Isaac makes china mugs with names painted on them. He charges a fixed fee for the mug, together with a fixed charge for each letter in the name. Penelope buys a mug for each of her children, Alexander and Lucia. She pays $12.60 for Alexander’s mug and $9.40 for Lucia’s mug. How much would Penelope have to pay for a mug with her own name on it?

Answer:

72

......................

Answer:

See below.

Step-by-step explanation:

In multiplication and division of two numbers:

equal signs equal positive

different signs equal negative

Now you can answer every question.

1. What is a negative times a positive different signs negative

2. A Positive times positive equal signs positive

3. A negative times a negative equal signs positive

4. What is a negative divided by a positive different signs negative

5. A Positive divided by positive equal signs positive

6. A negative divided by a negative equal signs positive

Answer:

1: - x + = -

2: + x + = +

3: - x - = +

4: - divided by a + is -

5: + divided by a + is +

6: - divided by a - is +

Answer:

0.325

Step-by-step explanation:

i don't get the question sorry...

rational

rational

irrational

irrational

irrational

the optimal solution to maximize Z is x1 = 25 and x2 = 0, with Z = 3000.

To solve the given linear programming model graphically, we need to plot the feasible region and identify the corner points to find the optimal solution. Here's the step-by-step process:

1. Plot the constraints:

  - Plot the line x1 = 40 (vertical line at x1 = 40).

  - Plot the line x2 = 10 (horizontal line at x2 = 10).

  - Plot the line 20x1 + 10x2 = 500 (which can be rewritten as 2x1 + x2 = 50).

  - Shade the feasible region that satisfies all the constraints.

2. Identify the corner points:

  - Determine the coordinates of the corner points where the boundary lines intersect.

3. Evaluate the objective function:

  - Calculate the value of the objective function Z = 120x1 + 80x2 for each corner point.

4. Determine the optimal solution:

  - Select the corner point that maximizes the objective function Z.

Here's the graphical representation of the feasible region:

      |

 40   |           C

      |          /

      |         /

      |        /

      |       /

      |      /

      |     /    Feasible Region

 10   |_____/_________________

      0   10  20  30  40  50

            0`

The corner points of the feasible region are:

A: (0, 0)

B: (0, 10)

C: (25, 0)

D: (20, 5)

Now, we evaluate the objective function Z = 120x1 + 80x2 for each corner point:

Z(A) = 120(0) + 80(0) = 0

Z(B) = 120(0) + 80(10) = 800

Z(C) = 120(25) + 80(0) = 3000

Z(D) = 120(20) + 80(5) = 2400

From the above calculations, we can see that the maximum value of Z occurs at point C: (25, 0).

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Answer:

04x=24

Step-by-step explanation:

04x=24

divide both sides by 4 to let x stand alone

04x÷4=24÷4

x=6

(a) For case a, the 95% confidence interval for β1 is (-48.25, -13.75) and the 90% confidence interval is (-46.37, -15.63).

(b) For case b, the 95% confidence interval for β1 is (-101.15, -28.85) and the 90% confidence interval is (-96.32, -33.68).

(c) For case c, the 95% confidence interval for β1 is (-17.35, 0.15) and the 90% confidence interval is (-15.92, 1.52).

To construct confidence intervals for β1, we need the values of β1, s (standard error of β1), SSxx (sum of squares of x), and n (sample size). The formula for the confidence interval is β1 ± tα/2 × (s / sqrt(SSxx)), where tα/2 is the critical value from the t-distribution for the desired confidence level.

(a) For case a, with β1 = -31, s = -4, SSxx = 35, and n = 10, we calculate the standard error as s / sqrt(SSxx) = -4 / sqrt(35) ≈ -0.676. With a sample size of 10, the critical value for a 95% confidence interval is t0.025,8 = 2.306, and for a 90% confidence interval is t0.05,8 = 1.860. Plugging the values into the formula, we get the 95% confidence interval as -31 ± 2.306 × (-0.676), which gives us (-48.25, -13.75), and the 90% confidence interval as -31 ± 1.860 × (-0.676), which gives us (-46.37, -15.63).

(b) For case b, with β1 = -65, SSE = 1,860, SSxx = 20, and n = 14, we calculate the standard error as sqrt(SSE / (n-2)) / \(\sqrt{ SSxx}\)≈ 20.00 / \(\sqrt{20}\)≈ 4.472. With a sample size of 14, the critical value for a 95% confidence interval is t0.025,12 = 2.179, and for a 90% confidence interval is t0.05,12 = 1.782. Plugging the values into the formula, we get the 95% confidence interval as -65 ± 2.179 ×4.472, which gives us (-101.15, -28.85), and the 90% confidence interval as -65 ± 1.782 × 4.472, which gives us (-96.32, -33.68).

(c) For case c, with β1 = -8.6, SSE = 135, SSxx = 64, and n = 18, we calculate the standard error as \(\sqrt{(SSE / (n-2) }\) / \(\sqrt{ SSxx}\) ≈ 135 / \(\sqrt{64}\) ≈ 2.813. With a sample size of 18, the critical value for a 95% confidence interval is t

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Answer:

Use the pythagorian theorm

Step-by-step explanation:

Answer:

x = 15/2

Step-by-step explanation:

the smaller triangle missing side by using pythagorean theorem

a^2 + b^2 = c^2

4^2 + b^2 = 5^2

b^2 = 25-16=9

b=3 the missing leg for the small triangle;

now use proportionality by saying \(\frac{4}{6}\) = \(\frac{3}{y}\); where y is the one leg in the larger triangle

y = 6*3/4 = 9/2

use pythogorean theorem again

a^2 + b^2 = x^2

6^2 + (9/2)^2 = x^2

36 + 81/4 = x^2

144/4 + 81/4 = x^2

225/4 = x^2

x = 15/2

Step-by-step explanation:

We can find the modulus/absolute value from the point -8.95 to each of the other points:

|(-9) - (-8.95)| = 0.05.

|(-8) - (-8.95)| = 0.95.

|(-7) - (-8.95)| = 1.95.

So what this tell us is that the point -8.95 is furthest away from -7 and is closest to -9. It is also much closer to -9 than to -8. (compare 0.05 with 0.95)

Hence the best answer is Point A. (A)

Answer:

x > 2

General Formulas and Concepts:

Step-by-step explanation:

Step 1: Translate

"Two" = 2

"minus" = subtraction

"a number x" = x

"is no more than" = <

"0" = 0

Step 2: Set up inequality

2 - x < 0

Step 3: Solve for x

Here we see that any value larger than 2 would work as a solution of x.

Answer:

-4

Step-by-step explanation:

if a=-10 and b=-6

a-b=-10- -6

=-10+6 which can be written as

=6-10

=-4

since -and-is+

The value of expression a-b if a= -10 and b= -6 is -4.

An expression is a combination of terms that are combined by using mathematical operations such as subtraction, addition, multiplication, and division.

The given expression is a-b.

Here, a= -10 and b= -6

Substitute, a= -10 and b= -6 in the given expression, we get

a-b= -10-(-6)

= -10+6

= -4

Therefore, the value of expression a-b if a= -10 and b= -6 is -4.

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Answer:

use the zero as an common multipal

Step-by-step explanation:

Answer:

1,3,4

Step-by-step explanation:

Answer:

equivalent fractions of 3/5 are 6/10, 9/15 and 12/20.

Step-by-step explanation:

hope this helped! have a good day<3

Answer:

1/6

Step-by-step explanation:

We know that 1/2 are apples and 1/3 are bananas

we also know that

apples+bananas+oranges=1

Which means that

1/2+1/3+oranges=1

Add 1/2 + 1/3 by getting the denominators equal

3/6+2/6=5/6

Which means that 5/6+oranges=1

1-5/6=1/6

1/6

write everything below this

1/2+1/3+oranges=1

1/2+1/3=5/6

5/6+oranges=1

oranges=1-5/6

oranges=1/6

The  probability that a product will operate properly within an expected time frame is the dimension of quality known as reliability

The probability is the ratio of the number of favorable outcomes to the total number of outcomes. The value of the probability is varies from zero to one

Here, the product will operate properly within an expected time frame is the dimension of quality

Reliability is expressed as the probability that a given item will perform its intended function with no failures for a given period of time under a given set of conditions that means the reliability is the complementary to the failure of probability

Therefore, the given statement is know as the reliability

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Let's solve your system by substitution.

2x−2y=−4;2x+y=11

Rewrite equations:

2x+y=11;2x−2y=−4

Step: Solve2x+y=11for y:

2x+y=11

2x+y+−2x=11+−2x(Add -2x to both sides)

y=−2x+11

Step: Substitute−2x+11foryin2x−2y=−4:

2x−2y=−4

2x−2(−2x+11)=−4

6x−22=−4(Simplify both sides of the equation)

6x−22+22=−4+22(Add 22 to both sides)

6x=18

6x/6 = 18/6

(Divide both sides by 6)

x=3

Step: Substitute3forxiny=−2x+11:

y=−2x+11

y=(−2)(3)+11

y=5(Simplify both sides of the equation)

Answer:

x=3 and y=5

The sum of the denominators of the two fractions is -28.

The sum of the denominators of the two fractions can be found by first finding the equivalent fractions for 2/3 and 5/11 that fit the given conditions, and then adding the denominators together.

To find the equivalent fraction for 2/3 with a sum of 45 for the numerator and denominator, we can use the equation:

x + y = 45, where x is the numerator and y is the denominator.

Since the fraction is equivalent to 2/3, we can also use the equation 2/3 = x/y.

Solving for x in the first equation gives us x = 45 - y, and substituting this into the second equation gives us 2/3 = (45 - y)/y.

Multiplying both sides by 3y gives us 2y = 135 - 3y, and solving for y gives us y = 27.

This means that the denominator of the equivalent fraction for 2/3 is 27.

To find the equivalent fraction for 5/11 with a difference of 30 between the numerator and denominator, we can use the equation:

x - y = 30, where x is the numerator and y is the denominator.

Since the fraction is equivalent to 5/11, we can also use the equation 5/11 = x/y.

Solving for x in the first equation gives us x = 30 + y, and substituting this into the second equation gives us 5/11 = (30 + y)/y.

Multiplying both sides by 11y gives us 5y = 330 + 11y, and solving for y gives us y = -55.

This means that the denominator of the equivalent fraction for 5/11 is -55.

Therefore, the sum of the denominators of the two fractions is 27 + (-55) = -28.

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Answer:

$0.22.

Step-by-step explanation:

To find the cost per ounce of juice, divide the total cost of 32 ounces of juice by the number of ounces:

7.04 ÷ 32 ounces = 0.22 per ounce

So, the cost per ounce of juice is approximately $0.22.

Answer:

0.22

Step-by-step explanation:

A logarithmic equation exists as an equation that uses the logarithm of an expression containing a variable. The value of the logarithmic equation x = log 2.97/log 1.13.

A logarithmic equation exists as an equation that applies the logarithm of an expression having a variable. To estimate exponential equations, first, see whether you can note both sides of the equation as powers of the same number.

Given: \($1.13^x = 2.97\)

Taking log on both sides, we get

log \($1.13^x\) = log 2.97

x log 1.13 = log 2.97

x = log 2.97/log 1.13

Therefore, the value of logarithmic equation x = log 2.97/log 1.13.

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Answer:

Number line graph with a closed circle on 120 and shading to the right.

Step-by-step explanation:

Because they have collected 30 dollars already and must collect at least 150 dollars, the closed circle would go on 120, going to the right. (150-30=120)

Since there are 130 people in the sport center and 121 people using any combination of facilities, we find that 130 - 121 = 9 people use exactly one of the facilities.

In the given sport center, there are 130 people utilizing various facilities. To determine how many people use exactly one of these facilities, we can use the principle of inclusion-exclusion.Total number of people using any facility: 61 (gym) + 68 (pool) + 60 (track)
However, this includes people who use multiple facilities, so we subtract the overlaps:Overlaps: 25 (gym & pool) + 30 (pool & track) + 19 (gym & track)
Now, we add back the people who use all three facilities, as they were subtracted twice: 6 (gym, pool, & track)
Combining these numbers, we get:(61 + 68 + 60) - (25 + 30 + 19) + 6 = 189 - 74 + 6 = 121.

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Answer:

12 books.

Step-by-step explanation:

6x+8=80

6x=72

x=12

The solution of the system of equations:

2x+2y+ 6z = 8

5x+6y + 5z = 3

5x + 6y + 3z = 5

Is the one in option a.

(x= 34, y = -27,z = -1)

Here we have the system of equations:

2x+2y+ 6z = 8

5x+6y + 5z = 3

5x + 6y + 3z = 5

If we subtract the third equation from the second one we will get:

(5x + 6y + 5z) - (5x + 6y + 3z) = 3 - 5

5z - 3z = -2

We just removed two of the variables, so we can now solve this linear equation for z so we get:

2z = -2

z = -2/2

z = -1

We know that the value of z is -1, that is enough to identify the correct option because only one of these has z = -1  which is the first one, so that is the correct option.

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a) To solve the recurrence relation an = an-1 + 3(n-1), a0 = 1, we can expand the recurrence relation iteratively.

a1 = a0 + 3(1-1) = 1 + 0 = 1

a2 = a1 + 3(2-1) = 1 + 3 = 4

a3 = a2 + 3(3-1) = 4 + 6 = 10

a4 = a3 + 3(4-1) = 10 + 9 = 19

...

We can observe a pattern from the values:

a0 = 1

a1 = 1

a2 = 4

a3 = 10

a4 = 19

We can notice that an = \(n^2 + 1.\) We can prove this by induction, but in this case, we can also recognize that the given recurrence relation generates the triangular numbers (1, 3, 6, 10, 15, ...), which are defined by the formula Tn = n(n+1)/2.

Thus, the solution to the recurrence relation is an = \(n^2 + 1.\)

b) For the recurrence relation an = an-1 + n(n-1), a0 = 3, we can again expand it iteratively:

a1 = a0 + 1(1-1) = 3 + 0 = 3

a2 = a1 + 2(2-1) = 3 + 2 = 5

a3 = a2 + 3(3-1) = 5 + 6 = 11

a4 = a3 + 4(4-1) = 11 + 12 = 23

...

Observing the values, we can notice that an =\(n(n^2 + 1).\)

Thus, the solution to the recurrence relation is an = \(n(n^2 + 1).\)

c) For the recurrence relation an = an-1 +\(3n^2\), a0 = 10, we expand it iteratively:

a1 = a0 + \(3(1^2)\) = 10 + 3 = 13

a2 = a1 + \(3(2^2) =\) 13 + 12 = 25

a3 = a2 + \(3(3^2)\)= 25 + 27 = 52

a4 = a3 + \(3(4^2)\)= 52 + 48 = 100

...

We can notice that an = \(n^3 + 10.\)

Thus, the solution to the recurrence relation is an = \(n^3 + 10.\)

These are the solutions to the given recurrence relations.

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The sum of the geometric series is 2199; option E.

S6 = a(rⁿ - 1) / r -1

= 1468(1/3^6 - 1) / (1/3 - 1)

= 1468(0.00137174211248 - 1) / -2/3

= 1468(-0.9986282578875) / -0.66666666666666

= -1,465.98628257885 / -0.66666666666666

= 2198.97942386829

Approximately,

S6 = 2199

Arithmetic series

Sn = n/2{2a + (n -1)d}

= 36/2 {2×27 + (36-1)-5/2}

= 18{54 + (35)-5/2}

= 18(54 + 175/2)

= 18(54 + 87.5)

= 18(141.5)

s36 = 2547

a36 = a + (n - 1) d

= 27 + (36 - 1)-5/2

= 27 + (35)-5/2

=27 + -175/2

= 27 - 87.5

= -60.5

S20 = n/2{2a + (n -1)d}

= 20/2{2×27 + (20-1)-5}

= 10(54 + (19)-5)

= 10{54 + (-95)}

= 10(54-95)

= 10(-41)

s20 = -410

Missing terms of the geometric sequence:

nth term = ar^n-1

448/135 = 63/80×r^(6-1)

448/135 = 63/80×r^5

r^5 = 448/135 ÷ 63/80

= 448/135 × 80/63

= 35,840/8,505

r = 5√35,840/5√8505

= 946.57/461.11

r = 2.05

Second term = a×r

= 63/80×2.05

= 1.614375

Third term = ar²

= 63/80×2.05²

= 63/80×4.2025

= 3.30946875

Fourth term = 63/80 × 2.05³

= 63/80×8.615125

= 6.7844109375

Therefore, none of these are correct

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Distribution agreements involve both parties mutually contributing to the distribution efforts.

A joint venture is another way of referring to a non-equity mode of entry with an alliance partner. An acquisition is another way of referring to an equity mode of entry, including, but not limited to, an acquisition. A license grants the right or permission to use the property, including intellectual property, of another. A distribution agreement is an agreement between at least two parties to join their efforts in an attempt to sell a product or service. The two main types of distribution agreements are sponsored and collaborative. In a sponsored distribution agreement, one party sponsors the other party's product or service, while in a collaborative distribution agreement, both parties work together to sell the product or service.

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The perimeter of each cookie is 14.42cm

The area of each cookie is 6.51 cm²

The number of dough batches required is 4.35 batches

The perimeter of each cookie is determined using the formula to find the length of each side:

l = √{(x₂ - x₁)² + (y₂- y₁)²}

For each pair of points:

O(0,0), A (2,3), B(4,0), C (2,-3)

MA = √(2² + 3²) = √13

AB = √{2² +(-3)²} = √13

BC= √{(2)² +(-3)²} =√13

CO = √{(-2)² +(3)²} = √13

Perimeter = 4 x length

Perimeter = 4 * √13

Perimeter = 14.42 cm

Since a parallelogram with equal sides is a rhombus, we can use the formula for the area of a rhombus:

Area = (diagonal 1 x diagonal 2)/2

Area = (diagonal 1 x diagonal 2)/2

Area = (3.61 x √(2) cm) x (3.61 x √(2) cm)/2

Area = 6.51 cm²

2. The area of the square dough = (30 cm)²

The area of the square dough = 900 cm²

One dough can make 900 cm²/6.51 cm² cookies = 138 cookies

Number of dough batches required = 600/1138

The number of dough batches required = 4.35 batches

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Based on the information provided regarding same as cash loans, Chelsea won't be charged interest for the first 6 months of the loan, nor will she have to make payments for the first 6 months. (Option D)

A Same-As-Cash Loan refers to a short-term lending solution in which no interest or monthly payment are required to be paid during a set “Same-As-Cash” period. At the end of a predetermined period, the loan is paid off. Hence, the customer owes no interest or monthly payments during a set promotional period and pays the same amount on the loan as they would have paid up front with cash. These are interest deferred loans in which the loans interest still accrues during that promotional period, however if the customer pays off the entire principal balance before the period ends, they are not required to pay that interest. The advantage of these loans is that customers may spend the same amount they would have if they had paid with cash up front. Hence, if Chelsea opts for loan that offered 6 months, same as cash, there would be no requirement of payment or interest charged for the 6 months.

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Answer:28

Step-by-step explanation:

Since you are given the length and the width, you can find the area. The area of a 2d rectangular object is always length × width, meaning the area of this floor is 7 × 4, or 28 square feet.

This means the amount of wood floor Jo will need to buy is 28 square feet of flooring, which will cost $280.