Which of the following statements is true for ∠a and ∠b in the diagram?

A) m∠a = m∠b

B) m∠a + m∠b = 90°

C) m∠a + m∠b = 180°

D) m∠a – m∠b = 90°

The solution is: In 86400 ways can the station air the movie marathon.

Given:

Number of total movies = 11

Number of science fiction movie = 6

Number of horror movie = 5

Computation:

Number of science fiction movies way air = 6!

so, we get,

Number of science fiction movies way air = 720

Number of horror movies way air = 5!

so, we have,

Number of horror movies way air = 120

The number of ways the station air the movie marathon is:

720 * 120

=86400

so, we get,

Final answer is 86400 ways.

Hence, The solution is: In 86400 ways can the station air the movie marathon.

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Answer:

R500

Step-by-step explanation:

20 books x R25 each = R500.

Answer:

To determine the number of cards necessary to build a tower with 100 stories, let's analyze the pattern observed in the given information.

From the information provided, we know that building 5 stories of cards required 40 cards. Now, let's examine the relationship between the number of stories and the number of cards used:

Number of stories: 5

Number of cards used: 40

To find the number of cards needed for 100 stories, we can calculate the ratio of the number of stories to the number of cards used for the 5-story tower and then apply that ratio to the target number of stories (100).

Ratio = Number of stories / Number of cards used

Ratio = 5 / 40

Now, we can use this ratio to calculate the number of cards needed for 100 stories:

Number of cards for 100 stories = Ratio * Number of stories

Number of cards for 100 stories = (5 / 40) * 100

Calculating the result:

Number of cards for 100 stories = (0.125) * 100

Number of cards for 100 stories = 12.5

Since it is not possible to use a fraction of a card, we need to round up to the nearest whole number. Therefore, we would need a minimum of 13 cards to build a tower with 100 stories using a similar pattern.

Please note that the actual number of cards required may vary depending on the specific construction technique and stability of the tower.

Answer:

20cm

Step-by-step explanation:

The exact value of the expression tan 15⁰ is determined as 2 - √3.

The exact value of the expression is calculated by applying trigonometry identity as shown below;

The trig ratio is simplified as;

SOH CAH TOA;

SOH ----> sin θ = opposite side / hypothenuse side

CAH -----> cos θ = adjacent side / hypothenuse side

TOA ------> tan θ = opposite side / adjacent side

The given trigonometry expression;

tan 15⁰

The expanded trigonometry expression;

tan 15⁰  = tan (60 - 45)

Apply tan addition formula;

tan(A - B) = (tan A - tan B) / (1 + tan A×tan B).

Simplify as follows;

tan (60 - 45) = (tan 60 - tan 45) / ( 1 + tan60 x tan45)

tan 60 = √3

tan 45 = 1

Substitute this value back into the tan formula;

tan (60 - 45) =  (√3 - 1 ) / ( 1 + √3)

Rationalize the surd expression as follows;

(√3 - 1 ) / (√3 + 1)  x (√3 - 1 ) / (√3 - 1 )

= ( 4 - 2√3) / 2

= 2 - √3

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The vertical asymptote of the equation does not exist, the horizontal asymptote of the equation is 1.

To calculate vertical asymptote,

Putting the denominator equal to zero,

x²+2x+3 = 0

Using Quadratic formulae,

b² - 4ac

where,

b = 2

a = 1

c = 3

putting value,

4-12 = -8<0

therefore, the solution is negative

Hence, no vertical asymptote of the given equation exists,

To calculate the horizontal asymptote,

the degrees of the numerator and denominator are the same. we can compare the coefficients of the highest power terms.

The coefficient of x² in the numerator is 1

Hence, the horizontal asymptote is y = 1.

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The quantity of milk that should be used for the given amount of flour would be = 11/25

The following steps are being taken to calculate the amount of milk that would be needed for the recipe.

The number of cups of flour for 1⅒ of milk = 5

The quantity of milk needed for 2cups of flour= X

That is;

1⅒milk = 5 flour

X milk = 2 flour

cross multiply;

X milk = 2×1⅒/5

= 11/25

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The Surface Area of cylinders are: 100 yd² , 264 m², 226  mm²

The Surface Area of Can is 219 cm².

We know the formula for Surface Area of Cylinder

= 2πrh

1. Radius = 2 yd

Height = 8 yd

So, Surface Area of Cylinder

= 2πrh

= 2 x 3.14 x 2 x 8

= 100 yd²

2. Radius = 7 m

Height = 6 m

So, Surface Area of Cylinder

= 2πrh

= 2 x 3.14 x 6 x 7

= 264 m²

3. Radius = 3 mm

Height = 12 mm

So,  Surface Area of Cylinder

= 2πrh

= 2 x 3.14 x 3 x 12

= 226  mm²

4. Radius = 3.5 cm

Height = 10 cm

So, Surface Area of Can

= 2πrh

= 2 x 3.14 x 3.5 x 10

= 219 cm²

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The scatter plot shows a [positive linear] association.

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

The image of the scatter plot

On the scatter plot, we can see that

The points appear to be on a straight line

Also, we can see that

As the x values increases the y values increases

This represents a positive linear association.

Hence, the association is a positive linear association.

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The variable that is contained in the given expression is y. Therefore, option C is the correct answer.

The given expression is 7y+2y² +3.

In the given expression there are 3 terms, so it is called trinomial.

In the term 7y, y is the coefficient of 7.

In the term 2y², y² is the coefficient of 2.

3 is the constant term.

Therefore, option C is the correct answer.

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The surface area of the dilated solid is 2,880 square units

Multiply each side of the shape by 4

Surface area of a rectangular prism = 2(LH + LW + WH)

Where,

Length, L = 8 × 4 = 32 units

Width, W = 6 × 4 = 24 units

Height, H = 3 × 4 = 12 units

Surface area of a rectangular prism = 2(LH + LW + WH)

= 2(32×12 + 32×24 + 24×12)

= 2(384 + 768 + 288)

= 2(1,440)

= 2,880 square units

Therefore, 2,880 square units is the surface area of the solid.

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Answer: 10/9, 0

Step-by-step explanation:

When it comes to long-term investment goals like early retirement, it is generally recommended to focus on investments that offer potential growth over an extended period of time. Here are some investment options and advice that could be beneficial for your friend:

Stock market investments: Investing in a diversified portfolio of stocks can provide the potential for long-term growth. Your friend can consider investing in individual stocks or exchange-traded funds (ETFs) that represent a basket of stocks.

Mutual funds: Mutual funds offer diversification by pooling money from multiple investors to invest in a variety of assets. They are managed by professionals who make investment decisions on behalf of the investors.

Index funds: Index funds are a type of mutual fund that aims to replicate the performance of a specific market index, such as the S&P 500. They offer broad market exposure and generally have lower expense ratios compared to actively managed funds.

Retirement accounts: Encourage your friend to take advantage of tax-advantaged retirement accounts like a 401(k) or an individual retirement account (IRA). These accounts provide tax benefits and can help grow savings faster.

Dollar-cost averaging: Advising your friend to invest regularly, regardless of market conditions, through a strategy called dollar-cost averaging can help mitigate the impact of market volatility. By investing a fixed amount at regular intervals, your friend will buy more shares when prices are low and fewer shares when prices are high.

Rebalancing: As time goes on, it's important to periodically review and rebalance the investment portfolio. This involves adjusting the asset allocation to maintain the desired level of risk and return. Regularly rebalancing ensures that the investments stay aligned with the financial goals and risk tolerance.

Emergency fund: Remind your friend about the importance of building an emergency fund with three to six months' worth of living expenses. This will provide a safety net and help prevent the need to tap into long-term investments during unforeseen circumstances.

Seek professional advice: Depending on your friend's knowledge and comfort level with investing, it may be helpful to recommend consulting with a financial advisor who can provide personalized advice based on their specific financial situation and goals.

Remember, investing involves risks, and it's crucial for your friend to carefully evaluate investment options, consider their risk tolerance, and have a long-term perspective. Regularly monitoring and adjusting the investment strategy over time will help ensure progress towards achieving their financial goals.

a ) The given expression from Sofia and Ella represents two different values.

b.) The fact about the surface area of prism that Ella's expression shows that is not in Sofia's expression is that the expression is according to the formula.

To determine the surface area of a rectangle prism, the formula that should be used would be given below:

That is;

Surface area of rectangular prism;

= 2(wl+hl+hw)

when the formula is multiplied out the following is gotten;

= 2wl + 2hl + 2hw

From Ella's expression,

2(3 cm x 4 cm) + 2(3 cm x 5 cm) + 2(4 cm x 5 cm). This follows the order of the formula. And it's final answer = 94cm²

From Sofia's expression,

(3 cm x 4 cm ) + (3 cm x 5 cm) + (4 cm x 5 cm) + (4 cm x 5 cm). This doesn't follow the order of the formula and therefore is not correct and not the same final value with Ella's expression.

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The equations of the circles that have centers on the x-axis are;

A. (x - 2)² + (y - 0)² = 22

B. (x - 0)² + (y - 0)² = 25

The equation of a circle is; (x - h)² + (y - k)² = r², where;

(h, k) = The coordinates of the center of the circle

r = The radial length of the circle

The center of the circle is on the x-axis when the y-coordinate of the center of the circle is; k = 0, therefore, the circle that have their centers on the x-axis are the circles with the term (y - 0)²

The option of the circle that has the term (y - 0)² are the first and second option, where the v is actually a y; option A and .

The correct option is therefore;

A. (x - 4)² + (y - 0)² = 22

B. (x - 0)² + (y - 0)² = 25

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To find the magnitude of the vector, we can use the Pythagorean theorem: ||V|| = sqrt((5 * √2 / 2)^2 + (5 * √2 / 2)^2) = 5.

To find the component form of a vector, you need to break it down into its x and y components. Let's say our vector V has a magnitude of 5 and is pointing in the direction of 45 degrees (measured from the positive x-axis).

To find its x component, we can use cosine: Vx = V cos(45) = 5 * √2 / 2. To find its y component, we can use sine: Vy = V sin(45) = 5 * √2 / 2. So the component form of vector V is (5 * √2 / 2, 5 * √2 / 2).

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Answer:

(a) 34 cm

Step-by-step explanation:

The formula for perimeter of a rectangle is

P = 2l + 2w, where

Thus, we can plug in 12 for l and 5 for w in the perimeter formula and simplify to find the perimeter of the rectangle:

P = 2(12) + 2(5)

P = 24 + 10

P = 34

Thus, the perimeter of a rectangle with a length of 12 cm and a width of 5 cm is 34 cm.

when the velocity is 348 meters per second, the approximate temperature is 18 degrees Celsius.

To find the temperature when the velocity is 348 meters per second, we can substitute the given velocity into the equation v = 20√273 + t and solve for t.

Given: v = 348 meters per second

Substituting this value into the equation:

348 = 20√273 + t

Now, let's solve for t. We can start by isolating the term with t:

t = 348 - 20√273

Calculating the value:

t ≈ 348 - 20 * 16.523

t ≈ 348 - 330.46

t ≈ 17.54

Rounding the answer to the nearest degree, we have:

t ≈ 18 degrees Celsius

Therefore, when the velocity is 348 meters per second, the approximate temperature is 18 degrees Celsius.

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Answer:

----------------------

Use the compound interest formula:

Where:

Plugging in the values, we get:

The relative frequency distribution is:

The correct option is A.

A relative frequency is the proportion of the total number of outcomes to the number of times a certain value of the data happens in the set of all outcomes.

The relative frequency distribution of the given data is constructed below:

Total number of students = 51 + 58 + 74 + 69 + 19

Total number of students = 271

The relative frequency of each class interval will be:

200-300; 51/271 * 100% = 18.82%

301-400; 58/271 * 100% = 21.40%

401-500; 74/271 * 100% = 27.30%

501-600; 69/271 * 100% = 25.46%

More than 600; 19/271 * 100% = 7.02%

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The product of matrices A and B are:

[tex]AB = \left[\begin{array}{ccc}-50&7\\44& -10\\\end{array}\right][/tex]

[tex]BA = \left[\begin{array}{ccc}-12&-30\\-16& -48\\\end{array}\right][/tex]

A matrix (plural matrices) is a set of numbers arranged in rows and columns so as to form a rectangular array.

The number of rows of a matrix can be determined by counting from top to bottom and the number of columns can be determined by counting from left to right.

The product of matrices A and B are:

AB = A * B

[tex]AB = \left[\begin{array}{ccc}-3&-8\\2& 8\\\end{array}\right] * \left[\begin{array}{ccc}6&3\\4& -2\\\end{array}\right][/tex]

To get the product, multiply each row by the column. That is:

(-3 * 6) + (-8 * 4) = -50

(-3 * 3) + (-8 * (-2)) = 7

(2 * 6) + (8 * 4) = 44

(2 * 3) + (8 * (-2)) = -10

[tex]AB = \left[\begin{array}{ccc}-50&7\\44& -10\\\end{array}\right][/tex]

BA =  B * A

[tex]BA = \left[\begin{array}{ccc}6&3\\4& -2\\\end{array}\right] * \left[\begin{array}{ccc}-3&-8\\2& 8\\\end{array}\right][/tex]

To get the product, multiply each row by the column. That is:

(6 * (-3)) + (3 * 2) = -12

(6 * (-8)) + (3 * 8) = -30

(4 * (-3)) + ((-2) * 2) = -16

(4 * (-8)) + ((-2) * 8) = -48

[tex]BA = \left[\begin{array}{ccc}-12&-30\\-16& -48\\\end{array}\right][/tex]

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The mean height of the plants whose heights are shown by the data set is 16 in.

To find the mean:

Sum of the values = 11 + 12 + 13 + 14 + 15 + 16 + 17 + 18 + 19 + 20 + 21 = 176

Total number of values = 11 (since there are 11 values in the data set)

Mean = Sum of the values / Total number of values

          = 176 / 11

          = 16

In other words, the mean of the given data set is 16 in and thus, the mean height of the plant is 16 in.

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The graph of the inequality is x < 0 and is plotted

Given data ,

Let the inequality equation be represented as A

Now , the value of A is

A = x is less than 0

So , on simplifying , we get

x < 0

Hence , the inequality of x is all numbers less than 0 without including 0

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Answer:

-----------------

Given that there are 3 designs, 2 sleeve lengths, and 6 color patterns, we can multiply these values together:

So, there are 36 different shirts available from this company.

There are 36 different types of shirt available for this company.

Given that;

Number of design Company has = 3

Number of color pattern available = 6

Types of shirt (short or long sleeves) = 2

Now, We need to find the number of different types of shirts are available from this company.

Since, the number of different types of shirts can be calculated by multiplying Number of design Company has with Number of color pattern available also multiplying with Types of shirt (short or long sleeves).

Hence, By framing in equation form we get;

the number of different types of shirts is,

⇒ 3 × 6 × 2

⇒ 36

Therefore, We get;

There are 36 different types of shirt available for this company.

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The required constant of proportionality is 5.

A graph is shown, we have to find out the constant of proportionality.
In the given case, the constant of proportionality is given by the slope of the curve.

So, the slope is given as,
m = rise/run

From the graph put the value  for any point, we choose (2, 10)

So,
m = 10/2
m = 5

Thus, the required constant of proportionality is 5.

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The system of equation of the tables used is 8x + 10y = 124 and x = y + 2

He used 8 round tables and 6 rectangular tables

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

Using the above as a guide, we have the following:

8x + 10y = 124

Where

x = round tables

y = rectangular tables

We understand that

He uses 2 more round tables than rectangular tables

This means that

x = y + 2

So, the system of equations is 8x + 10y = 124 and x = y + 2

The graph of the system is attached, where we have x = 8 and y = 6  

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The volume of the cylinder A = 1006.76 m³

The volume of the cylinder B = 2893.82 ft³

The volume of the cylinder C = 2712.96 in³

The volume of the cylinder D = 111.78 in³

The Volume of the cylinder = πr²h

Where r = radius , h = height

A) r = 15/2 = 7.5

h = 5.7

Volume = 3.14 × (7.5)² × 5.7

Volume = 1006.76

B) r = 8

height = 14.4

Volume = 3.14 × (8)² × 14.4

Volume = 2893.82

C) r = 6

h = 24

Volume = 3.14 × (6)² × 24

Volume = 2712.96

D) r = 2

h = 8.9

Volume = 3.14 × (2)² × 8.9

Volume = 111.78

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Answer:

Consider the following claim: Group behavior can increase the chances for an individual and a species to survive and reproduce.

Consider the following claim: Group behavior can increase the chances for an individual and a species to survive and reproduce.

Consider the following claim: Group behavior can increase the chances for an individual and a species to survive and reproduce.

Consider the following claim: Group behavior can increase the chances for an individual and a species to survive and reproduce.

Consider the following claim: Group behavior can increase the chances for an individual and a species to survive and reproduce.

Consider the following claim: Group behavior can increase the chances for an individual and a species to survive and reproduce.

Step-by-step explanation:

The values of

1. cosθ = √3/2

2. sinθ = √3/2

3. tanθ = 1

4. sec θ = 2/√3

5. cosec θ = 2/√3

6. cot θ = 1

The trigonometric functions are real functions which relate an angle of a right-angled triangle to ratios of two side lengths.

cosθ = adj/hyp

sinθ = opp/hyp

tanθ = opp/adj

sec θ = 1/cosθ

cosec θ = 1/sinθ

cot θ = 1/tanθ

We need to find the hypotenuse of the triangle

x² = 3² +3²

x = √9+9

x = √18

x = 2√3

cosθ = 3/2√3 = 6√3/12

= √3/2

2. sinθ = 3/2√3 = √3/2

3. tanθ = 3/3 = 1

4. sec θ = 2/√3

5. cosec θ = 2/√3

6. cot θ = 1

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The student that gets the rule of the transformation correctly is Raheem

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

Point N = (-2, -4)

Image of the point N = (2, 4)

This means that

N = (-2, -4)

N' = (2, 4)

From the above, we can see that

N' = -1 * N

This means that

N' = (-2, -4) * -1

So, we have

N' = (-2* -1 , -4 * -1)

So, the rule is (x * -1, y * 1)

Hence, the student that gets the rule correctly is Raheem

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Question

Four students are trying to find the rule that translates point N(-2,-4) to N'(2,4). Each student’s reasoning is shown below.

Raheem: The rule is (x * -1, y * -1)

Casey: The rule is (x + 2, y + 4)

Andrew: The rule is (x + 4, y + 0)

Lo: The rule is (x + 4, y + 8)

Which student is correct?

Raheem

Casey

Andrew