Solution:
Given that,
Gavin ran 10 MPH during Monday's workout
50% slower during Tuesday's workout
Therefore,
Speed in tuesday = 50 % slower than monday
Which means,
Speed in tuesday = 10 - 50 % of 10
Solve the above
[tex]\text{ Speed in tuesday } = 10 - \frac{50}{100} \times 10\\\\\text{ Speed in tuesday } = 10 - 0.5 \times 10\\\\\text{ Speed in tuesday } = 10 - 5\\\\\text{ Speed in tuesday } = 5\\\\[/tex]
Thus, he ran 5 mph in tuesday
Aldon and Jamal raised the same amount of money for the school fundraiser. Aldon
donated $40 and sold 12 tickets for the school raffle. Jamal donated $25 and sold
15 tickets for the raffle. What was the cost of each raffle ticket?
The cost of each raffle ticket was $5.
What is an expression?An expression is a number, or a variable, or a combination of numbers and variables and operation symbols.
Now it is given that,
Amount donated by Aldon = $40
Number of tickets sold by Aldon = 12
Amount denoted by Jamal = $25
Number of tickets sold by Jamal = 15
Let x be the cost of each raffle ticket.
So, Cost of tickets sold by Aldon = 12x
Cost of tickets sold by Jamal = 15x
So, Total amount raised by Aldon = 12x + 40
Total amount raised by Jamal = 15x + 25
∵ Aldon and Jamal raised the same amount of money for the school fundraiser
⇒ 12x + 40 = 15x + 25
Taking aliketerms together we get,
15x - 12x = 40 - 25
⇒ 3x = 15
Dividing both side by 3 we get,
x = $5
which is the required cost of each raffle ticket.
Thus, the cost of each raffle ticket was $5.
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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!
What is the value of x?
Answer:
5.14
Step-by-step explanation
6/x = 42/36
42x= 216
x= 5.14
You randomly draw marble from the bag of marbles contains seven blue marbles two Green marbles and one red marble what is P(not draw a blue marble)?
Answer:
3/10 probability as it is the same as getting 2gm +1rm =3m
Step-by-step explanation:
You add up the numbers 7+2+1=10m
A cubic box that holds 125 units
Answer: 5 units
Step-by-step explanation:
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.
How much money invested at 5% compounded continuously for 3 years will result in $852
Answer:
Step-by-step explanation:
Rate of interest is 5%.
Time =3years
Amount =$852
Then, we need to find P
Generally compound interest is given as
A=P(1+r/n)^nt
A=final amount
P=initial principal balance
r=interest rate
n=number of times interest applied per time period=12
t=number of time periods elapsed
A=P(1+r/n)^nt
852=P(1+0.05/12)^(12×5)
852=P(1+0.004167)^60
852=P(1.004167)^60
852=1.2834P
Then, P=852/1.2834
P=$663.88
Then the principal amount invested is $663.88
Approximately $664
What is the perimeter of a square with an area of 441 cm2?
Area of the square = side x side = side ^2
therefore to find a length of one side = Square root of the 441
sqrt of 441 = 21 cm
so the perimeter of a square is 21 x 4 = 84 cm
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
Find f(t-3) for f(×)=4x^2-8×+4
Answer:
4t^2-32t+64=4(t^2-8x+16)
Step-by-step explanation:
f(x)=4x^2-8x+4
f(t-3)=4(t-3)^2 - 8(t-3)+4=
4(t^2-2*t*3+9)-8t+24+4=
4(t^2-6t+9)-8t+28=
4t^2-24t+36-8t+28=
4t^2-32t+64=4(t^2-8x+16)
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
if cos x=2/3 and x is in quadrant 4 then sin x/2=
A. 1/3
B. Sqrt 1/6
C. -Sqrt 1/6
D. -1/3
Options are above will mark brainliest
Answer: B, [tex]\sqrt{\frac{1}{6} }[/tex]
Step-by-step explanation:
Using half-angle identities
Using half angle identities, we know that
[tex]sin\frac{x}{2} = +/- \sqrt{\frac{1-cosx}{2} }[/tex]
Plug in 2/3 for cosx
[tex]sin\frac{x}{2} = +/- \sqrt{\frac{1-2/3}{2} }[/tex]
[tex]sin\frac{x}{2} = +/- \sqrt{\frac{1/3}{2} }[/tex]
[tex]sin\frac{x}{2} = +/- \sqrt{\frac{1}{6} }[/tex]
Determining sign
Since the angle x is in quadrant 4 from 270 to 360 degrees, if we divide the angle by 2, the angle x should be somewhere from 135 to 180 degrees, which would all fall in quadrant 2
all sin values in quadrant 2 are positive
Final answer
[tex]sinx = \sqrt{\frac{1}{6} }[/tex]
If cos x=2/3 and x is in quadrant 4 then value of sin x/2 is -√(1/6), option C is correct.
What is Trigonometry?Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.
To find sin(x/2), we can use the half-angle formula for sine:
sin(x/2) = ±√[(1 - cos x)/2]
Since x is in quadrant 4, cosine is positive and sine is negative. We are given that cos x = 2/3
so we can substitute this value into the formula:
sin(x/2) = -√[(1 - 2/3)/2]
sin(x/2) = -√(1/6)
Hence, if cos x=2/3 and x is in quadrant 4 then sin x/2 is -√(1/6)
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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.
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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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
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.
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 :}
30 POINTS please help
Answer:
B :)
Step-by-step explanation:
estimated a 3 out of every 25 men are left handed
what percent of men are left ahnded
Answer:
12
Step-by-step explanation:
Percent means out of 100
We have 3/25
Multiply the top and bottom by 4
12/100
The percent is 12
Final answer:
Based on the estimate provided, 12% of men are left-handed, which is calculated by dividing 3 by 25 and then multiplying the result by 100.
Explanation:
To calculate the percentage of men who are left-handed based on the estimate that 3 out of every 25 men are left-handed, you can use the following steps:
Divide the number of left-handed men by the total number of men. In this case, 3 divided by 25 equals 0.12.Multiply the result by 100 to convert it to a percentage. So, 0.12 multiplied by 100 equals 12%.Therefore, based on the given estimate, 12% of men are left-handed.
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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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.
What's the snaller angle?
Answer:
the (2x) obviously because it is close to an acute angle and the (13x) is closer to a right angle
Step-by-step explanation:
A car traveled 63 miles on 3 gallons of gas. What proportion can you set up to determine how many miles, m, the car can travel on 7 gallons of gas?
Answer:Let x be the number of miles driven on 60 gallons of gas. By setting up and solving a proportion involving x, find the value of x for the car that you have chosen. State the type of car, the mileage, and show both the set up of the proportion and the steps
Step-by-step explanation:
Answer:
147 miles
Step-by-step explanation:
Let x be the number of miles travelled on 7 gallons, then proportion is of the form
[tex]\frac{miles}{gallons}[/tex], thus
[tex]\frac{63}{3}[/tex] = [tex]\frac{x}{7}[/tex] ( cross- multiply )
3x = 63 × 7 = 441 ( divide both sides by 3 )
x = 147
Thus the car can travel 147 miles on 7 gallons
21 3/4 as a improper fraction
Answer:
87/4
Step-by-step explanation:
Step 1: Convert 21 3/4 into an improper fraction
21 3/4 is same as 21 * 4/4 + 3/4
21 * 4/4 = 84/4
Step 2: Add them up
84/4 + 3/4
87/4
Answer: 87/4
Answer: 87/4
Step-by-step explanation:
Multiply:
21*4=84
Add:
84+3=87
Your answer should be: 87/4
The denominator stays the same
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
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+1)+(b-2)i=6+7i Solve for a and b
Answer:
a = 5 and b = 9Step-by-step explanation:
(a+1)+(b-2)i=6+7i
⇔
a + 1 = 6
and
b - 2 = 7
⇔
a = 5
and
b = 9
Write the equation of the line that passes through the point (-5,5) and has a slope of -8/5
A) y= -8/5 x - 3
B) y= -8/5x+3
C) 3x - 5y =0
D) 5x-3y=0
Answer:
A) y= -8/5x -3
Step-by-step explanation:
This is your current equation: y= -8/5x + b. I would plug in your point to the equation. It should look like this: 5= -8/5(-5)+b. Multiply -8/5 by -5 to get 8. This is what you should have: 5=8+b. Subtract 8 from both sides to get -3=b. So, this is your final answer: y= -8/5x -3. So, A is the correct answer. Hope this helped!
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!