Answer:
15 (rounded) 14.7 (not rounded)
Step-by-step explanation:
Answer:
15
Step-by-step explanation:
use the distance formula
d = √((x2-x1)^2 + (y2-y1)^2)
d = √((-4-3)^2 + (-8-5)^2)
d = √((-7)^2 + (-13)^2)
d = √(49 + 169)
d = √218
d = 14.76 ≅ 15
If sin θ = square root of three over two, which could not be the value of θ?
John finances his daughter's college education by making deposits into a fund earning interest at an annual effective rate of 8%. For 18 years he deposits X at the beginning of each month. In the 16th through the 19th years, he makes a withdrawal of 25,000 at the beginning of each year. The final withdrawal reduces the fund balance to zero. Calculate X.
Answer:
Monthly payment = 241.925
Step-by-step explanation:
Effective interest rate is the actual interest paid at the end of the year AFTER compounding. Most credit cards charge x% ("APR", annual percentage rate)annually. Since it is compounded monthly, each month the balance increases by (x//12)%, and by the end of the year, you will be paying effectively (x//12)^12 %, which is the effective interest rate.
Here, effective (annual) interest rate is 8%. We need the monthly rate, i.
(1+i)^12 = 1.08
Solving, we have i = 0.6434% monthly approximately
To balance the deposits and withdrawals, we note that the last withdrawal is the beginning of year 19, and the last deposit is the last month of year 18. We therefore conclude that the "future values" fall on the same day, and that they are equal.
We consider the annual deposits D (accumulated at the end of the year, and annual withdrawals W are in separate accounts. By the end of the operations, one will balance the other (they are equal).
We will need the following formula to calculate future value F given the periodic amount, A, interest rate per period, i, and the number of periods.
F(A,i,n) = A*((1+i)^n-1)/i
Step 1:
calculate the future value of the withdrawals
A = W = 25000 (annual withdrawal)
i = 8% (effective annual interest)
n = 4 years (beginning of 16,17,18,and 19th years)
F(A,i,n) = A*((1+i)^n-1)/i
= 25000( (1+0.08)^4 - 1)/(0.08)
= 112652.80
This is also the total deposit after eighteen years.
Step 2:
calculate the future value of the annual deposits D
A = D (total of annual deposits)
i = 8% (effective annual interest)
n = 18 years
Future value of deposits
F(A,i,n) = A*((1+i)^n-1)/i
= D( (1+0.08)^18 -1 ) / 0.08
= 37.45024373981167D
Since this must equal the total withdrawal, we equate the two to calculate D.
37.45024373981167D=112652.80
and solve for D
D = 112652.80 / 37.45024373981167
= $3008.0659
Step 3
Calculate monthly deposit, X
Effective interest rate is the actual interest paid at the end of the year AFTER compounding. Most credit cards charge x% ("APR", annual percentage rate)annually. Since it is compounded monthly, each month the balance increases by (x//12)%, and by the end of the year, you will be paying effectively (x//12)^12 %, which is the effective interest rate.
Here, effective (annual) interest rate is 8%. We need the monthly rate, i.
(1+i)^12 = 1.08
The actual monthly interest rate is therefore
i = 1.08^(1/12)-1
Over a 12 month period, (one year), the monthly amount X to accumulate an annual amount D (=$3008.0659) is therefore given by
D = X*((1+i)^n-1)/i
3008.0659 = X*(1.08-1)/(1.08^(1/12)-1)
or the monthly amount
X = $3008.0659 / ( 1.08^(1/12)-1)
= 241.925 per month.
=
Find an equation for the graph shown.
Answer:
y=-sin(x)
Step-by-step explanation:
y=-sin(x)
What are the measures of
∠
1
and
∠
2
? Show your work or explain your answers.
Answer:
Step-by-step explanation:
angle 2 is 75 degree because angle 2 and 75 dgeree are corresponding angles corresponding angles are always equal.
angle 1 + angle 2 = 180 degree (being linear pair)
angle 1 = 180 - 75
angle 1 = 105 degree
∠1 = 105° and ∠2 = 75°
What are parallel lines?"These are the lines in the same plane that are at equal distance from each other and never meet."
What is transversal?"It is a line that passes through two lines in the same plane at two distinct points."
What are corresponding angles?"The angles which are formed in matching corners or corresponding corners with the transversal when the transversal intersects two parallel lines."
For given question,
Line c and line d are parallel lines.
These parallel lines are intersected by a transversal.
We can observe that ∠2 and the angle that measures 75° are corresponding angles.
We know that the corresponding angles are congruent.
⇒ ∠2 = 75°
Also, the sum of all angles on either side of the line is 180°
⇒ ∠1 + ∠2 = 180°
⇒ ∠1 + 75° = 180°
⇒ ∠1 = 105°
Therefore, ∠1 = 105° and ∠2 = 75°
Learn more about parallel lines and transversal here:
https://brainly.com/question/17432060
#SPJ3
The base salary of 500$ per week plus a commission of 10.5% of sales
Answer:
salary = $ 500 + 0.105 sales
Step-by-step explanation:
Weekly Income = 500 + 0.105S where S= weekly sales
in x, y math format that's
y=500+0.105x
Economics often uses Q for quantity and Y for income
so,
Y=500+0.105Q
Hope this answer helps you :)
Have a great day
Mark brainliest
What is the equation of the line that passes through the point (−4,−8) and has a slope of 4?
Answer:
i hatee maths thank u
Step-by-step explanation:
What is the factorization of 81a6 - 100? (9a2 − 10)(9a3 + 10) (9a2 − 10)(9a3 − 10) (9a3 − 10)(9a3 + 10) (9a3 − 10)(9a3 − 10)
Answer:
(9a³ − 10)(9a³ + 10)
Step-by-step explanation:
Difference of squares
(9a³ − 10)(9a³ + 10)
Answer:
What is the factorization of 81a6 - 100?
(9a2 − 10)(9a3 + 10) (9a2 − 10)(9a3 − 10) (9a3 − 10)(9a3 + 10) <<< CORRECT (9a3 − 10)(9a3 − 10)
Step-by-step explanation:
Oct 2021 Edge
I need help.
The question is in the picture
Answer: In attached
Step-by-step explanation:
Use the given functions to set up and simplify
Attachment has your answer.
I’m not good at typing functions on this app so this image is all I could give.
Answer:
there you go..........
A group of 42 monkeys meet in the forest for a swinging competition. The monkeys divide into teams with 8 monkeys on each team. They make as many teams as they can, but not every monkey is in a team. How many teams of monkeys will there be? Answer must be a whole number. How many monkeys remain without a team? Answer must be a whole number.
Answer:
the a answer is five
Step-by-step explanation:
divide 42 by 8 and round it it up to the closest whole number
the cone and cylinder above have the same radius and height the volume of the cone is 222 cubic cm what is the volume of the cylinder
Answer:
Step-by-step explanation:
volume of cone v=1/3πr²h
volume of cylinder V=πr²h
V=3v
volume of cylinder=3×222=666 cubic cm.
Xavier shoots a basketball in which the height, in feet, is modeled by the equation, h(t) = -4t^2+10t +18, where t is time, in
seconds. What is the maximum height of the basketball?
Answer:
h = 24.25 feet
Step-by-step explanation:
Xavier shoots a basketball in which the height, in feet, is modeled by the equation.
[tex]h(t) = -4t^2+10t +18[/tex] ....(1)
For maximum height,
Put dh/dt=0
So,
[tex]\dfrac{dh}{dt}=\dfrac{d}{dt}(-4t^2+10t +18)\\\\=-8t+10[/tex]
So,
-8t = -10
t =1.25s
Put t = 1.25 s in equation (1)
[tex]h(t) = -4(1.25)^2+10(1.25) +18\\\\=24.25\ feet[/tex]
So, the maximum height of the basketball is equal to 24.25 feet.
The Solution to a system of linear equations is the _____
of their graphs.
Farah spent $13 on 4 items from the
snack stand at the airport. The
snack stand charges $7 per
sandwiches and $2 per bags of
snack mix. It she purchased a
combination of sandwiches and
snack mix bags, how many of each
food item did Farah purchase?
Answer:
Farah bought 1 sandwich which cost $7 and three snack mix bags which also cost (2 + 2 + 2)$
2+2+2+7=$13
what is the answer to
2/3x = − 1/2x + 5
Answer:
x = 30/7
Step-by-step explanation:
2/3x = − 1/2x + 5
multiply by 6 to clear the fractions
4x = -3x + 30
add 3x to both sides
7x = 30
Divide both sides by 7
x = 30/7
Please help ASAP with number 8 please
Answer:c
Step-by-step explanation:
Evaluate: 4+8 / 2 x (6 - 3)
Answer:
16
Step-by-step explanation:
4+8/2*(6-3) = 4+8/2*3 = 4+4*3 = 4+12 =16
Answer:
18
Step-by-step explanation:
4+8 /2 *(6-3)
=4+8/2 * 3
=(4+8)*3/2
=12*3/2
=36/2
=18
Solve simultaneous equation x-y=4 and x²+y²=10
Step-by-step explanation:
hear is your answer please check attachment
Mary has 2 blouses (1 Red and 1 blue) and 3 pair of slacks (1 yellow and 1 white and 1 green).
If Mary choose 1 blouse and 1 pair of slacks at random , what is the probability that the outfit she chooses will include a pair of green slacks?
Answer:
1/3, the information with the blouses is there to distract you
30. A model train is 4 inches long. If the
scale factor is 1 in : 48 it, what is the
actual length of the train?
F 192 feet
H 12 nches
G 12 feet
s 192 inches
(-32) +(-8) -(+40)+(40)+(78)-(46)
Answer:
or -32-8-40+40+78-46=-8
Step-by-step explanation:
Answer:
-8 is the answer!!!!
Step-by-step explanation:
you can use calculaTor
One year, the population of a city was 99,000. Several years later it was 82,170. Find the percent decrease.
Plz find the surface area
Answer:
What are the answers?
NEED HELP ASAP
The function f(x) = 7x + 1 is transformed to function g through a horizontal compression by a factor of 1/3. What is the equation of function g?
Substitute a numerical value for k into the function equation.
Step-by-step explanation:
x' = ⅓ x => x = 3x'
f'(x) = 7(3x')+1
= 21x' + 1
so g(x) = 21x + 1
Wendy has $17 to buy seed for her birdfeeders. Each bag of seed costs $2. How many bags of seed can she buy?
Answer:
It depends if there is tax or not, if there isn't she can buy 8 of them.
Step-by-step explanation:
$17 is the total so we need to see how many $2 fit in $17.
8×2=16, and 16 is the closest number we can get to.
Using the equation
[tex] \sqrt{x + 7} + 5 = x[/tex]
, are both x = 2 and x = 9 solutions or are one/both of them extraneous solutions? Explain.
Given:
The equation is:
[tex]\sqrt{x+7}+5=x[/tex]
To find:
Whether [tex]x=2[/tex] and [tex]x=9[/tex] both are solutions or one/both of them extraneous solutions.
Solution:
We have,
[tex]\sqrt{x+7}+5=x[/tex]
Subtract 5 from both sides.
[tex]\sqrt{x+7}=x-5[/tex]
Taking square on both sides, we get
[tex]x+7=(x-5)^2[/tex]
[tex]x+7=x^2-10x+25[/tex]
[tex]0=x^2-10x+25-x-7[/tex]
[tex]0=x^2-11x+18[/tex]
Splitting the middle term, we get
[tex]x^2-2x-9x+18=0[/tex]
[tex]x(x-2)-9(x-2)=0[/tex]
[tex](x-2)(x-9)=0[/tex]
[tex]x=2,9[/tex]
Now, substitute [tex]x=2[/tex] in the given equation.
[tex]\sqrt{2+7}+5=2[/tex]
[tex]\sqrt{9}+5=2[/tex]
[tex]3+5=2[/tex]
[tex]8=2[/tex]
This statement is false because [tex]8\neq 2[/tex]. So, 2 is an extraneous solution.
Substitute [tex]x=9[/tex] in the given equation.
[tex]\sqrt{9+7}+5=9[/tex]
[tex]\sqrt{16}+5=9[/tex]
[tex]4+5=9[/tex]
[tex]9=9[/tex]
This statement is true. So, 9 is a solution of given equation.
Therefore, 2 is an extraneous solution and 9 is a solution of given equation.
Work out the perimeter of this semicircle.
Take a to be 3.142
10 cm
Answer:
perimeter=1/2*2πr
Step-by-step explanation:
1/2*2*3.142*10
=31.42
Find the measure of angle c
Evaluate the expression 4q(q + 3w)^2 when q = 2 and w = 3
Answer:
512
Step-by-step explanation:
when q = 2, w = 3
4q(q + 3w)^2
= 4(2) ((2)+3(3))^2
= 512
grade 7 work please help
there is 2 questions 5 and 6
Answer:
For 5 the yellow square stays the same, while the blue adds 2 each time.
5. 1(2x) something like that.
6. 3 is 6 4 is 7 5 is 8
I have gotten too old for this, my bad somethings just dont make sense anymore.
Answer:
5.
a. 2 blue blocks added
b. 2 blue blocks are added on the top blue blocks
c.y = 2x +3
6.
a.
1,4
2,5
3,6
4,7
5,8
b. starting off with 4 triangles and ending with a bottom triangle a triangle is added first from the top, then the bottom for each increase (increment)
c. y = x+4
Step-by-step explanation:
all the answers are up
Is anyone good at Spanish ? I need help with Spanish homework. I’ll mark you brainliest
Answer:
...
Step-by-step explanation:
what help do you need ??