Answer:
B. $352.19 B. $9,126.53 D. $123,866.02Step-by-step explanation:
First of all, the formulas need to be written correctly, and you need to understand what the variables mean. Usually, the variables have these meanings:
A — the amount you're trying to find, often a payment or balanceP — the principal amount invested or borrowedr — the interest rate, often annual, sometimes the rate for the intervaln — the number of intervals in the year for purposes of interest compoundingt — the number of years (or intervals)Usually, an annual interest rate is quoted and compounding is annual (n=1), quarterly (n=4) or monthly (n=12). In some formulas, r is the monthly rate and n is the number of months (there is no "t" in such formulas).
When we say "written correctly", we mean that parentheses are needed around exponents and denominators. In the formulas you have here, necessary parentheses are missing or misplaced, so you cannot use these formulas directly in your calculator or spreadsheet. If you're copying formulas from a question where they're typeset, be aware of the grouping effect of fraction bars and superscripts and use parentheses accordingly.
In the first two problems, you're not given P directly. Rather, the principal invested is to be computed as 10% of the amount given as "earnings."
___
1. P = $147; r = 0.035; n = 12; t = 25.
A = P(1 + r/n)^(nt) = 147·(1 + .035/12)^(12·25) ≈ 147·1.002916667^300
A ≈ 352.19 . . . . matches choice B
___
2. P = $3600; r = 0.0625; n = 4; t = 15.
A = P(1 + r/n)^(nt) = 3600·(1 + .0625/4)^(4·15) ≈ 3600·1.01625^60
A ≈ 9126.53 . . . . matches choice B
___
3. P = $208; r = 0.05/12; n = 300. Here, r is the monthly rate, n is the number of months. Please note the correction of the formula. The variable "S" refers to the Sum of payments and interest. This is effectively the sum of a geometric sequence, so the formula should look familiar on that basis.
S = P((1 +r)^n -1)/r = 208·((1.004166667^300 -1)/0.004166667
S ≈ 123,866.02 . . . . matches choice D
Answer:
B. $325.19
B. $9,126.53
D. $123,866.02
Step-by-step explanation:
Hope this helps! Have an amazing day/restful night!
Find the equation of the perpendicular bisector of the given segment by following these steps. 1. Determine the slope of the given segment.
Answer:
The equation of the perpendicular bisector is 2x + 3y - 3 = 0
Step-by-step explanation:
* How to find the equation of a line from two points (x1 , y1)
and (x2 , y2) lie on it
- Find the slope of the line using the rule
The slope (m) = (y2 - y1)/(x2 - x1)
- Use the rule of the equation y - y1 = m (x - x1), where m is
the slope of the line and (x1 , y1) is a point on the line
* Remember if two line are perpendicular, then the product of
their slopes = -1, that means one of them is an additive inverse
and multiplicative inverse to the other
# Ex: if the slope of a line is a/b, then the slope of the
perpendicular to it is -b/a
* Now lets read the problem, we need the equation of the
perpendicular bisector to the line that passes through the
points (2 , 4) and (-2 , -2)
- Find the slope of the line in the graph by using the given points
# m = (-2 - 4)/(-2 - 2) = -6/-4 = 3/2
∴ The slope of the perpendicular line = -2/3 ⇒ multiplicative
inverse and additive inverse of it
* Bisector means intersect it in the mid-point of the given line
- The rule of the mid-point is [(x1 + x2)/2 , (y1 + y2)/2]
∴ The mid-point of the line is [(2 + -2)/2 , (4 + -2)/2] = (0 , 1)
* Now we have the slope and a point on the line, to find the
equation of the perpendicular bisector its slope is -2/3 and
a point (0 , 1)
∴ The equation: y - 1 = -2/3 (x - 0)
The equation : y - 1 = -2/3 x ⇒ Multiply both sides by 3
The equation : 3y - 3 = -2x ⇒ collect x , y in the same side
The equation : 2x + 3y - 3 = 0
* The equation of the perpendicular bisector is 2x + 3y - 3 = 0
Answer:3/2
Step-by-step explanation:
Using the linear equation 4x–3y=12, express: b x in terms of y
Answer:
y = [4(x-3)]/3
Step-by-step explanation:
4x = 12+3y
3y = 4x-12
y = [4(x-3)]/3
Best regards
Find the range of y=4sin2x+3
Answer:
[-1, 7]
Step-by-step explanation:
If you mean ...
y = 4sin(2x) +3
then you can substitute the range of the sine function into the equation and evaluate it to find the range of y.
The range of sin( ) is [-1, 1], so the range of y is ...
4[-1, 1] +3 = [4(-1)+3, 4(1)+3] = [-1, 7]
_____
Comment on the problem statement
The range of y = 4sin²(x)+3 will be different, and the range of 4sin(2x+3) will be different yet. It is usually a good idea to use parentheses around function arguments.
Answer:
-1,7
Step-by-step explanation:
got it right on odessyware
I'd appreciate an answer to this.
Here are the 30 best lifetime baseball batting averages of all time, arranged in order from lowest to highest.
Answer:
C. 0.366
Step-by-step explanation:
In this stemplot, it is apparent that the number on the right is the least-significant digit (thousandths digit) of the batting average. The two most-significant digits are to the left of the vertical line.
Hence the value 0.36 | 6 represents an average that is 36 hundredths plus 6 thousandths: 0.366.
Shavon has $23 to spend on school supplies. She buys a set of colored pencils for $5 and wants to spend the rest on notebooks. Each notebook costs $3.25. Circle symbols to create an inequity that models the the number of notebooks, n. Shavon can buy
Answer:
23-5≥3.25n
18≥3.25n
A granola recipe calls for 3/4 of a cup of peanuts and 2/3 of cup of raisins. how many cups of raisins should be used for every one cup of peanuts
Answer:
how many cups are needed for the recipe
Step-by-step explanation:
Please help someone..
Answer: [tex]\bold{\dfrac{1}{5}}[/tex]
Step-by-step explanation:
[tex]\dfrac{DF}{AK}=\dfrac{4}{20}=\large\boxed{\dfrac{1}{5}}[/tex]
What series of transformations from △ABC to △DEF shows that △ABC ≌ △DEF?
a). a reflection across the y-axis followed by a translation of 1 unit right and 2 units up
b). a clockwise rotation of 90º about the origin followed by a translation of 4 units right and 4 units up
c). a reflection across the x-axis followed by a translation of 1 unit right and 1 unit down
d). a reflection across the line y=x followed by a positive rotation of 270º about the center
Answer:
c). a reflection across the x-axis followed by a translation of 1 unit right and 1 unit down
Step-by-step explanation:
You want to know the transformations that map ΔABC onto ΔDEF.
TransformationsThe answer choices would ask us to consider some combination of the following transformations:
reflection across the y-axis: (x, y) ⇒ (-x, y)reflection across the x-axis: (x, y) ⇒ (x, -y)reflection across the line y=x: (x, y) ⇒ (y, x)clockwise rotation 90°: (x, y) ⇒ (y, -x)positive rotation 270°: (x, y) ⇒ (y, -x) . . . same as 90° CWtranslation by (h, k): (x, y) ⇒ (x+h, y+k) . . . h units right, k units upApplicationWe can apply these relations to the answer choices to see if they provide the desired mapping ...
A(-4, 1) ⇒ D(-3, -2)B(-6, 5) ⇒ E(-5, -6)C(-1, 2) ⇒ F(0, -3)a) Reflection across the y-axis, translation (1, 2)
A(-4, 1) ⇒ A'(4, 1) . . . reflection
A'(4, 1) ⇒ D(4+1, 1+2) = D(5, 3) . . . . not the correct point
b) Rotation CW 90°, translation (4, 4)
A(-4, 1) ⇒ A'(1, 4) . . . rotation 90° CW
A'(1, 4) ⇒ D(1+4, 4+4) = D(5, 8) . . . . not the correct point
c) Reflection across the x-axis, translation (1, -1)
A(-4, 1) ⇒ A'(-4, -1) . . . reflection
A'(-4, -1) ⇒ D(-4+1, -1+(-1)) = D(-3, -2) . . . . the correct location of D
d) Reflection across y=x, rotation CCW 270°
A(-4, 1) ⇒ A'(1, -4) . . . reflection
A'(1, -4) ⇒ D(-4, -1) . . . . not the correct point
The correct series of transformations is reflection across the x-axis followed by translation 1 right and 1 down.
Read the statement.
Doubling the dimensions of a rectangle increases the area by a factor of 4.
If p represents doubling the dimensions of a rectangle and q represents the area increasing by a factor of 4, which are true? Check all that apply.
p → q represents the original conditional statement.
~p → ~q represents the inverse of the original conditional statement.
q → p represents the original conditional statement.
~q → ~p represents the converse of the original conditional statement.
p → ~q represents the contrapositive of the original conditional statement.
Answer:
True, True , False , False , False
Step-by-step explanation:
Let us see the correction for the rest of the three False Statements
3) p→q represent the original conditional statement.
4) ~q → ~p represents the contrapositive of the original conditional statement
5) contrapositive of the original conditional statement will be ~q → ~p
There is one more implication called Converse of the original conditional statement . It is represented as q→p
Can someone please help me on this problem? I don’t know how to do it!!!
Answer:
(x^(11/4))(y^(5/9))
Step-by-step explanation:
The applicable rules of exponents are ...
(x^a)(x^b) = x^(a+b)
(x^a)/(x^b) = x^(a-b) . . . . . no surprise, since 1/x^b = x^-b
_____
Your expression simplifies to ...
x^((5/4) -(-5/4) -(-1/4)) · y^((1/18) -(-1/2))
= x^(5/4 +5/4 +1/4) · y^(1/18 +1/2)
= x^(11/4) · y^(1/18 +9/18)
= x^(11/4) · y^(5/9)
Members of the garner high school yearbook committee need to put 1,344 student photos on 24 pages in the yearbook they want to put the same number of students photos on each page how many student photos will they put on each page in the yearbook?
Answer:
56 photos per page
Step-by-step explanation:
1344 photos/(24 pages) = 1344/24 photos/page = 56 photos per page
Answer:
i need points to ask my question
Step-by-step explanation:
x-y-4z=-9
4x-3y-2z=-9
-x-3y-6z=-7
solve
Answer:
(x, y, z) = (-2, -1, 2)
Step-by-step explanation:
Your graphing calculator can usually solve systems of linear equations easily.
20 COINS
Cylinder A has radius r and height h as shown in the diagram. Cylinder B has radius 2r and height 2h. How many times greater is the surface area of Cylinder B than the surface area of Cylinder A?
The surface area of a cylinder is given by
[tex]A_A = 2\pi rh[/tex]
which is the surface area of cylinder A.
To compute the surface area of cylinder B, we have to map [tex](r,h)\mapsto (2r, 2h)[/tex] and we have the following formula
[tex]A_B = 2\pi(2r)(2h)[/tex]
If we manipulate the second expression, we have
[tex] A_B = 8\pi rh[/tex]
Which implies
[tex]\dfrac{A_B}{A_A} = \dfrac{8\pi rh}{2\pi rh} = 4 [/tex]
Given: circle k(O), DC ∥ AB , AC ∩ DB =0, m AD =124°Find: m∠C, m∠AOB.
Answer:
Part 1) The measure of angle C is [tex]62\°[/tex]
Part 2) The measure of angle AOB is [tex]56\°[/tex]
Step-by-step explanation:
step 1
Find the measure of angle C
we know that
The inscribed angle measures half that of the arc comprising
so
[tex]m<C=\frac{1}{2}(arc\ AD)[/tex]
we have
[tex]arc\ AD=124\°[/tex]
substitute
[tex]m<C=\frac{1}{2}(124\°)=62\°[/tex]
step 2
Find the measure of angle AOB
we know that
In the isosceles triangle ODC
∠D=∠C=62°
Remember that
The sum of the internal angles of a triangle must be equal to 180 degrees
so
∠D+∠C+∠DOC=180°
substitute the values
62°+62°+∠DOC=180°
∠DOC=180°-124°=56°
we have that
∠AOB=∠DOC -----> by vertical angles
so
∠AOB=56°
Find all pairs of natural numbers which can be the solution to the equation: x+y=11
Answer:
How many solution does ++=11
x
+
y
+
z
=
11
have where ,,
x
,
y
,
z
are non-negative integers. In light of the restrictions, its clear that ,,∈{0,1,2,..11}
x
,
y
,
z
∈
{
0
,
1
,
2
,
.
.11
}
. So, at face value I would assign a value for
x
and determine the different combinations that
y
and
z
can hold. For example,
For =0
x
=
0
, we have +=11
y
+
z
=
11
. With writing them out I found that there are 12
12
different assigned combinations for
y
and
z
that satisfy the equation. For =1
x
=
1
, I got 11
11
. Consequently, the pattern becomes clear whereby each one takes a value less by one. Hence, the number of solutions is 1+2+3+4+5+6+7..+12=78
1
+
2
+
3
+
4
+
5
+
6
+
7..
+
12
=
78
. I was wondering if there is an easier method perhaps with combinations equation (,)
C
(
a
,
b
)
..?
Step-by-step explanation:
Can someone help with 2.6
Answer:
B
Step-by-step explanation:
Theta is found using the sin-1 function. Start off with the sin of theta.
sin(theta) = opposite over hypotenuse.
sin(theta) = 3/8 = 0.375
Theta = Sin-1 (0.375)
Theta = 22.02 degrees.
Answer: B
How do i solve this?
Answer:
see below
Step-by-step explanation:
If the left-side tiles are numbered 1–7 from top to bottom, their order on the right is ...
7 — denominators factored
6 — common factors canceled
5 — make the left side have the same denominator as the right
3 — express the sum over the common denominator
2 — collect numerator terms
Decide if the answer to 5/7×6 is less than, greater than or equal to 6
less than
equal to
greater than
Answer:
less than
Step-by-step explanation:
The multiplying fraction (5/7) is less than 1 so its product with 6 will be less than 6.
___
5/7·6 = 30/7 = 4 2/7 < 6
The expression 5/7×6 results in a value that is less than 6. This is because the value of 5/7 is less than 1, and multiplying it by 6 gives a result that is consequently less than 6.
Explanation:To determine whether 5/7×6 is less than, greater than, or equal to 6, we perform the multiplication. Multiplying 5/7 by 6 can be viewed as 5 multiplied by 6, which equals 30, and then that result divided by 7. So the calculation is 30÷7, which equals approximately 4.29. Since 4.29 is less than 6, we can conclude that 5/7×6 is less than 6.
When solving mathematical problems involving multiplication and fractions, it's important to eliminate terms wherever possible to simplify the algebra and to check the answer to see if it is reasonable. Comparing the original fraction to 1 before the multiplication can help us understand whether the result will be greater or less than the number we're multiplying. In this case, since 5/7 is less than 1, multiplying it by 6 will give a result that is less than the original number, which is 6.
What is another way to describe an equilateral triangle?
A) acute
B) obtuse
C) right
D) scalene
I think it a but I sorry if it wrong
a semielliptic archway has a height of 15 feet at the center and a width of 50 feet. the 50 foot width consists of a two lane road. can a truck that is 12 feet high and 14 feet wide drive under the archway without going into the other lane?
The truck cannot drive under the archway since it is taller than the highest point of the archway.
Explanation:To determine if a truck can drive under the semielliptic archway without going into the other lane, we need to compare the height and width of the truck to the height and width of the archway. The truck has a height of 12 feet and a width of 14 feet. The highest point of the archway is at its center, which is 15 feet high. So, the truck will not fit under the archway since it is taller than the highest point of the archway.
Solve the triangle given two side lengths and one angle measure.
Answer:
B ≈ 64.9°C ≈ 45.1°c ≈ 82.2Step-by-step explanation:
The Law of Sines is helpful when you know one side and its opposite angle.
a/sin(A) = b/sin(B) = c/sin(C)
Rearranging gives you ...
B = arcsin(b/a·sin(A)) = arcsin(105/109·sin(70°)) ≈ 64.85138°
C = 180° -B -A = 45.14862°
c = a·sin(C)/sin(A) ≈ 82.23360
_____
Comment on the solution method
You can use the Law of Cosines if you like. The formulation would be ...
a² = b² + c² -2bc·cos(A) . . . . where a, b, and A are known
This gives a quadratic in c, the positive solution being the answer you're looking for. Then, either the law of sines or the law of cosines can be used to find one of the other two angles.
c = 105·cos[70°] + √[856 + 11025·cos[70°]²]
c ≈ 82.2336
HELP!!! I NEED AN ANSWER SOON!!!!! FIRST TO ANSWER WILL GET BRAINLIEST!!!!!!!!!!! THANKS IN ADVANCE!!!!!!!!!
Answer:
a= 84.83
Step-by-step explanation:
so remember this: my teacher taught me this amazing strategy to remember the formulas
C=πd : cherry pie delicious
a=πr² : apple pie are too
and to find the area of the saded area, we need to find the area of the big circle and subtract that by the smaller circle area.
so, area of the big circle:
fill in the variables for a=πr²
you get: a=π6²
follow the pemdas, the order of operations. now on the state test don't write pemdas as your answer because people are stupid and they dont take that answer
you do the exponent first then multiply by pie.
you get: 6²=36
36xπ=113.09733552923255658465516179806
round that answer to the nearest tenths and get: 113.1
now time to find the area of the smaller circle!!!
fill in a=πr² and get: a=π3²
its not 6 this time because that was the radius for the bigger circle. the smaller circles radius is half the size as the bigger circle so divide that by two and get 3.
now solve:
a=π3²
a=π9
a=28.274333882308139146163790449516
round and get: 28.27
now subtract the the bigger circles area and the smaller circles area:
113.1 is the bigger circles area
28.27 is the smaller circles area.
113.1 - 28.27 = 84.83
a=84.83
plz give me brainliesttt
For each hour he babysits, Anderson earns $1 more than half of Carey’s hourly rate. Anderson earns $6 per hour. Which equation can be used to solve for Carey’s hourly rate, c?
Answer:
10$ an hour
Step-by-step explanation:
1/2c=6-1
c=2(6-1)
c=10
Answer:
Carey's hourly rate to babysit is $10.
Step-by-step explanation:
Given is -
For each hour he babysits, Anderson earns $1 more than half of Carey’s hourly rate.
Let Carey's hourly rate to babysit be represented by 'c'
So, Anderson's hourly rate will be = [tex]\frac{c}{2}+1[/tex]
Also given that Anderson earns $6 per hour.
So, equaling both, we get;
[tex]6=\frac{c}{2}+1[/tex]
[tex]6=\frac{c+2}{2}[/tex]
[tex]c+2=12[/tex]
[tex]c=10[/tex]
Hence, Carey's hourly rate to babysit is $10.
Genise is making cookies. She needs 1 1/2 cups of flour for one batch, but she wants to make 2 1/2 batches. Write an equation that can be used to find how many cups of flour genise will need.
To calculate how many cups of flour Genise will need for 2 1/2 batches, multiply the amount of flour for one batch (1 1/2 cups) by the number of batches (2 1/2). This results in 3 3/4 cups of flour needed.
To find how many cups of flour Genise will need, we start by writing an equation that reflects the amount of flour needed for one batch times the number of batches she plans to make. Since she needs 1 1/2 cups of flour for one batch and she wants to make 2 1/2 batches, we set up the multiplication:
flour_needed = (cups of flour per batch) * (number of batches)
So the equation will be:
flour_needed = 1 1/2 * 2 1/2
Converting mixed numbers to improper fractions for easier multiplication, we have:
flour_needed = 3/2 * 5/2 = 15/4 cups
Then, we convert the improper fraction back to a mixed number, which is:
flour_needed = 3 3/4 cups of flour
PLEASE HELP ASAP
Shade the following: (B - A') intersects (A - C)
Step-by-step explanation:
Look at the picture.
A' - The complement of a set is the set of all elements in the given universal set U that are not in A.
B - A - The set difference of sets A and B is the set of all elements in A that are not in B.
A ∩ B - The intersection of sets A and B is the set of all distinct elements that are in both A and B.
What value is added to both sides of the equation x^2-2x=10 in order to solve by completing the square?
-2
-1
1
2
Answer:
1
Step-by-step explanation:
Add the square of half the x coefficient: (-2/2)^2 = 1.
In this formula, n represents the _____ .
a.
number of periods over which interest is calculated on the loan
b.
number of applicants for the loan
c.
number of years it will take to pay the loan back
d.
number of dollars the loan is for
Answer:
a. number of periods over which interest is calculated on the loan
Step-by-step explanation:
A formula should always be accompanied by an explanation of what it calculates and the meaning of each of its variables. This formula calculates P, the periodic payment on a loan of n periods at interest rate i (compounded) per period. The principal amount of the loan is PV.
___
The same formula can also be used to calculate an annuity from which payment P is received at the end of each of n periods. The amount invested is PV and the interest rate per period (compounded per period) is i.
'n' typically represents the number of periods over which interest is calculated in a loan. However, symbols' intended meanings can change depending upon the context.
Explanation:In most financial and mathematical formulas, the symbol 'n' typically represents the number of periods over which interest is calculated on a loan. It's relevant to note that these periods could be months, years, or any other agreed-upon timeframe. Hence, the correct answer to your question is (a).
However, it's important to state that the representation of variables can change with different contexts. In some scenarios, 'n' could be used to denote the number of years it will take to pay the loan back, but that is not as common as using 'n' for the number of periods.
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Ben is 12 years older than Ishaan. Ben and ishaan first met two years ago. Three years ago, Ben was 4 times as old as Ishaan.
Answer:
ok what is tthe question
Step-by-step explanation:
Technological advances in farming made it possible to increase the crop of potatoes from 1 acre by 4 tons. As a result, from a field of 320 acres 640 tons of potatoes more were collected than before from a field of 400 acres. How many tons of potatoes were collected before the new methods and how many after the introduction of the new technology?
The initial yield of potatoes per acre was 14 tons and after the introduction of the new technology, the yield increased to 18 tons. Therefore, 5600 tons were collected before the technological advances and 7200 tons were collected after.
Explanation:This problem involves understanding linear equations. Let's denote the initial yield of potatoes per acre as 'x' tons and the yield after the introduction of the new technology as 'y' tons.
It's given that technological advances increase the yield by 4 tons, so we have the equation: y = x + 4. The problem also states that from a 320 acre field 640 more tons were collected than before from a 400-acre field. So, we can write it as: 320y = 400x + 640.
Solve these two equations to find the values of x and y. The initial yield of potatoes per acre (x) was 14 tons while the yield after the introduction of the new technology (y) was 18 tons. Therefore, 5600 tons of potatoes were collected before the technological advances and 7200 tons were collected after.
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Before the new methods were introduced, 640 tons of potatoes were collected. After the introduction of the new technology, 0 tons were collected.
Explanation:To solve this problem, let's assume x is the number of tons of potatoes collected before the new methods were introduced, and y is the number of tons collected after the introduction of the new technology.
According to the given information, the new technology increased the crop of potatoes from 1 acre by 4 tons, so the increase in yield per acre is 4 tons.
From a field of 320 acres, 640 tons more were collected than before from a field of 400 acres. This means that the increase in yield from the reduced field of 320 acres is twice the increase in yield from the initial field of 400 acres.
Setting up the equation, we have:
(y - x) = 2(4)(320 - 400)
(y - x) = 2(4)(-80)
(y - x) = -640
We also know that the total increase in yield is 640 tons, so we have:
x + y = 640
To solve these equations, we can use substitution or elimination method. Solving for x in the second equation, we get:
x = 640 - y
Substituting x in the first equation, we have:
(y - (640 - y)) = -640
2y - 640 = -640
2y = 0
y = 0
Substituting y in the equation x + y = 640, we get:
x + 0 = 640
x = 640
Therefore, before the new methods were introduced, 640 tons of potatoes were collected, and after the introduction of the new technology, 0 tons were collected.
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40 points... Please help.
I am doing a project for geometry and need the ratio for both figures. The figure is a bird house and I am doubling the size. What would the ratio be?
Answer:
The ratio would be 1:2 my guy,if you're trying to triple the size, 1:3 if your trying to quadruple the size, it'd be 1:4, etc, etc