Use fundamental identities to find the values of the trigonometric functions for the given conditions. tan = − 15/8 and sin > 0
sin =
cos =
tan =
csc =
sec =
cot =

The situations that are both statistically fair and morally fair are Situation 2, Situation 3 and Situation 5

For a situation to be fair, the probability of every outcome must be equal.

Using the above definition, we can now analyze each option

Situation 1

Letters = 26

P(Vowel) = 5/26

P(Consonant) = 21/26

Both probabilities are not equal.

Hence, this situation is not fair

Situation 2

Participants = 4

P(Each) = 1/4

All probabilities are equal in the above scenario i.e. 1/4

Hence, this situation is fair

Situation 3

Cousins = 5

P(Each) = 1/5

All probabilities are equal in the above scenario i.e. 1/5

Hence, this situation is fair

Situation 4

Numbers = 5 i.e. 2 to 6

P(Prime) = 3/5

P(Composite) = 4/6

Both probabilities are not equal.

Hence, this situation is not fair

Situation 5

Roommates = 5

Cards = 5

Aces = 4

P(Each) = 1/5

All probabilities are equal in the above scenario i.e. 1/5

Hence, this situation is fair

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that's tuff you live in NC

The equation of a function f(x) =  x² -4x -12 in the vertex form is f(x) = (x -2)² -16 and the value of the a = 1, h = 2, and k = -16

Any equation of the form [tex]\rm ax^2+bx+c=0[/tex]  Where x is variable and a, b, and c are any real numbers where a ≠ 0 is called a quadratic equation.

We have a quadratic equation:

f(x) =  x² -4x -12

f(x) =  x² -4x -12 + 4 -4

f(x) = (x -2)² -16

Here a = 1, h = 2, and k = -16

Thus, the equation of a function f(x) =  x² -4x -12 in the vertex form is f(x) = (x -2)² -16 and the value of the a = 1, h = 2, and k = -16

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The shoelace drawer is 7.911 inches wider than the paperclip drawer.

The height of shoelace drawer is = 12.49 inches

The height of paperclip drawer is = 4.579 inches

Therefore the measurement difference between the two drawer is = 12.49 inches - 4.579 inches

= 7.911 inches

Therefore, the shoelace drawer is 7.911 inches wider than the paperclip drawer.

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Answer:

[tex]x+(\frac{1}{2} x + 12) =[/tex] number of postcards Simone has now

Step-by-step explanation:

x = the number of postcards in Simone's collection

Simone bought 12 more than half the number of postcards in her collection.

So Simone bought half her collection ( [tex]\frac{1}{2} *x = \frac{1}{2} x[/tex] ) plus 12 more postcards.

[tex](\frac{1}{2}x +12)[/tex] = number of postcards Simone bought

Write an expression to show how many pstcards she has now.

[tex]x+(\frac{1}{2} x + 12) =[/tex] number of postcards Simone has now

Let she has p no of postcards before .

She bought 12 more than the half of p

Currently she has

Answer:

The student is incorrect and for parallelograms to be equal, included angles between them too should be equal.Explanation:When two quadrilaterals MNOP=TQRS, then not only all corresponding sides are equal, all corresponding angles too are equal.As MNOP and TQRS are parallelograms their diagonals bisect each other. And as MO=TR and NP=QS, it is apparent (see figure below) that MX=XO=TY=YR and NX=XP=SY=YQ. And hence two sides of all the four triangles (in each of the parallelogram) are equal.However, the angles included between the two diagonals can change (as is seen from the figure below),and hence MNOP≠TQRS

Step-by-step explanation:

Answer:

7.5 kilometres

Step-by-step explanation:

In 30 minutes she ran 5 kilometres.

We know that 30 + 15 = 45, so we can divide the minutes and kilometres by 2.

So 30 divided by 2= 15 minutes.

And 5 kilometres divided by 2= 2.5 kilometres.

Now we just add the two distances, as we know that the minutes make 45.

2.5 + 5 = 7.5.

I hope this helps, have a lovely day.

The speed is the distance covered by an object at a particular time. The distance covered by Saima in 45 minutes is 7.5 km.

The speed is the distance covered by an object at a particular time. Therefore, it is the ratio of distance and time.

[tex]\rm{Speed = \dfrac{Distance}{Time}[/tex]

Given Samin can run 5 kilometres in 30 minutes. Therefore, the speed of Samin will be,

Speed = 5km/30min = 5/30 km per minute

The distance covered by Saima in 45 minutes will be equal to

Distance = 5/30 × 45 = 7.5 km

Hence, The distance covered by Saima in 45 minutes is 7.5 km.

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Answer: [tex]\frac{- 1}{11}[/tex]

Step-by-step explanation:

Note: the "." symbol stands for multiplication

Given,

[tex]\frac{2x+4}{3} \\[/tex]  - [tex]\frac{5x-7}{2}[/tex] = 5

First we the LCM = 6,

[tex]\frac{2(2x+4)}{2.3}[/tex] - [tex]\frac{3(5x-7)}{3.2}[/tex]= 5

Then, we join both sides, since they have same denominator

[tex]\frac{2(2x+4) - 3(5x-7)}{6}[/tex] = 5

Multiply again

[tex]\frac{4x+8 - 15x+21}{6}[/tex] = 5

Add the same numbers

[tex]\frac{-11x + 29}{6}[/tex] = 5

Transpose 6 to the other side

-11x + 29 = 5.6

-11x + 29 = 30

Transpose 29 to the other side

-11x = 30 -29

-11x = 1

Transpose 11 to the other side to get answer

x = [tex]\frac{-1}{11}[/tex]

Hope it helps! If you have any doubts, feel free to ask

Answer:

The Sum of supplementary angles is 180.

Therefore, <A + <B = 180

<A = 19<B

19<B + <B = 180

20<B = 180

<B = 9°

& <A = 19×9°

<A = 171°

The answer for the expression 0.5x=24 will be x=48

The linear equation is defined as the equation having a degree of one or the power of the variable will be one. Linear equation shows the staright line on the graph.

here the given equation is:-

0.5x=24

We can write 0.5 in fraction as 1/2

1/2x=24

x=48

Hence the answer for the expression 0.5x=24 will be x=48

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The highlighted part is known as the center of the circle. Then the correct option is C.

It is a locus of a point drawn an equidistant from the center. The distance from the center to the circumference is called the radius of the circle.

Identify the highlighted part of circle O shown below.

The mid-point of the diameter is known as the center of the circle.

The highlighted part is known as the center of the circle.

Thus, the correct option is C.

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Answer:

78%

Step-by-step explanation:

a percentage is equivalent to a number over 100.

43% is 43/100

72% is 72/100

87% is 87/100

etc.

to find the percentage of students who said their favorite color is red, we need to set up a cross-multiplication equation

390/500 = ?/100

390 times 100 is 39000

39000/500 = 78

78% of the students said their favorite color is red

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Answer: 1, 2, 5

Step-by-step explanation:

The first equation is true because angles in a triangle add to 180 degrees.

The second equation is true because both sides equal 180 degrees (left hand side is a straight angle, right hand side is the sum of angles in a triangle)

The third equation is not true because z = 180 - y, and 180-y+w+z is not 180.

The fourth equation is not true because z=180-y, and 180-y=w+y is not always true.

The fifth equation is true by the exterior angle theorem.

By graphing both functions, we will see that there are two intersections at (-1.41, -2.12) and (3.28, 7.27).

Here we must solve:

[tex]2^x - 2.5 = 2x + 0.7[/tex]

To do it, we can graph the functions:

[tex]y = 2^x - 2.5\\\\y = 2x + 0.7[/tex]

And see where do the curves intersect.

The graph can be seen below, in there we can see two intersections.

One at (-1.41, -2.12) and (3.28, 7.27).

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Explanation:

5.1 cm on paper corresponds to 5.1*100 = 510 meters in real life due to the scale 1 cm = 100 m.

11.9 cm on paper corresponds to 11.9*100 = 1190 meters in real life.

The 5.1 cm by 11.9 cm rectangle on paper corresponds to the real life counterpart of 510 meters by 1190 meters.

The actual area of the real life park is length*width = 510*1190 = 606,900 square meters

8π is the circumference

Answer:

114 feet

Step-by-step explanation:

To figure out the perimeter, we also need the width

The width can be found by dividing the area by the length

800/32 = 25

to find the perimeter, we use the equation 2L + 2W = P

L is the length

W is the width

2(32) + 2(25) = 64 + 50 = 114

114 feet is the perimeter

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To solve this formula, we can simply use the formula of half-life of a radioactive substance to calculate the decay rate.

The disintegration constant or decay rate is calculated as 0.385min^-1

The half-life of a radioactive substance is defined as the time taken for the initial mass of the substance to reach half it's starting mass.

The formula is given as

[tex]T_\frac{1}{2} = \frac{\ln2}{\lambda}[/tex]

Let's substitute the value into the equation and solve through

[tex]T_\frac{1}{2} = \frac{\ln2}{\lambda} \\\lambda = \frac{\ln2}{T_\frac{1}{2} } \\\lambda = \frac{0.693}{1.8} \\\lambda = 0.385[/tex]

The disintegration constant or decay rate is calculated as 0.385min^-1

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Step-by-step explanation:

5,200,000 = 5.2 × 10⁶

so, we have

(5.2 × 10⁶) × (8.3 × 10²) - (3.1 × 10⁸)

(5.2 × 8.3 × 10⁸) - (3.1 × 10⁸)

(43.16 × 10⁸) - (3.1 × 10⁸) = 40.06 × 10⁸ = 4.006 × 10⁹

The area of the shaded triangular section of the stained glass window is  72 square inches.

The first step is to determine the dimensions of each rectangle that makes up the  stained glass window.

Length of one rectangle = length of the window / number of rectangles along the length

36/4 = 9 inches

Width of one rectangle = width of the window / number of rectangles along the width

48/3 = 16 inches

Area of the shaded triangular section = 1/2 x area of one rectangle

1/2 ( length x width)

1/2 x (16 x 9) = 72 square inches.

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Answer:

144

Step-by-step explanation:

i took the test

a = amount invested at 7%

b = amount invested at 9%

we know the amount invested was ₹36000, thus we know that whatever "a" and "b" are, a + b = 36000.  We can also say that

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{a\% of b}\\ \cline{1-1} \\ \left( \cfrac{a}{100} \right)\cdot b \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{7\% of a}}{\left( \cfrac{7}{100} \right)a}\implies 0.07a~\hfill \stackrel{\textit{9\% of b}}{\left( \cfrac{7}{100} \right)b}\implies 0.09b[/tex]

since we know the interest earned from the invested was ₹2920, then we say that 0.07a + 0.09b = 2920.

[tex]\begin{cases} a + b = 36000\\\\ 0.07a+0.09b=2920 \end{cases} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{using the 1st equation}}{a + b = 36000\implies \underline{b = 36000-a}}~\hfill \stackrel{\textit{substituting on the 2nd equation}}{0.07a~~ + ~~0.09(\underline{36000-a})~~ = ~~2920} \\\\\\ 0.07a+3240-0.09a=2920\implies 3240-0.02a=2920\implies -0.02a=-320 \\\\\\ a=\cfrac{-320}{-0.02}\implies \boxed{a=16000}~\hfill \boxed{\stackrel{36000~~ - ~~16000}{20000=b}}[/tex]

Answer:

step 2

and then step 3 : the error neutralized the error of step 2

Step-by-step explanation:

sin(a + b) = sin(a)cos(b) + cos(a)sin(b)

and because

sin(-b) = -sin(b)

cos(-b) = cos(b)

we have

sin(a - b) = sin(a)cos(-b) + cos(a)sin(-b) =

= sin(a)cos(b) - cos(a)sin(b)

3pi/2 = 270° or -90°.

sin(3pi/2) = sin(270) = sin(-90) = -1

that means, it is the full radius straight down from the center of the circle.

cos(3pi/2) = cos(270) = cos(-90) = cos(90) = 0

so, step 1 is correct :

sin(A - 3pi/2) = sin(A)cos(3pi/2) - cos(A)sin(3pi/2) =

= sin(A)×0 - cos(A)×(-1) (correct step 2)

but as we see, the provided step 2 is incorrect.

it should have been the indicated

sin(A)×0 - cos(A)×(-1)

and NOT the provided

sin(A)×0 + cos(A)×(-1)

step 3 based on the erroneous step 2 should then have been

sin(A)×0 - (1)cos(A)

but instead another error with the sign was made that neutralized the error of step 2 and we got after this second mistake by pure chance the overall correct step 3

sin(A)×0 + (1)cos(A)

so, again, the first error was made in step 2.

but technically, there was also a consecutive error made in step 3 to bring everything back to the correct approach.

Answer:

799800000 larger

Step-by-step explanation:

So . . Subtract

800000000 - 200000 = 799800000

Answer: 799800000

Step-by-step explanation: For 8 x 10^8, do 10 x 10 x 10  10 x 10 x 10  10 x 10 to get 100,000,000 and x 8 is 800,000,000

For 2 x 10^5  do 10^5 ( 10 x 10 x 10 x 10 x 10) which is 100,000 and then x 2 is 200,000

Then subtract.

800,000,000 - 200,000 is 799800000

Step-by-step explanation:

[tex]\frac{1-\sin ^2\left(x\right)}{1+\sin \left(x\right)}=1-\frac{1}{\csc \left(x\right)}[/tex]

[tex]\frac{1-\sin ^2\left(x\right)}{1+\sin \left(x\right)}[/tex]

[tex]=1-\sin \left(x\right)[/tex]

⇒ [tex]\sin \left(x\right)=\frac{1}{\csc \left(x\right)}[/tex]

[tex]=1-\frac{1}{\csc \left(x\right)}[/tex]

Answer:

84.9

Step-by-step explanation:

Answer:

You use the quadartic foruala for this problem your fanial anwers is

x=1 + or - radical 37 / 6.

1+ radical 37 over 6 =1.180460422

To the nearest tenth =1.2

1-radical 37 over 6= -0.8471270884

To the nearest tenth=-0.8

Answer:

least to greatest:

1 1/10, 1.11, 1 2/5, 1.73, the square root of 3

Step-by-step explanation:

1 1/10 = 1.10

1.11 = 1.11

1 2/5 = 1.4

1.73 = 1.73

the square root of 3 is approximately 1.732