For some value of b, the expression 3(5x - 1) + b(2x - 7) is a constant. What is the constant?

The area of the composite figure is 24m², which is option C.

What is a composite figure?

A two-dimensional figure built up of fundamental two-dimensional shapes like triangles, rectangles, circles, semicircles, etc. is known as a composite shape or composite figure. To get the area of a composite shape, first determine the individual areas of every component. The total of the individual regions will then represent the area of the composite shape.

From the figure, we can see that from a big rectangle, 4 small identical squares of side 1m are cut from each corner.

We are asked to find the area of the rest of the rectangle which makes the composite figure.

W first find the area of the original rectangle.

Its length  = 5 + 1 + 1 = 7 m

Its breadth = 2 + 1 + 1 = 4 m

So the area of the rectangle = length * breadth = 7*4 = 28 m²

Now the side length of the square = 1 m

Area of one square = 1*1 = 1m²

So are of four identical squares = 4 * 1 = 4 m²

Therefore area of the composite figure = area of big rectangle - area of 4 squares = 28 - 4 = 24m²

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Answer:

24m^2 is ur answer

Step-by-step explanation:

Hope this helps

Answer:

60 degrees

Step-by-step explanation:

The solution to the given problem is 25/88. The solution has been obtained by applying BODMAS rule.

What is the BODMAS rule?

The letters BODMAS stand for Bracket, Of, Division, Multiplication, Addition, and Subtraction. An explanation of a mathematical expression's execution sequence is provided by the BODMAS. According to the BODMAS rule, brackets must be answered first, then powers or roots (i.e. of), Division, Multiplication, Addition, and finally Subtraction.

We are given an expression as (3/11 + 2/11) * 5/8

Now, as per the BODMAS rule, we will first solve the brackets.

On solving the brackets, we get

5/11 * 5/8

Now, on solving it further, we get

5/11 * 5/8 = 25/88

Hence, the solution to the given problem is 25/88.

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The dot product between u and v is 150.35 units²

In the problem given;

u = 10cos5

v = 16cos25

To find the dot product of two vectors, we need to find the product of the magnitude of the vectors and the cosine of the angle between them. Let's call the angle between the vectors θ.

The dot product of u and v is given by:

u•v = |u| * |v| * cos(θ)

where |u| and |v| are the magnitudes of vectors u and v. We are given the magnitudes of the vectors, which are |u| = 10 and |v| = 16.

To find cos(θ), we need to use the dot product formula with the given angle values:

cos(θ) = (u•v) / (|u| * |v|) = (|u| * |v| * cos(θ)) / (|u| * |v|)

Since u and v are both vectors in 2-dimensional space, we can use the law of cosines to find the angle between them:

cos(θ) = (u•v) / (|u| * |v|) = (u1 * v1 + u2 * v2) / (|u| * |v|)

where u1 and u2 are the components of vector u and v1 and v2 are the components of vector v.

To find the components of the vectors, we need to use the given angle values and the magnitudes of the vectors:

u1 = |u| * cos(5°) = 10 * cos(5°)

u2 = |u| * sin(5°) = 10 * sin(5°)

v1 = |v| * cos(25°) = 16 * cos(25°)

v2 = |v| * sin(25°) = 16 * sin(25°)

Substituting these values into the formula for cos(θ), we get:

cos(θ) = (u1 * v1 + u2 * v2) / (|u| * |v|) = (10 * cos(5°) * 16 * cos(25°) + 10 * sin(5°) * 16 * sin(25°)) / (10 * 16)

θ = 20°

u.v = 10 * 16 * cos 20

u.v = 150.35

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The probability that a randomly selected US teenager has either read Harry Potter and the Half Blood Prince or seen the movie is 84%.

To create a Venn diagram for this situation, you would need two circles that overlap in the middle. One circle would represent the 48% of teenagers who read the book, and the other circle would represent the 58% of teenagers who saw the movie. The overlap between the two circles would represent the 22% of teenagers who both read the book and saw the movie.

            +-----------------------------------------+

            |                                                 |

            |                    Read                    |

            |                   48% (R)                 |

            |                                                 |

            +--------------------+-------------------+

            |                         |                       |

            |                         |                       |

            |                         |                       |

            |    Both (B∩R)   |   Movie (M)   |

            |     22% (B)        |   58% (M)      |

            |                          |                      |

            |                          |                      |

            |                          |                      |

            +---------------------+------------------+

                              Not Read

                            30% (N∩M)

Here, R represents the event of reading the book, M represents the event of watching the movie, and B represents the event of both reading the book and watching the movie. The numbers in parentheses represent the percentage of US teenagers in each event. The area of each circle represents the total number of US teenagers.

To find the probability that a randomly selected US teenager has either read the book or seen the movie, you need to find the total area of the two circles (the 48% who read the book plus the 58% who saw the movie) and subtract the overlap (the 22% who both read the book and saw the movie). This gives you:

P(read or saw) = 48% + 58% - 22% = 84%

So the probability that a randomly selected US teenager has either read Harry Potter and the Half Blood Prince or seen the movie is 84%.

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The amount of money in the account after 2 years is $573.04.

What is compound interest?

Compound interest is the interest earned on an initial principal deposit as well as on the accumulated interest from previous periods. In other words, it is interest on interest.

To calculate the amount of money in the account after 2 years, we can use the formula for compound interest:

A = P(1 + r/n)ⁿᵗ

where A is the final amount, P is the principal amount (the initial deposit), r is the annual interest rate (as a decimal), n is the number of times the interest is compounded per year, and t is the time period (in years).

In this case, P = $500, r = 0.07 (7%), n = 1 (compounded annually), and t = 2.

Plugging these values into the formula, we get:

A = 500(1 + 0.07/1[tex])^{(1 \times 2)}[/tex]

A = 500(1.07)²

A = $573.04

Therefore, the amount of money in the account after 2 years is $573.04.

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Answer:

x = 62

Step-by-step explanation:

2x ÷ 2 = 124 ÷ 2

x = 124 ÷ 2 = 62

Step-by-step explanation:

since you know already that you need the law of cosine (which is nothing else than the generalization of Pythagoras from right-angled triangles to general triangles), why don't you just apply it ?

the law of cosine :

c² = a² + b² - 2ab×cos(C)

c is the side opposite of angle C, a and b are the other 2 sides.

our angle C is here now the angle QPR. the opposite side is QR = 3.

so, we have

3² = 2² + 4² - 2×2×4×cos(QPR) = 4 + 16 - 16×cos(QPR)

9 = 20 - 16×cos(QPR)

-11 = -16×cos(QPR)

cos(QPR) = -11/-16 = 11/16 = 0.6875

FYI : that means

angle QPR = 46.56746344...°

The value of the given function for x=122 is 5 and x=-346 is -7.

Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.

The given function is f(x)= ∛(x+3).

To find f(122):

Substitute x=122 in the given function, we get

f(122)=∛(122+3)

= ∛125

= ∛5³

= 5

To find f(-346):

Substitute x=-346 in the given function, we get

f(122)=∛(-346+3)

= ∛-343

= ∛(-7)³

= -7

Therefore, the value of the function for x=122 is 5.

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The value of the given ratio 3/4 : 1/2 is 3/2.

To get the value of a ratio, we just need to take the quotient between the first and second values.

For example, the value of a:b is a/b.

In this case we have the ratio:

3/4 : 1/2

Taking the quotient we will get:

(3/4)÷(1/2) = (3/4)*(2/1) = 6/4

                                    = 3/2

That is the value of the ratio.

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The value of x in the polygon is 30

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

Exterior angles = x, 2x, 4x, 5x, 8x, and 10x.

The sum of exterior angles of a polygon is 360

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

x + 2x + 4x + 5x + 8x + 10x = 360

Evaluate the like terms

30x = 360

So, we have

x = 12

Hence, the value of x is 12

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Answers: Each twin is 11 years old. Barb is 33 years old

Work Shown:

x = age of each twin

3x = Barb's age

x+x+3x = 5x = total of their ages = 55

5x = 55

x = 55/5

x = 11

Each twin is 11 years old. Barb is 3x = 3*11 = 33 years old.

Check: twin1+twin2+barb = 11+11+33 = 55

The answers are confirmed.

The line plot is attached based on the information given.

A line plot is a graph that shows data as dots or checkmarks above a number line to indicate how frequently each value occurs. Only numerical, discrete data, not continuous data, is shown using line graphs. Line plots categorize the data by showing how often each value appears on a number line. Small data sets make these graphs easy to make, and the revealed frequency patterns allow for interpretation.

Each mark on the line plot represents one of the distances Tomas rode. The number on the horizontal axis represents the day of the week and the vertical axis represents the distance in miles. The line plot shows that on most days, Tomas rode between 3 and 5 1/2 miles.

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The cumulative relative frequency distribution is a useful tool for summarizing data and making comparisons between classes. It can also be used to make predictions about future data values.

A cumulative relative frequency distribution is a table that shows the cumulative relative frequency of a set of data. A cumulative relative frequency is the sum of all relative frequencies up to a certain point in the data set. For example, if the first three entries in a data set are 20, 30, and 10, the cumulative relative frequency of the first entry would be 0.2, the cumulative relative frequency of the second entry would be 0.5, and the cumulative relative frequency of the third entry would be 1.0.

In a cumulative relative frequency distribution, the data is organized into classes, and each class has a relative frequency associated with it. The relative frequency is the fraction of the total number of items in the class compared to the total number of items in the data set. The cumulative relative frequency is the sum of the relative frequencies of all the classes up to that point.

For example, if there are five classes in a data set, the cumulative relative frequency of the first class would be the relative frequency of the first class. The cumulative relative frequency of the second class would be the sum of the relative frequencies of the first and second classes, and so on.

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After solving the expression from the given data we get that the cost of the book is £5.90.

Let's assume the cost of the book is "b" in pounds. From the information given, we can set up the following system of equations:

6x = 12.30 (Andy pays £12.30 for 6 sketch pads)

2x + b = 10 (Jo pays £10 for 2 sketch pads and 1 book). where x is the cost of one sketch pad in pounds. Solving the first equation for x, we get: x = 12.30/6 = 2.05

Substituting this value of x into the second equation, we get: 2(2.05) + b = 10

Simplifying this equation, we get: 4.10 + b = 10

Solving for b, we get: b = 5.90

Therefore, the cost of the book is £5.90.

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The equation of line p is y = (3/4)x + 13/2.

The equation of line q is y = (3/5)x + 23/5.

The equation of a line is given by:

y = mx + c

where m is the slope of the line and c is the y-intercept.

Example:

The slope of the line y = 2x + 3 is 2.

The slope of a line that passes through (1, 2) and (2, 3) is 1.

We have,

Line p passes through points (-2, 5) and (3, 8).
This means,

Slope = (8 - 5) / (3 + 2) = 3/4

m = 3/4

And,

Consider (-2, 5) = (x, y)

5 = (3/4) x -2 + c

5 = -3/2 + c

c = 5 + 3/2

c = 13/2

So,

y = (3/4)x + 13/2

Line q passes through the points (-1, 4) and (4, 7).

Slope = (7 - 4) / (4 + 1) = 3/5

m = 3/5

And,

Consider (-1, 4) = (x, y)

4 = (3/5) x (-1) + c

4 = -3/5 + c

c = 4 + 3/5

c = 23/5

So,

y = (3/5)x + 23/5

Thus,

The equation of line p is y = (3/4)x + 13/2.

The equation of line q is y = (3/5)x + 23/5.

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The complete question:

Find the equation of the Line p passes that passes through points (-2, 5) and (3, 8) and Line q that passes through points (-1, 4) and (4, 7).

It takes 1 hour, 20 mins for it to be safe to eat.

How to determine this

If a dish needs to remain at 185°F

And come out at 425°F

So, the difference = 425°F - 185°F

=240°F

If it decreases at 15°F for 5 minutes = 240/15

= 16°F for 5 minutes

= 16 * 5

= 80 minutes

And when converted to hour,

1 hour, 20 mins

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Answer:

5/6 (No option is suitable)

Step-by-step explanation:

Given information,

→ a = 1/2

→ b = 1/3

We have to find,

→ a + b

Let's solve the problem,

→ (1/2) + (1/3)

→ (3/6) + (2/6)

→ (3 + 2)/6

→ 5/6

Hence, the answer is 5/6.

Answer:ez

Step-by-step explanation: blah blah blah blah

Answer:

it has an error of 15 more then the actual temperature

Step-by-step explanation:

to find the change all you have to do is just subtract 340 -325 that is 15 so if the oven was 100 it would show 115

The number of chairs from number 27 to 66 in a row at an auditorium is calculated by using subtraction is 40.

To calculate the number of chairs in the row, we need to subtract the chair number of the first chair from the chair number of the last chair and add 1.

Number of chairs = (last chair number - first chair number) + 1

The first chair number is given as 27, and the last chair number is given as 66.

Substituting these values in the formula, we get:

Number of chairs = (66 - 27) + 1

Number of chairs = 40

Therefore, there are 40 chairs in the row, and the correct answer is option (3) 40.

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____ The given question is incorrect, the correct question is given below:

There are chairs from no, 27 to 66 in a row at an Auditorium. Then

how many chairs are there in the row ?

(1) 38

(2) 39

(3) 40

(4) 48

Were using the following formula to determine a line's equation using two points: Assuming (x1, y1) & (x2, y2) represent two important points on the line, y2 - y1 Equals m(x2 - x1).

A point in mathematics is symbolized by such a dot (.) and utilized to indicate an accurate location in space. It lacks all three dimensions—length, breadth, and height. It has no size, in other terms. A point's name is often written in all caps.

A straight line is mathematically represented by the equation y=mx+b. The y-intercept, or point at which line crosses the y-axis, is denoted by the letters "b," whereas the letters "m" denote the slope of the line.

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well, if a value goes from 88 to 20, it clearly decreased, hmmm 88 - 20 = 68, by 68 units.

so if we take 88(origin amount) to be the 100%, what's 68 off of it in percentage?

[tex]\begin{array}{ccll} amount&\%\\ \cline{1-2} 88 & 100\\ 68& x \end{array} \implies \cfrac{88}{68}~~=~~\cfrac{100}{x} \\\\\\ \cfrac{ 22 }{ 17 } ~~=~~ \cfrac{ 100 }{ x }\implies 22x=1700\implies x=\cfrac{1700}{22}\implies x\approx 77.3[/tex]

Answer: rs>4

Step-by-step explanation: The product of r and s just means rs. Then, when it says more than, you know its going to be a greater than sign: >. So your inequality would be rs>4

Answer:

56.549=56.5

Step-by-step explanation:

A = πr²/2 = 18 * π [in²] ≈ 56.549 [in²]

Answer: Let's assume the exchange rate between ZAR and EUR is given by E1, and the exchange rate between ZAR and CAD is given by E2.

First, let's calculate the cost of the CD in ZAR:

5 EUR * E1 = 5 * E1 ZAR

Next, let's calculate how much money Teboho will have left after purchasing the CD:

250 ZAR - 5 * E1 ZAR = 245 ZAR - 5 * E1 ZAR

Now, let's calculate the cost of the CD in CAD:

7 CAD * E2 = 7 * E2 ZAR

We need to determine the value of E1 and E2 in order to compare the prices. However, without knowing the current exchange rates, we cannot determine the best option for Teboho. If the exchange rate between ZAR and EUR is favorable and the cost of the CD in ZAR is lower than the cost of the CD in CAD, Teboho should order the CD from Germany. On the other hand, if the exchange rate between ZAR and CAD is favorable and the cost of the CD in CAD is lower than the cost of the CD in EUR, Teboho should order the CD from Canada.

Step-by-step explanation:

The probability that the player takes exactly 5 shots before missing one is approximately 0.0539, or 5.39%.

The probability of missing a free throw shot is 0.12, and the probability of making a free throw shot is 0.88 (which is 1 - 0.12).

To find the probability that the player takes exactly 5 shots before missing one, we can use the geometric distribution, which models the number of independent and identical Bernoulli trials needed to get a success.

In this case, a "success" is missing a free throw shot, and the "trials" are the number of shots the player takes before missing one. The probability of success (missing a shot) is p = 0.12, and the probability of failure (making a shot) is q = 0.88. The probability of taking exactly 5 shots before missing one is:

P(X = 5) = q^4 * p

where X is the random variable representing the number of shots the player takes before missing one.

Plugging in the values, we get:

P(X = 5) = (0.88)^4 * 0.12

= 0.0539

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The lemon are limiting ingredient  in lemonade recipe.

Here the limiting ingredient is lemon because here for 1 cup of sugar we have 1 lemon it's clearly seems that the juice of 1 lemon never melt the 1 cup of sugar that's why here limiting ingredient   is lemon.

A limiting reagent is a substance that is completely consumed upon completion of a chemical reaction. They are also called limiting agents or limiting reactants. According to the stoichiometry of a chemical reaction, a certain amount of reactants is required for the reaction to go to completion. Consider the following reactions involving the formation of ammonia.

[tex]3H_{2} +N_{2} - > 2NH_{3}[/tex]

In the above reaction, 3 moles of hydrogen gas are required to react with 1 mole of nitrogen gas to produce 2 moles of ammonia. But what if only 2 moles of hydrogen gas and 1 mole of nitrogen were available during the reaction? Not all nitrogen can be used in this case (because 3 moles of hydrogen gas are required to react all the nitrogen). Hydrogen gas is therefore called the limiting reagent for this reaction as it limits the reaction.

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The function g(x) = 5x²models the number of bulbs she will plant is  if the garden has a side length of 8 feet, Cindy will plant 320 tulip bulbs.

What is Function?

A function is a mathematical rule that assigns a unique output value for every input value. In other words, a function is a relation between a set of inputs and a set of possible outputs with the property that each input is related to exactly one output.

Functions are often denoted using function notation, such as f(x), where "f" is the name of the function and "x" is the input. The output of the function is denoted by f(x), which is read as "f of x" and represents the value of the function at the input value x.

To find the number of bulbs Cindy will plant if the garden has a side length of 8 feet, we need to evaluate the function g(8) = 5(8)²

Using the order of operations, we first need to square the side length, which gives us 8² = 64.

Then, we multiply 64 by 5 to get the total number of bulbs:

g(8) = 5(64) = 320

Therefore, if the garden has a side length of 8 feet, Cindy will plant 320 tulip bulbs.

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