Samantha was receiving an interest rate of 12% on her account.
What is Present value ?Present value is the present value of future cash flows discounted at a certain rate. Present value is based on the concept of the time value of money, where a dollar today is worth more than a dollar in the future.
PV = FV /(1 + r )ⁿ
Information provided to us ,
time period , n = 6 years
let " $x " be the present value of Samantha's account money.
After 6 years it becomes double that is
future value, F = $2x
let "r" be rate of interest was Samantha receiving on her account.
plugging all known values in above formula,
$x = $2x /(1+r)⁶
=> (1+r)^6 = 2
=> 1 + r = (2)^1/6 = 1.122
=> r = 1.122 - 1 = 0.122
=> r = 12%
So, rate of interest is 12% .
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Larry has decided that the above ground swimming
pools business is not the best way to earn a living
(see practice problem e). He now thinks the big
money is in rowing machines. If Larry switches jobs,
he will earn a 12% commission on all the machines he
sells. For Larry to receive $15,000 in commissions,
how many dollars worth of machines must he sell?
The amount of worth of machine Larry needs to sell to recieve 15,000 dollars is 125, 000 dollars.
How to find the worth of machine he can sell to earn a particular amount?Larry thinks the big money is in rowing machines. If Larry switches jobs,
he will earn a 12% commission on all the machines he sells. For Larry to
receive $15,000 in commissions, the worth of dollars of machines he must
sell can be computed as follows:
Therefore,
let
x = amount he will earn
Hence,
15, 000 = 12% of x
15,000 = 12 / 100 × x
15000 = 12x / 100
cross multiply
1500000 = 12x
divide both sides by 12
x = 1,500,000 / 12
x = 125,000
Therefore, he needs to sell $125, 000 worth of machine.
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in how many ways can a committee with 4 democrats and 2 republicans be formed from a group of 7 democrats and 5 republicans?
A committee with 4 democrats and 2 republicans formed from a group of 7 democrats and 5 republicans can be created in a total of 350 ways. Therefore, the option C holds true.
The calculation of the same has been shown as below,
A group has 7 Democrats and 5 Republicans.
Committee with 4 Democrats and 2 Republicans = 7C4 x 5C2
7C4 x 5C2 = 7! / (4! 3!) x 5! / (2! 3!)
7C4 x 5C2 =(7×6×5 / 3×2×1) x (5×4 / 2×1)
7C4 x 5C2 = 35 × 10
7C4 x 5C2 = 350
Therefore, a committee can be created in 350 ways.
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Complete Question
In how many ways can a committee with 4 Democrats and 2 Republicans be formed from a group of 7 Democrats and 5 Republicans?
A 105
B 924
C 350
D 1680
M = -21 divided by 0
By using the property of division, it can be calculated that M = -21 divided by 0 is not possible
What is division?
Division is the process by which value of single unit can be calculated from the value of multiple unit.
The number to be divided is known as dividend, the number by which the dividend is divided is the divisor, the result obtained is the quotient and the remaining part is the remainder.
There is a well known formula for division
Divisor x Quotient + Remainder = Dividend.
Anything divided by 0 is not possible.
M = -21 divided by 0 is not possible
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Use Infinite differences to write the linear function that represents the given data set.
The linear equation on the table is the one in option D.
y = 25*x + 45
How to write the linear function?
A general linear function is written as:
y = a*x + b
Where a is the slope and b is the y-intercept.
If we know two points on the line, (x₁, y₁) and (x₂, y₂), the slope can be written as:
a = (y₂ - y₁)/(x₂ - x₁)
Using the first two points, (0, 45) and (1, 70) we can get the slope:
a = (70 - 45)/(1 - 0) = 25
And because of the point (0, 45) we know that the y-intercept is b = 45, then the linear equation is:
y = 25*x + 45
So the correct option is D.
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Hamburger Heaven is having a lunch special where customers buy one 1/2-* 1 p
pound cheeseburger and get one free. If they set aside 48 pounds of meat,
how many 1/2-pound cheeseburgers can they make?
24
96
O 144
O48
Answer:
hshsjsjs
Step-by-step explanation:
shhshshsjdjdjdjdj
find the exact length of the curve. y = 3 + 4x3/2, 0 ≤ x ≤ 1
So the exact length of the curve is given by [tex]L=(1/36)*[\frac{37^{3/2}}{3/2} - 1][/tex]
Given the equation of curve:
[tex]y = 3+ 4x^\frac{3}{2}[/tex]
The length of the curve is given by [tex]L= \int\limits^a_b {\sqrt{1+(y^[/tex]
Where y^ is derivative of y with respect to x
So [tex]y= 4*(3/2) * \sqrt{x}= > 6 \sqrt{x}[/tex]
Given a=1 and b=0
So [tex]L= \int\limits^1_0 {\sqrt{1+(6\sqrt{x})^2 } } \, dx[/tex]
[tex]L= \int\limits^1_0 {\sqrt{1+36x } } \, dx[/tex]
let 1+36x be t
36dx = dt
As the value of x changes after the substitution of the value.
So now the L changes as:
[tex]L= 1/36 \int\limits{\sqrt{t } } \, dt[/tex]
[tex]L=1/36* \left \{ {{t=37} \atop {t=1}} \right. \frac{t^\frac{3}{2} }{\frac{3}{2} }[/tex]
[tex](1/36)*[\frac{37^{3/2}}{3/2} - 1][/tex]
the min value of t=1 and max value of t=37
[tex]L=(1/36)*[\frac{37^{3/2}}{3/2} - 1][/tex]
[tex]L=(1/36)*[\frac{37^{3/2}}{3/2} - 1][/tex]
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(a) The quadratic equation (x+2)² +3k-1=0 has two real and distinct roots, where k is a constant. Find the range of values of k.
Answer: This means that the range of values of k is k ∈ [-1/3, 1/3].
Step-by-step explanation: The quadratic equation (x+2)² +3k-1=0 can be written as (x+2)² = 1-3k. For the equation to have two real and distinct roots, the expression under the square root must be nonnegative. Therefore, we have the inequality 1-3k ≥ 0. Solving this inequality gives us -1/3 ≤ k ≤ 1/3. This means that the range of values of k is k ∈ [-1/3, 1/3].
Draw a line representing the "rise" and a line representing the "run" of the line. State the slope of the line in simplest form.
If f(x) =
√x-10+3, which inequality
x-10+3, which inequality can be used to find the domain of f(x)?
O
0x20
Ox-1020
O √x-10
x-10+320
Inequality can be used to find the domain of f(x) is [tex]$\quad x \geq 20$[/tex]
Interval Notation: [tex]$[20, \infty)$[/tex]
What is Domain definition?
The domain of a function is the set of input or argument values for which the function is real and defined.
Find non - negative values for radicals: [tex]$x \geq 20$[/tex]
The function domain
[tex]$$x \geq 20$$[/tex]
Range of[tex]$\sqrt{\frac{1}{2} x-10}+3:\left[\begin{array}{cc}\text { Solution: } & f(x) \geq 3 \\ \text { Interval Notation: } & {[3, \infty)}\end{array}\right]$[/tex]
Function range definition
The set of values of the dependent variable for which a function is defined
The range of an radical function of the form [tex]$c \sqrt{a x+b}+k$[/tex] is [tex]$f(x) \geq k$[/tex][tex]$k=3$[/tex]
[tex]$f(x) \geq 3$[/tex]
Axis interception points of [tex]$\sqrt{\frac{1}{2} x-10}+3$[/tex] : None
x - axis interception points of [tex]$\sqrt{\frac{1}{2} x-10}+3$[/tex] : None
y - axis interception point of [tex]$\sqrt{\frac{1}{2} x-10}+3$[/tex] : None
None
Extreme Points of [tex]$\sqrt{\frac{1}{2} x-10}+3: \quad$[/tex]Minimum (20,3)
First Derivative Test definition
Suppose that [tex]$x=c$[/tex] is a critical point of f(x) then, If [tex]$f^{\prime}(x) > 0$[/tex] to the left of [tex]$x=c$[/tex]and [tex]$f^{\prime}(x) < 0$[/tex] to the right of x=c then x=c is a local maximum. If [tex]$f^{\prime}(x) < 0$[/tex] to the left of [tex]$x=c$[/tex] and [tex]$f^{\prime}(x) > 0$[/tex] to the right of [tex]$x=c$[/tex] then [tex]$x=c$[/tex] is a local minimum. If [tex]$f^{\prime}(x)$[/tex] is the same sign on both sides of [tex]$x=c$[/tex] then [tex]$x=c$[/tex] is neither a local maximum nor a local minimum.
[tex]$$f^{\prime}(x)=\frac{1}{2 \sqrt{2} \sqrt{x-20}}$$[/tex]
Find intervals: Increasing:20 [tex]$ < x < \infty$[/tex]
Plug [tex]$x=20$[/tex] into [tex]$\sqrt{\frac{1}{2} x-10}+3: \quad 3$[/tex]
Minimum (20,3)
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81 of [60-{8*7-(13-3*5)}] find simply
Answer:
Step-by-step explanation:
81 of [60-{(8*7)-(13-(3*5))}] =
81 of [60-{56}-(13-15)] =
81 of [60-{56}-(-2) =
81 of [60-{56}+2] =
81 of [6] =
81% of 6 = 4.86
Jamie has 2 ½ packs of sunflower seeds to cover 150 sq ft. Based on this
information, what is the number of sq ft that 1 pack of sunflower seeds will
cover?
Answer:
60 ft.^2
Step-by-step explanation:
Known area/number of packs= A / number of packs for A, where A= area of interest
150/2.5=A/1
A=60
A dance squad needs at least $800 to buy new dance outfits. They have saved $350
already. -They are selling tickets to a dance performance for $10 each. They need to sell
x tickets to have enough money to buy the new dance outfits. Which inequality
represents the situation?
Answer:
x>=45 is the req. inequality
The inequality equation for the number of tickets to be sold is x ≥ 45
What is an Inequality Equation?Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.
In an inequality, the two expressions are not necessarily equal which is indicated by the symbols: >, <, ≤ or ≥.
Given data ,
Let the number of tickets to be sold be x
Let the total amount of money to be saved be = $ 800
The amount of money already saved = $ 350
So , the remaining amount of money = $ 800 - $ 350 = $ 450
The cost of each ticket = $ 10
So , the cost of x tickets = 10x
Now , the number of tickets to be sold to raise $ 450 is given by
10x ≥ 450 be equation (1)
On simplifying the equation , we get
Divide by 10 on both sides of the equation , we get
x ≥ 45
Therefore , the number of tickets to be sold is 45
Hence , the inequality is x ≥ 45
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original equations: S(p) = -200 + 50p and D(p) = 1060 - 55p please find the equilibrium price and quantity of the two equations. I think I already set up the equation for the equilibrium price here, though no guarantee that I did it right. Qd = 1060 - 55p = Qs = -200 + 50p
The equilibrium price is; $12
The quantity for the two equations is; 400
How to find the equilibrium price?
The equilibrium price formula is based on the demand and supply quantities; you will set quantity demanded (Qd) equal to quantity supplied.
The equilibrium price definition above is one that tells us that there is a price point that meets the needs of both supply and demand. In order to understand when those needs are met, we need to know how to find equilibrium price.
We are given;
Quantity supplied; S(p) = -200 + 50p
Quantity demanded; D(p) = 1060 - 55p
Thus, equilibrium price is p when;
S(p) = D(p)
-200 + 50p = 1060 - 55p
1060 + 200 = 55p + 50p
1260 = 105p
p = 1260/105
p = $12
S(p) = -200 + 50(12)
S(p) = 400
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The 2 digit number which become 5 by 6th of itelf when it digit are revered. The difference in the digit of the
number being 1, then the two digit number i
After solving the two digit number is 45.
In the given question,
The 2 digit number which become 5 by 6th of itself when it digit are revered.
The difference in the digit of the number being 1, then we have to find the two digit number.
Let the two digit number = 10y+x
When we reversed the number then the number is 10x+y
As given that;
10y+x = 5/6(10x+y)
Multiply by 6 on both side, we get
60y+6x = 50x+5y
Subtract 5y on both side, we get
55y+6x = 50x
Subtract 50x on both side, we get
55y-44x = 0
Divide by 11 on both side, we get
5y-4x = 0
4x-5y = 0......................(1)
It is given that the difference between the number is 1.
x-y = 1..................(2)
Multiply by 4 in equation 2
4x-4y = 4.........................(3)
Now subtract equation 3 and 1, we get
y = 4
Now putting the value of y in equation 2
x-4 = 1
Add 4 on both side, we get
x = 5
Since the number is 10y+x. So
10y+x = 10(4)+5
10y+x = 45
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PLEASE HELP QUICK!! WILL GIVE BRAINLIEST AND 25 POINTS!!
Find the value of x, round to the nearest degree.
Answer:
7
Step-by-step explanation:
4+3=7
7-4=3
7-3=4
Find the percent the first number is of the second.
(1.) 1.5 and 7.5,
(2.) 5ft 37.5ft
To find the percent that 1.5 is of 7.5, we need to divide 1.5 by 7.5 and multiply the result by 100% to convert it to a percentage:
1.5 / 7.5 = 0.2
0.2 * 100% = 20%
Therefore, 1.5 is 20% of 7.5.
To find the percent that 5ft is of 37.5ft, we need to divide 5 by 37.5 and multiply the result by 100% to convert it to a percentage:
5ft / 37.5ft = 0.1333
0.1333 * 100% = 13.33%
Therefore, 5ft is 13.33% of 37.5ft.
The area of the figure above is
blank + 25pi/4
Answer:
Add 75 for the blank number----------------------------
Divide the figure by three parts for easy calculation of its area:
Rectangle of 5 by 10 units, Square of 5 units,Quarter-circle of 5 units radius.Find each area and add up:
A = 5*10 + 5*5 + π*5²/4 A = 50 + 25 + 25π/4A = 75 + 25π/4The blank is 75.
If m<2 = 63°, then m<3 is:
63°.
27°
117°
None of these choices are correct.
Answer:
63°
Step-by-step explanation:
since they are in the form of vertically opposite angle.
HELPPP Determine the value of h in the equation one third plus h equals five thirds.
six thirds
fourth thirds
six over nine
four ninths
Answer:
h = [tex]\frac{4}{3}[/tex]
Step-by-step explanation:
[tex]\frac{1}{3}[/tex] + h = [tex]\frac{5}{3}[/tex] ( subtract [tex]\frac{1}{3}[/tex] from both sides )
h = [tex]\frac{5}{3}[/tex] - [tex]\frac{1}{3}[/tex] = [tex]\frac{4}{3}[/tex]
answer these questions. ( find the variables)
1. n + 7 = 10
2. c - 2+ = 7
3. a x 3 = 15
4. a / 5 = 9
5. 9z + 2 = 38
6. 17 + 3n = 47
7. 7y - 7 = 21
8. 3x + 90 = 147
9. 26/ y + 3 = 16
10. 147 - 3x + 90
Answer:
1)3
2)9
3)5
4)45
5)4
6)10
7)4
8)19
9)2
10)unable (no equal sign?)
Step-by-step explanation:
PLEASE HURRY! Brody works at the ticket booth at the movie theater and sold 25 adult tickets and several child tickets during the first hour at work. Each adult ticket costs $12, and each child ticket costs $6. Brody collected $360 during that hour.
How many child tickets did he sell?
___ child tickets
Answer:
10 Child Tickets
Step-by-step explanation:
25 x 12 = 300
So we need 60
6 x 10 = 60
Step-by-step explanation:
25 x 13 = 300
6 x 10 = 60300 + 60 = 360
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The function shown in the graph below is modeled by:
a linear function.
an exponential function.
a quadratic function.
how is 15×3/5 = 9
the slash is for the fraction
Answer:15x3 /=divide 5 = 9
Step-by-step explanation:
because if you do 15x3 it is 45 then you divide it by 5 and get 9 as your answer!
An office machine purchased new for $3600 loses $400 each year.
Assume the value continues to decrease the same amount
each year. If f(x) represents the value of the office machine
after x years, which linear function models the given situation?
The linear function models the given situation will be equal to f(x) = $3600 - $400(x).
What is an equation?Mathematical expressions with two algebraic symbols on either side of the equal (=) sign are called equations.
This relationship is illustrated by the left and right expressions being equal. The left-hand side equals the right-hand side is a basic, straightforward equation.
As per the given information in the question,
Original price of Machine = $3600
Price lost by the machine each year = $400
Then, the equation will be,
f(x) = $3600 - $400(x)
Here, x represents the number of years.
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Answer:
f(x) = −400x + 3600
The perimeter of a rectangle i 80 inche. The length of the rectangle i 12 inche. Which equation could repreent the width of the rectangle, w? Repone w = 2(80 – 12) w, = 2(80 – 12) w = (80 – 12) ÷ ÷ 2 w, = (80 – 12) divided by 2 w = 2(80 – 24) w , = 2(80 – 24) w = (80 – 24) ÷ ÷ 2
The perimeter of a rectangle i 80 inche. The length of the rectangle i 12 inchs then width is equal to 28 inch
What is length area and perimeter?
Firstly, the area of a shape is the surface or flat space that the shape covers whereas the perimeter of a shape represents the distance around its boundary. Secondly, the area is measured in square units, whereas the perimeter is measured in linear units.
given that the perimeter of a rectangle is 80 inch
we know that
perimeter = 2 ( L +B)
putting the values we get
80 = 2 ( 12 + B)
40= 12+B
B= 28
then the width is equal to 28inch
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Karen earns £12.80 an hour for a 35 hour week, time and a half on the next 6 hours and double time after that. How much does she earn for a 43 hour week?
Answer:
I hope the image helps!
A line that includes the point (0, 0) has a slope of 2. What is its equation in slope-intercept
form?
Write your answer using integers, proper fractions, and improper fractions in simplest form.
The equation of a line that passes through (0, 0) and has a slope of 2 is y = 2x.
How to represent equation in slope intercept form?Equation of a line can be represented in slope intercept form as follows
y = mx + b
where
m = slopeb = y-interceptA line that includes the point (0, 0) has a slope of 2. The equation of the line in slope intercept form is as follows:
y = 2x + b
using (0, 0) let's find y-intercept.
0 = 2(0) + b
Hence,
b = 0
Therefore, the equation is y = 2x
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A Web site sells baseball caps for $12 each. There's a $4 shipping charge no matter
how many hats you order. The equation c = 12h + 4 gives the total cost to buy h hats.
Which statement correctly describes what happens when h increases?
Answer:
0
Step-by-step explanation:
1 balls and bins throw n balls into m bins, where m and n are positive integers. Let x be the number of bins with exactly one ball. Compute var(x). Your final answer should not contain any summations
Using 1 balls and bins, n balls are thrown into m bins; m and n are positive numbers. the probability of any given bin containing one ball is n/m n * (1 - (1 - 1/m)^n) / m^2
Given that n is the number of balls and m is the number of bins, the probability of any given bin containing one ball is n/m. Therefore, the variance of x is equal to the variance of a binomial random variable with n trials and probability of success p = n/m.
By the formula for the variance of a binomial random variable, the variance of x is equal to n * (1 - (1 - 1/m)^n) / m^2.
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