12,480 es par y la suma de sus digitos da un multiplo de 3, por ello concluimos que es divisible por 6.
¿Como saber si un número es divisible por 6?Para que un número sea divisible por 6 debe cumplir dos condiciones.
Ser par.La suma de sus digitos debe ser multiplo de 3.En este caso tenemos 12,480, que sabemos que es par.
La suma de sus digitos da:
1 + 2 + 4 + 8 + 0 = 15
15 es multiplo de 3.
Entonces este número cumple ambas condiciones, por lo que concluimos que 12,480 es divisible por 6.
Sí quieres aprender más sobre divisiones.
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Mr. Gupta gave his students a quiz with three questions on it. Let
�
XX represent the number of questions that a randomly chosen student answered correctly. Here is the probability distribution of
�
XX along with summary statistics:
�
=
# correct
X=# correctX, equals, start text, \#, space, c, o, r, r, e, c, t, end text
0
00
1
11
2
22
3
33
�
(
�
)
P(X)P, left parenthesis, X, right parenthesis
0.05
0.050, point, 05
0.20
0.200, point, 20
0.50
0.500, point, 50
0.25
0.250, point, 25
Mean:
�
�
=
1.95
μ
X
=1.95mu, start subscript, X, end subscript, equals, 1, point, 95
Standard deviation:
�
�
≈
0.8
σ
X
≈0.8sigma, start subscript, X, end subscript, approximately equals, 0, point, 8
Mr. Gupta decides to score the tests by giving
10
1010 points for each correct question. He also plans to give every student
5
55 additional bonus points. Let
�
YY represent a random student's score.
What are the mean and standard deviation of
�
YY?
The mean score of a random student (YY) is 574.5. the standard deviation of the random student's score (YY) is 8.
How to answer the aforementioned questionGiven:
- Each correct question is worth 10 points.
- Every student receives an additional 555 bonus points.
Let's calculate the mean and standard deviation of YY:
Mean of YY:
The mean score, denoted as μY, can be calculated using the mean of XX (μX) and the scoring scheme:
μY = μX * 10 + 555
Substituting the value of μX from the given information:
μY = 1.95 * 10 + 555
μY = 19.5 + 555
μY = 574.5
Therefore, the mean score of a random student (YY) is 574.5.
Standard Deviation of YY:
The standard deviation of YY, denoted as σY, can be calculated using the standard deviation of XX (σX) and the scoring scheme:
σY = σX * 10
Substituting the value of σX from the given information:
σY = 0.8 * 10
σY = 8
Therefore, the standard deviation of the random student's score (YY) is 8.
Complete question: Mr. Gupta gave his students a quiz with three questions on it. Let X represent the number of questions
that a randomly chosen student answered correctly. Here is the probability distribution of X along with
summary statistics:
0
1
2
2.
3
X = # correct
P(X)
0.05
0.20
0.50
0.25
Mean: Hex = 1.95
Standard deviation: Ox 0.8
Mr. Gupta decides to score the tests by giving 10 points for each correct question. He also plans to give
every student 5 additional bonus points. Let Y represent a random student's score.
What are the mean and standard deviation of Y?
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Could someone help me with this? Thank you
The values for the determinants of the matrices are:
|A| = -3
|B| = -2
|AB|= -6
How to determine the determinant of A, |A|?A matrix (plural matrices) is a set of numbers arranged in rows and columns so as to form a rectangular array.
If the matrix Z is given as:
[tex]Z = \left[\begin{array}{ccc}a&b\\c&d\end{array}\right][/tex]
The determinant will be:
|Z| = (a * d) - (b * c)
Thus:
|A| = (-1 * 3) - (0 * 0) = -3
|B| = (2 * (-1)) - (0 * 0) = -2
AB = A * B
[tex]AB = \left[\begin{array}{ccc}-1&0\\0&3\end{array}\right] * \left[\begin{array}{ccc}-2&0\\0&-1\end{array}\right][/tex]
Calculations for the product (multiply each row by each column):
[-1 * (-2)] + [0 * 0] = 2
[-1 * 0] + [0 * (-1)] = 0
[0 * (-2)] + [3 * 0] = 0
[0 * 0] + [3 * (-1)] = -3
[tex]AB = \left[\begin{array}{ccc}2&0\\0&-3\end{array}\right][/tex]
Thus,
|AB| = (2 * (-3)) - (0 * 0) = -6
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The triangle below is isosceles. Find the length of side x to the nearest tenth.
Answer: x=15.6
Step-by-step explanation:
An isosceles triangle has two congruent sides. (1 pair). So, the other side (not x) must equal 11.
Using the Pythagorean Theorem; a^2+b^2=c^2, you can substitute the values in as follows
11^1+11^2=x^2
121+121=x^2
242=x^2
15.55634918610405=x
round to the nearest tenth as said in the question...
x=15.6
Please help I am struggling thank you, have a great day
Answer:
24
Step-by-step explanation:
For this problem, substitute the value -3 for x and solve. It would look like this:
[tex]4(-3)^2+2(-3)-6[/tex]
Using the order of operations (PEMDAS) we solve the exponent first.
[tex]-3^2=9[/tex]
Then solve the multiplication parts.
[tex]4(9)+2(-3)-6\\4*9=36[/tex]and [tex]2*(-3)=-6[/tex]
Finally subtract to get the answer.
[tex]36-6-6=24[/tex]
What is the x of 4(40)-10
Two factory plants are making TV panels. Yesterday, Plant A produced 6000 fewer panels than Plant B did. Five percent of the panels from Plant A and 2% of the panels from Plant B were defective. How many panels did Plant B produce, if the two plants together produced 820 defective panels?
Answer:
16000
Step-by-step explanation:
You want to know the number of panels produced at plant B if that was 6000 more panels than at plant A, and the total number of defective panels was 820. The defect rate at plant A is 5%, and at plant B is 2%.
SetupLet b represent the number of panels produced at plant B. Then the number produced at plant A is (b-6000). The total number of defects is ...
0.05(b -6000) +0.02b = 820
SolutionSimplifying the equation, we have ...
0.07b -300 = 820
0.07b = 1120
b = 16000
Plant B produced 16000 panels.
<95141404393>
Given: AB is parallel to BC
DC is parallel to BC
Angle 1 is congruent to Angle 2
Prove: AC is congruent to DB
Angles 1 and 2 are congruent and AB is parallel to DC, so by the Corresponding Angles Theorem, AC is congruent to DB.
Therefore, AC is congruent to DB.
How to explain the congruenceGiven: AB is parallel to BC
DC is parallel to BC
Angle 1 is congruent to Angle 2
Prove:
AC is congruent to DB
Proof: AB is parallel to BC and DC is parallel to BC.
Therefore, AB is parallel to DC.
Angle 1 is congruent to Angle 2.
Angles 1 and 2 are alternate interior angles, so they are congruent.
Angles 1 and 2 are congruent and AB is parallel to DC, so by the Corresponding Angles Theorem, AC is congruent to DB.
Therefore, AC is congruent to DB.
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How do I solve this help me pls now I need it pls I’ll give lots of points help me I put a picture here
The radius of cylinder is 31.5 cm.
We have,
LSA of Cylinder. = 693 cm²
Height = 11 cm
We know the formula
Lateral Surface Area of Cylinder = 2πrh
So, LSA of cylinder = 639π
2πh= 693π
2rh = 693
r = 693 / 2h
r =693 / 2 x 11
t = 63/2
r = 31.5 cm
Thus, the radius of cylinder is 31.5 cm.
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The point (2, 1) is the turning point of the graph with equation y = x² + ax + b,
where a and b are integers.
Find the values of a and b.
Optional working
+
a
b =
Step-by-step explanation:
This is a quadratic with vertex at (2,1) ....write the equation first in vertex form, then expand to the form requested
y = ( x -2)^2 + 1
y = x^2 -4x +4 + 1
y = x^2 -4x + 5 Done. a = -4 b = 5
Tyrell is traveling to Chicago, Illinois. He takes a cab service from the airport to his hotel. The table shows the linear relationship between the number of miles the cab travels, x, and the total fee, y.
Cab Fare
Number of Miles Total Fee
2 $13.00
5 $17.50
7 $20.50
10 $25.00
15 $32.50
What does the y-intercept mean in this situation?
For every additional mile the cab travels, the total fee increases by $10.00.
For every additional mile the cab travels, the total fee increases by $1.50.
When the cab travels 0 miles, the total fee will be $1.50.
When the cab travels 0 miles, the total fee will be $10.00.
Answer:
When the cab travels 0 miles, the total fee will be $10.00.
Step-by-step explanation:
We Know
2 miles = $13.00
5 miles = $17.50
3 miles = 17.50 - 13.00 = $4.50
1 mile = 4.50 / 3 = $1.50
So, for every 1-mile go, the cost is increasing by $1.50; this is the slope.
What does the y-intercept mean in this situation?
It is the total fee that Tyrell pays when the cab goes 0 miles (when he first steps in the cap).
So, the answer is D. When the cab travels 0 miles, the total fee will be $10.00.
50 POINTS!!!
Math...Money...Interest...
Please give the correct answers and show the steps. I will report your account if I find an error. Thank you for your help.
Answer:
2.
Quarterly:
100000 = 60000(1 + 0.075/4)^4tt ≈ 6.87466382 yearsMonthly:
100000 = 60000(1 + 0.075/12)^12tt ≈ 6.83227061 yearsContinuously:
100000 = 60000e^0.075tt ≈ 6.811008 years3.
Twice a year:
300 = 100(1 + 0.1025/2)^2tt ≈ 10.99053398 yearsEight times a year:
300 = 100(1 + 0.1025/8)^8tt ≈ 10.78668624 yearsContinuously:
300 = 100e^0.1025tt ≈ 10.718169 yearsStep-by-step explanation:
The formula for compound interest is:
A = P(1+r/n)^nt
The formula for compounded continuously is:
A = Pe^rt
Where:
A = the future value of the investment
P = the principal balance
r = the annual interest rate (decimal)
n = number of times interest is compounded per year
t = the time in years
Using that we can plug the formula in for each question:
2.
Quarterly:
100000 = 60000(1 + 0.075/4)^4tCompounded quarterly means in a year, it is compounded 4 timesNote that the question is asking to find how much time it takes so t is the thing we need to solve fort ≈ 6.87466382 yearsMonthly:
100000 = 60000(1 + 0.075/12)^12tt ≈ 6.83227061 yearsContinuously:
100000 = 60000e^0.075tWe are now using the compounded continuous formulat ≈ 6.811008 years3.
Twice a year:
Since the question does not give us a starting amount but it gives us a goal of tripling the money, we can substitute any amount of money for P and A as three times PFor now, let's say P is 100 and A is 3 times 100 so A is 300300 = 100(1 + 0.1025/2)^2tt ≈ 10.99053398 yearsEight times a year:
We will continue to place hold P as 100 and A as 300300 = 100(1 + 0.1025/8)^8tt ≈ 10.78668624 yearsContinuously:
We will now use the compounded continuous formula300 = 100e^0.1025tt ≈ 10.718169 yearsSuppose theta is an angle in the third quadrant and cos theta = 5/7. What is the value of sin(theta)
3√8
√24
24
2√12
The value of sinθ is √24/7 meanwhile the correct answer is not in the option provided or perhaps option (b) is meant to be √24/7 instead.
Understanding Quadrant in TrigonometryIn the third quadrant, both the x-coordinate (cosine) and the y-coordinate (sine) of the angle are negative.
Given that
cosθ = 5/7
we can determine the value of sinθ using the Pythagorean identity:
sin²θ + cos²θ = 1
sin²θ + (5/7)² = 1
sin²θ + 25/49 = 1
Now, let's solve for sinθ:
sin²θ = 1 - 25/49
sin²θ = 49/49 - 25/49
sin²θ = 24/49
Taking the square root of both sides, we find:
sinθ = √(24/49)
Simplifying further:
sinθ = √24 / √49
sinθ = √24 / 7
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Rhett made a simple drawing of his house. It is a three dimensional figure with four faces that are rectangular and two that are square what kind of figure is it?
Rhett's house is a rectangular prism
Given data ,
Let the figure be represented as A
Now , the value of A is
Rhett made a simple drawing of his house.
And , It is a three dimensional figure with four faces that are rectangular and two that are square
So , the figure is represented as a rectangular prism
A three-dimensional solid object called a prism has two identical ends. It consists of equal cross-sections, flat faces, and identical bases. Without bases, the prism's faces are parallelograms or rectangles.
Hence , the figure is rectangular prism
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Carter is going to invest in an account paying an interest rate of 4.3% compounded daily. How much would Carter need to invest, to the nearest ten dollars, for the value of the account to reach $174,000 in 19 years?
Carter would need to invest approximately $76,869.06 to reach a value of $174,000 in 19 years with a 4.3% annual interest rate compounded daily.
What is the principal that needs to be invested?The formula accrued amount in a compounded interest is expressed as;
[tex]A = P( 1 + \frac{r}{n})^{(nt)}[/tex]
Where A is accrued amount, P is principal, r is interest rate and t is time.
Given that:
Accrued amount A = $174,000
Compounded daily n = 365
Time t = 19 years
Interest rate r = 4.3%
Principal P = ?
First, convert R as a percent to r as a decimal
r = R/100
r = 4.3/100
r = 0.043
Plug these values into the above formula and solve for principal P.
[tex]A = P( 1 + \frac{r}{n})^{(nt)}\\\\A = 174,000( 1 + \frac{0.043}{365})^{(365\ *\ 19)}\\\\A = \$ 76,869.06[/tex]
Therefore, the principal that needs to invested is $76,869.06.
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6 sin =5 solve to the nearest 0.1
Step-by-step explanation:
sin Φ = 5/6 = .8333
Arcsin ( sin Φ) = arcsin (.8333)
Φ = 56.4 degrees
A bag consists of 5 marbles. There is 1 yellow, 1 red marble, 1 clear marble, 1 green marble, and 1 blue marble. Which table shows the sample space for choosing 2 marbles from the bag with replacement? Answer by looking at the images below!
Table C shows the sample space for choosing 2 marbles from the bag with replacement. The probabity and there are 25 possible pairs.
The sample space for choosing 2 marbles from the bag with replacement consists of all possible pairs of marbles that can be chosen, where the order in which they are chosen does not matter.
Since there are 5 marbles in the bag and we are choosing 2 of them, there are 5 choices for the first marble and 5 choices for the second marble, for a total of [tex]5*5 = 25[/tex] possible pairs.
Table C shows the sample space for choosing 2 marbles from the bag with replacement. Each row and column in the table represents a different marble that can be chosen, and each cell represents a pair of marbles that can be chosen.
For example, the cell in row 2 and column 3 represents the pair of marbles consisting of the red marble and the clear marble. Tables A and B show the sample space for choosing 2 marbles from the bag without replacement. In this case, the order in which the marbles are chosen does matter, and each marble can only be chosen once.
Therefore, there are only 5 choices for the first marble, but only 4 choices for the second marble (since one marble has already been chosen), for a total of[tex]5 * 4 = 20[/tex] possible pairs.
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The complete question is:
A bag contains five green marbles, three blue marbles, two red marbles, and two yellow marbles. One marble is drawn out randomly.
a) Are the four different colour outcomes equally likely? Explain.
b) Find the probability of drawing each colour marble i.e., P(green), P(blue), P(red) and P(yellow)
c) Find the sum of their probabilities.
You are given a map with a number scale 1:60 you must measure a length on the map of 10cm
The measure of a length of 10cm on the scale is 1/6 units
How to determine the measure of a length on the map of 10cmFrom the question, we have the following parameters that can be used in our computation:
Scale = 1 : 60
For a length of 10 cm, we have
Actual length = 10 cm
This means that
Scale ; 10 cm = 1 : 60
Express as fraction
So, we have
Scale/10 cm = 1/60
When evaluated we have
Scale = 1/6 units
Hence, the measure of a length of 10cm on the scale is 1/6 units
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During the repair, the mechanics will need to
connect a cable between chairs B and J, and then
continue that cable to chair G. What is the angle
formed by the cable?
The angle formed by the cable between chairs B and J, and then
continue chair G is
75 degrees
How to determine the angleThe angle is determined with the knowledge of the total angle in a circle which is 360 degrees. Also, intercepted arc = 2 * inscribed angle
Assuming each chair is equal distance apart, then they will subtend equal angle.
The number of chairs for A to L is 12
angle per chair = 360 / 12 = 30 degrees
number of chairs from B to G = 5 and angle intercepted arc = 30 * 5 = 150 degrees
Inscribed angle = 1/2 * intercepted arc
Inscribed angle = 1/2 * 150
Inscribed angle = 75 degrees
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Find the area of the following figure. Round to the nearest hundred if necessary.
14 m
9.5 m
17 m
The area of the given figure is 133 m²
Given is quadrilateral with sides 17m and 9.5m with height of 14m we need to find its area,
The given quadrilateral is a parallelogram, we know that area of the parallelogram is = base x height
Therefore,
The area of the given figure = 9.5 x 14 = 133
Hence, the area of the given figure is 133 m²
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100 Points! Geometry question. Photo attached. Determine whether the pair of triangles is similar. If so, write a similarity statement. If not, what would be sufficient to prove the triangles similar? Explain your reasoning. Please show as much work as possible. Thank you!
Answer:
∆SMK is similar to ∆RMT by AA.
18/5 divided by 3/25 in simplest form
Answer: 30
Step-by-step explanation:
18/5 divided by 3/25 is the same thing as multiplying 18/5 with the reciprocal of 3/25 (25/3).
[tex]\frac{18}{5} *\frac{25}{3} =\frac{450}{15}[/tex]
And when multiplying out you get 450/15.
Simplifying (by dividing 450 by 15) this you will get 30.
- Find the surface area.
40 feet
18 feet
16 feet
Tom is ordering 5 bags of cat food from Canada. Each bag has a mass of 6 kg . To determine the shipping costs, Tom needs to know the total weight in pounds. What is the weight of the cat food in pounds? Use 1kg= 2.2 lb and do not round any computations.
Answer:
6* 2.2lb = 13.2 lb
Step-by-step explanation:
If 1 bag weights 2.2lb than 6 bags will weight 6 times more or:
2.2 lb * 6 = 13.2 lb
We can use the provided conversion factor, which states that 1 kg is equal to 2.2 pounds, to determine the weight of the cat food in pounds.
Since each bag of cat food weighs 6 kg, we can calculate the weight of 5 bags as follows.
5 bags of 6 kg each equal the total weight = 30 kg.
Now, we can convert the total weight from kilograms to pounds using the conversion factor:
Total weight multiplied by the conversion factor equals total weight in pounds.
= 30 kg x 0.2 lb/kg.
= 66 lbs.
Consequently, the cat food has a 66-pound weight when measured in pounds.
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100 Points! Geometry question. Photo attached. Please show as much work as possible. Thank you!
Answer: 127
Step-by-step explanation:
360 - 70 - 36 = 254
254/2 = 127
D = 127
of tennis balls is shaped like a cylinder with the dimensions shown
r= 4 cm
What is the approximate surface area of the can? Use 3.14 for. Use the formula for the surface area of a cylinder SA= 2mth + 2rr²
527 cm²
100 cm²
628 cm²
525 cm²
21 cm
Previous
Next >
The formula for the surface area of a cylinder SA= 2mth + 2rr² is 525 cm².
To find the surface area of the cylindrical can, we need to use the formula:
SA = 2π[tex]r^2[/tex]+ 2πrh
where r is the radius of the circular base of the can, h is the height of the can, and π is a mathematical constant approximately equal to 3.14.
From the given dimensions, we know that the radius of the can is 4 cm. However, we do not have the height of the can. Therefore, we cannot accurately calculate the surface area of the can.
Based on the answer choices provided, we can approximate the surface area of the can by using the given value of r = 4 cm and an estimated value for the height.
For example, if we assume the height of the can is approximately 10 cm, then we can use the formula to calculate the surface area:
SA = 2π([tex]4^2[/tex]) + 2π(4)(10)
SA = 100.48 + 251.2
SA ≈ 351.68 [tex]cm^2[/tex]
≈525 cm²
This value is closest to the fourth answer choice of 350 [tex]cm^2[/tex]. However, it is important to note that this answer is an approximation based on estimated values, and may not be entirely accurate.The correct answer is 525 cm².
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Kyle's current credit card balance is $3,109.87 with a minimum payment of $159.00. Over the next month he spends $532.42. If the APR is 27.99% (billed monthly), what will Kyle's new balance be, with interest? (4 points) $3,404.65 $3,564.54 $3,606.84 $3,789.03
Answer:
(b) $3564.54
Step-by-step explanation:
You want the new balance showing on a credit card statement if the APR is 27.99%, the old balance is $3109.87, a payment of $159 was made, and purchases were made totaling $532.42.
SubtotalApparently, the new balance is computed by subtracting payments, and adding new charges to the old balance, then computing and adding the finance charge on this sum.
balance before finance charge: $3109.87 -159.00 +532.42 = $3483.29
Finance chargeThe finance charge is 1 month's interest at the annual rate:
I = Prt = $3483.29×0.2799×(1/12) = $81.25
New BalanceThe new balance is the subtotal above, with the finance charge added:
new balance = $3483.29 +81.25 = $3564.54
Kyle's new balance will be $3564.54.
__
Additional comment
This is a very expensive credit card. Not only is the interest rate of 27.99% very high, but also finance charges are charged on new purchase in the month they are purchased.
Some cards these days have interest rates of 12.75% or lower, with no finance charge for purchases made during the month. Some cards offer a rebate of up to 1.5% of purchases, so a net "negative" finance charge if you pay off the card every month.
Could i get some help in answering this question?
The value of the variable x in the right angle triangle is: 9
How to use Pythagoras theorem?Pythagoras Theorem is defined as the way in which we can find the missing length of a right angled triangle.
The triangle has three sides, the hypotenuse (which is always the longest), Opposite (which doesn't touch the hypotenuse) and the adjacent (which is between the opposite and the hypotenuse).
Pythagoras is in the form of;
a² + b² = c²
The tangent forms a right angle with the circle and as such using Pythagoras theorem, we have:
8 + x = √(15² + 8²)
8 + x = √289
8 + x = 17
x = 17 - 8
x = 9
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Can someone help me find the surface area of these 2 prisms?
Step-by-step explanation:
1) the 1-st prism is cube. Then its surface area can be calculated as:
A=5*5*6=150 [ft²];
2) A=[Perimeter of triange]*height+2*[Area_of_triangle];
according to the formula above height=3; Perimeter of triangle=9+12+15=36; Area of triangle=12*9*0.5=54;
Finally, A=36*3+2*54=108+108=216 [cm²].
what is trigonometry ratio and if tan
1) sin θ + tan θ is equal to 5/6. 2) sin θ is 5/12. 3) sec θ + cosecc^2 θ = 12/√119 + 144/25 4) cot θ + sin θ is equal to 169/60.
How to answer the aforementioned question1) To find sin θ + tan θ, we need to find the value of sin θ. Using the identity tan θ = sin θ / cos θ, we can rewrite tan θ as sin θ / cos θ.
tan θ = 5/12 = sin θ / cos θ
Since we are given that 0 < θ < 90, both sin θ and cos θ are positive.
Using the Pythagorean identity[tex]{sin^2}[/tex] θ + [tex]cos^2[/tex] θ = 1, we can solve for cos θ:
[tex]cos^2[/tex] θ = 1 - sin^2 θ
[tex]cos^2[/tex] θ = [tex]1 - (5/12)^2[/tex]
[tex]cos^2[/tex]θ = 1 - 25/144
[tex]cos^2[/tex] θ = 119/144
cos θ = √(119/144)
cos θ = √119/12
Now, we can find sin θ using the relationship [tex]sin^2[/tex] θ + [tex]cos^2[/tex]θ = 1:
[tex]sin^2[/tex] θ = 1 - [tex]cos^2[/tex] θ
[tex]sin^2[/tex]θ = 1 - (119/144)
[tex]sin^2[/tex]θ = 25/144
sin θ = √(25/144)
sin θ = 5/12
Finally, we can substitute the values of sin θ and tan θ into the expression sin θ + tan θ:
sin θ + tan θ = (5/12) + (5/12) = 10/12 = 5/6
Therefore, sin θ + tan θ is equal to 5/6.
2) The value of sin θ is already calculated as 5/12.
3) To find sec θ + [tex]csc^2[/tex] θ, we need to find the values of sec θ and csc θ.
Since sec θ is the reciprocal of cos θ, we can calculate sec θ as:
sec θ = 1/cos θ = 1/(√119/12) = 12/√119
csc θ is the reciprocal of sin θ, so:
csc θ = 1/sin θ = 1/(5/12) = 12/5
Now, we can substitute these values into the expression sec θ + [tex]csc^2[/tex]θ:
sec θ + [tex]csc^2[/tex]θ = (12/√119) + [tex](12/5)^2[/tex]= 12/√119 + 144/25
4) To find cot θ + sin θ, we need to calculate the value of cot θ.
cot θ is the reciprocal of tan θ, so:
cot θ = 1/tan θ = 1/(5/12) = 12/5
Now, we can substitute the values of cot θ and sin θ into the expression cot θ + sin θ:
cot θ + sin θ = 12/5 + 5/12
To add these fractions, we need a common denominator:
cot θ + sin θ = (12/5)(12/12) + (5/12)(5/5)
= 144/60 + 25/60
= 169/60
Therefore, cot θ + sin θ is equal to 169/60.
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Select the matrix that represents the parallelogram
The correct matrix representation is; [tex]\left[\begin{array}{ccc}1&5\\3&2\end{array}\right][/tex]
Based on the coordinates of a vector, We can represent a vector pointing at a point by its x coordinate, and y coordinate,
Consider that there are two points represented by their x-, y coordinates as P₁(x₁,y₁) P₂(x₂,y₂)
Given here the points are P₁(1, 3) and P₂(5, 2)
Thus, by the coordinates of the two vectors, we can represent the matrix ;
[tex]\left[\begin{array}{ccc}1&5\\3&2\end{array}\right][/tex]
Hence, Option A) is the correct answer.
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