Select the correct answer. What is the domain of the function f(x) = 2x + 5?

Answer:

Step-by-step explanation:          

\(49x^2-42x+(\frac{42}{2})^2=49x^2-42x+(\frac{42}{2} )^2\)    (completing the square)  

  \(49x^2-42x+441=49x^2-42x+21^2\)

                              \(=(7x-21)^2\)

So    \(49x^2-42x+441=(7x-21)^2\)

Solution: The required constant is 441.

Remember:    Completing the square IN \(ax^2+bx+c\) involves adding  \((\frac{b}{2} )^2\)     to both sides of the equation. THIS KEEPS IT BALANCED AND ALLOWS US TO MAKE A PERFECT SQUARE.    

There are 315 ways of distributing books (four identical math books and five identical history ) to three different students.

Let A, B be any finite sets. The number of ways to choose one element from A and one element from B is N(A)⋅N(B)..

We have, Total number of distinct students = 3

Total number of identical math books = 4

Identical History books = 5

let

Number of distinct ways to distribute identical four math books (n = 4) among three students(k= 3), N(M) = ⁽ⁿ⁺ᵏ⁻¹⁾Cₙ = ⁶C₄ = 6!/4!2! = 15

Number of distinct ways to distribute five history books (n= 5) among three students (k= 3) ,N(H) = ⁽ⁿ⁺ᵏ⁻¹⁾Cₙ = ⁷C₅ = 7!/5! 2! = 7× 3 = 21

Total different (distinguishable) ways can all the books be distributed to the students, N(A) = N(M)⋅N(H) = 15× 21 = 315 ways

Hence , required distribution ways are 315.

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The probability that they have an average weight of greater than 10 pounds and less than 15 pounds is 0.84134

In this question we have been given there are 250 dogs at a dog show who weigh an average of 15 pounds, with a standard deviation of 6 pounds. of 10 dogs are chosen at random.

We need to find the probability that they have an average weight of greater than 10 pounds and less than 15 pounds.

Given, μ = 12, σ = 8, n = 4

P(X > 8)

= P(z > (8 - 12 / 8/√4))

= P(z > -1)

= 1 - P(z ≤ -1)

= 1 - [1 - P(z ≤ 1)]

=  P(z ≤ 1)

= 0.84134

Therefore, the required probability is 0.84134

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Answer:

I think 270 because you rotated 3 times

Step-by-step explanation:

The concept is the Vertical Lines. The Vertical Lines are a pair of opposing, congruent angles created by intersecting lines. It is option A.

An upward line is a line on the direction plane where every one of the focuses on the line have a similar x-coordinate. Because they are perpendicular to the ground and extend toward the sky, vertical lines frequently convey a sense of height.

At the point when two straight lines cross each other vertical points are shaped. Every vertical angle is equal and congruent.

By super-imposing the two pairs of non-adjacent angles created by intersecting two lines, vertical angles are congruent.

Every vertical angle has the same length. We call angles congruent when their measurements are the same.

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Question:

Which of coming up next is best depicted as a couple of inverse points shaped by crossing lines?

A. Vertical angles

B. Supplementary angles

C. Complementary angles

D. Linear pair

I don't know if this is what you are looking for, but here is the graph of y=5.

Answer: Put the line Horizontally going through the point of 5 on the y axis.

Step-by-step explanation:

Dead asl (can't keep replying stop blowing my shii up)

YYYYYYYYYYYEEEEEEEEEEEEEERRRRRRRRRRRRRRRR WSG MAMAS I  MISSD U BRU FR ITS BEEN TOO LONG

The domain and range of y = arcsin x are [-1, 1] and [-π/2,π/2] respectively.

We know that the domain of the inverse trigonometric function is restricted to those values of x for which the inverse function exists.

The domain of y=arcsin x is [-1,1]. The range of y=arcsin x is [-π/2,π/2].y = arcsin x is an inverse trigonometric function which is the inverse of y = sin x.

It is defined asy = arcsin x ⇔ x = sin y, and - π /2 ≤ y ≤ π /2.If we put x = sin y, it is clear that - 1 ≤ x ≤ 1 and that y is an angle whose sine is x.

In other words, y = arcsin x ⇔ sin y = x.Since the range of the sin function is - 1 to 1, we know that the domain of y = arcsin x is also - 1 to 1.

Therefore, the domain of y = arcsin x is [-1, 1], and the range of y = arcsin x is [-π/2,π/2].

In trigonometry, the inverse trigonometric functions are a set of functions that calculate the angle of a right triangle based on the ratio of its sides.

For example, the inverse sine function (arcsin) calculates the angle of a triangle based on the ratio of its opposite side to its hypotenuse. The arcsin function is defined as y = arcsin x, where -1 ≤ x ≤ 1 and - π /2 ≤ y ≤ π /2.

This means that the domain of the arcsin function is [-1, 1] and the range is [-π/2,π/2].

When solving problems using inverse trigonometric functions, it is important to remember these domain and range restrictions.

In conclusion, the domain and range of y = arcsin x are [-1, 1] and [-π/2,π/2] respectively.

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Answer:

A ≈ 14.8 units²

Step-by-step explanation:

the area (A) of the triangle is calculated as

A = \(\frac{1}{2}\) yz sin Y ( that is 2 sides and the angle between them )

where x is the side opposite ∠ X and z the side opposite ∠ Z

here y = XZ = 4.3 and z = XY = 7 , then

A = \(\frac{1}{2}\) × 4.3 × 7 × sin79°

   = 15.05 × sin79°

   ≈ 14.8 units² ( to 1 decimal place )

Answer:

A

Step-by-step explanation:

The mean amount of snow per day is equal to 19 cm snow per day.

In Mathematics and Geometry, the mean for this set of data can be calculated by using the following formula:

Mean = [F(x)]/n

For the total amount of snow based on the frequency, we have;

Total amount of snow (s cm), F(x) = 5(8) + 15(10) + 25(7) + 35(2) + 45(3)

Total amount of snow (s cm), F(x) = 40 + 150 + 175 + 70 + 135

Total amount of snow (s cm), F(x) = 570

Now, we can calculate the mean amount of snow as follows;

Mean = 570/30

Mean = 19 cm snow per day.

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

Answer:

x       y

-2     4

-1       1

0       0

1         1

2        4

Step-by-step explanation:

Answer:

Y = -6X - 15

Step-by-step explanation:

-3 = -6(-2) + B

-3 = 12 + B

B= -15

Answer:

You didn't attach the options, but y = - 6x - 15

Step-by-step explanation:

Using the equation y = mx + b, you can plug in values that you have to solve for b, the y intercept. Since m is the slope and the slope is - 6, and you have a y and x value, you can write the equation as follows:

-3 = - 6 * -2 + b

Then solve for b

-3 = 12 + b

-15 = b

Then you rewrite the original formula with the values of m and b:

y = - 6x - 15

To write Acos(?0t) + Bsin(?0t) in the form r*sin(?0t - ?), we can use the identities. The relationship among R, r, ? and ? is:
R^2 = r^2 (1 + (A/B)^2), tan? = r/R = B/A

r = sqrt(A^2 + B^2)
tan? = B/A

Therefore, r = sqrt(A^2 + B^2) and tan? = B/A.

To determine the relationship among R, r, ? and ?, we can use the identity:

R^2 = r^2 + (tan?)^2

Therefore, R = sqrt(r^2 + (tan?)^2) and tan? = r/R. Substituting the expression for tan? from earlier, we get:

tan? = B/A = r/R

Solving for R, we get:

R = r/tan? = r/(B/A) = rA/B

And substituting the expression for R in terms of r and tan?, we get:

R = sqrt(r^2 + (r/R)^2) * A/B

Simplifying this expression, we get:

R^2 = r^2 + (A/B)^2 * r^2

R^2 = r^2 (1 + (A/B)^2)

Therefore, the relationship among R, r, ? and ? is:

R^2 = r^2 (1 + (A/B)^2)
tan? = r/R = B/A

To show that Acos(ω₀t) + Bsin(ω₀t) can be written in the form r*sin(ω₀t - θ), we can use trigonometric identities. We know that:

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

Comparing this to the given expression, we have:

Acos(ω₀t) + Bsin(ω₀t) = r*sin(ω₀t - θ) = r[sin(ω₀t)cos(θ) - cos(ω₀t)sin(θ)]

Now, let's equate the coefficients of sin(ω₀t) and cos(ω₀t):

A = -r*sin(θ)
B = r*cos(θ)

To find r and θ in terms of A and B, we can use the Pythagorean identity:

A² + B² = (-r*sin(θ))² + (r*cos(θ))² = r²(sin²(θ) + cos²(θ)) = r²

Therefore, r = √(A² + B²).

Now, to find θ, we can use the tangent function:

tan(θ) = -A/B

Now, for the second part, if Rcos(ω₀t - θ) = r*sin(ω₀t - θ), we can use the sine-to-cosine transformation:

Rcos(ω₀t - θ) = Rsin(ω₀t - θ + π/2)

This implies that:

R = r
θ + π/2 = θ'

So, the relationship among R, r, θ, and θ' is:

R = r
θ' = θ + π/2

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Answer:

k = \(\frac{1}{5}\)

Step-by-step explanation:

Given that r varies directly as p then the equation relating them is

r = kp ← k is the constant of variation

To find k use the condition r = 3 when p = 15, then

3 = 15k ( divide both sides by 15 )

\(\frac{3}{15}\) = k , that is

k = \(\frac{1}{5}\)

Answer:

k = 1/5

Step-by-step explanation:

The sine function that satisfies the given conditions is:
y = 4sin(3x - π) - 5

Let's break down the different parts of the equation:

1. Amplitude: The amplitude determines the maximum distance the graph reaches from its central axis. In this case, the amplitude is 4, so the graph will oscillate between 4 units above and 4 units below the central axis.

2. Period: The period determines the length of one complete cycle of the graph. In this case, the period is 3π, which means the graph will complete one full cycle every 3π units.

3. Phase Shift: The phase shift determines the horizontal shift of the graph. In this case, the phase shift is π, which means the graph will be shifted π units to the right.

4. Vertical Shift: The vertical shift determines the vertical displacement of the graph. In this case, the vertical shift is -5, which means the entire graph will be shifted 5 units downward.

So, the sine function with the given amplitude, period, phase shift, and vertical shift is y = 4sin(3x - π) - 5.

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Answer:

The first deal is the best deal. After the sales tax, the second deal is the better deal. I hope this helps!!

Answer:

978678

Step-by-step explanation:

kjgh

Answer:

Step-by-step explanation:

f(n) = n + 10

f(4) = 4 + 10 = 14

Answer: Well the range of how much it fills every 2 minutes is 5.2cm

Step-by-step explanation:

Answer: yes

Step-by-step explanation: 1.5+(-1.5)=1.5-1.5

Answer:

yes

Step-by-step explanation:

If a pollster wishes to estimate the number of left-handed scientists. The sample that is needed in order to be 95% confident that the sample proportion will not differ from the true proportion by more than 4% is: 176.71.

Using this formula to find the sample

n =Z²π (1-π) ÷ e²

Where:

n =sample size =?

Z =  Z -score for 95% confidence level =1.960

π = Population proportion = 0.08

e = Margin of error = 0.04

Let plug in the formula

n = 1.96² × 0.08 × (1 - 0.08) ÷ 0.04²

n =  3.8416× 0.08 × 0.92 ÷ 0.0016

n = 176.71

Therefore the sample is 176.71.

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Answer:

Either do 28+28+28, etc. 38 times, or follow the diagram I attached.

If you want to know more about what I did in the attachment, just ask <3

Answer:

Start by multiplying the ones: 6 times 28 is 168. Next, multiply the tens: 30 times 28 is 840. Add the products to get 1,008.

Step-by-step explanation:

The option that is least likely to be an application where statistics will be useful is "Choosing the wording of a corporate policy prohibiting smoking".

This is because statistics are generally used to analyze numerical data and make predictions or decisions based on that data.

However, choosing the wording of a corporate policy does not involve numerical data and therefore would not require the use of statistics.

The other options, such as deciding whether offering Rice Krispies improves restaurant sales, predicting whether an airfare is likely to rise or fall, and designing the most desirable features for a ski pass, all involve the analysis of numerical data and therefore would benefit from the use of statistics.

Statistics is the study of the collection, analysis, interpretation, presentation, and organization of data.

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The wave has:

Period = 3.5 seconds

Frequency = 1/3.5 = 0.29

Amplitude = 42 - 26 = 16 cm

We have,

Period:

The period of a wave refers to the time it takes for one complete cycle of the wave to occur.

T = 1 / f where f represents the frequency.

Frequency:

The frequency of a wave represents the number of complete cycles or oscillations of the wave that occur in a given time period.

f = 1 / T where T represents the period.

Amplitude:

The amplitude of a wave refers to the maximum displacement or distance from the equilibrium position of a particle in the wave.

Now,

The wave has:

Period = 3.5 seconds

Frequency = 1/3.5 = 0.29

Amplitude = 42 - 26 = 16 cm

Thus,

Period = 3.5 seconds

Frequency = 1/3.5 = 0.29

Amplitude = 42 - 26 = 16 cm

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(a) To find the probability that X is greater than 37, we use the cumulative standardized normal distribution table. First, we standardize the value by finding the z-score:

z = (37 - μ) / σ = (37 - 46) / 5 = -1.8

Using the table, we find the probability corresponding to the z-score of -1.8, which is 0.0359. However, we are interested in the probability that X is greater than 37, so we subtract this value from 1 to get 1 - 0.0359 = 0.9641.

(b) To find the probability that X is less than 41, we again standardize the value:

z = (41 - μ) / σ = (41 - 46) / 5 = -1.0

Using the table, we find the probability corresponding to the z-score of -1.0, which is 0.1587.

(c) To determine the X-value for which 9% of the values are less than, we need to find the corresponding z-score. We can use the inverse of the cumulative standardized normal distribution table to find the z-score that corresponds to a cumulative probability of 0.09. The z-score corresponding to a cumulative probability of 0.09 is approximately -1.34. We can then find the X-value by rearranging the formula for the z-score:

X = μ + (z * σ) = 46 + (-1.34 * 5) = 39.3

Rounding to the nearest integer, the X-value is 39.

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