A magic square is a square array of numbers arranged so that the numbers in all​ rows, all​ columns, and the two diagonals have the same sum. Create a​ 3-by-3 magic square using nine of the ten​ numbers, 20,​ 21, 22,​ 23, 24,​ 25, 26,​ 27, 28, and 29. Explain your solution and reasoning. List the strategies used.

Answer:

We get approximately 86.96%. T herefore, the teenager should charge his sister an annual simple interest rate of approximately 86.96%.

Step-by-step explanation:

Answer:

To calculate the interest rate that the teenager should charge his sister, we can use the formula:

I = P * r * t

where I is the interest earned, P is the principal (the amount borrowed), r is the interest rate, and t is the time period.

We know that the teenager wants to earn $25 in interest ($75 - $50). We also know that the principal is $50 and the time period is 15 weeks. Plugging these values into the formula, we get:

25 = 50 * r * (15/52)

Solving for r, we get:

r = 13.04%

Therefore, the teenager should charge his sister a simple interest rate of 13.04%. Rounded to the nearest hundredth, this is 13.05%.

hope it helps you

Answer:

Step-by-step explanation:

Given

the sample space for box A

green balls = 5

red balls= 7

sample size= 5+7= 12

the sample space for box B

green balls = 3

red balls= 3

yellow balls= 6

sample size= 3+3+6= 12

The probability of drawing a green ball from box A= 5/12

The probability of drawing a green ball from box B= 3/12= 1/4

Therefore the probability of picking a green ball from either of the boxes at random is =\(=\frac{5}{12} *\frac{1}{4}\)\(=\frac{5}{48}\)

Answer:

2.5n - 21.5

Step-by-step explanation:

\(-5(4 - \frac n2) + \frac1{16}(-32 + 8) \\ \\\to -5 \times 4 + 5 \times \frac n2 - \frac1{16} \times 32 + \frac1{16} \times 8 \\ \\\to -20 + \frac{5n}2 - \frac{32}{16} + \frac{8}{16} \\ \\\to -20 + 2.5n -2 + 0.5 \\ \\\to 2.5n - 21.5\)

Answer:

B

Step-by-step explanation:

Answer:

The two teachers are 13 feet apart

Step-by-step explanation:

Right Triangles

Ava, her math teacher, and her science teacher form a right triangle in which she is at the 90° vertex.

The distances from the three people must satisfy the Pythagora's theorem, where the distance between the two teachers (D) is the hypotenuse, thus:

\(D=\sqrt{5^2+12^2}\)

\(D=\sqrt{25+144}\)

\(D=\sqrt{169}\)

D = 13 feet

The two teachers are 13 feet apart

There are 12 month in a year :

6360 ÷ 12 = 530

Thus the labour earns Rs 530 in a month .

To find this out we will divide 6360 by 12 (as there are 12 months in an year) 6360/12 = 530 . Therefore answer = rs 530

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Answer:

The maximum possible daily profit is $11,500.

Step-by-step explanation:

Vertex of a quadratic function:

Suppose we have a quadratic function in the following format:

\(f(x) = ax^{2} + bx + c\)

It's vertex is the point \((x_{v}, f(x_{v})\)

In which

\(x_{v} = -\frac{b}{2a}\)

If a<0, the vertex is a maximum point, that is, the maximum value happens at \(x_{v}\), and it's value is \(f(x_{v})\)

In this question:

The maximum daily profit happens when \(x_{v}\) cars are sold. This profit is \(P(x_{v})\)

\(P(x) = -35x^{2} + 2100x - 20000\)

So \(a = -35, b = 2100\)

\(x_{v} = -\frac{2100}{2*(-35)} = 30\)

The maximum possible daily profit is:

\(P(30) = -35*30^2 + 2100*30 - 20000 = 11500\)

The maximum possible daily profit is $11,500.

Answer: \(\frac{11}{5}\)

Step-by-step explanation

(y2-y1)/(x2-x1)

which means (5-(-6))/-4-(-9)=\(\frac{11}{5}\)

There are 50 predicted rolls for 5 in 300 times of rolls.

A probability is a number that reflects the chance or likelihood that a particular event will occur.

Given that, Janet rolls a 6-sided number cube 300 times,

Probability = (Favourable Outcomes)/(Possible Outcomes)

Favourable Outcomes: 5 (1 total)

Possible Outcomes: 1,2,3,4,5,6 (6 total)

Probability of a 5 in any given roll of a die = 1/6

1/6x300 = 50 = 50 predicted roll with 5.

Hence, There are 50 predicted rolls for 5 in 300 times of rolls.

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The requried, Multiplies(with switching factors.) area given below,

a.

693 x 83 = 57489

83 x 693 = 57489

The answer is 57489.

b.

910 x 45 = 40950

45 x 910 = 40950

The answer is 40950.

c.

38 x 84 = 3192

84 x 38 = 3192

The answer is 3192.

d.

409 x 89 = 36401

89 x 409 = 36401

The answer is 36401.

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Answer:

1/10

Step-by-step explanation:

Answer:

The x intercept is -1 and the y intercept is 2.

Step-by-step explanation:

The intercepts are the points where the line crosses an axis. The line crosses the x axis at the point (-1,0) with the x value being -1. The line crosses the y axis at the point (0,2) with the y value being 2.

There is only 1 possible 11-card hand that can be formed from a 20-card deck.

To determine the number of 11-card hands possible with a 20-card deck, we can use the concept of combinations.

The number of combinations, denoted as "nCk," represents the number of ways to choose k items from a set of n items without regard to the order. In this case, we want to find the number of 11-card hands from a 20-card deck.

The formula for combinations is:

nCk = n! / (k!(n-k)!)

Where "!" denotes the factorial of a number.

Substituting the values into the formula:

20C11 = 20! / (11!(20-11)!)

Simplifying further:

20C11 = 20! / (11! * 9!)

Now, let's calculate the factorial values:

20! = 20 * 19 * 18 * ... * 2 * 1

11! = 11 * 10 * 9 * ... * 2 * 1

9! = 9 * 8 * 7 * ... * 2 * 1

By canceling out common terms in the numerator and denominator, we get:

20C11 = (20 * 19 * 18 * ... * 12) / (11 * 10 * 9 * ... * 2 * 1)

Performing the multiplication:

20C11 = 39,916,800 / 39,916,800

Finally, the result simplifies to:

20C11 = 1

Consequently, with a 20-card deck, there is only one potential 11-card hand.

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Answer:

She took 28 shots, 7 shots would be the remaining 25% so you multiply it by 4 to get 100% or 7 × 4 = 28

missed shots = 7 = 25%             since 75% are successful

proportionality table

25% ...............7

100% ........... = 7 x 100% : 25% = 28

total = 28 shots

Step-by-step explanation:

75 = 3 x 5 x 5    in prime factorization

Answer:

Step-by-step explanation:

3x5x5

Answer:

8 and 2/5 is 42/5 and its reciprocal is 5/42

Step-by-step explanation:

\(Reciprocal \: of \: \frac{42}{5} \: is \: \frac{5}{42} \).

\(\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\orange{:}}}}}\)

\(8 \frac{2}{5} \\ \\ = \frac{42}{5} \)

\(Hence, \:the\: reciprocal \: of \: \frac{42}{5} \: is \: \frac{5}{42}.\)

\(\large\mathfrak{{\pmb{\underline{\orange{Happy\:learning }}{\orange{!}}}}}\)

The length of the missing leg for the triangles are: x = 7.01, f = 5.4, and d = 15.1 using the Pythagoras rule.

The Pythagoras rule states that in a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. 

By Pythagoras rule we can evaluate for b as follows:

x = √(7.5² - 2.5²)

x = √50

x = x = 7.0711

f = √[(√78)² - 7²]

f = √(78 - 49)

f = √29

f = 5.3852

d = 2 × √(11² × 8²)

d = 2 × √53

d = 15.0996

Therefore, the length of the missing leg for the triangles are: x = 7.01, f = 5.4, and d = 15.1 using the Pythagoras rule.

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Answer:

∠ BDC = 29°

Step-by-step explanation:

the sides of a rhombus are congruent, so CD = ED and Δ EDC is therefore isosceles with base angles congruent , then

∠ BCD = ∠ BED = 61°

• the diagonals are perpendicular bisectors of each other , then

∠ CBD = 90°

the sum of the 3 angles in Δ BCD = 180°

∠ BDC + ∠ CBD + ∠ BCD = 180°

∠ BDC + 90° + 61° = 180°

∠ BDC + 151° = 180° ( subtract 151° from both sides )

∠ BDC = 29°

Answer:

Both are correct

Step-by-step explanation:

Answer: both are correct

Step-by-step explanation:

Both are correct

you can use either way to solve it.

Answer: The range is 20, Standard Deviation, σ: 6.8702256149271

Step-by-step explanation:

I hope it helped!

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A histogram of the weights of all 2,000 athletes would be a graph with two normal distributions, one for offense and one for defense.

The offense distribution would have a bell shaped curve centered at 200 pounds, with a range of 150-250 pounds. The defense distribution would have a bell shaped curve centered at 300 pounds, with a range of 250-350 pounds. Each of the distributions would have the same area, representing 1,000 athletes in each group. The total area of the histogram would represent the combined 2,000 athletes with weights ranging from 150-350 pounds. It is important to note that the histogram would not represent the exact weights of the athletes, but rather the relative frequency of each weight.

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Answer:

the last one

Step-by-step explanation:

there is no rhythm

The domain of the function g(x) is x >= 5

The complete question is added as an attachment

From the graph, we have the smallest value of x to be 5.

And the value of x increases to the right

This means that:

x >= 5

Hence, the domain of the function g(x) is x >= 5

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Answer:

0.8333 = 83.33% probability that the cycle time exceeds 50 minutes if it is known that the cycle time exceeds 45 minutes

Step-by-step explanation:

A distribution is called uniform if each outcome has the same probability of happening.

The uniform distributon has two bounds, a and b, and the probability of finding a value higher than x is given by:

\(P(X > x) = \frac{b - x}{b - a}\)

Uniformly distributed over the interval 40 to 75 minutes.

This means that \(a = 40, b = 75\)

It is known that the cycle time exceeds 45 minutes

This means that we can use \(a = 45\)

What is the probability that the cycle time exceeds 50 minutes?

\(P(X > 50) = \frac{75 - 50}{75 - 45} = 0.8333\)

0.8333 = 83.33% probability that the cycle time exceeds 50 minutes if it is known that the cycle time exceeds 45 minutes

The joint relative frequency is calculated by dividing the frequency of a specific subset (in this case, the number of adults who prefer watermelon) by the total number of data points.

Here, the specific subset is adults who prefer watermelon, which is 111. The total number of data points is the sum of all children and adults, regardless of fruit preference, which is 445.

So, to find the joint relative frequency of being an adult who prefers watermelon, you would divide 111 by 445.

Hence, the correct answer is:

C. Divide 111 by 445.

The total principal and interest payment that Nelson will have to pay after 2 months is $4665.50.

To calculate the total principal and interest payment, we need to determine the interest amount and add it to the principal.

First, let's find the interest amount:

Interest = Principal x Interest Rate x Time

Given:

Principal = $4650

Interest Rate = 2% per year

Time = 2 months

Since the interest rate is given on an annual basis, we need to convert the time from months to years. There are 12 months in a year, so 2 months is equivalent to 2/12 = 1/6 years.

Interest = $4650 x 0.02 x (1/6) = $15.50

Now, we can calculate the total principal and interest payment:

Total Payment = Principal + Interest

Total Payment = $4650 + $15.50 = $4665.50

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Answer:

b= 23.4,. γ = 70°, c= 28.9

Step-by-step explanation:

To solve the triangle with given α = 65°, β = 45°, and a = 30, we can use the law of sines:

b/sin(β) = a/sin(α)

b/sin(45°) = 30/sin(65°)

b ≈ 23.4

Then, to find angle γ, we can use the fact that the sum of angles in a triangle is 180°:

γ = 180° - α - β

γ ≈ 70°

To find side c, we can again use the law of sines:

c/sin(γ) = a/sin(α)

c/sin(70°) = 30/sin(65°)

c ≈ 28.9

Therefore, the solution is b = 23.4, γ = 70°, and c = 28.9.

Note that there is no other possible solution, as the given angles and side lengths do not allow for multiple triangles to be formed.