(03.02) If g(x) = x2 + 2, find g(3). (2 points) Group of answer choices 9 8 11 6

The given expression 2 sin(t) - 3 cos(t)  in the Form r sin(t + a), can be expressed as √13 sin(t - arctan(2/3)).

To express the given expression, 2 sin(t) - 3 cos(t), in the form r sin(t + a), we can use trigonometric identities to simplify and rewrite it.

Let's start by using the identity cos(a - b) = cos(a)cos(b) + sin(a)sin(b):

2 sin(t) - 3 cos(t) = r sin(t + a)

Here, r represents the magnitude or amplitude of the trigonometric function, and a represents the phase shift or the angle by which the function is shifted horizontally.

To find r and a, we need to manipulate the given expression to match the form r sin(t + a).

We can rewrite 2 sin(t) - 3 cos(t) as:

r [sin(t)cos(a) + cos(t)sin(a)]

By comparing the coefficients with the identity cos(a - b) = cos(a)cos(b) + sin(a)sin(b), we can determine that r = √(2^2 + (-3)^2) = √(4 + 9) = √13.

Next, we equate the coefficients of sin(t) and cos(t) to sin(a) and cos(a) respectively:

sin(a) = 2/√13

cos(a) = -3/√13

To find the value of a, we can use the arctan function:

a = arctan(sin(a)/cos(a)) = arctan((2/√13)/(-3/√13)) = arctan(-2/3)

Thus, we have expressed the expression 2 sin(t) - 3 cos(t) in the form r sin(t + a):

2 sin(t) - 3 cos(t) = √13 sin(t - arctan(2/3))

Note that the given value of 20464 and the letter "u" do not appear to be related to the given expression and can be ignored in this context.

In summary, the given expression 2 sin(t) - 3 cos(t) can be expressed as √13 sin(t - arctan(2/3)).

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the mean time between failures for the modified components is tested using the p-value method at a significance level of 0.05. The null hypothesis (H0) assumes that the mean time is 520 hours or less, while the alternative hypothesis (H1) suggests that the mean time is greater than 520 hours.

we will use the p-value method of hypothesis testing. The null hypothesis (H0) assumes that the mean time between failures for the modified components is 520 hours or less. The alternative hypothesis (H1) suggests that the mean time between failures is greater than 520 hours.

We start by calculating the sample mean and sample standard deviation of the given data. Using the sample mean and the assumed population mean of 520 hours, we can calculate the test statistic t, which follows a t-distribution with n-1 degrees of freedom (where n is the sample size).

Next, we determine the p-value associated with the obtained test statistic. The p-value represents the probability of observing a test statistic as extreme or more extreme than the calculated value, assuming the null hypothesis is true.

Comparing the p-value to the significance level of 0.05, if the p-value is less than 0.05, we reject the null hypothesis in favor of the alternative hypothesis. This would indicate that there is evidence to support the claim that the mean time between failures for the modified components is greater than 520 hours.

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Answer:

The correct answer is not shown in your picture. You must get a = 60.

Step-by-step explanation:

(1/2)a + (2/3)b = 50

b = 30

(1/2)a + (2/3)(30) = 50

(1/2)a + 20 = 50

(1/2)a + 20 - 20 = 50 - 20

(1/2)a = 30

2 * (1/2)a = 2 * 30

a = 60

The correct answer is not shown in your picture. You must get a = 60.

Answer: 3000 years

Step-by-step explanation:

Let y be the number of money and x be the number of years

So we have the equation

y= 6.5x + 10000

Now we put 29500 in the y

29500 = 6.5x + 10000

Subtracted 10000 from both sides

19500 = 6.5x

Divided both sides by 6.5

x = 3000 years

Answer:

so 240-90cm he cut off=195cm. Then 45x2=80cm so 195-90cm=105cm.

Therefore, 105 divided by 40=2.625 so he cut off 6 pieces of 40cm lengths overall

Step-by-step explanation:

Answer:

8.125 inches

Step-by-step explanation:

Ok so basically what you needed to do was this

Find out what was the value like this 3 1/4 = 3.25 and 2 1/2 = 2.5

Then you will do

3.25 x 2.5 and get your answer

8.125

There you go! Have a Wonderful Day

Answer:

2x-y-1=0

Step-by-step explanation:

.

a. Interest of the first year = $26.93

b. Balance after the first year = $1256.93

c. Interest for the second year = $27.52

d. Balance after the second year = $1284.45

Although a part of your question is missing, you might refer to this full question: Gerry deposited $1230 in an account that pays 2.19% simple interest for one year.

a. How much interest will he earn in one year?

b. What will be his balance after one year?

c. Gerry withdraws all of the principal and interest after the first year and deposits into another one-year account at the same rate. What will be his interest for the second year?

d. What will his balance be after two years?

Principal = $1230

Rate = 2.19%

Formula to be used:

Simple interest = (P*R*T)/100

where P = principal

R = rate

T = time in years

Calculating interest for the first year:

S.I = (1230*2.19*1)/100

S.I = 26.93

So, he will earn $26.93 as interest in the first year

And balance after the first year will be $1256.93

Solving for the second year:

P = 1256.93

S.I = (1256.93*2.19*1)/100

= 27.52

So, interest for the second year will be $27.52

And balance after the second year will be $1284.45

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Answer:

C. 1

Step-by-step explanation:

False, one of the most pieces of information with a var is whether each estimated coefficient for the lags is statistically significant (t-tests)

A statistical test called a t-test is employed to compare the means of two groups. It is frequently employed in hypothesis testing to establish whether a procedure or treatment truly affects the population of interest or whether two groups differ from one another.

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False. Each triangle in the STL file is defined by the vertices, but not necessarily by the inward pointing surface normal vector. The surface normal vector is often calculated based on the vertex positions.

False. The STL file is a mesh representation of the CAD model, and it does not contain all the information needed to fully reconstruct the original CAD model. It lacks information such as parametric features, assembly relationships, and design intent, making it difficult to recreate the exact original model.

The option "Increasing the heat exchange area for a heat exchanger" is NOT an advantage of using a lattice structure. Lattice structures are known for their lightweight properties, material-saving benefits, and simplified design and manufacturing processes.

However, increasing the heat exchange area for a heat exchanger is not typically associated with lattice structures. Heat exchangers usually rely on other design considerations, such as fin arrays or extended surfaces, to enhance heat transfer efficiency, rather than lattice structures.

Therefore, increasing heat exchange area is not a direct advantage of lattice structures.

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Answer:

x=1.5 y=-1/3

Step-by-step explanation:

2x-3y=4

2x+8=11

Let's subtract 8 from both sides of the second equation:

2x=3

x=1.5

Substituting this into the first equation, we get:

2(1.5)-3y=4

3-3y=4

-3y=1

y=-1/3

Answer: 3x^2 + 25x + 1

Step-by-step explanation:

3C + B

=> 3(x^2 + 8x + 3) + (x - 8)

=> 3x^2 + 24x + 9 + x - 8

=> 3x^2 + 25x + 1

Answer:

3(x^2-13x-10)

Step-by-step explanation:

You can only factor out 3, as that is the only thing these have in common.

Answer:

C?

I hope this helps, if not C than A- i get them mixed at times- Sorry

Step-by-step explanation:

♥ Hey Grey Here! ♥

The radioactive substance remaining after 43 hours is: 62.7273 mg by unitary method.

A single unit's value can be determined from the values of multiple units, and multiple units' values can be determined from the values of single units using the unitary method.

Now,

Given that 180 mg is present at t = 0 hours.

After t = 33 hours, substance left = 90mg

By unitary method, after = 1 hour, substance left = \(180-\frac{90}{33}=180 -\frac{30}{11}\)mg

The substance left after t = 43 hours = \(180 - \frac{30\times43}{11}= 180 - \frac{1290}{11}=180 - 117=62.7273mg\)

Hence, The radioactive substance remaining after 43 hours is: 62.7273 mg by unitary method.

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Answer:

11/9

Step-by-step explanation:

Answer:

Step-by-step explanation:

1. 2x

2. m^2 - 2

3. x^2 + 3x - 2

4. m - 2n + 3

You can just simply cancel out the given answers to the given problem.

1. 4x^2 - 2x = ___ (2x + 1)

4/2 = 2

x^2 - x is just x^2-1 so x.

= 2x

To check the answer, 2x (2x + 1) = 4x^2 - 2x

#1

\(\\ \rm\star\leadsto \underbrace{2x}(2x+1)\)

\(\\ \rm\star\leadsto 4x^2+2x\)

#2

\(\\ \rm\star\leadsto n\underbrace{(m^2-2)}\)

\(\\ \rm\star\leadsto m^2n-2n\)

#3

\(\\ \rm\star\leadsto x\underbrace{(x^2+3x-2)}\)

\(\\ \rm\star\leadsto x^3+3x^2-2x\)

#4

\(\\ \rm\star\leadsto 2mn\underbrace{(m-2n+3)}\)

\(\\ \rm\star\leadsto 2m^2n-4mn^2+6mn\)

Answer:

32

Step-by-step explanation:

I'm good at math hehe ggggggrhdgcdg

Answer:

24 ft

Step-by-step explanation:

10^2 = 100

6^2 = 36

100 - 36 = 64

\(\sqrt{64}\) = 8

b = 8 ft

10+6+8 = 24

Answer:

The answer is 2593.678

Step-by-step explanation:

The distance around the perimeter would be 120 ft.

Perimeter is the distance around the edge of a shape.

The complete question is

A garden is designed in the shape of a rhombus formed from 4 identical 30°-60°-90° triangles. The shorter distance across the middle of the garden measures 30 feet.

A rhombus is shown. Lines are drawn from each point to the opposite point to form 4 right triangles. The other 2 angle measures are 30 and 60 degrees. The base length of each triangle is 15 feet.

What is the distance around the perimeter of the garden?

let AE is the half of the diagonal AC.

AC = 30 ft.

So, AE = ½ * 30

AE = 15 ft

Now, using trigonometry

sin 30 = 15/AD

0.5= 15/AD

AD= 30 ft

Hence, distance around the perimeter would be: AD+AD+AD+AD=

=30 ft + 30 ft + 30 ft + 30 ft

= 120 ft.

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Answer:A

Step-by-step explanation: just took it

Answer:

3!

Explanation:

By calling a sunny weather "beautiful" and rainy weather "depressing", you're inserting your own opinion into the question- which makes it biased!

Answer:

8

Step-by-step explanation:

Step 1: Add 19 to both side

b-19+19=-11+19

b=8

Hope I helped:D

Answer: b = 8

Step-by-step explanation: To solve for b in this equation, we want to get b by itself on the left side of the equation.

Since 19 is being subtracted from b, to get b by itself,

we need to add 19 to the left side of the equation.

If we add 19 to the left side, we must also add 19 to the

right side in order to keep our equation balanced.

Notice that on the left side, -19 and +19 cancel

each other out so we're simply left with b.

On the right side, -11 + 19 equals 8.

So we have b = 8.

Answer:

not equivalent to meteorologists ratio

Step-by-step explanation:

meteorologists ratio is

rainy days : sunny days = 2 : 5

last months weather is

rainy days : sunny days

= 10 : 20 ( divide both parts by LCM of 10 )

= 1 : 2 ← not equivalent to 2 : 5

Answer:

a.

\(f(t) = 21000( {.918}^{t} )\)

b.

\(f(4) = 21000( {.918}^{4}) = 14913.86\)

A line beginning at point (0, 0) and continuing through the point (28, 7) describes the graph of the proportional relationship. 2nd option is the answer

Given: the proportional relationship

x 12 16 28

y  3  4   7

In order to know the beginning of the line, we need to find the y-intercept.

The equation of a line is of the form

y = mx + c

where m is the slope and c is the y-intercept.

m = y2-y1 /x2-x1

m = 4-3 / 16-12 = 1/4

y = mx + c

3 = 1/4(12) + c

3 = 3 + c

c = 0

Thus, the beginning of the line is (0, 0).

The coordinate of a line or graph is written in the form (x, y). Therefore, the line begins at point (0, 0) and continues through point (28, 7).

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Answer: 25 percent

Step-by-step explanation:

The price of the medicine was increased by 50%.

Given,

The price of some medication was increased from $8 to $12.

We need to find by what percentage the price of the medicine increased.

The formula used is given as:

Percentage increase = \(\frac{Final~amount - Initial~amount} {Initial ~amount}\) x 100

Find the initial amount.

= $8

Find the final amount.

= $12

Find the percentage increased.

= ($12 - $8) / $8 x 100

= 4/8 x 100

= 1/2 x 100

= 50%

Thus the price of the medicine was increased by 50%.

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The factorial of a number n is the product of all positive integers up to and including n

The factorial function is typically represented using the "!" symbol, such that n! represents the product of all positive integers up to and including n. For example, 5! = 5 x 4 x 3 x 2 x 1 = 120.

To represent the factorial function using product notation, we can write:

n! = ∏_{i=1}^n i

This means that we take the product of all positive integers from 1 to n, which is equivalent to computing n!. For example, using this notation, we can write:

5! = ∏_{i=1}^5 i = 1 x 2 x 3 x 4 x 5 = 120

Note that the product starts at i=1 and goes up to n, which includes all the positive integers we want to multiply together.

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Answer:

I think the area is 38

Step-by-step explanation:

area =38