Is 1,850 disvisbled by 2?

Answer:  -2x + 5y = 8

Step-by-step explanation:

Since the lines must be parallel, the slopes must be the same, so keep the coefficients of x and y

Substitute the values of x and y from the given coordinate  (6,4) to find the new constant, b, the y-intercept.

-2x + 5y = b

-2(6) + 5(4) = b

-12 + 20 = b

8 = b

Rewrite the original equation substituting the new b for the original -15

-2x + 5y = 8

Answer:

y=6/7

Step-by-step explanation:

-3=7y-9

-3+9=7y

6=7y

6/7=y

Answer:

18 1/6 I think I'm so so sorry if it's wrong

Step-by-step explanation:

Hope it helps :)

Brainliest pls?

Have a good day/night

A pair (x, p) is an equilibrium, if and only if x and p are optimal solutions to the standard form problem and its dual, respectively.

To show that a pair (x, p) is an equilibrium if and only if x and p are optimal solutions to the standard form problem and its dual, we need to demonstrate both directions of the equivalence.
First, let's assume that (x, p) is an equilibrium. An equilibrium occurs when the primal problem and its dual problem satisfy certain conditions. In this case, we have:
1. Primal problem:
  - Objective function: maximize \(c^T * x\) (where c is the cost vector and x is the decision variable)
  - Subject to: Ax = b (where A is the constraint matrix and b is the right-hand side vector)
2. Dual problem:
  - Objective function: minimize \(b^T * p\) (where p is the dual variable)
  - Subject to: \(A^T * p \geq c\) (where \(A^T\) is the transpose of A)
Now, if (x, p) is an equilibrium, it means that both the primal and dual problems are feasible, and their objective functions are equal. This implies that x and p are optimal solutions to their respective problems.
Conversely, let's assume that x and p are optimal solutions to the standard form problem and its dual, respectively. This means that x and p satisfy the feasibility conditions and optimize the objective functions of their respective problems.
Since x and p are optimal solutions, the objective functions of the primal and dual problems are equal. This condition ensures that (x, p) is an equilibrium.

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A pair (x, p) is an equilibrium if and only if x is an optimal solution to the standard form problem and p is an optimal solution to its dual. Both conditions must be satisfied for equilibrium.

To show that a pair (x, p) is an equilibrium, we need to prove two conditions: (1) x is an optimal solution to the standard form problem, and (2) p is an optimal solution to its dual.

First, assume that (x, p) is an equilibrium. This means that x is feasible and satisfies the constraints of the standard form problem. We can also assume that p is feasible and satisfies the constraints of the dual problem.

To prove condition (1), we can use contradiction. Suppose x is not an optimal solution. Then there exists another feasible solution x' that yields a better objective function value. However, this contradicts the definition of an equilibrium, so x must be an optimal solution.

Similarly, to prove condition (2), we can assume that p is not an optimal solution. Then there exists another feasible solution p' to the dual problem that yields a better objective function value. Again, this contradicts the definition of an equilibrium, so p must be an optimal solution.

Conversely, if x is an optimal solution to the standard form problem and p is an optimal solution to its dual, we can conclude that (x, p) is an equilibrium. This is because both x and p satisfy the necessary conditions for optimality.

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a) The probability of randomly selecting 4 males out of 7 spectators, given that 70% of the spectators are males, can be calculated using the binomial probability formula.

b) To find the probability that at most 5 of the randomly selected spectators are females, we need to calculate the cumulative probability of selecting 0, 1, 2, 3, 4, and 5 females from the total number of selected spectators.

a) To calculate the probability of selecting 4 males out of 7 spectators, we can use the binomial probability formula:

P(X = k) = C(n, k) * p^k * (1 - p)^(n - k)

Where:

- n is the total number of trials (number of people selected)

- k is the number of successful trials (number of males selected)

- p is the probability of success in a single trial (probability of selecting a male)

- C(n, k) is the binomial coefficient, calculated as C(n, k) = n! / (k! * (n - k)!)

In this case, n = 7, k = 4, and p = 0.70 (probability of selecting a male). Therefore, the probability of selecting 4 males out of 7 spectators is:

P(X = 4) = C(7, 4) * (0.70)^4 * (1 - 0.70)^(7 - 4)

b) To find the probability that at most 5 of the selected spectators are females, we need to calculate the cumulative probability of selecting 0, 1, 2, 3, 4, and 5 females. This can be done by summing the individual probabilities for each case.

P(X ≤ 5 females) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5)

To calculate each individual probability, we use the same binomial probability formula as in part a), with p = 0.30 (probability of selecting a female).

Finally, we sum up the probabilities for each case to find the probability that at most 5 of the selected spectators are females.

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Answer:The answer would be 8

Step-by-step explanation:You would have to do 8/-2+2 and that would leave you with 8 because -2+2 is 0.

False.

Hope This Helps You!

Good Luck Studying ^-^

Answer:

False

Step-by-step explanation:

Answer:

Step-by-step explanation:

passing through (¹/₂,0) and (-¹/₂,0) so:  ¹/₂ and -¹/₂ are roots of the equation

so:

     y = a(x - ¹/₂)(x-(-¹/₂))

     y = a(x - ¹/₂)(x +¹/₂)

     y = a(x² - ¹/₄)

and passing through (0,1) so:

     1 = a(0² - ¹/₄)

     1 = - ¹/₄a

     a = -4

therefore:

                 y = 4(x² - ¹/₄)

                 y = 4x² - 1

So the quadratic equation:   4x² - 1 = 0

Answer: A

Step-by-step explanation:

Answer:

The equation that shows inverse variation is (Choice C) y = (1/8)x.

Step-by-step explanation:

The equation that shows inverse variation is (Choice C) y = (1/8)x.

Landon would need to invest approximately $1,150 to reach a future value of $3,250 in 18 years with an interest rate of 6.6% compounded daily.

To determine how much Landon needs to invest, we can use the compound interest formula, which is:

A = P(1 + r/n)^(nt)

where A is the future value of the account, P is the principal amount (the amount Landon needs to invest), r is the interest rate (in decimal form), n is the number of times the interest is compounded per year, and t is the number of years.

In this case, the interest rate is 6.6% or 0.066, the account is compounded daily, so n = 365, and t = 18. We want to find the principal amount, P, that will result in a future value of $3,250.

Substituting these values into the formula, we get:

3,250 = P(1 + 0.066/365)^(365*18)

Simplifying the right-hand side of the equation, we get:

3,250 = P(1.000181)^6,570

Dividing both sides by (1.000181)^6,570, we get:

P = 3,250 / (1.000181)^6,570

Using a calculator, we can evaluate this expression to find that:

P ≈ $1,150.52

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Answer:

The volume of the cone is 75.36 cm³

Step-by-step explanation:

The rule of the volume of a cone is V = \(\frac{1}{3}\) π r² h, where

In the given figure

∵ The length of the radius of the cone is 3 cm

∴ r = 3 cm

∵ The length of the height of the cone is 8 cm

∴ h = 8 cm

→ Substitute the values of r and h in the rule of the volume above

∵ π ≅ 3.14

∵ V = \(\frac{1}{3}\) (3.14)(3)²(8)

∴ V = 75.36 cm³

∴ The volume of the cone is 75.36 cm³

We can be 95% confident that the true population mean BMI is between 25.368 and 29.032.

A 95% confidence interval for the population mean can be constructed using the t-distribution when the sample size is small (<30) or the population standard deviation is unknown.

In this case, we have a random sample of 46 people with a mean body mass index (BMI) of 27.2 and a standard deviation of 6.0.

Thus, we need to use the t-distribution to construct the confidence interval.

The formula for the confidence interval is as follows:

Upper limit of the confidence interval:27.2 + (2.013) (6.0/√46) = 29.032Lower limit of the confidence interval:27.2 - (2.013) (6.0/√46) = 25.368

Therefore, the 95% confidence interval for the population mean BMI is (25.368, 29.032).

This means that we can be 95% confident that the true population mean BMI is between 25.368 and 29.032.

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Step-by-step explanation:

\( = \frac{ {( - 3)}^{4} }{ {( - 3)}^{1} } \)

\( = {( - 3)}^{4 - 1} \)

\( = {( - 3)}^{3} \)

\( = ( - 3) \times ( - 3) \times ( - 3)\)

\( = - 27\)

Considering definition of probability, the probability that a student chosen from the class at random has either blonde hair or brown hair is 36.

Probability is the possibility that a phenomenon or an event will happen, given certain circumstances and it is expressed as a percentage.

The union of events is the event formed by all the elements of A and B. That is, the event AUB is verified when one of the two, A or B, or both occurs and it is read as "A or B".

The probability of the union of two compatible events is calculated as the sum of their probabilities subtracting the probability of their intersection:

P(A∪B)= P(A) + P(B) -P(A∩B)

Two events, A and B, are incompatible when they have no element in common and it is true that P(A∩B)=0. Then:

P(A∪B)= P(A) + P(B)

You know:

The probability that a student chosen from the class at random has either blonde hair or brown hair is calculated as:

P(blond hair or brown hair)= P(blond hair) + P(brown hair)

Then:

P(blond hair or brown hair)= 12 + 24

P(blond hair or brown hair)= 36

Finally, the probability in this case is 36.

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Answer:

12.

Step-by-step explanation:

Answer:

12

Step-by-step explanation:

the distance would be 12 because if you see the y values they are both -4 so they dont have any distance between them. Now if u look in the x values you will see different values -5 and 7 what u have to do now is do the equation 7 - - 5 which will be 12 because minus and minus will be plus so 7 plus 5 is 12, the distance between those points is 12.

Hope this answers ur question.

Answer:

10.5

Step-by-step explanation:

\( KET\cong KIT...... (given) \)

\( \therefore KE \cong KI.... (csct) \)

\( \therefore m(KE) =m(KI)\)

\( \therefore 10x-34= 4x + 29\)

\( \therefore 10x-4x= 34 + 29\)

\( \therefore 6x= 63\)

\( \therefore x=\frac{63}{6}\)

\( \therefore x=10.5\)

Answer:

\(y=8x-781\)

Here, \(x\) represents temperature and \(y\) denotes rate of chirping per minute.

Step-by-step explanation:

Let \(x\) represents temperature and \(y\) denotes rate of chirping per minute.

At \(106\)°F, a certain insect chirps at a rate of \(67\) times per minute.

Take \((x_1,y_1)=(106,67)\)

At \(108\)°F, they chirp \(83\) times per minute.

Take \((x_2,y_2)=(108,83)\)

Slope intercept form:

\(y-y_1=(\frac{y_2-y_1}{x_2-x_1})(x-x_1)\)

\(y-67=(\frac{83-67}{108-106})(x-106)\\\\y-67=(\frac{83-67}{108-106})(x-106)\\\\y-67=(\frac{16}{2})(x-106)\\\\y-67=8(x-106)\\y-67=8x-848\\y=8x+67-848\\y=8x-781\)

The formula holds for every real number r except 1 and integer n > 0, by mathematical induction.

To prove the formula for every real number r except 1 and integer n > 0:

Base case:

When n = 1,

\(\Σ^1_i=0 r^i = r^0 + r^1 = 1 + r\)

On the other hand,

\(r^1+1 - 1/r - 1 = r^2 - 1/r - 1 = (r^2r - 1 - r)/r = (r^3 - 1)/r\)

Therefore, the base case holds.

Induction Hypothesis:

Assume that the formula holds for some positive integer k, i.e.,

\(\Σ^k_i=0 r^i = r^(k+1) - 1/r - 1\)

Induction Step:

Consider the sum up to k+1:

\(\Σ^(k+1)_i=0 r^i = Σ^k_i=0 r^i + r^(k+1)\)

Using the induction hypothesis, we can substitute the formula for the sum up to k:

\(\Σ^(k+1)_i=0 r^i = r^(k+1) - 1/r - 1 + r^(k+1)\)

Simplifying the expression, we get:

\(\Σ^(k+1)_i=0 r^i = r^(k+2) - 1/r - 1\)

Therefore, the formula holds for every real number r except 1 and integer n > 0, by mathematical induction.

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The values of the variables in the equation will be:

1. a = -78

2. m = 209

3. p = -16

4. n = 1/5

5. r = 1/2

6. k = = -3/2

7. a = -13.5

8. p = 2

-6 = a/13

Cross multiply

a = 13 × -6

a = -78

m/11 =19

Cross multiply

m = 19 × 11

m = 209

p -1 = -17

p = -17 + 1

p = -16

3= 3/5n

5n = 3/3

5n = 1

Divide

n = 1/5

31/10= r+ 2⅗

r = 31/10 - 2 3/5

r = 31/10 - 13/5

r = 5/10

r = 1/2

-6/5 =⅘k

Divide

k = -6/5 × 5/4

k = -3/2

-12/5 = 1+a

a = -12.5 - 1

a = -13.5

p+ ½ = 5/2

p = 5/2 - 1/2

p = 2

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Answer:

115.395 min

Step-by-step explanation:

First we find the volume of 6 cm of water. We use the formula:

\(\pi *radius^2 *height\)

\(\pi *35^2*6 = 23,079 cm^3\)

1 L/min = 1000 cm^3 / min

0.2 L/min = 200 cm^3 /min

\(\frac{23,079}{200} = 115.395 min\)

Answer:

hope this helps :)

Step-by-step explanation:

The transformation T: R^3 → R^2 defined by T(x1, x2, x3) = (|x1|, 0) is not linear transformation as it violates the additivity and homogeneity properties of linearity.

To show that the transformation T: R^3 → R^2 defined by T(x1, x2, x3) = (|x1|, 0) is not linear, we need to demonstrate that it violates at least one of the two properties of linearity, namely, additivity and homogeneity.

Additivity: T(u + v) = T(u) + T(v) for all vectors u and v in R^3.

Let u = (1, 2, 3) and v = (4, 5, 6) be two vectors in R^3. Then,

T(u) = T(1, 2, 3) = (|1|, 0) = (1, 0)

T(v) = T(4, 5, 6) = (|4|, 0) = (4, 0)

T(u + v) = T(1+4, 2+5, 3+6) = T(5, 7, 9) = (|5|, 0) = (5, 0)

However,

T(u) + T(v) = (1, 0) + (4, 0) = (5, 0)

Since T(u + v) ≠ T(u) + T(v), the transformation T is not additive and hence not linear transformation.

Homogeneity: T(cu) = cT(u) for all vectors u in R^3 and all scalars c.

Let u = (1, 2, 3) be a vector in R^3, and let c = 2 be a scalar. Then,

T(u) = T(1, 2, 3) = (|1|, 0) = (1, 0)

T(cu) = T(2, 4, 6) = (|2|, 0) = (2, 0)

However,

cT(u) = 2(1, 0) = (2, 0)

Since T(cu) ≠ cT(u), the transformation T is not homogeneous and hence not linear.

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Answer:

-9.661

Step-by-step explanation:

I hope this is correct, if not feel free to let me know and I will fix it. I'm sorry in advance if this is incorrect.

Answer:

-9.661

Step-by-step explanation:

-a + -b

-a -b

Let a = 6.05  and b = 3.611

-6.05 - 3.611

-9.661

Answer:

Step-by-step explanation:

(3(18)+2(3.99)+45)(1.08)=(106.98)(1.08)=$115.54 (rounded to nearest cent)

Answer:

a. m∡ADB =  25°

b. m∡BDC =  35°

c. Used angle addition postulate.  It created the equation m∡ADB + m∡BDC = m∡ADC which helped solve for x°

Step-by-step explanation:

The angle addition postulate states the addition of smaller angles equals the overall angle OR m∡ADB + m∡BDC = m∡ADC

Given:

m∡ADB = x°

m∡BDC = x° + 10

m∡ADC = 60

m∡ADB + m∡BDC = m∡ADC; now substitute

x° + x° + 10 = 60

2x° = 50

x° = 25°; now plug back

m∡ADB = x° = 25°

m∡BDC = x° + 10 = 25° + 10° = 35°

I hope this helps

If simplify it would be -15 + 12i

Answer:

If the X in the middle is shown as multiplication, then the answer is -15 + 12i

EQUATION: (6 + 2iX6 - 21)

STEP 1:

SPLIT UP THE COMMON FACTORS

STEP 2:

SOLVE AS SHOWN

STEP 3:

ADD EVERYTHING TOGETHER

Answer:

Answer:

21.9

Step-by-step explanation:

Similarity Theorem

15/13=x/19

1.15384615=x/19

19*1.15384615=x

21.9230769=x

Final Answer

21.9

Proof answer

15/13=21.9/19

1.2= 1.2

Answer:

No

Step-by-step explanation:

substitute the x- coordinate of the point into each equation and if both have the value of the y- coordinate of the point then it is a solution.

y = 5(3) + 9 = 15 + 9 = 24 ≠ 9

y = 3 + 6 = 9

since the point does not satisfy both equations then it is not a solution of the system.

No

Step-by-step explanation:

y=5x+9

y=x+6

\(y = 5x + 9 \: \: - - - - - - (1) \\ y = x + 6 \: \: - - - - - - -(2) \\ from \: equation \: (2) \\ y - 6 = x \\ x = 6 + y - - - - - - (3)\\ y = 5x + 9 \\ y = 5(6 + y) + 9 \\ y = 30 + 5y + 9 \\ 5y - y = 30 + 9 \\ 4y = 39 \\ y = - \frac{39}{4} \\ y = 9.75 \\ \\ y = 9.75 \: into \: (2) \\y = x + 6 \\ 9.75 = x + 6 \\ 9.75 - 6 = x \\ x = 9.75 - 6 \\ x = 3.75\)

So the answer is NO