Answer:
Step-by-step explanation:
(x 3)(x – 3)
(x5 3)(x – 3)
(x3 3)(x2 – 3)
(x3 3)(x3 – 3)
Answer:
(x3 + 3)(x3 – 3)
Step-by-step explanation:
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.
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!
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
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
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:
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!
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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(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
Rani and her friends are raking leaves as a part of a school service project. The regular price of the supplies they need is 60$,but the store manager is giving them a 20% discount. Rani wants to know the sale price of the supplies.
Rani and her friends can purchase their supplies for $48 after a 20% discount on the original price of $60.
Explanation:Rani and her friends need to calculate the sale price of the supplies after a 20% discount. The original price is $60, and the discounts amount in money can be determined by multiplying this original cost by 20% or 0.20. This gives you a discount amount of $12. To determine the final price after the discount, you subtract the discount amount from the original price. Therefore: $60 - $12 = $48. Hence, the sale price of the supplies that Rani and her friends need is $48.
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If the base angle of the cone needs to measure 60° and the cone needs to be 24 inches tall, approximately how wide will the base of the resulting cone need to be?
A.
27.72 inches
B.
13.86 inches
C.
41.57 inches
D.
83.14 inches
Final answer:
Using the base angle and the height of the cone, we can use trigonometry to find that the width of the base of the cone needs to be approximately 41.57 inches, making option C the correct answer.
Explanation:
The question asks for the width of the base of a cone given that its base angle is 60° and its height is 24 inches. To solve this, we need to understand that the base angle of 60° creates a right-angled triangle when a line is drawn from the apex of the cone to any point on the base's circumference, with the height of the cone being one side of this triangle and half of the cone's base width being the other side.
Using trigonometry, specifically the tangent function, which is the opposite side (half the base width) over the adjacent side (height), we can solve for the base width. Given that tan(60°) = √3 and the height is 24 inches, the formula becomes √3 = (base width/2) / 24, solving for the base width gives us roughly 41.57 inches, which makes option C correct.
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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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
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
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.
The lengths of two sides of a triangle are 26
meters and 48 meters. What is the range of
possible lengths, in meters, for the third side,
x, of this triangle? Write your answers in the
boxes.
Answer:
[tex]22\ m < x < 74\ m[/tex]
Step-by-step explanation:
Let
x ----> the length for the third side
we know that
The Triangle Inequality Theorem states that the sum of any 2 sides of a triangle must be greater than the measure of the third side
Applying the triangle inequality theorem
1) [tex]26+48> x[/tex]
solve for x
[tex]74> x[/tex]
Rewrite
[tex]x < 74\ m[/tex]
2) [tex]26+x>48[/tex]
solve for x
subtract 26 both sides
[tex]x> 22\ m[/tex]
therefore
The range of possible lengths, in meters, for the third side is equal to
[tex]22\ m < x < 74\ m[/tex]
The range of the possible length of the third side of the triangle is 22 to 74 (exclusive)
Assume the lengths of a triangle are x, y and z.
The following are the possible inequalities that relate the side lengths
[tex]x + y > z[/tex]
[tex]y + z > x[/tex]
[tex]x + z > y[/tex]
The unknown side length is x.
So, we have:
[tex]x + 26 > 48[/tex]
[tex]48 + 26 > x[/tex]
[tex]x + 48 > 26[/tex]
Solve for x in the three inequalities
[tex]x + 26 > 48[/tex]
[tex]x > 22[/tex]
[tex]48 + 26 > x[/tex]
[tex]74 > x[/tex]
[tex]x + 48 > 26[/tex]
[tex]x > -22[/tex]
The values of x cannot be negative.
So, we ignore the inequality [tex]x > -22[/tex]
We are left with
[tex]74 > x[/tex] and [tex]x > 22[/tex]
Combine the inequalities
[tex]74 > x > 22[/tex]
Rewrite as:
[tex]22 < x < 74[/tex]
Hence, the range of the possible length is 22 to 74 (exclusive)
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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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A slot machine has 3 dials. Each dial has 30 positions, one of which is "Jackpot". To win the jackpot, all three dials must be in the "Jackpot" position. Assuming each play spins the dials and stops each independently and randomly, what are the odds of one play winning the jackpot?
1/30 = 0.03 or 3%
3/(30+30+30) = 3/90 = 0.33 or 33%
3/(30×30×30) = 3/27000 = 0.0001 or 0.01%
1/(30×30×30) = 1/27000 = 0.00003 or 0.003%
Answer:
3/(30×30×30) = 3/27000 = 0.0001 or 0.01%
Step-by-step explanation:
Answer:
here we have 3 dials in the slot machines and each dial has 30 position
so probability of getting a number of the each dial =
30
1
since all dials are independent so probability of getting same number would be
P ( getting jack pot) =
30
1
30
1
30
1
=
27000
1
= 0.003% option D is correct.
Step-by-step explanation:
Which statement is not true about the data shown by the box plot below?
a.
The interquartile range is 52.
b.
The median of the upper half of the data is 49.
c.
The median of the data is 37.
d.
Three fourths of the data is less than 49.
The false statement is "the median of the data is 37" because the IQR of the data is 20 option (a) is correct.
What is the box and whisker plot?A box and whisker plot is a method of abstracting a set of data that is approximated using an interval scale. It's also known as a box plot. These are primarily used to interpret data.
It is given that:
A box plot is shown in the picture;
As we know,
The interquartile range(IQR):
IQR = Q3 - Q1
IQR = 50 - 30
IQR = 20
From the box plot:
The median of the upper half of the data is 49.
The median of the data is 37.
Three-fourths of the data is less than 49.
Thus, the false statement is "the median of the data is 37" because the IQR of the data is 20 option (a) is correct.
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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
Simplify the expression and find the value, if x=2 : 5x-6-x+9
Answer:11
Step-by-step explanation:
5x-6-x+9
When x=2 we have
5(2)-6-2+9
10-6-2+9
10+9-6-2
19-6-2=11
Answer:
11
Step-by-step explanation:
5x - 6 - x + 9
4x + 3
x = 2
4(2) + 3 = 11
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:
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
One step equations
6r=42
R=7
I hope that help you! :)
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
Why is the reference angle the angle
the terminal side and the x-axis instead of the y-axis?
Answer:
If necessary, first "unwind" the angle: Keep subtracting 360 from it until it is lies between 0 and 360°. (For negative angles add 360 instead).
Sketch the angle to see which quadrant it is in.
Depending on the quadrant, find the reference angle:
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)
A cubic box that holds 125 units
Answer: 5 units
Step-by-step explanation:
This describes the relationship between one set of data that increases as another set of data increases. This is synonymous with directly related.
Answer:
Positive correlation
Step-by-step explanation:
Correlation:
Correlation is a technique that help us to find or define a linear relationship between two variables.It is a measure of linear relationship between two quantities. A positive correlation means that an increase in one quantity leads to an increase in another quantity A negative correlation means with increase in one quantity the other quantity decreases.Positive correlation means that the data sets are directly related with each other.Thus, the correct answer is
Positive correlation
Answer:
Negative Correlation
Step-by-step explanation:
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.