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?

Answers

Answer 1

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 question

Given:

- 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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Related Questions

A shirt company has 3 designs each of which can be made with short or long sleeves. There are 6 color patterns available. How many different shirts are available from this company?

Answers

Answer:

36 different shirts

-----------------

Given that there are 3 designs, 2 sleeve lengths, and 6 color patterns, we can multiply these values together:

3 designs × 2 sleeve lengths × 6 color patterns = 36

So, there are 36 different shirts available from this company.

There are 36 different types of shirt available for this company.

Given that;

Number of design Company has = 3

Number of color pattern available = 6

Types of shirt (short or long sleeves) = 2

Now, We need to find the number of different types of shirts are available from this company.

Since, the number of different types of shirts can be calculated by multiplying Number of design Company has with Number of color pattern available also multiplying with Types of shirt (short or long sleeves).

Hence, By framing in equation form we get;

the number of different types of shirts is,

⇒ 3 × 6 × 2

⇒ 36

Therefore, We get;

There are 36 different types of shirt available for this company.

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Help me with this problem please.

Answers

The product of matrices A and B are:

[tex]AB = \left[\begin{array}{ccc}-50&7\\44& -10\\\end{array}\right][/tex]

[tex]BA = \left[\begin{array}{ccc}-12&-30\\-16& -48\\\end{array}\right][/tex]

How to find the product of two matrices?

A matrix (plural matrices) is a set of numbers arranged in rows and columns so as to form a rectangular array.

The number of rows of a matrix can be determined by counting from top to bottom and the number of columns can be determined by counting from left to right.

The product of matrices A and B are:

AB = A * B

[tex]AB = \left[\begin{array}{ccc}-3&-8\\2& 8\\\end{array}\right] * \left[\begin{array}{ccc}6&3\\4& -2\\\end{array}\right][/tex]

To get the product, multiply each row by the column. That is:

(-3 * 6) + (-8 * 4) = -50

(-3 * 3) + (-8 * (-2)) = 7

(2 * 6) + (8 * 4) = 44

(2 * 3) + (8 * (-2)) = -10

[tex]AB = \left[\begin{array}{ccc}-50&7\\44& -10\\\end{array}\right][/tex]

BA =  B * A

[tex]BA = \left[\begin{array}{ccc}6&3\\4& -2\\\end{array}\right] * \left[\begin{array}{ccc}-3&-8\\2& 8\\\end{array}\right][/tex]

To get the product, multiply each row by the column. That is:

(6 * (-3)) + (3 * 2) = -12

(6 * (-8)) + (3 * 8) = -30

(4 * (-3)) + ((-2) * 2) = -16

(4 * (-8)) + ((-2) * 8) = -48

[tex]BA = \left[\begin{array}{ccc}-12&-30\\-16& -48\\\end{array}\right][/tex]

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50 Points! Multiple choice algebra question. Photo attached. Thank you!

Answers

The exact value of the cosine of θ is given as follows:

a) 3/5.

What are the trigonometric ratios?

The three trigonometric ratios are the sine, the cosine and the tangent, and they are obtained according to the rules presented as follows:

Sine of angle = opposite side/hypotenuse.Cosine of angle = adjacent side/hypotenuse.Tangent of angle = opposite side/adjacent side = sine/cosine.

Applying the Pythagorean Theorem, the hypotenuse length is given as follows:

x² = 6² + (-8)²

x² = 100

x = 10.

As the x-coordinate is used for the cosine, the cosine is given as follows:

cos(θ) = 6/10

cos(θ) = 3/5.

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if x+y+z=27 and x+y=17 then Z=

Answers

Answer:

Step-by-step explanation:

x+y+z=27

x+y=17

z=?

since x+y=17

then

17+z=27

z=27-17

z=10

Sofia and ella are both writing expressions to calculate the surface area of a rectangular prism however they wrote different expressions.

a. examine the expressions below, and determine if they represent the same value. explain why or why not.
sofia's expression
(3 cm x 4 cm ) + (3 cm x 5 cm) + (4 cm x 5 cm) + (4 cm x 5 cm)
ella's expression:
2(3 cm x 4 cm) + 2(3 cm x 5 cm) + 2(4 cm x 5 cm)

b. what fact about the surface area of a rectangular prism does ella's expression show more clearly than sofia's?

Answers

a ) The given expression from Sofia and Ella represents two different values.

b.) The fact about the surface area of prism that Ella's expression shows that is not in Sofia's expression is that the expression is according to the formula.

How to determine the surface area of a rectangular prism?

To determine the surface area of a rectangle prism, the formula that should be used would be given below:

That is;

Surface area of rectangular prism;

= 2(wl+hl+hw)

when the formula is multiplied out the following is gotten;

= 2wl + 2hl + 2hw

From Ella's expression,

2(3 cm x 4 cm) + 2(3 cm x 5 cm) + 2(4 cm x 5 cm). This follows the order of the formula. And it's final answer = 94cm²

From Sofia's expression,

(3 cm x 4 cm ) + (3 cm x 5 cm) + (4 cm x 5 cm) + (4 cm x 5 cm). This doesn't follow the order of the formula and therefore is not correct and not the same final value with Ella's expression.

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Stuck on this and cant move along until I get it correct. Please help.


Fill in the missing value.

The measure of angle F is ___°

Answers

The solution is:  the measure of angles 2, 3, and 4 are:

m∠2 = 95°

m∠3 = 85°

m∠4 = 95°

Vertical Angle Theorem:

When two straight lines intersect, the opposite vertical angles formed are always equal (congruent) to each other.

Therefore,

m∠3 = 85°

m∠2 = m∠4

Linear pair:

Two adjacent angles which, when combined, form a line, so the sum of a linear pair is 180°.

Therefore,

85° + m∠2 = 180°

m∠3 + m∠4 = 180°

If  85° + m∠2 = 180°

⇒ m∠2 = 180° - 85°

⇒ m∠2 = 95°

As  m∠2 = m∠4  then  m∠4 = 95°

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complete question:

Find the measure of angles 2, 3, and 4. input the measures then click done. i-ready

please help i missed a day of class i cant figure this out

(x+3)(x+7)=0

Problem answered, solution and why!

Answers

[tex](x+3)(x+7)=0\\x=-3 \vee x=-7\\\\x\in\{-7,-3\}[/tex]

5. (6 pts pts) The displacement of a spring vibrating in damped harmonic motion is given by
y = 4e-3t sin(2πt)
Find the times when the spring is at its equilibrium position (y = 0). '

Answers

The  times when the spring is at its equilibrium position (y = 0) are t = 0, 1/2, 1, 3/2, ... and so on.

To find the times when the spring is at its equilibrium position (y = 0), we can set the displacement equation equal to zero and solve for t:

[tex]4e^{(-3t)[/tex] sin(2πt) = 0

Since the product of two factors is zero if and only if at least one of the factors is zero, we have two cases to consider:

4[tex]e^{(-3t)[/tex] = 0

This equation has no solution since [tex]e^{(-3t)[/tex] is always positive and nonzero.

sin(2πt) = 0

The sine function is zero at integer multiples of π.

So, we can set 2πt equal to integer multiples of π:

2πt = 0, π, 2π, 3π, ...

Solving for t in each case, we get:

t = 0, 1/2, 1, 3/2, ...

Therefore, the times when the spring is at its equilibrium position (y = 0) are t = 0, 1/2, 1, 3/2, ... and so on.

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find the perimeter of a rectangle if: L= 12cm, W= 5cm.
(a) 34cm
(b) 21cm
(c) 14cm
(d) 17cm​

Answers

Answer:

(a) 34 cm

Step-by-step explanation:

The formula for perimeter of a rectangle is

P = 2l + 2w, where

P is the perimeter,l is the length,and w is the width.

Thus, we can plug in 12 for l and 5 for w in the perimeter formula and simplify to find the perimeter of the rectangle:

P = 2(12) + 2(5)

P = 24 + 10

P = 34

Thus, the perimeter of a rectangle with a length of 12 cm and a width of 5 cm is 34 cm.

Can someone answer and provide an explanation for these problems? Find the midpoint of the line segment with the given endpoints.

Answers

52)  The midpoint of the line segment is (-0.5, 9).

53) The midpoint of the line segment is (3, -8.5).

52) To find the midpoint of the line segment with endpoints (8,9) and (-9,9), we can use the midpoint formula. The midpoint formula states that the coordinates of the midpoint (x, y) are the average of the corresponding coordinates of the endpoints.

For the x-coordinate:

(x₁ + x₂) / 2 = (8 + (-9)) / 2 = (-1) / 2 = -0.5

For the y-coordinate:

(y₁ + y₂) / 2 = (9 + 9) / 2 = 18 / 2 = 9

Therefore, the midpoint of the line segment is (-0.5, 9).

53) To find the midpoint of the line segment with endpoints (8,-10) and (-2,-7), we apply the same process using the midpoint formula.

For the x-coordinate:

(x₁ + x₂) / 2 = (8 + (-2)) / 2 = 6 / 2 = 3

For the y-coordinate:

(y₁ + y₂) / 2 = (-10 + (-7)) / 2 = -17 / 2 = -8.5

Hence, the midpoint of the line segment is (3, -8.5).

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A given triangle has vertices at (-3, 1) (2, 4) and (5, -3). If the triangle were rotated 360 degrees clockwise, the new coordinates would be:

Answers

To rotate a point (x, y) 360 degrees clockwise, we can use the following formulas:

New x-coordinate = x * cos(θ) - y * sin(θ)
New y-coordinate = x * sin(θ) + y * cos(θ)

Since we want to rotate the entire triangle 360 degrees, each point will be transformed using these formulas.

Let's calculate the new coordinates for each vertex:

For the first vertex (-3, 1):
New x-coordinate = -3 * cos(360°) - 1 * sin(360°) = -3 * 1 - 1 * 0 = -3
New y-coordinate = -3 * sin(360°) + 1 * cos(360°) = -3 * 0 + 1 * 1 = 1

For the second vertex (2, 4):
New x-coordinate = 2 * cos(360°) - 4 * sin(360°) = 2 * 1 - 4 * 0 = 2
New y-coordinate = 2 * sin(360°) + 4 * cos(360°) = 2 * 0 + 4 * 1 = 4

For the third vertex (5, -3):
New x-coordinate = 5 * cos(360°) - (-3) * sin(360°) = 5 * 1 - (-3) * 0 = 5
New y-coordinate = 5 * sin(360°) + (-3) * cos(360°) = 5 * 0 + (-3) * 1 = -3

Therefore, after rotating the triangle 360 degrees clockwise, the new coordinates would be (-3, 1), (2, 4), and (5, -3), which are the same as the original coordinates.

I need help finding the Component form and Magnitude of the vector V.

Answers

To find the magnitude of the vector, we can use the Pythagorean theorem: ||V|| = sqrt((5 * √2 / 2)^2 + (5 * √2 / 2)^2) = 5.

To find the component form of a vector, you need to break it down into its x and y components. Let's say our vector V has a magnitude of 5 and is pointing in the direction of 45 degrees (measured from the positive x-axis).

To find its x component, we can use cosine: Vx = V cos(45) = 5 * √2 / 2. To find its y component, we can use sine: Vy = V sin(45) = 5 * √2 / 2. So the component form of vector V is (5 * √2 / 2, 5 * √2 / 2).

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A rectangular prism measures 8 inches in width, 12 inches in length, and 4 inches in height. What is the surface area of the prism?

Answers

Step-by-step explanation:

It has

two sides 8x12

two sides 12x4

two sides 4x8           total 352 in^2

Using the given scale 1:50, calculate the actual length of the wall if it is measured to be 15cm.​

Answers

Find the total square feet of the wall(s) by multiplying ceiling height by total wall length

First to find correct answer will get brainly

Answers

The surface area of the dilated solid is 2,880 square units

What is the surface area of the dilated solid?

Multiply each side of the shape by 4

Surface area of a rectangular prism = 2(LH + LW + WH)

Where,

Length, L = 8 × 4 = 32 units

Width, W = 6 × 4 = 24 units

Height, H = 3 × 4 = 12 units

Surface area of a rectangular prism = 2(LH + LW + WH)

= 2(32×12 + 32×24 + 24×12)

= 2(384 + 768 + 288)

= 2(1,440)

= 2,880 square units

Therefore, 2,880 square units is the surface area of the solid.

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A dentist was making note of her upcoming appointments with different aged patients and
the reasons for their visits.
Patients under 18
Patients 19-60
Patients over 60
Regular cleaning Broken tooth
Submit
5
3
3
2
6
2
What is the probability that a randomly selected appointment is not with a patient 19-60 or is
not for a broken tooth?
Simplify any fractions.

Answers

Probability that a randomly selected appointment is with patients over 60 years old and is for a regular cleaning = (5/21)

The probability of an event is calculated as the number of elements in that event divided by the total number of elements in the sample space.

For this question, we are told to find the probability that a randomly selected appointment is with patients over 60 years old and is for a regular cleaning.

Number of patients that are over 60 years and are for regular cleaning = 10

Total number of patients = 2 + 8 + 6 + 4 + 10 + 12 = 42

Probability that a randomly selected appointment is with patients over 60 years old and is for a regular cleaning = (10/42)

                                                                = (5/21)

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f(x) = x²/x² 2x+3 find Vertical asymptote find horizontal asymptote ​

Answers

The vertical asymptote of the equation does not exist, the horizontal asymptote of the equation is 1.

To calculate vertical asymptote,

Putting the denominator equal to zero,

x²+2x+3 = 0

Using Quadratic formulae,

b² - 4ac

where,

b = 2

a = 1

c = 3

putting value,

4-12 = -8<0

therefore, the solution is negative

Hence, no vertical asymptote of the given equation exists,

To calculate the horizontal asymptote,

the degrees of the numerator and denominator are the same. we can compare the coefficients of the highest power terms.

The coefficient of x² in the numerator is 1

Hence, the horizontal asymptote is y = 1.

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Help me solve this problem please

Answers

Answer:

450°

Step-by-step explanation:

Use the given data to make a box-and-whisker plot.
5, 4, 16, 21, 10, 6, 15

Answers

Answer:

To make a box-and-whisker plot, we first need to order the data from smallest to largest:

4, 5, 6, 10, 15, 16, 21

Next, we can find the median, which is the middle value of the ordered data set. In this case, the median is 10.

Then, we can find the lower quartile (Q1) and the upper quartile (Q3). The lower quartile is the median of the lower half of the data set, and the upper quartile is the median of the upper half of the data set. To find Q1 and Q3, we can split the data set into two halves:

4, 5, 6, 10 and 15, 16, 21

The median of the lower half is (5+6)/2 = 5.5, and the median of the upper half is (16+21)/2 = 18.5. Therefore, Q1 = 5.5 and Q3 = 18.5.

Now we can draw the box-and-whisker plot. The box represents the middle 50% of the data, with the bottom of the box at Q1 (5.5), the top of the box at Q3 (18.5), and the line inside the box at the median (10). The whiskers extend from the box to the smallest and largest values inthe data set that are not outliers. To determine whether there are outliers, we can use the following formula:

Outlier = Q1 - 1.5 * (Q3 - Q1) or Q3 + 1.5 * (Q3 - Q1)

Plugging in the values, we get:

Outlier = 5.5 - 1.5 * (18.5 - 5.5) = -13.25 or Outlier = 18.5 + 1.5 * (18.5 - 5.5) = 37.25

Since there are no values in the data set that are less than -13.25 or greater than 37.25, there are no outliers.

Therefore, the box-and-whisker plot for the given data is:

            |       4

     ___|___

    |              |

    |              |

    |        5.5 |-----  

    |              |      |

    |              |      |

    |------------|  10 |  

    |              |       |

    |      15.5 |------

    |       |      |

     ___|___

            |       21

The box spans from Q1 (5.5) to Q3 (18.5), with the median line inside the box at 10. The whiskers extend from the box to the minimum value of 4 and the maximum value of 21, since there are no outliers.

Hope this helps!

With a short time remaining in the​ day, a delivery driver has time to make deliveries at seven locations among the 8 locations remaining. How many different routes are​ possible? Question content area bottom Part 1 There are enter your response here possible different routes. ​(Simplify your​ answer.)

Answers

The number of different routes possible for the delivery driver, given the time to make deliveries at 7 out of the remaining 8 locations, is 8.

The number of different routes possible for the delivery driver can be calculated using combinatorics. Specifically, we need to determine the number of ways to choose 7 locations out of the remaining 8 locations. This can be found using the combination formula.

The combination formula, also known as "n choose k," is given by the expression C(n, k) = n! / (k! * (n-k)!), where n is the total number of items to choose from and k is the number of items to choose.

In this case, there are 8 locations remaining and the driver needs to choose 7 of them. Applying the combination formula, we have C(8, 7) = 8! / (7! * (8-7)!) = 8! / (7! * 1!) = 8.

Therefore, there are 8 possible different routes for the delivery driver to make deliveries at the remaining 8 locations, given that the driver has time to make deliveries at 7 of them.

To simplify the answer, we can state that there are 8 possible different routes for the driver.

In summary, the number of different routes possible for the delivery driver, given the time to make deliveries at 7 out of the remaining 8 locations, is 8.

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Please help I don’t understand thank you have a blessed day

Answers

By evaluation, the values of the rational function are f(11) = - 1 / 12 and f(- 2) = 1, respectively.

How to evaluate a rational function

In this problem we find the case of a rational function that must be evaluated at two different x-values: x = 11, x = - 2. The procedure is summarized below:

Write the entire expression.Substitute on x with the given value.Simplify the expression by algebra properties.

Now we proceed to present the complete procedure:

f(11) = 11 / (11 + 1) - 1

f(11) = 11 / 12 - 1

f(11) = 11 / 12 - 12 / 12

f(11) = (11 - 12) / 12

f(11) = - 1 / 12

f(- 2) = (- 2) / (- 2 + 1) - 1

f(- 2) = - 2 / (- 1) - 1

f(- 2) = 2 - 1

f(- 2) = 1

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At a conference of educators, there ore 189 people total, and 128 are teachers. If the rest are principals, then how many principals are present?

Answers

Answer:

61 principals

Step-by-step explanation:

189 total - 128 teachers = 61 principals

A jewlary shop sells 240 necklaces in a month 180 of the necklaces were sold in a via the shops website the rest were sold in a high street shop .
Work out the ratio of online sales to shop sales
Give ur answers in its simplest form

Answers

240-180= 60
180 were sold online and 60 were sold in shops
the ratio in its simplest form would be 3:1

What is the area of the shaded region?

Answers

Answer:

80 mm²

Step-by-step explanation:

Even for slanted triangles, the area is base x half height! The base is 10 mm, half the height is 8 mm, so the area is 8x10=80 mm.

1. Identify the variable that is contained in the expression.
7y+2y² +3

7
x
y
3

Answers

The variable that is contained in the given expression is y. Therefore, option C is the correct answer.

The given expression is 7y+2y² +3.

In the given expression there are 3 terms, so it is called trinomial.

In the term 7y, y is the coefficient of 7.

In the term 2y², y² is the coefficient of 2.

3 is the constant term.

Therefore, option C is the correct answer.

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Volume of Cone ___ mm3?

Answers

The volume of the cone is 301. 44mm³

How to determine the value

First, we need to know the formula

the formula that is used for calculating the volume of a cone is expressed as;

V = πr²h/3

Such that the parameters are;

V is the volume r is the radiush is the height of the cone

Substitute the values, we have;

Volume = 3.14 × 6² × 8/3

Multiply the values, we have;

Volume = 904.32/3

Divide the values

Volume = 301. 44mm³

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A triangle has sides with lengths of 3 miles, 4 miles, and 6 miles. Is it a right triangle

Answers

Yes, the given triangle is a right triangle.

We have,

This can be determined by applying the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

Now,

In this case, the squares of the side lengths are:

3² = 9

4² = 16

6² = 36

If the sum of the squares of the two shorter sides (9 + 16 = 25) is equal to the square of the longest side (36), then the triangle is a right triangle.

Thus,

In this case, since 25 is indeed equal to 36, the triangle with side lengths 3 miles, 4 miles, and 6 miles is a right triangle.

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Zara's car depreciates at a rate of 14% per year.

By what percentage has Zara's car depreciated after 5 years?

Give your answer to the nearest whole number.

NO SPAM.

Answers

Answer:

  53%

Step-by-step explanation:

You want to know the depreciation of car value after 5 years if it is 14% per year.

Multiplier

The multiplier of value each year is ...

  1 + growth rate = 1 + (-14%) = 0.86

When the value has been multiplied by that 5 times, it has been multiplied by ...

  0.86^5 ≈ 0.4704

This represents a change in value from the original value of ...

  0.4704 -1 = -0.5296 = -52.96% ≈ -53%

Zara's car has depreciated by 53% after 5 years.

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The sum of two numbers is -6. One number is 14 more than the other one. Find the numbers.

Answers

Answer:

The two numbers are -10 and 4

Step-by-step explanation:

[tex]x+y=-6\\y=14+x\\\\x+(14+x)=-6\\2x+14=-6\\2x=-20\\x=-10\\\\x+y=-6\\-10+y=-6\\y=4[/tex]


Find the exact values of the six trigonometric functions of the angle O shown in the figure.
sin(0) -
X
cos(0) -
tan(0) -
csc(0) -
sec(0)-
cot(0) -
0
3
3

Answers

The values of

1. cosθ = √3/2

2. sinθ = √3/2

3. tanθ = 1

4. sec θ = 2/√3

5. cosec θ = 2/√3

6. cot θ = 1

What is trigonometric ratio?

The trigonometric functions are real functions which relate an angle of a right-angled triangle to ratios of two side lengths.

cosθ = adj/hyp

sinθ = opp/hyp

tanθ = opp/adj

sec θ = 1/cosθ

cosec θ = 1/sinθ

cot θ = 1/tanθ

We need to find the hypotenuse of the triangle

x² = 3² +3²

x = √9+9

x = √18

x = 2√3

cosθ = 3/2√3 = 6√3/12

= √3/2

2. sinθ = 3/2√3 = √3/2

3. tanθ = 3/3 = 1

4. sec θ = 2/√3

5. cosec θ = 2/√3

6. cot θ = 1

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