On a grid, what is the
distance between two
points located at
(-4,-5) and (-1,-10)?

the expected total number of orange candies and the standard deviation for the total number of orange candies in the two samples, respectively, are 13.75 and 3.033. Option E is correct.

We are given that Ten percent of all Dynamite Mints candies are orange and 45 percent of all Holiday Mints candies are orange.

Two independent random samples, each of size 25, are selected - one from Dynamite Mints candies and the other from Holiday Mints candies and we are asked to find the expected total number of orange candies and the standard deviation for the total number of orange candies, respectively, in the two samples.

To solve this problem, we will use the formula for mean and variance of a binomial distribution.

Mean or Expected Value E(X) = np

Variance V(X) = np(1-p)The formula for standard deviation is as follows;

Standard deviation of X, σ(X) = √np(1 - p)The number of orange candies in each sample of size 25 is expected to be:

For Dynamite Mints: np = 25 × 0.1 = 2.5For Holiday Mints: np = 25 × 0.45 = 11.25Therefore, the expected total number of orange candies in the two samples is: 2.5 + 11.25 = 13.75The variance for Dynamite Mints is:

V(X) = np(1 - p) = 25 × 0.1 × (1 - 0.1) = 2.25The variance for Holiday Mints is:

V(X) = np(1 - p) = 25 × 0.45 × (1 - 0.45) = 6.9375Therefore, the total variance for the two samples is:

V(X1 + X2) = V(X1) + V(X2) = 2.25 + 6.9375 = 9.1875The standard deviation for the two samples is:

σ(X1 + X2) = √V(X1 + X2) = √9.1875 = 3.033

So, the expected total number of orange candies and the standard deviation for the total number of orange candies in the two samples, respectively, are 13.75 and 3.033. Option E is correct.

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The two smallest positive solutions for x in the equation 12cos(2π/5x) + 10 = 16 are x = 5/6 and x = 17/6. Therefore, the correct option is B) 5/6, 25/6.

To find the two smallest positive solutions for x in the equation 12cos(2π/5x) + 10 = 16, we need to solve the equation for x.

Let's start by isolating the cosine term:

12cos(2π/5x) = 16 - 10

12cos(2π/5x) = 6

Next, divide both sides of the equation by 12:

cos(2π/5x) = 6/12

cos(2π/5x) = 1/2

To find the values of x that satisfy this equation, we can take the inverse cosine (arccos) of both sides:

2π/5x = arccos(1/2)

To determine the two smallest positive solutions, we need to find the values of x that correspond to the acute angles whose cosine is 1/2.

The arccosine of 1/2 is π/3, so:2π/5x = π/3

Next, solve for x:

x = (π/3)(5/2π)

x = 5/6

Therefore, the first solution for x is 5/6.

To find the second solution, we can add 2π to the right-hand side of the equation:

x = (π/3)(5/2π) + 2π

x = 5/6 + 12π/6

x = 5/6 + 2

x = 5/6 + 12/6

x = 17/6

Therefore, the second solution for x is 17/6.

Option b

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Answer:

x=5/2 or  2.5

Step-by-step explanation:

1 Divide both sides by 22.

x=5/2

decimail form 2.5

​​  

The number of monthly payments that need to be made for a 2 ½ -year loan is 30. This is because there are 12 months in a year and 2 ½ years are equal to 30 months.

It's important to know the number of payments needed to be made when taking out a loan to ensure that the loan can be repaid in a timely manner. The number of monthly payments that need to be made for a 2 ½ -year loan is 30. This is because there are 12 months in a year and 2 ½ years are equal to 30 months. This information is important to know because it will allow you to budget your finances and ensure that you can make the necessary payments on time. It is important to note that some lenders may offer more flexible repayment schedules, so it's important to research the terms and conditions of the loan before signing the agreement. If you are unsure about the terms of a loan, it's always a good idea to seek the advice of a financial advisor. With the right information and planning, taking out a loan can be a responsible financial decision.

In conclusion, for a 2 ½ -year loan, 30 monthly payments need to be made. It is important to know this information to budget finances and make payments on time. It's important to research loan terms and seek the advice of a financial advisor to make informed financial decisions.

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Answer:

P(x) = (-0.2x² + 480x - 24480)

Step-by-step explanation:

1). Expression representing the "Cost" to produce the shirts is,

  C(x) = 160x + 24480

  Where 'x' represents the number of shirts.

  Cost to produce 900 printed shirts will be,

   C(900) = 160×900 + 24480

                = 144000 + 24480

                = Php 168480

2). Revenue generated by selling 900 shirts is,

   R(x) = 640x - 0.2x²

   For x = 900,

   R(x) = 640(900) - 0.2(900)²

          = 576000 - 162000

          = Php 414000

3). Expression for profit:

   Since, Profit = Revenue generated - Cost for production

   P(x) = R(x) - C(x)

          = (640x - 0.2x²) - (160x + 24480)

          = (640x - 160x) - 0.2x² - 24480

          = 480x - 0.2x² - 24480

  P(x) = (-0.2x² + 480x - 24480)

The amount of total cost at q* is 1.

To determine the production level that minimizes total cost, we need to find the value of q (production level) at which the derivative of the total cost function TC(q) is equal to zero. Let's begin by finding the derivative of TC(q):

TC(q) = 10 - 6q + q^2

To find the minimum point, we differentiate TC(q) with respect to q:

d(TC(q))/dq = -6 + 2q

Setting the derivative equal to zero and solving for q:

-6 + 2q = 0

2q = 6

q = 3

So the production level q* that minimizes the total cost is 3.

To find the amount of total cost at q*, we substitute q = 3 into the total cost function TC(q):

TC(q*) = 10 - 6(3) + (3)^2

TC(q*) = 10 - 18 + 9

TC(q*) = 1

Therefore, the amount of total cost at q* is 1.

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Answer:

y+2=5×

Step-by-step explanation:

because it is unlike term

Answer:

Ok I will help because i'm the nicest person you'll ever meet lol Ok anyway

there will be no step by step explanation

Direction variation:   and Not direction variation:

y= 3x

X= -1

and

Y= 4

now for the other one the non-direction---------------------> Y = (2/7)x

------------------------------------------------------------------------------> -0.5x = Y

------------------------------------------------------------------------------> Y= 2.2x + 7

TADA I'm finished and your welcome!!! :D

Answer:

d

Step-by-step explanation:

Supplementary angles sum to 180°

Sum the angles A and B and equate to 180m that is

16x - 7 + 21x + 2 = 180

37x - 5 = 180 ( add 5 to both sides )

37x = 185 ( divide both sides by 37 )

x = 5

Thus

∠ A = 16x - 7 = 16(5) - 7 = 80 - 7 = 73° → d

Answer:

5n + 3

Step-by-step explanation:

8 , 13 , 18

difference = 5

8 - 5(1) = 3

therefore nth term = 5n + 3

proof:

5(2) + 3 = 13

5(3) + 3 = 18

Step-by-step explanation:

Hey there!

The sequences are; 8,13,18,23.....

Common difference (d)= 5

Use formula: tn = t1+(n-1)d

Where d is the common difference and t1 is first sequence.

Or, tn = 8 + (n-1)5

= 8+5n -5

= 5n +3.

Therefore the required nth term is; tn = 5n+3.

Check;

1st term (t1) = 8 = 5×1+3=8 (true)

2nd term (t2) = 13 = 5×2+3=13 (true)

3rd term (t3)= 18 = 5×3+3=18 (true)

4th term (t4) = 23 = 5×4+3=23 (true).

Hope it helps..

Answer:

X=3

Step-by-step explanation:

Answer:

2(x+5)

Step-by-step explanation:

To find the values of x for which the two trinomials are equal, we need to set them equal to each other and solve for x.

For the trinomials 3x^2 - 4x + 3 and x^2 + x + 1:

3x^2 - 4x + 3 = x^2 + x + 1

By rearranging the equation and combining like terms, we get:

2x^2 - 5x + 2 = 0

Now, we can solve this quadratic equation by factoring, completing the square, or using the quadratic formula. In this case, the equation can be factored as:

(2x - 1)(x - 2) = 0

Setting each factor equal to zero, we have:

2x - 1 = 0   -->   2x = 1   -->   x = 1/2

x - 2 = 0   -->   x = 2

Therefore, the values of x for which the two trinomials are equal are x = 1/2 and x = 2.

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Answer:

ill help

Step-by-step explanation:

Answer:

Step-by-step explanation:

Solving for variables

1.......................................

2.......................................

3.......................................

4.......................................

here are your answer

d = 2/3

c = 3/2

y = 2/3

x = 4 2/19

have a good day

The minimum amount of emergency savings you should have is $130.

To determine the minimum amount of emergency savings you should have, we need to consider the essential expenses.

In this case, the gasoline expense and the credit card payment are marked as essential expenses.

Let's calculate the minimum amount of emergency savings required to cover these essential expenses.

Essential expenses:

Gasoline (essential) = $100

Credit card payment (essential) = $30

To calculate the minimum emergency savings required, we add up the essential expenses:

Minimum emergency savings = Gasoline (essential) + Credit card payment (essential)

Minimum emergency savings = $100 + $30

Minimum emergency savings = $130

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We need to evaluate the given expression, √3x + 7 - x, for two different values of x: (a) x = -2 and (b) x = 3.

For x = -2:

Plugging in the value of x, we have √3(-2) + 7 - (-2).

Simplifying this expression, we get √(-6) + 7 + 2.

Since the square root of a negative number is not defined in the real number system, the expression is undefined for x = -2.

For x = 3:

Plugging in the value of x, we have √3(3) + 7 - 3.

Simplifying this expression, we get √9 + 7 - 3.

The square root of 9 is 3, so we have 3 + 7 - 3.

Further simplification yields 7.

Therefore, for x = -2, the expression is undefined, and for x = 3, the expression evaluates to 7.

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Answer:

D the last one

Step-by-step explanation:

Answer:

∠VUR and ∠QRU

Step-by-step explanation:

Answer:

Hi there! I just answered this question and the situation represents a geometric sequence because the successive y-values have a common ratio of 0.7.

Step-by-step explanation:

Every year, the value of the computer decreases by 30%.

The value of the computer is originally $2,100. Determine the value of the computer after one year by subtracting 30% of the original value.

2,100 - 0.30(2,100) = 2,100 - 360 = 1,470

The cost of the computer after one year will be $1,470 and the original cost was $2,100. Find the ratio of these two values.

1,470/2,100 = 0.7!

Therefore, after one year, the value of the computer is 0.7 times the value of the computer the previous year. Since the value is decreasing 30% annually, this trend will continue each year.

So, the situation represents a geometric sequence because the successive y-values have a common ratio of 0.7.!

Hope this helps I was confused too!

Answer:

0.7

got it right.

New Simplex Tableau:

| Basis | x1 | x2

To use the simplex tableau method to solve the given linear programming problem, we need to convert it into standard form. The standard form includes non-negativity constraints and all inequalities as less than or equal to constraints. Let's rewrite the problem in standard form:

Maximize: Z = 2x1 + 5x2 + 4x3

Subject to:

x1 + x2 + 2x3 + x4 = 20

2x1 + x2 + x3 + x5 = 10

0x1 + x2 - x3 + x6 = 5

3x1 + 0x2 + 3x3 + x7 = 12

x1, x2, x3, x4, x5, x6, x7 ≥ 0

Now, let's construct the initial simplex tableau:

Basis x1 x2 x3 x4 x5 x6 x7 RHS

x4 1 1 2 1 0 0 0 20

x5 2 1 1 0 1 0 0 10

x6 0 1 -1 0 0 1 0 5

x7 3 0 3 0 0 0 1 12

Z -2 -5 -4 0 0 0 0 0

Next, we will perform iterations to find the optimal solution. The goal is to make the coefficients in the Z row non-negative. We will select the most negative coefficient as the pivot column and the smallest ratio of the RHS to the pivot column value as the pivot row.

Iteration 1:

Pivot Column: x2 (most negative coefficient)

Pivot Row: x6 (smallest ratio of RHS / pivot column value)

Perform row operations to make x6 a basic variable:

Row 3 = Row 3 / 1

Perform column operations to clear the pivot column:

Row 1 = Row 1 - 1 * Row 3

Row 2 = Row 2 - 1 * Row 3

Row 4 = Row 4 - 0 * Row 3

Row 5 = Row 5 + 5 * Row 3

New Simplex Tableau:

Basis x1 x2 x3 x4 x5 x6 x7 RHS

x4 1 0 3 1 0 0 0 15

x5 2 0 2 0 1 0 0 35

x2 0 1 -1 0 0 1 0 5

x7 3 0 3 0 0 0 1 12

Z -2 0 -3 0 0 5 0 20

Iteration 2:

Pivot Column: x3 (most negative coefficient)

Pivot Row: x4 (smallest ratio of RHS / pivot column value)

Perform row operations to make x4 a basic variable:

Row 1 = Row 1 - 3 * Row 4

Row 2 = Row 2 - 2 * Row 4

Row 3 = Row 3 - (-1) * Row 4

Row 5 = Row 5 - 3 * Row 4

Perform column operations to clear the pivot column:

Row 2 = Row 2 - 2 * Row 5

Row 1 = Row 1 - 3 * Row 5

Row 3 = Row 3 - (-1) * Row 5

Row 7 = Row 7 - 0 * Row 5

New Simplex Tableau:

| Basis | x1 | x2

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Answer:

34

Step-by-step explanation:

Answer:

x = tan (3/4) therefore you cannot use (4/3)

Step-by-step explanation:

tan = opp over adj

Answer:

[tex]-3x+y=10[/tex]

Step-by-step explanation:

To write this equation we first need to know what the standard form is. Standard form of a line is written as [tex]Ax + By = C[/tex]. To get this, we first need to put the equation into point slope form or [tex]y-y1 = m(x-x1)[/tex] where [tex]m[/tex] is slope and [tex](x1,y1)[/tex] is a point on the graph. Using the information we know we can make the equation [tex]y+2=4(x+3)[/tex].

Now that we have point slope form we need to convert it. To do this we need to first get rid of the parenthesis by distribution. This will give us [tex]y+2=3x+12[/tex]

Next, we know we need to get [tex]x[/tex] and [tex]y[/tex] on the same side of the equal sign. We do this by subtracting 3x on both sides to get [tex]-3x+y+2=12[/tex]

Finally, we can subtract 2 on both sides to put the equation into standard form. This will give us [tex]-3x+y=10[/tex]

Answer:

C

Step-by-step explanation:

A prime polynomial is simply an irreducible polynomial.

[tex]\mathbf{x + 9y^2}[/tex] is a prime polynomial

First, we test the options.

[tex]\mathbf{x + 9y^2}[/tex]

The above function cannot be reduced further.

Hence, [tex]\mathbf{x + 9y^2}[/tex] is a prime polynomial

[tex]\mathbf{3m + 9n}[/tex]

Factor out 3

[tex]\mathbf{3(m + 3n)}[/tex]

[tex]\mathbf{3m + 9n}[/tex] is not a prime because it can be factored as [tex]\mathbf{3(m + 3n)}[/tex]

[tex]\mathbf{8x^7 - 9x + 12x^2}[/tex]

Factor out x

[tex]\mathbf{x(8x^6 - 9 + 12x)}[/tex]

[tex]\mathbf{8x^7 - 9x + 12x^2}[/tex] is not a prime because it can be factored as [tex]\mathbf{x(8x^6 - 9 + 12x)}[/tex]

Hence, [tex]\mathbf{x + 9y^2}[/tex] is a prime polynomial

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Answer:

x = -2, 7

Step-by-step explanation:

1.Single out 6x^2 to x^2 by dividing 6 on both sides

= x^2-5x-14=0

2.Write -5x as a difference in order to factor

= x^2+2x-7x-14=0

3. Factor.

= (x+2)(x-7)

4. Set equal to 0

x+2=0

x=-2

x-7=0

x=7

The solution of the equation 6x² – 30x – 84 = 0 from least to greatest will be  –2 and 7.

It is a method for dividing a polynomial into pieces that will be multiplied together. At this moment, the polynomial's value will be zero.

The equation is given below.

6x² – 30x – 84 = 0

Then the factor of the equation will be

        x² – 5x – 14 = 0

x² – 7x + 2x – 14 = 0

x(x – 7) + 2(x – 7) = 0

       (x + 2)(x – 7) = 0

Then the solution will be

x = –2, 7

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Answer:

Step-by-step explanation:

Given

Solving for H

The solution of each of the quadratic equations are:

5) x = +3, -3

6) x = +3/2, -3/2

7) x = -4, 1/3

8) x = +9, -9

The general form of a quadratic equation is:

ax² + bx + c = 0

The quadratic formula to find the roots is:

x = [-b ± √(b² - 4ac)]/2a

5) The quadratic equation is given as 4x² - 36.

Thus:

x = [-0 ± √(0² - 4(4 * -36))]/2(4)

x = ±√4(4 * 36))/8

x = ±24/8

x = +3, -3

6) The quadratic equation is given as 64x² - 144

Thus:

x = [-0 ± √(0² - 4(64 * -144))]/2(64)

x = ±(√36864)/8

x = ±192/128

x = ±3/2

x = +3/2, -3/2

7) The quadratic equation is given as 3x² + 11x - 4

Thus:

x = [-11 ± √(11² - 4(3 * -4))]/2(3)

x = [-11 ± (√169)]/6

x = (-11 ± 13)/6

x = -4, 1/3

8) The quadratic equation is given as x² - 81

Thus:

x = [-0 ± √(0² - 4(1 * -81))]/2(1)

x = ±(√324)/2

x = ±18/2

x = ±9

x = +9, -9

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