Answer:
a) $20,771.76
b) $20,817.67
c) $20,484.80
d) $20,864.52
Step-by-step explanation:
Compound Interest Formula
[tex]\large \text{$ \sf A=P\left(1+\frac{r}{n}\right)^{nt} $}[/tex]
where:
A = final amountP = principal amountr = interest rate (in decimal form)n = number of times interest applied per time periodt = number of time periods elapsedPart (a): semiannually
Given:
P = $15,000r = 5.5% = 0.055n = 2t = 6 yearsSubstitute the given values into the formula and solve for A:
[tex]\implies \sf A=15000\left(1+\frac{0.055}{2}\right)^{2 \times 6}[/tex]
[tex]\implies \sf A=15000\left(1.0275}{2}\right)^{12}[/tex]
[tex]\implies \sf A=20771.76[/tex]
Part (b): quarterly
Given:
P = $15,000r = 5.5% = 0.055n = 4t = 6 yearsSubstitute the given values into the formula and solve for A:
[tex]\implies \sf A=15000\left(1+\frac{0.055}{4}\right)^{4 \times 6}[/tex]
[tex]\implies \sf A=15000\left(1.01375}\right)^{24}[/tex]
[tex]\implies \sf A=20817.67[/tex]
Part (c): monthly
Given:
P = $15,000r = 5.5% = 0.055n = 12t = 6 yearsSubstitute the given values into the formula and solve for A:
[tex]\implies \sf A=15000\left(1+\frac{0.055}{12}\right)^{12 \times 6}[/tex]
[tex]\implies \sf A=15000\left(1+\frac{0.055}{12}\right)^{72}[/tex]
[tex]\implies \sf A=20484.80[/tex]
Continuous Compounding Formula
[tex]\large \text{$ \sf A=Pe^{rt} $}[/tex]
where:
A = Final amountP = Principal amounte = Euler's number (constant)r = annual interest rate (in decimal form)t = time (in years)Part (d): continuous
Given:
P = $15,000r = 5.5% = 0.055t = 6 yearsSubstitute the given values into the formula and solve for A:
[tex]\implies \sf A=15000e^{0.055 \times 6}[/tex]
[tex]\implies \sf A=20864.52[/tex]
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What are the points if the slope is 4 and the point is (1,-1)
The points if the slope is 4 and the point is (1,-1) are (1,-1) and (2, 3)
What are linear equations?Linear equations are equations that have constant average rates of change, slope or gradient
How to determine the points?The given parameters are:
Slope = 4
Point = (1, -1)
The slope of 4 means that as x changes by 1, the value of y changes by 4
This means that, we have:
(x + 1, y + 4)
Substitute the known values in the above equation
(1 + 1, -1 + 4)
Evaluate
(2, 3)
Hence, the points if the slope is 4 and the point is (1,-1) are (1,-1) and (2, 3)
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Alex has a bag of marbles. Each marble is red or blue, and the ratio of red to blue marbles is 3 : 5. After Alex adds 10 red marbles to the bag, the ratio of red to blue marbles is 2 : 3. How many blue marbles are in Alex’s bag?
Solving a system of equations we will see that there are 150 blue marbles in the bag
How many blue marbles are in Alex’s bag?We know that initially, the ratio of red to blue marbles is 3:5
This means that if there are 8*n marbles in the bag, there are:
3*n red marbles.5*n blue marbles.Now, when he adds 10 red marbles, the new ratio is 2:3, this means that if now there are 5*m marbles, we have:
2*m red marbles3*m blue marbles.Where we will have two relations, so we have a system of equations:
3*n + 10 = 2*m
8*n + 10 = 5*m
With these two we can find the value of n and m.
To do that, we isolate m in the first equation:
m = (3*n + 10)/2
Now we can replace that in the other equation to get:
8*n + 10 = 5* (3*n + 10)/2
Now we can solve this for n:
2*(8*n + 10) = 5*(3n + 10)
16n + 20 = 15n + 50
n = 50 - 20 = 30
n = 30
And the number of blue marbles is:
5*n = 5*30 = 150
There are 150 blue marbles.
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A farmer with 1200 meters of fencing wishes to enclose a rectangular field and then divide it into two plots with a fence parallel to one of the sides. What are the dimensions of the field that produce the largest area
The perimeter of a given figure is a measure of the addition of each individual length of the sides of the figure. Thus the dimensions that would produce the largest area of the field are; length = 300 m, and width = 200 meters.
The perimeter of a given figure is a measure of the addition of each length of the sides of the figure. It always has the unit as that of the given sides of the figure.
So in the given question, the perimeter of the fence required = 1200 meters.
Thus, let the length of the enclosed rectangle be represented by l and its width by w. Thus,
Perimeter = 2l + 3w
1200 = 2l + 3w
Thus, let l be equal to 300, we have;
1200 = 2(300) + 3w
1200 - 600 = 3w
w = 200
Thus the dimensions of the field that would produce the largest area are; length = 300 m and width = 200 m.
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Find the inverse of the matrix
A=(3 4) and use it to solve the equation 3x+4y=1 5x+2y=3 simultaneously
(5 2)
By applying inverse of a matrix, we find that the solution of the system of linear equations is (x, y) = (5/7, - 2/7).
How to solve a system of equation with inverse matrices
In linear algebra, systems of linear equations with a unique solution can be represented by the following expression:
[tex]\vec A \cdot \vec x = \vec B[/tex] (1)
Where:
[tex]\vec A[/tex] - Matrix of dependent constants.[tex]\vec x[/tex] - Vector column of variables.[tex]\vec B[/tex] - Vector column of independent constants.The solution of such systems is defined by:
[tex]\vec x = \vec A^{-1}\cdot \vec B[/tex]
[tex]\vec x = \frac{1}{\det(\vec A)}\cdot adj\left(\vec A\right) \cdot \vec B[/tex], where [tex]\det \left(\vec A\right) \ne 0[/tex].
Where:
[tex]\det \left(\vec A\right)[/tex] - Determinant of the matrix of dependent constants.[tex]adj \left(\vec A\right)[/tex] - Adjoint of the matrix of dependent constants.For the case of [tex]\vec A \in \mathbb{R}_{2\times 2}[/tex], the inverse of [tex]\vec A[/tex] is:
[tex]\vec A^{-1} = \frac{1}{\det \left(\vec A\right)} \cdot \left[\begin{array}{cc}a_{22}&-a_{12}\\-a_{21}&a_{11}\end{array}\right][/tex] (2)
If we know that [tex]\vec A = \left[\begin{array}{cc}3&4\\5&2\end{array}\right][/tex] and [tex]\vec B = \left[\begin{array}{cc}1\\3\end{array}\right][/tex], then the solution of the system of linear equations is:
[tex]\vec A^{-1}= \frac{1}{(3)\cdot (2) - (5) \cdot (4)}\cdot \left[\begin{array}{cc}2&-4\\-5&3\end{array}\right][/tex]
[tex]\vec A^{-1} = -\frac{1}{14}\cdot \left[\begin{array}{cc}2&-4\\-5&3\end{array}\right][/tex]
[tex]\vec A^{-1} = \left[\begin{array}{cc}-\frac{1}{7} &\frac{2}{7} \\\frac{5}{14} &-\frac{3}{14} \end{array}\right][/tex]
[tex]\vec x = \left[\begin{array}{cc}-\frac{1}{7} &\frac{2}{7} \\\frac{5}{14} &-\frac{3}{14} \end{array}\right] \cdot \left[\begin{array}{cc}1\\3\end{array}\right][/tex]
[tex]\vec x = \left[\begin{array}{cc}\frac{5}{7} \\-\frac{2}{7} \end{array}\right][/tex]
By applying inverse of a matrix, we find that the solution of the system of linear equations is (x, y) = (5/7, - 2/7).
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Can someone tell me what this symbol means? Ty!!!
Answer:
Angle symbol
Angle ACB
Angle ACE
Angle DCE
What is the volume of the rectangular prism?
2 cm
2 cm
2 cm
Answer:
Step-by-step explanation:
Testing: h 0 : p = 0. 74 h0:p=0. 74 h α : p < 0. 74 hα:p<0. 74 your sample consists of 43 subjects, with 33 successes. calculate the test statistic
Test statistic is 0.42.
Given
Testing:
h0 : p = 0.74
h1 : p < 0.74
Successes x = 33
Subject n = 43
A test statistic is a number calculated by a statistical test. It describes how far your observed data is from the null hypothesis of no relationship between variables or no difference among sample groups.
It measures the accuracy of the predicted data distribution relating to the null hypothesis you use when analyzing data samples.
Test statistics z = [tex]\frac{p_{hat} - p}{\sqrt{\frac{p(1-p)}{n} } }[/tex]
Where [tex]p_{hat}[/tex] = Sample proportion = [tex]\frac{x}{n}[/tex]
p = population proportion
n = sample size
z = [tex]\frac{(\frac{33}{43})-0.74 }{\sqrt{\frac{0.74(1-0.74)}{43} } }[/tex]
z = 0.42
Hence,
Test statistics is 0.42..
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A softball player throws a ball into the air with an initial velocity of 32 feet per second. The ball is released at a height of 5 feet. The function h(t) = [tex]-16t^{2}[/tex]+32t+5 models the height h (in feet) of the ball as a function of the time t (in seconds) after it is thrown. Use the equation to find the time that the ball is in the air if the player lets the ball drop
The time that the ball is in the air if the player lets the ball drop is 2.145 sec
What is a quadratic equation?
A quadratic equation is an algebraic equation of the second degree in x. The quadratic equation in its standard form is ax²+ bx + c = 0, where a and b are the coefficients, x is the variable, and c is the constant term.
-16t²+32t+5
by comparing this equation to the standard form of the quadratic equation we get
a=-16 b=32 c=5
the time (t) needed for the ball to reach its maximum height using the axis of symmetry formula (x = -b/2a) for a parabola:
the time at which the ball reaches the maximum height using the axis of symmetry formula is (x=-b/2a)
t = -32/2×-16
t=1sec
by putting h(t) to zero and determining the time (t) when the ball hits the ground:
-16t²+32t+5=0
-16(t²+2t+5/16)=0
t²-2t-5/16=0
(t)²-2×1×t+(1)²-5/16=1
(t-1)²=21/16
t-1=√21/√16
t=1+4.58/4
t=1+1.145
t=2.245sec
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Determine how the strategies are similar. Picture below
Answer: Look at stwp by step
Step-by-step explanation:
Basically we can compare both equations to get that x = √7 and y = √2 so we can substitute that into 2x + 10y to get 2√7 + 10√2
In the figure below, ∠t= 133° . Find the measures of all remaining angle.
t is vertical to s because they share a point and are directly across from each other. vertical angles are congruent. therefore s=113 degrees
t and p are corresponding angles, which means they are congruent. this means p is also 113 degrees.
s and o are corresponding angles, so o is also 113 degrees.
t and u are supplementary. they share a straight line, so they add up to 180. you can find u by subtracting 113 from 180. 180-113= 67, so u is 67 degrees.
u and r are vertical angles, so r is 67 degrees.
r and m are corresponding, as well as u and q. therefore m and q both equal 67 degrees.
hope this helped :)
AB is tangent to ⊙C at point B and AD is tangent to ⊙C at point D.
Circle C is shown. Line segments C B and C D are radii. Line segments B A and D A are tangents to circle C. Angle B C D is 124 degrees.
What is m∠A?
34°
62°
56°
124°
[tex] {\qquad\qquad\huge\underline{{\sf Answer}}} [/tex]
As you can see in the quadrilateral ABCD, the two angles measure 90° (as they are tangents to circle c) and one of them is given 124°
we need to find the Angle BAD : let it be x ~
By angle sum property of Quadrilaterals,
[tex]\qquad \sf \dashrightarrow \: 90 + 90 + 124 + x = 360[/tex]
[tex]\qquad \sf \dashrightarrow \: x+30 4 = 360[/tex]
[tex]\qquad \sf \dashrightarrow \: x = 360 - 304[/tex]
[tex]\qquad \sf \dashrightarrow \: x = 56 \degree[/tex]
Hence, Angle m A = 56°
Answer: c
Step-by-step explanation:
simplify the expression 9^7/ 9^9 60 points
Answer:
1/9^2
Step-by-step explanation:
simplify
9^(7-9)
simplify further
9^-2
simplify even more
1/9^2
Answer:
9^16
Step-by-step explanation:
just took the test
Assumptions of a regression model can be evaluated by plotting and analyzing the ____________
The assumptions of a regression model can be evaluated by plotting and analyzing the error terms.
Important assumptions in regression model analysis are
There should be a linear and additive relationship between dependent (response) variable and independent (predictor) variable(s). There should be no correlation between the residual (error) terms. Absence of this phenomenon is known as auto correlation.The independent variables should not be correlated. Absence of this phenomenon is known as multi col-linearity.The error terms must have constant variance. This phenomenon is known as homoskedasticity. The presence of non-constant variance is referred to heteroskedasticity. The error terms must be normally distributed.Hence we can conclude that the assumptions of a regression model can be evaluated by plotting and analyzing the error terms.
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Find the total surface area. rectangular prism 2 A. 132 yd² B. 1,238 yd² C. 896 yd² D. 2,736 yd²
The total surface area is 1308 meters square
How to determine the total surface area?From the question, we have the following dimensions
Length = 19 m
Width = 16 m
Height = 10 m
The total surface area is then calculated as:
Total surface area = 2 * (Length * Width + Width * Height + Length * Height)
Substitute the known values in the above equation
Total surface area = 2 * (19 * 16 + 16 * 10 + 19 * 10)
Evaluate the expression
Total surface area = 1308
Hence, the total surface area is 1308 meters square
The question is incomplete, and the resources cannot be found online.
So, I used the attached figure to answer the question
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Answer:1,238yd squared
Step-by-step explanation:
How long is the arc intersected by a central angle of startfraction pi over 2 endfraction radians in a circle with a radius of 4.5 cm? round your answer to the nearest tenth. use 3.14 for pi.
7.1 cm long is the arc intersected by a central angle .
What is length of an arc?
The arc length of a circle can be calculated with the radius and central angle using the arc length formula. Length of an Arc = θ × r, where θ is in radian. Length of an Arc = θ × (π/180) × r, where θ is in degree.Given,
Central angle = π / 2
radius = 4.5 cm
we apply formula of length of arc.
length of the arc = angle × radius
= (π/2) × (4.5 cm)
Now put value of π = 3.14
length of the arc = (3.14 / 2) × (4.5) cm
= 7.065 cm ≈ 7.1 cm
Therefore, 7.1 cm long is the arc intersected by a central angle .
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Which equations for the line of best fit do not accurately represent the data in the scatter plot? Select all that apply.
Concluding, the equations that do not accurately represent the data in the scatter plot are B, C, and D.
Which equations do not accurately represent the data in the scatter plot?By looking at the scatter plot, we can see that as we read from left to right, the number of shoes sold (y variable) decreases.
Then the linear fit must have a negative slope, from that, we can discard options B and C.
Now, we also can see that the line starts almost at y = 70.
If you look at the option D, you can see that the constant term of that line is -70, so we can also discard that option.
Concluding, the equations that do not accurately represent the data in the scatter plot are B, C, and D.
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Your friend won't get many stars like this! What changes would you make to the equation to help your friend collect all the stars? Why are those changes going to work
The required equation that represents the line of best fit is y = 2x + 4
Finding the equation of a line of best fit.A line of best fit refers to a line through a scatter plot of data points that best expresses the relationship between those points.
From the given scatters plot, we only need to choose two points that aligns properly and create an equation of a line using the coordinates.
Using the following points (4, 12) and (2, 8)
The equation of the line will be in the form y = mx + b
where
m is the slope
b is the y-intercept
Determine the slope
Slope = y2-y1/x2-x1
Slope = 8-12/2-4
Sope = -4/-2
Slope = 2
Determine the y-intercept
Using the coordinate point (2, 8) and m = 2
8 = 2(2) + b
b = 8 - 4
b = 4
Hence the required equation that represents the line of best fit is y = 2x + 4
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The rate of inflation in the fictional land of sardonia is such that the price of a car costing 24000 dollars in u.s. currency will double in eleven years. what is the annual rate of inflation? what will be the price of this car in five years?
The annual rate of inflation is 35560.86%.
What is inflation?Inflation is defined as an increase in the overall price of goods and services in an economy.When the general price level rises, each unit of currency purchases fewer products and services; hence, inflation equates to a loss of money's purchasing power. Deflation, or a sustained reduction in the general price level of goods and services, is the inverse of inflation. The inflation rate, which is the annualized percentage change in a general price index, is the most commonly used metric of inflation.To find the annual rate of inflation:
48,000=24,000e^k(7)24,000 24,0002=e^k(7)ln2=lne^k7ln2=k77 7k=0.099 --> k=9.9%Now, sub in 4 and 0.099
=24,000e^(0.099)(4)=35560.86Therefore, the annual rate of inflation is 35560.86%.
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The correct question is given below:
The rate of inflation in the fictional land of Sardinia is such that the price of a car costing 24,000 dollars in U.S. currency will double in seven years. What is the annual rate of inflation? what will be the price of this car in four years?
please help this is a math question about geometry !!!! please view the attached images to see the question and the answer choices i am going to give 13 points and a brainlist thank you
Answer:
It is the second picture.
Step-by-step explanation:
A plot of land in the shape of a horizontal ellipse has a pole at each focus. the foci are 16 feet from the center. if the plot of land is 40 feet across one axis, how long is it across the other axis?
If a plot of land in the shape of a horizontal ellipse has a pole at each focus. the foci are 16 feet from the center. if the plot of land is 40 feet across one axis, how long is it across the other axis is: c. 24 feet.
Length across the other axisUsing Pythagoreans theorem formula
a²=b²+c²
Where:
c=16 feet
a=40/2=20 feet
Hence:
20²=b²+16²
b²=20²-16²
b²=400-256
b²=√144
b=12
2b=12×2
2b=24 feet
Therefore if the plot of land is 40 feet across one axis, how long is it across the other axis is: c. 24 feet.
The complete question is are:
A plot of land in the shape of a horizontal ellipse has a pole at each focus. The foci are 16 feet from the center. If the plot of land is 40 feet across one axis, how long is it across the other axis?
a. 34 feet
b. 46 feet
c. 24 feet
d. 30 feet
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Uan zhang bought a 10-year bond that pays 8. 25 percent semiannually for $911. 10. what is the yield to maturity on this bond? (roundyour percentage answer to two decimal places. )
The yield to maturity on this bond according to the trial-and-error approach is 9.66 percent.
According to the statement
we have given that the Uan zhang bought a 10-year bond that pays 8. 25 percent interest per 6 months.
And we have to find that the yield to maturity on this bond.
So, For this purpose,
The amount given is $911. 10.
Years to maturity = n = 10
Coupon rate = C = 8.25%
Semiannual coupon = $1,000 × (0.0825/2) = $41.25
Yield to maturity = i
Present value of bond = PB = $911.10
Use the trial-and-error approach to solve for YTM. Since the bond is selling at a discount, we know that the yield to maturity is higher than the coupon rate.
Try YTM = 9.4%:
= $522.90 + 391.54 ≅ $914.43
The YTM is approximately 9.66 percent. Using a financial calculator provided an exact YTM of 9.656 percent (2 × 4.828%).
So, The yield to maturity on this bond according to the trial-and-error approach is 9.66 percent.
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PLSSSS HELPPPP THANK YOUU IF YOU DOOO
Answer:
B
Step-by-step explanation:
Suppose it costs $43 to roll a pair of dice. you get paid $6 times the sum of the numbers that appear on the dice. is it a fair game?
The game is not fair as 6 times the expected sum is less than the cost, $43.
In the question, we are asked if the game is fair.
For the game to be fair, 6 times the expected sum for the pair from the game has to be greater than or equal to $43, that is,
6E(X) ≥ 43.
The expected sum for the pair, E(X) can be calculated using the formula,
E(X) = ∑x.p(x),
or, E(X) = 1/18 + 1/6 + 1/3 + 5/9 + 1/6 + 7/9 + 10/9 + 1 + 5/6 + 11/18 + 1/3,
or, E(X) = 107/18.
Now, 6E(X) = 6*(107/18) = 107/3 = 35.67.
Since, the total return from the game is $35.67, which is less than the cost of $43, the game is not fair.
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2(x+2y)^2 + 3(x+2y) +1
Answer:
[tex]3x+2y^2+2(x+y)+2y+1[/tex]
Step-by-step explanation:
1) Split the second term in [tex]2{(x+2y)}^{2}+3(x+2y)+1[/tex] into two terms.
1 - Multiply the coefficient of the first term by the constant term.
[tex]2\times1=2[/tex]
2 - Ask: Which two numbers add up to 3 and multiply to 2?
2 and 1.
3 - Split [tex]3x+2y[/tex] as the sum of [tex]2(x+y)[/tex] and [tex]x+2y[/tex].
[tex]2x+2y^2+2(x+y)+x+2y+1[/tex]
2) Collect like terms.
[tex](2x+x)+2y^2+2(x+y)+2y+1[/tex]
3) Simplify.
[tex]3x+2y^2+2(x+y)+2y+1[/tex]
Thank you,
Eddie
A palindrome is a string of characters the reads the same backwards as it does forwards. for example, "mam" is a 3-letter palindrome. how many 6-letter palindromes are there?
If a palindrome is a string of characters the reads the same backward as it does forwards then there are 120 such palindromes after solving through permutations.
Given that a palindrome is a string of characters the reads the same backwards as it does forwards.
We are required to find the number of 6 letter palindromes.
Permutations is basically finding how many ways in which the some numbers or things can be arranged. It is expressed as [tex]nP_{r}[/tex]=n!/(n-r)!.
If there are 6 letters then in a palindrome 3 alphabets are used here to form a 6 letter word.
=6[tex]P_{3}[/tex]
=6!/(6-3)!
=6*5*4*3!/3!
=120 palindromes.
Hence if a palindrome is a string of characters the reads the same backward as it does forwards then there are 120 such palindromes.
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Give the equation for a circle with the given center and radius. center at (-1, 3), radius = 4
Answer:
(x + 1)² + (y - 3)² = 16
Step-by-step explanation:
the equation of a circle in standard form is
(x - h)² + (y - k)² = r²
where (h, k ) are the coordinates of the centre and r is the radius
here (h, k ) = (- 1, 3 ) and r = 4 , then
(x - (- 1) )² + (y - 3)² = 4² , that is
(x + 1)² + (y - 3)² = 16
Answer:
(x+1)^2 + (y-3)^2 = 16
Step-by-step explanation:
The standard form of an equation of a circle with center (h,k) and radius r is (x-h)^2 + (y-k)^2 = r^2. Plugging in those values, we get (x-(-1))^2 + (y-3)^2= 4^2 = (x+1)^2 + (y-3)^2 = 16.
In the figure below, angle y and angle x form vertical angles. Angle y forms a straight line with the 60° angle and the 70° angle. A straight line is shown and is marked with three angles. The first angle measures 60 degrees. The second angle measures 60 degrees. The third angle is labeled y. The line between the 70 degree angle and angle y extends below the straight line. The angle formed is labeled angle x. Write and solve an equation to determine the measure of angle x.
The equation that solve for x is as follows;
70 + 60 + x = 180
How to find an angle?The equation that can be used to find the measure of angle x can be found as follows:
60 + 70 + y = 180
Therefore,
130 + y = 180
subtract 130 from both sides
130 - 130 + y = 180 - 130
y = 50°
70 + 60 + x = 180
130 + x = 180
x = 180 - 130
x = 50°
x and y are vertically opposite angles.
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Convert a normally distributed score of 80 with a mean of 70 and a standard deviation of 6 into a z score.
Answer:
5/3
Step-by-step explanation:
z = (Distributed score - Mean)/Standard deviation= (80-70)/6 = 5/3
Step-by-step explanation:
z = (specific score - mean) / standard deviation
in our case
z = (80 - 70)/6 = 10/6 = 5/3 = 1.666666... ≈ 1.67
as most z-tables round the z-scores to hundredths.
not to forget : the sign matters. so, don't worry, if you have e.g. a specific score of 60 :
(60 - 70)/6 = -10/6 = -5/3 = -1.666666... ≈ -1.67
you did not do anything wrong. that is all ok and valid.
A. Undefined b. Zero c.negative b. Positive
I believe the slope is negative. If it was positive then it would have been " / "
Answer:
C
Step-by-step explanation:
• A vertical line has an undefined slope
• A horizontal line has a slope of zero
• A line sloping downwards from left to right has a negative slope
• A line sloping upwards from left to right has a positive slope
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the line here slopes downwards from left to right and has a negative slope
O Yes
O No
2. (02.01 LC)
Is the following relation a function? (1 point)
{(3,-2), (1, 2), (-1,-4), (-1, 2)}
Answer:
No
Step-by-step explanation:
Each x can have only ONE y as its partner. In this relation, -1 has TWO different partners: in one point (-1,-4) the y is -4 and in another point (-1,2) the y is 2. Not a function.