Answer:
To calculate Mr. Chi's total tax bill, we need to find the amount of sales tax charged by each entity and add them together.
The state sales tax on the sale of a house is 3.2%, which means Mr. Chi will owe 0.032 x $289,300 = $9,267.20 in state sales tax.
The county sales tax on the sale of a house is 2.6%, which means Mr. Chi will owe 0.026 x $289,300 = $7,520.80 in county sales tax.
The city sales tax on the sale of a house is 1.8%, which means Mr. Chi will owe 0.018 x $289,300 = $5,207.40 in city sales tax.
Therefore, Mr. Chi's total tax bill will be $9,267.20 + $7,520.80 + $5,207.40 = $21,995.40.
Please help!
flynn is playing with a toy that is tied to his hand by a string. the toy falls toward the floor then risee back towards flynns hand, and repeats this motion, following the path illustrated by the given graph. (see pic)
use the graph to complete the function h(t) that models the toys height, in feet, above the floor t seconds after it has left flynns hand.
h(t)=____ (poss. answers- 2, 1.75, 3.5, 4) cos=(____pi^t) poss. answers- 6, 1/6, 1/3, 3)
+_____ (poss. answers- 1.75, 0.25, 2, 2.25)
Answer:
h(t) = 1.75 cos (π/6) + 2.25
Step-by-step explanation:
the amplitude of a regular cos graph is 1 (it alternates between +1 and -1 on the y-axis). that is, amplitude = (1 - -1)/2 = 2/2 = 1.
this graph has amplitude (4 - 0.5)/2 = 3.5/2 = 1.75.
the graph repeats for every sixth value on the x-axis (time axis).
in the x-axis direction, a cos graph that becomes 6 times larger is cos (π/6). a cos graph that becomes 6 times smaller is cos (6π).
so for our graph, it is cos (π/6).
what about the y-shift?
the graph has already been enlarged 1.75 times parallel to the y-axis.
it crosses the y-axis at 4. so the y-shift is 4 - 1.75 = 2.25.
so our graph is given by h(t) = 1.75 cos (π/6) + 2.25
Answer: got it right
h(t)=1.75, cos(1/3), + 2.25
Step-by-step explanation:
a circular feild has a diameter of 32 meters.
A farmer wants to build a fence around the edge of the feild.
Each metre of fence will cost £15.95
Work out the total cost of the fence
The circumference of a circle = pi x diameter
Circumference = 3.14 x 32 = 100.48 meters (rounded to two decimal places)
The farmer needs to build a fence around the edge of the field, which has a circumference of 100.48 meters. So the total length of fence needed is 100.48 meters.
Each meter of fence cost £15.95, therefore the cost of building the entire fence can be calculated as:
Total Cost = Length of fence x Cost per meter of fence Total Cost = 100.48 x £15.95 Total Cost = £1601.08
Therefore, it would cost the farmer a total of £1601.08 to build a fence around the edge of the circular field.
Answer:
$1603.47
Step-by-step explanation:
Plot the image of Figure ABCDEFGH after a dilation with scale factor 3. One of
the sides has been plotted for you.
Click twice to plot a segment.
Click a segment to delete it.
I can guide you on how to perform the dilation with a scale factor of 3 for the figure.
To perform a dilation with a scale factor of 3, you would multiply the coordinates of each point of the original figure by 3. This will result in the figure being enlarged by a factor of 3.
Let's assume the coordinates of the original figure ABCDEFGH are as follows:
A: (1, 1)
B: (4, 1)
C: (4, 4)
D: (1, 4)
E: (2, 2)
F: (3, 2)
G: (3, 3)
H: (2, 3)
To obtain the image of the figure after dilation with a scale factor of 3, multiply each coordinate by 3:
A': (3, 3)
B': (12, 3)
C': (12, 12)
D': (3, 12)
E': (6, 6)
F': (9, 6)
G': (9, 9)
H': (6, 9)
These new coordinates (A', B', C', D', E', F', G', H') represent the image of figure ABCDEFGH after the dilation with a scale factor of 3. You can plot these new coordinates on a graph or use a drawing tool to visualize the enlarged figure.
4(-2)² + 8(-2) + 3(-2) + 6 = ? Can you break down how you solved it
Answer:
Step-by-step explanation:
To solve the expression 4(-2)² + 8(-2) + 3(-2) + 6, we need to follow the order of operations, which is also known as PEMDAS (Parentheses, Exponents, Multiplication and Division - from left to right, Addition and Subtraction - from left to right).
First, we will simplify any calculations within parentheses:
4(-2)² + 8(-2) + 3(-2) + 6
(-2)² is equal to (-2) * (-2), which is 4:
4 * 4 + 8(-2) + 3(-2) + 6
Next, we perform the multiplication:
4 * 4 = 16
Now, we have:
16 + 8(-2) + 3(-2) + 6
Next, we continue with the multiplication:
8(-2) = -16
3(-2) = -6
Now, we have:
16 + (-16) + (-6) + 6
Finally, we simplify the addition and subtraction from left to right:
16 + (-16) = 0
0 + (-6) = -6
-6 + 6 = 0
Therefore, the expression 4(-2)² + 8(-2) + 3(-2) + 6 simplifies to 0.
HELP!!!!!!!!!!!!!!!!!!
Answer:
D 0.89275
Step-by-step explanation:
System C. Solve this system of equations using the provided table.
Answer:
Step-by-step explanation:
all you have to do is replace the x in each equation with the x in the table for example for the first one y1 would be -8 and y2 would be 28/3
Segment RT has endpoints R(-3,4) & T (-7,-3) what are the coordinates of the midpoint of RT?
d) √√(x²y²) = i. xy ii. xy² iii. x²y iv. x4y4
The expression √(x²y²) when simplified is i. xy
How to simplify the expressionFrom the question, we have the following parameters that can be used in our computation:
√(x²y²)
When the expression is expanded, we have
√(x²y²) = √(x² * √(y²)
Evaluae the exponents in the expression
So, we have
√(x²y²) = x * y
Evaluae the products in the expression
So, we have
√(x²y²) = xy
Hence, the expression when simplified is i. xy
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Reema wants to build a coat rack for the front hallway. The wall is 4 feet long, and the piece of wood she has for the the rack is 28 1/4 inches long. She wants to center the coat rack on the wall. There needs to be an equal amount of space, about 7 or 8 inches, between coat hooks. The first and last hooks should be no less than 1 3/4 inches from either end of the wood. How many hooks should Reema use? What is the distance between the hooks? What is the distance of each hook from the left edge of the wood?
Reema should use 3 hooks, with a distance of 7 inches between each hook, and each hook will be positioned 5 3/8 inches from the left edge of the wood.
To determine the number of hooks Reema should use, we first need to calculate the available space on the wood for the hooks.
The total length of the wall is 4 feet, which is equivalent to 48 inches. Reema wants to center the coat rack, so she will have an equal amount of space on either side.
Therefore, each side will have (48 - 28 1/4) / 2 = 9 3/8 inches of space.
Next, we need to determine the distance between the hooks.
Reema wants about 7 or 8 inches of space between each hook.
Let's choose 7 inches for consistency.
Since there will be (n - 1) spaces between n hooks, the total space taken by the spaces will be 7 [tex]\times[/tex] (n - 1) inches.
Now, let's subtract the space taken by the spaces from the available space on the wood: 9 3/8 - 7 [tex]\times[/tex] (n - 1) = 9 3/8 - 7n + 7 inches.
Reema wants the first and last hooks to be no less than 1 3/4 inches from either end of the wood.
Therefore, we subtract twice this distance from the remaining space: 9 3/8 - 7n + 7 - 2 [tex]\times[/tex] (1 3/4) = 9 3/8 - 7n + 7 - 3 1/2 inches.
Now we have the expression 9 3/8 - 7n + 7 - 3 1/2 inches representing the remaining space.
We want this value to be greater than or equal to zero, as it should not be negative.
Simplifying the expression, we have 18 7/8 - 7n - 3 1/2 inches ≥ 0.
Now we can solve this inequality to find the range of values for n, the number of hooks.
We can then determine the distance between the hooks by dividing the remaining space by the number of spaces, and the distance of each hook from the left edge of the wood by adding the space taken by the spaces to the distance between the hooks.
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A curve C and a straight-line L have respective equations.
y = 2x^2 - 6x + 5
and
2y + x = 4
Find the coordinates of the points of intersection between C and L. Given that the line L is parallel to the line P passing through the points of intersection. Find the equation of line P.
The equation of line P passing through the points of intersection is y = -1/2x + 2.
To find the coordinates of the points of intersection between curve C and line L, we need to solve the system of equations formed by their respective equations.
The equations are:
C: y = 2x^2 - 6x + 5 ...(1)
L: 2y + x = 4 ...(2)
We can solve this system by substituting the value of y from equation (1) into equation (2):
2(2x^2 - 6x + 5) + x = 4
4x^2 - 12x + 10 + x = 4
4x^2 - 11x + 6 = 0
To solve this quadratic equation, we can factorize it:
(4x - 3)(x - 2) = 0
Setting each factor to zero, we get:
4x - 3 = 0 --> x = 3/4
x - 2 = 0 --> x = 2
Now, substitute these x-values back into equation (1) to find the corresponding y-values:
For x = 3/4:
y = 2(3/4)^2 - 6(3/4) + 5
y = 9/8 - 18/4 + 5
y = 9/8 - 9/2 + 5
y = 9/8 - 36/8 + 40/8
y = 13/8
For x = 2:
y = 2(2)^2 - 6(2) + 5
y = 8 - 12 + 5
y = 1
Therefore, the coordinates of the points of intersection between C and L are (3/4, 13/8) and (2, 1).
Now, we need to find the equation of line P passing through the points of intersection.
We have two points on line P: (3/4, 13/8) and (2, 1).
First, let's find the slope of line P using the formula:
m = (y2 - y1) / (x2 - x1)
m = (1 - 13/8) / (2 - 3/4)
m = (-5/8) / (5/4)
m = -1/2
Now, we have the slope of line P, -1/2. We can use one of the points, let's say (3/4, 13/8), and the slope to find the equation of line P using the point-slope form:
y - y1 = m(x - x1)
Substituting the values:
y - 13/8 = -1/2(x - 3/4)
Simplifying:
y - 13/8 = -1/2x + 3/8
y = -1/2x + 3/8 + 13/8
y = -1/2x + 16/8
y = -1/2x + 2
Therefore, the equation of line P passing through the points of intersection is y = -1/2x + 2.
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The measured width of the office is 30mm. If the scale of 1: 800 is used, calculate the actual width of the building in metres
Answer:
Step-by-step explanation:
The figure below represents
marked central angle.
I
of a full circle. Find the measure of the marked central angle.
The measure of the marked central angle for the given circle is 160°.
Given a part of a circle.
This part is 4/9 of the full circle.
We have to find the marked central angle.
We know that,
Total circle can be represented as,
Total circle = 360°
Since the given figure is 4/9 part of the total circle, the marked central angle will be 4/9 of the total central angle.
Marked central angle = 4/9 × 360
= 160°
Hence the marked central angle is 160°.
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Please solve this
∫ (log(1 + x ^ 2))/((x + 1) ^ 2) dx
The final result of the integral is:
∫ (log(1 + x²) / (x + 1)²) dx = log(x + 1) - 2 (log(x + 1) / x) - 2Li(x) + C,
where Li(x) is the logarithmic integral function and C is the constant of integration.
We have,
To solve the integral ∫ (log(1 + x²) / (x + 1)²) dx, we can use the method of substitution.
Let's substitute u = x + 1, which implies du = dx. Making this substitution, the integral becomes:
∫ (log(1 + (u-1)²) / u²) du.
Expanding the numerator, we have:
∫ (log(1 + u² - 2u + 1) / u²) du
= ∫ (log(u² - 2u + 2) / u²) du.
Now, let's split the logarithm using the properties of logarithms:
∫ (log(u² - 2u + 2) - log(u²)) / u² du
= ∫ (log(u² - 2u + 2) / u²) du - ∫ (log(u²) / u²) du.
We can simplify the second integral:
∫ (log(u²) / u²) du = ∫ (2 log(u) / u²) du.
Using the power rule for integration, we can integrate both terms:
∫ (log(u² - 2u + 2) / u²) du = log(u² - 2u + 2) / u - 2 ∫ (log(u) / u³) du.
Now, let's focus on the second integral:
∫ (log(u) / u³) du.
This integral does not have a simple closed-form solution in terms of elementary functions.
It can be expressed in terms of a special function called the logarithmic integral, denoted as Li(x).
Therefore,
The final result of the integral is:
∫ (log(1 + x²) / (x + 1)²) dx = log(x + 1) - 2 (log(x + 1) / x) - 2Li(x) + C,
where Li(x) is the logarithmic integral function and C is the constant of integration.
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Rita's school is 5 kilometers west of her house and 5 kilometers south of her friend Jayce's
house. Every day, Rita bicycles from her house to her school. After school, she bicycles from
her school to Jayce's house. Before dinner, she bicycles home on a bike path that goes
straight from Jayce's house to her own house. How far does Rita bicycle each day? If
necessary, round to the nearest tenth
Given the circle below with secants TUV and XWV. If UV = 26, WV = 27 and
TU is 3 more than XW, find the length of TU. Round to the nearest tenth if
necessary.
The length of segment TU for the intersecting chords is determined as 28.
What is the length of TU?The length of segment TU is calculated by applying intersecting chord theorem for two chords in a circle as shown below.
From the given diagram we will have the following equation;
UV (UV + TU) = WV (WV + XW)
We know that TU is 3 more than XW;
TU = XW + 3
So our new equation becomes;
26( ( 26 + XW + 3) = 27( 27 + XW)
26(29 + XW) = 27 (27 + XW)
Simplify further as follows;
754 + 26XW = 729 + 27XW
754 - 729 = XW
25 = XW
The length of segment TU is calculated as;
TU = 3 + 25
TU = 28
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What are the approximate polar coordinates for the point with rectangular coordinates (–2, 4)? Give θ in degrees rounded to the nearest thousandth.
Use the remainder theorem to find P(2) for P(x)=-x^3+3x^2+6.
Specifically, give the quotient and the remainder for the associated division and the value of P(2).
Answer: The value of P(2) is equal to 26
Step-by-step explanation:
To find P(2) for the given polynomial P(x) = -x^3 + 3x^2 + 6, we can use the remainder theorem by dividing the polynomial by (x - 2).
-x^2 + 5x - 4
__________________________
x - 2 | -x^3 + 3x^2 + 0x + 6
(x^3 - 2x^2)
___________
5x^2 + 0x
(5x^2 - 10x)
____________
10x + 6
(10x - 20)
__________
26
The quotient is -x^2 + 5x - 4, and the remainder is 26.
Therefore, the value of P(2) is equal to the remainder, which is 26.
Show (AB)^-1 = B^-1 A^-1
The frequency table below shows the number of goals Real Madrid scored in each of their soccer games in April and May of 2022. Determine the total number of data values (games played) represented in the table.
Data (goals scored) Frequency
0 1
1 3
2 2
3 4
4 2
7 1
9 1
Provide your answer below:
FEEDBACK
There were 14 games played in total during April and May of 2022.
To determine the total number of data values (games played) represented in the frequency table,
Add all of the frequencies indicated in the table.
So, we have:
0 goals scored in 1 game
3 games with a single goal scored 2 goals scored in 2 games
4 games with three goals
2 games with four goals 1 game with 7 goals
And 1 game with 9 goals
Adding up all of these frequencies,
We get,
⇒ 1 + 3 + 2 + 4 + 2 + 1 + 1 = 14
Therefore,
There were 14 games played.
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The children's reading room of a library is shaped like a triangle. Two perpendicular sides of the room measure 12 feet and 17 feet. What's the area of the room?
a.29 squared feet
b.102 squared feet
c.120 squared feet
d.204 squared feet
Answer: B 102
Step-by-step explanation: The perpendicular sides of the room tells us that it is a right triangle.
To find our the area of the triangle you use the formula [tex]\frac{base*height}{2}[/tex]base*height/2
We plug in 12feet and 17 feet for the base and height
We get [tex]\frac{12*17}{2}[/tex]
12 and 2 cancel out so our new equation is 6*17 squared feet
So our answer is 102 square feet
an academy:
1. Explain the concept of conservation of energy and provide examples to illustrate its
application.
A small liberal arts college in the Northeast has 200 freshmen. Sixty of the freshmen are education majors. Suppose thirty freshmen are randomly selected (without replacement).
Find the standard deviation of the number of education majors in the sample. Round your answer to two decimal places, if necessary.
The standard deviation of the number of education majors in the sample is 0.3.
What is the standard deviation of education majors?The standard deviation of the number of education majors in the sample is calculated as follows;
σ = √ [(N - n) x n(N - k) / ((N - 1) x N²)]
Where
N is the total population size = 200 freshmenn is the sample size = 30 freshmenk is the number of successes in the population = 60 education majorsThe standard deviation of the number of education majors in the sample is calculated as;
σ = √[(200 - 30) x 30(200 - 60) / ((200 - 1) x 200²)]
= √[(170 x 30 x 140 / (199 x 40000)]
= √(714000 / 7960000)
= 0.3
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If KL = x + 8
, LM = 12
, and KM = 3x − 14
, what is KL?
Answer:
x = 17
Step-by-step explanation:
KL + LM = KM
x+8+12 = 3x-14
or, x+20 = 3x-14
or, 3x-x=20+14
or, 2x = 34
x = 17
Answer:
Step-by-step explanation:
3x-14=x+8+12
3x-x=8+12+14
2x=34
x=17
then
KL=(17)+8=25
Urgent please help I am running out of time thank you
Answer:
119
Step-by-step explanation:
For the following exercises, use Figure 2 to approximate the values.
I'm lost on number 15 and 17
Answer:
15. f(-2) = 2
17. f(x) = 1 for x = ±1.7
Step-by-step explanation:
You want various values of the function and its inverse relation for f(x)=x²-2.
Reading the graphThe value of f(x) is found by locating the value x on the x-axis and following the vertical line until it intersects the graph. Find the y-coordinate of that point.
The value of x for f(x) = k is found by locating k on the y-axis and following the horizontal line to the points of intersection with the graph. The x-coordinates of the points are the values of interest. Interpolation is often required.
15. f(-2)The graph intersects the vertical line at x=-2 where y = 2.
f(-2) = 2
17. f(x) = 1The horizontal line at y=1 intersects the graph in two places, located symmetrically about the y-axis. The leftmost point is approximately (-1.7, 1). The rightmost point is approximately (1.7, 1).
x ≈ -1.7 or +1.7
__
Additional comment
The instructions are to use the figure to answer the question. We interpret that to mean that you are to read the answers from the graph.
You can also use the figure to determine the equation for the graph (part of our problem statement, above). Then you can find the solutions by using the equation.
f(x) = 1
x² -2 = 1
x² = 3
x = ±√3 ≈ ±1.732 . . . . the values for problem 17
<95141404393>
Assume that the probability density function of a continuous random variant X is
[tex]f(x)\left \{ {{0,5x, 0\ \textless \ x\ \textless \ 2} \atop {0, else}} \right.[/tex]
try to compute:
(1) E(2X)
(2) E(X^2)
The calculated values of the expected values are E(2x) = 8/3 and E(x²) = 2
How to calculate the expected valuesFrom the question, we have the following parameters that can be used in our computation:
f(x) = 0.5x, 0 < x < 2
The expected value of 2x is calculated as
E(2x) = ∫2x * f(x) dx
So, we have
E(2x) = ∫2x * 0.5x dx
Evaluate
E(2x) = ∫x² dx
Integrate the function
So, we have
E(2x) = x³/3
Using the boundaries, we have
E(2x) = (2 - 0)³/3
Evaluate
E(2x) = 8/3
The expected value of x² is calculated as
E(x²) = ∫x² * f(x) dx
So, we have
E(x²) = ∫x² * 0.5x dx
Evaluate
E(x²) = ∫0.5x³ dx
Integrate the function
So, we have
E(x²) = 0.5x⁴/4
Using the boundaries, we have
E(x²) = 0.5 * (2 - 0)⁴/4
Evaluate
E(x²) = 2
Hence, the expected values are E(2x) = 8/3 and E(x²) = 2
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Please help with this Piece-Wise Function.
In "f(3)", we are told to use an x-value of 3.
Looking at the function, we can either pick a formula that is used when x≤0 or x>0.
Since 3 > 0, we need to use the formula paired with x > 0:
f(x) = x + 1 if x>0
So f(3) = 3 + 1 = 4.
The population of a city has decreased by 27% since it was last measured. If the current population is 7300, what was the previous population?
To find the previous population, we need to determine the population before the 27% decrease. Here's how we can calculate it:
Let's assume the previous population is P.
According to the problem, the current population is 7300, which represents 100% - 27% of the previous population:
(100% - 27%) * P = 7300
To simplify the equation, convert 27% to decimal form:
(100% - 0.27) * P = 7300
Simplifying further:
0.73P = 7300
Divide both sides of the equation by 0.73:
P = 7300 / 0.73
P ≈ 10000
Therefore, the previous population was approximately 10,000.
~~~Harsha~~~
Need help on finding g .
The numeric values for this problem are given as follows:
g(-1) = -2.g(2) = 0.g(3) = 0.5.How to obtain the numeric values of the function?The function in this problem is a piecewise function, meaning that it has different definitions based on the input x of the function.
For x between -2 and 2, the function is defined as follows:
g(x) = -(x - 1)² + 2.
Hence the numeric value at x = -1 is given as follows:
g(-1) = -(-1 - 1)² + 2 = -4 + 2 = -2.
For x at x = 2 and greater, the function is given as follows:
g(x) = 0.5x - 1.
Hence the numeric values at x = 2 and x = 3 are given as follows:
g(2) = 0.5(2) - 1 = 0.g(3) = 0.5(3) - 1 = 0.5.A similar problem, also featuring numeric values of a function, is given at brainly.com/question/28367050
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Solve the system with elimination
2x + 5y = 13
-4x - 3y = 9
Answer:
x = -6 and y =5
Step-by-step explanation:
2x + 5y = 13 (call this equation '1')
-4x - 3y = 9 (call this '2')
multiply '1' by 2
4x + 10y = 26 (call this '3')
eliminate by adding '2' and '3':
(-4 + 4)x + (-3 + 10)y = 9 + 26
7y = 35
y = 5
sub that into '1':
2x + 5(5) = 13
2x + 25 = 13
2x = 13 - 25 = -12
x = -6
sub both x = -6 and y =5 into '2' to make sure everything adds up:
-4(-6) - 3(5) = 24 - 15 = 9
so x = -6 and y = 5
