Answer:
We know that the total number of coins is 17.
N of the coins are nickels, and the rest of the coins are dimes.
Then the number of dimes is given by the difference between the total number of coins and the number of nickels, thus, there are:
17 - N dimes.
Each nickel has a value of $0.05
each dime has a value of $0.10
Then if you have N nickels and (17 - N) dimes, the total amount of money that you have is:
$0.05*N + (17 - N)*$0.10
This is the first expression, the second one comes if we simplify this.
First, we expand the second term:
$0.05*N + 17*$0.10 - N*$0.10
Now we can take the common factor N to get:
N*($0.05 - $0.10) + $1.70 = $1.70 - $0.05*N
$1.70 - $0.05*N is the simplified expression.
A mixture of jellybeans is to contain twice as many red as yellow, three times as many green as yellow, and twice as many pink as red. Red jelly beans cost $1.50 per pound, yellow cost $3.00 per pound, green cost $4.00 per pound, and pink only costs $1.00 per pound. How many pounds of each color jellybean should be in a 10 pound canister that costs $2.20 per pound?
(25 POINTS)Please help me, and show all of your work step by step.
Now say you invest $6,500 and the highest interest rate you can find is 2.5% compounded annually, but you would have to leave this investment in the account for a minimum of 5 years. If you decide to wait 5 years to buy the car, how much more money will you have to save to buy a car at the price of $8,000? Use the compound interest formula A = P(1 + i)^n.
A = accumulated amount
P = principle
i = interest rate
n = number of years
Answer:
$ 645.85
Step-by-step explanation:
First you would plug 6,500 into P. The plug 2.5% as 0.025 into i. And plug the years (5) into n.
A = 6500 (1 + 0.025)^5 = 7354.15
That is the amount that would be in the account at the end of the 5 years.
Then you take the cost of the car (8,000) and subtract the money left in the account (7,354.15).
8000 - 7354.15 = 645.85
Your final answer would be rounded to the nearest cent, or the hundredths place.
Bike speed of 21miles per hour. What is the speed per minute how many miles will the cyclist travel in 10 minutes
Answer:
First part: 0.35 miles per minute
Second part: 3.5 miles in 10 minutes
Step-by-step explanation:
Think about this as a fraction. Fractions can't be added nor subtracted unless they share the same denominator. So for this case, we have to turn hours into minutes. So 21 mph becomes 21 miles per 60 minutes. Then, we divide 60 from each side to find the speed per minute. 21/60 = 0.35, so the answer to the first part is 0.35 miles per minute.
Using what we got, we can answer the second part of the distance covered in 10 minutes. So, we just multiply 0.35 by 10 which is 3.5 miles covered in 10 minutes.
Help please, help me out
Answer:
2nd option x=-12.........
Polygon D is a scaled copy of Polygon C using a scale factor of 6.
How many times as large is the area of Polygon D compared to the area Polygon C?
Answer:
The area of D is 36 times bigger than C
Step-by-step explanation:
The scale factor is 1:6
We know the ratio of the areas is the ratio of the scale factor squared
1^2 : 6^2
1:36
The area of D is 36 times bigger than C
please me in math
[tex] \frac{a + 1}{a - 1} + \frac{ {a - 1}^{2} }{a + 1} [/tex]
Step-by-step explanation:
hope this helps you thank you
[tex]\boxed{ \sf{Answer}} [/tex]
[tex] \large{\sf\frac{a + 1}{a - 1} + \frac{ {a - 1}^{2} }{a + 1}} [/tex]
Use the algebraic identities ⟶
[tex]{\sf(a - b)(a + b) = {a}^{2} - b ^{2}} [/tex][tex]{\sf(a + b) {}^{2} = {a}^{2} + 2ab - {b}^{2}} [/tex][tex]{\sf(a - b) {}^{2} = {a}^{2} - 2ab + {b}^{2}} [/tex]Squaring on both the sides
[tex] {\sf\frac{(a + 1 {)}^{2} + ( {a - 1)}^{2} }{(a - 1)(a + 1)}} [/tex]
[tex]=\frac{ {a}^{2} + 2a + 1 + {a}^{2} - 2a + 1 }{ {a}^{2} - 1 } \\ = \frac{ {a}^{2} +\bcancel 2a + 1 + {a}^{2} - \bcancel2a + 1 }{ {a}^{2} - 1 } \\ = \frac{ {a}^{2} + {a}^{2} + 1 + 1 }{ {a}^{2} - 1}[/tex]
[tex]\large\boxed{\sf{⟹\frac{ {2a}^{2} + 2}{ {a}^{2} - 1 }}} [/tex]
ʰᵒᵖᵉ ⁱᵗ ʰᵉˡᵖˢ
꧁❣ ʀᴀɪɴʙᴏᴡˢᵃˡᵗ2²2² ࿐
How do I solve this?
Answer:
y = 0.8x – 2
Step-by-step explanation:
Slope (m) =
ΔY/ ΔX = 4 /5 = 0.8
y=.8x+b
plug in point
b=-2
In the American version of the Game Roulette, a wheel has 18 black slots, 18 red slots and 2 green slots. All slots are the same size. A person can wager on either red or black. Green is reserved for the house. If a player wagers $5 on either red or black and that color comes up, they win $10 otherwise they lose their wager. What is the expected value of playing the game once
Answer:
-$0.26
Step-by-step explanation:
Calculation to determine the expected value of playing the game once
Expected value= [18/(18+18+2) x $5)]- [20/(18+18+2) x $5]
Expected value= ($18/38 x $5) - (20/38 x $5)
Expected value= ($2.37-$2.63)
Expected value= -$0.26
Therefore the expected value of playing the game once is -$0.26
Helppppp please
What is the slope of the line shown below?
Answer:
A.
[tex]{ \tt{slope = \frac{ - 4 - 2}{ - 1 - 2} }} \\ \\ = { \tt{ \frac{ - 6}{ - 3} }} \\ = 2[/tex]
Evaluate the six trigonometric functions of the angle 0
# Sin θ = 9/15.
# Cos θ = 12/15.
# Cosec θ = 15/9.
# Sec θ = 5/4
Step-by-step explanation:
[tex]by \: using \: pythagorian \: triplets[/tex]
[tex] {a}^{2} + {b}^{2} = {c}^{2} [/tex]
[tex] {9}^{2} + {12}^{2} = {c}^{2} [/tex]
[tex]81 + 144 = {c}^{2} [/tex]
[tex]225 = {c}^{2} [/tex]
[tex]c = 15.[/tex]
[tex] \sin θ = \frac{9}{15} [/tex]
[tex] \cos θ = \frac{12}{15} = \frac{4}{5} [/tex]
[tex] \csc θ = \frac{15}{9} [/tex]
[tex] \secθ = \frac{5}{4} [/tex]
if anyone could help with any 3 or all of these questions it would be great!
Answer:
1. 90-68= 22
2. 90-80= 10
3. 90-3= 87
Step-by-step explanation:
A complement angle is found by their sum being 90 degrees. So, you are looking for the angle that would add to the given angle to = 90.
Consider the graph below.
Which of the following piecewise functions is shown in the given graph
Answer:
[tex]f(x)=\begin{cases}x^2 + 3; & \text{ } x<1 \\ -2\cdot x+5; & \text{ } x\geq 1 \end{cases}[/tex]
Step-by-step explanation:
The y-intercept (when x = 0) on the quadratic graph is 3, the upper quadratic graph does not intersect the x-axis, and the endpoint of the function has an open circle that stops at x = 1. The starting point extends to the boundaries of the graph
Therefore, the piecewise function shown in the quadratic graph is given as follows;
f(x) = x² + 3; x < 1
The straight line graph has a negative slope and starts at x = 1, with a closed circle, extending to higher values of x to the boundaries of the graph
Two points on the straight line graph are (1, 3) and (5, -5), therefore, the slope is (-5 - 3)/(5 - 1) = -2
The equation of the function is y - 3 = -2·(x - 1)
∴ y = f(x) -2·x + 2 + 3 = -2·x + 5
f(x) = -2·x + 5; x ≥ 1
The power 9 squared is equivalent to 81. What is the value of 9 Superscript negative 2?
Answer:
1/81
Step-by-step explanation:
9^2 = 81
We know that a^ -b = 1/a^b
9^-2
1/9^2
1/81
Answer:
1/81
Step-by-step explanation:
Edge
If b = -1, which one is the value of b^3?
Answer:
b=-1Put the value of b in b^3[tex] \\ \sf \longmapsto \: b {}^{3} \\ \\ \sf \longmapsto \: { - 1}^{3} \\ \\ \sf \longmapsto \: 1 \times - 1 \\ \\ \sf \longmapsto \: - 1[/tex]
Hence b^3=-1
What is the value of f(x) = 2 • 2 x for f(–2)?
Answer:
-8
Step-by-step explanation:
you know, all you have to do in such a case is simply taking the given -2 and put it, where there is "x" in the function expression and then calculate this. if necessary with a calculator.
2×2×x with x=-2 is
2×2×-2 = -8
Answer:
- 8
Step-by-step explanation:
f ( x ) = 2 . 2 x
f ( - 2 )
= 2 . 2 ( - 2 )
= 2 x 2 x ( - 2 )
= - 8
please help me with this question <3
9514 1404 393
Answer:
a) 30.7 million
b) 1.5% per year
c) 42.0 million
d) 2017
Step-by-step explanation:
a) The initial population is P(0) = 30.7 (million). The exponential term is 1 when t=0, so this number is the multiplier of the exponential term.
__
b) The growth factor is the base of the exponential term: 1.015. The growth rate is the difference between this and 1: 1.015 -1 = 0.015 = 1.5%.
The population is growing by 1.5% per year.
__
c) Fill in the value and do the arithmetic. t=2021 -2000 = 21.
P(21) = 30.7·1.015^21 ≈ 41.968 ≈ 42.0
The population in Canada in 2021 is predicted to be 42.0 million.
__
d) For this we need to solve for t when P(t) = 40.
40 = 30.7·1.015^t
40/30.7 = 1.015^t
Taking logarithms gives ...
log(40/30.7) = t·log(1.015)
t = log(40/30.7)/log(1.015) ≈ 17.773
In 2017, the population is predicted to be less than 40 million; in 2018, it is predicted to be more than 40 million. Canada should anticipate hitting 40 million people in 2017.
_____
Additional comment
The second attachment shows the prediction described here is a little high relative to the actuals in the last few years.
How long would it take for $5000 invested at 5% p.a. compound interest with yearly
rests to double in value?
5 years
7 years
10 years
14 years
Answer:
14
Step-by-step explanation:
10000 = 5000[tex](1.05)^{t}[/tex]
2 = [tex](1.05)^{t}[/tex]
ln(2) = t ln(1.05)
t = ln(2)/ln(1.05)
[tex]\frac{\ln \left(2\right)}{\ln \left(1.05\right)}=14.20669\dots[/tex]
For $5000 invested at 5% p.a. compound interest with yearly rests to double in value, The time will be 14 years. So, option D is correct.
How to find the compound interest?If n is the number of times the interest is compounded each year, and 'r' is the rate of compound interest annually,
then the final amount after 't' years would be:
[tex]a = p(1 + \dfrac{r}{n})^{nt}[/tex]
For $5000 invested at 5% p.a. compound interest with yearly
rests to double in value, we need to find the time.
So,
[tex]a = p(1 + \dfrac{r}{n})^{nt}[/tex]
[tex]10000 = 5000(0.05)^t\\\dfrac{10000 }{5000} = (0.05)^t\\2 = (0.05)^t\\ln(2) = t ln(1.05)\\t = \dfrac{ln(2)}{ln(1.05)}\\\\t = 14.21[/tex]
Hence, The time will be 14 years. So, option D is correct.
Learn more about compound interest here:
https://brainly.com/question/1329401
#SPJ2
answer nowwwwwwwwwwwwwwwwwwwwwwwwwwww
Answer:
7/6
Step-by-step explanation:
(7x/12)/(x/2)
=7/6
i need the last part of it pls help!
Answer:
CommutativeStep-by-step explanation:
Multiplication is Commutative. the term can be multiplied in either order. the product will be the same as the previous product.
OAmalOHopeO
What is the range of 58, 59, 57, 59, 55
Answer:
4
Step-by-step explanation:
Hi there!
Range = largest number from data given - smallest number from data given
From the given data, 58, 59, 57, 59, 55,
59 is the largest number and 55 is the smallest number
So the range = 59 - 55 = 4
Write an equation of a polynomial with the given characteristics: a quadratic function has x -intercepts of -3 and 1, and a y-intercept of (0,9).
Answer:
f(x) = -3(x+3)(x-1)
Step-by-step explanation:
x = -3 & 1; f(x) = 9
f(x) = a(x-r1)(x-r2)
f(0) = a(x-r1)(x-r2) = 9; 9 = a(0-(-3))(0-1)
9 = a(3)(-1); 9 = a(-3)
a = -3
f(x) = -3(x+3)(x-1)
Answer:
f(x) = -3x^2 - 6x + 9.
Step-by-step explanation:
As the x intercepts are - 3 and 1 we can write it as:
f(x) = a(x - 1)(x + 3) where a is a constant to be found.
As the - intercept is at (0, 9), x =0 when f(x) = 9 so we can also write:
a( 0 - 1)(0 + 3) = 9
(-1)(3)a = 9
a = 9 / -3
= -3.
So the equation is f(x) = -3(x - 1)(x + 3)
In expanded form it is
-3(x^2 + 2x - 3)
= -3x^2 - 6x + 9.
Solve for X
5x^2 + 6 =17x
Answer: x= 2/5 or x= 3
how?
Step 1: Subtract 17x from both sides
5x² + 6 -17x = 0
*PUT THEM IN ORDER* --> 5x² -17x + 6= 0
Step 2: Factor left side of equation:
(5x-2) (x-3) = 0
Step 3: Set factors equal to 0.
5x−2=0 or x−3=0
which gives us an answer of x= 2/5 or x=3
[tex]\huge\textsf{Hey there!}[/tex]
[tex]\mathsf{5x^2 + 6 =17x}\\\\\large\textsf{SUBTRACT 17x to BOTH SIDES}\\\\\mathsf{5x^2 + 6 - 17x = 17x - 17x}\\\\\mathsf{5x^2 - 17x + 6 = 0}\\\\\large\textsf{SET the LEFT SIDE to equal 0}\\\\\mathsf{(5x -2)(x -3)=0}\\\\\large\textsf{SET the FACTORS to EQUAL to 0}\\\\\mathsf{5x - 2 = 0\ or\ x - 3 = 0}\\\\\large\textsf{SIMPLIFY ABOVE AND YOU HAVE YOUR RESULT}\\\\\boxed{\boxed{\large\textsf{Answer: }\mathsf{\bf x = \dfrac{2}{3}\ or\ x = 3}}}\huge\checkmark[/tex]
[tex]\huge\textsf{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
A jet travels 490 miles in 5 hours. At this rate, how far could the jet fly in 10 hours? What is the rate of speed of the jet?
980 miles
Step-by-step explanation:
5 hours =490miles
1 hour =490/5=98miles
10hours = 98×10=980miles
Which function has a domain of all real numbers?
Answer:
c part ....
please mark brainlest
Simplify and state the restrictions.
I gotta test due and im having a hardd time lmk ty
Help!!!!!!!!!!!!!!!!
502.5 = -502.5
Now
x = -502.5
= -5025/10
= -1005/2 feet
Answered by Gauthmath must click thanks and mark brainliest
Translate sentence into equation
nine more than a product of a number and 4 is 8
Answer:
If x is the required number, equation will be 9+4x=8
DEFG is a cyclic quadrilateral. If ∠E = 27°, find ∠G.
For a cyclic quadilateral, the combination of opposite angles = 180°. So <G is opposite to <E so G must be 153°
What is the value of the expression -5pqr when
p = 3, q= -5, and r = 2?
Answer:
150
Step-by-step explanation:
-5pqr
Let p = 3, q= -5, and r = 2
-5(3)(-5)(2)
-15(-5)(2)
75(2)
150
[tex]\boxed{\large{\bold{\textbf{\textsf{{\color{pink}{☆Answer}}}}}}:)}[/tex]
See this attachment
Find the measure of angle BAC.
Answer:
[tex]\angle 72=BC-86/2[/tex]
[tex]144+86=BC[/tex]
[tex]BC=230[/tex]
[tex]BC=230/2[/tex]
[tex]\angle BAC= 115[/tex]°
~OAmalOHopeO
