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3 years ago

Find all of the solutions for the following equation. 2 sin 0 + 3 = sin 0 + 2

Mathematics

1 answer:

den301095 [7]3 years ago

3 0

Answer:

Step-by-step explanation:

$2 sin \theta+3=sin \theta+2\\sin \theta=-1=sin 270,sin(360n+270)\\\theta=270,360 n+270 where n is an integer.$

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Which of the following graphs represents the equation below? f(x) = x^2 + 4x

Sindrei [870]

Answer:

The graph in the attached figure

Step-by-step explanation:

we have

$f(x)=x^{2}+4x$

This is a vertical parabola open upward

The vertex is a minimum

step 1

Find the x-intercepts

The x-intercepts are the values of x when the value of the function is equal to zero

For f(x)=0

$0=x^{2}+4x$

Factor x

$0=x(x+4)$

The x-intercepts are (0,0) and (-4,0)

step 2

Find the y-intercept

The y-intercept is the values of the function when the value of x is equal to zero

For x=0

$f(x)=(0)^{2}+4(0)=0$

The y-intercept is (0,0)

step 3

Find the vertex

Convert the equation into vertex form

$f(x)=x^{2}+4x$

Complete the square

$f(x)=(x^{2}+4x+4)-4$

Rewrite as perfect squares

$f(x)=(x+2)^{2}-4$

The vertex is the point (-2,-4)

therefore

using a graphing a graphing tool

The graph in the attached figure

7 0

3 years ago

Use the information provided to write the standard form equation of each parabola. (Plzzzz help me)

Nikolay [14]

Answer:

I think you are in a test..You should do by your own

8 0

3 years ago

The formula for the circumference of a circle is C = 2r, where r is the radius and C is the circumference. The equation solved f

Marat540 [252]

Answer:

It should be 8

Step-by-step explanation:

C = 2r

16 =2r

r =16/2

r =8

7 0

3 years ago

Which expression is equivalent to 3^4 times 3^-9

creativ13 [48]

Answer: 3^4 · 3^-9 = 3^4 · 1/3^9

Step-by-step explanation:

3 0

3 years ago

The attendance at baseball games at a certain stadium is normally distributed, with a mean of 30,000 and a standard deviation of

lakkis [162]

Answer:

a) 0.964

b) 0.500

c) 0.885

d) $x \geq 32467.5$

e) 0.997

Step-by-step explanation:

We are given the following information in the question:

Mean, μ = 30000

Standard Deviation, σ = 1500

We are given that the distribution of attendance at stadium is a bell shaped distribution that is a normal distribution.

Formula:

$z_{score} = \displaystyle\frac{x-\mu}{\sigma}$

a) P(attendance is greater than 27,300)

P(x > 27300)

$P( x > 27300) = P( z > \displaystyle\frac{27300 - 30000}{1500}) = P(z > -1.8)$

$= 1 - P(z \leq -1.8)$

Calculation the value from standard normal z table, we have,

$P(x > 27300) = 1 - 0.036 = 0.964 = 96.4\%$

b) P(attendance greater than or equal to 30000)

$P(x > 30000) = P(z > \displaystyle\frac{30000-30000}{1500}) = P(z \geq 0)\\\\P( z \geq 0) = 1 - P(z \leq 0)$

Calculating the value from the standard normal table we have,

$1 - 0.500 = 0.500 = 50\%$

c) P(attendance between 27000 and 32000)

$P(27000 \leq x \leq 32000) = P(\displaystyle\frac{27000 - 30000}{1500} \leq z \leq \displaystyle\frac{32000-30000}{1500}) = P(-2 \leq z \leq 1.33)\\\\= P(z \leq 1.33) - P(z < -2)\\= 0.908 - 0.023 = 0.885 = 88.5\%$

$P(27000 \leq x \leq 32000) = 88.5\%$

e) P(attendance less than 33000)

P(x < 33000)

$P( x < 33000) = P( z < \displaystyle\frac{33000 - 30000}{1500}) = P(z < 2)$

Calculating the value from the standard normal table we have,

P(x < 33000) = 0.997 = 99.7%

d) We have to find x such that:

$P( X > x) = P( z > \displaystyle\frac{x - 30000}{1500}) = 0.95$

Calculating the value from the standard normal table we have,

P(z = 1.645) = 0.95

Thus,

$\displaystyle\frac{x - 30000}{1500} \geq 1.645\\\\x \geq 32467.5$

The attendance should be greater than or equal to 32467.5 to be in the top 5% of all games.

6 0

4 years ago