Answer:
- 14π/9; 108°; -√2/2; √2/2
Step-by-step explanation:
To convert from degrees to radians, use the unit multiplier [tex]\frac{\pi }{180}[/tex]
In equation form that will look like this:
- 280° × [tex]\frac{\pi }{180}[/tex]
Cross canceling out the degrees gives you only radians left, and simplifying the fraction to its simplest form we have [tex]-\frac{14\pi }{9}[/tex]
The second question uses the same unit multiplier, but this time the degrees are in the numerator since we want to cancel out the radians. That equation looks like this:
[tex]\frac{3\pi }{5}[/tex] × [tex]\frac{180}{\pi }[/tex]
Simplifying all of that and canceling out the radians gives you 108°.
The third one requires the reference angle of [tex]\frac{3\pi }{4}[/tex].
If you use the same method as above, we find that that angle in degrees is 135°. That angle is in QII and has a reference angle of 45 degrees. The Pythagorean triple for a 45-45-90 is (1, 1, √2). But the first "1" there is negative because x is negative in QII. So the cosine of this angle, side adjacent over hypotenuse, is [tex]-\frac{1}{\sqrt{2} }[/tex]
which rationalizes to [tex]-\frac{\sqrt{2} }{2}[/tex]
The sin of that angle is the side opposite the reference angle, 1, over the hypotenuse of the square root of 2 is, rationalized, [tex]\frac{\sqrt{2} }{2}[/tex]
And you're done!!!
Find the value of x.
Answer:
x = 5
Step-by-step explanation:
The sum of the side lengths shown is ...
(2x) + (3x +2) + (4x +1) = 9x +3
That is the perimeter of the inscribed triangle. That triangle is similar to triangle ABC by a scale factor of 1:2, so the perimeter of ΔABC is ...
2(9x +3) = 96 = 18x +6
90 = 18x . . . . subtract 6
90/18 = x = 5 . . . . . divide by the coefficient of x
What is the distance between the center and edge of a circle called
Answer: The radius
Step-by-step explanation:
The radius is the distance between the center point of the circle and a edge, it is half of the diameter which is the straight line passing through the center point.
Anna and Tamara have four suitcases. Anna's suitcases' weights are represented by x + 4 and 4x - 5. Tamara's suitcases' weights are represented by -3x + 2 and 2x + 4. Write an algebraic expression that represents the total weight of all the suitcases.
Answer:
4x + 5
Step-by-step explanation:
x + 4 + 4x - 5 - 3x + 2 + 2x + 4
= 4x + 5
The algebraic expression that represents the total weight of all the suitcases (Anna's and Tamara's) is 6x + 5.
To find the total weight of all the suitcases, we need to add the weights of Anna's four suitcases and Tamara's four suitcases.
Anna's suitcases' weights: x + 4 and 4x - 5
Tamara's suitcases' weights: -3x + 2 and 2x + 4
The total weight can be represented by the algebraic expression:
Total weight = (x + 4) + (4x - 5) + (-3x + 2) + (2x + 4)
Now, let's simplify the expression:
Total weight = x + 4x - 3x + 2x + 4 - 5 + 2 + 4
Total weight = 6x + 5
So, the algebraic expression that represents the total weight of all the suitcases is 6x + 5.
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Jenny bought a new car for $25,995. The value of the car depreciates by 16 percent each year. Which type of function could model the value of the car? A. Exponential B. Can't be determined C. Linear D. Quadratic
Answer:
an exponential function
Step-by-step explanation:
Use a function of the same form as the compound amount formula:
A = P(1+r)^5, where r is the appreciation or depreciation rate and P is the initial value. This is definitely an exponential function.
The given function could model the value of the car as an exponential function.
We have given that,
Jenny bought a new car for $25,995. The value of the car depreciates by 16 percent each year.
We have to determine which type of function could model the value of the car.
Use a function of the same form as the compound amount formula
A = P(1+r)^5,
where r is the appreciation or depreciation rate and P is the initial value. This is definitely an exponential function.
Therefore the given function could model the value of the car as an exponential function.
Therefore the option A is correct
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I NEED HELP FAST PLEASE!!! 21 points!!!
Solve -5(3 n + 4) = 40.
-4
-3
3
4
Answer:
The answer is -4.
Step-by-step explanation:
-5(3n+4)=40
-15n - 20 = 40
15n = 60
-4.
Identify the equation of the circle B with center B(4,−6) and radius 7. HELP ASAP!!
Answer:
(x − 4)2 + ( y + 6)2 = 49
Step-by-step explanation:
The equation of a circle with center (h, k) and radius r is (x − h)2 + (y − k)2 = r2.
Define h, k and r using the given values. So, h = 4, k = −6 and r = 7.
Substitute the values into the equation of a circle:
(x − 4)2 + (y − (−6))2 =72
Simplify.
(x − 4)2 + (y + 6)2 = 49
Therefore, the equation of the circle B with center B(4, -6) and radius 7 is (x − 4)2 + (y + 6)2 = 49.
The equation of the circle B with center B(4,−6) and radius 7 is[tex]\rm (x-4)^2+(y+6)^2=49[/tex], the corrcet option is B.
What is the equation of the circle?A circle can be represented as;
[tex]\rm (x-h)^2+(y-k)^2=r^2[/tex]
Where h and k are the centers of the circle and r is the radius of the circle.
The equation of circle B with center B(4,−6) and radius 7.
Substitute all the values in the equation
[tex]\rm (x-h)^2+(y-k)^2=r^2\\\\\rm (x-4)^2+(y-(-6))^2=7^2\\\\\rm (x-4)^2+(y+6)^2=49[/tex]
Hence the equation of circle B with center B(4,−6) and radius 7 is[tex]\rm (x-4)^2+(y+6)^2=49[/tex], the correct option is B.
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Write an equation of a line in slope-intercept form that is perpendicular to the line 2x -3y = 12 and passes through the point (2, 6).
For this case we have by definition, that the equation of a line in the slope-intersection form is given by:
[tex]y = mx + b[/tex]
Where:
m: It's the slope
b: It is the cutoff point with the y axis
We have the following line:
[tex]2x-3y = 12\\2x-12 = 3y\\y = \frac {2} {3} x-4[/tex]
If the line we wish to find is perpendicular to the one given, then its slope is given by:
[tex]m_ {2} = \frac {-1} {m_ {1}}\\m_ {2} = \frac {-1} {\frac {2} {3}}\\m_ {2} = - \frac {3} {2}[/tex]
Then the line is:
[tex]y = - \frac {3} {2} x + b[/tex]
We substitute the point:
[tex]6 = - \frac {3} {2} (2) + b\\6 = -3 + b\\b = 6 + 3\\b = 9[/tex]
Finally, the equation is:
[tex]y = - \frac {3} {2} x + 9[/tex]
Answer:
[tex]y = - \frac {3} {2} x + 9[/tex]
Please dont ignore, Need help!!! Use the law of sines/cosines to find..
Answer:
16. Angle C is approximately 13.0 degrees.
17. The length of segment BC is approximately 45.0.
18. Angle B is approximately 26.0 degrees.
15. The length of segment DF "e" is approximately 12.9.
Step-by-step explanation:
16By the law of sine, the sine of interior angles of a triangle are proportional to the length of the side opposite to that angle.
For triangle ABC:
[tex]\sin{A} = \sin{103\textdegree{}}[/tex],The opposite side of angle A [tex]a = BC = 26[/tex], The angle C is to be found, andThe length of the side opposite to angle C [tex]c = AB = 6[/tex].[tex]\displaystyle \frac{\sin{C}}{\sin{A}} = \frac{c}{a}[/tex].
[tex]\displaystyle \sin{C} = \frac{c}{a}\cdot \sin{A} = \frac{6}{26}\times \sin{103\textdegree}[/tex].
[tex]\displaystyle C = \sin^{-1}{(\sin{C}}) = \sin^{-1}{\left(\frac{c}{a}\cdot \sin{A}\right)} = \sin^{-1}{\left(\frac{6}{26}\times \sin{103\textdegree}}\right)} = 13.0\textdegree{}[/tex].
Note that the inverse sine function here [tex]\sin^{-1}()[/tex] is also known as arcsin.
17By the law of cosine,
[tex]c^{2} = a^{2} + b^{2} - 2\;a\cdot b\cdot \cos{C}[/tex],
where
[tex]a[/tex], [tex]b[/tex], and [tex]c[/tex] are the lengths of sides of triangle ABC, and[tex]\cos{C}[/tex] is the cosine of angle C.For triangle ABC:
[tex]b = 21[/tex],[tex]c = 30[/tex], The length of [tex]a[/tex] (segment BC) is to be found, andThe cosine of angle A is [tex]\cos{123\textdegree}[/tex].Therefore, replace C in the equation with A, and the law of cosine will become:
[tex]a^{2} = b^{2} + c^{2} - 2\;b\cdot c\cdot \cos{A}[/tex].
[tex]\displaystyle \begin{aligned}a &= \sqrt{b^{2} + c^{2} - 2\;b\cdot c\cdot \cos{A}}\\&=\sqrt{21^{2} + 30^{2} - 2\times 21\times 30 \times \cos{123\textdegree}}\\&=45.0 \end{aligned}[/tex].
18For triangle ABC:
[tex]a = 14[/tex],[tex]b = 9[/tex], [tex]c = 6[/tex], andAngle B is to be found.Start by finding the cosine of angle B. Apply the law of cosine.
[tex]b^{2} = a^{2} + c^{2} - 2\;a\cdot c\cdot \cos{B}[/tex].
[tex]\displaystyle \cos{B} = \frac{a^{2} + c^{2} - b^{2}}{2\;a\cdot c}[/tex].
[tex]\displaystyle B = \cos^{-1}{\left(\frac{a^{2} + c^{2} - b^{2}}{2\;a\cdot c}\right)} = \cos^{-1}{\left(\frac{14^{2} + 6^{2} - 9^{2}}{2\times 14\times 6}\right)} = 26.0\textdegree[/tex].
15For triangle DEF:
The length of segment DF is to be found, The length of segment EF is 9, The sine of angle E is [tex]\sin{64\textdegree}}[/tex], andThe sine of angle D is [tex]\sin{39\textdegree}[/tex].Apply the law of sine:
[tex]\displaystyle \frac{DF}{EF} = \frac{\sin{E}}{\sin{D}}[/tex]
[tex]\displaystyle DF = \frac{\sin{E}}{\sin{D}}\cdot EF = \frac{\sin{64\textdegree}}{39\textdegree} \times 9 = 12.9[/tex].
Your gross pay is $2,759.00. Your involuntary deductions are FICA (7.65%), federal withholding (12%), and state withholding (7%). How much are you allowed for housing and fixed expenses?
After calculating the total involuntary deductions for FICA, Federal withholding, and State withholding, we subtract this total from the gross pay to determine the amount available for housing and fixed expenses, which is $2023.63.
Explanation:To find out how much you are allowed for housing and fixed expenses, we first need to calculate the total involuntary deductions. This is done by applying the given percentages to the gross pay.
For the FICA it would be: $2759.00 * 7.65% = $211.16
Federal withholding would be: $2759.00 * 12% = $331.08
And for the State withholding: $2759.00 * 7% = $193.13
You'll then add all the deductions together: $211.16 + $331.08 + $193.13 = $735.37
The final step is to subtract the total deductions from the gross pay: $2759.00 - $735.37 = $2023.63
Hence, you are allowed $2023.63 for housing and fixed expenses.
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To calculate the amount allowed for housing and fixed expenses, subtract the involuntary deductions from the gross pay which is $2,023.19
Explanation:To calculate the amount allowed for housing and fixed expenses, we need to subtract the involuntary deductions from the gross pay. First, calculate the FICA deduction by multiplying the gross pay by 7.65% (0.0765). Next, calculate the federal withholding by multiplying the gross pay by 12% (0.12). Finally, calculate the state withholding by multiplying the gross pay by 7% (0.07). Subtract the sum of these deductions from the gross pay to find the amount allowed for housing and fixed expenses.
Gross pay: $2,759.00
FICA deduction: $2,759.00 x 0.0765 = $211.60
Federal withholding: $2,759.00 x 0.12 = $331.08
State withholding: $2,759.00 x 0.07 = $193.13
Amount allowed for housing and fixed expenses:
$2,759.00 - $211.60 - $331.08 - $193.13
= $2,023.19
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Planes S and R both intersect plane T .
Which statements are true based on the diagram? Check all that apply.
[A] Plane S contains points B and E.
[B] The line containing points A and B lies entirely in plane T.
[C] Line v intersects lines x and y at the same point.
[D] Line z intersects plane S at point C.
[E] Planes R and T intersect at line y.
False
As indicated in Figure A below, Plane S contains only point B (remarked in red). Point E (remarked in blue) lies on plane R.
[B] The line containing points A and B lies entirely in plane T.True
As indicated in Figure B below, the line containing points A and B lies entirely in plane T. That line has been remarked in red and it is obvious that lies on plane T.
[C] Line v intersects lines x and y at the same point.False
As indicated in Figure C below, line v intersects lines x and y, but line x in intersected at point B while line y (remarked in red) is intersected at point A (remarked in blue), and they are two different points, not the same.
[D] Line z intersects plane S at point C.True
As indicated in Figure D below, line z that has been remarked in yellow, intersects plane S at point C that has been remarked in blue.
[E] Planes R and T intersect at line y.True
As indicated in Figure E below, planes R and T intersect at line y. The line of intersection has been remarked in red.
The length of a rectangle is 6 1/2 inches and the width is 3 3/4 inches. What is the ratio, using whole numbers, of the length to the width?
Answer:The length is 13/2, while the width is 15/4, after combination. Ratio of length to width is then (13/2)/(15/4) = 26/15.
Please help ill give brainlist
Answer:
N⊥M
Step-by-step explanation:
If N║ P and P⊥M then N⊥M
Which situation results in the final value of zero? E the temperature after a decrease of 5°F from a temperature of -5°F. Be the height of an airplane after taking off from brown level and rising 1000 feet. See the amount of money received and change after making a $10 purchase with the $20 bill. D the distance above sea level after increasing 24 m after depth of 24 m below sea level.
Answer:
It's D.
Step-by-step explanation:
That would be D.
-24 + 24 = 0.
Answer:
The correct option is D) The distance above sea level after increasing 24 m after depth of 24 m below sea level.
Step-by-step explanation:
Consider the provided information.
We need to find Which situation results in the final value of zero.
Option A) E the temperature after a decrease of 5°F from a temperature of -5°F.
Decreasing means we need to subtract 5°F from the existing temperature.
E=-5°F-5°F=-10°F
Hence, now the temperature is -10°F.
Therefore, it is not the correct option.
Option B) The height of an airplane after taking off from ground level and rising 1000 feet.
If the airplane was at the ground level then we consider the height of the airplane was 0 feet above the ground.
After taking off it is rising 1000 feet above the ground level that means the overall rising is 1000 feet.
Therefore, it is not the correct option. As final value is not 0.
Option C) See the amount of money received and change after making a $10 purchase with the $20 bill.
If you purchase something which cost you $10 and you are purchasing it with the $20 bill.
The money you will received is: $20-$10=$10
Which is not 0.
Therefore, it is not the correct option.
Option D) The distance above sea level after increasing 24 m after depth of 24 m below sea level.
The previous position of the object was 24 m below sea level
It can be written as -24m as the distance is below sea level.
Now the object Increasing 24 m, therefore,
-24+24=0
Hence, the final value is zero.
Therefore, the correct option is D) The distance above sea level after increasing 24 m after depth of 24 m below sea level.
Determine the fourth term of the sequence defined by the formula:
t1=2a
t2=3a−1
Tn = 2tn−1−3tn−2+1,n ≥ 3
1
−9a+2
-1
−5a+4
Answer:
B. -9a+2
Step-by-step explanation:
You are given the sequence
[tex]t_1=2a,\\ \\t_2=3a-1,\dots\\ \\t_n=2t_{n-1}-3t_{n-2}+1,\ n\ge 3[/tex]
According to the given rule, find [tex]t_3,\ n=3[/tex]
[tex]t_3=2t_2-3t_1+1=2\cdot (3a-1)-3\cdot 2a+1=6a-2-6a+1=-1[/tex]
and [tex]t_4,\ n=4[/tex]
[tex]t_4=2t_3-3t_2+1=2\cdot (-1)-3(3a-1)+1=-2-9a+3+1=-9a+2[/tex]
Jan typically earns $575 per week. She has $172.50 withheld from her paycheck each week. What percent is being withheld from her paycheck? Type your answer as a percentage using the % symbol.
Answer:
30%
Step-by-step explanation:
What your problem is asking basically is how many percent is the withholding of her earnings each week. We just divide what is withheld by the earnings.
[tex]\dfrac{172.50}{575}=0.3[/tex]
Because we need it in percentage, we then multiply it by 100%.
0.30 x 100% = 30%
Answer:
30%
Step-by-step explanation:
For what value of x does (the equation is in the picture)
1
3
12
no solution
the answer is.... no solution
An equation is formed of two equal expressions. For the given equation 64³ˣ=512²ˣ⁺¹² no solution for x exists.
What is an equation?An equation is formed when two equal expressions are equated together with the help of an equal sign '='.
The above equation 64³ˣ=512²ˣ⁺¹² can be solved in the following manner as stated below,
64³ˣ = 512²ˣ⁺¹²
(8²)³ˣ=(8³)²ˣ⁺¹²
8⁶ˣ = 8⁽⁶ˣ⁺³⁶⁾
6x = 6x +36
6x - 6x = 36
0 = 36
As the value of x can not be defined, it can be concluded that the equation has no solution.
Hence, for the given equation no solution for x exists.
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What three digit number would need no ungrouping to subtract from?
Answer:
999
Step-by-step explanation:
Regrouping used to be called borrowing. Since no single column can have a digit larger than 9, then you would have the number 999 where you would never have to "borrow", or "regroup
Final answer:
A three-digit number that requires no ungrouping for subtraction should have each digit greater than the corresponding digit in the number being subtracted. For example, subtracting 234 from 453 requires no ungrouping because each digit in 453 is greater than the corresponding digit in 234.
Explanation:
The student's question pertains to the process of subtraction without requiring ungrouping, also known as regrouping or borrowing, when subtracting from a three-digit number. To avoid ungrouping, the number we subtract from should have each digit larger than the corresponding digit of the number being subtracted. For simplicity, let's consider subtracting a three-digit number of the form XYZ, where X, Y, and Z are individual digits. To ensure there's no need for ungrouping, the number from which we are subtracting should have each place value (hundreds, tens, and ones) greater than or equal to those in XYZ.
For example, if we take the number 453 and subtract 234 from it, no ungrouping is needed because 4 is greater than 2, 5 is greater than 3, and 3 is greater than 4. Hence, any three-digit number with digits greater than those of the subtrahend in the corresponding place values would satisfy the condition of needing no ungrouping to subtract from. By following this rule, the process of subtraction becomes straightforward without the complication of borrowing across place values.
Which of the following is an infinite series?
A. 4 + 8 + 16 + 32
B. 2 − 6 + 18 − 54 + . . .
C. 3, 13, 23, 33, . . .
D. 3, –6, 12, –24, 48
Given the recursive formula below, what are the first 4 terms of the sequence?
A. 17, –6, –3, 0
B. 17, 22, 39, 56
C. 17, 39, 105, 303
D. 17, 63, 201, 615
Answer:
for the first question it would be A. 4+8+16+32 because infinite series are such as :
9,18,36,72,144,288
10,20,40,80,160,
so basically its multiplying *2
I cant do #2 without seeing the formula
How would adding a score of 0 to this data affect the mean and median game scores - i ready lesson ......Choice of measures of center or variability
Answer:
I need to know the data to answer the question
Step-by-step explanation:
Adding a score of 0 to your data will lower both the mean and median, and could potentially increase the standard deviation and affect the percentile rankings.
Explanation:Adding a score of 0 to your data set will affect both the mean (average) and the median (middle value) of the scores. Thus, adding a zero will decrease the mean. The median is the middle score when all the scores are arranged in order. If you add a score that is lower than the current median score, the median will either stay the same or decrease, depending on the number of scores. If the number of scores is odd, the median will remain the same, if the number is even, the median will decrease.
The standard deviation is a measure of the variability or dispersion of a set of scores. If all values are the same, the standard deviation is zero. The standard deviation is small when the scores are close to the mean and larger when the scores vary more from the mean. Adding a score of zero could increase the standard deviation, depending on the other scores.
The percentiles in your data represent the value below which a given percent of data falls. Adding a score of 0 could potentially affect the percentile rankings of the other scores.
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Please help me with this
Answer:
Step-by-step explanation:
The formula for this is
x° = [tex]\frac{1}{2}[/tex](major arc - minor arc)
The measure around the outside of a circle is 360°. We have the minor arc as 120°. So the major arc is 360 - 120 = 240. Fitting that into the formula:
x° = [tex]\frac{1}{2}[/tex](240 - 120)
x° = [tex]\frac{1}{2}[/tex](120)
x° = 60
Jenna's packing company uses a machine to fill boxes of raisins. Due to a defect in the machine, the actual weight of the raisins packed differs by a maximum of 5 ounces from the desired weight of 15 ounces.
Select the correct inequality and number line that model the situation above.
Graphs in this order: B, C, D, E, A
Answer:
your answer is a
Step-by-step explanation:
The correct inequality and number line that model the situation above is:
10 ≤ weight of boxes ≤ 20
and the correct graph is: Graph A
Step-by-step explanation:The desired weight of raisins is: 15 ounces.
As the weight of the raisins packed differs by a maximum of 5 ounces.
This means that the weight of the raisins packed could either be less by 5 ounces or more by 5 ounces.
i.e. Weight of raisins could be minimum= 15-5=10 ounces.
and weight of raisins could be maximum= 15+5=20 ounces.
Hence, the inequality that will hold true is:
10 ≤ weight of boxes ≤ 20
and the graph that describe this situation is attached to the answer.
(30 points! I just need someone to correctly answer this, please.)
Graph the system of equations on graph paper to answer the question.
{y=1/3x−2 y=−3x−12
What is the solution for this system of equations?
Step-by-step explanation:
y = ⅓x − 2
y = -3x − 12
The first line has a y-intercept of -2 and a slope of ⅓.
The second line has a y-intercept of -12 and a slope of -3.
The graph looks like this: desmos.com/calculator/raouxrikbg
From the graph, we see they intersect at (-3, -3).
A cat is watching a bird in a tree nearby the tree is approximately 20 feet from the cat ground distance if the cats line of sight makes a 25 degrees with the ground when he has his eye on the bird how high up is bird in the tree
Answer:
X=20Tan(25)
Step-by-step explanation:
So because the cat is looking at the tree it is a strait line making a right triangle with the tree. The cat spots the bird 25 degrees up in the tree making a triangle. Then use SohCahToa, and because u have the adjacent side use Tangent because you are missing the opposite side of the angle. There are a few other ways to find it but that is the simplest way to perform this, GOOD LUCK!
Find cscx if sinx+cotx cosx= sqrt3
Answer:
The answer is (d) ⇒ cscx = √3
Step-by-step explanation:
∵ sinx + (cotx)(cosx) = √3
∵ sinx + (cosx/sinx)(cosx) = √3
∴ sinx + cos²x/sinx = √3
∵ cos²x = 1 - sin²x
∴ sinx + (1 - sin²x)/sinx = √3 ⇒ make L.C.M
∴ (sin²x + 1 - sin²x)/sinx = √3
∴ 1/sinx = √3
∵ 1/sinx = cscx
∴ cscx = √3
Answer:
d. [tex]\sqrt{3}[/tex]
Step-by-step explanation:
see attachment, it's correct :))
A square pyramid has a height h h and a base with side length b b . The side lengths of the base increase by 50%. Write a simplified expression that represents the volume of the new pyramid in terms of b b and h h . An expression is .
Answer:
the new pyramid in terms of b and h.
Step-by-step explanation:
the new pyramid
If C is the midpoint of KN what is KC?
A. 18
B. 4.5
C. 19
D. 9
Answer:
19
Step-by-step explanation:
If C is the midpoint of KN, then KC = CN
So we can equate the expressions
[tex]KC= 2x+10[/tex]
[tex]CN= 4x+1[/tex]
KC = CN
[tex]2x+10=4x+1[/tex]
Subtract 2x on both sides
[tex]2x-2x+10=4x-2x+1[/tex]
[tex]10=2x+1[/tex]
Subtract 1 on both sides
[tex]9=2x[/tex]
Divide both sides by 2
[tex]x=4.5[/tex]
Now we find out KC
[tex]KC= 2x+10[/tex]
[tex]KC= 2(4.5)+10[/tex]
[tex]KC= 19[/tex]
a) Using your equation from step 2d, estimate the GPA of a student who studies for 15 hours a week. Justify your answer. The equation is y=0.149x+0.89
Answer:
The predicted GPA is then y = 0.149(15) + 0.89 = 3.125
Step-by-step explanation:
Although you don't specifically say so, the equation you provide here is probably a "best fit" equation based upon data: GPA versus number of hours of study per week.
Here, y = 0.149x + 0.89 and the number of study hours of interest is 15.
The predicted GPA is then y = 0.149(15) + 0.89 = 3.125
The GPA is 3.125 who studies for 15 hours a week if the line of the best fit is y=0.149x+0.89
What is the line of best fit?A mathematical notion called the line of the best fit connects points spread throughout a graph. It's a type of linear regression that uses scatter data to figure out the best way to define the dots' relationship.
[tex]\rm m = \dfrac{n\sum xy-\sum x \sum y}{n\sum x^2 - (\sum x)^2}\\\\\rm c = \dfrac{\sum y -m \sum x}{n}[/tex]
We have a line of best fit:
y = 0.149x + 0.89
Plug x = 15 hours
y = 0.149(15) + 0.89
y = 3.125
Thus, the GPA is 3.125 who studies for 15 hours a week if the line of the best fit is y=0.149x+0.89
Learn more about the line of best fit here:
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The probability of drawing two red candies without replacement is 1335 , and the probability of drawing one red candy is 25 . What is the probability of drawing a second red candy, given that the first candy is red?
The probability would be 50 because 25+25=50
Yvonne is a salesperson who earns a fixed amount of $1,850 per month. She also earns a commission of 4% on the amount of goods that she sells. If she wants to earn more than $2,300 in one month, how many dollars (x) in goods must she sell?
Answer:
$11,250
Step-by-step explanation:
Yvonne earns a fixed amount of $1,850 per month and want to earn $2,300. The difference is
[tex]\$2,300-\$1,850=\$450.[/tex]
This difference is her commission. If she earns the commission of 4% on the amount of goods that she sells, then
$x - 100%
$450 - 4%
Make a proportion:
[tex]\dfrac{x}{450}=\dfrac{100}{4}\Rightarrow 4x=45,000\\ \\x=\dfrac{45,000}{4}\\ \\x=\$11,250[/tex]
Yvonne must sell $11,250
The graph of y=cosx is transformed to y=a cos (x−c)+d by a vertical compression by a factor of 1/3 and a translation 2 units down. The new equation is:
y=3cosx+2
y=1/3cos(x−2)
y=1/3cosx−2
y=1/3cosx+2
ANSWER
[tex]y = \frac{1}{3} \cos(x) - 2[/tex]
EXPLANATION
If the graph of y=cosx is transformed to y=a cos (x−c)+d by a vertical compression by a factor of 1/3 and a translation 2 units down,
then
a=1/3
and d=-2.
The 'c' is a phase shift since it is not given, it means it is zero.
Therefore the new equation is:
y=1/3cos(x-0)−2
This simplifies to:
y=1/3cosx−2
The correct option is C.
Answer:
The new equation is y = 1/3 cos(x) - 2 ⇒ 3rd answer
Step-by-step explanation:
* Lets revise the trigonometry transformation
- If the equation is y = a cos(x - c) + d
# a is the scale factor of a vertical stretch or compression
# c is the phase shift (negative is to the right, positive is to the left)
# d is the vertical shift
- If y = cos(x)
∴ a = 1 , c = 0 , d = 0
* Now lets solve the problem
∵ There is a vertical compression by a factor of 1/3
∴ a = 1/3
∵ There is a translation 2 units down (vertical translation)
∴ d = -2
∵ There is now phase shift (horizontal translation)
∴ c = 0
* Now lets write the new equation
∴ y = 1/3 cos(x) - 2
* For more understand look to the attached color graph
- The red is y = cos(x)
- The blue is y = 1/3 cos(x) - 2