Answer:
You are better off investing today in the mutual fund and earn 8.2 percent semiannually for 10 years.
Step-by-step explana
We will need to calculate the interest generated in both of these scenarios to determine which one is the best.
In scenario 1
Periods= 10 years * 2= 20 periods (since rate is biannual)
Principal= $12,000
Rate= 8.2%
Using the formula
Interest= Principal * Rate * Time
Interest= 12,000* 0.082 * 20
Interest= $19,680
In scenario 2
Principal= $11,000
Rate= 10%
Period= 8 years ( two years have already passed, so we calculate for 8 years since we want to see gain after 10 years)
Interest= 11,000* 0.10 * 8
Interest= $8,800
So imvesting $12,000 at interest rate of 8.2% biannually for 10 years is a better option.Answer:
You are better off investing today in the mutual fund and earn 8.2 percent semiannually for 10 years.
Explanation:
We will need to calculate the interest generated in both of these scenarios to determine which one is the best.
In scenario 1
Periods= 10 years * 2= 20 periods (since rate is biannual)
Principal= $12,000
Rate= 8.2%
Using the formula
Interest= Principal * Rate * Time
Interest= 12,000* 0.082 * 20
Interest= $19,680
In scenario 2
Principal= $11,000
Rate= 10%
Period= 8 years ( two years have already passed, so we calculate for 8 years since we want to see gain after 10 years)
Interest= 11,000* 0.10 * 8
Interest= $8,800
So imvesting $12,000 at interest rate of 8.2% biannually for 10 years is a better option.
How many sets of three consecutive integers are there in which the sum of the three integers equals their product?
Answer:
3
Step-by-step explanation:
since the 3 integers are consecutive, we are dealing with x, x+1, x+2.
and their sum is the same as their product :
x + (x + 1) + (x + 2) = x(x + 1)(x + 2)
3x + 3 = x(x² + 3x + 2) = x³ + 3x² + 2x
x³ + 3x² - x - 3 = 0
this is a polynomial of third degree.
and as such it has 3 solutions.
of course, it could be that some of them are the same or are even in the realm of complex numbers (i = sqrt(-1)), but usually these 3 solutions are different real numbers.
I tried x=1 just to see, and, hey, it is a solution for this equation.
x = 1 means that the other 2 consecutive integers are 2 and 3.
and indeed, 1+2+3 = 1×2×3 = 6.
now it is easier to find the other 2 solutions, as a zero solution can be expressed as a factor of the whole expression.
for x = 1 the factor term is (x - 1), as this term is then turning 0, when x = 1.
I can divide the main expression by this factor and then analyze the quotient about the other 2 solutions.
x³ + 3x² - x - 3 : x - 1 = x² + 4x + 3
- x³ - x²
----------------
0 4x² - x
- 4x² - 4x
-----------------------
0 + 3x - 3
- 3x - 3
---------------------------
0 0
so, the original expression can be written as
(x² + 4x + 3)(x - 1).
now we need to find the 2 zero solutions for x²+4x+3
the general solution to a quadratic equation is
x = (-b ± sqrt(b² - 4ac))/(2a)
in our case
a = 1
b = 4
c = 3
so,
x = (-4 ± sqrt(4² - 4×1×3))/(2×1) =
= (-4 ± sqrt(16 - 12))/2 = (-4 ± sqrt(4))/2 =
= (-4 ± 2)/2 = -2 ± 1
x1 = -2 + 1 = -1
x2 = -2 - 1 = -3
so, we have the additional solutions :
-1 0 1
-3 -2 -1
-1 + 0 + 1 = -1×0×1 = 0
-3 + -2 + -1 = -3×-2×-1 = -6
and there we have it fully proven :
there are 3 different sets of 3 consecutive integers with the same sum as product.
Elena gets paid $60 every time she babysits, and she donates the same amount of this money to charity every time she gets paid. Elena will babysit 7 times this month, and she wants to make sure she keeps at least $420 from this month’s earnings.
The inequality 7(60 - x) ≥ 420 represents this situation.Solve this inequality and explain what the solution represents in this context.
Answer:
It's good
Step-by-step explanation:
7 x 60 = 420.
So, she will get the complete money
What is the degree of the polynomial below?
7x5+6x2 + 4x + 2
Answer: 5
Step-by-step explanation:
7x^5 has the highest degree of the polynomial
Answer:
5
Step-by-step explanation:
The highest power(Exponent) of variable x is the degree of the polynomial
Highest power = 5
Degree of the polynomial = 5
True or False: Every fraction has a limited number of equivalent fractions.
A
True
B
False
Answer: False
Step-by-step explanation: Numbers are infinite, They go on forever. 2/3 can be 20/30, 200/300, etc.
Answer
B)False
Step-by-step explanation:
Every fraction has an infinite number of equivalent fractions.
For example, the equivalent fractions for 1/2 are 2/4, 3/6, 4/8, 5/10, 6/12, and infinite others. Hence, there are infinite equivalent fractions for a every single fraction.
write the phrase as an expression.
the sum of 12 and a number h
Answer:12+h
Step-by-step explanation:
Charlotte has joined the a Frequent Coffee Buyer program with a local cafe. The program costs $5 per month which allows her to get a discounted coffee price of $2.5 per cup. Answer the questions below regarding the relationship between the of number of cups of coffee purchased and the total monthly cost.
The independent variable, x, represents the
number of coffee cups purchased
, and the dependent variable is the
total monthly cost
, because the
number of coffee cups purchased
depends on the
total monthly cost
.
A function relating these variables is A(x) =A(x)=
.
So A(10) =A(10)=
, meaning 1010
.
The equation will be A(x) = 5 + 2x and the independent variable will be the number of coffee cups that are purchased.
How to calculate the equationSince the program costs $5 per month which allows her to get a discounted coffee price of $2.5 per cup.
The independent variable x, represents the number of coffee cups purchased. The dependent variable is the total monthly cost.
The function is A(x) = 5 + 2x. The cost for 10 cups will be:
= 5 + 2x
= 5 + 2(10)
= 5 + 20
= 25
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The means and mean absolute deviations of Sidney’s and Phil’s grades are shown in the table below. Means and Mean Absolute Deviations of Sidney’s and Phil’s Grades Sidney Phil Mean 82 78 Mean Absolute Deviation 3. 28 3. 96 Which expression represents the ratio of the difference of the two means to Sidney’s mean absolute deviation? StartFraction 82 over 3. 28 EndFraction StartFraction 4 over 3. 28 EndFraction StartFraction 4 over 0. 68 EndFraction StartFraction 82 over 0. 68 EndFraction.
Answer:
4/3.28
Step-by-step explanation:
Answer:
4/3.28
Step-by-step explanation:
I need help pls help me
First Method:
Round [tex]\frac{3}{5}[/tex] to the closest integer, which is 1.
Round [tex]\frac{3}{4}[/tex] to the closest integer, which is also 1.
So 1 + 1 = 2.
Answer for method 1: 2
Second Method:
[tex]\frac{3}{5}[/tex] + [tex]\frac{3}{4}[/tex] = [tex]\frac{3*4}{5*4} + \frac{3*5}{4*5} = \frac{12}{20}+\frac{15}{20}=\frac{27}{20}[/tex]
[tex]\frac{27}{20}[/tex] is around 1
Answer for method 2: 1
The closest answer is 1.
Determine the GCF of 12y, 15y?, and 6y
Answer:
3y
Step-by-step explanation:
All three expressions have the factor 3, and all three have the factor y. Thus, the GCF is 3y.
PLEASE ANSWER HURRY WHICH ONE IS IT?
Answer:
x = cd-by/ a
Step-by-step explanation:
ax + by / c = d
ax + by = cd
ax = cd-by
x = cd-by/a
Answer:
B
Step-by-step explanation:
You can multiply both sides by c to remove the fraction part.
d(c) = ax + by/c(c)
dc = ax + by
Then subtract "by" from both sides to isolate x.
dc - by = ax - by + by
dc - by = ax
Then divide both sides by a to completely isolate the variable x.
(dc - by)/a = ax/a
(dc - by)/a = x
B
At lunch, the meal cost $55 and the sales tax of 3.58 was added to the bill. What was the tax rate for meals in this city?
Answer:
this is what to do
Step-by-step explanation:
The formula for calculating the sales tax on a good or service is selling price x sales tax rate, and when calculating the total cost of a purchase, the formula is total sale amount = selling price + sales tax.
Examine this system of equations. Which numbers can be multiplied by each equation so that when the two equations are added together, the x term is eliminated?
One-fifth x + three-fourths y = 9
Two-thirds x minus five-sixths y = 8
A. –10 times the first equation and 3 times the second equation
B. 10 times the first equation and 3 times the second equation
C. –3 times the first equation and 5 times the second equation
D. 3 times the first equation and 5 times the second equation
Answer:
The first equation must be multiplied by 18 and second equation must be multiplied by 8
Step-by-step explanation:
To eliminate x, on the addition of two equations, we multiply the first equation by -10, and the second equation by 3. Thus, option (A) –10 times the first equation and 3 times the second equation, is the right choice.
What is a system of equations?A system of equations is a set of equations, involving similar variables used to solve for the variables simultaneously.
How to solve the question?In the question, we are asked for the numbers which when multiplied by the two equations respectively, eliminate x, when the equations are added.
The two equations are:
(1/5)x + (3/4)y = 9 ... (i),
(2/3)x - (5/6)y = 8 ... (ii).
We know that to eliminate a variable from a system of equations, their coefficients need to be equal and the sign needs to be opposite.
In the question, we are asked to eliminate x.
The coefficients of x are (1/5) and (2/3).
To equalize the coefficients, we make them equal to their LCM.
LCM of (1/5) and (2/3) is 2.
To make (1/5) as 2, we need to multiply it by 10.
To make (2/3) as 2, we need to multiply it by 3.
For opposite signs, we will make of this negative.
The option with our calculations is A. –10 times the first equation and 3 times the second equation.
Thus, to eliminate x, on the addition of two equations, we multiply the first equation by -10, and the second equation by 3. Thus, option (A) –10 times the first equation and 3 times the second equation, is the right choice.
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In triangle PQR, A and B are points on side QR such that they trisect QR. Prove that, ar( triangle PBR) = 0.5 ar( triangle PQB).
pls give the answer with steps...pls help me guys
Explanation:
We assume the problem statement is telling us that the order of points on segment QR is Q, A, B, R, and that QA = AB = BR. This means that
QB = QA +AB = 2BR
BR = 1/2(QB)
The area of the triangles will be ...
A = 1/2bh
For triangle PQB, the area is ...
ar(PQB) = 1/2(QB)h . . . . . h is the perpendicular distance from QR to P
For triangle PBR, the area is ...
ar(PBR) = 1/2(BR)h = 1/2(1/2QB)h . . . . h is the same as above
ar(PBR) = 1/2ar(PQB)
__
Essentially, you're showing the base of the smaller triangle is 1/2 the base of the larger one and using that to show the area of the smaller triangle is 1/2 the area of the larger one. (Both have the same height.)
HELP ASAP
what is the length of bd. round your answer to the nearest hundredth
Answer:
BD = 4.99 units
Step-by-step explanation:
Consider the triangle ABD only. The angle formed is 31 degrees which occurs between two sides that are AD and BC. We know that for a right angled triangle, the angle can always be taken as an angle between hypotenuse and base. Thus, The perpendicular sides is then 3 units, where base is BD and Hypotenuse is AD Using formula for tanθ tanθ = Perpendicular/Base tan31 = 3/BD 0.601 = 3/BD BD = 3/0.601 BD = 4.99 units
answer the following question
Answer:
Step-by-step explanation:
1) Total = 30 students
Girls : Boys = 2 : 1
Total part = 2 + 1 = 3
Fraction of girls = 2/3
[tex]Number \ of \ girls = \dfrac{2}{3}*30 = 2*10 = 20\\\\\\Number \ of \ boys = 30 - 20 = 10[/tex]
Answer: 20 girls and 10 boys
2) Total pens = 24
Red :Blue : Black = 3 : 4 : 1
Total parts = 3 + 4 + 1 = 8
[tex]Number \ of \ red \ pens = \dfrac{3}{8}*24=3*3 = 9\\\\\\Number \ of \ blue \ pens = \dfrac{4}{8}*24=4*3=12\\\\\\Number \ of \ black \ pens = \dfrac{1}{8}*24=1*3=3[/tex]
Answer: 9 red pens
12 blue pens
3 black pens
3) Total people = 180
Adults : boys : girls = 3 : 2 : 7
Total parts = 3 + 2 + 7 = 12
[tex]Number \ of \ adults = \dfrac{3}{12}*180=3*15=45\\\\\\Number \ of \ boys = \dfrac{2}{12}*180=2*15=30\\\\\\Number \ of \ girls = \dfrac{7}{12}*180=7*15=105\\\\[/tex]
Answer: 45 adults ; 30 boys and 105 girls
4)Total vehicles = 12000
Cars : trucks : motorcycles = 13 : 8 : 3
[tex]Number \ of \ cars = \dfrac{13}{24}*12000=13 *500 = 6500\\[/tex]
6500 cars drove through on that day
[tex]b) Number \ of \ trucks = \dfrac{8}{24}*1200 = 8*500 = 4000[/tex]
4000 trucks
Which is greater 3yd or 30ft
Answer: 30 feet is greater
Step-by-step explanation:
3 yards is 9 feet (1 yard is 3 feet). 9 < 30. 30 feet is more than 9 feet, and 9 feet is equal to 3 yards so 30 feet is greater than 3 yards
plz help me i’ll give like 50 points!
Answer:
We will be using the Pythagorean theorem for the first 2 and SOH CAH TOA for the other 3.
a^2 + b^2 = c^2
sin(t) = b/c; cos(t) = a/c; tan(t) = b/a
#4) a^2 + 9^2 = (3sqrt(10))^2 #5 9^2 + 27^2 = c^2
a^2 + 81 = 90 81 + 729 = c^2
a^2 = 9 810 = c^2
a = 3 9sqrt(10) = c
#6 27 + 3 = 30 #9 cos(90) = 8/c
8/-0.45 = c
| 17 | = c [not the exact value]
#7 8^2 + b^2 = 17^2 #8 2^2 + 15^2 = c^2
64 + b^2 = 289 4 + 225 = c^2
b^2 = 225 229 = c^2
b = 15 [not the exact value] 15.3 = c [not the exact value]
Sorry if something doesn't make sense and felt kind of rushed. Feel free to comment down below my answer if you have any questions and I'll try to clarify it the best I can.
Please help I will give a brainly
2(x - 6) + 6 = 4x - 4
Multiply 2 with x - 6
2x - 12 + 6 = 4x - 4
2x - 6 = 4x - 4
Change the position of them
2x - 4x = -4 + 6
- 2x = 2
Take -2 to other side and divide
[tex]x \: \: = \frac{2}{ - 2} [/tex]
x = -1 answer
Write an equation in slope intercept form that has a slope of \frac{3}{2}
2
3
goes through these two points.
\left(2,-6\right)\&\left(4,-3\right)(2,−6)&(4,−3)
Mrs. Smith bought an 88 pound pumpkin so she could make a pie. The pumpkin cost Mrs. Smith $ 6 . 80$6.80. How much did the pumpkin cost per pound?
Answer:
$.08 per pound
Step-by-step explanation:
Take the total cost and divide by the number of pounds
6.80 / 88 lbs
$.077272727 per pound
Rounding to the nearest cent
$.08 per pound
what’s the linear equation for 8 miles in 32 min
What is the degree of the polynomial?
Answer:
5
Step-by-step explanation:
6x^2 + 7x^3 + 8x^5 +9
Write in order from highest power to lowest power
8x^5 + 7x^3 + 6x^2 +9
The highest power ( largest exponent) is 5
The degree of the polynomial is 5
samantha was training for a marathon each week she ran she increased her distance by 2km if she ran 5km the first week after how many weeks will be able to run 15km?
Answer:
5 weeks
Step-by-step explanation:
x(number of weeks)
5+2x=15
2x=10
x=5
(verification)
5+2*5=15
15=15
How do I solve this?
360÷9=40°
2x+40=180
2x=180-40
2x=140
x=140÷2
x=70
angle is
2×70=140°
The circle has a diameter of 16 inches. What is the area of the circle, rounded to the nearest square inch?
A circle with diameter 16 inches.
A) 64
B) 79
C) 201
D) 804
Statement:
The circle has a diameter of 16 inches.
To find out:
The area of the circle.
Solution:
Diameter of the circle = 16 inches.Radius of the circle = Diameter ÷ 2 = 16 inches ÷ 2 = 8 inchesπ = 3.14 We know, area of a circle = πr² where r is the radius.Therefore, the area of the circle= 3.14 × (8)² square inches= 3.14 × 64 square inches= 200.96 square inches= 201 square inches [rounded to the nearest square inch]Answer:
C) 201 square inches
Hope you could understand.
If you have any query, feel free to ask.
Answer:
[tex]Solution,\\Here,\\Diameter(d)=16 inches\\radius(r)=16inches/2=8inches\\Now, \\ Area=\pi r^{2} \\ Area=3.14*(8inches)^{2} \\ Area=3.14*64inches^{2} \\Area=200.96inches^{2} =201inches^{2}[/tex]
Hence, Option c is correct.
There are two concentric spheres of radii 3 units and 6 units. What is the volume, in cubic units, of the region within the larger sphere and not within the smaller sphere
Check the picture below.
we can simply get the volume of the larger sphere, then the volume of the smaller sphere and subtract it from that of the larger sphere and what's leftover is the region between both.
[tex]\stackrel{\textit{\large volumes}}{\stackrel{\textit{sphere with r=6}}{\cfrac{4\pi (6)^3}{3}}~~ -~~\stackrel{\textit{sphere with r = 3}}{\cfrac{4\pi (3)^3}{3}}}\implies 288\pi -36\pi \implies 252\pi \approx \stackrel{cubic~units}{791.68}[/tex]
The region within the larger sphere and not within the smaller sphere is 789.02 cubic units.
What is the volume of a sphere?The volume of sphere is the measure of space that can be occupied by a sphere. If the radius of the sphere formed is r and the volume of the sphere is V. Then, the volume of the sphere is given by: Volume of Sphere, V = (4/3)πr³
Given that, there are two concentric spheres of radii 3 units and 6 units.
Now,
Volume of sphere with radius 3 units is
V₁ = 4/3×3.14×3³
= 4/3×3.14×27
= 4×3.14×9
= 113.04 cubic units
Volume of sphere with radius 6 units is
V₂ = 4/3×3.14×6³
= 4/3×3.14×216
= 902.06 cubic units
Now, difference is 902.06-113.04
= 789.02 cubic units
Therefore, the region within the larger sphere and not within the smaller sphere is 789.02 cubic units.
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Rewrite the following expression.
10
3
OA (23)
O B.
Oc. (alia
10
OD.
1
Answer:
[tex]the \: answer \: is \: c \: \\ {x}^{ \frac{10}{3} } = \sqrt[3]{ {x}^{10} } = {x}^{3} \sqrt[3]{x} \\ {x}^{3 } \times {x}^{ \frac{1}{3} } = {x}^{3 + \frac{1}{3} } = {x}^{ \frac{10}{3} } [/tex]
Item 3
What is the value of m in this proportion?
1235=13m
m=
solve pls brainliest
Answer:
3/8 = 9/24
1/3 = 8/24
3/8 > 1/3
Step-by-step explanation:
3/8 = 9/24 (multiply both numerator and denominator by 3)
1/3 = 8/24 (multiply both numerator and denominator by 8)
9/24 > 8/24
I NEED ANSWERR PLEASE AND FAAST
Look at the pics
Step-by-step explanation:
