divide using a calculator or long division.
-1 / 8 = -0.125
Best of Luck!
At his last track meet, Eli ran the 400-meter dash in 54 seconds. His friend Kimberly bet him that he couldn't run a whole kilometer at that pace, but Eli is determined to prove her wrong. How many minutes would he have to run at this pace to win the bet?
Write your answer as a whole number, decimal, or simplified fraction. Do not round.
Answer:
Eli has to run for 2.25 minutes at this pace to win the bet.
Step-by-step explanation:
At his last track meet, Eli ran the 400-meter dash in 54 seconds.
So, the speed of Eli's run is [tex]\frac{400}{54} \times 60 = 444.44[/tex] meters per minute.
Now, if Eli is determined to run a whole kilometer with the same speed, then it will take Eli to run 1 kilometer within [tex]\frac{1000}{444.44} = 2.25[/tex] minutes.
Hence, Eli has to run for 2.25 minutes at this pace to win the bet. (Answer)
If you were calculating the volume of a cube that has a side length of 8 inches, how would you write the calculations in exponential form? What are 2 more ways to read the exponent verbally.
Answer: 8^3, Eight to the third power, Eight times eight times eight.
To calculate the volume of a cube with a side length of 8 inches, you write the calculation in exponential form as V = 8^3, which is read as '8 cubed' or '8 to the third power', resulting in a volume of 512 cubic inches.
Explanation:To calculate the volume of a cube using a side length of 8 inches, you can write the calculation in exponential form as V = 8^3. This represents the volume (V) as the length of a side of the cube (8 inches) raised to the power of 3. In exponential form, 8^3 is 8 cubed or 8 to the third power, both of which mean 8 multiplied by itself twice more (8 x 8 x 8).
Therefore, the volume of the cube would be 512 cubic inches because 8 x 8 x 8 equals 512.
help please, ive been sitting on this chair for 2 hours
Answer:
Step-by-step explanation:
We need to analyze the surface
Look at the L shape, it has a mirror image at the back, which is symmetrical to the front side
Then,
area of rectangle = length × breadth
The L shape can be divided into two plane shape
1. A rectangle of length 10in and breadth 6in,
Then, A=l×b=10×6 = 60in²
2. To a square of side a=4in
Then, A=s²=4²=16in²
Then, the total area of one side of the L shape is
A=60+16=76in²
Also, the total area of the two L shape is =2×76
A=152in²
Then, let look at the back side of the solid and the front side, they are also symmetrical.
It forms a rectangle of length 10in and breadth 6in
Then, A= l×b=10×6=60in²
Area of the two sides is =60×2
A=120in²
The total are of the front and back side is 120in²
A=120in²
Let take a look at the top and bottom, they are also symmetrical and has a dimension of length 10in and breadth 6in
Then, A=l×b=10×6=60in²
So, total area =2×60 =120in²
The total area of the shape is the total area of top+ total are of the sides + total area of the L shape
Total area=152+120+120=392in²
A(total)=392in²
Then, the total area of the solid shape is 392in²
The first option is correct
The endpoint of a diameter of a circle are (-4,2) and (12,10). What is the y-coordinate for the center of the circle
Answer:
6
Step-by-step explanation:
The center of the circle is the midpoint of the diameter. The midpoint can be found by averaging the coordinates of the end points:
((-4, 2) +(12, 10))/2 = ((-4+12)/2, (2+10)/2) = (4, 6)
The y-coordinate of the center is 6.
The center of the circle has a y-coordinate of 6, determined by averaging the y-coordinates (2+10)/2 of the diameter's endpoints (-4,2) and (12,10).
Explanation:The y-coordinate for the center of a circle can be determined by finding the midpoint of the y-coordinates of the diameter's endpoints. Given the endpoints (-4,2) and (12,10), the midpoint can be found by averaging the y-coordinates: (2 + 10) / 2 = 12 / 2 = 6. Therefore, the y-coordinate of the center of the circle is 6.
You start driving north for 21 miles, turn right, and drive east for another 20 miles.
How many miles must you travel to return directly back to your starting point?
Answer:
40
Step-by-step explanation:
add 21 + 20
hope this helps :)
If h = 24 units and r = 8 units, what is the volume of the cone shown above?
Use 3.14 for π
Answer:
1,607 volume
Step-by-step explanation:
3200 dollars is placed in an account with an annual interest rate of 8.25%. To the nearest tenth of a year, how long will it take for the account value to reach 9600 dollars?
Answer:13.9
Step-by-step explanation:
Using the compound interest formula, it will take approximately 14.9 years for an account with a $3,200 initial deposit and an 8.25% annual interest rate to grow to $9,600.
Explanation:To find out how long it will take for an account with an initial value of $3,200 and an annual interest rate of 8.25% to grow to $9,600, we can use the future value formula for compound interest:
The formula is FV = PV (1 + r)^n, where:
FV is the future value of the money after n years,PV is the present value or initial amount (which is $3,200),r is the annual interest rate (which is 0.0825), andn is the number of years.To find n when FV is $9,600, we rearrange our formula to solve for n:
n = log(FV / PV) / log(1 + r)
Now, plug in the values:
n = log(9600 / 3200) / log(1 + 0.0825)
n = log(3) / log(1.0825)
n ≈ 14.9 years
So, it will take approximately 14.9 years for the account value to reach $9,600.
what is 100 miles in 2.5 hours
Answer:
40 Miles Per Hour
Step-by-step explanation:
If this is traveling 100 Miles in 2.5 hours...
100/2.5 = 40
You would have to go 40 Miles Per Hour.
Answer:40
Step-by-step explanation:
A farm stand wants to sell fruit to local grocery stores in packages with
baskets of grapes, worth $5 apiece, and baskets of plums, worth $10 apiece.
The owner wants each package to include 35 baskets total, and he wants to
sell each package for $290. How many baskets of grapes and how many
baskets of plums should he put in each package?
O
A. 12 grapes, 23 plums
OB. 10 grapes, 5 plums
O
C. 5 grapes, 10 plums
O
D. 23 grapes, 12 plums
A.12 grapes, 23 plums
Step-by-step explanation:
1. solve all the equations by multiplying each number by how much each item is worth
2. A: 290 =(12× 5)+(10×23)
B: 100 =(10×5)+(5×10)
C:125 =(5×5)+(10×10)
D:235 =(23×5)+(12×10)
True or false: f(x) is a function.
2
MV
f(x)
Answer:
False, since x values cannot have more than one y value.
Step-by-step explanation:
Because if you were to plot the points on a graph, and do the vertical line test, there will be points that cross one another making it not a function.
Hope I Helped
the equation of a line β is 2x-3y=6
find the gradient of β
Answer:
2/3
Step-by-step explanation:
Rewrite the equation into the form of y=mx+c
m is the gradient of the line.
2x-3y=6
3y= 2x-6 (bring y terms to one side, the rest to the other)
y= 2/3x -2 (÷3 throughout)
Thus the gradient is 2/3.
if a circle has a diameter of 12.8 cm, what is the radius
Answer:
6.4cm
Step-by-step explanation:
The radius of a circle with a diameter of 12.8 cm is 6.4 cm.
Explanation:The diameter of a circle is twice the length of its radius, so to find the radius of a circle given its diameter, you simply divide the diameter by 2.
In this case, the diameter is 12.8 cm, so the radius would be 12.8 cm / 2 = 6.4 cm.
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What's the distance between (–4, 3) and (4, 3)?
Answer:
The distance between (-4, 3) and (4, 3) is 8
Step-by-step explanation:
Distance formula: [tex]\sqrt{(x2 - x1)^2 + (y2 - y1)^2)}[/tex]
Distance: [tex]\sqrt{(4 - (-4)^2 + (3 - 3)^2}[/tex]
Distance: [tex]\sqrt{(4 + 4)^2 + (0)^2}[/tex]
Distance: [tex]\sqrt{8^2} \\[/tex]
Distance: 8
Answer: The distance between (-4, 3) and (4, 3) is 8
HELP PLEASE BE QUICK
Answer:
Option A, V = π(7)^2h
Step-by-step explanation:
The formula for the volume of a cylinder: V = πr^2h
Step 1: Since the give us diameter we need to find radius
radius = diameter/2
radius = 14/2
radius = 7
Answer: Option A, V = π(7)^2h
Answer:
A
Step-by-step explanation:
Volume of a cylinder = pi r2 h
Where pi = 3.14
Radius r = diameter/2
Diameter given is 14,
So radius = 24/2 = 7
Height h
Volume = pi(7)^2 h
If f(x) = -3x – 9 and g(x) = (x+7,
what is (fºg)(-6)?
Helppp
Answer:
-12
Step-by-step explanation:
we know that
(fºg)(x)=f(g(x))
To find out the composite function f(g(x)) substitute the variable x in the function f(x) by the function g(x)
we have
[tex]f(x)=-3x-9[/tex]
[tex]g(x)=x+7[/tex]
so
[tex]f(g(x))=-3(x+7)-9[/tex]
For x=-6
substitute
[tex]f(g(-6))=-3(-6+7)-9[/tex]
[tex]f(g(-6))=-3(1)-9[/tex]
[tex]f(g(-6))=-12[/tex]
1. y = 6x
2x + 3y = -20
Step-by-step explanation:
[tex]y = 6x[/tex]
[tex]2x + 3y = -20[/tex]
To solve this system of equations, let's multiply the first equation by [tex]-3[/tex] to get a [tex]3y[/tex] term in each equation:
[tex]-3y = -18x[/tex]
Now, let's add the two equations together:
[tex](2x + 3y) + (-3y) = -20 + (-18x)[/tex]
[tex]2x = -20 - 18x[/tex]
[tex]20x = -20[/tex]
[tex]x = -1[/tex]
Now, we can plug in this value of [tex]x[/tex] into either equation to solve for [tex]y[/tex]:
[tex]y = 6x[/tex]
[tex]y = 6(-1)[/tex]
[tex]y = -6[/tex]
or
[tex]2x + 3y = -20[/tex]
[tex]2(-1) + 3y = -20[/tex]
[tex]-2 + 3y = -20[/tex]
[tex]3y = -18[/tex]
[tex]y = -6[/tex]
Therefore, the solution to this system of equations is [tex](-1, -6)[/tex].
Answer:
x = -1
y = -6
Step-by-step explanation:
y = 6x
2x + 3y = -20
Substitute the first expression into the second one
We have
2x + 3y = -20
2x + 3(6x) = -20
2x + 18x = -20
20x = -20
Divide both sides by 20 to isolate x
20x/20 = -20/20
x = -1
Remember the first expression
y = 6x
Therefore
y = 6(-1)
y = 6 x -1
y = -6
Check
2(-1) + 3(-6) = -20
-2 + -18 = -20
-2 - 18 = -20
-20 = -20
So our answer is correct
Can someone help me with theses problems?
Answer:
17. 50
18. 150
19. 240
20. 20
21. 60
22. 240
23. 150
24. -240
25. 222
26. 75
27. 300
28. 340
29. 175
30. 265
31. 298
32. 118
Step-by-step explanation:
How you find co-terminal is by adding or subtracting 360 degrees to the value you are given.
If it is a positive number like #18. all you do is subtract 510 - 360 = 150 until you get to a value between 0 degrees and 360 degrees.
The same thing applies to negative numbers. Like #21. You will add 360 + (-660) until you get to a number between 0 degrees and 360 degrees.
-660 + 360 = -300 (this is not a value in between 0 and 360 so we must add 360 again)
-300 + 360 = 60 (this is a value in between 0 and 360) (this is the co-terminal angle)
That is the idea of finding co-terminal angles.
30 POINTS please help
Answer:
B :)
Step-by-step explanation:
what is the square root of -25
Answer:
the square root of -25 is 5i
Answer:
5i
Step-by-step explanation
All negative roots have i, which is an imaginary number.
i^2=-1.
Following this, the square root of -25 is 5i.
To double check:
5i*5i=5*5*i*i
25*-1=-25
What should be added to 6 7/15 to get 8 1/5?
Answer:
-6/7
Step-by-step explanation:
So the question basically is asking, 6x7/15+x=8/7 so find the value of X.
We multiply 7/15 by six because the question says 6 7/15 and we multiply 8 by 1/7 to get 8/7. Hope that was useful!
find the equation of the tangent to the curve at x=3 for parametric equations
x = t + 1/t
y = t^2 + 1/(t^2) when t is greater than 0
Answer:
y = 6x − 11
Step-by-step explanation:
x = t + (1/t), y = t² + (1/t²)
If we square x:
x² = t² + 2 + (1/t²)
x² = y + 2
When x = 3, y = 7.
Taking derivative with respect to time:
2x = dy/dx
dy/dx = 6
So the equation of the tangent line is:
y − 7 = 6 (x − 3)
y − 7 = 6x − 18
y = 6x − 11
What is the value of x?
Answer:
5.14
Step-by-step explanation
6/x = 42/36
42x= 216
x= 5.14
Mindy buys 12 cupcakes. Nine of the
cupcakes have chocolate frosting and the
rest have vanilla frosting. What fraction
the cupcakes have vanilla frosting?
Answer:
1/4
Step-by-step explanation:
9 Chocolate cupcakes, 9/12
3 Cupcakes are the remaining cupcakes, over 12 it's 3/12
Then Simplify, 3/12
by dividing
3 divided by 3 equals 1
12 divided by 3 equals 4
then use the simplified version 1/4
To check:
add 3/12 + 9/12
and it equals all 12 cupcakes
Final answer:
There are 3 cupcakes with vanilla frosting out of 12 total, resulting in the fraction 3/12, which simplifies to 1/4 for the cupcakes with vanilla frosting.
Explanation:
The student's question is asking us to find what fraction of the cupcakes have vanilla frosting. Mindy buys 12 cupcakes in total and 9 of them have chocolate frosting. To find how many have vanilla frosting, we subtract the chocolate frosted cupcakes from the total:
12 cupcakes - 9 chocolate frosted cupcakes = 3 vanilla frosted cupcakes
To express this as a fraction, we take the number of vanilla frosted cupcakes (which is 3) over the total number of cupcakes (which is 12).
Therefore, the fraction of cupcakes that have vanilla frosting is 3/12, which can be simplified to 1/4.
A total of 492 tickets were sold for the school play. They were either adult tickets or student tickets. The number of student tickets sold was three times the number of adult tickets sold. How many adult tickets were sold?
Answer:
164 adult tickets
Step-by-step explanation:
164×3 = 492 tickets
Really hope this helped! :)
Final answer:
A total of 123 adult tickets were sold for the school play, with the total number of tickets sold being 492 and student tickets being three times the number of adult tickets.
Explanation:
To solve the problem of how many adult tickets were sold at the school play when a total of 492 tickets were sold and the number of student tickets was three times the number of adult tickets, we set up a system of equations. Let A be the number of adult tickets and S be the number of student tickets sold.
Steps to solve this question:
The total number of tickets sold was 492: A + S = 492
The number of student tickets was three times the number of adult tickets: S = 3A
We can substitute the second equation into the first to find the number of adult tickets:
A + 3A = 492
4A = 492
A = 492 / 4
A = 123
Therefore, 123 adult tickets were sold for the school play.
multiply 72 x 25/100
Answer:
18
Step-by-step explanation:
Answer:
18
Step-by-step explanation:
What is X in this equation?
3x+55=9x-5
Please Explain.
Answer:
x = 10
Step-by-step explanation:
3x + 55 = 9x - 5 (add 5 to both sides)
3x + 55 + 5 = 9x - 5 + 5
3x + 60 = 9x (subtract 3x from both sides)
60 = 9x - 3x
60 = 6x (rearrange)
6x = 60 (divide both sides by 6)
x = 60/6
x = 10
Answer:
x=10
Step-by-step explanation:
[tex]\mathrm{Subtract\:}55\mathrm{\:from\:both\:sides}\\3x+55-55=9x-5-55[/tex]
[tex]\mathrm{Simplify}\\3x=9x-60[/tex]
[tex]\mathrm{Subtract\:}9x\mathrm{\:from\:both\:sides}\\3x-9x=9x-60-9x[/tex]
[tex]\mathrm{Simplify\:}again\\-6x=-60[/tex]
[tex]\mathrm{Divide\:both\:sides\:by\:}-6\\\frac{-6x}{-6}=\frac{-60}{-6}[/tex]
[tex]\mathrm{\:Simplify\:one\:more\:time}\\x=10[/tex]
I hope this helps you out!
Have a wonderful afternoon!
Which is better to buy? - A 3lbs. bag of apples for $2.99 or a 5lbs. bag for $4.99?
IS THERE AN OPTION TO SAY THEY ARE EQUAL IF THERE IS THEN THAT IS THE ANSWER :}
In a fraternity with 40 members , 18 take mathematics, 5 take both mathematics and physics, and 8 take neither mathematics nor physics. How many take physics but not mathematics?
Answer: 14
Step-by-step explanation:
The number of fraternity members taking physics but not mathematics is 27, calculated using inclusion-exclusion principle: 18 members take math, 5 take both math and physics, and 8 take neither.
Let's use the principle of inclusion-exclusion to solve this problem.
Total fraternity members (n) = 40
Members taking mathematics (M) = 18
Members taking both mathematics and physics (B) = 5
Members taking neither mathematics nor physics (N) = 8
To find the number of members taking physics but not mathematics (P).
We can start by using the formula for the number of elements in the union of two sets:
n(M ∪ P) = n(M) + n(P) - n(B)
Since the total members are 40, the equation becomes:
18 + n(P) - 5 = 40
Solving for n(P):
n(P) = 40 - 18 + 5
n(P) = 27
Therefore, 27 members take physics but not mathematics.
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Which is the length of the arc MPN expressed in terms of pie?
The calculated length of the arc MPN is 79/9π units
Finding the length of arc MPN
From the question, we have the following parameters that can be used in our computation:
Central angle = 360 - 44 = 316 degrees
Radius = 5 units
Using the above as a guide, we have the following:
arc MPN = central angle/180 * π * Radius
Substitute the known values in the above equation, so, we have the following representation
arc MPN = 316/180 * π * 5
Evaluate
arc MPN = 79/9π
Hence, the length of the arc is 79/9π units