The axis of symmetry for the quadratic function y = x^2 - 9x + 20 is x = 4.5.
To find the axis of symmetry for a quadratic function, we can use the formula x = -b/2a, where the quadratic function is in the form y = ax^2 + bx + c.
Identify the coefficients of the quadratic function:
In the given function y = x^2 - 9x + 20, we can see that a = 1, b = -9, and c = 20.
Apply the formula for the axis of symmetry:
The axis of symmetry is given by x = -b/2a. Plugging in the values of a and b from the quadratic function:
x = -(-9)/(2 * 1)
x = 9/2
x = 4.5
Therefore, the axis of symmetry for the quadratic function y = x^2 - 9x + 20 is x = 4.5.
The axis of symmetry is a vertical line that passes through the vertex of the parabolic graph. In this case, the vertex is located at the point (4.5, f(4.5)), where f(4.5) represents the value of the quadratic function when x = 4.5.
By finding the axis of symmetry, we can determine the x-coordinate of the vertex, which is the maximum or minimum point of the parabola. In this case, since the coefficient of the x^2 term is positive, the parabola opens upward, and the vertex represents the minimum point of the function.
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Two numbers are in the ratio 10: 16. When 4 is added to each, the ratio of resulting numbers is 4 to 6. Find the numbers
The two numbers are 20 and 32.
Let's assume the two numbers in the ratio 10:16 are 10x and 16x, where x is a common factor.
According to the given information, when 4 is added to each number, the ratio becomes 4:6. This means that the new numbers are (10x + 4) and (16x + 4).
To find the numbers, we can set up an equation based on the given ratios:
(10x + 4) / (16x + 4) = 4/6
To simplify the equation, we can cross-multiply:
6(10x + 4) = 4(16x + 4)
Expanding both sides:
60x + 24 = 64x + 16
Bringing like terms together:
60x - 64x = 16 - 24
-4x = -8
Dividing both sides by -4:
x = 2
Now that we have the value of x, we can substitute it back into the original ratios to find the numbers:
The first number = 10x = 10 * 2 = 20
The second number = 16x = 16 * 2 = 32
Therefore, the two numbers are 20 and 32.
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Answer:
Let the two numbers be 10x and 16x.
When 4 is added to each, the resulting numbers are (10x + 4) and (16x + 4).
According to the problem, the ratio of (10x + 4) to (16x + 4) is 4:6.
We can write this as:
(10x + 4)/(16x + 4) = 4/6
Cross-multiplying, we get:
6(10x + 4) = 4(16x + 4)
Simplifying the equation, we get:
60x + 24 = 64x + 16
48 = 4x
x = 12
Therefore, the two numbers are:
10x = 120
16x = 192
So the two numbers are 120 and 192.
Write equations of a line in slope intercept form going through the points 2,1 and -1,-5
Answer:
Equation of the line in slope-intercept form: y = 2x - 3
Step-by-step explanation:
The general equation of the sloe-intercept form of a line is given by:
y = mx + b, where
(x, y) is any point on the line,m is the slope,and b is the y-intercept.Step 1: Find m, the slope:
We can find m, the slope of the line using the slope formula, which is given by:
m = (y2 - y1) / (x2 - x1), where:
Thus, we can plug in (2, 1) for (x1, y1) and (-1, -5) for (x2, y2) to find m, the slope of the line:
m = (-5 - 1) / (-1 - 2)
m = (-6) / (-3)
m = 2
Thus, the slope of the line is 2.
Step 2: Find b, the y-intercept of the line:
We can find b, the y-intercept of the line by plugging in any of the two points for (x, y) and 2 for m in the slope-intercept form. Let's use (2, 1) for (x, y):
1 = 2(2) + b
1 = 4 + b
-3 = b
Thus, the y-intercept of the line is -3.
Therefore, the equation of a line in slope-intercept form passing through the points (2, 1) and (-1, -5) is y = 2x - 3
Find the measure of the indicated angle.
101°
S
T
V
?
P
U
125°
The measure of the indicated internal angle in the circle is 113 degrees.
What is the measure of the missing angle?The inscribed angle theorem states that an angle x inscribed in a circle is half of the central angle 2x that subtends the same arc on the circle.
It is expressed as:
Internal angle = 1/2 × ( x + y )
From the image:
Intercepted arc TU = x = 125 degrees
Intercepted arc SP = y = 101 degrees
Internal angle = ?
Plug the given values into the above formula and solve for the internal angle:
Internal angle = 1/2 × ( x + y )
Internal angle = 1/2 × ( 125 + 101 )
Internal angle = 1/2 × 226
Internal angle = 113°
Therefore, the internal angle is 113 degrees.
Option B) 113° is the correct answer.
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what is one and half right angle
Answer: 135°
Step-by-step explanation:
1 and 1/2 right angle.
1 right angle is 90°
1/2 of a right angle = 45°
so 1 and 1/2= 90+45=135°
The amount of oil imported to Country A from Country B in millions of barrels per day can be approximated by the equation
y = 0.069x + 1.24, where x is the number of years since 2000. Solve this equation for x. Use the new equation to determine in which
year the approximate
number of oil barrels imported from Country B per day will be 1.93 million.
In approximately the year 2001 (or the 1.373rd year since 2000), the approximate number of oil barrels imported from Country B per day will be 1.93 million.
To solve the equation y = 0.069x + 1.24 for x, we need to isolate x on one side of the equation. Let's rearrange the equation:
y = 0.069x + 1.24
Subtract 1.24 from both sides:
y - 1.24 = 0.069x
Divide both sides by 0.069:
(y - 1.24) / 0.069 = x
Now we have x isolated on one side of the equation. We can use this equation to determine the year in which the approximate number of oil barrels imported from Country B per day will be 1.93 million.
Let's substitute y = 1.93 into the equation:
(x - 1.24) / 0.069 = 1.93
Multiply both sides by 0.069:
x - 1.24 = 0.069 * 1.93
x - 1.24 = 0.13317
Add 1.24 to both sides:
x = 0.13317 + 1.24
x = 1.37317
Now we have the value of x, which represents the number of years since 2000. To determine the year, we add the value of x to 2000:
Year = 2000 + 1.37317
Year ≈ 2001.373
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Given the geometric sequence an with the following information, find a9.
The value of ninth term (a₉) is equal to: B. 8/729.
How to calculate the nth term of a geometric sequence?In Mathematics and Geometry, the nth term of a geometric sequence can be calculated by using this mathematical equation (formula):
aₙ = a₁rⁿ⁻¹
Where:
aₙ represents the nth term of a geometric sequence.r represents the common ratio.a₁ represents the first term of a geometric sequence.From the second term of this geometric sequence, we have:
-24 = a₁r
a₁ = -24/r
From the fifth term of this geometric sequence, we have:
8/9 = a₁r⁴
8/9 = a₂ × r³
8/9 = -24 × r³
r³ = -8/216
r = -∛1/27
r = -1/3
Now, we can determine ninth term as follows;
a₁ = -24/(-1/3)
a₁ = 72
a₉ = a₁r⁸
a₉ = 72(-1/3)⁸
a₉ = 72/6,561
a₉ = 8/729
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Find the slip and y-intercept of the line.
Answer:
Slope: 1/2
y-intercept: (0, 4.5)
Slope Intercept = y = mx + b
Slope Intercept = y = 1/2x + 4.5
Step-by-step explanation:
The slope is 1/2 based on our rule, "Rise over Run" Based on the two points listed on the graph, we can say that we "rise" once and "run" twice. This makes our slope 1/2.
The y-intercept is where the line crosses the y-axis. If use our slope, we can determine that if we "rise" half of our slope in the opposite direction (0.5) and run half of our run in the opposite direction (1) we will intersect at (0, 4.5).
With this information, we can construct our slope-intercept equation:
The slope-intercept formula is as follows: y = mx + b
m is our slope, and b is out y-intercept.
y = 1/2x + 4.5
Hector is taking surfing classes with a surfing instructor. He has to pay a surf board rental fee and a fee per-hour that he works with the instructor. He has a coupon for a certain percent off the total cost. The expression (1−x)(125+80y) represents his cost after the coupon.
The expression (1 - x)(125 + 80y) gives us the final cost for Hector after applying the coupon, taking into account the surfboard rental fee and the fee per hour for the surfing classes with the instructor.
(1 - x): This represents the remaining percentage after applying the coupon. If the coupon offers a discount of x percent, then (1 - x) represents the percentage of the total cost that Hector has to pay.
(125 + 80y): This represents the original cost without any discounts or coupons. The term 125 represents the surfboard rental fee, and 80y represents the fee per hour that Hector works with the instructor (where y is the number of hours).
(1 - x)(125 + 80y): Multiplying the two terms together gives us the cost after applying the coupon. The expression (1 - x)(125 + 80y) represents the product of the remaining percentage after the coupon and the original cost.
Therefore, the expression (1 - x)(125 + 80y) gives us the final cost for Hector after applying the coupon, taking into account the surfboard rental fee and the fee per hour for the surfing classes with the instructor.
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What is different about multiplying and dividing two signed numbers?
Multiplying two signed numbers results in a product, and the sign of the product depends on the signs of the multiplied numbers.
Multiplying and dividing two signed numbers differ in terms of the rules and properties that apply to each operation. Here are the key differences:
1. Product vs. Quotient:
When multiplying two signed numbers, the result is called the product. It represents the total of repeated addition or combining equal groups. For example, multiplying -3 by -4 gives a product of 12.
When dividing two signed numbers, the result is called the quotient. It represents the ratio or partitioning of one quantity into equal parts. For example, dividing 12 by -4 gives a quotient of -3.
2. Signs of the Result:
In multiplication, the sign of the product depends on the signs of the multiplied numbers. If the signs are the same (both positive or both negative), the product is positive. If the signs are different (one positive and one negative), the product is negative. For example, (-3) * (-4) = 12, and (-3) * 4 = -12.
In division, the sign of the quotient depends on the signs of the dividend and divisor. If both numbers have the same sign, the quotient is positive. If the numbers have different signs, the quotient is negative. For example, 12 / (-4) = -3, and (-12) / (-4) = 3.
3. Properties:
Multiplication has properties like the commutative property (changing the order of the factors doesn't change the product) and the associative property (changing the grouping of factors doesn't change the product). For example, (-3) * (-4) = (-4) * (-3) = 12.
Division, on the other hand, has specific properties like the division property of zero (dividing any number by zero is undefined) and the division property of one (dividing a number by one leaves the number unchanged). For example, 12 / 1 = 12.
In summary, multiplying two signed numbers results in a product, and the sign of the product depends on the signs of the multiplied numbers. Dividing two signed numbers results in a quotient, and the sign of the quotient depends on the signs of the dividend and divisor. Additionally, multiplication has properties like commutativity and associativity, while division has properties specific to the division operation.
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Match each quadratic function given in factored form with its equivalent standard form listed on the left.
f(x) = (x + 2)(x – 6)
f(x) = (x – 4)(x + 3)
f(x) = (x – 12)(x + 1)
f(x) = (x – 3)(x + 4)
A. f(x) = x2 – 11x – 12
B. f(x) = x2 – 4x –12
C. f(x) = x2 + x – 12
D. f(x) = x2 – x – 12
The standard form which are equivalent to the specified factored form of the quadratic equations are;
f(x) = (x + 2)·(x - 6) → B. f(x) = x² - 4·x -12
f(x) = (x - 4)·(x + 3) → D. f(x) = x² - x - 12
f(x) = (x - 12)·(x + 1) → A. f(x) = x² - 11·x - 12
f(x) = (x - 3)·(x + 4) → C. f(x) = x² + x - 12
What is the factored form of a quadratic function?The factored form of a quadratic function is the expression of the function as the product of the linear factors, which is the form; y = (x + p)·(x + q)
The factored form of the quadratic equations can be expanded to find the equivalent standard form as follows;
f(x) = (x + 2) × (x - 6) = x² - 6·x + 2·x - 12 = x² - 4·x - 12
f(x) = (x - 4) × (x + 3) = x² - 4·x +3·x - 12 = x² - x - 12
f(x) = (x - 12) × (x + 1) = x² - 12·x + x - 12 = x² - 11·x - 12
f(x) = (x - 3) × (x + 4) = x² - 3·x + 4·x - 12 = x² + x - 12
Therefore, we get;
A. f(x) = x² - 11·x - 12 ⇒ f(x) = (x - 12) × (x + 1)
B. f(x) = x² - 4·x - 12 ⇒ f(x) = (x + 2) × (x - 6)
C. f(x) = x² + x - 12 ⇒ f(x) = (x - 3) × (x + 4)
D. f(x) = x² - x - 12 ⇒ f(x) = (x - 4) × (x + 3)
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Please answer ASAP i will brainlist
The expression log 3x⁹y⁴ can be written as a sum of logarithms:
log(3x⁹y⁴) = log(3) + 9log(x) + 4log(y)
How to write the expression log3x⁹y⁴ as a sum of logarithmsTo express log(3x⁹y⁴) as a sum and/or difference of logarithms, we use the logarithmic properties.
Using the power rule of logarithms, we can write the expression as:
log(3x⁹y⁴) = log(3) + log(x⁹) + log(y⁴)
we can further simplify so that the variables will be to the first degree as follows;
log(3x⁹y⁴) = log(3) + 9log(x) + 4log(y).
Therefore, the expression log(3x⁹y⁴) can be written as a sum of logarithms:
log(3x⁹y⁴) = log(3) + 9log(x) + 4log(y)
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To determine which student is most likely to win the student council election, 100 students from the school are randomly asked who they intend to value for. This experimental design is using a _____ to gather its results.
A.confounding variable
B. Sample survey
C. Simulated model
D. Census
The experimental design described is using a sample survey to gather results, providing a cost-effective and efficient way to estimate the likelihood of winning for different candidates in the student council election. B Sample survey Option B
The experimental design described in the scenario, where 100 students from the school are randomly asked who they intend to vote for in the student council election, is using a Sample Survey to gather its results.
A sample survey involves selecting a subset, or sample, of individuals from a larger population and collecting data from that sample to make inferences about the entire population. In this case, the 100 students randomly chosen from the school represent the sample, while the larger population would be all the students in the school.
The use of a sample survey is a common and practical approach when the population size is large, as it would be impractical or time-consuming to survey every individual in the population (which would be a census). By randomly selecting a sample, the goal is to obtain a representative subset that reflects the characteristics and opinions of the larger population.
The purpose of this sample survey is to gauge the voting intentions of the students and make predictions about the likely winner of the student council election based on the responses obtained from the sample. The results from the 100 students surveyed would be analyzed to estimate the proportion of the larger population that supports each candidate, and the candidate with the highest estimated proportion of support would be considered the most likely to win the election.
Therefore, the experimental design in question is using a Sample Survey to gather its results and make predictions about the likely winner of the student council election.
Option b
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XZ is the perpendicular bisector of segment WY. Solve for k. Enter a NUMBER only.
The calculated value of k on the line is 9
How to determine the value of kFrom the question, we have the following parameters that can be used in our computation:
XZ is the perpendicular bisector of segment WY
This means that
WX = XY
substitute the known values in the above equation, so, we have the following representation
3k - 4 = 2k + 5
So, we have
3k - 2k = 4 + 5
Evaluate
k = 9
Hence, the value of k is 9
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sarah was cutting fabric for a quilt. she cut 5 pieces that were 19 1/8 inches long. when she finished cutting she had a piece that was 2 1/4 inches long. how long was the piece she cut for the quilt.
The length of the fabric Sarah cut for the quilt is 97.875 inches.
To determine the length of the fabric Sarah cut for the quilt, we need to add up the lengths of the individual pieces she cut.
Number of pieces cut: 5
Length of each piece: 19 1/8 inches
Length of the remaining piece: 2 1/4 inches
To find the total length, we can multiply the length of each piece by the number of pieces and add the length of the remaining piece.
Length of each piece = 19 1/8 inches = 19 + 1/8 inches = 19.125 inches
Length of the remaining piece = 2 1/4 inches = 2 + 1/4 inches = 2.25 inches
Total length = (Length of each piece) [tex]\times[/tex] (Number of pieces) + Length of the remaining piece
Total length = 19.125 inches [tex]\times[/tex] 5 + 2.25 inches
Total length = 95.625 inches + 2.25 inches
Total length = 97.875 inches
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A piece of buttered toast falls to the floor 26 times. The toast landed buttered side up 9 times. Which statement below is correct?
A. The experimental probability that the toast lands buttered side up is 17/26.
B. A simulation could be carried out using odd digits to represent the buttered side landing up and even digits representing the buttered side landing down.
C. The experimental probability that the toast lands buttered side down is 17/26.
D. The theoretical probability that the toast lands buttered side up is 9/26.
Answer:
D. The theoretical probability that the toast lands buttered side up is 9/26.
Forgive me if im wrong....
Step-by-step explanation:
One month Jina rented 6 movies and 2 video games for a total of $30. The next month she rented 3 movies and 5 video games for a total of $36. Find the
rental cost for each movie and each video game.
Rental cost for each movie:
$11
Rental cost for each video game: $
X
Ś
Answer:
Rental cost for each movie = $3.25
Rental cost for each video game = $5.25
Step-by-step explanation:
We can find the rental cost for each movie and each video game using a system of equations where:
M represents the rental cost for each movie,and V represents the rental cost for each video game.First equation:
Since Jina rented 6 movies and 2 video games for a total of $30, our first equation is given by:
6M + 2V = 30
Second equation:
Since Jina also rented 3 movies and 5 video games for a total of $36, our second equation is given by:
3M + 5V = 36
Method to solve: Elimination:
We can solve this with eliminate. First, we need to multiply the second equation by -2. Then, we must add the two equations to eliminate the Ms and solve for V:
Multiplying the entire second equation by -2:
-2(3M + 5V = 36)
-6M - 10V = -72
Adding the two equations:
6M + 2V = 30
+
-6M - 10V = -72
(6M - 6M) + (2V - 10V) = (30 - 72)
-8V = -42
Solving for V:
(-8V = -42) / -8
V = 5.25
Thus, the rental cost for each video game is $5.25.
Solving for M:
We can now find M by plugging in 5.25 for V in any of the two equations in our system.
Let's use the first equation:
Plugging in 5.25 for V in 6M + 2V = 30 to solve for M:
6M + 2(5.25) = 30
(6M + 10.50 = 30) - 10.50
(6M = 19.50) / 6
M = 3.25
Thus, the rental cost for each movie is $3.25.
In the first quarter of 2020, a nation's posted the following statistics and wants to now what the GDP for the first quarter is. Use the data below to calculate that GDP.
Consumers purchased $50 billion of goods and services.
Businesses invested $10 Billion back into their businesses and held $5 Billion of goods produced during the year in their inventories.
Federal, state, and local governments spent $70 Billion throughout the year.
The nation exported $90 Billion worth of goods and services while importing $100 Billion.
The GDP for the first quarter of 2020 is $120 billion.
To calculate the GDP (Gross Domestic Product) for the first quarter of 2020, we need to consider the components of GDP: consumption (C), investment (I), government spending (G), and net exports (NX). The formula for GDP is:
GDP = C + I + G + NX
Given the following statistics for the first quarter of 2020:
Consumers purchased $50 billion of goods and services (C = $50 billion).
Businesses invested $10 billion back into their businesses and held $5 billion of goods produced during the year in their inventories (I = $10 billion).
Federal, state, and local governments spent $70 billion throughout the year (G = $70 billion).
The nation exported $90 billion worth of goods and services while importing $100 billion.
To calculate net exports (NX), we subtract the value of imports from the value of exports:
NX = Exports - Imports
NX = $90 billion - $100 billion
NX = -$10 billion (negative value indicates a trade deficit)
Now, we can substitute the given values into the GDP formula:
GDP = C + I + G + NX
GDP = $50 billion + $10 billion + $70 billion + (-$10 billion)
GDP = $120 billion.
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On a coordinate plane, a point is 4 units to the left and 1 unit down.
For the point shown:
The x-coordinate is
.
The y-coordinate is
.
The point is in quadrant
.
.
The point has an x-coordinate of -4 and a y-coorindate of -1, and it is on the third quadrant.
In which quadrant is the point?First, remember that for a point (x, y):
if x >0, y > 0, then the point is in quadrant I.if x <0, y > 0, then the point is in quadrant II.if x < 0, y < 0, then the point is in quadrant III.if x >0, y < 0, then the point is in quadrant IV.For the point that is 4 units to the lefft and 1 unit down (of the origin) it is written as:
(-4, -1)
Then we can see that this point is on the quadrant III.
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A red giant loses a solar mass in 300,000 years vía a super wind. After a 0.6 million years, it has a mass of 11
The original mass of the red giant was approximately 13.67 solar masses (MSun).
How to solve for the original massAfter 0.8 million years (0.8 * 10⁶ years), the red giant's mass is 11 MSun. This means that it has lost a certain amount of mass over this time period.
The mass loss can be calculated by multiplying the mass loss rate by the time period:
Mass loss = Mass loss rate * Time
Mass loss = (1 MSun / 300,000 years) * (0.8 * 10^6 years)
Mass loss = 2.67 MSun
Now, we can find the original mass by subtracting the mass loss from the current mass:
M original = M current + Mass loss
M original = 11 MSun + 2.67 MSun
M original = 13.67 MSun
Therefore, the original mass of the red giant was approximately 13.67 solar masses (MSun).
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A red giant loses a solar mass in 300,000 years via a superwind. After 0.8 million years, it has a mass of 11MSun. What was its original mass?
Triangle D has been dilated to create triangle D′. Use the image to answer the question.
image of a triangle labeled D with side lengths of 6, 8, 10 and a second triangle labeled D prime with side lengths of 18, 24, 30
Determine the scale factor used.
1/2
2
3
1/3
Answer:
To determine the scale factor used, we can compare the corresponding side lengths of the two triangles.
In triangle D, the side lengths are 6, 8, and 10.
In triangle D', the corresponding side lengths are 18, 24, and 30.
To find the scale factor, we can divide the corresponding side lengths of triangle D' by the corresponding side lengths of triangle D.
Side length ratio:
18/6 = 3
24/8 = 3
30/10 = 3
The ratio of corresponding side lengths is consistent at 3 for each pair. Therefore, the scale factor used is 3.
So, the correct answer is 3.
Step-by-step explanation:
Step 1: Identify the corresponding side lengths of the two triangles.
In triangle D, the side lengths are given as 6, 8, and 10.
In triangle D', the corresponding side lengths are given as 18, 24, and 30.
Step 2: Calculate the ratio of each corresponding side length of D' to D.
For the first pair of corresponding sides:
18/6 = 3
For the second pair of corresponding sides:
24/8 = 3
For the third pair of corresponding sides:
30/10 = 3
Step 3: Analyze the ratios obtained.
Since all three ratios are equal to 3, it indicates a consistent scale factor between the corresponding side lengths of the two triangles.
Step 4: Determine the scale factor.
The scale factor is the constant ratio by which each corresponding side length is multiplied to obtain the corresponding side length of the larger triangle. In this case, since the ratio is 3 for all pairs, the scale factor used is 3.
So, the step-by-step explanation confirms that the scale factor used is 3.
Answer:
The scale factor is 3
Step-by-step explanation:
For triangle D to be dilated into triagle D', each side of D is multiplied by 3,i.e,
6 * 3 = 18
8 * 3 = 24
10 * 3 = 30
Therefor, the scale factor to turn triangle D to D' is 3
A three-column table is given.
Part A C D
Part 14 28 63
Whole B 40 90
What is the value of B in the table?
You acquire a $15,000 unsubsidized loan at 6.8% interest. You will graduate 4 years later.
a) How much simple interest accumulated while you are still in school for an unsubsidized loan?
b) If you capitalized the loan, what will be the balance when you graduate?
c) After you graduate, you will begin making payments on your loan at 6.8% compounded monthly for 10 years. What is the monthly payment for this loan?
d) How much interest will be paid for this loan?
e) Explain what it means of the loan is not capitalized.
f. Now suppose you acquire the same loan of $15,000 at 6.8% compounded monthly for 10 years but it is subsidized. What is the monthly payment for this loan?
g) How much interest will you pay for the subsidized loan?
h) What is the difference in savings for the subsidized loan?
Answer:
a) For an unsubsidized loan of $15,000 at 6.8% interest for 4 years, the simple interest accumulated while you are still in school is **$4,080**.
b) If you capitalized the loan, the balance when you graduate would be **$20,322.68**.
c) After you graduate, you will begin making payments on your loan at 6.8% compounded monthly for 10 years. The monthly payment for this loan is **$174.30**.
d) The total amount of interest paid for this loan is **$10,118.00**.
e) If the loan is not capitalized, it means that the interest accrued during the in-school period is not added to the principal balance of the loan. Instead, it is paid off separately after graduation.
f) For a subsidized loan of $15,000 at 6.8% compounded monthly for 10 years, the monthly payment for this loan is **$163.19**.
g) The total amount of interest paid for this subsidized loan is **$9,782.80**.
h) The difference in savings for the subsidized loan is **$335.20**.
The table represents the function f(x). x 0 1 4 9 16 f(x) -4 -3 -2 -1 0 If g(x) =4/x-8 , which statement is true? A. The y-intercept of g(x) is less than the y-intercept of f(x). B. The y-intercept of g(x) is equal to the y-intercept of f(x). C. The x-intercept of g(x) is equal to the x-intercept of f(x). D. The x-intercept of g(x) is greater than the x-intercept of f(x).
The y-intercept of g(x) is less than the y-intercept of f(x). The y-intercept of g(x) is -1/2, which is greater than the y-intercept of f(x), which is -4. So, the correct answer is A. The y-intercept of g(x) is less than the y-intercept of f(x).
To determine the y-intercept and x-intercept of the function g(x) = 4/(x - 8), we need to find the values of x for which g(x) equals zero and the value of g(x) when x equals zero.
First, let's find the x-intercept of g(x), which is the value of x for which g(x) equals zero. Setting g(x) = 0 and solving for x, we have:
0 = 4/(x - 8)
This equation has no solutions because a fraction can only be zero if its numerator is zero, but in this case, the numerator (4) is always non-zero. Therefore, g(x) does not have an x-intercept.
Next, let's find the y-intercept of g(x), which is the value of g(x) when x equals zero:
g(0) = 4/(0 - 8)
g(0) = 4/(-8)
g(0) = -1/2
Therefore, the y-intercept of g(x) is -1/2.
Now, let's compare the y-intercepts of g(x) and f(x). From the given table, we see that the y-intercept of f(x) is -4.
Since -4 is not equal to -1/2, we can conclude that statement B, "The y-intercept of g(x) is equal to the y-intercept of f(x)," is false.
To summarize, the correct answer is: A. The y-intercept of g(x) is less than the y-intercept of f(x).
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graph the following inequality -2y+3<5
The graph of the inequality -2y + 3 < 5 is a shaded region below the line y = -1.
1. Start by rewriting the inequality with y on the left side: -2y + 3 < 5.
2. Subtract 3 from both sides of the inequality: -2y < 2.
3. Divide both sides of the inequality by -2. Since we are dividing by a negative number, the inequality sign flips: y > -1.
4. This means that y must be greater than -1 to satisfy the inequality.
5. To graph this inequality, draw a number line and mark -1 with an open circle (since y is not equal to -1).
6. Shade the region to the right of -1, since y must be greater than -1.
7. Since there are no other variables or coefficients in the inequality, the line y = -1 is a horizontal line passing through -1 on the y-axis.
8. Indicate on the graph that the line itself is not part of the solution by making it a dashed line instead of a solid line.
9. Therefore, the graph of the inequality -2y + 3 < 5 is a shaded region below the line y = -1.
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In sampling distributions the mean is consistently _____ the population mean
A. Lower than
B. Higher than
C. Identical to
D. Unrelated to
In sampling distributions, the mean is consistently identical to the population mean. (Option C)
This concept is a fundamental property of sampling distributions and is rooted in the principles of probability and statistical theory. A sampling distribution is a theoretical distribution that represents the possible values of a statistic (such as the mean or proportion) calculated from different samples drawn from the same population. The mean of a sampling distribution is an average of the sample means, and it provides an estimate of the population mean.
When random samples are drawn from a population, the mean of each sample will vary due to random sampling variability. However, as the sample size increases, the distribution of sample means tends to converge around the population mean. This phenomenon is known as the Central Limit Theorem.
According to the Central Limit Theorem, as sample sizes become large (typically n > 30), the sampling distribution of the mean becomes approximately normal, with a mean that is identical to the population mean. In other words, on average, the sample means will be equal to the population mean. This property holds true regardless of the shape, spread, or other characteristics of the population distribution.
Therefore, the correct answer is C. Identical to.
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What is the mid point of the line segment? (Geometry) I’m pretty stuck on this and I’m unsure how to do it properly.
The line segment is calcilated by the formula represented mathematically as (x1+x2/2, y1+y2/2), The midpoint is (5,5).
The midpoint of a line segment is the point on the line that is halfway between the endpoints of the line.
To find the midpoint of a line segment, you need to average the x-coordinates of the endpoints and the y-coordinates of the endpoints.
In other words, the x-coordinate of the midpoint is the average of the x-coordinates of the endpoints, and the y-coordinate of the midpoint is the average of the y-coordinates of the endpoints.
The midpoint formula can be represented mathematically as (x1+x2/2, y1+y2/2)
Where (x1, y1) and (x2, y2) are the coordinates of the endpoints of the line segment.
Let's illustrate this with an example:
Suppose we have a line segment with endpoints (2,3) and (8,7).
To find the midpoint of the line segment, we use the formula (x1+x2/2, y1+y2/2)(2+8/2, 3+7/2)(10/2, 10/2)
The midpoint is (5,5).
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A. Pascal's triangle:
1
1 1
1 2 1
1 3 3 1
1 4 6 4 1
1 5 10 10 5 1
B. Matrix to find the inverse of:
[0 -4 0]
[3 7 1]
[0 1 7]
1. The terms of Pascal's triangle consists of different combination arrangements. This special triangle contains triangular arrays of binomial coefficients. There are many interesting patterns in Pascal's triangle. Examine the rows, columns, and diagonals of Pascal's triangle and state the different patterns you see among the numbers.
2. Summarize the requirements that distinguish each of the conic sections (i.e. ellipse, hyperbola, parabola, etc.)
3. Find the inverse of the matrix B.
4. Ocean tides can be modeled by a sinusoidal function. Suppose that there is a low and high tide every 12 hours, and that high tide in Seattle occurs at 1:00 a.m. and 1:00 p.m. with the low tides 6 hours after high tides. Also suppose that the water level at high tide is 10 ft above the water level at low tide.
a. Find a formula for the function y=ℎ(t) that computes the height of the tide above low tide at time t. (In other words, y=0 corresponds to low tide.)
b. What is the height of the tide at 11:00 a.m?
5. In a video game an object represented by the point (7,3) is rotated counterclockwise 190 degrees about an origin. Find the new coordinates that represent the point.
6. The point (2, 4) lies on the terminal arm of an angle of rotation. Name the point in each of the other quadrants which has the same reference angle.
Dave's Taxi
C = 1.8x
Pete's Cab
C = 1.5x + 5
Rick's
Rickshaw
C=1.9x-3.5
Jenny wants to get a lift to the Airport.
The distance to the Airport is 20 miles
C is the cost of the trip when x = the number of miles.
Jenny has £40.
How much change would she have if she took the cheapest service?
We know that 20 miles is the distance to tbe airport. So, we should start by substituting the x on each expression with 20.
This way we can find the cost of each ride.
Dave
C=1.8x
C=1.8(20)
C=36
Dave's ride would cost 36 pounds .
Pete
C=1.5x+5
C=1.5(20)+5
C= 30+5
C=35
Pete's ride would cost 35 pounds.
Rick
C=1.9x-3.5
C=1.9(20)-3.5
C=38-3.5
C=34.5
Rick's ride would cost 34.5 pounds.
The cheapest ride would be Rick's Rickshaw.
Now, we just figure out the change .
Jenny has 40 pounds
So, subtracting with the cheapest rate of 34.5:
40-34.5=5.5
Answer. Jenny would get 5.5 pounds in change if she took the cheapest ride.
why is the sky blue? why is the water blue?
The sky appears blue because of Rayleigh scattering while water appears blue due to selective absorption and scattering of light.
Why does the sky appear blue and the water blue?The blue color of the sky is a result of Rayleigh scattering which occurs when the Earth's atmosphere scatters shorter wavelengths of light (blue and violet) more efficiently than longer wavelengths (red and orange).
When sunlight enters the atmosphere, the blue light is scattered in all directions by the molecules and tiny particles present in the air creating the blue appearance of the sky.
Similarly, water appear blue due to selective absorption and scattering of light. Water molecules selectively absorb colors from the visible light spectrum and absorb longer wavelengths (such as red) more effectively than shorter wavelengths (such as blue).
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In the quadrilateral below, angles DAB and BCD are the same size. What is the size of angle DAB? A D 226° 38° B
The size of angle DAB in the quadrilateral is 48°.
How to find the size of angle DAB?The sum of the interior angles of a quadrilateral is 360°. We can say:
[tex]\angle \text{A} +\angle\text{B} + \angle\text{C} + \angle\text{D} = 360^\circ[/tex]
[tex]\angle \text{A} +38^\circ + \angle\text{C} + 226^\circ = 360^\circ[/tex]
[tex]\angle \text{A} + \angle\text{C} + 264^\circ = 360^\circ[/tex]
[tex]\angle \text{A} + \angle\text{C} = 360^\circ- 264^\circ[/tex]
[tex]\angle \text{A} + \angle\text{C} = 96[/tex]
Since angles DAB and BCD are the same size. This implies ∠A = ∠C. Thus:
[tex]\angle\text{A} + \angle\text{A} = 96[/tex]
[tex]2\angle\text{A} = 96[/tex]
[tex]\angle\text{A} = \dfrac{96}{2}[/tex]
[tex]\angle\text{A} = 48^\circ[/tex]
Therefore, the size of angle DAB is 48°.
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