Add 1/6 +3/4 + 2/3. Simplify the answer and write it as a mixed number, if possible.

It should be noted that the probability that a student will earn at least one 5 will be 0.3152.

Test P(x). P(at least one 5)

1. 0.4. 0.2

2. 0.45. 0.36

3. 0.15. 0.488

Therefore, the probability that a student in the AP curriculum will earn at least one 5 will be:

= (0.4 × 0.2) + (0.45 × 0.36) + (0.15 × 0.488)

= 0.3152

In conclusion, the correct option is 0.3152.

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Answer:

5.524 in 2 significant figures rounding the value to 2 non zero numbers.

5.524 = 5.5 (2 significant figures)

Answer:

  a.  2/5; reduction

Step-by-step explanation:

It appears that C is the center of dilation, so C' and C are coincident. The scale factor is ...

  P'C'/PC = 4/10 = 2/5 . . . scale factor

The scale factor is less than 1, so the dilation is a reduction in size.

Answer:

2 : 3

Step-by-step explanation:

bananas to apples = 8 : 12

simplify by dividing both values by highest common factor of 4:

8 ÷ 4 : 12 ÷ 4 = 2 : 3

Answer: 1. x=2,-5/3

Step-by-step explanation:

Answer:

C 30 degrees

Step-by-step explanation:

Sum of interior angles of a triangle = 180°

⇒ ∠UST + 78 + 72 = 180

⇒ ∠UST = 180 - 78 - 72

⇒ ∠UST = 30°

Answer:

$54

Step-by-step explanation:

Original Price = $90

Discounted = 40%

Percent to decimal 40% = .40

$90 x .40=36 ( 36 is the Discount)

$90 - 36=54

Sale Price = $54

Hence, Sale Price = $54

[RevyBreeze]

Answer:

x³ + 1

Step-by-step explanation:

to evaluate (f ￮ g)(x) , substitute x = g(x) into f(x)

f(g(x) )

= f(x³)

= x³ + 1

Explanation:

When x is zero or larger, then |x| = x.

An example: |9| = 9

This applies to |3x| as well, so |3x| = 3x when [tex]x \ge 0[/tex]

Step-by-step explanation:

[tex]y = \frac{4}{x} + \sqrt{x + 0.2} - 5x[/tex]

[tex]x = \frac{4}{5} [/tex]

[tex]y = \frac{4}{1} \div \frac{4}{5} + \sqrt{ \frac{4}{5} + 0.2} - 5 \times \frac{4}{5} [/tex]

[tex] \frac{4}{1} \times \frac{5}{4} + \sqrt{0.8 + 0.2} - 4[/tex]

[tex]5 + \sqrt{1} - 4[/tex]

[tex]5 + 1 - 4 \\ 6 - 4 = 2[/tex]

Answer:

Second quadrant

Step-by-step explanation:

Quadrant I ranges from [tex]0^\circ<\theta<90^\circ[/tex]

Quadrant II ranges from [tex]90^\circ<\theta<180^\circ[/tex]

Quadrant III ranges from [tex]180^\circ<\theta<270^\circ[/tex]

Quadrant IV ranges from [tex]270^\circ<\theta<360^\circ[/tex]

Answer:

-6

Step-by-step explanation:

Answer:

-6

Step-by-step explanation:

3(-2)(-1)(-1)= -6

[RevyBreeze]

Answer:

We cannot calculate this probability because the sampling distribution is not normal.

Step-by-step explanation:

Since the parent population is not normally distributed, the small sample size will result in a sampling distribution that isn't normal.

Answer:

square root of 4 is 2, 1/2 of 2 is 1

Step-by-step explanation:

Answer:

$240000

Step-by-step explanation:

[tex]p = 200000[/tex]

[tex]t = 4[/tex]

[tex]r = 5 \: percent\: per \: anum[/tex]

[tex]si = \frac{p \times r \times t}{100} [/tex]

[tex] = \frac{200000 \times 5 \times 4}{100} [/tex]

[tex] = 2000 \times 5 \times 4[/tex]

[tex] = 2000 \times 20[/tex]

[tex] = 40000[/tex]

[tex]amount = si + principle[/tex]

[tex] = 200000 + 40000 = 240000[/tex]

The total amount after 4 years is $240,000

Simple interest rate is the interest that is paid only on the principal portion of a the amount that is saved.

Total amount = principal + interest

Interest = principal x time x interest rate

200,000 x 0.05 x 4 = $40,000

Total amount = 200,000 + 40,000 = $240,000

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ratio remains same.

[tex]\\ \tt\longrightarrow \dfrac{2}{14}=\dfrac{7}{2z}[/tex]

[tex]\\ \tt\longrightarrow 4z=14(7)[/tex]

[tex]\\ \tt\longrightarrow 4z=98[/tex]

[tex]\\ \tt\longrightarrow z=98/4[/tex]

[tex]\\ \tt\longrightarrow z=24.5[/tex]

Answer:

276.25

Step-by-step explanation:

37.50 x 5.5 = 206.25

206.25+ 70 = 276.25

Answer:

x = 269

explanation:

solve:

5 * x = 1345

x = 1345/5

x = 269

Therefore x is 269.

note: changing sides changes multiplication(*) to division(/) and division(/) to multiplication(*).

Answer:

x = 269

Step-by-step explanation:

For this question, they are asking you to create a problem out of the information given. For this problem, we will require the use of division. Before we can solve, we need to create the problem first.

Because the problem says 5 multiplied by x, we have to multiply these two. (Important:) Anytime you are multiplying a coefficient (5 in this case) by a variable (x in this case) we have to put the coefficient in front of the variable, like this:

5x _ ___.

Now that we know that, the question states that this basically equals 1345. With that said, that just gave us the rest of the problem. Now let's put it together:

5x = 1345.

Now we can solve. To single out the variable (x) to find our answer, divide 5 into 1345:

5x = 1345

5        5

So, 1345 ÷ 5 = 269. After that, we are left with x and 269 (because the 5 was canceled out with the division). So, the answer is:

x = 269.

I hope that this helps.

Answer:

a

Step-by-step explanation:

5/3 is 1.6666667

8/5 is 1.6

therefore 5/3 > 8/5

The equation of a line that is tangent to the graph of f and parallel to the given line is; y = 3x + 2 and y = 3x - 2

The given equation of the line is 3x - y + 3 = 0

In slope intercept form, this can be rewritten as;

y = 3x + 3

Therefore, the slope of this line will be 3 since in y = mx + c, m is the slope. Thus, the slope of the parallel line will be  3

We will be looking for the value of x when the derivative of f(x) equals 3.

f(x) = x³ and so f'(x) = 3x²

Thus;

3x² = 3

x² = 3/3

x² = 1

x = 1 or -1

Thus;

y = 1³ or y =-1³

y = 1 or -1

Equation of tangent is;

y - 1 = 3(x - 1)

y - 1 = 3x - 3

y = 3x - 2

or y - (-1) = 3(x - (-1))

y + 1 = 3x + 3

y = 3x + 2

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taking a peek at the picture, we can see that the U-turn or vertex occurs at the point (2 , -9), and we can also see that the graph passes through the point say (5 , 0).

[tex]~~~~~~\textit{vertical parabola vertex form} \\\\ y=a(x- h)^2+ k\qquad \begin{cases} \stackrel{vertex}{(h,k)}\\\\ \stackrel{"a"~is~negative}{op ens~\cap}\qquad \stackrel{"a"~is~positive}{op ens~\cup} \end{cases} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\stackrel{vertex}{(2~~,~-9)}\qquad y=a(x-2)^2-9\qquad \qquad \textit{we know that} \begin{cases} x=5\\ y=0 \end{cases} \\\\\\ 0=a(5-2)^2-9\implies 9=9a\implies \cfrac{9}{9}=a\implies 1=a~\hfill \\\\\\ y=1(x-2)^2-9\implies \boxed{y=(x-2)^2-9}[/tex]

Answer:

We cant see the writing it is too small

Step-by-step explanation:

Answer:

1. 103        

2. 156

3. 114
4. 115.14

5. 140

6. 123.8

7. 120.28

8. 107

Step-by-step explanation:

Answer:

hope it helps you :)) !

Answer: 10

Step-by-step explanation:

Answer:

x = 10i - 10i

Step-by-step explanation:

3x^2 + 300 = 0

3(x^2 + 300) = 0

x^2 + 100 = 0

x^2 = -100

x = -100 (sqr root)

x = 10i - 10i

Hope this is more of the answer you where looking for.

Answer:

10

Step-by-step explanation:

it just is

Answer:

sin theta = .923

Step-by-step explanation:

see image. An angle in standard position has one side glued to the x-axis, and the other side-the terminal side- rotating around the origin. When it gets to (-5, 12) in your problem, it stops there. 5, 12are the legs of a right triangle and they are recognizable as part of a pythagorean triple 5,12,13. So the hypotenuse is 13. Sin is OPP/HYP. So that is 12/13. Its in the 2nd quadrant, so it should be positive. We used the reference angle, bc the actual angle is the >90° angle from the positive x-axis to thru (-5,12). It calcs the same tho.

sin theta = 12/13

= 0.923

Answer:

  (c)  0.923

Step-by-step explanation:

The coordinates of a point on the unit circle are (cos(θ), sin(θ)). That is, the y-coordinate of a point on the terminal ray will have the same sign as the sine of the angle. Here, the sign of the sine is positive, eliminating the first two answer choices.

We know that cos(θ) < sin(θ) for reference angles greater than 45°, where both values are √2/2 ≈ 0.707. Since 5 < 12, that means the angle of interest here will have a sine that is more than 0.707. Only one of the positive answer choices is in this range: sin(θ) ≈ 0.923.

_____

Additional comment

The value of sin(θ) is precisely ...

  sin(θ) = y/√(x²+y²) = 12/√(25+144) = 12/13

  sin(θ) = 0.923076...(6-digit repeat)

Answer:

  (c)  (6, -3)

Step-by-step explanation:

Reflection over both axes is the same as reflection across the origin, or rotation 180° about the origin. It has the effect of negating both coordinates:

  (x, y) ⇒ (-x, -y) . . . . . reflection over both axes

The coordinates of A are (-6, 3), so the coordinates of A' will be ...

  A(-6, 3) ⇒ A'(6, -3)