Answer:
6) $35,198.32
7) $43,492.33
Step-by-step explanation:
To solve both these problems, we can use the formula for compound interest:
[tex]\boxed{\begin{minipage}{8.5 cm}\underline{Compound Interest Formula}\\\\$ A=P\left(1+\frac{r}{n}\right)^{nt}$\\\\where:\\\\ \phantom{ww}$\bullet$ $A =$ final amount \\ \phantom{ww}$\bullet$ $P =$ principal amount \\ \phantom{ww}$\bullet$ $r =$ interest rate (in decimal form) \\ \phantom{ww}$\bullet$ $n =$ number of times interest is applied per year \\ \phantom{ww}$\bullet$ $t =$ time (in years) \\ \end{minipage}}[/tex]
Question 6Given values:
P = $8,000r = 10% = 0.1n = 4 (quarterly)t = 15 yearsSubstitute the given values into the formula and solve for A:
[tex]A=8000\left(1+\dfrac{0.1}{4}\right)^{4\cdot 15}[/tex]
[tex]A=8000\left(1+0.025\right)^{60}[/tex]
[tex]A=8000\left(1.025\right)^{60}[/tex]
[tex]A=35198.3179905[/tex]
[tex]A=35198.32[/tex]
Therefore, the balance of Anisha's account after 15 years will be $35,198.32.
[tex]\hrulefill[/tex]
Question 7Given values:
P = $32,500r = 6% = 0.06n = 1 (annually)t = 5 yearsSubstitute the given values into the formula and solve for A:
[tex]A=32500\left(1+\dfrac{0.06}{1}\right)^{1\cdot 5}[/tex]
[tex]A=32500\left(1+0.06\right)^{5}[/tex]
[tex]A=32500\left(1.06\right)^{5}[/tex]
[tex]A=43492.331272[/tex]
[tex]A=43492.33[/tex]
Therefore, Kevin will pay a total of $43,492.33 over the course of the 5 year loan (assuming he doesn't pay any of the loan back over those 5 years).
Solve A and B please
a. The standard deviation of the tuition is $150.
b. The shape of this distribution is a normal distribution, which is a bell-shaped curve.
How to calculate the value(a) The mean tuition is $100 per credit hour * 15 credit hours per semester + $150 lab fee = $1650 per semester.
The standard deviation of the tuition is l:
= ✓(100² + 150²) =
= ✓22500
= $150.
(b) The shape of this distribution is a normal distribution, which is a bell-shaped curve. The mean is the center of the distribution, and the standard deviation is the width of the distribution. The majority of the tuitions will be close to the mean, with fewer and fewer tuitions as you move further away from the mean.
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Please someone help me 28th this, eleven people are entered in a race if there are no ties in how many ways can first and second place come?
Helppppp pleaseeeeeeee
To achieve a 1 in row 1, column 1, divide row 1 by 4 in the given matrix, resulting in the updated matrix. This row operation preserves the system of linear equations represented by the matrix.
To get a 1 in row 1, column 1 of the given matrix, you can perform the following valid row operation:
R1 = (1/4) * R1
This operation scales row 1 by a factor of 1/4, resulting in the new matrix:
1 , -3/4 , -43/4
3 , -2 , -30
By dividing each element in row 1 by 4, the value in row 1, column 1 becomes 1. This row operation maintains the equivalence of the system of linear equations represented by the matrix.
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Silverton County is home to a declining population of sage grouse, an endangered species of land bird similar to turkeys. Every decade, the Silverton Wildlife Center publishes its estimate of the county's sage grouse population. The most recent estimate, published this year, concluded that there are about 115,000 sage grouse in the county, and the population is expected to decrease by a factor of 1/4 each decade.
Write an exponential equation in the form y=a(b)x that can model the estimated population of sage grouse in Silverton County, y, in x decades.
Use whole numbers, decimals, or simplified fractions for the values of a and b.
The exponential equation that models the estimated population of sage grouse in Silverton County is: [tex]y = 115,000 * (1/4)^x[/tex]
How to write an exponential equation in the form y=a(b)x that can model the estimated population of sage grouse in Silverton CountyGiven that the population is expected to decrease by a factor of 1/4 each decade, we know that the common ratio, b, is 1/4.
Since the most recent estimate is about 115,000 sage grouse, we can assign this value to the initial population, a.
Therefore, the exponential equation that models the estimated population of sage grouse in Silverton County is: [tex]y = 115,000 * (1/4)^x[/tex]
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3 pitchers of berry were made and 1/5 serving size how many were made
The total number of berry pitchers made is 15/5 or 3.
If the serving size of berry pitchers is 1/5, it means that each pitcher represents 1/5 of a full serving. To determine the total number of pitchers made, we need to calculate how many times 1/5 fits into the whole serving.
Let's assume that the total number of pitchers made is represented by "x". We can set up the following equation:
x * 1/5 = 3
To solve for "x," we multiply both sides of the equation by 5:
5 * (x * 1/5) = 5 * 3
This simplifies to:
x = 15/5
Thus, the total number of berry pitchers made is 15/5 or 3.
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solve 6x²-42=0 with the exact values of x
Answer:
X=-√7 and √7
Step-by-step explanation:
To solve the equation 6x² - 42 = 0, we can begin by rearranging it to isolate the variable term:
6x² = 42
Then, we can divide both sides by 6:
x² = 7
To get the exact values of x, we need to take the square root of both sides:
x = ±√7
Therefore, the exact values of x are √7 and -√7.
Nicole correctly calculates that the Coach will spend $14,800 after 12 months if he chooses the Five-Year Plan. She then claims the total cost of the Five-Year Plan will be $74,000, because 5x $14,800 $74,000. The Coach says that Nicole made a mistake. Do you agree that Nicole made a mistake? Explain your reasoning. ANSWER FAST WHOEVER GIVES CORRECT ANSWER I WILL GIVE BRAINLIST!
I agree that Nicole made a mistake because the total cost of the Five year plan is $ 34, 000 and not $ 74, 000.
How was the mistake made ?The total cost of the Five year plan would be:
= Payment per month for the five year plan x Number of months in year x number of years + Down payment
= 400 x 12 x 5 + 10, 000
= 4, 800 x 5 + 10, 000
= $ 34, 000
The mistake that Nicole made was to multiply the $ 14, 800 that was the cost of the five year plan in one year, by five years. This was wrong because it meant including a new down payment in every one of the five years instead of just once.
She should have multiplied $4, 800 by 5 years and then added the down payment which is paid just once.
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I need to know how to solve number 4 in order to get a solution
Answer: 11x16x5=880
This means the answer is C
Assume that a sample is used to estimate a population proportion p. Find the margin of error E that corresponds to
the given statistics and confidence level. Round the margin of error to four decimal places
98% confidence; the sample size is 800. of which 40% are successes
The error E = ± 4.04 %
Sample data = ( p ).
success p = success percentage = 40 %
confidence interval CI = 98%
sample size n = 800
margin of error E:
The margin of error "E" for estimation of population proportion ( p ) is given by:
E = z - critical √(p(1-p)/n)
P ( Z < Z-critical ) = a/
a = 1 - CI
P ( Z < Z-critical ) = (1 - 0.98) / 2
P ( Z < Z-critical ) = 0.01
Z-critical = 2.33
The error E = ± 4.04 %
Thus, the correct answer is E=± 4.04 %
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Points z1 and z2 are shown on the graph. (10 points)
complex plane, point z sub 1 at 4 to the right of the origin and 6 units up, point z sub 2 at 5 units to the left of the origin and 2 units up
Part A: Identify the points in standard form and find the distance between them.
Part B: Give the complex conjugate of z2 and explain how to find it geometrically.
Part C: Find z2 − z1 geometrically and explain your steps.
Answer:
Part A: The point z1 is at (4, 6) and the point z2 is at (-5, 2). The distance between them is √((4-(-5))^2 + (6-2)^2) = √(9^2 + 4^2) = √(81 + 16) = √97.
Part B: The complex conjugate of z2 is (-5, -2). Geometrically, it can be found by reflecting the point z2 across the x-axis.
Part C: To find z2 − z1 geometrically, you can draw a vector from z1 to z2. The coordinates of this vector are (-5-4, 2-6) = (-9, -4). So z2 − z1 = -9 - 4i.
Jane is converting the given equation in Standard Form to the General Form. At which step did she make her first mistake?
Answer:
Step 4
Step-by-step explanation:
In step 3, 16 + 9 = 25, so step 4 should subtract 25 from both sides. Also, y² became -y² in step 4 which is incorrect.
Answer: Step 4
Use the Distributive Property to find (g−7)(g−2) all i need is the answer
Answer: [tex]g^2-9g+14[/tex]
Step-by-step explanation:
(g-7)(g-2)
[tex]g^2 - 2g-7g+14[/tex]
[tex]g^2-9g+14[/tex]
Use FOIL method.
tamikas math teachers plots student grades on their weekly quizzes against the number of hours yhe say they study on the pair of coordinate axes and then draws the lines of best fits. what is the meaning of the x-value on the line when y = 100
The x-value on the line when y = 100 represents the estimated number of hours a student would need to study to achieve a quiz grade of 100.
We have,
Assuming that the line of best fit represents the trend between the number of hours students study and their quiz grades,
The x-value on the line when y = 100 represents the estimated number of hours a student would need to study to achieve a quiz grade of 100.
In other words,
If a student studies for this amount of time, they are predicted to achieve a quiz score of 100 based on the trend shown by the line of best fit.
Thus,
The x-value on the line when y = 100 represents the estimated number of hours a student would need to study to achieve a quiz grade of 100.
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Find the area of the regular polygon below and round your answer to the nearest tenth.
Explain your reasoning. Show all your work.
1) What is the perimeter of the regular polygon?
2) What is the apothem length? Show all your work and explain how you found the apothem.
3) What is the area of the regular polygon? Show your work.
7 sides each side is 10 in long
The area of the regular polygon is 311.5 in2.
We are given that;
A polygon
Now,
To find the perimeter of the regular polygon, we need to multiply the number of sides by the length of each side. The polygon has 7 sides and each side is 10 in long, so the perimeter is 7 * 10 = 70 in.
To find the apothem length, we need to use some trigonometry.
The central angle is 360/7 degrees, since there are 7 equal angles in a regular polygon. Half of the side length is 5 in, since each side is 10 in long. The apothem is the adjacent side of the right triangle. We can use the tangent function to find the apothem: tan(360/14) = 5/a, where a is the apothem. Solving for a, we get a = 5/tan(360/14) ≈ 8.9 in.
To find the area of the regular polygon, we need to plug in the values of P and a into the formula A = (1/2)P*a.
A = (1/2)708.9 ≈ 311.5 in2.
Therefore, by the area the answer will be 311.5 in2.
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Please help!! I don’t understand trigonometric functions
The horizontal transformations are defined as follows:
cos(ax).
They are classified as follows:
Stretch if |a| < 1.Compression if |a| > 1.The vertical transformations are defined as follows:
acos(x).
They are classified as follows:
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If sin 0 - cos 0 = 1, prove that sin 0 + cos 0=1.
The trigonometric value equation is solved and sin ( 0 )° + cos ( 0 )° = 1
Given data ,
Let the trigonometric relation be represented as A
Now , the value of A is
sin ( 0 )° - cos ( 0 )° = 1
From the trigonometric relation , we get
sin 0 = 0
cos 0 = 1
So , the equation is
sin ( 0 )° + cos ( 0 )° = 1
Hence , the equation is solved
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Books in the clearance section at Reading Central Bookmart cost $6.00 for paperbacks and $12.00 for hardbacks. Which inequality best describes the number of paperback books, p, and the number of hardback books, h, that can be purchased for $53.00 or less?
A.
12p + 6h > 53
B.
6p + 12h < 53
C.
12p + 6h < 53
D.
6p + 12h < 53
solve by using elimination. 12x + 36y = −3
−12x − 36y = 0
The given system of equations has no solution.
Given that a system of equations, 12x + 36y = −3 and −12x − 36y = 0, we need to solve it,
We know for a system of equations =
a₁x + b₁y = c₁ and a₂x + b₂y = c₂
If a₁ / a₂ = b₁ / b₂ = c₁ / c₂ then the system has infinite solutions.
If a₁ / a₂ = b₁ / b₂ ≠ c₁ / c₂ then the system has no solutions.
If a₁ / a₂ ≠ b₁ / b₂ then the system has a unique solution.
comparing the coefficients given,
-12/12 = -1
-36/36 = -1
-3/0 = -3
We get here the condition of a₁ / a₂ ≠ b₁ / b₂, which means that the system has no solution.
Hence the given system of equations has no solution.
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l want the steps.
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The first derivative of the parametric curve is:
dx/dt = [tex]-1/(t-1)^2[/tex] and dy/dt = [tex](2t(t-1) - t^2)/(t-1)^2.[/tex]
How to solve1. To find the first derivative of the parametric curve x = 1/(t-1) and [tex]y = t^2/(t-1)[/tex], we can use the chain rule.
2. Let's differentiate each component separately.
3. Differentiating x with respect to t, we have:
dx/dt = [tex]-1/(t-1)^2[/tex]
4. Differentiating y with respect to t, we have:
dy/dt = [tex](2t(t-1) - t^2)/(t-1)^2[/tex]
5. Therefore, the first derivative of the parametric curve is:
dx/dt = [tex]-1/(t-1)^2[/tex] and dy/dt = [tex](2t(t-1) - t^2)/(t-1)^2.[/tex]
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Type in the parent function for a quadratic equation to make your parabola go through the points shown
The parent function for the quadratic equation is y = x²
How to determine the parent function for the quadratic equationFrom the question, we have the following parameters that can be used in our computation:
The graph
From the graph, we have the following points
vertex = (0, 0)
Points = (±1, 1) and (±2, 4)
The equation for the quadratic function is represented as
y = a(x - h)² + k
Where vertex = (h, k)
So, we have
y = a(x - 0)² + 0
Evaluate
y = ax²
Using the points, we have
a(1)² = 1
Evaluate
a = 1
So, we have
y = x²
Hence, the parent function for the quadratic equation is y = x²
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Please help quickly! (Will mark Brainliest)
Hello!
area
= (b x h)/2
= (18in x 7in)/2
= 126in²/2
= 63in²
Answer:
63 in²
Step-by-step explanation:
1/2 bh=area of the triangle
Solve:{2x-y=5
{4x+2y=-2
The table describes the quadratic function h(x).
x h(x)
−3 −2
−2 −3
−1 −2
0 1
1 6
2 13
3 22
What is the equation of h(x) in vertex form?
h(x) = (x + 2)2 − 3
h(x) = (x + 1)2 − 2
h(x) = (x − 1)2 + 2
h(x) = (x − 2)2 + 3
The equation of h(x) in vertex form is given as follows:
h(x) = (x + 2)² - 3.
How to define the quadratic function given it's vertex?The quadratic function of vertex(h,k) is given by the rule presented as follows:
y = a(x - h)² + k
In which:
h is the x-coordinate of the vertex.k is the y-coordinate of the vertex.a is the leading coefficient.The vertex is the turning point of the function, where it changes from decreasing to increasing, or vice versa, hence it's coordinates are given as follows:
(-2,-3).
Then the equation is:
h(x) = a(x + 2)² - 3.
When x = 0, h(x) = 1, hence the leading coefficient a is obtained as follows:
1 = a(2)² - 3
4a = 4
a = 1.
Hence the equation is:
h(x) = (x + 2)² - 3.
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Prove: If A and B are m × n matrices such that Ax = Bx for all x ∈ R
n, then A = B.
From matrix property it can be showed that A=B.
Given,
If A,B and x are matrices with x≠0 and AX=BX
Now,
X must be non-singular matrix because
A[tex]XX^{-1}[/tex]=B[tex]XX^{-1}[/tex]
AI = BI
= I( identity matrix )
⇒A = B
Hence Proved, A = B .
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Given: Isosceles trapezoid ABCD with diagonals BD and AC Identify the missing reason in the proof.
The statement thet complete the proof of the congruent triangles is (a) SAS criterion
How to determine the statement thet complete the proof of the congruent trianglesFrom the question, we have the following parameters that can be used in our computation:
The incomplete proof
In the proof, we have
AD ≅ BC --- side length
DC ≅ DC --- side length
∠ADC ≅ ∠BCD -- angle
This means that the triangles are congruent by the SAS theorem
The SAS theorem is defined by "If two sides in one triangle are congruent to two sides in another triangle and the included angle in both are congruent, then the two triangles are congruent"
This means that they are congruent by the SAS congruent
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Answer: A. SAS criterion.
Step-by-step explanation: Angle : ∠ADC ≅ ∠BCD Side length : AD ≅ BC Side length : DC ≅ DC
Because of this △ADC ≅ △BCD by SAS criterion.
The length of a rectangle measures two more than three times the width if the area is 40 ft.² find the dimensions of the rectangle
Answer:Therefore, the dimensions of the rectangle are 14 ft by 4 ft.
Let's use variables to represent the length and width of the rectangle. We know from the problem that:Length = 3 times the width + 2
Area = 40 ft²We can use the formula for the area of a rectangle to set up an equation:Area = length x widthSubstituting in the values we have:40 = (3w + 2)wExpanding the brackets and simplifying:40 = 3w² + 2wRearranging into a quadratic equation form:3w² + 2w - 40 = 0We can solve for w using the quadratic formula:w = (-2 ± sqrt(2² - 4(3)(-40))) / (2 x 3)
w = (-2 ± sqrt(484)) / 6
w = (-2 ± 22) / 6The two possible solutions are w = 4 and w = -6.67. Since width cannot be negative, we take the positive solution: w = 4 ft.To find the length, we can use the formula we established earlier:Length = 3w + 2
Length = 3(4) + 2
Length = 14 ft
In Austin TX the cost of housing for a family of four is $1600 per month. How much more would the family need to bring home annually in order to cover the cost of increased housing
The family would need to bring home an additional $2400 annually to cover the increased cost of housing.
The family would need to bring home annually to cover the cost of increased housing need to calculate the total cost of housing for a year and subtract the current annual cost of housing.
The current monthly cost of housing is $1600 so the annual cost is:
$1600/month x 12 months = $19,200/year
Let's assume the family needs to cover an increased housing cost of $200 per month.
The new monthly cost of housing would be:
$1600/month + $200/month = $1800/month
The new annual cost of housing would be:
$1800/month x 12 months = $21,600/year
The family would need to bring home annually to cover this increased cost need to subtract the current annual cost of housing from the new annual cost of housing:
$21,600/year - $19,200/year = $2400/year
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solve the following for x 2log a x- log a(x-1) =log a(x-2)
The solution to the equation [tex]2log_a(x) - log_a(x-1) = log_a(x-2)[/tex] is
x = 2/3.
To solve the equation [tex]2log_a(x) - log_a(x-1) = log_a(x-2)[/tex] for x, We can employ algebraic manipulation and logarithmic characteristics.
Apply logarithmic properties.
Using the logarithmic property[tex]log_a(b) - log_a(c) = log_a(b/c),[/tex] we can rewrite the equation as:
[tex]log_a(x^2) - log_a(x-1) = log_a(x-2).[/tex]
Combine the logarithms.
Applying the logarithmic property [tex]log_a(b) - log_a(c) = log_a(b/c),[/tex] we can combine the logarithms on the left-hand side:
[tex]log_a[(x^2)/(x-1)] = log_a(x-2).[/tex]
Take the logarithms out.
We can do away with the logarithms because the base of the equation is the same.
[tex](x^2)/(x-1) = x-2.[/tex]
Streamline the equation.
We can eliminate the denominator and simplify the equation by multiplying both sides by (x-1):
[tex]x^2 = (x-2)(x-1).[/tex]
Expand and simplify.
Expanding the right-hand side, we have:
[tex]x^2 = x^2 - 3x + 2[/tex]
Rearrange the equation.
Rearranging the equation, we get:
0 = -3x + 2.
Do the x math.
We must isolate x on one side of the equation in order to find its value. Taking 2 away from both sides:
3x = 2.
Finally, divide both sides by 3:
x = 2/3.
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The following figure shows a cube. Which expression represents the surface area of the cube? Choose 1 answe B 6-10 5 5-5-5 25 + 25 + 25 + 25 + 25 + 25 5+5+5+5+5+5
The expression that represents the surface area of the cube is 25 + 25 + 25 + 25 + 25 + 25
Calculating the expression that represents the surface area of the cube?From the question, we have the following parameters that can be used in our computation:
The cube
The side length of the cube is
Side length = 5
The surface area of the cube is calculated as
SA = 6 * Side length²
So, we have
SA = 6 * 5²
Expand
SA = 6 * 25
Further expand
SA = 25 + 25 + 25 + 25 + 25 + 25
Hence, the expression that represents the surface area of the cube is 25 + 25 + 25 + 25 + 25 + 25
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Complete question
The following figure shows a cube. Which expression represents the surface area of the cube? Choose 1 answer
(a) 5 5 - 5 - 5
(b) 25 + 25 + 25 + 25 + 25 + 25
(c) 5 + 5 + 5 + 5 + 5 + 5
The figure is attached
What do you know about the graphs of polynomials with positive end behavior compared to the graphs of polynomials with negative end behavior?
If "positive" end behavior:
1. The graph hits the x-axis
2. The arrows point in opposite directions
3. The arrows point in the same direction
4. The right arrow is up
5. The graph hits the y-axis
6. The right arrow is down
If "negative" end behavior:
1. The graph hits the x-axis
2. The right arrow is down
3. The graph hits the y-axis
4. The right arrow is up
5. The arrows point in the same direction
6. The arrows point in opposite directions
The correct statements are:
If "positive" end behaviour:
The arrows point in the same direction.
The right arrow is up.
The graph hits the y-axis.
If "negative" end behaviour:
The arrows point in opposite directions.
The right arrow is down.
The graph hits the X-axis.
In mathematics, a graph is a visual representation of a set of data, which consists of points, called vertices or nodes, and lines connecting them, called edges or arcs.
Graphs are often used to represent mathematical functions, data sets, or relationships between objects, and they can be used to model real-world phenomena.
Graphs can be drawn on a coordinate plane or in a more abstract form, and they can be used to analyze and understand complex systems and relationships.
The correct statements are:
If "positive" end behaviour:
The arrows point in the same direction.
The right arrow is up.
The graph hits the y-axis.
If "negative" end behaviour:
The arrows point in opposite directions.
The right arrow is down.
The graph hits the X-axis.
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