If f(x) = 12x² - 5 and g(x) = x + 7 find(fºg)(x).
I need help asap please and thank you

Answer:

Step-by-step explanation:

if ∠1=∠2

2x+12=3x+3

3x-2x=12-3

x=9

∠1=2×+12=30°

∠2=30°

∠VXW=30+30=60°

Answer:

1/2

Step-by-step explanation:

If y is the √3/2 on the unit circle, x must be either 1/2 or -1/2.

Answer:

im thinking 25 or 24

Step-by-step explanation:

sorry if i made you get it wrong

The probability of observing a value from the Lorentzian distribution more than 1, 2, and 3 half-widths from the mean was found by numerical integration to be approximately 32.2%, 4.6%, and 0.33%, respectively.

The Lorentzian distribution is given by:

f(x) = (1/π) (γ/2) / ((x - x0)² + (γ/2)²)

where x0 is the location parameter (mean) and γ is the scale parameter (half-width at half-maximum, HWHM).

To find the probability of observing a value from the Lorentzian distribution that is more than k half-widths from the mean, we need to perform the following definite integral:

P(k) = ∫[x0 - k(γ/2), x0 + k(γ/2)] f(x) dx

a. More than 1 half-width from the mean (k = 1):

P(1) = ∫[x0 - (γ/2), x0 + (γ/2)] f(x) dx

To solve this integral, we can use a trigonometric substitution:

Let x - x0 = (γ/2) tan θ, then dx = (γ/2) sec² θ dθ.

Substituting into the integral, we get:

P(1) = (1/π) ∫[-π/4, π/4] dθ = 1/2

Therefore, the probability of observing a value from the Lorentzian distribution that is more than 1 half-width from the mean is 1/2 or 50%.

b. More than 2 half-widths from the mean (k = 2):

P(2) = ∫[x0 - γ, x0 + γ] f(x) dx

Using the same trigonometric substitution as before, we get:

P(2) = (1/π) ∫[-π/2, π/2] cos² θ dθ

Using the identity cos² θ = (1 + cos 2θ)/2, we can simplify the integral to:

P(2) = (1/2) + (1/π) ∫[0, π/2] cos 2θ dθ

Integrating, we get:

P(2) = (1/2) + (1/π) [sin π - sin 0] / 2 = (1/2) + 1/π

Therefore, the probability of observing a value from the Lorentzian distribution that is more than 2 half-widths from the mean is approximately 0.818 or 81.8%.

c. More than 3 half-widths from the mean (k = 3):

P(3) = ∫[x0 - (3γ/2), x0 + (3γ/2)] f(x) dx

Using the same substitution as before, we get:

P(3) = (1/π) ∫[-π/3, π/3] (3/2) sec² θ dθ

Simplifying, we get:

P(3) = (1/π) [tan π/3 - tan (-π/3)] / 2 = (1/π) √3 / 2

Therefore, the probability of observing a value from the Lorentzian distribution that is more than 3 half-widths from the mean is approximately 0.910 or 91.0%.

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Given :

Work done by a segment dx of a cable :

dW = 8dx x = 8x dx

So, work done by whole cable :

\(W=\int\limits^{450}_0 {8x} \, dx\\\\W = 4x^2|_0^{450}\\\\W = 4( 450^2)\\\\W= 810000\ ft- lb\)

Now, work done to bring coal up :

\(W'=900\times 450\ ft-lb\\\\W'=405000\ ft-lb\)

Therefore, total work done is ( 810000 + 405000 ) = 1215000 ft-lb .

Hence, this is the required solution.

The integers in the set S: {−2, −3, −4, −5} which would make the inequality 4p − 7 ≥ 9p + 8 true are: S:{−3, −4, −5}

In order to determine which integers are true with respect to a solution of the given inequality, we would have to test the given integers by substituting their values into the inequality as follows;

For integers (-2, -3), we have:

4p − 7 ≥ 9p + 8

4(-2) − 7 ≥ 9(-2) + 8

-8 - 7 ≥ -18 + 8

-15 ≥ -10 (False).

For integers (-2, -3), we have:

4p − 7 ≥ 9p + 8

4(-3) − 7 ≥ 9(-3) + 8

-12 - 7 ≥ -27 + 8

-19 ≥ -21 (True).

For integers (-3, -4), we have:

4p − 7 ≥ 9p + 8

4(-3) − 7 ≥ 9(-3) + 8

-12 - 7 ≥ -27 + 8

-19 ≥ -21 (True).

For integers (-3, -4), we have:

4p − 7 ≥ 9p + 8

4(-4) − 7 ≥ 9(-4) + 8

-16 - 7 ≥ -36 + 8

-23 ≥ -28 (True).

For integers (-4, -5), we have:

4p − 7 ≥ 9p + 8

4(-4) − 7 ≥ 9(-4) + 8

-16 - 7 ≥ -36 + 8

-23 ≥ -28 (True).

For integers (-4, -5), we have:

4p − 7 ≥ 9p + 8

4(-5) − 7 ≥ 9(-5) + 8

-20 - 7 ≥ -45 + 8

-23 ≥ -37 (True).

Therefore, -3, -4, and -5 are integers that would make the inequality true.

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Least time required to reach the point Q as per the distance and the speed rate is equal to 2 hours.

As given in the question,

Nearest point on the coast is 2 miles far away

rate of the row = 1mile per hour

Walk at the rate of 3 miles per hour

Let 'x' hours be the least time to reach point Q.

Time = distance / speed

Time taken to reach the point Q = [√ 1 + ( 3 - x)² ]/ 3

Time taken to reach the coast = (√ 4 + x² ) / 1

Total  time taken 't' = (√ 4 + x² ) / 1 + [√ 1 + ( 3 - x)² ]/ 3

To find least time dt/dx = 0

t  = (√ 4 + x² ) / 1 + [√ 1 + ( 3 - x)² ]/ 3

⇒dt/dx = [ x / √ 4 + x² ] + ( 3 - x) / √( 10 -6x + x² )

⇒x / √ 4 + x² = ( x - 3) / √( 10 -6x + x² )

Squaring both the side we get,

x² / (4 + x²) = ( x - 3)² / ( 10 -6x + x² )

⇒3x² -24x +36 =0

⇒ x² -8x + 12 = 0

⇒ x = 2 or 6 hours

Therefore , the least time taken to reach the point Q is equal to 2 hours.

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Answer:

$3.60

Step-by-step explanation:

Answer:

The relation is not a function.

Step-by-step explanation:

The x-values of the relation are repetitive, making it not a function.

Answer:

Not a function

Step-by-step explanation:

-1 is used more than once

Answer:

21f=12m

Step-by-step explanation:

Lidal's price is better

Step-by-step explanation:

Lidal

4 for £2.04

1 for £2.04/4= £0.51= 51 p

Oldi

9 for £4.68

1 for £4.68/9= £0.52= 51 p

Lidal offers better price per roll

Answer:

x = -3

Step-by-step explanation:

2/3x + 4 = 2

2/3x = 2 - 4

2/3x = -2

2x = -2 * 3

2x = -6

x = -6/2

x = -3

Note that given the angle of elevation, the distance from pont A to Point B is approximately 627.6ft.

See the attached image.

As shown in the attached figure:

L = AO Tan 8°

L = 1035 * Tan 8°

L = 1035 * 0.14054083470239144683811769343281

L = 1035 * 0.14054083470239144683811769343281

L = 145.46 Feet


BO = L/Tan 5°
BO =  145.459763917 / 0.08748866352592400522201866943496
BO = 1662.61270952
BO = 1662.6 Feet

Since AB = BO-AO
AB = 1662.6-1035

AB = 627.6 Ft.

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The weight before the party could be any positive number

The weight of the bag of ice after the party was 7/8 pounds. So we can set up an equation:

x - weight used at the party = 7/8

We know that the weight used at the party is the weight before the party minus the weight after the party.

So we can substitute 3x for the weight before the party:

3x - (7/8) = weight used at the party

We don't know the exact weight used at the party, but we do know that it was less than or equal to the weight before the party.

So we can set up another inequality:

weight used at the party ≤ 3x

Putting it all together:

3x - (7/8) ≤ 3x

Simplifying:

-(7/8) ≤ 0

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The solution is, The volume is 1,260 in³ & The surface area is 864 in^2.

In mathematics, volume is the space taken by an object. Volume is a measure of three-dimensional space. It is often quantified numerically using SI derived units or by various imperial or US customary units. The definition of length is interrelated with volume.

here, we have,

First, let's find the volume

Volume = length × width × height

30 × 6 × 7 = 1260

The volume is 1,260 in³

Surface Area:

Small squares: 84

(7 × 6) · 2

Smaller rectangles: 360

(30 × 6) · 2

Bigger rectangles: 420

(30 × 7) · 2

Now, let's add all

84 + 360 + 420 = 864

The surface area is 864 in^2.

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We are given the radius of the scoop and asked to find the volume of ice cream in one scoop. By using the formula for the volume of a sphere and substituting the given radius, we can calculate the volume. The final answer is approximately 33.49 cubic inches.

a) The problem asks for the volume of ice cream in one scoop.

b) The given fact is that the radius of the scoop is 2 inches.

c) The formula to be used is the volume of a sphere, which is given by V = (4/3)πr³, where V is the volume and r is the radius.

d) Number Sentence:

  - Given: Radius (r) = 2 inches

  - Formula: V = (4/3)πr³

  - Substituting the value: V = (4/3)π(2)³

  - Simplifying: V = (4/3)π(8)

  - Evaluating: V = (4/3)(3.14)(8)

  - Multiplying: V = 33.49333333 (approx.)

e) Final answer: The volume of ice cream in one scoop is approximately 33.49 cubic inches.

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ANSWER:

a)

b)

EXPLANATION:

Given:

a) When x = -4, let's go ahead and solve for y;

When x = 0, let's go ahead and solve for y;

When x = 4, let's go ahead and solve for y;

b) Using the above values, we can go ahead and the equation as seen below;

Answer:yes!

Step-by-step explanation:

Answer:

correct

Step-by-step explanation:

Answer:

3n-8

Explanation:

multiply n by 3 then subtract 8

Answer:

3 - 8 x n

Step-by-step explanation:

8 less than 3 -> 3 - 8

Times a number, n -> x n

Expression -> 3 - 8 x n

Answer: Mark needs 110 ft. fencing to surround all 4 gardens.

The value of the expression a(b + c) when a = 2, b = 3, and c = 4 is 14.

Given the expression in the question:

a( b + c )

Also, a = 2, b = 3, and c = 4

To evaluate the expression a( b + c ) when a = 2, b = 3, and c = 4, we substitute these values into the expression:

Hence:

a( b + c )

Plug in a = 2, b = 3, and c = 4

2( 3 + 4 )

First, we simplify the parentheses by adding 3 and 4:

2( 7 )

Next, we multiply 2 and 7:

14

Therefore, the value of a(b + c) is 14 .

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Comparing the ratios in form of fraction, the ratio 1:3 is the largest.

The ratio is defined as the comparison of two quantities of the same units that indicates how much of one quantity is present in the other quantity. We use the ratio formula while comparing the relationship between two numbers or quantities. The general form of representing a ratio of between two quantities say 'a' and 'b' is a: b, which is read as 'a is to b'.

In the ratios given, we have 2:9, 3:18 and 1:3

Let's write these in form of fraction to the decimal and determine which is the largest.

i)

2:9 = 2/9 = 0.22

ii)

3:18 = 3/18 = 0.1666 ≅ 0.17

iii)

1:3 = 1/3 = 0.33

From the above fractions, the ratio 1:3 is the largest.

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To simplify the expression, we need to remember that the cosine function has the following identity:

Which gives an expression for the cosine of a sum of angles. In this case we have the following original expression:

If we compare this expression to the right side of the identity given above, we notice that we have a similar structure but, in this case, instead of alpha we have 3x and instead of beta we have x; for this reason, let:

Then we have, according to the identity given above:

Therefore, the expression given simplifies to:

Answer:

4

Step-by-step explanation:

the total height is 12 and the first half of the shape has a height of 8 so the other part is 4.

The equation of the least-squares line predicting wins from payroll is:

y = -6.37 + 0.1*x

The equation of the least-squares line predicting wins from payroll can be calculated using the following formula:

y = b0 + b1*x

where y is the dependent variable (number of wins), x is the independent variable (payroll in millions of dollars), b0 is the y-intercept of the line, and b1 is the slope of the line.

To calculate the values of b0 and b1, you can use the following formulas:

b1 = r*(\(\frac{sy}{sx}\))

b0 = mean(y) - b1*mean(x)

where r is the correlation coefficient between x and y, sx is the standard deviation of x, and sy is the standard deviation of y.

Using the values provided in the table, we can calculate the equation of the least-squares line as follows:

b1 = 0.393*(\(\frac {3.12}{12.34}\)) = 0.1

b0 = 7.75 - 0.1*142.1 = -6.37

Therefore, the equation of the least-squares line predicting wins from payroll is:

y = -6.37 + 0.1*x

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The value of 0.045 × 2.05 / 0.0025 in standard form is 3.69 × 10.

To perform the calculation and express the answer in standard form, follow these steps:

Multiply 0.045 by 2.05:

0.045 × 2.05 = 0.09225

Divide the result by 0.0025:

0.09225 / 0.0025

= 36.9

Convert the answer to standard form by writing it as a decimal multiplied by a power of 10:

36.9 = 3.69 × 10

Therefore, the value of 0.045 × 2.05 / 0.0025 in standard form is 3.69 × 10.

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We are given a six-sided die and we are asked to determine the probability of getting a number less than 3. To do that, let's remember that the probability is defined as the quotient between the number of desired outcomes and the total number of outcomes. Since there are 2 number in the die that are less than 3 (1, 2) there are 2 possible desired outcomes and since the die has 6 sides, there are 6 possible outcomes, therefore, the probability is: