A gardening company sells clay flower pots and plastic flower pots. There must be at least 2 pots in each shipment, but there cannot be more than 8 in a shipment. Additionally, the shipment must weigh less than 100 pounds. Each shipment container weighs 20 pounds, and there is 1 pound of packing material. A clay flower pot weighs 15 pounds, whereas a plastic flower pot weighs 7.5 pounds.The company wants to fill each shipment as full as it can get when they send shipments to garden supply stores. There is similar demand for each type of pot. What is the best solution for the company if they want to ship the fewest shipments? Justify your reasoning.

Answer:

800 N

Step-by-step explanation:

I don’t know I just submitted it and that was the answer

Answer:

C(3, −3), D(−2, −3)

Step-by-step explanation:

The distance from point A to point B is 5 units.

The width of the rectangle is 5 units.

The length must be 6 units to have an area of 30 square units.

Points C and D must be 6 units below points A and B.

Their coordinates must be (-2, -3) and (3, -3).

Answer: C(3, −3), D(−2, −3)

Answer:

Hello! answer: 80

Step-by-step explanation:

8 × 4 = 32 32 ÷ 2 = 16 16 × 4 = 64

4 × 4 = 16 64 + 16 = 80 therefore 80 is the answee Hope that helps!

Answer:

\(80~in^2\)

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hope it helps...

have a great day!!

On a number line, 7.05 would be located

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

Number = 7.05

The analysis of its position s as follows:

So, the true statements are B and C.

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The algebraic expression "difference of 4 and a number" where the number is letter x is represented as 4 - x.

Algebra is an elementary branch of mathematics that deals with the numbers and the basic mathematics operations of addition, subtraction, division and multiplication. Algebraic expression involves arithmetic where the use of unknown quantities along with numbers.

From the question, we have the mathematical statement "difference of 4 and a number" and the number is "a number" is represented with the letter x.

the word difference in mathematics implies Subtraction (-)

Therefore, the mathematical statement "difference of 4 and a number" is represented as 4 - x.

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9514 1404 393

Answer:

  π/360 radians/minute

Step-by-step explanation:

The angular velocity is ...

  (2π radians)/(12 h) = (π rad)/(6× 60 min) = π/360 rad/min

Answer:

83.29% probability that at least 2 flights arrive late.

Step-by-step explanation:

For each flight, there are only two possible outcomes. Either it arrives late, or it does not arrive late. The probability of a flight arriving late is independent of other flights. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)

In which \(C_{n,x}\) is the number of different combinations of x objects from a set of n elements, given by the following formula.

\(C_{n,x} = \frac{n!}{x!(n-x)!}\)

And p is the probability of X happening.

80 % of its flights arriving on time.

So 100 - 80 = 20% arrive late, which means that \(p = 0.2\)

15 Southwest flights

This means that \(n = 15\)

Find the probability that at least 2 flights arrive late.

Either less than two arrive late, or at least 2 do. The sum of the probabilities of these outcomes is 1. So

\(P(X < 2) + P(X \geq 2) = 1\)

We want \(P(X \geq 2)\)

Then

\(P(X \geq 2) = 1 - P(X < 2)\)

In which

\(P(X < 2) = P(X = 0) + P(X = 1)\)

So

\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)

\(P(X = 0) = C_{15,0}.(0.2)^{0}.(0.8)^{15} = 0.0352\)

\(P(X = 1) = C_{15,1}.(0.2)^{1}.(0.8)^{14} = 0.1319\)

\(P(X < 2) = P(X = 0) + P(X = 1) = 0.0352 + 0.1319 = 0.1671\)

Then

\(P(X \geq 2) = 1 - P(X < 2) = 1 - 0.1671 = 0.8329\)

83.29% probability that at least 2 flights arrive late.

Answer:

Step-by-step explanation:I need the same answer lol

Answer:

Step-by-step explanation:

Answer:

Line BE and Line AB

Step-by-step explanation:

On the graph you can see that these two lines cross each other.

x - 9 ≤ 2(9 - x)

x - 9 ≤ 18 - 2x

3x - 9 ≤ 18

3x ≤ 27

x ≤ 9

(just handle it like an equation)

Using one CFL bulb for one year would cost approximately $12.62.

We have,

We already calculated the cost of electricity for using one CFL-style bulb for one year as $8.76.

Let's now calculate the cost of the bulb for one year of use.

If one CFL-style bulb lasts for 10,000 hours, then it will last for:

10,000/24 = 416.67 days or approximately 1.14 years if used for 8 hours a day.

So, for one year of use, we would need,

1/1.14 = 0.8772 or approximately 1 CFL bulb.

The cost of using one CFL bulb for one year would be the cost of the bulb ($5.58) plus the cost of electricity ($8.76) divided by the lifespan of the bulb in years (1.14).

So,

Cost of using one CFL bulb for one year

= ($5.58 + $8.76)/1.14

= $12.62

Thus,

Using one CFL bulb for one year would cost approximately $12.62.

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Answer:

f(5) = 17

Step-by-step explanation:

Pretty easy :)

just pluggin f(5).

f(5) = 3(5) + 2

f(5) = 15+2

f(5) = 17.

:)

Answer:

0 muffins and 8 cookies

6 muffins and 4 cookies

Explain:

These are the only two combinations of muffins and cookies that Jordan could have sold to earn $24. If Jordan sold 0 muffins and 8 cookies, they would have earned $24 because 0 x $3 + 8 x $2 = $24. If Jordan sold 6 muffins and 4 cookies, they would have earned $24 because 6 x $3 + 4 x $2 = $24.

If one number is increased by a factor of 12 and the other is decreased by a factor of 4, the product of the two numbers will be multiplied by a factor of 3.

Let's suppose we have two numbers, A and B, and we want to know how their product will change if one number is increased by a factor of 12 and the other is decreased by a factor of 4.

The initial product of the two numbers is:

A x B

If we increase A by a factor of 12, the new value of A will be 12A. If we decrease B by a factor of 4, the new value of B will be B/4. Therefore, the new product of the two numbers will be:

(12A) x (B/4) = (12/4) x A x B = 3AB

So the new product of the two numbers will be three times the initial product. In other words, if one number is increased by a factor of 12 and the other is decreased by a factor of 4, the product of the two numbers will increase by a factor of 3.

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The measure of a different interior angle of the triangle is 52 degrees.

A right angled triangle is a triangle with one of the angles as 90 degrees.

The sum of the interior angle of a triangle is 180 degrees.

Given the data in the question;

Since the sum of the interior angle of a triangle is 180 degrees.

Angle a + Angle b + Angle c = 180

38 + Angle b + 90 = 180

Angle b + 128 = 180

Angle b = 180 - 128

Angle b = 52 degrees.

Therefore, the measure of the second angle is 52 degrees.

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If Gavin contributes towards a Pension fund (7,5% of his Basic Salary), then his net salary will be reduced by the amount he contributed towards pension fund i.e. R652.5.

1.1 Name of employee is Gavin Pillay. 1.2 UIF stands for Unemployment Insurance Fund. UIF is a benefit to provide short-term relief to workers who lose their jobs, or can't work due to illness, maternity or adoption leave. 1.3 The UIF paid by Gavin is calculated correctly.

Firstly, we need to calculate Gross Salary of Gavin, which is given as: Basic Salary + Overtime + M = R8700 + R1200 + R3201 = R13101Then, calculate total deductions from gross salary.

Total Deductions = PAYE + UIF = R1200 + 87 = R1287Hence, Gavin's net salary = Gross salary - Total Deductions = R13101 - R1287 = R11814Therefore, UIF paid by Gavin is calculated correctly as R87.1.4 This payslip is for the month of May i.e.

31/05/2023.1.5 Basic salary of Gavin = R8700. Deduct 7.5% of his basic salary to calculate his pension fund contribution. Pension Fund Contribution = 7.5/100 x R8700 = R652.5.1.6

Total deductions of Gavin includes PAYE, UIF and pension fund contribution.

Therefore, Total Deductions = PAYE + UIF + Pension Fund Contribution = R1200 + R87 + R652.5 = R1939.5.1.7

Gavin's age can not be determined as his date of birth is not provided.1.8 Address of Gavin's workplace is 21 Halsted Road, Pietermaritzburg?

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Answer:

x = 24

Step-by-step explanation:

\(\frac{4}{3}\)x + \(\frac{1}{6}\)x = 36

Make the denominator the same by multiplying the first fraction by 2 to make both denominators 6.

\(\frac{8}{6}\)x + \(\frac{1}{6}\)x = 36

Now we can calculate the numerators and keep the denominators the same.

\(\frac{9}{6}\)x = 36

Find x.

\(\frac{6}{6}\)x = \(\frac{6}{9}\) × 36

x = 24

Answer:

a) 20.44% probability that none of the selected adults say that they were too young to get tattoos.

b) 35.90% probability that exactly one of the selected adults says that he or she was too young to get tattoos.

c) 56.34% probability that the number of selected adults saying they were too young is 0 or 1.

d) No

Step-by-step explanation:

For each adult, there are only two possible outcomes. Either they say they were too young when they got their tattoos, or they don't say that. Each adult is independent of each other. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)

In which \(C_{n,x}\) is the number of different combinations of x objects from a set of n elements, given by the following formula.

\(C_{n,x} = \frac{n!}{x!(n-x)!}\)

And p is the probability of X happening.

18% say that they were too young when they got their tattoos.

This means that \(p = 0.18\)

Eight adults who regret getting tattoos are randomly selected

This means that \(n = 8\)

a. Find the probability that none of the selected adults say that they were too young to get tattoos.

This is P(X = 0).

\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)

\(P(X = 0) = C_{8,0}.(0.18)^{0}.(0.82)^{8} = 0.2044\)

20.44% probability that none of the selected adults say that they were too young to get tattoos.

b. Find the probability that exactly one of the selected adults says that he or she was too young to get tattoos.

This is P(X = 1).

\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)

\(P(X = 1) = C_{8,1}.(0.18)^{1}.(0.82)^{7} = 0.3590\)

35.90% probability that exactly one of the selected adults says that he or she was too young to get tattoos.

c. Find the probability that the number of selected adults saying they were too young is 0 or 1.

Either a. or b.

20.44 + 35.90 = 56.34

56.34% probability that the number of selected adults saying they were too young is 0 or 1.

d. It we randomly select 9 adults. Is 1 a significantly low number who day that they were too young to get tattoos?

Now \(n = 9\)

It is significantly low if it is more than 2.5 standard deviations below the mean.

The mean is \(E(X) = np = 9*0.18 = 1.62\)

The standard deviation is \(\sqrt{V(X)} = \sqrt{n*p*(1-p)} = \sqrt{9*0.18*0.82} = 1.15\)

1 > (1.62 - 2.5*1.15)

So the answer is no.

Answer:

3/8

Step-by-step explanation:

hope it helps :)

Answer:

Step-by-step explanation:

Assuming that the given dimensions of 13, 13, 13 refer to the base of the rectangular pyramid, we can calculate the surface area of the pyramid as follows:

First, we need to calculate the area of the rectangular base, which is simply length x width:

Area of rectangular base = 13 x 13 = 169 square units

Next, we need to calculate the area of each triangular face of the pyramid. Since the rectangular base has two sets of parallel sides, there are two types of triangular faces: the isosceles triangles on the sides and the right triangles on the front and back.

To calculate the area of the isosceles triangles, we need to first find the length of the slant height, which can be found using the Pythagorean theorem:

a² + b² = c²

where a and b are the base and height of the triangle (both equal to 13 in this case), and c is the slant height.

13² + 13² = c²

338 = c²

c ≈ 18.38

Now that we have the slant height, we can calculate the area of each isosceles triangle using the formula:

Area of isosceles triangle = (1/2) x base x height

Area of isosceles triangle = (1/2) x 13 x 18.38

Area of isosceles triangle ≈ 119.14 square units

To calculate the area of each right triangle, we need to use the same slant height of 18.38, along with the height of the pyramid, which is also 13. Then we can use the formula:

Area of right triangle = (1/2) x base x height

Area of right triangle = (1/2) x 13 x 18.38

Area of right triangle ≈ 119.14 square units

Since there are two of each type of triangular face, the total surface area of the pyramid is:

Surface area = area of rectangular base + 2 x area of isosceles triangle + 2 x area of right triangle

Surface area = 169 + 2 x 119.14 + 2 x 119.14

Surface area = 546.28 square units

Therefore, the surface area of the rectangular pyramid with base dimensions of 13 x 13 and height of 13 is approximately 546.28 square units.

Answer:

\(x = 36\)

Step-by-step explanation:

\(3x + x + x = 180\)

\(5x = 180\)

\(x = 36\)

the length of side a is 91 ft (rounded to the nearest whole foot) and the length of side b is 132 ft (rounded to the nearest whole foot). The area of the triangle is approximately 6007 sq ft.

Given: The hypotenuse of the right triangle,

c = 159 ft; angle A = 34°

We know that, in a right-angled triangle:

\($$\sin\theta=\frac{\text{opposite}}\)

\({\text{hypotenuse}}$$$$\cos\theta=\frac{\text{adjacent}}\)

\({\text{hypotenuse}}$$\)

We know the value of the hypotenuse and angle A. Using trigonometric ratios, we can find the length of sides in the right triangle.We will use the following formulas:

\($$\sin\theta=\frac{\text{opposite}}\)

\({\text{hypotenuse}}$$$$\cos\theta=\frac{\text{adjacent}}\)

\({\text{hypotenuse}}$$$$\tan\theta=\frac{\text{opposite}}\)

\({\text{adjacent}}$$\) Length of side a is:

\($$\begin{aligned} \sin A &=\frac{a}{c}\\ a &=c \sin A\\ &= 159\sin 34°\\ &= 91.4 \text{ ft} \end{aligned}$$Length of side b is:$$\begin{aligned} \cos A &=\frac{b}{c}\\ b &=c \cos A\\ &= 159\cos 34°\\ &= 131.5 \text{ ft} \end{aligned}$$\)

Now, we have the values of all sides of the right triangle. We can calculate the area of the triangle by using the formula for the area of a right triangle:

\($$\text{Area} = \frac{1}{2}ab$$\)

Putting the values of a and b:

\($$\begin{aligned} \text{Area} &=\frac{1}{2}ab\\ &=\frac{1}{2}(91.4)(131.5)\\ &= 6006.55 \approx 6007 \text{ sq ft}\end{aligned}$$\)

Therefore, the length of side a is 91 ft (rounded to the nearest whole foot) and the length of side b is 132 ft (rounded to the nearest whole foot). The area of the triangle is approximately 6007 sq ft.

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From trigonometric ratio, we used the tangent of the angle to determine that the flagpole is leaning by an angle of 47.12°

The six trigonometric ratios are sine (sin), cosine (cos), tangent (tan), cotangent (cot), cosecant (cosec), and secant (sec). In geometry, trigonometry is a branch of mathematics that deals with the sides and angles of a right-angled triangle. Therefore, trig ratios are evaluated with respect to sides and angles.

In the question, we can assume the point of view and the flagpole makes a right angle triangle.

Since we have the opposite and adjacent, we can find the acute angle by using the tangent of the angle

tanθ = opposite / adjacent

tan θ = 14 / 13

θ = tan⁻¹(14/13)

θ = 47.12°

The flagpole is leaning with an acute angle of 47.12 degrees

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We can conclude that the hypotheses of the Existence and Uniqueness Theorem are satisfied in any rectangular region in the ty-plane that does not contain the curve t² + y² = -1.

The Existence and Uniqueness Theorem for first-order ordinary differential equations states that if a differential equation of the form y' = f(t, y) satisfies the following conditions in some rectangular region in the ty-plane:

1. f(t, y) is continuous in the region.

2. f(t, y) satisfies a Lipschitz condition in y in the region, i.e., there exists a constant L > 0 such that |f(t, y₁) - f(t, y₂)| ≤ L|y₁ - y₂| for all t and y₁, y₂ in the region.

then there exists a unique solution to the differential equation that passes through any point in the region.

In the case of the differential equation y' = (y cot(2t)) / (t² + y² + 1), we have:

f(t, y) = (y cot(2t)) / (t² + y² + 1)

This function is continuous everywhere except at the points where t² + y² + 1 = 0, which is the curve t² + y² = -1 in the ty-plane. Since this curve is not included in any rectangular region, we can say that f(t, y) is continuous in any rectangular region in the ty-plane.

To check if f(t, y) satisfies a Lipschitz condition in y, we can take the partial derivative of f with respect to y and check if it is bounded in any rectangular region. We have:

∂f/∂y = cot(2t) / (t² + y² + 1) - (2y² cot(2t)) / (t² + y² + 1)²

Taking the absolute value and simplifying, we get:

|∂f/∂y| = |cot(2t) / (t² + y² + 1) - (2y² cot(2t)) / (t² + y² + 1)²|

= |cot(2t) / (t² + y² + 1)| * |1 - (2y² / (t² + y² + 1)))|

Since 0 ≤ (2y² / (t² + y² + 1)) ≤ 1 for all t and y, we have:

1/2 ≤ |1 - (2y² / (t² + y² + 1)))| ≤ 1

Also, cot(2t) is bounded in any rectangular region that does not contain the points where cot(2t) is undefined (i.e., where t = (k + 1/2)π for some integer k). Therefore, we can find a constant L > 0 such that |∂f/∂y| ≤ L for all t and y in any rectangular region that does not contain the curve t² + y² = -1.

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Answer:

1: 10+6 x 6 = 96cm

2: 14 + 8 x 5 = 110cm

3: 9 + 14 x 20 = 460cm

Step-by-step explanation:

Hope this helps.

Answer: 13P3= 1716

Step-by-step explanation:

Answer:

8000

Step-by-step explanation:

10000 x 20% = 2000

10000-2000= 8000

Both figures have an area of 4 units squared, so yea, the area is the same.

The area of a square of side length S is equal to S squared, for the square, we can see that:

S = 2 units.

Then the area is:

A = (2 units)² = 4 square units.

For the triangle, we know that the area is equal to:

A = B*H/2

Where B = base, H = height.

We can see that:

B = 2 units.

H = 4 units.

Then:

A = (2 units)*(4 units)/2= 4 square units.

So yea, both have the same area.

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