In a metallurgical process Ti reacts with C to form TIC with AG = -183000 + 11.4T. V, Si and Cr are added separately. In the final process we want to form TIC as soon as possible. For every 6000 J exothermally produced it will take 3 minutes. Which one of the above elements will we have to use if the process temperature is 927°C? V + C = VC AG = -83600 + 6.6T Si + C = SiC AG = -53400 + 24.2T 3Cr + 2C = Cr3 C₂ AG = -87020 - 16.5T

Answer:

x=0,1,±2

Step-by-step explanation:

x^3(x^2-5)=-4x

x^2(x^2-5)=-4

Take x^2=a, we have

a*(a-5)=-4, a^2-5a+4=0, (a-1)(a-4)=0, a=1,4

x^2=0, 1, 4. x=0,1,±2

Answer:

x = 1 and x = 2

Step-by-step explanation:

\( {x}^{5} - 5 {x}^{3} = - 4x \\ {x}^{4} - 5 {x}^{2} + 4 = 0 \\ ( {x}^{2} - 4)( {x}^{2} - 1)=0\)

x² = 4 or x² = 1

Since x > 0, the negative integers are rejected and the solutions to this equations are x = 1 and x = 2

Answer:

A coordinate plane with a line passing through (0, negative 4) and (2, 0).

Step-by-step explanation:

rewrite the equation in standard form (Ax+By=C). the equation in standard form is 2x-y=4. to find the intercepts, let one of the values equal 0.

y intercept (let x equal 0)

2x-y=4

2(0)-y=4

-y=4

divide both sides by -1

y=-4

the y intercept is (0,-4)

x intercept (let y equal 0)

2x-y=4

2x-0=4

2x=4

divide both sides by 2

x=2

the x intercept is (2,0)

Answer:

Option C. A coordinate plane with a line passing through (0, negative 4) and (2, 0) or known as the hird graph.

Step-by-step explanation:

EDG

The protagonist, a detective, stumbles upon a series of crimes connected to the labeled tickets.

Box A: The plot that matches Box A is a thrilling mystery. The protagonist, a detective, stumbles upon a series of crimes connected to the labeled tickets.

As the detective investigates, they discover that the tickets with the number "1" are linked to a notorious gang involved in illegal activities. The tickets labeled "2" lead the detective to a secret society that uses the tickets for initiation rituals.

The plot unfolds as the detective races against time to unravel the connections between the tickets and bring the culprits to justice.

Box B: The plot that matches Box B is a heartwarming tale of friendship and adventure. The protagonist, a young child, finds one of the tickets labeled "3" and realizes it grants them access to a magical world. In this world, they meet a group of unique and colorful characters who also possess tickets labeled "5."

Together, they embark on a journey to restore harmony to their realm, battling against an evil force that seeks to exploit the power of the tickets. Through their shared experiences, the group learns valuable lessons about courage, loyalty, and the true meaning of friendship.

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Answer: B, Randomly select 6 graduate students and 24 undergrad students for the survey.

Step-by-step explanation: This guarantees that each type is proportionately represented in the survey.

Not A because it risks too many or too few graduate students. It is not C because again, it risks too many or too few graduate students. It is not D because each section has about 50 students and the professor only wants 30 in his sample.

Answer:

Step-by-step explanation:

B

9. H is a subspace of R3 as it contains a 2s vector [0, 2s, 0].

10. H is a subspace of R3 as it consists of the zero vector [0, 0, 0].

11. W is a subspace of R3 as it is spanned by the vectors [1,0,0] and [1,1,0].

12.W is a subspace of R4 as it is spanned by the vectors [1,2,0,0] and [0,-1,4,0].

9. To find a 2s vector v in R3 such that H is a subspace of R3, we can choose v = [0, 2s, 0]. This vector satisfies the condition of H being a subspace since it is of the form 2s, and any scalar multiple of v will also be of the form 2s, which is within H. Therefore, H is a subspace of R3.

0. Let H be the set of all vectors of the form [0, 0, 0]. To show that H is a subspace of R3, we can use the method from Exercise 9. By choosing v = [0, 0, 0],

we can see that H is closed under scalar multiplication and addition, as any scalar multiple or sum of the zero vector will still result in the zero vector. Therefore, H is a subspace of R3.

11. Let W be the set of all vectors of the form [b, c, 0], where b and c are arbitrary. To show that W is a subspace of R3, we need to find vectors u and v such that W is spanned by (u, v).

We can choose u = [1, 0, 0] and v = [0, 1, 0]. Any vector in W can be expressed as a linear combination of u and v, and therefore W is spanned by (u, v). This shows that W is a subspace of R3.

12. Let W be the set of all vectors of the form [s, 2s - t, 4t] in R4. To show that W is a subspace of R4, we can use the method from Exercise 11. By choosing u = [1, 2, 0, 0] and v = [0, -1, 4, 0],

we can observe that any vector in W can be expressed as a linear combination of u and v. Hence, W is spanned by (u, v), indicating that W is a subspace of R4.

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Answer:

1/2 is the answer

Step-by-step explanation:

Answer:

1/2 is the anwser

The Euler equation represents the relationship between current-period consumption and future-period consumption in the optimum. It is derived from intertemporal optimization in economics.

In the context of consumption, the Euler equation can be expressed as:

u'(Ct) = β * u'(Ct+1)

where:

- u'(Ct) represents the marginal utility of consumption in the current period,

- Ct represents current-period consumption,

- β is the discount factor representing the individual's time preference,

- u'(Ct+1) represents the marginal utility of consumption in the future period.

This equation states that the marginal utility of consumption in the current period is equal to the discounted marginal utility of consumption in the future period. It implies that individuals make consumption decisions by considering the trade-off between present and future utility.

Note: The Euler equation assumes a constant discount factor and a utility function that is differentiable and strictly concave.

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Answer:  see proof below

Step-by-step explanation:

Given: A + B + C = π               → A = π - (B + C)

                                               → B = π - (A + C)

                                               → C = π - (A + B)

Use Sum to Product Identity: sin A - sin B = 2 cos [(A + B)/2] · sin [(A - B)/2]

Use the following Cofunction Identity: cos (π/2 - A) = sin A

Proof LHS → RHS:

LHS:                        sin A - sin B + sin C

                             = (sin A - sin B) + sin C

\(\text{Sum to Product:}\quad 2\cos \bigg(\dfrac{A+B}{2}\bigg)\cdot \sin \bigg(\dfrac{A-B}{2}\bigg)+2\cos \bigg(\dfrac{C}2{}\bigg)\cdot \sin \bigg(\dfrac{C}{2}\bigg)\)

\(\text{Given:}\qquad 2\cos \bigg(\dfrac{\pi -(B+C)}{2}+\dfrac{B}{2}}\bigg)\cdot \sin \bigg(\dfrac{A-B}{2}\bigg)+2\cos \bigg(\dfrac{C}2{}\bigg)\cdot \sin \bigg(\dfrac{C}{2}\bigg)\\\\\\.\qquad \qquad =2\cos \bigg(\dfrac{\pi -C}{2}\bigg)\cdot \sin \bigg(\dfrac{A-B}{2}\bigg)+2\cos \bigg(\dfrac{C}2{}\bigg)\cdot \sin \bigg(\dfrac{C}{2}\bigg)\)

\(.\qquad \qquad =2\cos \bigg(\dfrac{\pi}{2} -\dfrac{C}{2}\bigg)\cdot \sin \bigg(\dfrac{A-B}{2}\bigg)+2\cos \bigg(\dfrac{C}2{}\bigg)\cdot \sin \bigg(\dfrac{C}{2}\bigg)\)

\(\text{Cofunction:} \qquad 2\sin \bigg(\dfrac{C}{2}\bigg)\cdot \sin \bigg(\dfrac{A-B}{2}\bigg)+2\cos \bigg(\dfrac{C}2{}\bigg)\cdot \sin \bigg(\dfrac{C}{2}\bigg)\)

\(\text{Factor:}\qquad 2\sin \bigg(\dfrac{C}{2}\bigg)\bigg[ \sin \bigg(\dfrac{A-B}{2}\bigg)+\cos \bigg(\dfrac{C}{2}\bigg)\bigg]\)

\(\text{Given:}\qquad 2\sin \bigg(\dfrac{C}{2}\bigg)\bigg[ \sin \bigg(\dfrac{A-B}{2}\bigg)+\cos \bigg(\dfrac{\pi -(A+B)}{2}\bigg)\bigg]\\\\\\.\qquad \qquad =2\sin \bigg(\dfrac{C}{2}\bigg)\bigg[ \sin \bigg(\dfrac{A-B}{2}\bigg)+\cos \bigg(\dfrac{\pi}{2} -\dfrac{(A+B)}{2}\bigg)\bigg]\)

\(\text{Cofunction:}\qquad 2\sin \bigg(\dfrac{C}{2}\bigg)\bigg[ \sin \bigg(\dfrac{A-B}{2}\bigg)+\sin \bigg(\dfrac{A+B}{2}\bigg)\bigg]\)

\(\text{Sum to Product:}\qquad 2\sin \bigg(\dfrac{C}{2}\bigg)\bigg[ 2\sin \bigg(\dfrac{A}{2}\bigg)\cdot \cos \bigg(\dfrac{B}{2}\bigg)\bigg]\\\\\\.\qquad \qquad \qquad \qquad =4\sin \bigg(\dfrac{A}{2}\bigg)\cdot \cos \bigg(\dfrac{B}{2}\bigg)\cdot \sin \bigg(\dfrac{C}{2}\bigg)\)

\(\text{LHS = RHS:}\quad 4\sin \bigg(\dfrac{A}{2}\bigg)\cdot \cos \bigg(\dfrac{B}{2}\bigg)\cdot \sin \bigg(\dfrac{C}{2}\bigg)=4\sin \bigg(\dfrac{A}{2}\bigg)\cdot \cos \bigg(\dfrac{B}{2}\bigg)\cdot \sin \bigg(\dfrac{C}{2}\bigg)\quad \checkmark\)

Answer:

(x+5) ^2 -20

Step-by-step explanation:

x² + 10x + 5

We are completing the square

Take 10, divide by 2, then square the result

10/2 = 5, 5^2 = 25

Add 25 , then subtract 25 to keep the equation the same

x² + 10x +25 - 25 + 5

(x² + 10x +25) -25+  5

(x+5) ^2 -20

The probability that one or fewer workers will leave within the first year is 0.472

To calculate the probability, we sum up the probabilities of exactly 0 and exactly 1 employee leaving within the first year.

P(X ≤ 1) = P(X = 0) + P(X = 1)

Using the binomial probability formula, we can calculate each term:

P(X = 0) = (36 choose 0) * (0.18^0) * (0.82^36)

P(X = 1) = (36 choose 1) * (0.18^1) * (0.82^35)

Let's calculate these probabilities:

P(X = 0) = (1) * (1) * (0.82^36) = 0.155

P(X = 1) = (36) * (0.18) * (0.82^35) = 0.317

Now, we can sum up these probabilities:

P(X ≤ 1) = P(X = 0) + P(X = 1) = 0.155 + 0.317 = 0.472

Therefore, the probability that one or fewer workers will leave within the first year is 0.472 (rounded to three decimal places).

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From the given information, total surplus in a market is equal to the sum of consumer surplus and producer surplus.

Consumer surplus is the difference between the highest price a consumer is willing to pay for a good or service (the "reservation price") and the actual price they pay. Producer surplus is the difference between the lowest price a producer is willing to accept for goods or services and the actual price they receive.

When a market is in equilibrium, the price and quantity are such that the quantity demanded equals the quantity supplied. At this point, total surplus is maximized, since all trades that benefit both consumers and producers have taken place. The total surplus represents the net benefit to society from the production and consumption of the good or service in the market.

In other words, total surplus is the sum of the gains from trade that accrue to consumers and producers in the market, and it represents the difference between the value that buyers and sellers place on the good or service and the resources that were actually used to produce it.

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\(m\angle E=\sin \dfrac{\sqrt{10}}{2\sqrt5}=\sin \dfrac{\sqrt2}{2}=45^{\circ}\)

Josh will pay a loan origination fee of $2,100 if the lender charges a fee of 0.75%.

To calculate the loan origination fee, we need to multiply the loan amount by the lender's fee percentage.

Loan origination fee = Loan amount x Lender's fee percentage

In this case, the loan amount is $280,000 and the lender's fee percentage is 0.75%.

Loan origination fee = $280,000 x 0.0075

Loan origination fee = $2,100

Therefore, Josh will have to pay a loan origination fee of $2,100.

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Answer:

the divisors of 63 are

Step-by-step explanation:

1,3,7,9,21,63

Answer:

Fraction Form: 2/6 or 1/3

or Decimal Form: .333

or Percent Form: 33.333?%

Step-by-step explanation:

The divisors of 63 that are 1-6 is 1 and 3

So there are TWO numbers out of SIX.

We would turn that into the fraction 2/6 and then simplify (optional) it to 1/3.

Then we use 2/6 to convert it to multiple forms if needed.

Answer:

Step-by-step explanation:

I=prt/100

5000×2×2=20000÷10

I=2000

Answer:

the answer would be y^6/x^2

Step-by-step explanation:

so (Y) to the sixth power over (X) to the second power

Using it's concept, the domain of function m is given as follows:

-∞ < x < ∞.

The domain of a function is the set that contains all the values of the input. In a graph, it is the set that contains all values of x of function.

In this problem, the function is defined for all real values of x, as it keeps increasing to left and right, hence the domain of function m is given as follows:

-∞ < x < ∞.

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The probability that at least one calculator will be defective is 0.7305.

The probability that at least one of the calculators is defective can be calculated using the formula:

P(at least one defective calculator) = 1 - P(no defective calculator)

The probability of selecting a defective calculator from the group of defective calculators is 16/46.

Since the calculators are selected randomly, the probability of selecting a non-defective calculator is 30/46.

Therefore, the probability of selecting 4 non-defective calculators from the group of 46 calculators is:

30/46 × 29/45 × 28/44 × 27/43 = 0.2695 (rounded to 4 decimal places)

Using the formula above, we can calculate the probability that at least one calculator will be defective:

P(at least one defective calculator) = 1 - P(no defective calculator)P(no defective calculator)

                                                         = 1- 0.2695 P(at least one defective calculator)

                                                         = 1 - 0.2695

                                                         = 0.7305

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Answer:

Step-by-step explanation:none

Answer: $648

Step-by-step explanation:

The experimental probability of an event is the ratio of the number of successful outcomes to the number of trials performed. In this case, the experimental probability of the spinner landing on red is given as 1/8, which means that for every 8 spins, it should land on red 1 time.

Option D : The experimental probability of the spinner landing on red is given as 1/8. If it landed on red 6 times, then the number of trials is

8 * 6 = 48.

The experimental probability of an event is the ratio of the number of successful outcomes to the number of trials performed. In this case, the experimental probability of the spinner landing on red is given as 1/8, which means that for every 8 spins, it should land on red 1 time.

To determine the number of trials that were performed, we need to know how many times the spinner landed on red. In this case, it landed on red 6 times.

Using the experimental probability,

Trials = Red spins * (1 / Experimental probability)

= 6 * (1 / 1/8)

= 6 * 8

= 48

Therefore, the number of trials performed is 48.

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Answer:

19

Step-by-step explanation:

18 x 6 = 108

19 + 13 + 25 + 14 + 18 = 89

108 - 89 = 19

The equation of the plane through the origin and the points (2, –4, 6) and (5, 1, 3) is - 9x + 12y + 11 x = 0.

The general equation of a plane through (0, 0, 0) is a(x - 0) + b(y - 0) + c(z - 0) = 0

Since the plane passes though the origin, the equation of the plane is given by ( x, y, z ) = 0. Simplify it so that you write the equation of the plane in the form a x + b y + c z = 0

ax + by + cx = 0...(1)

It will pass through B(2, -4, 6) and C(5, 1, 3) if

a(2) + b(-4) + c(6) = 0

2a - 4b + 6c = 0

a - 2b + 3c = 0 ...(2)

a(5) + b(1) + c(3) = 0

5a + b + 3c = 0 ... (3)

Solving (2) and (3) by cross-multiplication, we have

\(& \frac{a}{-6-3}=\frac{b}{15-3}=\frac{c}{1+10} \\\)

\(& \Rightarrow \frac{a}{-9}=\frac{b}{12}=\frac{c}{11}=\lambda\) (say) }

\(& \Rightarrow\) a = - 9 \(\lambda\), b = 12 \(\lambda\)  and c = 11 \(\lambda\)

Substituting the values of a, b and c in (1), we get

- 9 \(\lambda\) x + 12 \(\lambda\) y + 11 \(\lambda\) x = 0

- 9x + 12y + 11 x = 0

which is the required equation of the plane.

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The answer is "x = 1/7"

Given that square ABCD is a rectangle and angle ADC is 7x-1 degrees

To find the value of x, we will use the formula for angles in a rectangle which says that opposite angles in a rectangle are equal and are each 90° in measure.

So, ∠ABC = 90°We also know that the sum of angles in a triangle is 180°.

Let's find the value of angle ADC using the above formula: ∠A + ∠B + ∠C = 180°

As square ABCD is a rectangle,

angles A and B are each 90°∠A + ∠B + ∠C = 180°90° + 90°

+ ∠C = 180°180° + ∠C = 180°

∠C = 180° - 180°∠C = 0°

Therefore, ∠ADC is equal to 0°And we are given that ∠ADC = 7x - 1°

Therefore, 7x - 1 = 0⇒ 7x = 1⇒ x = 1/7

So, the value of x is 1/7

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Answer: 2

Step-by-step explanation:

To graph the solution to the inequality -5 + x ≥ -3 on the number line, we first need to isolate x.

Adding 5 to both sides of the inequality, we get:

x ≥ 2

This means that any value of x greater than or equal to 2 will satisfy the inequality. To graph this solution on a number line, we draw a closed circle at the point 2 and shade all the points to the right of 2, including the point 2 itself.

The resulting graph looks like this:

     ------•-------------------------------->

           2

The shaded region on the right of 2 represents all the values of x that make the inequality true.

The monthly rate for the given loan is 1.0118%.The annual rate for this loan is 12.1423%.

Given loan: $150,000

Payment per month: $1,770

Duration of loan: 10 years

Interest = ?

The formula for monthly payment is given by:

\(PV = pmt x (1 - (1 + r)^-n) / r\)

Where, PV is the present value, pmt is the payment per period, r is the interest rate per period and n is the total number of periods.Solving the above formula for r will give us the monthly rate for the loan.

r = 1.0118%The monthly rate for the given loan is 1.0118%.The annual rate can be calculated using the following formula:

Annual rate = \((1 + Monthly rate)^12 - 1\)

Annual rate = 12.1423%

The annual rate for this loan is 12.1423%.The effective annual rate can be calculated using the following formula:

Effective annual rate =\((1 + r/n)^n - 1\)

Where, r is the annual interest rate and n is the number of times interest is compounded per year.If interest is compounded monthly, then n = 12

Effective annual rate = (1 + 1.0118%/12)^12 - 1

Effective annual rate = 12.6801%

The effective annual rate for this loan is 12.6801%.

Total amount paid after 10 years = Monthly payment x Number of payments

Total amount paid after 10 years = $1,770 x 120

Total amount paid after 10 years = $212,400

The total amount paid after 10 years is $212,400.

The future value for this loan can be calculated using the following formula:

FV = PV x (1 + r)^n

Where, PV is the present value, r is the interest rate per period and n is the total number of periods.If the loan is paid off in 10 years, then n = 120 (12 payments per year x 10 years)

FV = $150,000 x (1 + 1.0118%)^120

FV = $259,554.50

The future value for this loan is $259,554.50.

Thus, the monthly rate for the loan is 1.0118%, the annual rate for this loan is 12.1423%, the effective annual rate for this loan is 12.6801%, the total amount paid after 10 years is $212,400 and the future value for this loan is $259,554.50.

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The table(s) that show that  y vary directly with x are the first, second and third tables.

Direct variation serves as the mathematical relationship between two variables which is been  expressed using  equation whereby  one of the variable is equal to a constant times the other.

It should be noted that the Direct Variation  serves as the  relationship between two variables , hence The table(s) that show that  y vary directly with x are the first, second and third tables.

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Answer: 7/8 + 4/8 = Exact form- 11/8

                                   Decimal form- 1.375

               17/25 - 9/25 = Exact form- 8/25

                                       Decimal form- 0.32

                63/46 - 81/46 = Exact form- -9/23

Step-by-step explanation: Hope this helped.

Cartesian equation is\(4y^2 = x\ or\ y^2 = x/4\)We know that the polar equation of the form \(r = f(\Theta)\)can be obtained by converting the Cartesian equation x = g(y) into polar coordinates.

To convert the equation, \(x = 4y^2\) into polar coordinates, we need to replace x and y with their respective polar coordinates.

We know that \(x = r\ cos\ \Theta\) and \(y = r\ sin\ \Theta\), where r is the radial distance and θ is the polar angle.

So, the Cartesian equation can be expressed as follows:\(4(r\ sin\ \theta)^2 = r\ sin\ \theta\⇒\\\ 4r^2 sin^2 \theta = r\ cos\ \theta\⇒ \\r = 4\ cos\ \theta sin^2 \theta\)

Therefore, the polar equation for the curve represented by the given Cartesian equation is \(r = 4\ cos\ \theta\ sin^2\ \theta\).The polar equation for the curve represented by the given Cartesian equation \(x = 4y^2\ is\ r = 4\ cos\ \theta\ sin\ \theta\).

To convert the given Cartesian equation\(r = 4 \cos\ \theta \sin^2 \theta\)\(x = 4y^2\) into polar coordinates, we need to replace x and y with their respective polar coordinates.

Using the equation \(x = r\ cos\ \theta\)and \(y = r\ sin\ \theta\), we get \(4(r\ sin\ \theta)^2 = r\ cos\ \theta\), which simplifies to \(r = 4\ cos\ \theta \sin^2 \theta\).

Hence, the polar equation for the curve represented by the given Cartesian equation is r = 4 cos θ sin² θ.

Therefore, the polar equation for the given Cartesian equation \(x = 4y^2\)is \(r = 4\ cos \ \theta\ sin^2 \theta\).

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The solution of 20% of 90 is, 18

We have,

Use the grid to create a model to solve the percent problem.

Here, We can simplify as,

= 20% of 90

= 20/100 x 90

= 18

Therefore, The solution of 20% of 90 is, 18

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