g(a) = 4a - 5; Find a when g(a)=-37

Answer:

B

Step-by-step explanation:

put both sides under square root.

x^2 + y^2 = 64

sqrt ( x^2 + y^2 ) = sqrt(64)

x + y = 8

r = 8.

\(\underline{r^2=x^2+y^2} \\\\\\ x^2+y^2=64\implies r^2=64\implies r=\sqrt{64}\implies r=8\)

Answer:

the two points are (-3,-3

Step-by-step explanation:

You must first check if the line is a straight line two the you check the intersection of the two points and the write it

If 6 human resource managers are randomly selected, the probability that at least 2 of them say job applicants should follow up within two weeks is; 81.047%

The binomial probability is defined as the probability of exactly x successes on n repeated trials, with p probability

The general formula of binomial probability distribution is;

P(X = x) = ⁿCₓ * pˣ * (1 - p)⁽ⁿ ⁻ ˣ⁾

where;

p is probability of success

n is number of trials or sample size

x is number of successful trials

Thus,  If 6 human resource managers are randomly selected, the probability that at least 2 of them say job applicants should follow up within two weeks is;

P(X ≥ 2) = 1 - (P(0) + P(1))

P(0) = ⁶C₀ * 0.43⁰ * (1 - 0.43)⁽⁶ ⁻ ⁰⁾ = 0.0343

P(1) = ⁶C₁ * 0.43¹ * (1 - 0.43)⁽⁶ ⁻ ¹⁾ = 0.15524

P(X ≥ 2) = 1 - (0.0343 + 0.15524)

P(X ≥ 2) = 0.81047 = 81.047%

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The centroid of the region bounded by the curves y = 2 sin(3x), y = 2 cos(3x), x = 0, and x = 12 is approximately (x, y) = (6, 0).

To find the centroid of the region bounded by the given curves, we need to determine the x-coordinate (x-bar) and y-coordinate (y-bar) of the centroid. The x-coordinate of the centroid is given by the formula:

x-bar = (1/A) * ∫[a,b] x * f(x) dx,

where A represents the area of the region and f(x) is the difference between the upper and lower curves.

Similarly, the y-coordinate of the centroid is given by:

y-bar = (1/A) * ∫[a,b] 0.5 * [f(x)]^2 dx,

where 0.5 * [f(x)]^2 represents the squared difference between the upper and lower curves.

Integrating these formulas over the given interval [0, 12] and calculating the areas, we find that the x-coordinate (x-bar) of the centroid is equal to 6, while the y-coordinate (y-bar) evaluates to 0.

Therefore, the centroid of the region is approximately located at (x, y) = (6, 0).

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Answer:

25

Step-by-step explanation:

let x = the amount of money that shelly has.

let y = the amount of money that john has.

if shelly give john 5 dollars, then they both have the same amount of money.

this leads to the equation:

x-5 = y+5

if john give shelly 5 dollars, then shelly has twice as much money as john has.

this leads to the equation:

x+5 = 2(y-5)

solve for x in each equation to get:

x-5 = y+5 leads to:

x = y+10

x+5 = 2(y-5) leads to:

x+5 = 2y-10 which becomes:

x = 2y-15

you have 2 expressions that are equal to x.

they are:

x = y+10

x = 2y-15

you can set these expressions equal to each other to get:

y+10 = 2y-15

subtract y from both sides of this equation and add 15 to both sides of this equation to get:

y = 25

since x = 2y-15, this leads to:

x = 2(25)-15 which becomes:

x = 35

the equation x = y + 10 leads to the same answer of:

y =35

you have:

x = 25

y = 35

The volume of a rectangular prism is always greater than or equal to the volume of a pyramid with the same height and base.

How to find the volume of a rectangular prism and pyramid?

The formula for the volume of a rectangular prism is:

Volume = Length * Width * Height

The formula for the volume of a pyramid is:

Volume = (Base Area * Height) / 3

The volume of a rectangular prism is always greater than or equal to the volume of a pyramid with the same height and base.

This is because the volume of a rectangular prism is calculated by multiplying its three dimensions together, whereas the volume of a pyramid is calculated by multiplying the base area by the height and dividing the result by 3.

Hence, the volume of the rectangular prism is greater than the volume of the pyramid with the same height and base. This is because the rectangular prism has additional volume in the form of its width, which the pyramid does not have.

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Answer:

4 + x×9 >= 22

Step-by-step explanation:

that is the word by word "translation".

Answer:

5:10

or if they prefer it simplified 1:2

Step-by-step explanation:

It asks to write the number of cherry pies sold(5) to the number of apple pies sold (10).

Exactly how it is written is how it should be answered (5:10)

Now if they ask for it to be simplified, we know that five goes into 5 once and twice into 10 thus giving the expression 1:2

Step-by-step explanation:

FIRST find the hypotenuse  CB

 sin B = .5 =  opposite leg/ hypotenuse

            .5 = 3x/CB

             CB = 3x/.5 = 6x

Now you can use the Pythagorean theorem

   (6x)^2 = (3x)^2 +  AB ^2

AB ^2 = 36x^2 - 9x^2

AB ^ 2 = 27 x^2

AB = x sqrt 27

AB = 3x sqrt 3

OR

If sin = 1/2    cos = sqrt(3) /2     Using  CB = 6x as before

 AB  =    sqrt (3)/2 * 6x =   3x sqrt 3

Answer:

1/16 out of the entire thing.

Step-by-step explanation:

1/4 of 1/4 is the same as 1/4 x 1/4.

1/4 x 1/4 = 1/16.

Answer:

A.

Step-by-step explanation:

The Answer is A

The expression for the area under the curve y = x^3 from 0 to 1, as a limit, is A = 1/4.

(a) To find an expression for the area under the curve y = x^3 from 0 to 1 using Definition 2, we need to approximate the area using a sum and then take the limit as the number of approximating rectangles approaches infinity.

Let's divide the interval [0, 1] into n equal subintervals. The width of each subinterval will be Δx = 1/n. We can choose any point within each subinterval as the representative x-value for that subinterval. Let's choose the right endpoint of each subinterval as our representative x-value.

The right endpoint of the ith subinterval will be x_i = iΔx = i/n, where i ranges from 1 to n. The corresponding y-value for each x_i is y_i = (i/n)^3.

The area of each rectangle can be approximated as the product of the width and height of the rectangle, which is ΔA_i = Δx  y_i = (1/n)  (i/n)^3.

The total area under the curve can be approximated by summing up the areas of all the rectangles:

A = Σ(ΔA_i) = Σ[(1/n)  (i/n)^3] for i = 1 to n.

(b) The formula given in Appendix E states that the sum of the cubes of the first n integers is [n(n+1)/2]^2. Therefore, we have:

1^3 + 2^3 + 3^3 + ... + n^3 = [n(n+1)/2]^2.

Using this formula, we can rewrite the expression for the area under the curve as a limit:

A ≈ Σ[(1/n)  (i/n)^3] for i = 1 to n

= (1/n^4)  [1^3 + 2^3 + 3^3 + ... + n^3]

= (1/n^4)  [n(n+1)/2]^2.

Taking the limit as n approaches infinity, we have:

A = lim(n→∞) [(1/n^4) [n(n+1)/2]^2]

= lim(n→∞) [(n^2(n+1)/2)^2 / n^4]

= lim(n→∞) [(n^4 + 2n^3 + n^2) / 4n^2]

= lim(n→∞) [(1 + 2/n + 1/n^2) / 4]

= (1 + 0 + 0) / 4

= 1/4.

Therefore, the expression for the area under the curve y = x^3 from 0 to 1, as a limit, is A = 1/4.

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Answer:

Just Chill no need to take tension.

Step-by-step explanation:

ok so u need to like add stuff yk

like just see other answers

a. The resultant magnetic field at point P due to currents in the two wires can be determined by vector addition of the individual magnetic fields.

b. Reversing the direction of currents in both wires would result in a reversed direction of the resultant magnetic field at point P.

a. To construct the vector diagram showing the direction of the resultant magnetic field at point P due to currents in the two wires, we can use the right-hand rule for determining the magnetic field direction around a wire carrying current.

For Wire 1, which has the current coming towards us (out of the plane of the paper), the magnetic field direction can be determined by wrapping the right-hand fingers around the wire in the direction of the current, and the thumb will point in the direction of the magnetic field. Let's say the direction of the magnetic field for Wire 1 is from left to right.

For Wire 2, which has the current going into the plane of the paper, we apply the right-hand rule again. Wrapping the right-hand fingers around the wire in the direction opposite to the current, the thumb will point in the direction of the magnetic field. Let's say the direction of the magnetic field for Wire 2 is from right to left.

At point P, which is equidistant from the two wires, the magnetic fields due to the currents in the wires will combine. The resultant magnetic field direction at point P can be found by vector addition. Drawing the vectors representing the magnetic fields for Wire 1 and Wire 2, with opposite directions, we can add them head-to-tail. The resultant vector will show the direction of the resultant magnetic field at point P.

b. If the currents in both wires were instead directed into the plane of the page (such that the current moved away from us), the directions of the magnetic fields due to the currents in the wires would be reversed compared to the previous case.

For Wire 1, the magnetic field direction would be from right to left, and for Wire 2, it would be from left to right. Following the same process as in part a, we would draw the vectors representing the magnetic fields for Wire 1 and Wire 2 in their respective reversed directions. Adding them head-to-tail would give us the resultant vector indicating the direction of the resultant magnetic field at point P in this scenario.

Complete Question:

Two wires lie perpendicular to the plane of the paper, and equal electric currents pass through the paper in the directions shown. Point P is equidistant from the two wires.

a. Construct a vector diagram showing the direction of the resultant magnetic field at point P due to currents in these two wires. Explain your reasoning.

b. If the currents in both wires were instead directed into the plane of the page (such that the current moved away from us), show the resultant magnetic field at point P.

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based on the alternating series test, the series ∑((-1)^(n-1)*b_n) is convergent.

To test the series ∑((-1)^(n-1)*\(b_n\)), n = 1, for convergence or divergence using the alternating series test, we need to check two conditions:

1. The sequence {\(b_n\)} is positive and monotonically decreasing (i.e., b_n > 0 and \(b_n\) ≥ b_(n+1) for all n).

2. The limit of \(b_n\) as n approaches infinity is 0 (i.e., lim(n→∞) \(b_n\) = 0).

Given the series ∑((-1)^(n-1)*\(b_n\)) = 1/2 - 1/3 + 1/4 - 1/5 + 1/6 - ...

Let's evaluate the two conditions:

1. The sequence {\(b_n\)} = {1/2, 1/3, 1/4, 1/5, 1/6, ...} is positive since all terms are reciprocals of positive numbers. Now, we need to check if it is monotonically decreasing.

\(b_n\) ≥ b_(n+1) for all n:

1/2 ≥ 1/3

1/3 ≥ 1/4

1/4 ≥ 1/5

1/5 ≥ 1/6

Since {b_n} is positive and monotonically decreasing, the first condition is satisfied.

2. To check the second condition, we need to evaluate the limit of \(b_n\)as n approaches infinity:

lim(n→∞) \(b_n\) = lim(n→∞) (1/n) = 0

Since the limit of \(b_n\) as n approaches infinity is 0, the second condition is satisfied.

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We have to blend two mixtures of ethanol (E7 and E10) to make an E9 mixture.

We know that the amount of E10 mixture is 4000 gal.

Let x be the amount of E7 mixture.

As we have x gallons of E7 and 4000 gallons of E10, the volume of the E9 mixture will be (x+4000).

The volume of ethanol in the E7 mixture will be 0.07*x gallons.

The volume of ethanol in the E10 mixture is 0.1*4000 = 400 gallons.

The volume of ethanol in the E9 mixture will be 0.09*(x+4000) gallons.

As the sum of the ethanol volume in the E7 and E10 mixtures has to be equal to the ethanol in the E9 mixture, we can write:

We can use this equation to solve for x:

Then, the volume of the E7 mixture has to be 2000 gallons.

Answer: 2000 gallons of E7 mixture.

Answer: x∈(-∞,-2√6-2)U(2√6-2,+∞)

Step-by-step explanation:

\(\displaystyle\\y=\frac{1}{4} (x+2)^2-6\\y > 0\\Hence,\\\frac{1}{4}(x+2)^2-6 > 0 \\\\\frac{1}{4}(x+2)^2-6+6 > 0+6\\\\\frac{1}{4}(x+2)^2 > 6\\\)

Multiply both parts of the equation by 4:

\((x+2)^2 > 24\)

Extract the square root of both parts of the inequality:

\(|x+2| > \sqrt{24} \\|x+2| > \sqrt{4*6} \\|x+2| > 2\sqrt{6}\)

Expand the modulus - we get a set of inequalities:

\(\displaystyle\\\left [{{x+2 > 2\sqrt{6}\ \ \ \ (1) } \atop {-(x+2) > 2\sqrt{6} \ \ \ (2)}} \right.\\\)

Multiply both parts of inequality (2) by -1 and reverse the sign of the inequality:

\(\displaystyle\\\left [ {{x+2-2 > 2\sqrt{6}-2 } \atop {x+2 < -2\sqrt{6} }} \right. \ \ \ \ \ \left [ {{x > 2\sqrt{6}-2 } \atop {x+2-2 < -2\sqrt{6} -2}} \right. \ \ \ \ \ \left [ {{x > 2\sqrt{6}-2 } \atop {x < -2\sqrt{6}-2 }} \right.\)

Thus,

\(x\in(-\infty,-2\sqrt{6}-2)U(2\sqrt{6} -2,+\infty)\)

Answer:

1. 918

2. 2880

3. 2678

4. 22554

5. 66014

6. 44208

Answer:

x=16

Step-by-step explanation:

16+18+10=44

18+10+x=28+x

44-28=x

x=16

Ashley used 8/25 of the spool for her project.

To determine the fraction of the spool that Ashley used for her project, we need to multiply the fraction of the spool she had (4/5) by the fraction she used (2/5):

(4/5) * (2/5) = 8/25

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A new sample size of at least 537 fish to estimate the true mean length with a margin of error of 0.5 centimeters and 95% confidence.

To determine the size of a new sample so that the true mean length is estimated with a margin of error of 0.5 centimeters with 95% confidence, we need to find the standard error of the mean and use it in the formula for the margin of error.

The formula for the margin of error is: ME = z * (σ/√n)

where z is the z-score corresponding to the desired confidence level, σ is the standard deviation of the population, and n is the sample size.

We can estimate the standard deviation of the population using the sample variance, which is given as 34.9.

The standard deviation is the square root of the variance, so σ = √34.9

= 5.91.

To find the standard error of the mean, we divide the standard deviation by the square root of the sample size:

SEM = σ/√n

= 5.91/√n We want the margin of error to be 0.5 centimeters, so we can set up the equation:

0.5 = z * (5.91/√n)

To solve for n, we need to know the value of z for a 95% confidence level.

This corresponds to a z-score of 1.96. Substituting this into the equation gives: 0.5 = 1.96 * (5.91/√n)

Simplifying and solving for n gives: √n = 1.96 * (5.91/0.5) √n

n =(23.18)

n = 537

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This value is approximate.

============================================================

Explanation:

Let's focus on the 48 degree angle. This angle combines with angle ABC to form a 90 degree angle. This means angle ABC is 90-48 = 42 degrees. Or in short we can say angle B = 42 when focusing on triangle ABC.

Now let's move to the 17 degree angle. Add on the 90 degree angle and we can see that angle CAB, aka angle A, is 17+90 = 107 degrees.

Based on those two interior angles, angle C must be...

A+B+C = 180

107+42+C = 180

149+C = 180

C = 180-149

C = 31

----------------

To sum things up so far, we have these known properties of triangle ABC

Let's use the law of sines to find side b, which is opposite angle B. This will find the length of side AC (which is the distance from the storm to station A).

b/sin(B) = c/sin(C)

b/sin(42) = 24/sin(31)

b = sin(42)*24/sin(31)

b = 31.1804803080182 which is approximate

b = 31.2 miles is the distance from the storm to station A

Make sure your calculator is in degree mode.

The weather station A is 31.2 miles from the storm

From the triangle shown:

m<B = 90° - 48°

m<B = 42°

m<A = 17° + 90°

m<A = 107°

m<A + m<B + m<C = 180° (Sum of angles in a triangle)

107° + 42° + m<C = 180°

m<C = 180° - 149°

m<C = 31°

The distance between the weather stations A and B = 24 miles

That is, AB = 24 miles

The storm is at point C

The length AC is found by using the rule of sines:

\(\frac{sinC}{AB}=\frac{sinB}{AC} \\\\\frac{sin31}{24}=\frac{sin42}{AC} \\\\\frac{0.515}{24} = \frac{0.669}{AC} \\\\0.02146=\frac{0.669}{AC}\\\\AC=\frac{0.669}{0.02146} \\\\AC=31.2 miles\)

The weather station A is 31.2 miles from the storm

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According to the information we can infer that the compound that will have the longeset wavelength absorption is 1, 3, 5, 7 octatetraene (option a).

The compound 1, 3, 5, 7 octatetraene absorbs light with the longest wavelength among the given options. This is because the longer the conjugated system in a compound, the longer the wavelength of light it can absorb. 1, 3, 5, 7 octatetraene has a larger conjugated system compared to the other compounds listed, which results in its ability to absorb light with longer wavelengths.

Note: This question is incomplete. Here is the complete question:
Which of the following compounds absorbs light with the longest wavelength ?

(a) 1, 3, 5, 7 octatetraene

(b) 1, 3, 5-octatriene

(c) 1, 3-butadiene

(d) 1, 3, 5-hexatriene

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Answer:

no

Step-by-step explanation:

If f(4) = 7 then the inverse of the function f⁻¹(7) is 4.

Function is a combination of different types of variable and constants in which for the different values of x the value of function y is unique.

The given function is,

f(4) = 7

According to inverse function property,

if f(x) = y, then f⁻¹(y) = x

The inverse of function,

f⁻¹(7) = 4

The inverse of the function f(4) = 7 is f⁻¹(7) = 4.

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The first one is C

The second one is YES

To get equation b from a, you have to divide by three, which is the non zero constant.

Both equations do give the same answer because if you divide first one(a) by 3, you will end up with the second(b).

Hope this helps

Answer:

6 units

Step-by-step explanation:

use imagination to separate the triangle from the square.

2*2 is 4 which is the volume of the square part

2*2/2 is the volume of the triangle which divides out to be 2

2+4=6

The formula that can be used to find the area (a) of a parallelogram is: a = base × height.

Which formula can be used to find the area (a) of a parallelogram with a base length of 14 centimeters and a height represented by 'h' centimeters?

The answer states that the formula to find the area of a parallelogram is "a = base × height" based on the given information of a base length of 14 centimeters and a height represented by 'h' centimeters.

This formula is derived from the geometric properties of a parallelogram, where the area is equal to the product of the base length and the corresponding height.

By substituting the given values into the formula, we can calculate the area of the parallelogram in square centimeters.

The formula assumes that the height is perpendicular to the base and that the given values accurately represent the dimensions of the parallelogram.

It's important to note that without a specific value for 'h', the exact area cannot be determined, but the formula provides a general method to calculate it.

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Answer:

Step-by-step explanation:

Simplify by factoring both trinomials:

Answer:

675 ÷ 3 - ( 225 - 144)

675 ÷ 3 - (81)

225 - 81

144

I hope it's helps you

Answer:

\(675 \div 3 - (15 - 12) {}^{2} \\ \\ 675 \div 3 - (225 - 144) \\ \\ 675 \div 3 - 81 \\ \\ 225 - 81 \\ \\ = 144\)