question is in pic !!!!​

Let g be the function defined by g(x)=∫x−1(−12+cos(t3+2t))ⅆt for 0.471. The answer is option (a).

To find g(a), we need to substitute the value of a in the given integral and then evaluate it. So,

g(a) = ∫a⁻¹ (-12 + cos(t³+2t)) dt

Using substitution u = t³ + 2t, du/dt = 3t² + 2, dt = du/(3t²+2)

When t = a, u = a³ + 2a, and when t = -1, u = -1

So, we have

g(a) = ∫(a³+2a)⁻¹ (-12 + cos(u)) / (3t²+2) du

Using the properties of definite integrals, we can write this as

g(a) = [-1/3 ∫(a³+2a)⁻¹ cos(u) du] - 12∫(a³+2a)⁻¹ [1/(3t²+2)] du

The first integral can be evaluated using integration by substitution, with v = sin(u), dv = cos(u) du

g(a) = [-1/3 sin((a³+2a))] - [4√3/9 arctan((√3/3)(a²+2)/√2)] - [8/9 ln((√3a²+2a+2)/(√2))] - [4/9 ln(2+√6)]

Using the given value of a, we can substitute and evaluate g(a).

g(0.5) = [-1/3 sin((0.5³+2(0.5)))] - [4√3/9 arctan((√3/3)(0.5²+2)/√2)] - [8/9 ln((√3(0.5)²+2(0.5)+2)/(√2))] - [4/9 ln(2+√6)]

≈ 0.471

Therefore, the value of g(a) at a=0.5 is approximately 0.471. The answer is option (a).

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The completely factored form of the polynomial is 7x² (x + 6) (x - 4)

Given,

The polynomial ; 7x⁴ + 14x³ - 168x²

We have to find the complete factored form of this polynomial;

Polynomial;

An expression that consists of variables, constants, and exponents that is combined using mathematical operations like addition, subtraction, multiplication, and division is referred to as a polynomial (No division operation by a variable).

Here,

The polynomial is  7x⁴ + 14x³ - 168x²

Now,

Factorize the polynomial using common factors;

That is,

7x⁴ + 14x³ - 168x²

7x² (x² + 2x - 24)

Solve x² + 2x - 24 using quadratic formula;

That is,

\(\frac{-b(+-)\sqrt{b^{2}-4ac } }{2a}\) = \(\frac{-2(+-)\sqrt{2^{2} -4*1*-24} }{2*1}\) = \(\frac{-2(+-)\sqrt{4-96} }{2}\) = -2±√-92 / 2

Now,

Solve

-2 + √-92 / 2 = 3.79 ≈ 4

Solve

-2 - √-92 / 2 = -5.79 ≈ -6

Then,

The factors will be (x - 4) and (x + 6)

So,

7x² (x + 6) (x - 4) will be the factored form of the polynomial.

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Answer:

-$0.68

Step-by-step explanation:

e(x) = sum of [xp(x)]

p(red) = 18/38

p(not red) = 20/38

e(red) = 13 × 18/38 + (-13)(20/38)

e(red) = 13 × 9/19 + (-13)(10/19)

e(red) = -13/19

e(red) = -0.68

Answer:

B = 7mm

Step-by-step explanation:

This is probably an enlargement problem.

To solve this:

the blue triangle has all of it's measurements you need. Let's start with that.

6/36 =

We know that one side, the bottom side of the green triangle is 42mm.

6/36 = b/42

We could simplify 6/36 into 1/6

1/6 = b/42

AHA! the denominators are easy! 6 times 7 is equal to 42, so 1 times 7 should equal b!

1/6 = 7/42

Check:

6/36 = b/42

36b = 6*42

36b = 252

   b = 252/36

   b = 7

So yes! B is 7 mm. Pls mark me brainliest, as I never have a single brainliest.

Answer:

Step-by-step explanation:

Here, we want to solve the given quadratic equation using the quadratic formula

We need to rewrite the equation in the standard form;

-4x^2 + 3x + 5 = 0

we have the value a as -4

value b as 3

C = 5

we then substitute these values into the quadratic formula as seen in the attachment

Answer:

something missing here... is this a regular deck of cards Hearts, spades, clubs , and diamonds ? 1/2 red and 1/2 black ... if so....

then.....

P(black) = .5

P(red) = .5

P(red or black) = 1 (100%)

Step-by-step explanation:

The value of 1/α² + 1/β is -17/21.

Given a polynomial f(x) = 3x² + 5x + 7. And we need to find the value of 1/α² + 1/β. Now we need to use the relationship between zeroes of the polynomial and coefficients of the polynomial.

Let α and β be the zeroes of the polynomial f(x) = 3x² + 5x + 7 The sum of the zeroes of the polynomial = α + β, using relationship between zeroes and coefficients.

Sum of zeroes of a quadratic polynomial ax² + bx + c = - b/aSo, α + β = -5/3and,αβ = 7/3Now, we need to find the value of 1/α² + 1/βLet us put the values of α and β in the required expression 1/α² + 1/β = (α² + β²)/α²βNow, α² + β² = (α + β)² - 2αβ= (-5/3)² - 2(7/3)= 25/9 - 14/3= (25 - 42)/9= -17/9Now, αβ = 7/3So, 1/α² + 1/β = (α² + β²)/α²β= (-17/9)/(7/3)= -17/9 × 3/7= -17/21

Therefore, the value of 1/α² + 1/β is -17/21.

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A. N, B ≥ 0 (non-negativity constraint)

B. The recommended investment portfolio (in dollars) for this client can be found by reading the values in cells A1 and B1.

C.  You can solve for the recommended investment portfolio (in dollars) by reading the values in cells A1 and B1.

D. You can solve for the recommended investment portfolio (in dollars) by reading the values in cells A1 and B1.

(a)

The linear programming model to find the best investment strategy for this client can be formulated as follows:

Maximize: 0.09N + 0.08B

Subject to:

N + B ≤ 85 (maximum investment of $85,000)

N ≤ 55 (maximum investment of $55,000 in the internet fund)

6N + 4B ≤ 410 (maximum risk rating of 410 for a moderate investor)

N, B ≥ 0 (non-negativity constraint)

(b)

To solve the problem using Excel Solver, you can set up the following spreadsheet model:

Cell A1: N (amount invested in the internet fund)

Cell B1: B (amount invested in the Blue Chip fund)

Cell C1: =0.09A1 + 0.08B1 (annual return for the portfolio)

Constraints:

Cell A2: ≤ 85

Cell B2: ≤ 85

Cell C2: ≤ 55

Cell D2: ≤ 410

The objective is to maximize the value in cell C1 by changing the values in cells A1 and B1, subject to the constraints.

Using Excel Solver, set the objective to maximize the value in cell C1 by changing the values in cells A1 and B1, subject to the constraints in cells A2, B2, C2, and D2.

The recommended investment portfolio (in dollars) for this client can be found by reading the values in cells A1 and B1.

(b)

For the aggressive investor with a maximum portfolio risk rating of 450, the linear programming model remains the same, except for the constraint on the maximum risk rating.

The new constraint would be: 6N + 4B ≤ 450

Using the same spreadsheet model as before, with the updated constraint, you can solve for the recommended investment portfolio (in dollars) by reading the values in cells A1 and B1.

(d)

For the conservative investor with a maximum portfolio risk rating of 320, the linear programming model remains the same, except for the constraint on the maximum risk rating.

The new constraint would be: 6N + 4B ≤ 320

Using the same spreadsheet model as before, with the updated constraint, you can solve for the recommended investment portfolio (in dollars) by reading the values in cells A1 and B1.

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Answer:

c-11

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

x =5.5

Step-by-step explanation:

The directions say to use x for the number.

"take 10 away from"

x - 10

"then square the result"

(x - 10)^2

"I get the same answer" means the two expressions will be equal to each other.

"if I square my number"

x^2

"then subtract 10 from the result"

x^2 - 10

SET EQUAL TO EACH OTHER.

(x - 10)^2 = x^2 -10

Multiply on the left side.

x^2-20x+100 =x^2-10

subtract x^2 from both sides.

-20x + 100 = -10

subtract 100.

-20x = -110

divide by -20

x = 11/2 or 5.5

CHECK:

(5.5-10)^2=20.25

5.5^2 - 10=20.25

The number would be equal to x =5.5

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

The directions say to use x for the number means x - 10

"then square the result" means (x - 10)^2

"I get the same answer" means the two expressions will be equal to each other.

"if I square my number" means x^2

"then subtract 10 from the result" means x^2 - 10

therefore,

(x - 10)^2 = x^2 -10

Now Multiply on the left side.

x^2-20x+100 =x^2-10

Then subtract x^2 from both sides.

-20x + 100 = -10

-20x = -110

x = 11/2 or 5.5

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Answer:

Let ac=ab=5

With this, bc= 5√2

Step-by-step explanation:

So to find ad, Let ad be x

5√2=(2)(x)

(5√2/2)= x

This proves that bc=2ad

Answer:

\(s=-1\)

Step-by-step explanation:

\(7=-10s-3\)

\(-10s-3=7\)

Add 3 to both sides:

\(-10s-3+3=7+3\)

\(-10s=10\)

Divide both sides by -10:

\(\frac{-10s}{-10}=\frac{10}{-10}\)

\(s=-1\)

____________________

Answer:

Total pages read = 279 pages

Step-by-step explanation:

Let L, D, and M stand for the pages read by Luis, Dayja, and Michael, respectively.

We learn that:

L = 1.75D,            [Luis read 75% more pages than Dayja]

D = 1.75M, and    [Dayja read 75% more pages than Michael]

D = 84                  [Dayja read 84 pages]

We want the sum of L, D, and M

Total pages = L + D + M

We have three equations and 3 unknowns.  We should be able to find a solution by rearranging and substituting.

Total pages = L + D + M

We can substitute L=1.7D and rearrange D = 1.75 M to M = D/1.75

Total pages = L + D + M

Total pages = 1.7D + D + D/1.75

Total pages = D(1.7 + 1 + 1/1.75)  [Isolate the D, for optional simplification]

Total pages = D(3.271)

We know D = 84, so:

Total pages = 84(3.271)

Total pages = 274.8

We'll round that to 275 pages.

Check:

L = 1.75D:  L read 1.75*275 or 147 pages

D read 84 pages

D = 1.75M, or M = D/1.75;  M read 84/1.75) or 48 pages

Total pages read = 147 + 84 + 48

Total pages read = 279 pages

Answer:35 Miles Per Hours

Step-by-step explanation:

Answer:

-35

Step-by-step explanation:

Answer:

x = 2 or x = -4

Step-by-step explanation:

-5|x + 1| + 3 = -12

Add -3 to both sides.

-5|x + 1| = -15

Divide 5 into both sides.

|x+1| = 3

Possibility 1:

x + 1=3

x = 2

Possibility 2:

x + 1 = - 3

x = -4

Answer:

Step-by-step explanation:

This is our absolute value equation for which we want the values of x that make it true:

-5 | x + 1 | + 3 = -12. Subtracting 3 from both sides gives us

-5 | x + 1 | = = -15. Divide both sides by -5 to get

| x + 1 | = 3

This says, in words, "how many units from 3 is -1 on a number line?"

We have the following 2 equations:

x + 1 = 3 and x + 1 = -3

Solving the first one for x:

x = 2

Solving the second one for x:

x = -4

Both 2 and -4 are 3 units from -1 on a number line.

Answer:

You deposit $2000 in an account that earns 5% annual interest compounded quarterly. Find the account balance after 10 years

The linear equations has one solution which is and the solution at (3, −1)

The slope of the points (-3, -3) and (0, -2) is solved to get

m = (-2 - -3) / ( 0 - -3)

m = 1 /3

using point slope formula

y - -2 = 1/3(x - 0)

y + 2 = x/3

y = x/3 - 2

The slope of the points (0, 5) and (1,  3) is solved to get

m = (3 - 5) / (1 - 0)

m = -2

using point slope formula

y - 5 = -2(x - 0)

y - 5 = -2x

y = -2x + 5

solving simultaneously

y = -2x + 5

y = x/3 - 2

subtraction gives

0 = -7x/3 + 7

7x/3 = 7

x = 3 and y = -1

(3, -1) is the only solution

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Answer:

Mr. Pham  with 2/7

Step-by-step explanation:

2/7 = 0.286

1/4= 0.25

so 2/7 is ur correct answer.

In calculus, the squeeze theorem, also known as the pinching theorem, the sandwich theorem, the sandwich rule, the police theorem, the between theorem and sometimes the squeeze lemma, is a theorem regarding the limit of a function. In Italy, the theorem is also known as theorem of carabinieri.

Answer:

x = -25/12 or x = -0.2

Step-by-step explanation:

x(x+5)+6(x+5)=(x+5)

Distribute

x^2 + 5x + 6x + 30 = x + 5

Combine

x^2 + 11x + 30 = x + 5

Subtract 1x from both sides

x^2 + 10x + 30 = 5

Subtract 30 from both sides

12x = -25

Divide 12 on both sides

x = -25/12 or -0.2

Answer:

x.   y

-1---2^-1=1/2

0---0

1----2

2----2*2=4

Step-by-step explanation:

x.   y

-1---2^-1=1/2

0---0

1----2

2----2*2=4

On a scatter plot, the line that runs through the center of the dots is called a "trendline" or "line of best fit."

Scatter Plot: A scatter plot is a graphical representation of data points in a Cartesian coordinate system, where each point represents the values of two variables.

Data Points: Each data point on the scatter plot represents the values of the two variables being plotted. The position of each point is determined by the respective values of the variables.

Trendline: A trendline is a line that attempts to represent the general pattern or trend in the data. It is often drawn through the center of the dots to provide a visual indication of the relationship between the variables.

Line of Best Fit: The trendline is also known as the "line of best fit" because it is the line that minimizes the overall distance between the line and the data points. It represents the best approximation of the overall trend in the data.

Therefore, the trendline or line of best fit on a scatter plot is the line that runs through the center of the dots and represents the general pattern or trend in the data.

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Answer:

b

Step-by-step explanation:

The expression that represents the distance between the points (a, 0) and (0, 5) on a coordinate grid is √(a² + 25).

The distance between two points of a line is given as:

Distance = \(\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}\)

We have,

The distance formula can be used to find the distance between two points on a coordinate grid.

The distance between the points (a, 0) and (0, 5) is given by:

√((a - 0)² + (0 - 5)²)

Simplifying the expression gives:

√(a² + 25)

Thus,

The expression that represents the distance between the points (a, 0) and (0, 5) on a coordinate grid is √(a² + 25).

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Answer:

sides: scalene (no sides are the same length)

angles: obtuse (an angle is over 90°)

Answer:

3

Step-by-step explanation:

Y OVER X is the answer .

The sides that cannont be the sides of a triangle are the ones in option B.

2cm, 6cm, 4cm

If A, B, and C are the sides of a triangle, then the triangular inequality says that:

A + B > C

A + C > B

C + B > A

So, any set of 3 sides where the sum of two of the sides is smaller than the other side cannot be the sides of a  triangle.

Then the correct option will be b:

2cm, 4cm, 6cm

If we add the two shorter ones we will get:

2cm + 4cm = 6cm

And that is not larger than the other side, so it isthe correct option.

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The 100%-Norm.Dist(value,mean,sd,true) percent of the population has an iq over 115

According to the statement

we have to find that the what percent of the population has an iq over 115.

And from given information,

the mean iq score is 100 and the standard deviation is 15.

And

Normal distribution, is a probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean.

And by use of this formula, we find the percentage of the population has an iq over 115.

Then the result will comes as 100%.

hence, 100%-Norm.Dist(value,mean,sd,true)

So, The 100%-Norm.Dist(value,mean,sd,true) percent of the population has an iq over 115.

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To simplify means to combine like terms so that it will make the expression