The amount that Peyton would need to invest for the value of the account to reach $39,000 in 17 years is given as follows:
A(0) = $19,097.58.
How to model continuous compounding?The balance of an account after t years, using continuous compounding, is modeled by the equation presented as follows:
[tex]A(t) = A(0)e^{kt}[/tex]
In which:
A(0) is the initial amount.k is the continuous compounding rates.The parameters for this problem are given as follows:
A(t) = 39000, t = 17, k = 0.042.
Hence the investment is obtained as follows:
[tex]A(0)e^(0.042 \times 17) = 39000[/tex]
[tex]A(0) = \frac{39000}{e^(0.042 \times 17)}[/tex]
A(0) = $19,097.58.
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3. When kx³ + x² - 5x -5 is divided by x + 1, its remainder is 0. Hence, the value of k is?
Answer:
k = 1
Step-by-step explanation:
given a polynomial f(x) divided by (x + h) with a remainder of 0 , then (x + h) is a factor of f(x) and f(- h) = 0
here the polynomial is divided by (x + 1)
then substitute x = - 1 into the polynomial and equate to zero
k(- 1)³ + (- 1)² - 5(- 1) - 5 = 0
- k + 1 + 5 - 5 = 0
- k + 1 = 0 ( subtract 1 from both sides )
- k = - 1 ( multiply both sides by - 1 )
k = 1
A store purchases mixing bowls from
the manufacturer for $8 each.
Calculate the sticker price for the
bowls in order to achieve a 60%
gross margin.
A. $13.33
C. $12.00
B. $15.50
D. $20.00
Helpppp
A desktop is shaped like a semicircle with a diameter of 28 inches. What is the area of the desktop? Round your answer to the nearest square inch, if necessary
The area of the desktop is 307.72 square inches.
What is the area of the desktop?Remember that the area of a semicircle of radius R is given by the formula:
A = (pi/2)*R²
Where pi = 3.14
Here we know that the diameter is 28 inches, then the radius is:
R = 28in/2 = 14 inches
Replacing that in the formula for the area we will get:
A= (3.14/2)*(14 in)²
A = 307.72 in²
That is the area of the desktop.
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NEED HELP ASAP
Which ordered pair represents the point labeled A?
The x axis starts at negative 3, with tick marks every one unit up to positive 3. The y-axis starts at negative 3, with tick marks every one unit up to three. Point A is left two units and up one unit from the origin. Point B is right two units and up one unit from the origin. Point C is down two units from the origin. Point D is left one unit and down one unit from the origin.
(−2, 1)
(−1, −1)
(0, −2)
(2, 2)
Help!!!! Please
Asap
Answer:
events at A and B are independent because P(A)(B)≠P(A)
In ABC, AB = 24.1, AC = 15.7, and BC = 25.3. What is LA?
The measure of angle A in triangle ABC is approximately 113.8 degrees.
To find the measure of angle A (LA) in triangle ABC, we can use the Law of Cosines:
c² = a² + b² - 2ab*cos(C)
where c is the length of the side opposite to angle C, and a and b are the lengths of the other two sides.
In this case, we want to find LA, which is opposite to side a (BC). So we can rewrite the Law of Cosines as:
cos(A) = (b² + c² - a²) / 2bc
Plugging in the values we have:
cos(A) = (24.1² + 15.7² - 25.3²) / (2 * 24.1 * 15.7)
cos(A) = -0.3694
Now we need to find the inverse cosine (cos⁻¹) of -0.3694 to get the measure of angle A:
A = cos⁻¹(-0.3694)
Using a calculator, we get:
A ≈ 113.8 degrees
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cual va en los espacios
The function value of f(f(7)) is -13.
We have,
x 9 -11 7 11 -6 -13
f(x) 11 4 -6 -1 -15 -5
From the table,
Using the given table, we can see that:
f(93) is not in the list of x values, so we cannot find its inverse.
Therefore,
We cannot evaluate [tex]f^{-1}(f(93)).[/tex]
f(7) is in the list of x values, and its corresponding function value is f(7) = -6. Therefore,
We can evaluate f(f(7)) by finding the function value corresponding to -6.
i.e
f(-6) = -13
Now,
The function value of f(f(7)).
= f(-6)
= -13
Thus,
The function value of f(f(7)) is -13.
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When cooking rice, the grain is 1/2 of the part to water. Write the ratio that represents this.
• Rice:Water = 2:1
Water:Ratio = 1:2
Rice:Water = 1:2
The matrix associated with the solution to a system of linear equations in x, y, and z is given. Write the solution to the system, if it exists.
The solution to the system of linear equations, would be :
x = -1 - zy = - 4 - 4 zz = zHow to find the solution ?We can rewrite the system of linear equations to be:
x + 0 y + z = - 1
0 x + y + 4 z = - 4
0x + 0y + 0z = 0
The simple version is:
x + z = -1
y + 4z = -4
0 = 0
Therefore, the solution can be written as:
x = -1 - z
y = -4 - 4z
z = z
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using the data on this scatter plot
Answer:
[tex] - 8(45) + 482 = - 360 + 482 = 122[/tex]
An educational researcher devised a wooden toy assembly project to test learning in 6-year-olds. The time in seconds to assemble the project was noted, and the toy was disassembled out of the child's sight. Then the child was given the task to repeat. The researcher would conclude that learning occurred if the mean of the second assembly times was less than the mean of the first assembly times.
Find the 99% confidence interval for the difference in means.
Child
2
3
4
Trial 1
108 140
154
115
Trial 2
99
118 154
96
5
130
108
107
102
110
0 0.7
0-07<4-4 < 23.5
0-29
O 29
Homework part2 need help asap
The key features of the given quadratic functions are listed below.
What is the graph of a quadratic function?In Mathematics and Geometry, the graph of any quadratic function would always form a parabolic curve because it is a u-shaped. Based on the first quadratic function, we can logically deduce that the graph is an upward parabola because the coefficient of x² is positive and the value of "a" is greater than zero (0) i.e 3 > 0.
For the quadratic function y = 3x² - 5, the key features are as follows;
Axis of symmetry: x = 0.
Vertex: (0, -5).
Domain: [-∞, ∞]
Range: [-5, ∞]
For the quadratic function y = -2x² + 12x - 15, the key features are as follows;
Axis of symmetry: x = 3.
Vertex: (3, 3).
Domain: [-∞, ∞]
Range: [-∞, 3]
For the quadratic function y = -x² + 1, the key features are as follows;
Axis of symmetry: x = 0.
Vertex: (0, 1).
Domain: [-∞, ∞]
Range: [-∞, 1]
For the quadratic function y = 2x² - 16x + 30, the key features are as follows;
Axis of symmetry: x = 4.
Vertex: (4, -2).
Domain: [-∞, ∞]
Range: [-2, ∞]
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How many deciliters are in 12 decaliters?
1,200 deciliters
120 deciliters
0.12 deciliters
0.012 deciliters
if 6 article are sold for 20 rupees then there is aloss of20% inorder to gain 20% what must be the number of articals sold for 20 rupess
The number of article sold for Rupees 20 to gain a profit of 20% is equal to 4.
Number of article sold for Rupees 20 = 6
Percent of loss in selling 6 article for Rupees 20 = 20%
Let us start by finding the cost price of one article.
We know that if 6 articles are sold for 20 rupees,
then the selling price of one article is equal to,
Selling price of 1 article = 20/6
⇒ Selling price of 1 article = 3.33 rupees
There was a loss of 20% when 6 articles were sold for 20 rupees.
This means that the cost price of 6 articles is equal to,
Cost price of 6 articles
= Selling price of 6 articles / (1 - Loss%)
= 20 / ( 1 - 20% )
= 20 / (1 - 0.2)
= 25 rupees
To gain 20% profit, the selling price of the articles should be equal to,
Profit% is 20% = 0.2
Selling price of 6 articles
= Cost price of 6 articles × (1 + Profit%)
= 25 × (1 + 0.2)
= 30 rupees
Now , the selling price of one article to calculate how many articles can be sold for 20 rupees,
Selling price of 1 article
= Selling price of 6 articles / 6
= 30 / 6
= 5 rupees
This implies,
The number of articles that can be sold for 20 rupees to gain a 20% profit is equal to,
Number of articles
= 20 / 5
= 4 articles
Therefore, 4 articles must be sold for 20 rupees to gain a 20% profit.
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Please Help
A line has a slope of -7 and passes through the point (2,7). Write its equation in slope intercept form.
A line has a slope of 1 and passes through the point (-1,-7). Write it’s equation in slope intercept form
A line have a slope of 1/2 and passes through the point (6,7). Write it’s equation in slope intercept form.
A line has a slope of -2/3 and passes through the point (9,0). Write It’s equation in slope intercept form
A line has a slope of 5 and passes through the point (5,19).
Write it’s equation in slope intercept form
Write all answers using integers, proper fractions, and improper fractions in simplest form
A linear equation in slope intercept form for each of this line are as follows;
y = -7x + 21y = x - 8y = x/2 + 4y = -2x/3 + 6y = 5x - 6How to determine an equation of this line?In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical equation (formula):
y - y₁ = m(x - x₁)
Where:
x and y represent the data points.m represent the slope.At data point (2, 7) and a slope of -7, a linear equation in slope intercept form for this line can be calculated by using the point-slope form as follows:
y - 7 = -7(x - 2)
y - 7 = -7x + 14
y = -7x + 21
y = 5x - 6
At data point (-1, -7) and a slope of 1, a linear equation in slope intercept form for this line can be calculated by using the point-slope form as follows:
y - (-7) = 1(x - (-1))
y + 7 = x + 1
y = x - 8
At data point (6, 7) and a slope of 1/2, a linear equation in slope intercept form for this line can be calculated by using the point-slope form as follows:
y - 7 = 1/2(x - 6)
y - 7 = x/2 - 3
y = x/2 + 4
At data point (9, 0) and a slope of -2/3, a linear equation in slope intercept form for this line can be calculated by using the point-slope form as follows:
y - 0 = -2/3(x - 9)
y - 0 = -2x/3 + 6
y = -2x/3 + 6
At data point (5, 19) and a slope of 5, a linear equation in slope intercept form for this line can be calculated by using the point-slope form as follows:
y - 19 = 5(x - 5)
y - 19 = 5x - 25
y = 5x - 6
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Meena has a pair of blue jeans with the design below on its back pockets.
60°
60°
Which of the following best describes the triangle with the given measures?
OA. obtuse isosceles triangle
OB. acute equilateral triangle
OC. obtuse equilateral triangle
OD. acute isosceles triangle
B
In geometry, an equilateral triangle is a triangle in which all three sides have the same length. In the familiar Euclidean geometry, an equilateral triangle is also equiangular.
An equilateral triangle can never be obtuse.
Solve the following differential equations:
The general solution to the differential equation based on the information is y(x) = (1/2) x^4 e^(-3x) + C e^(-3x)
How to explain the equationBased on the information, dy/dx + 3y = 2x³ e^(-3x)
The integrating factor is e^(∫3 dx) = e^(3x),
e^(3x) dy/dx + 3e^(3x) y = 2x^3 e^(3x - 3x)
d/dx (e^(3x) y) = 2x^3
e^(3x) y = ∫2x^3 dx = (1/2)x^4 + C
C is an arbitrary constant of integration.
y = (1/2) x^4 e^(-3x) + C e^(-3x)
The equation will be y(x) = (1/2) x^4 e^(-3x) + C e^(-3x)
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Offering 100 points to the first person to answer correctly. Need asap - PLEASE!
Three friends, Jessa, Tyree, and Ben, are collecting canned food for a culinary skills class. Their canned food collection goal is represented by the expression 12x2 − 2xy + 3. The friends have already collected the following number of cans:
Jessa: 3x2
Tyree: 5x2 − 8
Ben: 2xy + 4
Part A: Write an expression to represent the amount of canned food collected so far by the three friends. Show all your work. (5 points)
Part B: Write an expression that represents the number of cans the friends still need to collect to meet their goal. Show all your work. (5 points)
An expression that represents the amount of canned food collected so far by the three friends is 8x² + 2xy - 4.
An expression that represents the number of cans the friends still need to collect to meet their goal is 4x² - 4xy + 2.
How to write the required expressions?From the information provided above, we can logically deduce the following number of canned food collection expressions for each friend:
Jessa; 3x²
Tyree: 5x² - 8
Ben: 2xy + 4
Canned food collection goal: 12x² - 2xy - 2
Therefore, an expression that represents the total amount of canned food collected so far by the three friends can be calculated and written as follows;
Total amount collected so far = 3x² + 5x² - 8 + 2xy + 4
Total amount collected so far = 8x² + 2xy - 4
In order to meet the goal, they need to collect this amount:
Remaining canned foods = 12x² - 2xy - 2 - (8x² + 2xy - 4)
Remaining canned foods = 12x² - 2xy - 2 - 8x² - 2xy + 4
Remaining canned foods = 4x² - 4xy + 2
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HURRY DUE TONIGHT PLEASE EXPLAIN
Danielle was completing her science project and mixed saline solutions A and B. Brand A was a six gallon 18% saline solution and she ended up with an 18 gallon 8% saline solution mixture. Find the percent of saline solution in brand B.
A. 21%
B. 3%
The percentage of saline solution in brand B is 3%.
Let x be Percentage of saline solution in brand B
We know that the overall volume of saline solution in the combination is 18% of 6 gallons plus x% of (18 - 6) gallons since Danielle blended brands A and B to make a total of 18 gallons of 8% saline solution.
Then the equation is given as,
0.18(6) + 0.01x(18 - 6) = 0.08(18)
Simplifying and solving for x, we get:
1.08 + 0.12x = 1.44
0.12x = 0.36
x = 3
Therefore, the percentage of saline solution in brand B is 3%.
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GCM for 16 and 32 I- resdy
The Greatest common Factor of 16 and 32 is 16
What is greatest common factor?Greatest common factor is the largest factor that all the numbers share. For example, 12, and 18 have three common factors: 2, 3and 6 the greatest is 6.
Similarly the factors of 16 and 32 are shown below;
factors of 16 are : 2,4,8,16
factors of 32 are : 2,4,8,16,32
The common factors are: 2,4,8,16
and the largest number among the common factors is 16
Therefore the greatest common factor of 16 and 32 is 16
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What is one of the stages in Cooley's looking-glass self theory?
O A.
OB.
O C.
O D.
We imagine how we look to other people.
We pretend to be someone else we admire.
We spend time looking at ourselves in the mirror.
We discard past patterns and adapt new ones.
One of the stages in Cooley's looking-glass self theory is A. We imagine how we look to other people.
What is Cooley's theory ?As per Cooley's theory, our self-concept is shaped through a social interchange in which we envision how others perceive us, evaluate that perception and then deliberate on how those assessments influence our self-esteem.
All these components are part of the "looking-glass self" process, consisting of three stages: 1) fantasising about how one appears to others 2) pondering over the judgments made based on appearance and 3) evolution of the self-image influenced by such judgements. Notably, imagining one's outward persona forms an integral element of this psychological principle.
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Someone help me do this ols
The values of the variables x and y for the cyclic quadrilateral are 9 and 17 respectively.
How to evaluate for the variables in the cyclic quadrilateralThe figure is a cyclic quadrilateral since it four side vertices lie on the circumference of the circle. The sum of the interior angles of a cyclic quadrilateral is also 360°. Also opposite angles of a cyclic quadrilateral add up to 180°
Thus;
11x + 8 + 8x + 1 = 180° {opposite angles of a cyclic quadrilateral}
19x + 9 = 180°
19x = 180° - 9 {collect like terms}
19x = 171
x = 171/19
x = 9
Also;
6y - 4 + 5y - 3 = 180°
11y - 7 = 180°
11y = 180 + 7
11y = 187
y = 187/11
y = 17
Therefore, the values of the variables x and y for the cyclic quadrilateral are 9 and 17 respectively.
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Help a girl out
Use your brain powers
Triangle GHI is similar to triangle SQR. Therefore, option A and E are correct answers.
Given that, in triangle GHI, ∠G=104°, ∠H=45° and ∠I=31°.
In triangle QRS, ∠Q=45°, ∠R=31° and ∠S=104°.
In triangle XYZ, ∠X=104°, ∠Y=45° and ∠Z=31°.
Consider triangle GHI and triangle QRS
∠G=∠S=104°
∠H=∠Q=45°
∠I=∠R=31°
ΔGHI is similar to ΔSQR
Consider triangle XYZ and triangle QRS
∠X=∠S=104°
∠Z=∠Q=45°
∠Y=∠R=31°
ΔXYZ is similar to ΔSRQ
Consider triangle XYZ and triangle GHI
∠X=∠G=104°
∠Z=∠H=45°
∠Y=∠I=31°
ΔXYZ is similar to ΔGIH
Therefore, option A and E are correct answers.
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Freezer a has interior dimensions of 1‘ x 1‘ x 5‘ and sells for $499.99 freezer B has interior dimensions of 1.5‘ x 1.5‘ x 4‘ and sells for $149.99 which freezer is a better buy in terms of dollars per cubic foot.
Freezer B is better to buy in terms of dollars per cubic foot.
We have,
Dimensions of Freezer A = 1 ft x 1 ft x 5 ft
Sale price of Freezer A = $499.99
Dimensions of Freezer B = 1.5 ft x 1.5 ft x 4 ft
Sale price of Freezer B = $149.99
Now, Dollars per cubic foot for Freezer A
= (1 x 1 x 5)/ 499.99
= 0.01
and, Dollars per cubic foot for Freezer B
= (1.5 x 1.5 x 4)/ 149.99
= 0.06
Thus, Freezer B is better to buy in terms of dollars per cubic foot.
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3
1
Jill walked on Tuesday 3-miles. On Wednesday, she walked 1
less than on Tuesday. Which equati
5
4
total number of miles Jill walked, w, on Tuesday and Wednesday?
0 = 3/3² + 1² = w
The equation that shows the total number of miles Jill walked, w, on Tuesday and Wednesday is w = 3 + 2
Calculating the equation shows the total number of milesFrom the question, we have the following parameters that can be used in our computation:
Tuesday = 3 miles
Wednesday = 1 less than Tuesday
This means that
Wednesday = 3 miles - 1 mile
Evaluating the like terms, we have
Wednesday = 2 miles
The equation shows the total number of miles Jill walked, w, on Tuesday and Wednesday is represented as
w = Tuesday + Wednesday
Substitute the known values in the above equation, so, we have the following representation
w = 3 + 2
Evaluate
w = 5
Hence, the equation is w = 3 + 2 and the number of miles s 5
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Find the measure of the angle X in the figure.
The unknown measure in the line segment is as follows:
∠x = 141 degrees
How to find the measure of angles?When line segment intersect, angle relationships are formed such as vertical angles, adjacent angles etc.
Therefore, let's find the angle x in the line intersection as follows:
Therefore, the angle x comprises of angle 90 degrees and angle 50 degrees.
The sum of angle 90 degrees and 50 degrees is equals to angle x
Hence,
x = 51 + 90
x = 141 degrees
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50 students in the fourth grade class list of their hair and eye colors in the table below are the events green eyes and brown hair independent
Answer:
câu này là 500 nhen
The question is attached
The rules for the two graphs above are: A. first graph: y = 3 + x; second graph : y = 6 + x.
How to determine an equation of this line?In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical equation (formula):
y - y₁ = m(x - x₁)
Where:
x and y represent the data points.m represent the slope.First of all, we would determine the slope of graph 1;
Slope (m) = (y₂ - y₁)/(x₂ - x₁)
Slope (m) = (4 - 3)/(1 - 0)
Slope (m) = 1/1
Slope (m) = 1
At data point (0, 3) and a slope of 1, a linear equation for this line can be calculated by using the point-slope form as follows:
y - y₁ = m(x - x₁)
y - 3 = 1(x - 0)
y = x + 3
Next, we would determine the slope of graph 2;
Slope (m) = (y₂ - y₁)/(x₂ - x₁)
Slope (m) = (7 - 6)/(1 - 0)
Slope (m) = 1/1
Slope (m) = 1
At data point (0, 6) and a slope of 1, a linear equation for this line can be calculated by using the point-slope form as follows:
y - y₁ = m(x - x₁)
y - 6 = 1(x - 0)
y = x + 6
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When cooking rice, the grain is 1/2 of the part to water. Write the ratio that represents this.
• Rice:Water = 2:1
Water:Ratio = 1:2
Rice:Water = 1:2
Answer:
Rice:Water = 1:2
Step-by-step explanation:
Samantha stores all of her important paperwork in the file cabinet shown below.
A locker measurement at the bottom as 2 one by 6 ft 2, side as 1 and a half ft, and length as 2 2 by 3 ft.
*Picture not drawn to scale
What is the volume of the file cabinet?
A.
7 2/9
cu ft
B.
6 1/12
cu ft
C.
4 1/36
cu ft
D.
2 17/24
cu ft
The volume of the file cabinet in this problem is given as follows:
V = 8 and 7/10 cu ft.
How to obtain the volume of a rectangular prism?The volume of a rectangular prism, with dimensions length, width and height, is given by the multiplication of these dimensions, according to the equation presented as follows:
Volume = length x width x height.
The dimensions for this problem are given as follows:
2.167 ft, 1.5 ft and 2.67 ft.
Hence the volume of the prism is given as follows:
V = 2.167 x 1.5 x 2.67
V = 8.7 ft³.
As a mixed number, the volume is given as follows:
V = 8 and 7/10 cu ft.
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