the fraction with the lowest value is 1/12.
Company revenue quadratic function.
Angel
The revenue, in billions of dollars, for a company in the year 2002 was $2.7 billion. One year later, in 2003, the revenue had risen to $3.4 billion. In 2005, the revenue climbed to $3.9 billion, before falling to $2.7 billion in 2008. The revenue, r, in billions of dollars, for the company, is a quadratic function of the number of years since 2002, x. what is the vertex of the function?
To find the quadratic function that represents the revenue of the company as a function of the number of years since 2002, we can use the vertex form of a quadratic function:
r(x) = a(x - h)^2 + k
where a is the coefficient of the quadratic term, h is the x-coordinate of the vertex, and k is the y-coordinate of the vertex.
We can use the given revenue values to set up a system of three equations:
2.7 = a(0 - h)^2 + k
3.4 = a(1 - h)^2 + k
2.7 = a(6 - h)^2 + k
Subtracting the first equation from the second, and the first equation from the third, we get:
0.7 = a(1 - h)^2
0 = a(6 - h)^2
Since a cannot be zero (otherwise we wouldn't have a quadratic function), we can divide the second equation by the first to get:
6 - h = 10
which gives us h = -4.
Substituting h = -4 into the first equation, we get:
2.7 = a(0 - (-4))^2 + k
2.7 = 16a + k
Substituting the revenue value for 2005, we get:
3.9 = a(3 - (-4))^2 + k
3.9 = 49a + k
Solving for a and k, we get:
a = -0.1
k = 4.3
Therefore, the quadratic function that represents the revenue of the company as a function of the number of years since 2002 is:
r(x) = -0.1(x + 4)^2 + 4.3
The vertex of this function is at (-4, 4.3).
Angel
What is the sum of the numbers in the sequence 3, −4, 5, −6, . . . , 101?
We can notice that the sequence alternates between adding an odd number and subtracting an even number. The first term is 3, which is odd, so the sequence starts by adding an odd number. The second term is -4, which is even, so the sequence then subtracts an even number. This pattern continues, so the sum of the sequence can be written as:
3 - 4 + 5 - 6 + ... + 101
We can group the terms into pairs:
(3 - 4) + (5 - 6) + ... + (99 - 100) + 101
Each pair of terms adds up to -1, so we can simplify the expression to:
-1 -1 -1 ... -1 + 101
where there are 50 pairs of -1's. The sum of 50 -1's is -50, so the sum of the sequence is:
-50 + 101 = 51
Therefore, the sum of the numbers in the sequence 3, −4, 5, −6, . . . , 101 is 51.
Angel
What is 12 7/8 - 56/17?
To subtract mixed numbers like 12 7/8, we first need to convert it to an improper fraction. We can do this by multiplying the whole number by the denominator of the fraction, and adding the result to the numerator. This gives us:
12 7/8 = (12 × 8 + 7)/8 = 103/8
Now we can subtract 56/17 from 103/8. To do this, we need to find a common denominator for the two fractions. The least common multiple of 8 and 17 is 136, so we can rewrite the fractions with this denominator:
103/8 = (103/8) × (17/17) = 1751/136
56/17 = (56/17) × (8/8) = 448/136
Now we can subtract the two fractions:
1751/136 - 448/136 = (1751 - 448)/136 = 1303/136
We can simplify this fraction by finding a common factor to divide both the numerator and denominator. Since both 1303 and 136 are relatively prime, we cannot simplify it any further. Therefore, the final answer is:
12 7/8 - 56/17 = 1303/136
Angel
A circle in the xy-plane has a diameter with endpoints (2,4) and (2,14). An equation of this circle is (x-2)^2+(y-9)^2=r^2 ,where r is a positive constant. What is the value of r?
The center of the circle is the midpoint of the diameter, which is at (2, (4+14)/2) = (2, 9). We can substitute this center point into the equation of the circle to get:
(x - 2)^2 + (y - 9)^2 = r^2
(2 - 2)^2 + (9 - 9)^2 = r^2
0 + 0 = r^2
So we see that r = 0. Therefore, the equation of the circle is just:
(x - 2)^2 + (y - 9)^2 = 0
This describes a single point in the xy-plane, which is the center of the circle. Note that this point is already on the given diameter, so it makes sense that the radius is zero.
Angel
which number has which number has the lowest value? 1/6 1/3 - 1/9 1/3 - 1/6 1/4 - 1/6the lowest value?
To compare these fractions, we can first find a common denominator for all of them. The least common multiple of 2, 3, and 4 is 12, so we can rewrite the fractions with this denominator:
1/6 = 2/12
1/3 - 1/9 = (3/12) - (1/12) = 2/12
1/3 - 1/6 = (2/6) - (1/6) = 1/6
1/4 - 1/6 = (3/12) - (2/12) = 1/12
So the fractions can be ordered as follows, from least to greatest:
1/12 < 1/6 < 2/12 = 1/3 - 1/9 < 1/3 - 1/6
Therefore, the fraction with the lowest value is 1/12.
the eiffel tower is 300 m tall. when you are standing at a certain place in paris, it subtends an angle of 6. how far are you, then, from the eiffel tower?
The distance between the Eiffel tower and the location where the observer is standing is 2869.2929 meters.
Therefore, you are 2869.2929 meters away from the Eiffel tower.
The Eiffel Tower is 300m tall. If a person is standing at a certain location in Paris, the tower subtends an angle of 6 degrees. To calculate the distance from the Eiffel tower, trigonometry is used. Here's how you can calculate the distance between the Eiffel tower and the location you are standing in Paris;
Let AB be the height of the Eiffel Tower, which is 300 m.
Let AC be the distance between the observer and the base of the Eiffel Tower.
Let the angle of elevation at A be θ = 6 degrees.
Now, from the diagram, it is clear that;
Tan θ = AB/AC
Therefore, AC = AB/Tan θ
Substituting values, we get:
AC = 300/Tan 6 degrees
AC = 300/0.104528
AC = 2869.2929 meters.
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I need helppppppppp please help me
Find the exact values of the five remaining trigonometric functions of theta.
21. sec theta = √3, where sin theta 0
Answer:
The secant function is defined as the reciprocal of the cosine function. So if `sec(theta) = √3`, then `cos(theta) = 1/√3`. Since `sin^2(theta) + cos^2(theta) = 1`, we can solve for `sin(theta)`:
`sin^2(theta) + cos^2(theta) = 1`
`sin^2(theta) + (1/√3)^2 = 1`
`sin^2(theta) + 1/3 = 1`
`sin^2(theta) = 2/3`
`sin(theta) = ±√(2/3)`.
Since it is given that `sin theta > 0`, we can conclude that `sin(theta) = √(2/3)`.
Now that we have the values of sine and cosine, we can find the remaining trigonometric functions:
`tan(theta) = sin(theta)/cos(theta)`
`= (√(2/3)) / (1/√3)`
`= √(6)/3`
`cot(theta) = cos(theta)/sin(theta)`
`= (1/√3)/(√(2/3))`
`= √6 / 6`
`csc theta = 1/sin theta`
`= 1/(√(2/3))`
`= √6 / √4`
So, in summary:
- sec theta = √3
- cos theta = 1 / √3
- sin theta = √(2 / 3)
- tan theta = √6 / 3
- cot theta = √6 / 6
- csc theta = √6 / √4
Is there anything else you would like to know?
im giving brainliest to whoever gets it RIGHT
A patient has a choice between four different prescription plans through their health insurance. The options are:
Option A: $105 monthly premium with a $15 co-pay per prescription
Option B: $100 monthly premium with a $20 co-pay per prescription
Option C: $115 monthly premium with a $10 co-pay per prescription
Option D: $110 monthly premium with a $12 co-pay per prescription
Which option is the most expensive if the patient fills 7 prescriptions each month?
Option A
Option B
Option C
Option D
The most expensive health insurance plan for someone who fills 7 prescriptions each month is Option B, which has a total monthly cost of $240.
Explanation:To identify the most expensive health insurance plan, we need to calculate the total cost for each option per month. The total cost can be found by adding the monthly insurance premium to the product of the co-pay per prescription and the number of prescriptions per month.
Option A: Total cost = $105 (premium) + 7(prescriptions) x $15 (co-pay) = $210Option B: Total cost = $100 (premium) + 7(prescriptions) x $20 (co-pay) = $240Option C: Total cost = $115 (premium) + 7(prescriptions) x $10 (co-pay) = $185Option D: Total cost = $110 (premium) + 7(prescriptions) x $12 (co-pay) = $194From the calculations, Option B is the most expensive plan as it cost $240 per month.
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How can we help the park manager to draw a departure timetable
To make a departure timetable:
The simplest: download a predefined template from Microsoft Excel.
To create a template: select A1:E2 > Merge and Center > click WEEKLY SCHEDULE > select Center Alignment.
Add borders and titles. Type the time in A3. In A4 and A5, enter time > fill cell > add days > save template.
1. Start Excel and open a new blank workbook.
2. Select the range A1:E2 and on the Home tab, select Merge and Center in the Alignment group.
3.
Type "WEEKLY SCHEDULE" in A1:E2, change the font size to 18, and select Center Alignment in the Alignment group.
4. Select cells F1:H2, on the Home tab, in the Font group, select the Border drop-down menu, and then select All Borders.
5. Enter “Daily Start Time” into F1, “Time Interval” into G1, and “Start Date” into H1.
Select the Select All icon (between 1 and A on the worksheet), then double-click the line dividing two columns to resize all cells to fit the contents.
6. Select cell A3 and enter "TIME".
7. Select cell A4 and enter the time you want the program to start.
To follow this example, enter "7:00".
8. In cell A5, enter the next interval to be listed in the plan. To follow this example, enter "7:30". Select A4:A5 and drag the fill handle down to fill the time increment for the rest of the day.
9. In cell B3, enter the day of the week you want the schedule to start. To follow this example, enter "SUNDAY".
10. Drag the fill handle to the right to automatically fill the calendar with the remaining days of the week.
11. Select row 3. Make the font bold and change the font size to 14.
12. Change the hour font size in column A to 12.
13. Choose the Select All icon or press Ctrl+A and choose Center from the Alignment group on the Home tab.
14. Select cells A1:H2. In the Font group on the Home tab, select the Fill Color drop-down list and choose a fill color for the selected cells.
15. Select the body of the program. Select the Border drop-down menu in the Font group and select All Borders.
16. Save the program that we have made as time table.
Complete Question:
How can we help the park manager to draw a departure timetable in excel?
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Which linear equations have an infinite number of solutions? Check all that apply.
(x – 3\7) = 2\3 (3\2x – 9\14 )
8(x + 2) = 5x – 14
12. 3x – 18 = 3(–6 + 4. 1x)
1\2(6x + 10) = 7(3\7x – 2)
4. 2x – 3. 5 = 2. 1 (5x + 8)
the linear equations that have an infinite number of solutions are (x – 3/7) = 2/3 (3/2x – 9/14), 3x – 18 = 3(–6 + 4.1).
To determine which linear equations have an infinite number of solutions, we need to check if the equations are equivalent. Two linear equations are equivalent if they have the same slope and y-intercept, or if they represent the same line.
Let's check each of the given equations:
(x – 3/7) = 2/3 (3/2x – 9/14)
Multiplying both sides by 14, we get:
14x - 6 = 28/3x - 6
Multiplying both sides by 3, we get:
42x - 18 = 28x - 18
Subtracting 28x and adding 18 to both sides, we get:
14x = 0
Dividing both sides by 14, we get:
x = 0
Substituting x = 0 into the original equation, we get:
(-3/7) = (-9/14)
The left-hand side is equal to the right-hand side, which means the equation is true for all values of x. Therefore, this equation has an infinite number of solutions.
8(x + 2) = 5x – 14
Expanding the left-hand side, we get:
8x + 16 = 5x - 14
Subtracting 5x and subtracting 16 from both sides, we get:
3x = -30
Dividing both sides by 3, we get:
x = -10
Substituting x = -10 into the original equation, we get:
8(-8) = 5(-10) - 14
-64 = -64
The left-hand side is equal to the right-hand side, which means the equation is true for x = -10. Therefore, this equation has exactly one solution.
3x – 18 = 3(–6 + 4.1x)
Expanding the right-hand side, we get:
3x - 18 = -18 + 12.3x
Subtracting 3x and adding 18 to both sides, we get:
0 = 0.3x
Dividing both sides by 0.3, we get:
x = 0
Substituting x = 0 into the original equation, we get:
-18 = -18
The left-hand side is equal to the right-hand side, which means the equation is true for all values of x. Therefore, this equation has an infinite number of solutions.
1/2(6x + 10) = 7(3/7x – 2)
Expanding both sides, we get:
3x + 5 = 3x - 14
This equation simplifies to 5 = -14, which is not true for any value of x. Therefore, this equation has no solutions.
2x – 3.5 = 2.1(5x + 8)
Expanding the right-hand side, we get:
2x - 3.5 = 10.5x + 16.8
Subtracting 2x and adding 3.5 to both sides, we get:
0 = 8.5x + 20.3
This equation simplifies to 0 = 0, which is true for all values of x. Therefore, this equation has an infinite number of solutions.
Therefore, the linear equations that have an infinite number of solutions are (x – 3/7) = 2/3 (3/2x – 9/14), 3x – 18 = 3(–6 + 4.1).
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If a matrix A is 5 x 3 and the product AB is 5 x 7, what is the size of B?
Matrix Multiplication
Two matrices may be multiplied if and only if the first matrix has the same number of columns as there are rows in the second matrix. Suppose the first matrix has dimensions of a×b and the second matrix has dimensions of c×d, we can say that b=c and their product will have dimensions of a×d
Answer:
Matrix B is a 3 × 7 matrix.
Find the cross product a ⨯
b. A = 4, 5, 0 , b = 1, 0, 3 verify that it is orthogonal to both a and
b. (a ⨯
b. · a = (a ⨯
b. · b =
The cross product a ⨯b: A = 4, 5, 0 , b = 1, 0, 3
cross product {15, -12, -5}
dot products with 'a' and 'b': 0 and 0
For vectors a = {4, 5, 0} and b = {1, 0, 3}, you want the cross product and verification that the cross product is orthogonal to both 'a' and 'b'.
Cross product:
The cross product of 4i+5j+0k and 1i+0j+3k is the determinant :
[tex]\left[\begin{array}{ccc}i&j&k\\4&5&0\\1&0&3\end{array}\right][/tex]
= 15i - 12j -5k
As a list of coefficients, the cross product is c = {15, -12, -5}.
Orthogonal
Vectors are orthogonal if their dot product is 0.
a· c = {4, 5, 0}·{15, -12, -5} = (4·15) -(5·12) +(0·(-5)) = 60 -60 = 0
b· c = {1, 0, 3}·{15, -12, -5} = (1·15) +(0·(-12)) +(3·(-5)) = 15 -15 = 0
The dot products are both zero, so the cross product is orthogonal to both of the vectors that created it.
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help
im stuck on this question
Answer:
Step-by-step explanation:
Line A passes through (5,1) and (0,-2). So
gradient line A =[tex]=\frac{-2-1}{0-5} =\frac{3}{5}[/tex]
Since the lines are parallel they have equal gradients, so [tex]m=\frac{3}{5}[/tex].
The line passes through point P and so has y-intercept = 3 (so c=3).
So the equation of the new line is:
[tex]y=\frac{3}{5} x+3[/tex]
please solve question with explanation *TEST REVISION*
Answer:
x = - 2 [tex]\frac{1}{4}[/tex]
Step-by-step explanation:
10(5x + 12) = 2(5x + 15) Distribute the 10 and the 2
10(5x) + 10(12) = 2(5x) + 2(15)
50x + 120 = 10x + 30 Subtract 10x from both sides
50x - 10x +120 = 10x - 10x + 30
40x + 120 = 30 Subtract 120 from both sides
40x + 120 - 120 = 30 - 120
40x = -90 Divide both sides by 40
[tex]\frac{40x}{40}[/tex] = [tex]\frac{-90}{40}[/tex]
x = [tex]\frac{-9}{4}[/tex] or - 2[tex]\frac{1}{4}[/tex]
Helping in the name of Jesus.
simplify: |x-120| when x<-120
Answer: If x is less than -120, then x-120 will be less than zero, so we have:
|x-120| = -(x-120)
And since x is less than -120, we have:
|x-120| = -(x-120) = -x + 120
Therefore, the simplified expression for |x-120| when x<-120 is -x + 120.
Step-by-step explanation: I would reallyyyyyyyyyyyyyyyyy apreciate brainliest
I need some help better understanding Area Volume/Differential Equations, as ive been stuck on this single string of questions in my workbook for some time now, any and all help would be appreciated.
"Let R be the region in quadrant 1 bounded by y=3sin(2x) and y=e^x "
1) Find the area of R
2) Let S be the solid generated by rotating R around the x-axis. Find the volume of S.
3) Let Q be the solid generated by rotating R around the horizontal line y=5. Find the volume of Q
4) Let P be the solid whose base is R and whose cross sections perpendicular to the x-axis are semicircles. Find the volume of P.
Answer:
Refers to the attachment given below!
Step-by-step explanation:
If u have R125 in a box and remove half of the total for each day how long will it take for there to be only 25 cents
This gives a result of t = 10, meaning that it will take 10 days for the amount of money in the box to be reduced to 25 cents.
If there are R125 in a box and half of the total is removed each day, it will take 10 days to reduce the total to 25 cents. This is because the total amount is being halved each day, and the amount remaining at the end of each day is the amount left at the start of the day, divided by two. This can be expressed mathematically using the formula[tex]R125/(2^t)[/tex] = 25, where t is the number of days.If we solve the equation for t, we get t = log2(R125/25). This gives a result of t = 10, meaning that it will take 10 days for the amount of money in the box to be reduced to 25 cents.To calculate this process over the 10 days, we can use the formula [tex]R125/(2^t)[/tex] for each day, where t is the day number. Starting at day 0, the amount remaining would be R125. At the end of day 1, the amount remaining would be R125/2 = R62.50. At the end of day 2, the amount remaining would be R62.50/2 = R31.25. This process continues until at the end of day 10, the amount remaining would be R0.25.
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Apply the Cauchy-Goursat Theorem to show that Jc f(z) dz = 0 when the contour C is the unit circle with counterclockwise (positive) orientation, where (a) f(z) = ze-%, (b) f(2) (c) f(z) tan 2. 22 + 2 Let C1 be the positively oriented boundary of the square whose vertices lie On the lines I El and y = +l and Cz be the positively oriented circle |2| = 4. Explain why Jc f(2) dz Jc_ f(2) dz when + 2 (a) f(2) (6) f(2) (c) f(2) sin( 2/2)` Let C denote the positively oriented boundary of the square whose sides lie along I = 12 and y +2 Use a Cauchy Integral Formula (Generalised version Or not) to evaluate the following integrals: COS - dz cosh z d tan(2/2) d2 (6) (c) c 2 (22 (a) First show that for AnY real constant ( d= = 2t4. Using the parameterisation writo (ie integral in part (a) in terms of 0. Then with the aid of Euler icentitV lerive the formula 4C coska sin 0) d0 = x, Bonus: Use the following method to derive the integration formila (with b > OJ:
The Cauchy Integral Formula (Generalized version), we have: ∫C [tex]z^2[/tex] dz = ∫C[tex]z^2[/tex]/(z - 0) dz
To apply the Cauchy-Goursat Theorem, we need to check if the function f(z) is analytic inside the contour C, i.e., it should be differentiable everywhere inside C.
(a) Let f(z) =[tex]ze^(-z)[/tex]. Then, f(z) is entire, i.e., differentiable everywhere in the complex plane. Hence, it is analytic inside the unit circle C. Now, applying the Cauchy-Goursat Theorem, we have:
∮C f(z) dz = 0
(b) Let f(z) = 2. Since 2 is a constant, it is analytic everywhere in the complex plane. Hence, it is analytic inside the unit circle C. Now, applying the Cauchy-Goursat Theorem, we have:
∮C f(z) dz = f(0) × 2πi = 0 (since C does not enclose the origin)
(c) Let f(z) = z tan(2π/2). Since tan(2π/2) is not analytic at z = ±i, f(z) is not analytic inside the unit circle C. Hence, we cannot apply the Cauchy-Goursat Theorem directly to evaluate the integral ∮C f(z) dz.
To evaluate the integral ∮C f(z) dz, we can use the Cauchy Integral Formula (Generalized version) which states that for any analytic function f(z) and any closed contour C, we have:
∮C f(z)/(z - a) dz = 2πi f(a)
where a is any point inside the contour C.
For (a), let's use the Cauchy Integral Formula to evaluate the integral. We have:
f(z) = z[tex]e^{-z[/tex]
∮C f(z) dz = ∮C f(z)/(z - 0) dz (since f(0) = 0)
= 2πi f(0) = 0
For (b), we can use the Cauchy-Goursat Theorem as f(z) = 2 is analytic everywhere inside the circle |z| = 4. Hence, we have:
∮C2 dz = 2πi f(0) = 2πi × 2 = 4πi
For (c), we need to use the Cauchy Integral Formula to evaluate the integral. We have:
f(z) = z tan(π/2)
∮C f(z) dz = ∮C f(z)/(z - i) dz (since i is inside C)
= 2πi f(i) = 2πi × i × tan(π/2) = -2πi
Thus, we have:
∮C f(z) dz ≠ ∮C f(z) dz in general.
Now, let C be the positively oriented boundary of the square whose sides lie along x = ±2 and y = ±2.
(a) Using the Cauchy Integral Formula (Generalized version), we have:
∫C cos(z) dz = ∫C cos(z)/(z - π/2) dz
= 2πi cos(π/2) = 0
(b) Using the Cauchy Integral Formula (Generalized version), we have:
∫C cosh(z) dz = ∫C cosh(z)/(z - 0) dz
= 2πi cosh(0) = 2πi
(c) Using the Cauchy Integral Formula (Generalized version), we have:
∫C [tex]z^2[/tex]dz = ∫C [tex]z^2[/tex]/(z - 0) dz.
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In the 2021 football season, the Riverside Red Dragon's manager gathered the points scored by the team during the regular season games. The following data set shows the values collected by the manager.
{17, 0, 28, 17, 17, 20, 28, 11, 17, 22, 24, 33, 20, 31, 20, 3}
Which of the following stem-and-leaf plots correctly graphs the data set?
2021 Riverside Red Dragon Football Season Points
0 0 3
1 1 7 7 7 7
2 0 0 0 2 4 8 8
3 1 3
Key 1|1 = 11
2021 Riverside Red Dragon Football Season Points
0 0 3
1 1 7
2 0 2 4 8
3 1 3
Key 1|1 = 11
2021 Riverside Red Dragon Football Season Points
1 1 7
2 0 2 4 8
3 0 1 3
Key 1|1 = 11
2021 Riverside Red Dragon Football Season Points
1 1 7 7 7 7
2 0 0 0 2 4 8 8
3 0 1 3
Key 1|1 = 11
Each data point's ones digit is displayed in the second column, while its tens digit is displayed in the first column. Each "1|1" in the key denotes the value "11" in the data collection.
what is statistical data ?The term "statistical data" refers to numerical data that is gathered from a sample or population in order to characterise or draw conclusions about a larger group. Observational studies, surveys, experiments, and other techniques can all be used to gather statistical data, as can data from already-existing records and databases. Many approaches and methodologies, including data visualisation, inferential statistics, and descriptive statistics, can be used to examine statistical data. Measures of central tendency (mean, median, mode), indicators of dispersion (standard deviation, range, interquartile range), and graphical representations are some examples of the key characteristics of a dataset that are summarised and described using descriptive statistics (histograms, box plots, scatter plots). A bigger population can be inferred from a sample of data using inferential statistics, on the other hand.
given
The stem-and-leaf plot that depicts the data set accurately is as follows:
Season Points for the 2021 Riverside Red Dragon Football
0 0 3
1 1 7 7 7 7
2 0 0 0 2 4 8 8
3 1 3
Key 1|1 = 11
This stem-and-leaf plot depicts the frequency distribution of the data set in an accurate manner.
Each data point's ones digit is displayed in the second column, while its tens digit is displayed in the first column. Each "1|1" in the key denotes the value "11" in the data collection.
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A disk is shaped like a flat circular plate. Its radius is 4.25 inches. What is the area of 5/6 of the disk? Write your answer in terms of pi.
Answer:
5/6π(4.25 in)^2
Step-by-step explanation:
Step 1: Calculate the full area of the disk using the formula for the area of a circle: A = π × r2
A = π × (4.25 inches)2
A = 56.41π inches2
Step 2: Calculate 5/6 of the full area.
A = (5/6) × 56.41π inches2
A = 47.01π inches2
Therefore, the area of 5/6 of the disk is 47.01π inches2.
a card is drawn from a standard deck of 52 playing cards. what is the probability that the card will be a spade or a jack? express your answer as a fraction or a decimal number rounded to four decimal places.
A card is drawn from a standard deck of 52 playing cards. the probability that the card will be a spade or a jack is 17/52 or 0.3269 (rounded to four decimal places).
The total number of playing cards in a deck is 52. Out of these 52 playing cards, there are 4 suits, and each of these suits includes 13 cards.
Hence, there are 4 types of cards, and each of these types includes 13 cards. Therefore, there are 52/4 = 13 cards per type.A card is drawn from the deck of 52 playing cards.
The probability that it will be a spade or a jack is given below:
The probability of a spade card is 13/52 or 1/4, since there are 13 spade cards in the deck of 52 playing cards.
The probability of a jack card is 4/52 or 1/13, since there are 4 jacks in the deck of 52 playing cards.
Therefore, the probability that the card will be a spade or a jack is (13/52) + (4/52) = 17/52 or 0.3269 (rounded to four decimal places).
Thus, the probability that the card will be a spade or a jack is 17/52 or 0.3269 .
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errors-in-variables bias a. is only a problem in small samples. b. arises from error in the measurement of the dependent variable. c. arises from error in the measurement of the independent variable. d. is particularly severe when the source is an error in the measurement of the dependent variable.
Errors -in -variables bias represents the option c. arises from error in the measurement of the independent variable.
In a regression model Errors -in -variables bias is not only a problem in small samples.
It can affect large samples as well.
This can lead to biased estimates of the regression coefficients.
This can lead to biased and inconsistent estimates of the regression coefficients and standard errors.
Even if the error in the dependent variable is zero-mean.
Even if the measurement error in the dependent variable is negligible.
The problem is not limited to small samples.
And can be particularly severe when the measurement error in the independent variable is large.
Therefore, the errors -in - variables bias arises from the option c. arises from error in the measurement of the independent variable.
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Can you help me with this math problem?
Answer:
-1239/1961
Step-by-step explanation:
You want cos(A+B) given that tan(A) = 45/28 and cos(B) = 12/37.
Tangent formulasHere, we'll use the tangent relations ...
tan(A+B) = (tan(A) +tan(B))/(1 -tan(A)tan(B))tan(x)² +1 = sec(x)² = 1/cos(x)²ApplicationThe tangent of angle B can be found from ...
tan(B)² = 1/cos(B)² -1
tan(B)² = 1/(12/37)² -1 = 1225/144
tan(B) = 35/12
Now the tangent of the angle sum is ...
tan(A+B) = (tan(A) +tan(B))/(1 -tan(A)tan(B))
= (45/28 +35/12)/(1 -(45/28)(35/12)) = (95/21)/(1 -75/16) = -1520/1239
CosineNote that the tangent of this sum of two first-quadrant angles is negative. That means the result is a second-quadrant angle, so the cosine will also be negative.
cos(A+B) = -1/√(tan(A+B)² +1)
cos(A+B) = -1/√((1520/1239)² +1)
cos(A+B) = -1239/1961
__
Additional comment
Some calculators maintain enough internal accuracy that you can obtain the answer directly from ...
cos(arctan(45/28) +arccos(12/35))
The one shown in the attachment is not able to provide the ratio of integers equal to the floating point value it computes for this.
I need help with this ,can someone please answer it for me
Answer:
h=
[tex] \frac{15}{4} [/tex]
Step-by-step explanation:
Divide both sides by 8:
[tex]2 - 7 + 4h = \frac{80}{8} [/tex]
Divide 80 by 8 to get 10:
[tex]2 - 7 + 4h = 10[/tex]
subtract 7 from 2 to get -5:
[tex] - 5 + 4h = 10[/tex]
add 5 to both sides:
[tex]4h = 10 + 5[/tex]
Add 10 and 5 to get 15:
[tex]4h = 15[/tex]
divide both sides by 4.:
[tex]h = \frac{15}{4} [/tex]
Hopefully this helps! :)
(a) If a matrix A is 5 x 3 and the product AB is 5x7, what is the size of B?
If a matrix A is 5 x 3 and the product AB is 5x7, the size of B is 3x7.
The product of two matrices A and B, denoted as AB, is possible only if the number of columns of A is equal to the number of rows of B. In this case, A is 5x3, which means it has 3 columns.
And since the product AB is 5x7, it means the resulting matrix has 7 columns. Therefore, the number of columns of B must be equal to 7. And since A has 3 columns, the number of rows of B must be equal to 3 for the product to be possible.
Thus, the size of B is 3x7.
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A parabola opening up or down has vertex (0,– 5) and passes through (– 2,– 4). Write its equation in vertex form. Simplify any fractions. Y= Submit
The equation of the parabola in vertex form is: y = (1/4)x² - 5. We can calculate it in the following manner.
Since the parabola opens either up or down, its vertex form is given by:
y = a(x - h)² + k
where (h, k) is the vertex of the parabola and "a" is a constant that determines the direction and shape of the parabola.
Using the given vertex (0, -5), we have:
h = 0 and k = -5
Substituting the vertex coordinates into the vertex form, we get:
y = a(x - 0)² - 5
y = ax² - 5
To determine the value of "a", we use the given point (–2, –4) on the parabola. Substituting these coordinates into the equation, we get:
-4 = a(-2)² - 5
-4 = 4a - 5
1 = 4a
a = 1/4
Substituting this value of "a" into the equation for the parabola, we get:
y = (1/4)x² - 5
Therefore, the equation of the parabola in vertex form is:
y = (1/4)x² - 5
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6x1/2=
PLEASE HELP MEEEEEEEEEEEEEEE IT DO TOMORROW SO PLEASE I WILL GIVE U 10 POINTS!!!!!!!!!!!!!!!!!!
Answer:
3
Step-by-step explanation:
Please help i dont understand and i will mark brainliest please give a small explanation
Answer:
Step-by-step explanation:
To find the volume of a figure, you need to multiply the length, width, and height of the figure.
State what each variable may be so that the equation is true. You must have at least one negative number. Explain how you chose the values for a and b. 2^a • 2^b = 2^0
We can solve [tex]2^{a}[/tex] x[tex]2^{b}[/tex] = [tex]2^{0}[/tex] by recognizing that [tex]2^{0}[/tex]equals 1 and simplifying the equation to [tex]2^{a+b}[/tex] = 1.
EquationsTo solve [tex]2^{a}.2^{b}=2^{0}[/tex] for a and b, we must first recognize that 2^0 equals 1, which means that the equation can be rewritten as [tex]2^{a}.2^{b}=1[/tex]. Therefore, we can simplify the equation to [tex]2^{a+b}[/tex] = 1.
Since 2 raised to any negative power is a fraction, we need at least one of the exponents to be negative.
We could also choose other values that make either a or b negative, such as a = -2 and b = 2, or a = -3 and b = 3. The key is to have one negative exponent and one positive exponent so that their sum equals zero.
In summary, we can solve [tex]2^{a}.2^{b}=1[/tex]by recognizing that [tex]2^{0}[/tex] equals 1 and simplifying the equation to [tex]2^{a+b}[/tex] = 1. We must have at least one negative exponent to satisfy the equation, and we can choose various values for a and b as long as their sum equals zero.
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can someone answer this for me?
Answer:
B) x=12
Step-by-step explanation:
theres a 50/50 shot at getting heads, half of 24 is 12
Given sinA = 8\sqrt{73} and that angle
A is in Quadrant I, find the exact value of
tan tanA in simplest radical form using a rational denominator.
The value of [tex]$\tan A$[/tex] in its simplest radical form is [tex]8/3$.[/tex]
What is radical form?
Radical form refers to a mathematical expression that includes radicals, which are symbols that indicate a root of a number.
To find the value of [tex]$\tan A$[/tex], we first need to determine the value of [tex]\cos A$.[/tex]
Using the Pythagorean identity, we have:
[tex]$$\sin^2 A + \cos^2 A = 1$$[/tex]
Substituting the given value of [tex]$\sin A$[/tex], we get:
[tex]$$\left(\frac{8}{\sqrt{73}}\right)^2 + \cos^2 A = 1$$[/tex]
Simplifying the left-hand side, we get:
[tex]$\frac{64}{73} + \cos^2 A = 1$$$$\cos^2 A = \frac{9}{73}$$$$\cos A = \frac{3}{\sqrt{73}}$$[/tex]
Since angle [tex]$A$[/tex] is in the first quadrant, both [tex]$\sin A$[/tex] and [tex]$\cos A$[/tex] are positive.
Therefore, we have:
[tex]$$\tan A = \frac{\sin A}{\cos A} = \frac{8/\sqrt{73}}{3/\sqrt{73}} = \frac{8}{3}$$[/tex]
So the value of [tex]$\tan A$[/tex] in its simplest form is [tex]8/3$.[/tex]
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At the beginning of spring, Samuel planted a small sunflower in his backyard. The sunflower's height in inches,h,after w weeks, is given by the equation h=3.25w+19. What could the number 3.25 represent in the equation?
In equation h=3.25w+19, the number 3.25 represents the rate of change in the height of the sunflower per week (w), and the constant term of 19 represents the initial height of the sunflower when it was first planted.
The equation h=3.25w+19 is in slope-intercept form, which means that it can be written as y=mx+b, where y represents the dependent variable (in this case, the height of the sunflower), x represents the independent variable (the number of weeks since the sunflower was planted), m represents the slope of the line, and b represents the y-intercept (the value of y when x=0).
In this equation, the slope is 3.25, which means that for each additional week that passes since the sunflower was planted, its height increases by an average of 3.25 inches. So, the number 3.25 represents the rate of change of the height of the sunflower with respect to time.
This means that for every additional week that passes since the sunflower was planted, the height of the sunflower increases by 3.25 inches on average.
The equation also includes a constant term of 19, which represents the initial height of the sunflower when it was first planted, before any weeks had passed.
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Given: QS bisects PR at T, QR is parallel to PS. Prove PQRS is a parallelogram
The proof involves showing that the bisecting line QS and the parallel sides QR and PS create pairs of congruent angles, which then proves that opposite sides are parallel. Therefore, PQRS is a parallelogram.
Proof:
Since QS bisects PR at T, we know that PT = RT and QT = TS.
Also, QR is parallel to PS. Therefore, angle QTS is congruent to angle RPT (alternate interior angles).
Using the same reasoning, we can show that angle PST is congruent to angle QRP (alternate interior angles).
Now, we have two pairs of congruent angles in the quadrilateral PQRS, which means that the opposite sides are parallel.
Therefore, PQRS is a parallelogram.
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Write a system of equations to describe the situation below, solve using any method, and fill in the blanks.
Mario's Pizza just received two big orders from customers throwing parties. The first customer, Karen, bought 6 regular pizzas and 7 deluxe pizzas and paid $226. The second customer, Malik, ordered 6 regular pizzas and 9 deluxe pizzas, paying a total of $270. What is the price of each pizza?
Each regular pizza costs blank $, and each deluxe pizza costs blank$.
The system of equations given consisted of two equations, both of which represented the cost of the pizzas ordered by the two customers, Karen and Malik. each regular pizza costs $41 and each deluxe pizza costs $22.
System of equations:
6r + 7d = 226
6r + 9d = 270
Solving:
6r + 7d = 226
6r + 9d = 270
-6r -6r
7d -9d = -44
d = -44/2
d = -22
6r + (-22) = 226
6r = 248
r = 248/6
r = 41
Each regular pizza costs $41, and each deluxe pizza costs $22.
The system of equations given consisted of two equations, both of which represented the cost of the pizzas ordered by the two customers, Karen and Malik. To solve this system of equations, we first subtracted 6r from both equations, leaving us with 7d and -9d on one side. We then divided both sides by -2, leaving us with d = -22. We then added 22 to the other equation, leaving us with 6r = 248. Finally, we divided both sides by 6, leaving us with r = 41. Thus, each regular pizza costs $41 and each deluxe pizza costs $22.
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