Answer:
the answer is A.616.39
Step-by-step explanation:
Megan can withdraw $615.21 per month for 5 years from the new account.
Option B is the correct answer.
What is an equation?An equation contains one or more terms with variables connected by an equal sign.
Example:
2x + 4y = 9 is an equation.
2x = 8 is an equation.
We have,
To solve this problem, we need to use the formula for the future value of an annuity:
[tex]FV = P [(1 + r/n)^{n\times t} - 1]/(r/n)[/tex]
where:
P = payment per period
r = interest rate per period
n = number of compounding periods per year
t = number of years
FV = future value of the annuity
First, we can calculate the future value of Megan's semiannual payments after 10 years:
P = $1,624.13
r = 1.5%/2 = 0.0075 (semiannual interest rate)
n = 2 (semiannual compounding periods)
t = 10 years
So,
[tex]FV = 1,624.13 \times[(1 + 0.0075/2)^{2\times10} - 1]/(0.0075/2)[/tex]
= $21,070.58
Next, we need to calculate the future value of this amount when transferred to the new account:
r = 2.3% / 12 = 0.00191667 (monthly interest rate)
n = 12 (monthly compounding periods)
t = 5 years (60 months)
FV
[tex]= $21,070.58 \times (1 + 0.00191667)^{60}[/tex]
= $24,526.41
Finally, we need to calculate the monthly payment Megan can withdraw for 5 years from this account, assuming the balance is depleted at the end of the 5 years:
P = ?
r = 2.3% / 12 = 0.00191667 (monthly interest rate)
n = 12 (monthly compounding periods)
t = 5 years (60 months)
Using the formula for the present value of an annuity:
[tex]P = FV \times (r/n) / [(1 + r/n)^{n\timest} - 1][/tex]
[tex]= $24,526.41 \times (0.00191667) / [(1 + 0.00191667)^{60} - 1][/tex]
= $615.21
Therefore,
Megan can withdraw $615.21 per month for 5 years from the new account.
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How many degrees are there in angle C?
** multiple choice question
There are 50 degrees in angle c
Answer: A. 50°
Step-by-step explanation:
Since the measure angles of a triangle add up to 180° and the right triangle=90°, therefore when you subtract 180-90-40, you get 90-40, which then equals to 50°.
write the comparison below as a ratio in it's simplest form using a fraction, a colon and the word to. _____ 15 dollars to 27 dollars
Answer:
Step-by-step explanation:
15/27 - 5/9
5:9
5 to 9 ratio
Kane is saving money. He starts with $14. The next day he has $21 and the third day he has $28. Assuming this pattern continues, what is the equation for the nth term of the arithmetic sequence?
Answer:
x+7
Step-by-step explanation:
let x= the amount of money he got that day
he gains $7/day
x+7
FRUIT The circle graph shows the results of a survey about students’ favorite fruit. If 300 students were surveyed, how many students chose bananas as their favorite type of fruit?
a.
222 students
b.
78 students
c.
26 students
d.
132 students
Answer:
B 78 students
Step-by-step explanation:
The answer is d. 132 students
A company that produces video games has hired you to set the sale price for its newest game. based on the production costs and consumer demands , the company has concluded that the equation p(x) = -0.3x^2 + 45x - 1000 represents the profit p (in dollars) for x individual games sold. What will the company's profit be if 100 games are sold?
Answer: 500 dollars
You just plug in 100 to the x’s in the equation
The company's profit be if 100 games are sold is $41100
The profit function is given as:
[tex]p(x) = -0.3x^2 + 45x - 1000[/tex]
When the number of games is 100, it means that
x = 100
So, we substitute 100 for x in the profit function
[tex]p(x) = -0.3x^2 + 45x - 1000[/tex] becomes
[tex]p(100) = -0.3(100)^2 + 45(100) - 1000[/tex]
Evaluate the exponents
[tex]p(100) = -0.3(10000) + 45(100) - 1000[/tex]
Open all brackets
[tex]p(100) = -3000 + 45100 - 1000[/tex]
Evaluate like terms
[tex]p(100) = 41100[/tex]
Hence, the company's profit be if 100 games are sold is $41100
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Ivan is putting books in his bookcase. He has
already put 74 books in the bookcase but he has
225 books. How many more books does he have to
put in the bookcase?
Answer:
151
Step-by-step explanation:
because 225-74 =151
151 books
There are 225 books, and 74 have already been placed on the shelf. Subtract 225 minus 74 to find that Ivan needs to place 151 more books on the shelf.
Which of the following conditions make a pair of triangles congruent?
Answer:
SSS, SAS, ASA, AAS, and HL. These tests describe combinations of congruent sides and/or angles that are used to determine if two triangles are congruent.
Step-by-step explanation:
Elijah spends 5 hours each week working out in a pool. This is twice the
amount of time he spends working out in the weight room. How much time
does he spend in the weight room each week?
Answer: he spends 2.5 hours in the weight room each week.
Step-by-step explanation: 2.5 multiplied by 2 (which is the twice amount of time spent working out in the pool) is 5.
So the answer is 2.5
what are regular and irregular numbers
Do you mean irrational?
Paul bought a concert ticket for $25. He sold the ticket at a 35% markup. How much did Paul sell the ticket for? *
Answer:
33.75
Step-by-step explanation:
find 35 % of 25 then add that to 25.
He sold the ticket at $33.75.
What is Markup ?Markup is the amount by which a product is sold above its cost price.
It is given that
Cost Price of the ticket is $25
Selling price = ?
Markup = 35%
Selling Price = 1.35 * 25 = $33.75
Therefore he sold the ticket at $33.75.
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If 1 dish of craft paint covers an area of 720 square centimeters, how many dishes of paint are required to paint the top surface and the lateral faces of the table shown in the diagram? Ignore the bottom of the tabletop and the legs.
(540 + 540 + 900 + 900) + (2160) = (Surface area of Lateral faces) + (Top) = 5040 sq cm.
5040 / 720 = dishes of craft paint = 7 dishes
Answer:
7 dishes
Step-by-step explanation:
what is the quotient of 7^2/2x+6 divided by 3x-5/x+3
[tex]\bf \cfrac{7^2}{2x+6}\div \cfrac{3x-5}{x+3}\implies \cfrac{7^2}{2x+6}\cdot \cfrac{x+3}{3x-5}\implies \cfrac{49}{2~~\begin{matrix} (x+3) \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}}\cdot \cfrac{\begin{matrix} x+3 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix} }{3x-5}\implies \cfrac{49}{2(3x-5)}[/tex]
A bag contains 10 pieces of flavored candy 4 lemon 3 strawberrys 2 grape and 1 cherry one piece of candy will be randomly picked from the bag what is the probability the candy picked is not grape flavored
Answer:
The probability that the candy picked is not grape flavored would be 4/5
Step-by-step explanation:
We are given that a bag contains 10 pieces of flavored candy. 4 lemon, 3 strawberry, 2 grape and 1 cherry. The probability that the candy picked is not grape flavored is calculated as;
(number of candy that are not grape flavored)/ ( total number of candy in the bag)
= (4+3+1)/(10)
= 8/10
=4/5
Therefore, the probability that the candy picked is not grape flavored would be 4/5
To find the probability that a randomly picked candy is not grape flavored, we will follow these steps:
1. Count the total number of pieces of candy in the bag. This is the sum of all the different flavors of candy:
- 4 lemon candies
- 3 strawberry candies
- 2 grape candies
- 1 cherry candy
The total number is 4 + 3 + 2 + 1 = 10 candies.
2. Count the number of candies that are not grape flavored. Since there are 2 grape candies, the number of candies not grape flavored is the total minus the grape candies:
10 (total candies) - 2 (grape candies) = 8 candies that are not grape flavored.
3. Calculate the probability of picking a non-grape flavored candy. Probability is the number of favorable outcomes divided by the total number of possible outcomes. In our case, the favorable outcomes are the instances where we pick a non-grape flavored candy, and the total possible outcomes are picking any candy from the bag:
Probability (not grape flavored) = Number of non-grape flavored candies / Total number of candies
Probability (not grape flavored) = 8 / 10
4. Simplify the fraction, if needed. In this case, the fraction 8/10 can be simplified to 4/5 by dividing both the numerator and denominator by the greatest common divisor, which is 2.
Therefore, the probability of picking a candy that is not grape flavored from the bag is 4/5, or 80% if expressed as a percentage.
is 3-6x=y proportional
Answer:
Step-by-step explanation:
Answer:
No
Step-by-step explanation:
The equation of a proportional relation is of the form
y = kx,
where k is a number.
Here you have
3 - 6x = y,
which can be rewritten as
y = -6x + 3
Because of the +3, your equation is not for the form y = kx, and it is not a proportional relation.
Which is the better buy?
A. 3-yard piece of cotton cloth for $4.41
B. 3-foot piece of cotton cloth for $1.05
Answer:
Step-by-step explanation:
It’s is a because if you divide 4.41 divide by 3 you will get 1.47
Step-by-step explanation:
1 yard = 3 feet
So 3 yards = 9 feet
$4.41 / 9 feet = $0.49 per foot
$1.05 / 3 feet = $0.35 per foot
The second one is cheaper, so that's the better buy.
simplify
[tex](x^{2} + 3x - 4) + (4^{2} - 5) - (7x + 3)[/tex]
X^2-4x+4 is the answer, to save you points next time, use an app called M8thw8y
First you want to drop the parenthesis. If there is a “+” sign, you do not have to change anything. If there is a “-“ sign, you have to distribute the negative in order to simplify, so imagine you are distributing -1 to 7x + 3 to make it -7x -3.
So, you now have x^2 + 3x - 4 + 16 -5 - 7x -3. (I evaluated the 4^2 to 16)
Now, what you want to do now is to combine like terms. Notice that there is only one x^2, so it is the same. There are two terms that have “x”. 3x and -7x react like normal numbers and they form -4x. The numbers who don’t have x on them you combine like terms.
Answer is x^2 - 4x - 12
What is the value of m in the equation 1/2m-3/4n=16, when n = 8?
A. 20
B. 32
C. 44
D. 48
Answer:
44
Step-by-step explanation:
0.5 m - 0.75 n = 16
Substitute n = 8 into the equation
0.5 m - ( 0.75 × 8 ) = 16
0.5 m - 6 = 16
( Add 6 to both sides )
0.5 m = 26
( Divide by 0.5 )
m = 52
2. What percent of rolling a 2
3 probability of getting HH
Answer:
2. The correct answer option is 25%.
3. The experimental probability is 3% greater than the theoretical probability.
Step-by-step explanation:
2. We are given that a number cube is rolled 20 times out of which 5 times it lands on the number 2.
We are to find the experimental probability of getting the number 2.
P (2) = [tex]\frac{5}{20} \times 100 =\frac{1}{4} \times 100[/tex] = 25%
3. The theoretical Outcomes are: HH HT TH TT
So theoretical probability of getting HH = [tex]\frac{1}{4} \times 100[/tex] = 25%
Total number of outcomes = [tex]28+22+34+16[/tex] = 100
So experimental probability of getting HH = [tex]\frac{28}{100} \times 100[/tex] = 28%
Therefore, the experimental probability is 3% greater than the theoretical probability.
Which of the following piecewise functions is graphed above?
The answer is:
The piecewise function that represents the graph, is the option A (first option):
f(x) (piecewise function):
[tex]8; x\leq -1\\\\x^{2} -4x+1;-1<x<5\\\\-x+1\geq 5[/tex]
Why?To find the correct option, we need to look for the piecewise function that contains the following functioncs existing in the determined domains (inputs).
From the graph, we know that we need the following functions:
- A horizontal line, which exists from -∞ to -1, givind as input 8.
The function will be:
[tex]y=8[/tex]
Then, the piecewise function it will be:
[tex]8; x\leq -1[/tex]
- A quadratic function (convex parabola) which y-intercept is equal to 1, exists from -1 to 5, and it vertex (lowest point for this case) is located at (2,-3)
The function will be:
[tex]y=x^{2}-4x+1[/tex]
Finding the y-intercept, we have:
[tex]y=0^{2}-4*80)+1[/tex]
[tex]y=1[/tex]
Finding the vertex of the parabola, we have:
[tex]x_{vertex}=\frac{-b}{2}\\\\x_{vertex}=\frac{-(-4)}{2}=\frac{4}{2}=2[/tex]
[tex]y_{vertex}=x_{vertex}^{2}-4x_{vertex}+1[/tex]
[tex]y_{vertex}=2^{2}-4*2+1=4-8+1=-3[/tex]
The vertex of the parabola is located at the point (2,-3).
Then, for the piecewise function it will be:
[tex]x^{2} -4x+1;-1<x<5[/tex]
- A negative slope function, which evaluated at x equal to 5 (input), gives as output -4.
The function will be:
[tex]y=-x+1[/tex]
Proving that it's the correct equation by evaluating "x" equal to 5, we have:
[tex]y=-5+1[/tex]
[tex]y=-4[/tex]
It proves that the equation is correct.
Then, for the piecewise function it will be:
[tex]-x+1\geq 5[/tex]
Hence, we have that the piecewise function that represents the graph, is the option A (first option):
f(x) (piecewise function):
[tex]8; x\leq -1\\\\x^{2} -4x+1;-1<x<5\\\\-x+1\geq 5[/tex]
Have a nice day!
What is the solution to this system of equations?
x + 2y − z = 3
2x − y + 2z = 6
x − 3y + 3z = 4
Answer: The system of equations has no solutions.
Step-by-step explanation:
Identify the equation as:
[tex]x + 2y - z=3[/tex] [Equation 1]
[tex]2x -y + 2z=6[/tex] [Equation 2]
[tex]x - 3y + 3z=4[/tex] [Equation 3]
Multiply [Equation 1] by -2 and add this to [Equation 2] :
[tex](-2)(x + 2y - z)=3(-2)[/tex]
[tex]\left \{ {{-2x - 4y +2z=-6} \atop {2x -y + 2z=6}} \right.\\ ..........................\\-5y+4z=0[/tex]
Find another equation of two variables: Multiply [Equation 3] by -2 and add this to [Equation 2]:
[tex](-2)(x - 3y + 3z)=4(-2)[/tex]
[tex]\left \{ {{2x -y + 2z=6} \atop {-2x +6y -6z=-8}} \right.\\........................\\5y-4z=-2[/tex]
Then you get this new system of equations. When you add them, you get:
[tex]\left \{ {{-5y+4z=0} \atop {5y-4z=-2}} \right.\\..................\\0=-2[/tex]
Since the obtained is not possible, the system of equations has no solutions.
The solution to the system of equations x + 2y - z = 3, 2x - y + 2z = 6, and x - 3y + 3z = 4 is (-1, 1, 2) utilizing substitution method.
Explanation:The subject of this question is to find a solution to the system of linear equations. We can solve this system by methods of either substitution, elimination or matrix - but let's use substitution. First, let's isolate x in the first equation: x = 3 - 2y + z. Then we substitute x into the second and the third equation:
2(3 - 2y + z) − y + 2z = 6(3 - 2y + z) − 3y + 3z = 4
After simplifying these equations, we find y = 1 and z = 2. Plugging these back into x = 3 - 2y + z, we get x = -1. Therefore, the solution to the system is (-1, 1, 2).
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Four expressions are shown below:
4(8x + 2)
4(7x + 3)
32x + 8
28x + 12
Which two expressions are equivalent to 4(7x + 2 + x)?
It’s the first one and the third one
Answer: A and C
Step-by-step explanation:
What are the zeros of the quadratic function f(x) = 6x2 + 12x – 7?
x = –1 – and x = –1 +
x = –1 – and x = –1 +
x = –1 – and x = –1 +
x = –1 – and x = –1 +
It an expression or a way of saying f(x)=6x2+12-7
Answer:
[tex]x=-1+\frac{\sqrt{78} }{6}[/tex] and
[tex]x=-1-\frac{\sqrt{78} }{6}[/tex]
Step-by-step explanation:
[tex]f(x) = 6x^2 + 12x - 7[/tex]
To find out the zeros of the quadratic function, we apply quadratic formula
[tex]x=\frac{-b+-\sqrt{b^2-4ac}}{2a}[/tex]
From the given f(x), the value of a=6, b=12, c=-7
Plug in all the values in the formula
[tex]x=\frac{-12+-\sqrt{12^2-4(6)(-7)}}{2(6)}[/tex]
[tex]x=\frac{-12+-\sqrt{312}}{2(6)}[/tex]
[tex]x=\frac{-12+-2\sqrt{78}}{2(6)}[/tex]
Now divide each term by 12
[tex]x=-1+-\frac{\sqrt{78} }{6}[/tex]
We will get two values for x
[tex]x=-1+\frac{\sqrt{78} }{6}[/tex] and
[tex]x=-1-\frac{\sqrt{78} }{6}[/tex]
Find the perimeter of an isosceles triangle ABC. Side AB=4, and the base BC=3. Angles B & C are both 70 degrees.
Answer:
11 units
Step-by-step explanation:
Since ∆ABC is isosceles, it means that at least two sides are congruent/equal in length.
Sides CA and AB are congruent, since BC is the base. So, CA = 4.
That means the perimeter is 4 + 4 + 3 = 11 un
find the measure of an angle between 0 and 360 coterminal coterminal with the given angle 495 degrees
Answer:
135 degrees
Step-by-step explanation:
Coterminal means it ends at the same spot around the circle.
To calculate the resulting angle we need to reduce/increase the started value to arrive to a value between 0 and 359 degrees.
If the starting angle is greater or equal to 360, we subtract 360 until we get below 360.
If the starting angle is below 0, we add 360 until we get equal or greater than 0.
So, starting with 495, we subtract 360 a first time....
A = 495 - 360 = 135
We're already in the desired range (0-359)... so we have our answer.
A tank measure 30 centimeters by 30 centimeters by 50 centimeters. It is filled with water from a tap that flows at a rate of 6 liters per minute. How long would it take to fill 4/5 of the tank with water? Give your answer in minutes and seconds.
Answer:
6 minutes
Step-by-step explanation:
There are two ways you can simplify this problem:
1. change the dimensions to 3 dm × 3 dm × 5 dm, because 1 L = 1 dm³
2. Adjust the 5 dm dimension to 4/5 that value: 4 dm. Then you're filling a whole volume that is 3 dm × 3 dm × 4 dm = 36 dm³ = 36 L.
__
At the rate of 6 L/min, the tank will be filled to the desired level in ...
(36 L)/(6 L/min) = 6 min . . . . and 0 seconds
_____
A decimeter is 0.1 m = 10 cm, so 1 cubic decimeter is (10 cm)³ = 1000 cm³ = 1 liter. Using decimeters as the unit of measure in volume problems can make conversion to liters trivial.
The cost of a cell phone varies directly with the number of minutes it is used. If it costs $52.36 to talk for
175 minutes, what is the cost to talk for 325 minutes?
Answer:
$97.24
Step-by-step explanation:
You can use a direct proportion.
175 is to $52.36 as 325 minutes is to x.
Use two ratios of minutes/dollars:
175/52.36 = 325/x
Cross multiply.
175x = 52.36 * 325
175x = 17,017
x = 17,017/175
x = 97.24
Answer: $97.24
(1.1•10^-5)(3 •10^-2)
A. 4.1 • 10 ^-7
B. 4.1 • 10^10
C. 3.3 • 10^-7
D. 3.3 • 10^10
Answer:
C. 3.3 • 10^-7
Step-by-step explanation:
(1.1•10^-5)(3 •10^-2)
Multiply the numbers out front of the powers of ten, then add the exponents on the powers of 10
1.1 * 3 * 10 ^(-5+-2)
3.3 ^ (-7)
Answer:
C
Step-by-step explanation:
What is the length of the altitude of the equilateral triangle below
Answer:
Step-by-step explanation:
Recall that an equilateral triangle has three equal interior angles, all 60°. Let b represent the length of the base. Draw a dashed line from the upper vertex to the base, perpendicularly. This dashed line represents the height or altitude of the triangle.
Now construct a triangle whose opposite side is this altitude, whose hypotenuse is b (and whose base is (1/2)b).
The altitude (opp) is then given by sin Ф = opp / hyp = opp / b. Solving this for the altitude (opp), we get b·sin 60°:
alt (opp) √3
------------- = ------
hyp 2
b·√3
so that 2 alt = b·√3, or alt = ------------
2
Thus, for any equilateral triangle of side length b, the height of the triangle is
√3
alt = height = b · ------
2
Please note: Your problem statement refers to "the equilateral triangle below." It's important that you share such illustrations, along with all instructions. In this case your question was general enough so that I could use the definitions of "sine," "equilateral," etc., to come up with a general answer.
Answer:
do u have a pic i can see
Step-by-step explanation:
You purchase an item at a store and have a total of $153.60.The cashier then adds a 5% tax to your total. If you pay with two 100$ bills how much change will you get back?
Answer:
38.72 change
Step-by-step explanation:
153.6 x 1.05 = 161.28
100 x 2 = 200
200-161.28 = 38.72
Answer:
42.36
Step-by-step explanation:
Determine whether f(x) = -5x2 - 10x + 6 has a maximum or a minimum
value. Find that value and explain how you know.
Answer:
The function has a maximum
The maximum value of the function is
[tex]f (-1) = 11[/tex]
Step-by-step explanation:
For a quadratic function of the form:
[tex]ax ^ 2 + bx + c[/tex] where a, b and c are the coefficients of the function, then:
If [tex]a <0[/tex] the function has a maximum
If [tex]a> 0[/tex] the function has a minimum value
The minimum or maximum value will always be at the point:
[tex]x=-\frac{b}{2a}\\\y=f(-\frac{b}{2a})[/tex]
In this case the function is: [tex]f(x) = -5x^2 - 10x + 6[/tex]
Note that
[tex]a = -5,\ a <0[/tex]
The function has a maximum
The maximum is at the point:
[tex]x=-\frac{-10}{2(-5)}[/tex]
[tex]x=-1[/tex]
[tex]y=f(-1)[/tex]
[tex]y= -5(-1)^2 - 10(-1) + 6[/tex]
[tex]y= 11[/tex]
The maximum value of the function is
[tex]f (-1) = 11[/tex]
The function [tex]f(x) = -5x^2 - 10x + 6[/tex] has a maximum value at the vertex of its parabola. The maximum value is f(x) = 11 when x = -1.
To determine whether the quadratic function [tex]f(x) = -5x^2 - 10x + 6[/tex] has a maximum or a minimum value, we need to examine the coefficient of the [tex]x^2[/tex]term. The general form of a quadratic function is [tex]f(x) = ax^2 + bx + c.[/tex] If 'a' is negative, the parabola opens downwards, and the function has a maximum value at its vertex. In this case, 'a' is -5, which is negative, so the function has a maximum value.
To find the vertex of the parabola, we use the formula for the x-coordinate of the vertex, which is given by -b/(2a). Here, a = -5 and b = -10. Plugging these values into the formula gives us:
x = -(-10) / (2 * (-5))
x = 10 / -10
x = -1
Now that we have the x-coordinate of the vertex, we can find the y-coordinate (the maximum value) by substituting x = -1 into the original function:
[tex]f(-1) = -5(-1)^2 - 10(-1) + 6[/tex]
f(-1) = -5(1) + 10 + 6
f(-1) = -5 + 10 + 6
f(-1) = 5 + 6
f(-1) = 11
Therefore, the maximum value of the function [tex]f(x) = -5x^2 - 10x + 6[/tex] is 11 when x = -1. This is the value at the vertex of the parabola, confirming that it is the maximum value since the parabola opens downwards.