In a parallelogram, opposite angles are congruent.
This means that the four angles of the parallelogram are:
[tex]L = x+40,\quad M = 3x,\quad N = x+40,\quad O = 3x[/tex]
Moreover, the sum of the interior angles of a polygon with n sides is 180(n-2). So, the sum of the interior angles of a parallelogram is 360.
This means
[tex]L+M+N+O = 360 \iff 2(x+40)+2(3x) = 2x+80+6x = 360 \iff 8x = 280 \iff x = 35[/tex]
And since [tex]O=3x[/tex], we have [tex]O=3\cdot 35=105[/tex]
Answer:
Angle O(3x) is =105 degrees or C
LOOK AT PHOTO PLEASE
The slope of the line in the graph is ____
The y-intercept is______
The equation of the line is y=_____ x=_____
The slope of the graph is 3
The y-intercept is -4
The equation of the line is y=3x-4 it shouldn’t be y= then x=
Answer:
The slope is 3
The y-intercept is -4
The equation of the line is y=3 x=-4
Step-by-step explanation:
:)
ADE and ABC are similar which best explains why the spike of the line between point A and D is the same as the slope between points A and B
The same slope between line AD and line AB results from the property of similar triangles. This property states that corresponding sides are proportional, which also applies to the slopes of these sides. Hence, the slopes are equivalent.
Explanation:The reason the slope of the line between point A and D is the same as the slope between points A and B derives from the concept of similar triangles in geometric math. In similar triangles, corresponding sides are proportional. This proportionality is carried over to the slopes of the lines that form these sides. Slope is defined by the change in y (vertical change) over the change in x (horizontal change). In similar triangles, these changes are proportional meaning the division, or the slope will be the same.
Consider this using Figure A1 Slope and the Algebra of straight lines where they indicate that the slope is the same all along a straight line. This also applies to the lines of similar triangles. Therefore, if triangles ADE and ABC are similar, then the slope of line AD will be the same as the slope of line AB because the ratios of their changes in y over changes in x are equal.
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Find the common difference of the following arithmetic sequence 35,32,29,26...
Answer: they are all being subtracted by 3
Step-by-step explanation:
35-3=32
32-3=29
29-3=26
The common difference in the arithmetic sequence 35, 32, 29, 26... is 3.
To find the common difference in an arithmetic sequence, you subtract one term from the following term. In this case, the sequence is 35, 32, 29, 26... To find the common difference, subtract 32 from 35, which equals 3. Therefore, the common difference in this sequence is 3.
#18 please help me thank you
Answer:
The solutions of the equation is 0 , π , 2π
Step-by-step explanation:
* Lets revise some identities in the trigonometry
- tan²x + 1 = sec²x
- tan²x = sec²x - 1
* Now lets solve the equation
∵ tan²x sec²x + 2sec²x - tan²x = 2
* Lets replace tan²x by sec²x - 1
∴ (sec²x - 1) sec²x + 2sec²x - (sec²x - 1) = 2 ⇒ open the brackets
∴ sec^4 x - sec²x + 2sec²x - sec²x + 1 = 2 ⇒ add the like terms
∴ sec^4 x -2sec²x + 2sec²x + 1 = 2 ⇒ cancel -2sec²x with +2sec²x
∴ sec^4 x + 1 = 2 ⇒ subtract 1 from both sides
∴ sec^4 x = 1 ⇒ take root four to both sides
∴ sec x = ± 1 ⇒ x is on the axes
∵ sec x = 1/cos x
∵ sec x = 1 , then cos x = 1
∵ sec x = -1 , then cos x = -1
∵ 0 ≤ x ≤ 2π
∵ x = cos^-1 (1)
∴ x = 0 , 2π ⇒ x is on the positive part of x-axis
∵ x = cos^-1 (-1)
∴ x = π ⇒ x is on the negative part of x-axis
* The solutions of the equation is 0 , π , 2π
How do I solve this?
Answer:
[tex]\large\boxed{4\sqrt{-81}+\sqrt{-25}=41i}[/tex]
Step-by-step explanation:
[tex]i=\sqrt{-1}\\\\\sqrt{-81}=\sqrt{(81)(-1)}=\sqrt{81}\cdot\sqrt{-1}=9i\\\\\sqrt{-25}=\sqrt{(25)(-1)}=\sqrt{25}\cdot\sqrt{-1}=5i\\\\4\sqrt{-81}+\sqrt{-25}=4(9i)+5i=36i+5i=41i[/tex]
Which of the following shows 27⁄54 written in prime factored form to help in reducing the fraction to simplest form?
A. 1⁄2
B. 9×3 ⁄9×6
C. 27×1 ⁄27×2
D. 3×3×3⁄3×3×3×2
Answer:
3×3×3⁄3×3×3×2
Step-by-step explanation:
27 = 3×3×3
54 = 3×3×3×2
The prime factored form of 27⁄54 is thus;
3×3×3⁄3×3×3×2
Answer:
D= 3×3×3/2×3×3×3
Step-by-step explanation:
A prime factored form breaks the number into prime numbers that give the same value when multiplied
27= 3×3×3
54=2×3×3×3
To get the simplest form of a fraction you proceed with division.
=3×3×3 / 2×3×3×3.............................cancel 3 in the numerator and denominator
= 1/2
144^14/144^2
A.144^16
B.144^12
C.144^28
D.144^14/244^2
Answer:
B. 144^12
Step-by-step explanation:
[tex]{144}^{14} \div {144}^{2} \\ = {144}^{14 - 2} \\ = {144}^{12} [/tex]
The simplified exponent form of the given expression 144^14/144^2 would be 144^12.
What are exponential functions?When the expression of function is such that it involves the input to be present as an exponent (power) of some constant, then such function is called exponential function. There usual form is specified below. They are written in several such equivalent forms.
The given expression can be solved by exponentially
[tex]\dfrac{144^{14}}{144^2}\\\\144^{14} \times144^{-2}}\\\\144^{14-2} \\\\144^{12}[/tex]
Therefore the simplified exponent form of the given expression would be 144^12.
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Give the scale factor, perimeter ratio, and area ratio of figure A to figure B
Answer:
Scale factor: 4/7
perimeter ratio: 4:7
area: I don't know the height of the two
Step-by-step explanation:
What is the expanded form of the series represented below?
A. -3 + 2 + 7 + 12 + 17
B. -3 + 3 + 8 + 13 + 18
C. 2 + 7 + 12 + 17 + 22
D. 5 + 2 + (-1) + (-4) + (-7)
Answer:
See below
Step.-by-step explanation:
Choice A has first term -3 and common difference 5. The formula for the kth term is -3 + (k - 1)5. It is an arithmetic series.
The required expanded form for the Sum is:
5
S5 = ∑ [-3 + (k - )5)]
k = 1
Answer:
Expanded form of the series is:
A. -3 + 2 + 7 + 12 + 17
Step-by-step explanation:
when k=1 -3+(k-1)5= -3
when k=2 -3+(k-1)5= -3+5=2
when k=3 -3+(k-1)5= -3+10=7
when k=4 -3+(k-1)5= -3+15=12
when k=5 -3+(k-1)5= -3+20=17
Hence, value of [tex]S_{5}= -3+2+7+12+17[/tex]
Hence, expanded form of the series is:
A. -3 + 2 + 7 + 12 + 17
Justin walked his dog 5 miles in
5
4 hours. How many miles per hour did Justin and his dog walk?
Answer:
Is the 5 separate or to gather like 45
Justin and his dog walked at approximately 0.093 miles per hour.
Explanation:To find the number of miles per hour, Justin and his dog walked, we need to divide the total distance walked (5 miles) by the total time taken (54 hours). So, 5 miles / 54 hours = 0.093 miles per hour.To find out how many miles per hour Justin and his dog walked, we need to divide the total distance walked by the total time spent. In this case, Justin walked 5 miles in 54 hours. Therefore, the speed is calculated as follows: 5 miles ÷ (54) hours = 4 miles per hour. This means Justin and his dog walked at a speed of 4 miles per hour.
Therefore, Justin and his dog walked at approximately 0.093 miles per hour.
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Use the given information to match the answers. ABC is a right triangle. 1. If a = 3 and c = 6, then b = 2. If a = 4 and b = 6, then c = 3. If b = 2 and c = 3, then a =
i need the answers quickly please
Final answer:
Using the Pythagorean theorem, we solved for the missing sides of a right triangle in three scenarios, finding b approximately as 5.20, c approximately as 7.21, and a approximately as 2.24.
Explanation:
To solve for the missing sides of a right triangle, we use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b). The theorem is mathematically represented as a² + b² = c². Let's use this to solve the given problems.
For a = 3 and c = 6, to find b, we use the equation 3² + b² = 6². After calculation, b = √(36 - 9), which simplifies to b = √27 or approximately 5.20.
If a = 4 and b = 6, to find c, the equation is 4² + 6² = c². Solving for c gives us c = √(16 + 36), which is c = √52 or approximately 7.21.
For b = 2 and c = 3, to find a, we apply the formula a² + 2² = 3². This leads to a² = 9 - 4, so a = √5 or about 2.24.
The width of a rectangle is fifteen feet less than its length. If the area of the rectangle is 54 square feet, find the width.
Answer:
3 ft
Step-by-step explanation:
It is because 3 times 18 is 54 and 3 is 15 less than 18
The width of a rectangle is 3 feet .
What is area of rectangle?The area can be defined as the amount of space covered by a flat surface of a particular shape. It is measured in terms of the "number of" square units (square centimeters, square inches, square feet, etc.)
According to the question
Let length of rectangle = x
The width of a rectangle is fifteen feet less than its length.
i.e,
Width of a rectangle = x - 15
Now,
Area of the rectangle = 54 square feet .
Length * Width = 54
x (x - 15 ) = 54
[tex]x^{2}[/tex] - 15x - 54 = 0
[tex]x^{2}[/tex] - (18-3)x - 54 = 0
[tex]x^{2}[/tex] - 18x + 3x - 54 = 0
x(x-18) +3(x-18) = 0
(x-18) (x+3) = 0
x= 18 , -3
length of rectangle = 18 feet
Width of a rectangle = 18 - 15
= 3 feet
Hence, The width of a rectangle is 3 feet .
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Find the slope of the line on the graph.
Write your answer as a fraction or a whole
number, not a mixed number or decimal.
Answer:
-1/3
Step-by-step explanation:
You can do rise over run, and, in this case is going to be 1\3.
The slope of the line is 1.
To do this, we'll use the coordinates of two points on the line: Point 1 at (0,6) and Point 2 at (-6,0).
The slope of a line is given by the formula:
[tex]\[ m = \frac{{y_2 - y_1}}{{x_2 - x_1}} \][/tex]
1. Identify the coordinates:
- Point 1: [tex]\( (x_1, y_1) = (0, 6) \)[/tex]
- Point 2: [tex]\( (x_2, y_2) = (-6, 0) \)[/tex]
2.Calculate the change in x and change in y:
- Change in x: [tex]\( x_2 - x_1 = -6 - 0 = -6 \)[/tex]
- Change in y:[tex]\( y_2 - y_1 = 0 - 6 = -6 \)[/tex]
3. Apply the slope formula:
[tex]\[ m = \frac{{y_2 - y_1}}{{x_2 - x_1}} = \frac{{-6}}{{-6}} = 1 \][/tex]
Therefore, the slope of the line is 1.
Jane had R Beanie Babies. She gave 8 of them to her friend. Later her grandma bought her 5 more Beanie Babies than she had in the beginning. How many Beanie Babies did Jane have in the beginning, if now she has 27 of them?
Jane had 10 Beanie Babies in the beginning.
The number of Beanie Babies Jane had in the beginning.
- She gave 8 to her friend, leaving her with [tex]\( x - 8 \)[/tex] Beanie Babies.
- Her grandma bought her 5 more, so she then had [tex]\( x + 5 \)[/tex] Beanie Babies.
- Combining the Beanie Babies she had at the beginning, the ones she gave away, and the ones her grandma bought her, the total is 27.
- Solving the equation [tex]\( x - 8 + (x + 5) = 27 \)[/tex], we find [tex]\( x = 10 \)[/tex], the number of Beanie Babies Jane had in the beginning.
Jane had 20 Beanie Babies in the beginning.
To calculate:
1. Let's denote the number of Beanie Babies Jane had in the beginning as [tex]\( x \).[/tex]
2. She gave 8 of them to her friend, leaving her with [tex]\( x - 8 \)[/tex] Beanie Babies.
3. Her grandma bought her 5 more Beanie Babies than she had in the beginning, so she now has [tex]\( x + 5 \)[/tex] Beanie Babies.
4. Given that she now has 27 Beanie Babies, we can set up the equation:
[tex]\[ x - 8 + (x + 5) = 27 \][/tex]
Now, let's solve for [tex]\( x \):[/tex]
[tex]\[ 2x - 3 = 27 \][/tex]
[tex]\[ 2x = 30 \][/tex]
[tex]\[ x = 15 \][/tex]
However, this is the number of Beanie Babies Jane had after her grandma bought her 5 more. To find out how many she had in the beginning, we need to subtract 5 from [tex]\( x \):[/tex]
[tex]\[ x = 15 - 5 = 10 \][/tex]
So, Jane had 10 Beanie Babies in the beginning.
- Let [tex]\( x \)[/tex] be the number of Beanie Babies Jane had in the beginning.
- She gave 8 to her friend, leaving her with [tex]\( x - 8 \)[/tex] Beanie Babies.
- Her grandma bought her 5 more, so she then had [tex]\( x + 5 \)[/tex] Beanie Babies.
- Combining the Beanie Babies she had at the beginning, the ones she gave away, and the ones her grandma bought her, the total is 27.
- Solving the equation [tex]\( x - 8 + (x + 5) = 27 \)[/tex], we find [tex]\( x = 10 \)[/tex], the number of Beanie Babies Jane had in the beginning.
Complete question
Jane had R Beanie Babies. She gave 8 of them to her friend. Later her grandma bought her 5 more Beanie Babies than she had in the beginning. How many Beanie Babies did Jane have in the beginning, if now she has 27 of them?
Which of the following is not a property of the sample standard deviation s?
A. Sensitive to changes in the distribution
B. Calculated based on the mean
C. Larger than the population standard deviation o D. Resistant to extreme data values
E. All of the above.
The property of the sample standard deviation that is not accurate is 'D. Resistant to extreme data values'. The sample standard deviation is indeed sensitive to extreme data values. The other properties listed are true about the sample standard deviation.
Explanation:The property of the sample standard deviation (s) that is not accurate from the given options is 'D. Resistant to extreme data values'. The sample standard deviation is sensitive to extreme values, not resistant. In other words, if there are outliers or extreme values in the data, the sample standard deviation will tend to be larger, reflecting the increased variability.
Let's quickly review the other options for clarity. 'A. Sensitive to changes in the distribution' and 'B. Calculated based on the mean' are true properties of the sample standard deviation. The standard deviation, whether for a sample or a population, measures the spread or dispersion of the data points about the mean. Therefore, it changes with the distribution and is calculated based on the mean. 'C. Larger than the population standard deviation σ' is typically true, unless the sample perfectly represents the population.
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The sample standard deviation is C. larger than the population standard deviation o.
Explanation:The sample standard deviation, denoted as s, is a measure of spread that quantifies how much the data values deviate from the mean. It is calculated based on the mean. However, it is not necessarily larger than the population standard deviation, o, as it depends on the specific data set.
The other options are not correct:
A. The sample standard deviation is sensitive to changes in the distribution, as it considers the individual data values and their deviations from the mean.B. The sample standard deviation is calculated based on the mean, as it involves calculating the deviations of individual data values from the mean.D. The sample standard deviation is not resistant to extreme data values, as it considers each data value and its deviation from the mean.E. All of the above is not the correct answer, as the correct answer is C.
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Find the total surface area of this object.
Answer:
60
Step-by-step explanation:
Use the formula for the surface area and plug in the given numbers. See work for more.
origami is the Japanese art of paper folding the diagram below represents an unfolded paper kabuto a samuri warriors helmet which of the following are pairs of congruen segments? check all that apply
Answer: FR and NR
NO and NM
RC and RO
Step-by-step explanation: just did it on apex. good luck!
Answer:
The correct options are A, C and D.
Step-by-step explanation:
The given figure shows an unfolded paper. It is a square sheet.
Here the line of symmetry are diagonals FN, AK and midline CM, OI. All of these lines are intersecting at point R.
Diagonals of square bisect each other, therefore R is midpoint of FN.
[tex]FR\cong NR[/tex]
[tex]AO\cong ON[/tex] (OI is line of symmetry)
[tex]PO\neq ON[/tex]
[tex]RC\cong RO[/tex] (AK is line of symmetry)
[tex]NO\cong NM[/tex] (FN is line of symmetry)
[tex]DV\cong HV[/tex] (FN is line of symmetry)
[tex]DV\neq EW[/tex]
Therefore the correct options are A, C and D.
Write a rule for the function represented in the table
Answer:
i think that it is y=5n
Step-by-step explanation:
Given: ABCD is a rectangle, < ABX is congruent to < XBC
PROVE: ABCD is a square
Figure is labeled ABCD clockwise with A starting in the upper left hand corner. Diagnosis AC and BD intersect at X
Answer:
im not sure were you got this but are there any pictures?
Step-by-step explanation:
The figure ABCD represents a square
What is the area of a square?A square is a four sided quadrilateral with all of the side having equal lengths. The total internal angle of a square is 360° with each side perpendicular to each other.
A square is a 4 sided polygon where all the sides are of equal length.
The area of the square is the square of any one of its side
Let a be the side of the square
Area of the square = a²
Given data ,
Let the figure be represented as ABCD
Now , the coordinates of ABCD are noted clockwise
And , the diagonals of the quadrilateral are AC and BD
Now , the diagonals AC and BD intersect at X
where the measure of angle ∠ABX = measure of ∠XBC
So , the diagonals are equal and the angles are equal
And , the figure represents a square
where the sides AB = BC = CD = AC
Hence , the figure is a square by SAS congruency
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if 5lb of cheese cost 18.50, how much would 1 lb cost
Answer:
3.70
Step-by-step explanation:
18.50 ÷ 5 = 3.70
fairly simple math but can be confusing depending upon how its asked, you just have to find the words that describe what you have to do and check your math to make sure
Find the angle between vector u=2i+sqrt(11)j and v=-3i-2j to the nearest degree
Answer: Last option 155°
Step-by-step explanation:
We have the components of the vectors u and v.
Then, to find the angle between them, perform the following steps:
1) Calculate the scalar product u * v
If [tex]u = 2i + \sqrt{11}j[/tex] and [tex]v = -3i-2j[/tex]
Then, the product scalar u * v is:
[tex]u * v = (2)(-3) + (\sqrt{11})(-2)[/tex]
[tex]u * v = -6-2\sqrt{11}[/tex]
[tex]u * v = -12.633[/tex]
2) Calculation of the magnitude of both vectors.
[tex]| u | = \sqrt{(2) ^ 2 + (\sqrt{11})^2}\\\\| u | = \sqrt{4+11}\\\\| u | = \sqrt{15}[/tex]
[tex]| v | = \sqrt{(- 3) ^ 2 + (- 2) ^ 2}\\\\| v | = \sqrt{9 +4}\\\\| v | = \sqrt{13}[/tex]
3) Now that you know the product point between the two vectors and the magnitude of each, then use the following formula to find an angle
[tex]u * v = | u || v |cos(\alpha)[/tex]
[tex]-12.633 = \sqrt{15}\sqrt{13}*cos(\alpha)\\\\cos(\alpha) = \frac{-12.633}{\sqrt{15}\sqrt{13}}\\\\arcos(\frac{-12.633}{\sqrt{15}\sqrt{13}}) = \alpha\\\\\alpha =155\°[/tex]
Someone please answer this
The two lines with the equations are the same length.
Set the two equations to equal and solve:
3x +3 = 6x - 57
Add 57 to each side:
3x +60 = 6x
Subtract 3x from each side:
60 = 3x
Divide both sides by 3:
x = 20
Answer:
x= 20
Step-by-step explanation:
Please help with this question!!!!
Answer:
D) The number line with a solid dot and the arrow going to the right of 3.
Step-by-step explanation:
x - 5 >/= -2
x >/= 3
x is greater than or equal to 3.
For this case we must find the solution of the following inequality:
[tex]x-5\geq-2[/tex]
So:
If we add 5 to both sides of the inequality we have:
[tex]x-5 + 5\geq - 2 + 5\\x\geq - 2 + 5\\x\geq 3[/tex]
Thus, the solution is given by all values of x greater than or equal to 3.
Answer:
Option D
taxidistance between (0,0) and (7,3)
For this case we have that by definition, the distance between two points is given by:
[tex]d = \sqrt {(x_ {2} -x_ {1}) ^ 2+ (y_ {2} -y_ {1}) ^ 2}[/tex]
We have to:
[tex](x_ {1}, y_ {1}) = (0,0)\\(x_ {2}, y_ {2}) = (7,3)[/tex]
Substituting:
[tex]d = \sqrt {(7-0) ^ 2 + (3-0) ^ 2}\\d = \sqrt {(7) ^ 2 + (3) ^ 2}\\d = \sqrt {49 + 9}[/tex]
[tex]d = \sqrt {58}\\d = 7.62[/tex]
ANswer:
[tex]d = 7.62[/tex]
Answer:
The Answer Is 10.
Step-by-step explanation:
| x2-x1 | + | y2-y1 | = taxidistance.
(0, x1), (0, y1), (7, x2), (3, y2)
Substitute.
| 7-0| + | 3-0 | = 10
Write a recursive formula for the sequence –2, 4, –8, 16, ...
please help and thank you
Answer:
see explanation
Step-by-step explanation:
A recursive formula allows us to calculate any term in the sequence from the previous term.
These are the terms of a geometric sequence with r being the common ratio between consecutive terms.
r = 4 ÷ - 2 = - 8 ÷ 4 = 16 ÷ - 8 = - 2
Multiplying a particular term by - 2 gives the next term in the sequence.
Hence recursive formula is
[tex]a_{n+1}[/tex] = - 2 [tex]a_{n}[/tex] with a₁ = - 2
-2,4,-8,16,...
a₁ = -2
a₂ = -2a₁
a₃ = -2a₂
..................
=> aₙ₊₁ = -2•aₙ, with a₁ = -2
Identify the vertex of the graph. Tell whether it is a minimum or maximum A. (-1, -2); maximum B. (-2,- 1); maximum C. (-2, -1); minimum D. (-1, -2); minimum
Answer:
D
Step-by-step explanation:
The vertex is the turning point of the graph.
This is at (- 1, - 2)
The graph changes from decreasing to increasing at (- 1, - 2)
Hence is a minimum at (- 1, - 2)
The graph of the parabola is minimum at (-2, -1).
Parabola
The path of an object that is thrown in the air and falls back to the earth.
GivenA graph of the parabola is given.
How to find maximum and minimum?
a. At ( -1, -2 ), the parabola is minimum.
b. At ( -2, -1 ), point does not satisfy.
c. At ( 2, 1 ), the point does not satisfy.
d. At ( 1, 2 ), the point does not satisfy.
Thus, the graph of the parabola is minimum at (-2, -1).
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In a freshman high school class of 80 students, 22 students take Consumer Education, 20 students take French, and 4 students take both. Which equation can be used to find the probability, P, that a randomly selected student from this class takes Consumer Education, French, or both?
Answer:
First subtract the number of students who take both subjects from the number of students who take Consumer Education
22-4=18
Then,
subtract the number of students who take both subjects from the number of students who take French
20-4=16
Now,
Add 18,16 and 4 and subtract the sum from the total number of students in the class
=80-(18+16+4)
=80-38
=42
Step-by-step explanation:
Answer: P= 11/40 + 1/4 + 1/20
5600 dollars is placed in an account with an annual interest rate of 8.5%. To the nearest year, how long will it take for the account value to reach 15000 dollars?
It takes about 20 years
It will take approximately 13 years for the account value to reach $15,000.
To find the time it takes for the account value to reach $15,000, we used the formula for compound interest and rearranged it to solve for [tex]\(t\).[/tex] Then, we substituted the given values into the formula and calculated the time to be approximately 12.82 years. Rounding to the nearest year gives us 13 years.
To calculate the time it takes for the account value to reach $15,000 with an annual interest rate of 8.5%, we can use the formula for compound interest:
[tex]\[A = P(1 + r/n)^{nt}\][/tex]
Where:
- [tex]\(A\)[/tex] is the future value of the investment/loan, including interest.
- [tex]\(P\)[/tex] is the principal investment amount (the initial deposit or loan amount).
- [tex]\(r\)[/tex] is the annual interest rate (in decimal).
- [tex]\(n\)[/tex] is the number of times that interest is compounded per year.
- [tex]\(t\)[/tex] is the time the money is invested for, in years.
In this case, [tex]\(P = 5600\)[/tex], [tex]\(A = 15000\)[/tex], [tex]\(r = 0.085\)[/tex] (8.5% expressed as a decimal), and [tex]\(n = 1\)[/tex] (compounded annually).
We need to solve for [tex]\(t\)[/tex], so rearranging the formula:
[tex]\[t = \frac{\log(A/P)}{n \cdot \log(1 + r/n)}\][/tex]
Substituting the given values:
[tex]\[t = \frac{\log(15000/5600)}{1 \cdot \log(1 + 0.085/1)}\][/tex]
[tex]\[t[/tex] ≈ [tex]\frac{\log(2.6786)}{\log(1.085)}[/tex]
[tex]\[t[/tex] ≈ [tex]\frac{0.4285}{0.0334}[/tex]
[tex]\[t[/tex] ≈ [tex]12.82[/tex]
To the nearest year, it will take approximately 13 years for the account value to reach $15,000.
To find the time it takes for the account value to reach $15,000, we used the formula for compound interest and rearranged it to solve for \(t\). Then, we substituted the given values into the formula and calculated the time to be approximately 12.82 years. Rounding to the nearest year gives us 13 years.
Complete question
5600 dollars is placed in an account with an annual interest rate of 8.5%. To the nearest year, how long will it take for the account value to reach 15000 dollars?
The table below shows the three-day rain forecast
for Friday, Saturday and Sunday in Aberystwyth.
Day Probability of rain
Friday
70%
Saturday
70%
Sunday
70%
a) Work out the probability that it will rain on all three days.
b) Work out the probability that it will rain on exactly two consecutive days.
Answer:
a=0.343
Step-by-step explanation:
70/100=0.7
0.7x0.7x0.7=0.343
Rotation 90 clokwise HELP PLEASE
Answer:
Step-by-step explanation:
I assume you want to rotate each point about the origin.
To rotate a point (x, y) 90° clockwise about the origin:
(x, y) → (y, -x)
For point A:
(-5, 0) → (0, 5)
For point B:
(-5, 3) → (3, 5)
For point C:
(0, 4) → (4, 0)