Answer:
To find the final balance of an account earning interest compounded continuously, you can use the formula:
A = Pe^(rt)
where A is the final account balance, P is the initial principal (or starting) amount, r is the interest rate, and t is the time (in years) for which the interest is being calculated.
Substituting in the given values:
A = 550 * e^(0.066 * 10)
Therefore, the final balance would be approximately $1064.14.
Answer:
C) $1064.14
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{8.5 cm}\underline{Continuous Compounding Formula}\\\\$ A=Pe^{rt}$\\\\where:\\\\ \phantom{ww}$\bullet$ $A =$ final amount \\\phantom{ww}$\bullet$ $P =$ principal amount \\\phantom{ww}$\bullet$ $e =$ Euler's number (constant) \\\phantom{ww}$\bullet$ $r =$ annual interest rate (in decimal form) \\\phantom{ww}$\bullet$ $t =$ time (in years) \\\end{minipage}}[/tex]
Given:
P = $550r = 6.6% = 0.066t = 10 yearsSubstitute the given values into the continuous compounding formula and solve for A:
[tex]\implies A=550e^{0.066 \times 10}[/tex]
[tex]\implies A=550e^{0.66}[/tex]
[tex]\implies A=550(1.93479233...)[/tex]
[tex]\implies A=1064.13578...[/tex]
Therefore, the balance of the account after 10 years would be $1064.14.
N=
Help me please!!! Asap thanks so much :)
Answer:
n = 100
Step-by-step explanation:
the area (A) of the sector is calculated as
A = area of circle × fraction of circle
given A = 40π , then
πr² × [tex]\frac{n}{360}[/tex] = 40π
π × 12² × [tex]\frac{n}{360}[/tex] = 40π
144π × [tex]\frac{n}{360}[/tex] = 40π ( divide both sides by π )
144 × [tex]\frac{n}{360}[/tex] = 40 ( multiply both sides by 360 to clear the fraction )
144n = 14400 ( divide both sides by 144 )
n = 100
Please help meeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee
Answer:
a) x = 1.5 or x = -0.3
b) x = 5 or x = -8
Explanation:
Quadratic formula:
[tex]\sf x = \dfrac{ -b \pm \sqrt{b^2 - 4ac}}{2a} \quad when \:\: ax^2 + bx + c = 0[/tex]
Here given equation: 5x² - 6x - 2 = 0
Identify variable constants: a = 5, b = -6, c = -2
Putting these values into equation:
[tex]\sf x = \dfrac{ -(-6) \pm \sqrt{(-6)^2 - 4(5)(-2)}}{2(5)}[/tex]
[tex]\sf x = \dfrac{ 6 \pm \sqrt{36 + 40}}{10}[/tex]
[tex]\sf x = \dfrac{ 6 \pm \sqrt{76}}{10}[/tex]
[tex]\sf x = \dfrac{ 3\pm \sqrt{76}}{5}[/tex]
[tex]\sf x = \dfrac{ 3+ \sqrt{76}}{5} \quad or \quad \dfrac{ 3- \sqrt{76}}{5}[/tex]
In one decimal point:
[tex]\sf x = 1.5 \quad or \quad -0.3[/tex]
b) Here use "middle term split" method
⇒ x² + 3x = 40
relocate
⇒ x² + 3x - 40 = 0
The factors of 40 are 8 and 5
⇒ x² + 8x - 5x - 40 = 0
factor common terms
⇒ x(x + 8) - 5(x + 8) = 0
collect into groups
⇒ (x - 5)(x + 8) = 0
set to zero
⇒ x - 5 = 0 or x + 8 = 0
relocate
⇒ x = 5 or x = -8
Step-by-step explanation:
a) The quadratic formula can help find answers to a quadratic equation when it is equal to 0. The formula is [tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex] for a quadratic equation of the form [tex]ax^2+bx+c=0[/tex].
In this question, a is 5, b is -6, and c is -2. Let's put them in the equation and solve.
[tex]x=\frac{6\pm\sqrt{(-6)^2-4(5)(-2)}}{2(5)}\\x=\frac{6\pm\sqrt{36+40}}{10}\\x=\frac{6\pm\sqrt{76}}{10}\\x=\frac{6\pm2\sqrt{19}}{10}\\x=\frac{3\pm\sqrt{19}}{5}[/tex]
This means that the value of x is both [tex]\frac{3+\sqrt{19}}5[/tex] and [tex]\frac{3-\sqrt{19}}5[/tex], since both values make x equal to 0. Putting both into the calculator, we get that [tex]x=1.5[/tex] or [tex]x=-0.3[/tex].
b) We can easily solve this equation using factoring, which turns a quadratic into two factors, and finds the solutions by setting both to 0. This will only work if the quadratic is equal to 0.
[tex]x^2+3x-40=0[/tex]
Now, we have to find two numbers that add to 3 and multiply to -40. The numbers 8 and -5 work, as 8-5=3 and 8*-5 is -40.
we can now make our factors x+8 and x-5
[tex](x+8)(x-5)=0[/tex]
If two numbers, say A and B, are being multiplied and equal 0, then either A is 0, or b is 0, or both. Similarly, if x+8 and x-5 are being multiplied and equal 0, either x+8 = 0, or x-5=0.
[tex]x+8=0\\x=-8[/tex] [tex]x-5=0\\x=5[/tex]
This makes our solutions x=-8 and x=5.
If you are not familiar with factoring or the process I have went through above, I highly recommend learning about it.
7. In a regular polygon, adjacent interior and exterior angles are congruent
What is the name of the polygon?
(1) triangle
(2) rectangle
(4) hexagon
lor
(3) square
Answer:
This would be true for a rectangle and a square.
Step-by-step explanation:
Rectangles and square have 90 angles. The exterior angles would also equal 90 because 90 + 90 is 180. An interior angle and the exterior angle are supplements (add together to 180).
Are the ratios 2:1 and 14:6 equivalent?
yes
no
Answer:
Step-by-step explanation:
To check this, we need to know whether
2
1
=
3
2
We have,
2
1
=
2×3
1×3
=
6
3
and
3
2
=
3×2
2×2
=
6
4
We find that
6
3
<
6
4
, which means that
2
1
<
3
2
.
Therefore, The ratio 1:2 is not equivalent to the ratio 2:3
Answer:
No, they aren't equal.
Step-by-step explanation:
Which equation has an a-value of 1 a b-value of -3 and a c-value of -5
The equation which has the values as given in the task content is; y= x² -3x -5.
What is the quadratic equation with the given values?By convention, the general form representation of a quadratic equations is;
y = ax² + bx +c.
Hence, it follows that when the equation has an a-value of 1 a b-value of -3 and a c-value of -5, the equation is; y= x² -3x -5.
Read more on quadratic equations;
https://brainly.com/question/1214333
#SPJ1
Joe is thinking of an integer. The opposite of his number is greater than
the number itself. Which of the following must be true of Joe’s number?
Answer: Joe's number is a negative number.
Since the number's opposite is greater in value, the number's value is in the negatives.
On a coordinate plane, line k l goes through (negative 6, 8) and (6, 0). point m is at (negative 4, negative 2). which point could be on the line that is parallel to line kl and passes through point m?
The equation of the line parallel to the line KL passing through the points (-6, 8) and (6, 0), and going through the point M (-4, -2) is 2x + 3y = -6. The point satisfying this equation is (-6, 2). Thus, the 2nd option is the right choice.
Slope of the line KL = (8 - 0)/(-6 - 6) = 8/(-12) = -2/3.
Using the formula of the slope of the line passing through the points (x₂, y₂) and (x₁, y₁), as m = (y₂ - y₁)/(x₂ - x₁).
The slope of the line parallel to the line KL will be equal to the slope of KL.
Thus, the slope of the required line is m = -2/3.
The required line also passes through point M (-4, -2).
Thus, the equation of the required line will be,
y - (-2) = (-2/3)(x - (-4)) {Using the equation of the line passing through the point (x₁, y₁) and a slope m, as y - y₁ = m(x - x₁)},
or, y + 2 = (-2/3)(x + 4),
or, 3(y + 2) = -2x - 8,
or, 2x + 3y = -6.
From the given points, only the point (-6, 2) satisfies the equation.
Thus, the equation of the line parallel to the line KL passing through the points (-6, 8) and (6, 0), and going through the point M (-4, -2) is 2x + 3y = -6. The point satisfying this equation is (-6, 2). Thus, the 2nd option is the right choice.
Learn more about parallel lines at
https://brainly.com/question/13763238
#SPJ4
The provided question is incomplete. The complete question is:
"On a coordinate plane, line K L goes through (negative 6, 8) and (6, 0). Point M is at (negative 4, negative 2). Which point could be on the line that is parallel to line KL and passes through point M?
(–10, 0)
(–6, 2)
(0, –6)
(8, –10)"
A number is chosen at random from the first 100 positive integers. find the probability that the number is divisible by 5. 1/10 1/5 1/4
The probability that the number chosen is divisible by 5 is; 1/5.
What is the probability that the number chosen is divisible by 5?It follows from the task content that the number of possible outcomes in the probability event is; 100. Additionally, the number of required outcomes is 20 as only 20 numbers are divisible by 5.
Ultimately, the required probability is; 20/100 = 1/5.
Read more on probability;
https://brainly.com/question/7965468
$SPJ1
Please help. will give brainliest
Answer:
the 4th answer option. W = 153°, P = 71°
Step-by-step explanation:
PQRS ~ TUVW
that means both figures are similar.
and that means that the angles at the corresponding vertexes are the same, and all 4 corresponding sides (and any other pair of corresponding lines like diagonals) have the same scaling factor.
we see due to the proportions of the different parts of the shapes
U corresponds to Q.
T corresponds to P.
W corresponds to S.
V corresponds to R.
therefore, as the angle at S = 153°, so is W.
and as the angle at T = 71°, so is P.
[tex]\frac{2x}{x+1} +\frac{3(x-1)}{x} =5[/tex]
Answer:
[tex]x=-3[/tex]
Step-by-step explanation:
Given equation:
[tex]\dfrac{2x}{x+1}+\dfrac{3(x+1)}{x}=5[/tex]
Make the denominators the same:
[tex]\implies \dfrac{2x}{x+1} \cdot\dfrac{x}{x}+\dfrac{3(x+1)}{x} \cdot \dfrac{x+1}{x+1}=5[/tex]
[tex]\implies \dfrac{2x^2}{x(x+1)}+\dfrac{3(x+1)^2}{x(x+1)} =5[/tex]
Combine the fractions:
[tex]\implies \dfrac{2x^2+3(x+1)^2}{x(x+1)} =5[/tex]
Multiply both sides by x(x+1):
[tex]\implies 2x^2+3(x+1)^2 =5x(x+1)[/tex]
Expand the brackets:
[tex]\implies 2x^2+3(x^2+2x+1) =5x^2+5x[/tex]
[tex]\implies 2x^2+3x^2+6x+3 =5x^2+5x[/tex]
Combine like terms:
[tex]\implies 5x^2+6x+3=5x^2+5x[/tex]
Subtract 5x² from both sides:
[tex]\implies 6x+3=5x[/tex]
Subtract 5x from both sides:
[tex]\implies x+3=0[/tex]
Subtract 3 from both sides:
[tex]\implies x=-3[/tex]
Learn more about algebraic fractions here:
https://brainly.com/question/27943438
https://brainly.com/question/27979364
Refer to Table 9-8. Suppose that the data in the table above reflect the price levels in the economy. What is the inflation rate in between 2017 and 2018
The inflation rate between 2017 and 2018 is 2.86%.
What is the inflation rate?
Inflation rate is used to determine the rate at which the general price levels in an economy is increasing with the passage of time.
The inflation rate = (2018 CPI / 2017 CPI) - 1
(180 / 175) - 1 = 0.0286 = 2.86%
To learn more about CPI, please check: https://brainly.com/question/26382640
#SPJ1
Which set describes the domain of p(h)? {h| 0 ≤ h ≤ 40} {h| 0 ≤ h ≤ 60} {p(h)| 0 ≤ p(h) ≤ 1,400} {p(h)| 0 ≤ p(h) ≤ 1,800}
The set {h| 0 ≤ h ≤ 60} describe the domain of p(h).
According to the statement
We have given that the brenton gets paid $20 per hour for the first 40 hours he works in a week. For any hours above that, he is paid overtime at $30 per hour.
and we have to find that the those set which describes the domain of p(h).
So,for this purpose
In this case, the domain represents the set of hours he is permitted to work
From the question, we understand that he cannot work more than 60 hours
This means that, the least number of hours to work is 0, and the highest is 60
So, the domain is 0 to 60
When represented properly, the domain of P(h) is (b) {h| 0 ≤ h ≤ 60}.
So, The set {h| 0 ≤ h ≤ 60} describe the domain of p(h).
Learn more about Domain here https://brainly.com/question/1770447
Disclaimer: This question was incomplete. Please find the full content below.
Question:
Brenton’s weekly pay, P(h) , in dollars, is a function of the number of hours he works, h. He gets paid $20 per hour for the first 40 hours he works in a week. For any hours above that, he is paid overtime at $30 per hour. He is not permitted to work more than 60 hours in a week. Which set describes the domain of P(h)? {h| 0 ≤ h ≤ 40} {h| 0 ≤ h ≤ 60} {P(h)| 0 ≤ P(h) ≤ 1,400} {P(h)| 0 ≤ P(h) ≤ 1,800
#SPJ4
Answer:
B.{h|0<h<60}
Step-by-step explanation:
solve for x
A)8
B)9
C)-9
D)-8
Answer:
C) -9
Step-by-step explanation:
x + 19 must be half x + 29 because triangles RBC and RST are similar by SAS and RB is half of RS and RC is half of RT.
2(x + 19) = x + 29
2x + 38 = x + 29
x + 38 = 29
x = -9
PLEASE HELP ASAP!!!!
The location of the points on Cartesian plane are listed below:
Figure 1: A(x, y) = (0, 4), B(x, y) = (5, 0)
Figure 2: A(x, y) = (8.5, 4), B(x, y) = (2.5, 1.5)
How to write coordinates in a rectangular system
A point on a Cartesian plane can be represented by rectangular system of coordinates with the form:
(x, y)
Where:
x - Distance along the x-axis respect to origin.y - Distance along the y-axis respect to origin.Now we proceed to represent each point:
Figure 1: A(x, y) = (0, 4), B(x, y) = (5, 0)
Figure 2: A(x, y) = (8.5, 4), B(x, y) = (2.5, 1.5)
To learn more on Cartesian planes: https://brainly.com/question/27927590
#SPJ1
Quick algebra 1 question for 25 points!
Only answer if you know the answer, quick shout-out to Dinofish32, tysm for the help!
Yes
It's inverse variationSee
3 contractors took 8hours
4 contractors took 6hours
We observe
No of contracter increases hence time decreasesSo it's inverse variation
Answer:
[tex]\fbox {Yes}[/tex]
Step-by-step explanation:
An inverse variation can be seen when two factors are compared, if one factor is seen to be increasing, then naturally the factor should be decreasing.
Here, as the number of contractors increase, the time taken to complete the work decreases.
∴ Hence, this represents an inverse variation.
Line a is perpendicular to line b. if the slope of line a is 7 what is the slope of line b
Answer:
1/7
Step-by-step explanation:
When 2 lines are perpendicular the gradient of one is the reciprocal of the other :
If the gradient of A was 2 the gradient of B would be 1/2.
If the gradient of a is 7 the gradient of b would be 1/7 .
Hope this helped and have a good day
Oops, looks like I’m stuck. Can someone please explain to me in detail why 1 plus 1 isn’t 3? (Giving brainliest to the lengthiest and best answer)
By assuming that 1 + 1 = 3, we will reach an absurd.
How to prove that 1 + 1 isn't 3?
To do this, we need to reach an absurd.
Let's assume that we are working with integer numbers, and let's assume that 1 + 1 is equal to 3.
Then we can write:
1 + 1 = 3
Now, if we subtract 1 in both sides, we get:
(1 + 1) - 1 = 3 - 1
1 = 2
Now we can subtract 1 again so we get:
1 - 1 = 2 - 1
0 = 1
This is an absurd, then the statement:
1 + 1 = 3
is false.
So we conclude that:
1 + 1 isn't 3.
If you want to learn more about math statements:
https://brainly.com/question/1885950
#SPJ1
In a right triangle, one acute angle is 22 degrees less than 3 times the other acute angle. What is the measure of the larger acute angle
The measure of the acute angles are 62° and 28° .
What is the larger acute angle in a right triangle?The Triangle Angle Sum Theorem states that the sum of all interior angles in a triangle is . Additionally, the Right Triangle Acute Angle Theorem states that the two non-right angles in a right triangle are acute; that is to say, the right angle is always the largest angle in a right triangle.Let x represent the measure of one of the acute angles of the right angle triangle.
Let y represent the measure of the other acute angle of the right angle triangle.
One of the acute angles in a right triangle measures 22 degrees less than 3 times the other acute angle. This means that
x = 3y - 22
The sum of two acute angles in a right triangle is 90 degrees.
We write as
x + y = 90 - - - - - - - (1)
Substituting x = 3y - 22 into equation 1, it becomes
3y - 22 + y = 90
4y = 90 + 22= 112
y = 112/4 = 28
x = 90 - y = 90 - 28
x = 62
Learn more about acute angle in a right triangle
brainly.com/question/4174850
#SPJ4
Ali and Baba discovered an underground palace and set out to map all the treasure in it. After carefully mapping the interior, they found that the palace had a vault filled with treasure chests. In each chest, they found either 7 gold bars or 11 silver bars. There were 90 bars in total. How many of them were gold bars?
Answer:
396 gold bars
Step-by-step explanation:
first of all we will find numbers of gold bar 7*99
which is 693 and
we will find number of silver bars 11*99
which is 1089
then 1089-693=
396
If there are 4 green apple and 3 red apples, what's the probability that a red apple is picked?
Answer: 3/7
Step-by-step explanation:
The volume of a cone is 37x³ cubic units and its height is x units.
Which expression represents the radius of the cone's base, in units?
3x
6x
О Злх2
97X2
The radius of the cone's base in the unit is 9*7x².
Which expression represents the radius of the cone's base, in units?Given:
The volume of a cone is 3*7x³ cubic units Its height is x units.To find:
The expression represents the radius of the cone's base, in units.Solution:
As we know, the volume of the cone formula is
V = πr²h/3
So, lets us compare the above formula with the given expression;
πr²h/3 = 3*7x³
Here, h is represented as x, we get;
πr²x/3 = 3*7x³
πr²/3 = 3*7x²
r²= 9*7x²
Hence, the radius of the cone's base, in units, is 9*7x².
To learn more about volume, refer to:
https://brainly.com/question/3390425
#SPJ9
A classroom contains an equal number of boys and girls. if 10 girls leave, twice as many boys as girls remain. what was the original number of students present?
the answer of this question is 38 and i hope it s correct
Help please!!!!
Will give brainliest
The amplitude, Period, Horizontal Shift and Vertical Shift of both graphs are as detailed below.
How to interpret features of trigonometric Graphs?
3)a. Amplitude is the distance between the center line and the positive or negative peak of the graph. Thus, the amplitude is 0.5.
b. The period is the time it takes for the graph to repeat or complete one cycle and in this graph, it is 3.
c. Looking at the graph, ideally the coordinate (3, -1.5) should have been on the y-axis which is at (0, -1.5). This means it was shifted by 3 units to the right side.
d. The positive peak should be equal to the negative peak but in this case, it is not so and as such the center should be on the x-axis which means that the graph was shifted down vertically by 2 units.
4) a. Amplitude is the distance between the center line and the positive or negative peak of the graph. Thus, the amplitude is 3 - 1 = 2
b. The period is the time it takes for the graph to repeat or complete one cycle and in this graph, it is 6.
c. Looking at the graph, ideally the coordinate (4, -1) should have been on the y-axis which is at (0, -1). This means it was shifted by 4 units to the right side.
d. The positive peak should be equal to the negative peak but in this case, it is not so and as such the center should be on the x-axis which means that the graph was shifted up vertically by 1 unit.
Read more about trigonometric graph features at; https://brainly.com/question/17075439
#SPJ1
Find the mode of the following data: 18, 17, 12, 14, 8, 21, 10, 11, 19, 20, 10, 5, 17, 12, 10, 20  A. 16  B. 14  C. 13  D. 10
Answer:
D.10
Step-by-step explanation:
Mode is the number that is repeated the most as we can see the number 10 is there 3 times in the data. 13 isn't there, 14 is only there once and 16 is also not there
The ratio of oil vinegar in a certain salad dressing is 8:5. How much oil must be blended with 7 liters of vinegar for that recipe?
can someone pls help me on this
Answer:
The answer is X=3/4 or -1/2
Drag the values to the correct locations to write this series using sigma notation and find the sum of the terms. Not all values will be used.
45 + [45 − 2.5] + ⋯ + [45 − 4(2.5)]
Answer:
[tex]\displaystyle \\\sum_{k=0}^4 45-2.5k=200[/tex]
Step-by-step explanation:
We start off with the term 45 and decrease by 2.5 each term, ending with four 2.5's subtracted from 45.
Therefore, our index starts at k=0 and ends at 4. The general term can be defined then as [tex]\displaystyle \\\sum_{k=0}^4 45-2.5k[/tex] and evaluating yields 200.
You are _____ to commit a Type I error using the 0.05 level of significance than using the 0.01 level of significance. Group of answer choices more likely less likely equally likely twice as likely
More likely -You are more likely to commit a Type I error
According to statement
we have to find the type 1 error by using the significant levels.
we are commit a MORE LIKELY to find the error by rejecting a true null hypothesis using the 0.05 level of significance than using the 0.01 level of significance.
So, More likely -You are more likely to commit a Type I error
Learn more about HYPOTHESIS here https://brainly.com/question/11555274
#SPJ4
make m the subject!
Quick algebra 1 question for 50 points!
Only answer if you know the answer, quick shout-out to Yeony2202, tysm for the help!
Answer:
Yes.
Step-by-step explanation:
Yes, the given line can be used to make reasonable predictions of the number of cheese pizzas that will be sold, since the scatter points clearly show a trend.
As time goes on, the number of pizzas sold is getting bigger, and the trend is what created the line.
The data was taken over 8 consecutive weeks, so we can assume that it can be used in our prediction.
Since the trend has been pretty consistent over periods of time, we can expect it to continue in the upcoming weeks.