True or false: f(x) is a function. 0 3 4 2 8 12 0 f(x) A. True B. False​

Answer:

Proof in explanation

Step-by-step explanation:

Trigonometric Identities

The basic trigonometric identity is:

[tex]\sin^2\theta+\cos^2\theta=1[/tex]

We'll use it and some basic algebra to prove that, given:

[tex]a sin^3\theta+b cos^3\theta=sin\theta cos\theta[/tex]

And

[tex]a\sin\theta-b\cos\theta=0[/tex]

Then

[tex]a^2+b^2=1[/tex]

From the equation:

[tex]a\sin\theta-b\cos\theta=0[/tex]

We have:

[tex]a\sin\theta=b\cos\theta\qquad [1][/tex]

The equation

[tex]a sin^3\theta+b cos^3\theta=sin\theta cos\theta[/tex]

Can be rewritten as

[tex]a\sin\theta \sin^2\theta+b \cos^3\theta=\sin\theta \cos\theta[/tex]

Replacing [1]:

[tex]b\cos\theta \sin^2\theta+b \cos^3\theta=\sin\theta \cos\theta[/tex]

Taking the common factor:

[tex]b\cos\theta (\sin^2\theta+ \cos^2\theta)=\sin\theta \cos\theta[/tex]

The expression in parentheses is 1, thus:

[tex]b\cos\theta =\sin\theta \cos\theta[/tex]

Dividing by [tex]\cos\theta[/tex]

[tex]b=\sin\theta[/tex]

Replacing in

[tex]a\sin\theta=b\cos\theta[/tex]

We have

[tex]a\sin\theta=\sin\theta\cos\theta[/tex]

Dividing by [tex]\sin\theta[/tex]

[tex]a=\cos\theta[/tex]

Now:

[tex]a^2+b^2=(\cos\theta)^2+(\sin\theta)^2[/tex]

This expression is 1, thus it's proven:

[tex]\boxed{a^2+b^2=1}[/tex]

Answer:

The probability is [tex]P(X | B) = 0.91[/tex]

Step-by-step explanation:

Generally the probability of the perpetrator being X  is equal  to the probability of the perpetrator being Y (given that both fugitives appear equally likely to be the perpetrator )

This can be mathematically represented as

         [tex]P(X) = P(Y) = \frac{1}{2}[/tex]

Let G represent the event that  the blood type of the sample is  type A

Generally if X has a blood type A then it is almost certain that the perpetrator is  X compared to Y

This can be mathematically represented as

        [tex]P(G | X) = 1[/tex]  

( Here this means  the probability of the sample being of type A given that the X has a blood type A )

Given that the sample belonging to Y  accidentally destroyed

   Then the probability that Y is innocent given that the blood type of  Y is of type  A

 This can be mathematically represented as

         [tex]P(G | Y) = 10\%[/tex]

         [tex]P(G | Y) = 0.10[/tex]

Generally according to  Bayes rule  the probability that person X is the perpetrator  mathematically as

         [tex]P(X | G) = \frac{P(G|X) * P(X)}{ P(G|X) * P(X) + P(G | Y ) * P(Y)}[/tex]

       [tex]P(X | B) = \frac{1 * 0.5 }{ 1 * 0.5 + 0.10 * 0.5}[/tex]

        [tex]P(X | B) = 0.91[/tex]

Answer:

The first one is incorrect

Step-by-step explanation:

3^2 - 5 + 2

9 - 5 + 2

4+2 = 6 (not 42)

Answer:

It is D because if 3 to the second power is 9-5=4+2=6

Step-by-step explanation:

Answer:

Between 67 and 103 beats per minute

Step-by-step explanation:

The minimum would be 80. That means that the minimum sum would have to be 320 among the four numbers.

85+81+87=253

320-253=67 so 67 will be the minimum

now, we should see the maximum. It will be 89 so the sum of the four numbers cannot be anymore than 89*4 which is 356

So, 356-253=103

yay savvas, my favorite

A. between 67 and 103 beats per minute inclusive

Step-by-step explanation:

What I did was I just started from the top and tried out the mean with 69 and saw that that was 80, so that was right. Then I tried 103, and that was 89, so that's obviously the max. So it was pretty simple. I do not know the way you are supposed to do it. That's what I came on here for, but none of the answers anyone but was right..

Answer:

First map, 1cm:10km

Distance between cleveland and cincinnati :

[tex]40 \times 10km = 400km[/tex]

Second map, 1cm: 50km

[tex] \frac{400km}{50km} = 8[/tex]

Therefore, the distance between the two places in second map will be 8 cm.

The distance between the two places on the second map will be 8 cm.

The ratio between a distance on a map and its corresponding distance on the ground is referred to as the "map scale." One kilometer on the ground is equal to one centimeter on a map with a scale of 1:100,000.

Given that the scale on the first map is 1 cm to 10 km. The distance from Cleveland to Cincinnati is 40 cm. The scale on the second map is 1 cm to 50 km.

The distance from Cleveland to Cincinnati on the second map will be calculated as below:-

40 X 10 = 400 KM

Second map, 1cm: 50km

( 400 / 50 ) = 8 cm

Therefore, the distance between the two places on the second map will be 8 cm.

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Answer:

The probability that neither test is positive

P(A⁻ ∩ B⁻ ) = 0.0108

Step-by-step explanation:

Step(i) :-

Given  the two tests are independently

Test A has probability 0.91 of being positive if the illegal drug has been used

P(A) = 0.91

Test B has probability 0.88 of being positive if the illegal drug has been used

P(B) = 0.88

If   events are independently then ,

[tex]P(A n B) = P(A) P(B)[/tex]

Step(ii):-

The probability that neither test is positive (and thus Al gets to keep his job)

[tex]P(A^{-} n B^{-} ) = P(A^{-} ) P(B^{-} )[/tex]

P(A⁻ ∩ B⁻ ) = P(A⁻ ) P(B⁻ )

                  = ( 1- P(A) ) ( 1 - P(B))

                 =  (1 - 0.91 ) ( 1 - 0.88 )

                = (0.09) (0.12)

               = 0.0108

The probability that neither test is positive

P(A⁻ ∩ B⁻ ) = 0.0108

Answer:

c

Step-by-step explanation:

5.26×10³=5260 which is less than 6000 and greater than 600

Answer:

The square root of fifty is 7.10 rounded

Step-by-step explanation:

It would be around 7 on the number line. Hope this helps!!

Answer:

12%

Explanation:

The $18 don't matter in this problem.

120/1000 is not a lot so it would be predicted to be 12% due to the amount.

Answer:

a. 0.158

b. 0.01942

Step-by-step explanation:

For part a we define probability that the randomly selected person is if 65 years or more than that

a.

Probability of under age = 22.8% = 0.228

Probability of those from age 18 to 64 = 61.4% = 0.614

1-0.228-0.614

= 0.158

b.

P(uninsured) = p(those not up to 18) * p(those uninsured or under 18) + p(those age 18-64) * p(uninsured or under 18) + p(being 64plus) x P(uninsured or 64 plus)

= 0.228 x 0.051 + 0.614 x 0.124 + 0.158 x 0.011

= 0.011628 + 0.076136 + 0.001738

=0.089502

P(65 of older|uninsured) = p(64+) x P(uninsured or 64 plus)

= 0.157 x 0.011/0.089502

= 0.001738/0.089502

= 0.01942

a. The probability that a randomly selected person in the United States is 65 or older is 0.158

b. In the case when the person is  an uninsured American so the probability is 0.01942

a.

Since

Probability of under age = 22.8% = 0.228

And,

Probability of those from age 18 to 64 = 61.4% = 0.614

So, the probabilities of 65 or older is

= 1 - 0.228-0.614

= 0.158

b.

Now

P(uninsured) = p(those not up to 18) × p(those uninsured or under 18) + p(those age 18-64) × p(uninsured or under 18) + p(being 64plus) × P(uninsured or 64 plus)

= 0.228 × 0.051 + 0.614 × 0.124 + 0.158 × 0.011

= 0.011628 + 0.076136 + 0.001738

=0.089502

So,

P(65 of older|uninsured) = p(64+) × P(uninsured or 64 plus)

= 0.157 × 0.011 ÷ 0.089502

= 0.001738 ÷ 0.089502

= 0.01942

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Answer:

6x^3-38x^2+65x-21

Step-by-step explanation:

Answer:

A:B:C = 5:5:7 or 5x : 5x : 7x

Cindy ate 30 Skittles less than Ann and Ben together

-----> 7x = 5x + 5x - 30

-3x = -30

x = 10

5x = 50

7x = 70

They ate 50+50+70 = 170 of them

Answer:

170

Step-by-step explanation:

because it is

Answer:

y=−x2+8x−7

Step-by-step explanation:

Answer: y - 5 = -5/6 (x - 18)

Step-by-step explanation:

The point-slope form of a linear equation is written using the slope of the line and one point in the line. From part A, the slope of the line representing this situation is m = -5/6.

Since x represents the number of 10-student groups and y represents the number of 12-student groups, the combination of 18 groups of 10 students and 5 groups of 12 students is represented by the point (18,5).

Answer:

Step-by-step explanation:

Answer:

[tex]\sin(\theta)=-\sqrt5/5\text{ and } \csc(\theta)=-\sqrt5\\\cos(\theta)=2\sqrt5/5\text{ and } \sec(\theta)=\sqrt5/2\\\tan(\theta)=-1/2\text{ and } \cot(\theta)=-2[/tex]

Step-by-step explanation:

First, let's determine which quadrant our angle θ lies in.

Remember ASTC, where:

Everything is positive in QI,

Only sine (and cosecant) is positive in QII,

Only tangent (and cotangent) is positive in QIII,

And only cosine (and secant) is positive in QIV.

Since our tangent is negative, and our cosine is positive, this means that our θ must be in QIV.

In QIV, sine is negative, tangent is negative, and cosine is positive.

With that, let's figure out the remaining trig ratios.

We know that:

[tex]\tan(\theta)=-1/2[/tex]

Remember that tangent is the ratio of the opposite side to the adjacent side.

Let's figure out our hypotenuse using the Pythagorean Theorem:

[tex]a^2+b^2=c^2[/tex]

Substitute 1 for a and 2 for b (we can ignore the negative since we're squaring anyways). This yields:

[tex](1)^2+(2)^2=c^2[/tex]

Square:

[tex]1+4=c^2[/tex]

Add:

[tex]c^2=5[/tex]

Take the square root:

[tex]c=\sqrt{5}[/tex]

So, our square root is √5.

So, our three sides are: Opposite=1, Adjacent=2, and Hypotenuse=√5.

Sine and Cosecant:

Remember that:

[tex]\sin(\theta)=opp/hyp[/tex]

Substitute 1 for the opposite and √5 for the hypotenuse. This yields:

[tex]\sin(\theta)=1/\sqrt5[/tex]

Rationalize:

[tex]\sin(\theta)=\sqrt5/5[/tex]

And since our angle is in QIV, we add a negative:

[tex]\sin(\theta)=-\sqrt5/5[/tex]

Cosecant is simply the reciprocal of sine. So:

[tex]\csc(\theta)=-\sqrt5[/tex]

Cosine and Secant:

Remember that:

[tex]\cos(\theta)=adj/hyp[/tex]

Substitute 2 for the adjacent and √5 for the hypotenuse. This yields:

[tex]\cos(\theta)=2/\sqrt5[/tex]

Rationalize:

[tex]\cos(\theta)=2\sqrt5/5[/tex]

Since our angle is in QIV, cosine stays positive.

Secant is the reciprocal of cosine. So:

[tex]\sec(\theta)=\sqrt5/2[/tex]

Tangent and Cotangent:

We were given that:

[tex]\tan(\theta)=-1/2[/tex]

To find cotangent, flip:

[tex]\cot(\theta)=-2[/tex]

And we're done!

Answer:

c

Step-by-step explanation:

Answer:

A) {x: x ≥ 3}

Step-by-step explanation:

took the test

Domain: (−∞,∞),{x|x∈R}

Range: [3,∞),{y|y≥3}

Answer:

70

Step-by-step explanation:

complementary angles are 2 angles that add up to 90, the first angle is already 20 so just subtract 90-20 to find other angle

Answer:

2 ounces are in 2 ounces

Step-by-step explanation:

Answer:2

Step-by-step explanation:

Answer:

3y=1-2x....

y=1/3-2/3x.....m=-2/3

y=-2/3x+b replacement(-5,7)

b=11/3

y=-2/3x+11/3

Step-by-step explanation:

Answer:

10r

Step-by-step explanation:

8r - 9r +11r

-r +11r

10r

Answer:

135 miles

Step-by-step explanation:

So first we have to find the difference of 83 and 100. So 100-83=27. So for miles, she can spend 27 dollars. Now, since per mile it costs 20 cents or 1/5 of a dollar, every time she drives 5 miles she'll have to pay one more dollar. So One dollar = 5 miles. Then we do the total amount of money she can spend on miles (27) and multiply that by the amount of miles per dollar (5) and we get 135 miles. So she can drive 135 miles.

Answer:

Step-by-step explanation:

it is an angle that adds up to 90 degrees.

Answer:

Complementary angles are two angles that, when their measurements are added together, add up to be 90°.

Step-by-step explanation:

For example, two angles that measure 31° and 59° respectively would be complementary angles.

Hope this helps!

Answer:

12

Step-by-step explanation:

15×0.8= 12

you're multiplying the total number of questions with the score as a decimal

Answer:

78.67

Step-by-step explanation:

The computation of the average for a student is shown below:

= Different Weights × different activities

= (3% × 81) + (9% × 90) + (9% × 92) + (17% × 86) + (17% × 71) + (17% × 93) + (28% × 62)

= 2.43 + 8.1 + 8.28 + 14.62 + 12.07 + 15.81 + 17.36

= 78.67

Hence, the average of the student is 78.67

We simply applied the above formula

Answer:

Its 3

Step-by-step explanation:

Add them all together and divide by 6

Answer:

The correct answer is 1/2 = ?/100

Step-by-step

The circle is divided into 2 halves and the angle is 100 degrees

Answer:

b. -1/2

Step-by-step explanation:

the slope is negative so we can get choices a and c out. and you go down 1 over 2

Answer:

yes you are correct

Step-by-step explanation:

6 times 6 times 6 times 7 times 7 times 7 is 74088

The required volume of the given figure is 7 cubic units.

Volume is defined as the mass of the object per unit density while for geometry it is calculated as profile area multiplied by the length at which that profile is extruded.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
The volume of the given 1 cube is 1 cubic unit,

Now,
In the figure,
There are 7 cubes,
So the volume is given as = 1 × 7  = 7 cubic units.

Thus, the required volume of the given figure is 7 cubic units.

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