Answer:
The passenger train is traveling at 45 mph, and the freight train is traveling at 27 mph.
Step-by-step explanation:
Let's assume the speed of the passenger train is represented by x mph.
According to the given information, the freight train leaves the depot 2 hours before the passenger train. Therefore, when the passenger train starts, the freight train has already been traveling for 2 hours.
Let's represent the speed of the freight train as (x - 18) mph, which is 18 mph slower than the passenger train.
Now, we know that the passenger train overtakes the freight train in 3 hours. This means that the passenger train traveled for 3 hours, while the freight train traveled for 3 + 2 = 5 hours.
Since speed = distance/time, we can set up the following equation based on the distances covered by each train:
Distance covered by passenger train = Distance covered by freight train
Using the formula, distance = speed × time, we get:
x × 3 = (x - 18) × 5
Simplifying the equation:
3x = 5x - 90
90 = 5x - 3x
90 = 2x
Dividing both sides by 2:
45 = x
So, the speed of the passenger train is 45 mph.
The speed of the freight train is 45 - 18 = 27 mph.
I need help solving these problems please.
Answer: i dont know what this is but i do believe its the second one
Step-by-step explanation:
Please help. Any unnecessary answers will be reported. Show your work.
King Arthur's Sword has a blade that is made of a regular hexagon and a regular pentagon. What is the amplitude of the tip of King Arthur's Sword?
The total amplitude of the tip of King Arthur's sword is s + [tex]\sqrt{3}[/tex]t/2.
Given that the length of the line segment connecting the centre of the regular hexagon to one of its vertices as the length of the line segment connecting centre of the regular pentagon to one of its vertices.
To find the amplitude by adding these two lengths.
For the regular hexagon, the distance from the centre to a vertex is equal to the radius of the circumscribed circle. The radius of the circumscribed circle is equal to length of a side.
Therefore, the amplitude of the hexagon is s.
For a regular pentagon, divide it into three triangles. One of these triangles is an isosceles triangle where the base is the side of the pentagon and the other two sides are radii of the circumscribed circle.
The amplitude of pentagon is the height of the isosceles triangle.
In an isosceles triangle, the height(h) is calculated from formula
h = [tex]\sqrt{3}[/tex]t/2.
Therefore, the amplitude of the pentagon is [tex]\sqrt{3}[/tex]t/2.
Hence, the total amplitude of the tip of King Arthur's sword is s + [tex]\sqrt{3}[/tex]t/2.
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Assumptions: Tax depreciation is straight-line over three years. Pre-tax salvage value is 25 in Year 3 and 50 if the asset is scrapped in Year 2. Tax on salvage value is 40% of the difference between salvage value and book value of the investment. The cost of capital is 20%.
Based on the given assumptions and calculations, the net present value (NPV) of the investment in the new piece of equipment is -$27,045.76, indicating that the investment is not favorable.
To calculate the after-tax cash flows for each year and evaluate the investment decision, let's use the following information:
Assumptions:
Tax depreciation is straight-line over five years.
Pre-tax salvage value is $10,000 in Year 5 and $15,000 if the asset is scrapped in Year 4.
Tax on salvage value is 30% of the difference between salvage value and book value of the investment.
The cost of capital is 12%.
Given:
Initial investment cost = $50,000
Useful life of the equipment = 5 years
To calculate the depreciation expense each year, we divide the initial investment by the useful life:
Depreciation expense per year = Initial investment / Useful life
Depreciation expense per year = $50,000 / 5 = $10,000
Now, let's calculate the book value at the end of each year:
Year 1:
Book value = Initial investment - Depreciation expense per year
Book value [tex]= $50,000 - $10,000 = $40,000[/tex]
Year 2:
Book value = Initial investment - (2 [tex]\times[/tex] Depreciation expense per year)
Book value [tex]= $50,000 - (2 \times$10,000) = $30,000[/tex]
Year 3:
Book value = Initial investment - (3 [tex]\times[/tex] Depreciation expense per year)
Book value = $50,000 - (3 [tex]\times[/tex] $10,000) = $20,000
Year 4:
Book value = Initial investment - (4 [tex]\times[/tex] Depreciation expense per year)
Book value [tex]= $50,000 - (4 \times $10,000) = $10,000[/tex]
Year 5:
Book value = Initial investment - (5 [tex]\times[/tex] Depreciation expense per year)
Book value [tex]= $50,000 - (5 \times $10,000) = $0[/tex]
Based on the assumptions, the salvage value is $10,000 in Year 5.
If the asset is scrapped in Year 4, the salvage value is $15,000.
To calculate the tax on salvage value, we need to find the difference between the salvage value and the book value and then multiply it by the tax rate:
Tax on salvage value = Tax rate [tex]\times[/tex] (Salvage value - Book value)
For Year 5:
Tax on salvage value[tex]= 0.30 \times ($10,000 - $0) = $3,000[/tex]
For Year 4 (if scrapped):
Tax on salvage value[tex]= 0.30 \times ($15,000 - $10,000) = $1,500[/tex]
Now, let's calculate the after-tax cash flows for each year:
Year 1:
After-tax cash flow = Depreciation expense per year - Tax on salvage value
After-tax cash flow = $10,000 - $0 = $10,000
Year 2:
After-tax cash flow = Salvage value - Tax on salvage value
After-tax cash flow = $0 - $0 = $0
Year 3:
After-tax cash flow = Salvage value - Tax on salvage value
After-tax cash flow = $0 - $0 = $0
Year 4 (if scrapped):
After-tax cash flow = Salvage value - Tax on salvage value
After-tax cash flow = $15,000 - $1,500 = $13,500
Year 5:
After-tax cash flow = Salvage value - Tax on salvage value
After-tax cash flow = $10,000 - $3,000 = $7,000
Now, let's calculate the net present value (NPV) using the cost of capital of 12%.
We will discount each year's after-tax cash flow to its present value using the formula:
[tex]PV = CF / (1 + r)^t[/tex]
Where:
PV = Present value
CF = Cash flow
r = Discount rate (cost of capital)
t = Time period (year)
NPV = PV Year 1 + PV Year 2 + PV Year 3 + PV Year 4 + PV Year 5 - Initial investment
Let's calculate the NPV:
PV Year 1 [tex]= $10,000 / (1 + 0.12)^1 = $8,928.57[/tex]
PV Year 2 [tex]= $0 / (1 + 0.12)^2 = $0[/tex]
PV Year 3 [tex]= $0 / (1 + 0.12)^3 = $0[/tex]
PV Year 4 [tex]= $13,500 / (1 + 0.12)^4 = $9,551.28[/tex]
PV Year 5 [tex]= $7,000 / (1 + 0.12)^5 = $4,474.39[/tex]
NPV = $8,928.57 + $0 + $0 + $9,551.28 + $4,474.39 - $50,000
NPV = $22,954.24 - $50,000
NPV = -$27,045.76
The NPV is negative, which means that based on the given assumptions and cost of capital, the investment in the new piece of equipment would result in a net loss.
Therefore, the investment may not be favorable.
Please note that the calculations above are based on the given assumptions, and additional factors or considerations specific to the business should also be taken into account when making investment decisions.
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The complete question may be like :
Assumptions: Tax depreciation is straight-line over five years. Pre-tax salvage value is $10,000 in Year 5 and $15,000 if the asset is scrapped in Year 4. Tax on salvage value is 30% of the difference between salvage value and book value of the investment. The cost of capital is 12%.
You are evaluating an investment in a new piece of equipment for your business. The initial investment cost is $50,000. The equipment is expected to have a useful life of five years.
Using the given assumptions, calculate the after-tax cash flows for each year and evaluate the investment decision by calculating the net present value (NPV) using the cost of capital of 12%.
helpppppppppppppppppoooo
The probability that a given student said math was their favorite subject was 3.44
The mathematical notion of probability measures the possibility of an event happening. A number between 0 and 1 is used to indicate it, with 0 denoting impossibility (the event won't happen) and 1 denoting certainty (the event will unquestionably happen). In probability theory, the probability of an event is determined based on a set of assumptions or information available. It is calculated by dividing the number of favorable outcomes by the total number of possible outcomes.
Here, the total outcome is 299 and favorable outcome is 87.
Hence, the probability is 299/87 = 3.44
Therefore, probability that a given student said math was their favorite subject was 3.44.
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50 Points! Multiple choice algebra question. Photo attached. Thank you!
Answer:
B. 3188.5 cubic inches.
Step-by-step explanation:
The volume of a cone is calculated using the following formula:
Volume = (1/3) * π * r² * h
Where:
π is the mathematical constant pi, approximately equal to 3.14.r is the radius of the base of the cone.h is the height of the cone.In this problem, we are given that r = 17 inches and S.h = 20 inches.
First we need to find height h.
py using Pythagorous theorem,we get
c²=a²+b²
here c= slight height and a is radius
20²=17²+b²
20²-17²=b²
111=b²
b=√(111)
Plugging these values into the formula, we get:
Volume = ⅓*π* 17² *√(111) = 3188.5 cubic inches
Therefore, the volume of the cone is 3188.5 cubic inches.
Need help solving this problem try to exclude steps if can
The transformed vertices are;
A'' => (-7, -1)
B'' => (-7, 4)
C''=> (-9,4)
D''=> (-9, -1)
Here, we have,
given that,
we have to translate by (x,y) => (x-5, y+4)
so, the rectangle will be transformed as;
the transformed vertices are;
A' => ( 4-5, 3+4) => (-1, 7)
B' => (9-5, 3+4) => (4,7)
C'=>(9 -5, 5 +4 ) => (4, 9)
D'=> (4 -5, 5+4 ) => (-1, 9)
now, For clockwise rotation of a triangle by 90 degree, then x coordinate is similar to the y coordinate of original point and y coordinate is negative times of x coordinate of original point.
So (x,y) changes to (-y,x).
the transformed vertices are;
A'' => ( 4-5, 3+4) => (-1, 7) => (-7, -1)
B'' => (9-5, 3+4) => (4,7) => (-7, 4)
C''=>(9 -5, 5 +4 ) => (4, 9) => (-9,4)
D''=> (4 -5, 5+4 ) => (-1, 9)=> (-9, -1)
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A group of students was asked to pick a favorite primary color. The results are shown in the table.
Red Green Blue Total Male 12 24 4 40 Female 15 30 5 50 Total 27 54 9 90
Question
Which statement correctly explains the association between being male and favoring the color blue?
Answer options with 5 options
A.
There is a negative association because the number of males who responded to the survey is less than the number of females.
B.
There is a negative association because the number of males who chose blue is less than the number of females who chose blue.
C.
There is a negative association because the number of males who chose blue is the smaller than the number of males who chose the other colors.
D.
There is no association because the percent of males who chose blue is equal to the percent of females that chose blue.
E.
There is no association because the percent of individuals who are male and chose blue is not equal to the percent of individuals who are female and chose blue.
The correct statement that explains the association between being male and favoring the color blue is:
B. There is a negative association because the number of males who chose blue is less than the number of females who chose blue.
In the given table, it can be observed that out of the total 90 students surveyed, 9 students (4 males and 5 females) decided the color blue as their favorite primary color. Since the number of males (4) who selected blue is less than the number of females (5) who chose blue, there is a negative association between being male and favoring the color blue.
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9. The table shows the results from a study in which some patients were treated with a new
medical drug for sleeping disorders and others received a common sleeping pill. Use a 0.05
significance level to find the critical value needed to test for independence between the type of
sleeping pill and the presence of any adverse health condition.
Adverse health
condition reported
No adverse health
condition reported
00.004
03.841
00.751
0.100.
New Sleeping Pill Common Sleeping Pill
135
132
145
122
(1 point)
The critical value of the chi-squared statistic with a significance level of 0.05 is 3.84. Therefore, the correct answer is option B.
The null hypothesis in this case would be that there is independence between the type of sleeping pill and the presence of any adverse health condition.
The critical value needed to test for this is the chi-squared statistic with a significance level of 0.05.
To calculate the critical value, we first need to calculate the degrees of freedom, which is calculated by (rows-1) * (columns-1). In this case, the degrees of freedom is (2-1)*(2-1) = 1.
The critical value of the chi-squared statistic with a significance level of 0.05 is 3.84. This means that if the calculated chi-squared statistic is greater than 3.84, then we can reject the null hypothesis and claim that there is a significant relationship between the type of sleeping pill and the presence of any adverse health condition.
Therefore, the critical value of the chi-squared statistic with a significance level of 0.05 is 3.84. Therefore, the correct answer is option B.
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Find the perimeter and area of the shaded figure below
The perimeter of shaded figure is 10 unit.
We know,
The perimeter of a figure is the total distance around its boundary. To calculate the perimeter, you need to sum the lengths of all the sides of the figure.
From the figure
length of rectangle = 4 unit
width of rectangle = 1 unit
Now, the perimeter of shaded figure
= 2 (l + w)
= 2 (4 +1 )
= 2 x 5
= 10 unit
Thus, the perimeter of figure is 10 unit.
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Martin's school is due west of his house and due south of his friend Hayley's house. The
distance between the school and Hayley's house is 12 kilometers and the straight-line
distance between Martin's house and Hayley's house is 13 kilometers. How far is Martin's
house from school?
The distance between Martin's house and the school is 5 kilometers.
How to solve for distanceTo find the distance between Martin's house and the school, we can use the Pythagorean theorem.
Let's represent the distance between Martin's house and the school as x kilometers.
According to the given information:
Distance between Martin's house and Hayley's house (hypotenuse) = 13 kilometers
Distance between the school and Hayley's house (one side of the right triangle) = 12 kilometers
Using the Pythagorean theorem, we have:
x[tex]x^2 + 12^2 = 13^2[/tex]
Simplifying the equation:
[tex]x^2 + 144 = 169x^2 = 169 - 144x^2 = 25[/tex]
Taking the square root of both sides:
x = √25
x = 5
Therefore, the distance between Martin's house and the school is 5 kilometers.
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Triglycerides are a type of fat in the bloodstream. The mean triglyceride level in the United States is 134 milligrams per deciliter. Assume the triglyceride levels of the population of the United States are normally distributed, with a standard deviation of 35 milligrams per deciliter. You randomly select a person from the United States. What is the probability that the person's triglyceride level is less than 80?
The probability that a aimlessly named person's triglyceride position is lower than 80 milligrams per deciliter is roughly0.0618 or6.18.
To calculate the probability that a aimlessly named person's triglyceride position is lower than 80 milligrams per deciliter, we can use the conception of standard normal distribution.
First, we need to regularize the value of 80 using the z- score formula z = ( x- μ)/ σ Where x = 80( the value we want to calculate the probability for) μ = 134( mean triglyceride position) σ = 35( standard divagation) Plugging in the values, we get z = ( 80- 134)/ 35 z = -54/ 35 z ≈-1.543
Next, we need to find the corresponding area under the standard normal distribution wind for a z- score of-1.543. We can use a standard normal distribution table or a calculator to find this area.
Looking up the z- score in the table or using a calculator, we find that the area to the left wing of z = -1.543 is roughly0.0618.
thus, the probability that a aimlessly named person's triglyceride position is lower than 80 milligrams per deciliter is roughly0.0618 or6.18.
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A set of data is represented in the stem plot below.
Stem plot with stems of 3, 4, 5, 6, 7, 8, 9. Leaf for stem of 3 is 5. Leaves for stem of 4 are 4, 5. Leaves for stem of 5 are 3, 6. Leaves for stem of 6 are 2, 5. Leaves for stem of 7 are 5, 5, 6. Leaves for stem of 8 are 2, 5. Leaf for stem of 9 is 2.
Key: 3 | 5 = 35
Part A: Find the mean of the data. Show each step of work. (2 points)
Part B: Find the median of the data. Explain how you determined the median. (2 points)
Part C: Find the mode of the data. Explain how you determined the mode. (2 points)
Part D: Compare your values for mean, median, and mode from parts A, B, and C. Which value would best represent the data, and why? Explain using complete sentences. (4 points)
In this dataset, the mean is approximately 65.77, the median is 65, and the mode is 5 and 75.
Part A: Finding the mean of the data:
To find the mean, we need to calculate the average of all the data points.
Step 1: Identify the stems and their corresponding leaves:
3 | 5
4 | 4, 5
5 | 3, 6
6 | 2, 5
7 | 5, 5, 6
8 | 2, 5
9 | 2
Step 2: Assign numerical values to each stem-leaf combination:
3 | 5 = 35
4 | 4 = 44, 5 = 45
5 | 3 = 53, 6 = 56
6 | 2 = 62, 5 = 65
7 | 5 = 75, 5 = 75, 6 = 76
8 | 2 = 82, 5 = 85
9 | 2 = 92
Step 3: Calculate the sum of all the numerical values:
35 + 44 + 45 + 53 + 56 + 62 + 65 + 75 + 75 + 76 + 82 + 85 + 92 = 855
Step 4: Determine the count of all the data points:
The count is the total number of data points, which can be determined by adding up the frequencies of each stem-leaf combination:
1 (stem 3) + 2 (stem 4) + 2 (stem 5) + 2 (stem 6) + 3 (stem 7) + 2 (stem 8) + 1 (stem 9) = 13
Step 5: Calculate the mean by dividing the sum of all values by the count:
Mean = Sum of all values / Count = 855 / 13 = 65.77 (rounded to two decimal places)
The mean of the data is approximately 65.77.
Part B: Finding the median of the data:
To determine the median, we need to arrange the data in ascending order and find the middle value.
Arranging the data in ascending order: 35, 44, 45, 53, 56, 62, 65, 75, 75, 76, 82, 85, 92
There are 13 data points, the median will be the value in the middle. In this case, the middle value is the 7th value, which is 65.
The median of the data is 65.
Part C: Finding the mode of the data:
The mode represents the value(s) that occur with the highest frequency.
From the stem-leaf plot, we can see that the leaves with the highest frequency are 5 and 75. Both of these frequencies occur twice.
The mode of the data is 5 and 75.
Part D: Comparing the mean, median, and mode:
In this dataset, the mean is approximately 65.77, the median is 65, and the mode is 5 and 75.
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find the unit vector of n=(4,-3)
The unit vector for n = (4, -3) is V = (4/5, -3/5)
How to find the unit vector for the given vector?An unit vector will be a vector that has the same direction than the given one, but a magnitude of 1 unit.
Then we can define the vector V = k*n
Where k > 0 is a real number, then the unit vector is:
V = (4k, -3k)
But notice that this must have a magnitude of 1, then:
1 = √( (4k)² + (-3k)²)
1 = √25k²
1 = 5k
1/5 = k
Then the unit vector is:
V = (4/5, -3/5)
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A refrigerator and 2 fans cost $1219. 2 refrigerators and 3 fans cost $2155. Find the cost of 1 refrigerator.
Answer:
$653
Step-by-step explanation:
:]
Let's use x to represent the cost of one refrigerator and y to represent the cost of one fan.
The equations become:
Equation 1: x + 2y = 1219
Equation 2: 2x + 3y = 2155
Using the same substitution method:
From Equation 1, we have:
x = 1219 - 2y
Substitute this expression for x in Equation 2:
2(1219 - 2y) + 3y = 2155
Simplify the equation:
2438 - 4y + 3y = 2155
-y = 2155 - 2438
-y = -283
===> y = 283
Now substitute the value of y back into Equation 1 to find x:
===> x + 2(283) = 1219
===> x + 566 = 1219
===> x = 1219 - 566
===> x = 653
Therefore, the cost of one refrigerator is $653.
An expression is shown. 2 + 2(x – 3) – 5x Which expression is equivalent to the expression shown? –3x – 4 –3x – 1 –x – 12 –x – 3
The other options provided, -3x - 1, -x - 12, and -x - 3, do not match the simplified form of the given expression. Only -3x - 4 corresponds to the original expression after simplification. It is important to carefully distribute and combine like terms to simplify expressions correctly.
The expression shown is 2 + 2(x – 3) – 5x. To find an equivalent expression, we need to distribute the 2 to both terms inside the parentheses, resulting in 2x - 6. Now we can simplify the expression further:
2 + 2x - 6 - 5x
Combining like terms, we have:
(2x - 5x) + (2 - 6)
This simplifies to:
-3x - 4
Hence, the expression -3x - 4 is equivalent to 2 + 2(x – 3) – 5x.
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the function g(x) is a transformation of the cube root parent function, f(x) = exponent 3 square root x, what function is g(x)?
The function g(x) in the context of this problem is given as follows:
A. [tex]g(x) = \sqrt[3]{x + 4} + 3[/tex]
What is a translation?A translation happens when either a figure or a function is moved horizontally or vertically on the coordinate plane.
The four translation rules for functions are defined as follows:
Translation left a units: f(x + a).Translation right a units: f(x - a).Translation up a units: f(x) + a.Translation down a units: f(x) - a.The parent function in this problem is given as follows:
[tex]f(x) = \sqrt[3]{x}[/tex]
The translated function was moved 4 units left and 3 units up, hence the function is defined as follows:
[tex]g(x) = \sqrt[3]{x + 4} + 3[/tex]
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What is the quotient of 5x³+2x2-6x-5 divided by x+2?
O 5x²-8x+10+ 25/(x+2)
O 5x²-8x+10-25/(x+2)
O 5x2+12x+18+ 31/(x+2)
O 5x²+12x+18 - 31/(x+2)
PLS HELP I BEG
The correct option is: 5x² - 8x + 10 - 25/(x + 2)
Given that we need to determine, what is the quotient of 5x³+2x2-6x-5 divided by x+2,
Long division can be used to determine the polynomial 5x³+2x2-6x-5 divided by x + 2.
Here is how to accomplish it:
5x² - 8x + 10
____________________
x + 2 | 5x³ + 2x² - 6x - 5
- (5x³ + 10x²)
_________________
-8x² - 6x
- (-8x² - 16x)
_______________
10x - 5
- (10x + 20)
___________
-25
The quotient is 5x² - 8x + 10, and the remainder is -25/(x + 2).
Therefore, the correct option is: 5x² - 8x + 10 - 25/(x + 2)
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Which expression is equal to x-9/x-4 + x^2-x+5/x-4
Answer: The expression can be simplified by combining the fractions with a common denominator:
(x - 9)/(x - 4) + (x^2 - x + 5)/(x - 4)
To add these fractions, we need to find a common denominator, which in this case is (x - 4). Therefore, we can rewrite each fraction with the common denominator:
[(x - 9) + (x^2 - x + 5)] / (x - 4)
Simplifying the numerator:
(x - 9 + x^2 - x + 5) / (x - 4)
Combining like terms:
(x^2 - 2x - 4) / (x - 4)
Hence, the simplified expression is (x^2 - 2x - 4) / (x - 4).
50 Points! Multiple choice geometry question. Photo attached. Thank you!
The equation of the parabola with the given focus (2, 7) and directrix y = -1 is [tex](x - 2)^2 = 12(y - 3)^2[/tex].Option C.
To find the equation of the parabola with a focus and directrix, we can use the standard form of the equation of a parabola:
For a vertical parabola:
[tex](x - h)^2 = 4p(y - k),[/tex]
where (h, k) is the vertex, and p is the distance from the vertex to the focus and directrix.
In this case, the focus is given as (2, 7), which means the vertex is also (2, 7) since the focus and vertex lie on the axis of symmetry. Additionally, the directrix is given as y = -1, which means the directrix is a horizontal line.
First, let's determine the distance from the vertex to the focus and directrix, which is the value of p. The distance is the absolute difference between the y-coordinate of the focus (7) and the y-coordinate of the directrix (-1):
p = |7 - (-1)| = 8.
Now we can substitute the values of the vertex (h, k) = (2, 7) and p = 8 into the standard form equation:
[tex](x - 2)^2 = 4(8)(y - 7).[/tex]
Simplifying further:
[tex](x - 2)^2 = 32(y - 7).[/tex]
Expanding the equation:
[tex]x^2 - 4x + 4 = 32y - 224.[/tex]
Rearranging the terms:
[tex]x^2 - 4x - 32y + 228 = 0.[/tex]
Therefore, the equation of the parabola with the given focus (2, 7) and directrix y = -1 is [tex](x - 2)^2 = 12(y - 3)^2.[/tex] SO Option C is correct.
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100 Points! Geometry question. Photo attached. Find the area of the figure. Round to the nearest tenth if necessary. Please show as much work as possible. Thank you!
Answer:
150 m²
Step-by-step explanation:
You want the total area of a figure consisting of a 12 m wide rectangle 5 m high with a triangle above that bringing the total height to 20 m.
Rectangle areaThe area of the rectangle is the product of its length and width:
A = LW
A = (12 m)(5 m) = 60 m²
Triangle areaThe area of the triangle is half the product of its base and height.
A = 1/2bh
A = 12/(12 m)(20 -5 m) = 90 m²
Total areaThe area of the whole figure is the sum of the areas of its parts:
total area = rectangle area + triangle area
total area = 60 m² +90 m² = 150 m²
The area of the figure is 150 m².
__
Additional comment
Since you know a triangle's area is equivalent to the area of a rectangle that has half the height, the 15 m high triangle can be considered as a rectangle 7.5 m high. Adding that to the 5 m area of the rectangle already there gives the equivalent area as that of a rectangle 12 m wide and 5+7.5 = 12.5 m high: (12 m)(12.5 m) = 150 m².
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pls answer this question, I don't understand it.
The two numbers could be 0.43× 10⁻⁵ and, 0.06× 10⁻³.
Here, we have,
given that,
the product of two number in scientific notation is: 0.0258 × 10⁻⁸
now, let the two numbers be:
0.43× 10⁻⁵ and, 0.06× 10⁻³
we get,
0.43× 10⁻⁵ × 0.06× 10⁻³
= 0.43 × 0.06× 10⁻⁵ × 10⁻³
= 0.43 × 0.06 × 10⁻⁵⁻³
=0.43 × 0.06× 10⁻⁸
=0.0258 × 10⁻⁸
Hence, The two numbers could be 0.43× 10⁻⁵ and, 0.06× 10⁻³.
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Use the space below to show your work.
45 points PLEASE HELP
The total number of each type of ball:
Football: Given as 8
Basketball: 18
Baseball: 40
Softball: 15
For basketball:
2 + 2(8) = 18
First, we evaluate the expression inside the parentheses: 2(8) = 16
Then, we add 2 to the result: 16 + 2 = 18
So, the total number of basketballs is 18.
For baseball:
5(8) = 40
We simply multiply 5 by 8 to get the total number of baseballs, which is 40.
For softball:
6 + 1/2(18) = 24
First, we evaluate the expression inside the parentheses: 1/2(18) = 9
Then, we add 6 to the result: 9 + 6 = 15
So, the total number of softballs is 15.
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The probability that a point chosen randomly inside the rectangle and is inside the Square or Trapezoid is 2/15.
We know that, probability of an event
= Number of favourable outcomes/Total number of outcomes.
Here, area of a rectangle = Length × Breadth
= 15×8
= 120 square units
Area of a triangle = 1/2 × Base × Height
= 1/2 ×(√10²-6²)×6
= 0.5×8×6
= 24 square units
Area of a trapezium = 1/2 (Sum of parallel sides)×Height
= 1/2 ×(5+7)×2
= 12 square units
Area of a square = side² = 2²
= 4 square units
(a) Probability of landing in trapezium or Square = 12/120 + 4/120
= 16/120
= 2/15
(b) Probability of landing inside the rectangle but outside the triangle = 16/120
= 2/15
Therefore, the probability that a point chosen randomly inside the rectangle and is inside the Square or Trapezoid is 2/15.
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the next 3 terms of 10,13,17,238
What is the exact length of HG in cms
The given triangle is a right angled triangle, therefore the rules of basic Trigonometry can be used here to find the solution.
Considering angle G, lets find sin 45°[tex]\qquad\displaystyle \tt \dashrightarrow \: \sin(45 \degree) = \frac{opposite \:\: side}{hypotenuse} [/tex]
[ sin 45° = 1/√2 ]
[tex]\qquad\displaystyle \tt \dashrightarrow \: \frac{1}{ \sqrt{2} } = \frac{b}{x} [/tex]
[tex]\qquad\displaystyle \tt \dashrightarrow \: x = b \sqrt{2} \: \: cm[/tex]
So, the side HG is b√2 cm long
Find the measure of each interior and exterior angle of a regular 30-gon
To find the measure of each interior and exterior angle of a regular 30-gon, we can use the formula:
Interior angle = (n - 2) * 180° / nExterior angle = 360° / nIn this case, we have a regular 30-gon, so n = 30.
Let's calculate the measures:
Interior angle = (30 - 2) * 180° / 30 = 28 * 180° / 30 = 168°Exterior angle = 360° / 30 = 12°Therefore, each interior angle of the regular 30-gon measures 168°, and each exterior angle measures 12°.
What is the meaning of "free variables"?
Free variables are variables used to represent parameters
What are free variables?Free variables are placeholders or symbols in mathematics and logic that are not constrained by any quantifiers or other specified conditions within an expression, formula, or equation.
When the expression is evaluated, they stand for values that can change or be given different values. In equations or functions, free variables are frequently employed to represent unknowns or parameters.
Free variables enable flexibility and generality in mathematical reasoning since they can be given various values to investigate various situations or solutions. In contrast, bound variables have a specific scope within a certain context or statement and are constrained by quantifiers.
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50 Points! Multiple choice geometry question. Photo attached. Thank you!
The total area of the quadrilateral DEFG is determined as 154 cm² .
option A.
What is the total area of the quadrilateral?The total area of the quadrilateral DEFG is calculated by applying the following method.
Consider triangle GDE in the quadrilateral;
base of the triangle = 16 cm
height of the triangle = 8 cm
Area of the triangle GDE = ¹/₂ x base x height
Area of the triangle GDE = ¹/₂ x 16 cm x 8 cm
Area of the triangle GDE = 64 cm²
Consider triangle GEF in the quadrilateral;
base of the triangle = 18 cm
height of the triangle = 10 cm
Area of the triangle GEF = ¹/₂ x base x height
Area of the triangle GEF = ¹/₂ x 18 cm x 10 cm
Area of the triangle GEF = 90 cm²
The total area of the quadrilateral DEFG is calculated as;
Area = 64 cm² + 90 cm²
Area = 154 cm²
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a. Prices at Store A are 21% higher than at Store B
i. If the price at store A was $583, what was the price at store B?
ii. If the price at store B was $1200, what was the price at store A?
b. If there were 11,000 members in 2020 and 12,500 in 2021, what was the percent increase?
The answers are given as:
Ai. The price at Store B would be $583 / 1.21 = $481.82
ii. The price at Store A would be $1200 * 1.21 = $1452.
b. The percent increase in membership from 2020 to 2021 is 13.64%
How to solveA.
i. If the price at Store A was $583, the price at Store B would be $583 / 1.21 = $481.82 (approximately).
ii. If the price at Store B was $1200, the price at Store A would be $1200 * 1.21 = $1452.
b. The percent increase in membership from 2020 to 2021 is ((12,500 - 11,000) / 11,000) * 100 = 13.64% (approximately).
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What is the radian measure of a 45 degree angle in a circle of radius 24 ft
To convert from degrees to radians, we use the conversion factor that 180 degrees is equal to π radians (or π/180 radians per degree).
Given that the angle is 45 degrees, we can calculate the radian measure as follows:
Radian measure = (45 degrees) * (π/180 radians per degree)
Radian measure = 45π/180
Simplifying further:
Radian measure = π/4
Therefore, the radian measure of a 45 degree angle is π/4.