Answer:
Step-by-step explanation:
[tex]P(\text{not vanilla})=1-\frac{3}{22}=\frac{19}{22}[/tex]
Odds are 19 to 3.
PLEASE HELPP: 2.11.2 Project: Performance Task: The Parallax Problem (For San Francisco)
The Scenario: You’re looking for a sponsor to pay for you to participate in a sailboat race. Now that you’ve solved the parallax problem, use the same skills you used there to write a proposal that shows that you can win the race.
The Project: Use the information provided in the performance task to estimate your travel costs and to calculate your average speed and the speed of last year’s winner. Use the questions below to help you gather information to write your proposal
3. What is the distance between buoy A and B? (5 points)
4. What are the lengths of the other two triangle legs? (4 points: 2 points each)
Remember what you know about the shape of the Race Course.
5. What is the total length of the race course? (4 points: 3 for calculation, 1 for answer)
Part VIII: Calculate the winner’s speed. (10 points)
1. What was the winner’s speed during last year’s race? (5 points: 3 points for speed. 2 points for conversion to knots).
2. How does the winner’s speed compare with your average speed? How much faster or slower are you? (5 points)
Part IX: Write your proposal. (8 points)
Now it’s time to make your proposal to the sponsor. Your sponsor will have their logo on your boat, so they want to be sure it’s likely to do well. The sponsor also needs to know what the expenses and risks are, so they know how much their investment in you will cost.
1. Complete the table to summarize the results of your study. (4 points)
Category:
Race:
Risk Analysis:
Itemized Travel Cost
Safety hazards
Competitive Analysis:
My time and speed
Last year's winning time and speed
Reward Analysis:
My chances of winning
2. Write a summary paragraph explaining why the sponsor should accept your proposal. (4 points)
The proposal is as follows
Part III - The distance between buoys A and B is 12.8 kilometers.
Part IV - The length of the other two triangle legs are 10.2 kilometers and 8.4 kilometers.
Part V - The total length of the race course is 31.4 kilometers.
Part VIII - The winner's speed during last year's race was 10.8 knots.
See the proposal attached.
Why the sponsor should accept your proposalDear Sponsor,
I'm seeking sponsorship for the San Francisco sailboat race.
With a proven track record and the determination to win, your investment of $5,500 covers travel costs and potential hazards.
By associating your brand with a winning sailor, you'll gain significant exposure to thousands of spectators. Join me in this thrilling race for success.
Sincerely,
[Your Name]
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What number completes the sequence below? Enter your answer in the input
box at the bottom.
8————-4
16————8
24———-12
32———-?
Answer here
Answer:
The number is 16
Step-by-step explanation:
This follows a multiplication rule,
4 times 1 = 4
4 times 2 = 8
4 times 3 = 12
4 times 4 = 16
So, the number is 16
Purchasing a Car
Now you have to decide how to save enough money to purchase a used car in three years. You have the
$1000 that you saved up and you plan to continue working. According to your estimates, you can save an
additional $60 per month to put towards the car purchase. After conducting some research at the banks,
you have decided on two options (see below). You need to figure out which option will yield the most
money after the three years.
Option #1-CD for 3 years
Interest rate of 3% compounded monthly.
No money can be added to the CD.
However you can save your money on the side.
Option # 2-CD for 1 year
Interest rate of 2% compounded quarterly.
You can add money at the end of each year.
You will renew it each year for 3 years.
Work Shown:
Answer:
Step-by-step explanation:
To determine which option will yield the most money after three years, let's calculate the final amount for each option.
Option #1 - CD for 3 years:
Principal (initial investment) = $1000
Interest rate = 3% per year (compounded monthly)
No additional money can be added
To calculate the final amount, we can use the formula for compound interest:
A = P * (1 + r/n)^(n*t)
Where:
A = Final amount
P = Principal (initial investment)
r = Interest rate (as a decimal)
n = Number of times the interest is compounded per year
t = Number of years
For Option #1:
P = $1000
r = 3% = 0.03 (as a decimal)
n = 12 (compounded monthly)
t = 3 years
A = $1000 * (1 + 0.03/12)^(12*3)
Calculating the final amount for Option #1, we get:
A = $1000 * (1 + 0.0025)^(36)
A ≈ $1000 * (1.0025)^(36)
A ≈ $1000 * 1.0916768
A ≈ $1091.68
Option #2 - CD for 1 year:
Principal (initial investment) = $1000
Interest rate = 2% per year (compounded quarterly)
Money can be added at the end of each year
To calculate the final amount, we need to consider the annual additions and compounding at the end of each year.
First Year:
P = $1000
r = 2% = 0.02 (as a decimal)
n = 4 (compounded quarterly)
t = 1 year
A = $1000 * (1 + 0.02/4)^(4*1)
A ≈ $1000 * (1.005)^(4)
A ≈ $1000 * 1.0202
A ≈ $1020.20
At the end of the first year, the total amount is $1020.20.
Second Year:
Now we add an additional $60 to the previous amount:
P = $1020.20 + $60 = $1080.20
r = 2% = 0.02 (as a decimal)
n = 4 (compounded quarterly)
t = 1 year
A = $1080.20 * (1 + 0.02/4)^(4*1)
A ≈ $1080.20 * (1.005)^(4)
A ≈ $1080.20 * 1.0202
A ≈ $1101.59
At the end of the second year, the total amount is $1101.59.
Third Year:
Again, we add $60 to the previous amount:
P = $1101.59 + $60 = $1161.59
r = 2% = 0.02 (as a decimal)
n = 4 (compounded quarterly)
t = 1 year
A = $1161.59 * (1 + 0.02/4)^(4*1)
A ≈ $1161.59 * (1.005)^(4)
A ≈ $1161.59 * 1.0202
A ≈ $1185.39
At the end of the third year, the total amount is $1185.39.
Comparing the final amounts:
Option #1: $1091.68
Option #2: $1185.39
Therefore, Option #2 - CD for 1 year with an interest rate of 2% compounded quarterly and the ability to add money at the end of each year will yield the most money after three years.
A graph has time driven (hours) on the x-axis, and Distance Driven (miles) on the y-axis. Points are grouped closely together an increase slightly. Points (2, 225) and (8, 75) are outside of the cluster.
The scatterplot shows the time driven on a trip compared to the distance driven. Inspect the scatterplot to determine if it has outliers.
How many outliers does the data set have?
The point
is an outlier in the data se
The data set has two outliers, namely the points (2, 225) and (8, 75).
Based on the given information about the scatterplot, we can observe that most of the points are grouped closely together and show a slight increase.
There are two points that lie outside of this cluster, specifically (2, 225) and (8, 75).
To determine if these points are outliers, we need to consider their deviation from the general pattern exhibited by the majority of the data points.
If these points deviate significantly from the overall trend, they can be considered outliers.
In this case, since (2, 225) and (8, 75) lie outside of the cluster of closely grouped points and do not follow the general pattern, they can be considered outliers.
These points are noticeably different from the majority of the data points and may have influenced the overall trend of the scatterplot.
The data set has two outliers, namely the points (2, 225) and (8, 75).
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50 Points! Multiple choice geometry question. Photo attached. Thank you!
Answer:
B. Lenghts of the diagonals
Step-by-step explanation:
Devaughn's age is three times Sydney's age. The sum of their ages is 80 . What is Sydney's age?
[tex]\qquad\displaystyle \rm \dashrightarrow \: let \: \: Sydney's \: \: age \: \: be \: \: 'y'[/tex]
[tex]\qquad\displaystyle \tt \dashrightarrow \: Devaughn's \: \: age \: \: will \: \: be \: \: 3y[/tex]
Sum up ;
[tex]\qquad\displaystyle \tt \dashrightarrow \: 3y + y = 80[/tex]
[tex]\qquad\displaystyle \tt \dashrightarrow \: 4y = 80[/tex]
[tex]\qquad\displaystyle \tt \dashrightarrow \: y = 80 \div 4[/tex]
[tex]\qquad\displaystyle \tt \dashrightarrow \: y = 20[/tex]
So, Sydney's age is 20 years, n that of Devaughn is 20 × 3 = 60 years
Answer:
Sydney= 20, Devaughn= 60
Step-by-step explanation:
Let Sydney's age be 'x'
Devaughn's age = 3 times x = 3x
We Know That
The sum of their ages is 80.
So,
3x + x = 80
4x = 80
If we shift the 4 to the 80 side
x = 80/4
x = 20
So, Sydney's age is 20
Therefore, Devaughn's age =
3x = 3 times x
= 3 times 20
= 60
in this chart, × is the length of a persons forearm in centimeters and y is the persons height in centimeters. the question is if someones forearm (x) is 24.5 cm, how tall would they be? how do i find this? and how would i make a linear regression graph? thanks
The height of a person whose length of forearm is 24.5 cm is equal to 163.38 centimeters.
How to construct and plot the data in a scatter plot?In this exercise, we would plot the length of forearm on the x-axis of a scatter plot while height would be plotted on the y-axis of the scatter plot through the use of Microsoft Excel.
On the Microsoft Excel worksheet, you should right click on any data point on the scatter plot, select format trend line, and then tick the box to display a linear equation for the line of best fit on the scatter plot;
y = 3.01x + 89.63
Based on the equation of the line of best fit above, the height of a person whose length of forearm is 24.5 cm can be determined as follows;
y = 3.01x + 89.63
y = 3.01(24.5) + 89.63
y = 163.375 ≈ 163.38 centimeters.
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Last year, Ali biked b miles. This year, he biked 358 miles. Using b, write an expression for the total number of miles he biked
What is the slope of the Line y=-3x+2
Answer:
m = -3
Step-by-step explanation:
The slope-intercept form is y = mx + b
m = the slope
b = y-intercept
The equation is y = -3x + 2
m = -3
So, the slope of the line is -3
Answer:
The slope is -3
Step-by-step explanation:
You were given the easiest form of linear equation, the slope-intercept form, because these are the ones that directly tell you the slope and the y-intercept.
y=mx+b, Where m is the slope and b is the y-intercept.
Find the center of the ellipse defined by the equation... 100 points
Answer:
(-4,4)
Step-by-step explanation:
You rewrite the terms:
(x + 4)^2 => [x - (-4)]^2
(y - 4)^2 => [y - (4)]^2
so h = -4 and k = 4
so center of ellipse is (h,k) or (-4,4)
Answer:
Center = (-4, 4)
Step-by-step explanation:
The standard form of the equation of an ellipse with center (h, k) is:
[tex]\boxed{\dfrac{(x-h)^2}{a^2}+\dfrac{(y-k)^2}{b^2}=1}[/tex]
The given equation is:
[tex]\dfrac{(x+4)^2}{25}+\dfrac{(y-4)^2}{9}=1[/tex]
Comparing the given equation with the standard form, we can see that h = -4 and k = 4. Therefore, the center (h, k) of the ellipse is (-4, 4).
A parabola can be drawn given a focus of ... 100pts
Answer:
The parabola has a vertex at (3, -4), has a p-value of -6 and it opens downwards.
Step-by-step explanation:
The given directrix of the parabola is y = 2, which is a horizontal line.
This means that the parabola is vertical, with a vertical axis of symmetry.
The focus of a parabola is a fixed point located inside the curve. The y-coordinate of the given focus is y = -10. As this is below the directrix, it means that the parabola opens downwards.
The standard form of a vertical parabola is:
[tex]\boxed{(x-h)^2=4p(y-k)}[/tex]
where:
Vertex = (h, k)Focus = (h, k+p)Directrix: y = (k - p)Axis of symmetry: x = hAs the focus is (3, -10), then:
[tex](h, k+p)=(3,-10)[/tex]
[tex]\implies h = 3[/tex]
[tex]\implies k+p=-10[/tex]
As the directrix is y = 2, then:
[tex]k - p=2[/tex]
To find the value of k, sum the equations involved k and p to eliminate p:
[tex]\begin{array}{crcccr}&k &+& p& =& -10\\+&k& -& p& = &2\\\cline{2-6}&2k&&& =& -8\\\cline{2-6}\\\implies &k&&&=&-4\end{array}[/tex]
To find the value of p, substitute the found value of k into one of the equations:
[tex]-4-p=2[/tex]
[tex]p=-4-2[/tex]
[tex]p=-6[/tex]
Therefore, the values of h, k and p are:
h = 3k = -4p = -6The parabola has a vertex at (3, -4), has a p-value of -6 and it opens downwards.
The parabola has a vertex at (3, -4), has a p-value of -6 and it opens downwards.
How to determine the equation and vertex of a parabola?In Mathematics, the standard form of the equation of the directrix lines for any parabola is given by this mathematical equation:
(x - h)² = 4p(y - k).
Where:
h and k are the vertex.p is a point.Since the directrix is horizontal, the axis of symmetry would be vertical. This ultimately implies that, we would have the following parameters;
directrix is y = 2
Focus, (h, k + p) = (3, -10)
Next, we would determine the value of k as follows;
k + p = -10 .......equation 1
k - p = 2 .......equation 2
By solving the equations simultaneously, we have:
2k = -8
k = -4
For the value of p, we have the following from equation 2:
k - p = 2
-4 - p = 2
p = -4 - 2
p = -6
In conclusion, we can logically deduce that the parabola opens downward because the p-value is negative.
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Triangle ABC with vertices at A(4, 3), B(3, −2), C(−3, 1) is dilated using a scale factor of 1.5 to create triangle A′B′C′. Determine the vertex of point A′.
The vertex of point A' in the dilated triangle A'B'C' is (6, 4.5).
1. Start by calculating the distance between the vertices of the original triangle ABC:
- Distance between A(4, 3) and B(3, -2):
Δx = 3 - 4 = -1
Δy = -2 - 3 = -5
Distance = √((-[tex]1)^2[/tex] + (-[tex]5)^2[/tex]) = √26
- Distance between B(3, -2) and C(-3, 1):
Δx = -3 - 3 = -6
Δy = 1 - (-2) = 3
Distance = √((-6)² + 3²) = √45 = 3√5
- Distance between C(-3, 1) and A(4, 3):
Δx = 4 - (-3) = 7
Δy = 3 - 1 = 2
Distance = √(7² + 2²) = √53
2. Apply the scale factor of 1.5 to the distances calculated above:
- Distance between A' and B' = 1.5 * √26
- Distance between B' and C' = 1.5 * 3√5
- Distance between C' and A' = 1.5 * √53
3. Determine the coordinates of A' by using the distance formula and the given coordinates of A(4, 3):
- A' is located Δx units horizontally and Δy units vertically from A.
- Δx = 1.5 * (-1) = -1.5
- Δy = 1.5 * (-5) = -7.5
- Coordinates of A':
x-coordinate: 4 + (-1.5) = 2.5
y-coordinate: 3 + (-7.5) = -4.5
4. Thus, the vertex of point A' in the dilated triangle A'B'C' is (2.5, -4.5).
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Find the value of the combination. 10C0 0 1 10
The formula to find the value of a combination is
[tex]C(n, r) = n! / (r!(n-r)!),[/tex]
where n represents the total number of items and r represents the number of items being chosen at a time. 10C0 is 1
In the combination,
n = 10 and r = 0,
so the formula becomes:
C(10,0) = 10! / (0! (10-0)!) = 10! / (1 x 10!) = 1 / 1 = 1
This means that out of the 10 items, when choosing 0 at a time, there is only 1 way to do so. In other words, choosing 0 items from a set of 10 items will always result in a single set. This is because the empty set (which has 0 items) is the only possible set when no items are chosen from a set of items. Therefore, the value of the combination 10C0 is 1.
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If FE =14 find the length of BC
Please give a very in-depth explanation and I will mark Brainliest!!
HI Your answer is 42
I have calculated it you can trust me
Well you have marked right in the pic
PLEASE MARK AS BRAINLIEST
Given that p(x)=2(5−x)2+1 , what is the value of p(-4)? Responses
Answer:
37
Step-by-step explanation:
x=-4
=2(5-(-4)2+1
=2(5+4)2+1
=2(9)2+1
=18(2)+1
=36+1
=37
GEOMETRY 50POINTS
FIND x
Combining the results of a given triangle, we can conclude that the value of 'x' must be greater than -22 and also less than 52. So, the possible range for 'x' is -22 < x < 52.
To find the value of 'x' in a triangle with side lengths 'x', 37, and 15, we can use the triangle inequality theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the remaining side.
In this case, we have:
x + 37 > 15 (Sum of x and 37 is greater than 15)
x + 15 > 37 (Sum of x and 15 is greater than 37)
37 + 15 > x (Sum of 37 and 15 is greater than x)
From the first inequality, we can subtract 37 from both sides:
x > 15 - 37
x > -22
From the second inequality, we can subtract 15 from both sides:
x > 37 - 15
x > 22
From the third inequality, we can subtract 15 from both sides:
52 > x
Combining the results, we can conclude that the value of 'x' must be greater than -22 and also less than 52. So, the possible range for 'x' is -22 < x < 52.
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Cecilia se compra un libro con la cuarta parte de su dinero y un cómic con la mitad del dinero que le quedaba. Al salir de la librería se da cuenta que le sobraron $8. ¿Cuál es la ecuación para conocer la cantidad de dinero que tenía en un inicio?
The equation to determine the initial amount of money Cecilia had is x = 0.
Let's denote the initial amount of money Cecilia had as "x" dollars.
According to the given information, Cecilia spent one-fourth (1/4) of her money on a book, which is (1/4)x dollars. After buying the book, she had (x - (1/4)x) dollars left.
Next, Cecilia spent half (1/2) of the remaining money on a comic, which is ((1/2)x - 8) dollars. After buying the comic, she had ((x - (1/4)x) - ((1/2)x - 8)) dollars remaining.
Since she had $8 left, we can set up the equation:
((x - (1/4)x) - ((1/2)x - 8)) = 8
To simplify the equation, we can first combine like terms:
(x - (1/4)x - (1/2)x + 8) = 8
Now, let's solve the equation step by step:
(x - (1/4)x - (1/2)x + 8) = 8
Multiplying the fractions by their common denominator, which is 4, we get:
(4x - x - 2x + 32) = 32
Simplifying further:
(x + 32) = 32
Subtracting 32 from both sides:
x = 0
Therefore, the equation to determine the initial amount of money Cecilia had is x = 0.
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Find the volume of the solid obtained by rotating the region
bounded by the graphs y=(x-4)^3,the x-axis, x=0, and x=5
about the y-axis? (Express numbers in exact form. Use symbolic
notation and fractions where needed.)
Answer:
Step-by-step explanation:
To find the volume of the solid obtained by rotating the region bounded by the graphs y = (x - 4)^3, the x-axis, x = 0, and x = 5 about the y-axis, we can use the method of cylindrical shells.
The formula for the volume of a solid obtained by rotating a region bounded by the graph of a function f(x), the x-axis, x = a, and x = b about the y-axis is given by:
V = 2π ∫[a, b] x * f(x) dx
In this case, the function f(x) = (x - 4)^3, and the bounds of integration are a = 0 and b = 5.
Substituting these values into the formula, we have:
V = 2π ∫[0, 5] x * (x - 4)^3 dx
To evaluate this integral, we can expand the cubic term and then integrate:
V = 2π ∫[0, 5] x * (x^3 - 12x^2 + 48x - 64) dx
V = 2π ∫[0, 5] (x^4 - 12x^3 + 48x^2 - 64x) dx
Integrating each term separately:
V = 2π [1/5 x^5 - 3x^4 + 16x^3 - 32x^2] evaluated from 0 to 5
Now we can substitute the bounds of integration:
V = 2π [(1/5 * 5^5 - 3 * 5^4 + 16 * 5^3 - 32 * 5^2) - (1/5 * 0^5 - 3 * 0^4 + 16 * 0^3 - 32 * 0^2)]
Simplifying:
V = 2π [(1/5 * 3125) - 0]
V = 2π * (625/5)
V = 2π * 125
V = 250π
Therefore, the volume of the solid obtained by rotating the region bounded by the graphs y = (x - 4)^3, the x-axis, x = 0, and x = 5 about the y-axis is 250π cubic units.
The following is a list of shoe sizes for a group of 13 people.
4.5, 9.5, 8, 6.5, 10, 7, 8.5, 6, 7.5, 9, 6, 7, 11
Which of the following box plots best represents the numerical data?
A box plot using a number line from 3 to 12.25 with tick marks every one-fourth unit. The box extends from 6.25 to 9.25 on the number line. A line in the box is at 7.5. The lines outside the box end at 4.5 and 11. The graph is titled Shoe Sizes, and the line is labeled Size of Shoe.
A box plot using a number line from 3 to 11.25 with tick marks every one-fourth unit. The box extends from 6.25 to 8.75 on the number line. A line in the box is at 7.25. The lines outside the box end at 4.5 and 10. The graph is titled Shoe Sizes, and the line is labeled Size of Shoe.
A box plot using a number line from 3 to 13 with tick marks every one-half unit. The box extends from 6.5 to 9 on the number line. A line in the box is at 7.5. The lines outside the box end at 4.5 and 12. The graph is titled Shoe Sizes, and the line is labeled Size of Shoe.
A box plot using a number line from 3 to 12.5 with tick marks every one-fourth unit. The box extends from 6.25 to 8.75 on the number line. A line in the box is at 7.5. The lines outside the box end at 4.5 and 10.5. The graph is titled Shoe Sizes, and the line is labeled Size of Shoe.
The box plot that best represents the numerical data is: A. A box plot using a number line from 3 to 12.25 with tick marks every one-fourth unit. The box extends from 6.25 to 9.25 on the number line. A line in the box is at 7.5. The lines outside the box end at 4.5 and 11. The graph is titled Shoe Sizes, and the line is labeled Size of Shoe.
How to complete the five number summary of a data set?In order to determine the five-number summary for the survey, we would arrange the data set in an ascending order:
4.5,6,6,6.5,7,7,7.5,8,8.5,9,9.5,10,11
Based on the information provided about the list of shoe sizes for a group of 13 people, we would use a graphical method (box plot) to determine the five-number summary for the given data set as follows:
Minimum (Min) = 4.5.
First quartile (Q₁) = 6.25.
Median (Med) = 7.5.
Third quartile (Q₃) = 9.25.
Maximum (Max) = 11.
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What is the major difference between Grades 4 and 5 in terms of the teaching of probability?
Answer:
In Grade 4, students are introduced to the concept of chance and the idea that different situations have different probabilities of occurring. They learn that for many situations, there are a finite number of different possible outcomes. However, at this stage, students are not expected to calculate the probability of events occurring. In Grade 5, students continue to build on their understanding of probability and may begin to learn more advanced concepts and techniques for calculating probabilities.
Step-by-step explanation:
B=(3,5,6,9) and C=(2,4,6,8) Find (A). A/B (B). B/C C. A/C (D). C/A
Answer:
The question isn't clear. Can you provide more information or context? What is A? Is it a set or a number? Without this information, I can't provide a meaningful answer.
Let p(x) = a1x^2 + b1x +c1 and q(x) = a2x^2 + b2x + c2 be polynomials in P2. Define an inner product in P2 as follows {p,q} = 5a1a2 + 4b1b2 + 3c1c2.
Given p(x) =5x^2 + (-1)x + (-3) and q(x) = 2x^2 + (4)x +(-3). Evaluate the following expressions
1. p(x) - q(x) = 3x^2 - 5x
2. {p - q, p-q} = 145
3. llp-qll = sqrt({p-q,p-q}) = sqrt(145)
For part 1, I know the answer and how to get it.
For part 2, I know the answer but I'm not sure how to get to it
Answer:
Step-by-step explanation:
To evaluate the expression {p - q, p - q}, which represents the inner product of the polynomial (p - q) with itself, you can follow these steps:
Given p(x) = 5x^2 - x - 3 and q(x) = 2x^2 + 4x - 3.
Subtract q(x) from p(x) to get (p - q):
(p - q)(x) = (5x^2 - x - 3) - (2x^2 + 4x - 3)
= 5x^2 - x - 3 - 2x^2 - 4x + 3
= (5x^2 - 2x^2) + (-x - 4x) + (-3 + 3)
= 3x^2 - 5x
Now, calculate the inner product of (p - q) with itself using the given inner product formula:
{p - q, p - q} = 5(a1)(a2) + 4(b1)(b2) + 3(c1)(c2)
= 5(3)(3) + 4(-5)(-5) + 3(0)(0)
= 45 + 100 + 0
= 145
Therefore, the value of {p - q, p - q} is 145.
please answer i am stuck
omari's monthly taxable income is ksh 24200. calculate the tax charged on omari's monthly earning
The tax charged on Omari's monthly earning of Ksh 24,200 is Ksh 3,340.
To calculate the tax charged on Omari's monthly earning, we need to consider the tax brackets and rates applicable in the specific tax system or country. Since you haven't specified a particular tax system, I will provide a general explanation.
Assuming we have a simplified progressive tax system with three tax brackets:
For the first tax bracket, let's say income up to Ksh 10,000 is taxed at a rate of 10%.
For the second tax bracket, income between Ksh 10,001 and Ksh 20,000 is taxed at a rate of 15%.
For the third tax bracket, income above Ksh 20,000 is taxed at a rate of 20%.
To calculate the tax charged on Omari's monthly earning of Ksh 24,200, we can divide it into the respective tax brackets:
Ksh 10,000 falls in the first tax bracket. So, the tax for this portion is 10% of Ksh 10,000, which is Ksh 1,000.
Ksh 20,000 - Ksh 10,000 = Ksh 10,000 falls in the second tax bracket. The tax for this portion is 15% of Ksh 10,000, which is Ksh 1,500.
The remaining amount, Ksh 24,200 - Ksh 20,000 = Ksh 4,200, falls in the third tax bracket. The tax for this portion is 20% of Ksh 4,200, which is Ksh 840.
Now, we can sum up the taxes for each bracket:
Total Tax = Tax in the first bracket + Tax in the second bracket + Tax in the third bracket
Total Tax = Ksh 1,000 + Ksh 1,500 + Ksh 840
Total Tax = Ksh 3,340
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please answer i am stuck
The correct answer choice is: A. The system has exactly one solution. The solution is (13, 5).
The correct answer choice is: A. all three countries had the same population of 5 thousand in the year 2013.
How to solve this system of equations and interpret the answer?Based on the information provided above, the population (y) in the year (x) of the counties listed are approximated by the following system of equations:
-x + 20y = 87
-x + 10y = 37
y = 5
where:
y is in thousands.x = 10 corresponds to 2010.By solving the system of equations simultaneously, we have the following solution:
-x + 20(5) = 87
x = 100 - 87
x = 13
-x + 10(5) = 37
x = 50 - 37
x = 13
Therefore, the system of equations has only one solution (13, 5).
For the year when the population are all the same for three countries, we have:
x = 2010 + (13 - 10)
x = 2013
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Suppose that an object is thrown upward from ground level with an initial velocity of 160ft/sec. Its height after t seconds is a function h given by h(t)=-16t^2 +160t.
a) Find an equivalent expression for h(t) by factoring out a common factor with a negative coefficient.
b) Check your factoring by evaluating both expressions for h(t) at t=1.
The factored expression is
a) The factored expression for h(t) is -16t(t - 10), obtained by factoring out a common factor of -16 and a common factor of t from the original expression -16t^2 + 160t.
b) Both the original expression -16t^2 + 160t and the factored expression -16t(t - 10) yield the same result of 144 when evaluated at t = 1, confirming the correctness of the factoring.
a) To factor out a common factor with a negative coefficient from the expression h(t) = [tex]-16t^2 + 160t[/tex], we can rewrite it as:
h(t) = [tex]-16(t^2 - 10t)[/tex]
Now, let's focus on factoring the quadratic expression inside the parentheses. We can factor out a common factor of t:
h(t) = -16t(t - 10)
Therefore, the factored expression for h(t) is -16t(t - 10).
b) To check the factoring by evaluating both expressions for h(t) at t = 1, we substitute t = 1 into the original expression and the factored expression and compare the results.
Using the original expression:
h(1) = [tex]-16(1)^2 + 160(1)[/tex]
h(1) = -16 + 160
h(1) = 144
Using the factored expression:
h(1) = -16(1)(1 - 10)
h(1) = -16(1)(-9)
h(1) = 144
Both expressions yield the same result of 144 when evaluated at t = 1. Therefore, the factoring is correct.
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labor-hours and its standard cost card per unit is as follows:
Direct material: $ pounds at $11.00 per pound
Direct labor: 3 hours at $12 per hour
Variable overhead: 3 hours at $7 per hour
Total standard variable cost per unit
The company also established the following cost formulas for its selling expenses:
sales salaries and commissions
shipping expenses
Fixed Cost per
Month
$ 280,000
$ 260,000
$ 55.00
36.00
$112.00
Variable
Cost per
Unit Sold
$ 20.00
$ 11.00
The planning budget for March was based on producing and selling 21,000 units. However, during March the company
actually produced and sold 26.600 units and incurred the following costs:
a Purchased 154.000 pounds of raw materials at a cost of $9.50 per pound. All of this material was used in production.
b. Direct laborers worked 63,000 hours at a rate of $13.00 per hour
e Total variable manufacturing overhead for the month was $510,930
d Total advertising sales salaries and commissions, and shipping expenses were $286,000, $495,000, and $195,000,
respectively
6 What direct labor cost would be included in the company's flexible budget for March?
The direct labor cost included in the Preble Company's flexible budget for March is $819,000.
How to compute Preble Company's direct labor cost?To find the direct labor cost included in the company's flexible budget for March, we shall estimate the actual direct labor cost incurred during the period.
Given:
Actual production and sales =n26,600 units
Actual direct labor rate = $13.00 per hour
Actual direct labor hours worked = 63,000 hours
Direct labor cost = Actual direct labor rate × Actual direct labor hours worked
Direct labor cost = $13.00/hour × 63,000 hours
Direct labor cost = $819,000
Hence, the direct labor cost included in the company's flexible budget for March would be $819,000.
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Find the exact value of cos 105⁰.
a. √√√2-√6
4
b.
√2+√6
4
C.
4
d. √2+√6
4
Answer:
[tex]\dfrac{\sqrt{2}-\sqrt{6} }{4} }[/tex]
Step-by-step explanation:
Find the exact value of cos(105°).
The method I am about to show you will allow you to complete this problem without a calculator. Although, memorizing the trigonometric identities and the unit circle is required.
We have,
[tex]\cos(105\°)[/tex]
Using the angle sum identity for cosine.
[tex]\boxed{\left\begin{array}{ccc}\text{\underline{Angle Sum Identity for Cosine}}\\\\\cos(A+B)=\cos(A)\cos(B)-\sin(A)\sin(B)\end{array}\right}[/tex]
Split the given angle, in degrees, into two angles. Preferably two angles we can recognize on the unit circle.
[tex]105\textdegree=45\textdegree+60\textdegree\\\\\\\therefore \cos(105\textdegree)=\cos(45\textdegree+60\textdegree)[/tex]
Now applying the identity.
[tex]\cos(45\textdegree+60\textdegree)\\\\\\\Longrightarrow \cos(45\textdegree+60\textdegree)=\cos(45\textdegree)\cos(60\textdegree)-\sin(45\textdegree)\sin(60\textdegree)[/tex]
Now utilizing the unit circle.
[tex]\boxed{\left\begin{array}{ccc}\text{\underline{From the Unit Circle:}}\\\\\cos(45\textdegree)=\dfrac{\sqrt{2} }{2}\\\\\cos(60\textdegree)=\dfrac{1}{2}\\\\\sin(45\textdegree)=\dfrac{\sqrt{2} }{2}\\\\\sin(60\textdegree)=\dfrac{\sqrt{3} }{2} \end{array}\right}[/tex]
[tex]\cos(45\textdegree)\cos(60\textdegree)-\sin(45\textdegree)\sin(60\textdegree)\\\\\\\Longrightarrow \Big(\dfrac{\sqrt{2} }{2}\Big)\Big(\dfrac{1 }{2}\Big)-\Big(\dfrac{\sqrt{2} }{2}\Big)(\dfrac{\sqrt{3} }{2}\Big)[/tex]
Now simplifying...
[tex]\Big(\dfrac{\sqrt{2} }{2}\Big)\Big(\dfrac{1 }{2}\Big)-\Big(\dfrac{\sqrt{2} }{2}\Big)(\dfrac{\sqrt{3} }{2}\Big)\\\\\\\Longrightarrow \Big(\dfrac{\sqrt{2} }{4} \Big)-\Big(\dfrac{\sqrt{6} }{4} \Big)\\\\\\\therefore \cos(105\textdegree)= \boxed{\boxed{\frac{\sqrt{2}-\sqrt{6} }{4} }}[/tex]
Which expression is equivalent to 10f - 5f + 8 +6g +4?
The given expression, 10f - 5f + 8 + 6g + 4, simplifies to 5f + 12 + 6g when like terms are combined.
To simplify the expression 10f - 5f + 8 + 6g + 4, we can combine like terms by adding or subtracting coefficients that have the same variables:
10f - 5f + 8 + 6g + 4
Combining the terms with 'f', we have:
(10f - 5f) + 8 + 6g + 4
This simplifies to:
5f + 8 + 6g + 4
Next, we can combine the constant terms:
8 + 4 = 12
Thus, the simplified expression is:
5f + 12 + 6g
This expression is equivalent to 10f - 5f + 8 + 6g + 4.
In summary, the expression 10f - 5f + 8 + 6g + 4 simplifies to 5f + 12 + 6g after combining like terms.
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what is five times five
Answer:
25
Step-by-step explanation:
5+5+5+5+5=25
Answer:25
Step-by-step explanation: