Determine which integer in the solution set will make the equation true. t − 42 = −14 S: {−56, −28, 3, 28}

Applying the Lagrange interpolation formula, we construct a polynomial that passes through the four given points. Evaluating this polynomial at x = 1 yields the approximation for f(1).we evaluate P(1) to obtain the approximation for f(1).

To approximate f(1) using Lagrange interpolating polynomials, we consider the four given function values: f(0) = 0, f(2) = -1, f(3) = 1, and f(4) = -2. The Lagrange interpolation formula allows us to construct a polynomial of degree 3 that passes through these points.The Lagrange interpolation formula states that for a set of distinct points (x₀, y₀), (x₁, y₁), ..., (xn, yn), the interpolating polynomial P(x) is given by:P(x) = Σ(yi * Li(x)), for i = 0 to n,

where Li(x) represents the Lagrange basis polynomials. The Lagrange basis polynomial Li(x) is defined as the product of all (x - xj) divided by the product of all (xi - xj) for j ≠ i.Using the given function values, we can construct the Lagrange interpolating polynomial P(x) that passes through these points.

Learn more about interpolation formula click here: brainly.com/question/30766137

#SPJ11

Answer:

Given, the annual profit equation is f(n) = 65n - 0.04n².

When the number of pizzas sold, n = 300, the annual profit will be:

f(300) = 65(300) - 0.04(300)²

= 19500 - 0.04(90000)

= 19500 - 3600

= $15,900

Therefore, the annual profit if the pizza maker sells 300 pizzas is $15,900. Answer: D.

Step-by-step explanation:

Answer:

37.50

Step-by-step explanation:

2/5x + 15 = 30

2/5x = 15

x = 15 ( 5/2)

x = 37.50

The value of the equations are

a) y = -2x² + 1

b) f ( x ) = y = x² + 6x + 14

Graphs behave differently at various x-intercepts. Sometimes the graph will cross over the x-axis at an intercept. Other times the graph will touch the x-axis and bounce off.

Identify the even and odd multiplicities of the polynomial functions' zeros.

Using end behavior, turning points, intercepts, and the Intermediate Value Theorem, plot the graph of a polynomial function.

The graphs cross or are tangent to the x-axis at these x-values for zeros with even multiplicities. The graphs cross or intersect the x-axis at these x-values for zeros with odd multiplicities

Given data ,

Let the equation be represented as A and B

Now , the value of A is

y = -2x² + 1   be equation (1)

The equation A is that of a parabolic curve and it is a U-shaped plane curve where any point is at an equal distance from a fixed point

The graph of the parabola is downward (or opens down), when the value of a is less than 0, a < 0.

Now , the value of B is

y = x² + 6x + 14   be equation (2)

The equation B is that of a parabolic curve and it is a U-shaped plane curve where any point is at an equal distance from a fixed point

The graph of parabola is upward (or opens up) when the value of a is more than 0, a > 0.

Hence , the equation of graphs are solved

To learn more about graph of polynomial click :

https://brainly.com/question/16957172

#SPJ1

(b) So the equilibrium points are (0, 0), (1, 0), (0, 1), and (1, 1).

(a) To find the vertical (x-) nullcline, we set dy/dt = 0 and solve for x:

dy/dt = y(1 - y^4 - x) = 0

This equation is satisfied when y = 0 or 1 - y^4 - x = 0. So the vertical nullcline consists of two parts: y = 0 and x = 1 - y^4.

To find the horizontal (y-) nullcline, we set dx/dt = 0 and solve for y:

dx/dt = x(1 - x^3 - y) = 0

This equation is satisfied when x = 0 or 1 - x^3 - y = 0. So the horizontal nullcline consists of two parts: x = 0 and y = 1 - x^3.

(b) Equilibrium points are the points where both dx/dt and dy/dt are zero. From the previous equations, we can see that the equilibrium points occur when either x = 0 or x = 1 - y^4, and either y = 0 or y = 1 - x^3.

Substituting these values into the equations, we have four possible cases:

Case 1: x = 0 and y = 0

Case 2: x = 1 and y = 0

Case 3: x = 0 and y = 1

Case 4: x = 1 - y^4 and y = 1 - x^3

Solving these equations, we find the equilibrium points:

Case 1: (x, y) = (0, 0)

Case 2: (x, y) = (1, 0)

Case 3: (x, y) = (0, 1)

Case 4: (x, y) = (1, 1)

To know more about equations visit:

brainly.com/question/10724260

#SPJ11

Answer:

The slope of this graph is 1. Well, 1/1 is equal to 1 so I think you should just put 1 as your answer.

Step-by-step explanation:

Answer:

\(\frac{7}{8}\)

Step-by-step explanation:

\(\frac{1}{4}\ + \frac{10}{16}\\)

\(= \frac{4}{16}\ + \frac{10}{16}\\\)

\(= \frac{14}{16} \\\)

\(= \frac{7}{8}\)

hope it helps :)

mark brainliest!

Answer:

B

Step-by-step explanation:

If you look at the graph/chart, it starts at 1,000, so half of that is 500, so you go down to 500, and go straight down to see the number of time under it (In this case, is 1 minute) so you know it is one minute

Answer:

x=18

Step-by-step explanation:

y=3x-4

3x-4=y

3x-4=50

3x=50+4

3x=54

x=54÷3

x=18

1001 ways are there to distribute the money of Uncle Henry to his nieces and nephews.

He may donate the entire sum to one child (five ways).

He could give each youngster two bucks (one way).

He may offer $0.00, $1.00, $2.00, $3.00, and $4.00 in five different ways.

Henry will put the dividers on the left and the banknotes on the right. Money to the left of the first divider goes to the youngest kid, money between the first and second dividers goes to the child after that, and so on.

For example, the first kid receives $1, the second receives $2, the third receives $1, the fourth receive nothing, and the fifth receives $6.

It is merely a matter of selecting the number of arrangements of 10 bills and four dividers using this model:

\(\frac{14 !}{(10 !)(4 !)}=1,001, \text { or: } 14 C 4=1,001\)

For more questions on Permutation and Combination

https://brainly.com/question/28065038

#SPJ4

There are 1001 ways to distribute Uncle Henry's money to his nieces and nephews.

He might give one youngster the full amount (five ways).

He could give each child two dollars (one way).

He can make five separate offers of $0.00, $1.00, $2.00, $3.00, and $4.00.

Henry will arrange the banknotes on the right and the dividers on the left. The youngest child receives the money to the left of the first divider, the following child receives the money between the first and second dividers, and so forth.

The first child gets $1, the second gets $2, the third gets $1, the fourth gets nothing, and the fifth gets $6, for instance. Using this model, it is only a matter of choosing the quantity of arrangements of 10 bills and 4 dividers.

Learn more about Permutation distribute Visit: brainly.com/question/28065038

#SPJ4

The z-score to test the hypothesis that the part is coming out longer than usual is approximately 1.61.

Sample mean = x = 12.20 cm

Population mean = μ = 12.05 cm

Standard deviation = σ = 0.350 cm

Sample size = n = 14

A hypothesis is an informed prediction regarding the solution to a scientific topic that is supported by sound reasoning. there is the expected result of the experimentation even if there is not proved in an experiment.

Calculating the z-score -

\(z = (x - u) / (\alpha / \sqrt n)\)

Substituting the values -

\(z = (12.20 - 12.05) / (0.350 / \sqrt{14)\)

= z = 0.15 / (0.350 / √14)

= 0.093

Substituting the value again into the formula:

z = 0.15 / 0.093

= 1.61

Read more about hypothesis on:

https://brainly.com/question/30484892

#SPJ4

Answer:

x = 55.866 ft.

Step-by-step explanation:

39^2 + 40^2 = x^2

1521 + 1600 = 3121

sqrt(3121) = 55.8659

Rounded = 55.866

Make sure to add the ft.

Answer:

Step-by-step explanation:

a²+b²=c²

39²+40²=c²

3121=c²

c=√3121

c=55.866 to 3.d.p

Answer: 1

Step-by-step explanation:  I know the answer.

1 costume needs

5costume needs

When the cylindrical tank is standing upright on one of its bases, the oil would be 6 feet deep.

Question: A right cylindrical oil tank is 20 feet tall and its circular bases have diameters of 8 feet each. When the tank is lying flat on its side (not on one of the circular ends), the oil inside is 6 feet deep. How deep, in feet, would the oil have been if the tank had been standing upright on one of its bases? Express your answer as a decimal to the nearest tenth.

To find the depth of the oil when the tank is standing upright on one of its bases, we can use the concept of similar triangles.

Step 1: Find the height of the tank when it is standing upright.
The height of the tank is 20 feet.

Step 2: Find the radius of the tank.
The radius is half of the diameter, so the radius is 8/2 = 4 feet.

Step 3: Find the height of the oil when the tank is upright.
We can set up a proportion using the similar triangles formed by the tank and the oil.
The height of the oil when the tank is lying flat is 6 feet.
Let x represent the height of the oil when the tank is upright.
We can set up the following proportion: 4/6 = 4/x.

Step 4: Solve the proportion to find the height of the oil when the tank is upright.
Cross-multiply: 4x = 6 * 4.
Simplify: 4x = 24.
Divide both sides by 4: x = 24/4.
Simplify: x = 6.

Therefore, when the tank is standing upright on one of its bases, the oil would be 6 feet deep.

To know more about cylindrical tank refer here:

https://brainly.com/question/25562559

#SPJ11

Given, Y is a discrete random variable with probability mass function p(y). Variance of aY + b can be found out using the following formula: Variance of aY + b = E [(aY + b)2] - [E (aY + b)]2

Now, let's calculate E [(aY + b)2]:E [(aY + b)2]

= E [a2 Y2 + 2abY + b2]

= a2 E [Y2] + 2ab E [Y] + b2

Thus, we have E [aY + b]2

= a2 E [Y2] + 2ab E [Y] + b2.

Now, let's calculate [E (aY + b)]2:[E (aY + b)]2

= [a E (Y) + b]2

= a2 E [Y2] + 2ab E [Y] + b2

Thus, we have [E (aY + b)]2

= a2 E [Y2] + 2ab E [Y] + b2.

Now, we can find variance of aY + b using these two equations: Variance of aY + b = E [(aY + b)2] - [E (aY + b)]2

= a2 E [Y2] + 2ab E [Y] + b2 - [a2 E [Y2] + 2ab E [Y] + b2]

= a2 E [Y2] - a2 E [Y2]

= a2 (E [Y2] - E [Y]2)

Therefore, the final equation is: Variance of aY + b = a2 (E [Y2] - E [Y]2)

= a2 V(Y)Hence, we proved that V(aY + b)

= a2V(Y) where a & b are constant.

To know more about probability visit:

https://brainly.com/question/31828911

#SPJ11

Answer:

Step-by-step explanation:

On Saturday, Rosa and her family drove 260 miles in 4 hours.

In order to find mph, you must divide 260 miles by 4 hours.

She drove 65 mph on Saturday.

On Sunday, Rosa and her family drove 300 miles in 5 hours.

In order to find mph, you must divide 300 by 5 hours.

She drove 60 mph on Sunday.

Therefore, Rosa and her family drove faster on Saturday by 5 mph.

Answer:

C. 64

Hope that helps you

The value of the angle x is calculated as: ∠x = 64

Let the intersect of line SV and RT be Y

Sides RTU forms a triangle, and the sum of the interior angles of a triangle is 180.

Since RT = TU, ∠TRU  = ∠TUR = z

114 + z + z = 180

114 + 2z = 180

2z = 180 - 114

2z = 66

z = 66/2

z = 33

Line STU is a straight line and the angle of a straight line is 180. Thus:

114 + ∠STR  = 180

∠STR = 180 - 114

∠STR = 66

Also, sides SYT is forms a triangle and the sum of all interior angles of a triangle is 180. Thus:

66 + 31 + ∠SYT = 180

97 + ∠SYT = 180

∠SYT = 180 - 97

∠SYT = 83

But ∠SYT = angle RYV = 83

sides RYV form a triangle and the sum of all interior angles of a triangle is 180

33 + 83 + ∠x = 180

116 +  ∠x = 180

∠x = 180 - 116

∠x = 64

Read more about Missing Angle at: https://brainly.com/question/28293784

#SPJ2

Using system of linear equations he will require 20kg of 15% copper and 30kg of 70% copper to produce an alloy of 48% in 50kg

The system of linear equations is the set of two or more linear equations involving the same variables. Here, linear equations can be defined as the equations of the first order, i.e., the highest power of the variable is 1. Linear equations can have one variable, two variables, or three variables.

To solve this problem, we need to write a system of linear equations and find the equivalent amount of the metal required to make the desired amount of the alloy.

0.15x + 0.7y = 0.48(50) ..eq(i)

0.15x + 0.7y = 24 ...eq(i)

x + y = 50 ...eq(ii)

solving equation (i) and (ii)

x = 20, y = 30

He needs 20kg of 15% copper and 30kg of 70% copper to get 48% of 50kg of alloy.

Learn more on system of linear equation here;

https://brainly.com/question/13729904

#SPJ1

1. 6(3-8)-10

=6(-5)-10

=-30-10

=-40

2.30(3)+15(10)

=90+150

=240

3. 2(3)(3+32+32)

=6(67)

=402

Answer:

5a. V = (1/3)π(8²)(15) = 320π in.³

5b. V = about 1,005.3 in.³

The approximate solution for the system of equations is x = -48/29

From the question, we have the following parameters that can be used in our computation:

f(x) = 5/8x + 2

g(x) = -3x - 4

To calculate the solution for the system of equations, we have the following

f(x) = g(x)

Substitute the known values in the above equation, so, we have the following representation

5/8x + 2 = -3x - 4

Multiply through by 8

So, we have

5x + 16 = -24x - 32

Evaluate the like terms

29x = -48

Evaluate

x = -48/29

Hence, the solution is x = -48/29

Read more about system of equations at

https://brainly.com/question/13729904

#SPJ1

The long-run cost function is C(q) = 2w(sqrt[rw(q^3)]). The profit-maximizing output can be found by minimizing this cost function with respect to q.

Part a: Deriving the long-run cost function C(q):

To derive the long-run cost function, we need to find the minimum cost of producing a given output level q using the given production function.

Given the production function q = F(L, K) = (KL)^(1/3), we can rewrite it as K = (q^3)/L.

Now, let's express the cost function C(q) in terms of q. We have the cost function as C(q) = wL + rK, where w is the wage rate and r is the rental rate.

Substituting the expression for K in terms of q, we get C(q) = wL + r[(q^3)/L].

To minimize the cost function, we can take the derivative of C(q) with respect to L and set it equal to zero:

dC(q)/dL = w - r[(q^3)/(L^2)] = 0.

Simplifying the equation, we have w = r[(q^3)/(L^2)].

Solving for L, we get L^2 = r(q^3)/w.

Taking the square root, we have L = sqrt[(r(q^3))/w].

Substituting this value of L back into the cost function equation, we get:

C(q) = w(sqrt[(r(q^3))/w]) + r[(q^3)/sqrt[(r(q^3))/w]].

Simplifying further, we have:

C(q) = 2w(sqrt[rw(q^3)]).

So, the long-run cost function C(q) is given by C(q) = 2w(sqrt[rw(q^3)]).

Part b: Solving the long-run profit maximization problem directly:

To solve the profit maximization problem directly, we need to maximize the expression:

max K, L [F(L, K) - wL - rK].

Taking the derivative of the expression with respect to L and K, and setting them equal to zero, we can solve for the optimal values of L and K.

The first-order conditions are:

dF(L, K)/dL - w = 0, and

dF(L, K)/dK - r = 0.

Differentiating the production function F(L, K) = (KL)^(1/3) with respect to L and K, we get:

(1/3)(KL)^(-2/3)K - w = 0, and

(1/3)(KL)^(-2/3)L - r = 0.

Simplifying the equations, we have:

K^(-2/3)L^(1/3) - (3/2)w = 0, and

K^(1/3)L^(-2/3) - (3/2)r = 0.

Solving these two equations simultaneously will give us the optimal values of L and K.

Part c: Using the derived long-run cost function:

In Part a, we derived the long-run cost function as C(q) = 2w(sqrt[rw(q^3)]).

To find the profit-maximizing output, we can minimize the long-run cost function C(q) with respect to q.

Taking the derivative of C(q) with respect to q and setting it equal to zero, we can solve for the optimal value of q.

dC(q)/dq = w(sqrt[rw(q^3)]) + (3/2)w(q^2)/(sqrt[rw(q^3)]) = 0.

Simplifying the equation, we have:

(sqrt[rw(q^3)])^2 + (3/2)(q^2) =

0.

Solving this equation will give us the profit-maximizing output q.

Learn more about long-run cost function here :-

https://brainly.com/question/30882146

#SPJ11

Answer:

A.) 375/1000, B) 75/200,  D.) 3/8

Step-by-step explanation:

A number can be represented in many forms depending on the situation, it can be represented in form of ratio, decimals, fraction e.t.c.

Given the number 0.375 which is in its decimal form, this number can also be represented in the form of a fraction.

\(a)0.375=\frac{0.375}{1} \\ \\multiplying\ by\ \frac{1000}{1000}\ gives:\\\\\frac{0.375}{1}*\frac{1000}{1000}= \frac{375}{1000}\\\\ b) 0.375=\frac{0.375}{1} \\ \\multiplying\ by\ \frac{1000}{1000}\ gives:\\\\\frac{0.375}{1}*\frac{1000}{1000}= \frac{375}{1000}=\frac{5(75)}{5(200)} =\frac{75}{200} \\\\d) 0.375=\frac{0.375}{1} \\ \\multiplying\ by\ \frac{1000}{1000}\ gives:\\\\\frac{0.375}{1}*\frac{1000}{1000}= \frac{375}{1000}=\frac{125(3)}{125(8)}=\frac{3}{8} \\\)

Step-by-step explanation:

It is worked out step by step.

The value of x is 29° and it's a supplementary angles.

Supplementary angles simply means the angles that have a sum that is equal to 180°

In this case, we have been given two angles. It's important to equate them together. This will be illustrated as:

2x + 15 + 5x - 38 = 180

Collect like terms

7x - 23 = 180

Collect like terms

7x = 180 + 23

7x = 203

Divide

x = 203/7

x = 29°

The complete question is written below.

Learn more about angles on:

brainly.com/question/25716982

#SPJ1

Complete question

Given angle P is 2x + 15. and angle Q is 5x - 38. Prove that they are supplementary

The values are: -9, 7, -2, Undefined, Undefined, 8, Undefined, Undefined.

Let's match each expression with its corresponding value:

Expression: -9

Value: -9

Expression: 7

Value: 7

Expression: -2

Value: -2

Expression: Undefined

Value: Undefined

Expression: h(3.999)

Value: Undefined

Expression: h(4)

Value: 8

Expression: h(4.0001)

Value: Undefined

Expression: h(9)

Value: Undefined

Now let's explain the reasoning behind each value:

The expression -9 represents the number -9, so its value is -9.

Similarly, the expression 7 represents the number 7, so its value is 7.

The expression -2 represents the number -2, so its value is -2.

When an expression is labeled as "Undefined," it means that there is no specific value assigned or that it does not have a defined value.

For the expression h(3.999), its value is undefined because the function h(x) is not defined for the input 3.999.

The expression h(4) has a value of 8, indicating that when we input 4 into the function h(x), it returns 8.

Similarly, the expression h(4.0001) has an undefined value because the function h(x) is not defined for the input 4.0001.

Lastly, the expression h(9) also has an undefined value because the function h(x) is not defined for the input 9.

For more such questions on values

https://brainly.com/question/843074

#SPJ8

Justin buys 4 hot dogs ad 5 pop corn boxes at the baseball game.

Equation is an expression which is used to show the relationship between two or more variables and numbers.

Let x represent the number of hot dogs and y represent the boxes of popcorn.

Justin buys a total of 9 snacks. Hence:

He buys popcorn 3 less than twice as many hot dogs. Hence:

Solving equations 1 and 2 simultaneously gives:

x = 4, y = 5

Justin buys 4 hot dogs ad 5 pop corn boxes at the baseball game.

Find out more on equation at: https://brainly.com/question/13763238

A water park water ride would pump 4,00,000 gallon of water in 100 minutes.

In this question, we have been given a water park water ride pump 8000 gallon of water every 2 minute.

So, the amount of water pumped in 1 minute would be,

8000/2 = 4000 gallon

We need to find the amount of water the ride would pump in 100 minute.

By unitary method the required amount would be,

A = 4000 * 100

A = 4,00,000 gallon

Therefore, the ride would pump 4,00,000 gallon of water.

Learn more about Unitary method here:

https://brainly.com/question/22056199

#SPJ4