Draw a circle with radius 4cm.
What is the length of the diameter of the circle?
How many sectors of 90° will fit inside the circle?
Draw five radii inside your circle that are equally spaced out around the circumference. Join up the ends of the radii to create a shape inside your circle.
What is the name of the shape that you have created inside your circle?
How long are the chords that are joining the radii together?
How big is the angle of each sector?
If you did the same as above with sectors of 45°, what shape would you create inside your circle?

The maximum weight occurs when x = 0 and y = 0, and the maximum weight is W = 0.

In calculus, the derivative is a fundamental concept that measures the rate of change of a function with respect to its input variable. The derivative of a function at a particular point gives the instantaneous rate of change of the function at that point.

The derivative of a function f(x) with respect to its input variable x is denoted by f'(x) or df/dx. It is defined as the limit of the difference quotient as the change in x approaches zero:

f'(x) = lim (h → 0) [(f(x+h) - f(x)) / h]

Intuitively, the derivative of a function at a particular point gives the slope of the tangent line to the graph of the function at that point. This slope can be positive, negative, or zero, depending on whether the function is increasing, decreasing, or constant at that point.

To find the maximum weight, we need to find the critical points of the function.

First, we find the partial derivatives of the weight function with respect to x and y:

∂W/∂x = 8y(20 - 2x - 2y)

∂W/∂y = 8x(20 - x - 4y)

Setting these partial derivatives equal to zero, we get:

8y(20 - 2x - 2y) = 0

8x(20 - x - 4y) = 0

Solving for x and y, we get two critical points:

x = 0, y = 0

x = 10, y = 5

To determine which of these critical points correspond to a maximum, we use the second partial derivative test.

The second partial derivatives of W with respect to x and y are:

∂²W/∂x² = -32y

∂²W/∂y² = -32x

At the critical point (0,0), both second partial derivatives are negative, which means that it is a maximum.

At the critical point (10,5), both second partial derivatives are positive, which means that it is a minimum.

Therefore, the maximum weight occurs when x = 0 and y = 0, and the maximum weight is W = 0.

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Answer:

Option B

3&5, 4&6

Step-by-step explanation:

An interior angle is an angle inside a shape

The area of the regular polygon which is given above would be = 64.5 cm². That is option D.

To calculate the area of the given regular polygon will require the use of this formula such as:

Area = 1/2(a×p)

where;

a = length of an apothem = 4.3 cm

p = perimeter = 6×5 = 30cm

Area = 1/2 ( 4.3×30)

= 129/2

= 64.5 cm²

Therefore, in conclusion the area of the regular polygon which is a hexagon with 6 sides would be = 64.5 cm².

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a) The speed at which the car gets maximum gas mileage is given as follows: 48 miles per hour.

b) The max gas mileage is given as follows: 29.5 miles per gallon.

The gas mileage is modeled as a function of the velocity x according to the quadratic function presented as follows:

m(x) = -0.028x² + 2.688x - 35.012.

The coefficients are given as follows:

a = -0.028, b = 2.688, c = -35.012.

The leading coefficient a is negative, hence the vertex represents the point at which the maximum mileage is obtained.

The velocity is given as follows:

x = -b/2a

x = -2.688/[2(-0.028)]

x = 48 miles per hour.

The max gas mileage is obtained as follows:

m(48) = -0.028(48)² + 2.688(48) - 35.012.

m(48) = 29.5 miles per gallon.

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Answer:

Step-by-step explanation:

(y^2)/1600-(x^2)/81=1. y21600−x281=1 y 2 1600 - x 2

Answer: y21600x281=1 y 2 1600 - x 2

Step-by-step explanation: for sure chfjjgffjfj ;)

Joel cannot buy 2 games and 6 puzzles and satisfy the constraints was solved by using inequality.

The total cost of x puzzles and y games must be less than or equal to $96, which gives us the first inequality: 8x + 12y ≤ 96

The second inequality: x + y ≥ 9.

An inequality is a mathematical statement that compares two quantities or expressions and shows the relationship between them using one of the following symbols: <, >, ≤, or ≥. For example, "x > 5" is an inequality that states that x is greater than 5.

In the given question,

Part A:

Let x be the number of puzzles Joel can buy and y be the number of games Joel can buy.

The total cost of x puzzles and y games must be less than or equal to $96, which gives us the first inequality: 8x + 12y ≤ 96

Joel needs to buy at least 9 gifts, which means that the total number of gifts must be greater than or equal to 9. Since x represents the number of puzzles and y represents the number of games, the total number of gifts is x + y. This gives us the second inequality: x + y ≥ 9

We also know that Joel can only buy puzzles or games, not both. Therefore, x and y must be either both integers or both half-integers (such as 1.5 or 2.5), but they cannot be mixed. This gives us the third inequality:

x, y are both integers or both half-integers

Part B:

To see if Joel can buy 2 games and 6 puzzles and satisfy the constraints, we can substitute x = 6 and y = 2 into the inequalities:

8x + 12y ≤ 96

8(6) + 12(2) ≤ 96

72 ≤ 96

This inequality is true, so the first constraint is satisfied.

x + y ≥ 9

6 + 2 ≥ 9

8 ≥ 9

This inequality is not true, so the second constraint is not satisfied. Therefore, Joel cannot buy 2 games and 6 puzzles and satisfy the constraints.

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a. The probability that it is not a 10-peso coin is  [tex]\frac{12}{17}[/tex].

b. The probability that it is a 5-peso coin is [tex]\frac{3}{17}[/tex] .

What is probability?

The mathematical notion of probability is used to determine the likelihood of an event. It is only helpful for estimating the likelihood that an event will happen. A scale from 0 to 1, where 0 denotes impossibility and 1 denotes a specific occurrence.

We are given that a purse contains five 10-peso coins, three 5-peso coins, and nine 1-peso coins.

Total coins = 5 + 3 + 9 = 17

a. Probability of getting a 10 peso coin is

P (A) = [tex]\frac{5}{17}[/tex]

Probability of not getting a 10 peso coin is

⇒Probability = 1 - P (A)

⇒Probability = 1 - [tex]\frac{5}{17}[/tex]

⇒Probability = [tex]\frac{12}{17}[/tex]

b. Probability of getting a 5 peso coin is [tex]\frac{3}{17}[/tex] .

Hence, the required probabilities have been obtained.

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Answer: 5

Step-by-step explanation:

A = Lw (area of rectangle is length times width)

A = 15 (Area is 15)

L = 2x + 5 (length is 2 times a number plus another 5)

w = x - 4 (width is 4 less than that number

Plug in the values:

15 = (2x + 5)(x - 4)

FOIL

15 = 2x2 - 8x + 5x - 20

simplify:

15 = 2x2 - 3x - 20

Subtract 15

0 = 2x2 - 3x - 35

Factor out the quadratic. We know that one number has to be 7 and the other 5 so that they multiply together to make 35, and that one of them has to be negative so that it's actually -35.

That means we have m * n = -35

We also need it set up so that so that 2m + n = -3:

2 * -5 + 7 = -3

0 = (2x + 7)(x - 5)

So:

0 = 2x + 7, or 0 = x - 5

x = -7/2 or 5

We cannot have a negative length, so x = 5

Check:

15 = (2 * 5 + 5) (5 - 4)

15 = 15 * 1

15 = 15

By answering the presented question, we may conclude that As a result, fraction the answer is nine thirty-fifths.

A whole can be represented by any number of equal sections or fractions. In standard English, fractions represent the number of units of a specific size. 8, 3/4. A whole contains fractions. In mathematics, numbers are stated as the ratio of the numerator to the denominator. Each of these is an integer in simple fractions. A fraction exists in the numerator or denominator of a complex fraction. True fractions have numerators that are smaller than their denominators. A fraction is a sum that represents a piece of a total. You may assess it by dividing it up into smaller chunks. Half of a whole number or object, for example, is represented as 12.

We can simplify both fractions to have a common denominator of 12 for the first problem:

Four-sixths = Eighteenths

Three-twelfths + three-twelfths = three-twelfths

As a result, the phrase becomes: 8/12 - 3/12 = 5/12

As a result, the answer is five-twelfths.

For the second case, we may reduce both fractions again such that they have a common denominator of 16:

Seventy-eighths = fourteenteenths

Nineteenths + nineteenths = nineteenths

As a result, the equation becomes: 14/16 - 9/16 = 5/16.

As a result, the answer is five-sixteenths.

We can simplify both fractions to obtain a common denominator of 35 for the third problem:

Two-fifths = 14-thirty-fifths

One-seventh Equals thirty-fifths

As a result, the phrase becomes: 14/35 - 5/35 = 9/35

As a result, the answer is nine thirty-fifths.

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Answer:

83

Step-by-step explanation:

The expression follows the order of operations (PEMDAS): Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction, in that order.

First, simplify what is inside the parentheses: 3 x 9 = 27

Next, multiply 3 by 27: 3 x 27 = 81

Finally, add 2 to 81: 2 + 81 = 83

Therefore, the expression 2+3(3x9) equals 83.

The result of this expression is 83

To solve them we have to start from the inside to out, that is, parentheses, brackets...
And proceed to signal resolution:

[tex]\begin{array}{l}\sf 2+3\tiny\text{$\times$}(3\times9)\\\sf 2+3\tiny\text{$\times$}(27)\\\sf 2+81\\\bf 83\end{array}[/tex]

We get the result 83

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The  inferences from the results of the random sample  that are reasonable is: C. The percentage of all bags produced that contain less than 11 ounces is likely to fall between 15% and 25%.

From the sample of 250 bags, we know that 50 of them contain only 10.9 ounces of coffee. Let's calculate the percentage of bags in the sample that contain less than 11 ounces:

50/250 = 0.2 = 20%

Now let's consider each inference:

A. It cannot be inferred that 5% of the bags from a second random sample will contain more than 11 ounces. The sample only provides information about the bags in the sample, not the entire population.

B. It is possible that a second random sample of bags will show a lower percentage of bags with only 10.9 ounces, but it cannot be concluded with certainty based on the given information.

C. It is reasonable to estimate that the percentage of all bags produced that contain less than 11 ounces is likely to fall between 15% and 25%. This is because out of a sample of 250 bags, 50 bags contained 10.9 ounces, which is 20% of the sample.

D. It is not necessarily likely that the company's claim is true because 20% of the bags in the sample contain 10.9 ounces. The sample provides information about the bags in the sample, not the entire population.

E. It is not necessarily unlikely that the company's claim is true because 20% of the bags in the sample contain 10.9 ounces. The sample provides information about the bags in the sample, not the entire population.

Therefore, the correct inferences from the given information are C. The percentage of all bags produced that contain less than 11 ounces is likely to fall between 15% and 25%.

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Answer:

Therefore, 3 bakers can make 30 loaves of bread in 2 hours.

Therefore, 5 bakers can make 30 loaves of bread in 2 hours.

Therefore, 6 bakers can make 30 loaves of bread in 1.25 hours.

Therefore, 15 bakers can make 30 loaves of bread in 2 hours.

Step-by-step explanation:

In the number of bakers, it would take 2 hours to make 30 loaves of bread.

A proportion is an equation in which two ratios are set equal to each other.

Let h be the number of hours needed for a given number of bakers to make 30 loaves. Then we have:

2 bakers can make 30 loaves in 1 hour, so 1 baker can make 15 loaves in 1 hour.

Therefore:

3 bakers can make 45 loaves in h hours, so 45/3 = 15 loaves can be made in 1 hour. Thus, 3 bakers can make 30 loaves in 2 hours.

5 bakers can make 75 loaves in h hours, so 75/5 = 15 loaves can be made in 1 hour. Thus, 5 bakers can make 30 loaves in 2 hours.

6 bakers can make 90 loaves in h hours, so 90/6 = 15 loaves can be made in 1 hour. Thus, 6 bakers can make 30 loaves in 2 hours.

15 bakers can make 225 loaves in h hours, so 225/15 = 15 loaves can be made in 1 hour. Thus, 15 bakers can make 30 loaves in 2 hours.

Therefore, regardless of the number of bakers, it would take 2 hours to make 30 loaves of bread.

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Answer:

216.49

Step-by-step explanation:

you have two right triangles, for the left one

[tex]tan(64)=\frac{113}{a}[/tex]

[tex]a=\frac{113}{tan(64)}[/tex]
for the one on the right

[tex]tan(35)=\frac{113}{b}[/tex]

[tex]b=\frac{113}{tan(35)}[/tex]

The total value of X is the sum

[tex]\frac{113}{tan(35)} +\frac{113}{tan(64)}=216.4945073[/tex]

so 216.4945073

The relationship between the diameter of a circle and it's circumference is presented in this problem.

The circumference of a circle of radius r is given by the equation presented as follows:

[tex]C = 2\pi r[/tex]

The radius of a circle represents the distance between the center of the circle and a point on the circumference of the circle, while the diameter of the circle is the distance between two points on the circumference of the circle that pass through the center. Hence, the diameter’s length is twice the radius length.

The diameter is twice the radius, hence, for a circle with diameter 35 in, the radius is given as follows:

r = 0.5 x 35

r = 17.5 in.

Then the circumference of the circle is given as follows:

C = 2 x pi x 17.5

C = 109.9 in.

The problem is incomplete, hence the relation between the diameter of a circle and it's circumference is presented.

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Answer:

-3/2

Step-by-step explanation:

cubed roots of -27 is -3

cubed root of 8 is 2

Answer:

0.7

Step-by-step explanation:

Answer: 0.7

Step-by-step explanation: The tenths place in decimals is the number directly to the right of the decimal. the 5 next to the six is greater than or equal to 5 meaning you can round up the 6 to a 7.

Step-by-step explanation:

Interchange just means to switch really. The first 3 will stay the same be cause they are the same numbers.

The last one will be (2,8) because that's (8,2) but with the numbers switched

The value of the perimeter:

1. 97. 3 units

2. 27. 8 units

The formula for the perimeter of a triangle is expressed as;

P = a + b + c

Given that;

From the diagram shown, we have that;

Using the tangent identity;

tan 44 = BC/29

find the value and cross multiply

BC = 28. 00

Also, AC ²= 29² + 28²

AC = √1625 = 40. 3

Then, the perimeter = 29 + 28. 00 + 40. 3 = 97. 3 units

For the second diagram;

Note that the perimeter of a rectangle is expressed as 2(length + width)

Substitute the values

Perimeter =2 ( 4 + 3) = 14 units

For triangle;

sin 45 = 4/t

cross multiply

t = 5. 7 units

To determine the adjacent side;

5.7² - 4² = x²

32. 5 - 16 = a²

a = √16. 49

a = 4. 1

Then, the perimeter = perimeter of rectangle + perimeter of triangle

= 14 + 13. 8

= 27. 8 units

Note that no specific unit was given as thus, we used 'units' as the measuring scale.

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Answer:

It depends on the equation in question. If Maggie is referring to an equation in the form of x = y, then adding 8 to both sides would still result in the same value of x and y being equal. For example, if the equation is 2x - 5 = 7, then adding 8 to both sides would result in 2x - 5 + 8 = 7 + 8, which simplifies to 2x + 3 = 15. In this case, adding 8 to both sides would not maintain equality.

However, if the equation is in the form of an inequality such as x < y or x > y, adding the same value to both sides may not maintain the inequality. For example, if the inequality is 2x - 5 < 7, then adding 8 to both sides would result in 2x - 5 + 8 < 7 + 8, which simplifies to 2x + 3 < 15. In this case, adding 8 to both sides would still maintain the inequality.

Therefore, whether or not adding 8 to both sides of an equation would still result in equality depends on the equation in question and the mathematical operation being performed.

Yes.  Yes I do.

If you think of an equation as a balance, where both sides have equal weight, then adding the same amount to both sides or taking away the same amount from both sides will still maintain that balanced weight.

We call this the addition property of equality:

    If a = b, then a+c = b+c for any expression c.

We estimate that Jordan will drive a distance of approximately 4668.3 miles during the entire 7-day road trip.

Distance and displacement are two key words in mechanics that, although having similar sounds, have distinct definitions and meanings. How much of an object's path is covered by a moving object is measured in terms of distance. Whereas "How much route is covered by the item in a specific direction" is measured by displacement, The main distinction between distance and displacement is therefore that the former is a scalar quantity while the latter is a vector quantity.

Given that, the distance travelled is  666.9 miles.

The same distance is travelled for 7 days thus,

distance = Distance per day x Number of days

distance = 666.9 miles/day x 7 days

distance = 4668.3 miles

Hence, we estimate that Jordan will drive approximately 4668.3 miles during the entire 7-day road trip.

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On solving the provided question, we can say that Hence, the solution to the system of equations is x = 19/8 and y = 5/8.

A math equation is a technique that links two statements and utilises the equals sign (=) to express equivalence. In algebra, an equation is a mathematical statement that proves the equivalence of two mathematical expressions. For example, in the computation 3x + 5 = 14, the equal sign inserts a gap between the numbers 3x + 5 and 14. A mathematical formula may be used to explain the link between the two phrases written on either side of a letter. The logo and the programme are usually the same. For example, 2x - 4 equals 2.

4x + 4y = 12 is obtained by multiplying the first equation by four.

To remove y, combine the first and second equations: (4x + 4y) + (4x - y) = 12 + 7, which simplifies to 8x = 19.

Divide both sides of the equation by 8 to find x: x = 19/8.

To find y, plug the value of x into either equation: y = 3 - x = 3 - 19/8 = 5/8.

Hence, the solution to the system of equations is x = 19/8 and y = 5/8.

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Answer:

I think

Step-by-step explanation:

The number 3 in the equation h(t) = -16t² + 6t+ 3 represents option 2 - the height from which the ball is thrown.

What is an equation?

A mathematical definition of an equation is a claim that two expressions are equal when they are joined by the equals sign ("=").

The equation h(t) = -16t² + 6t+ 3 gives the height of the ball as a function of time.

The constant term in this equation is 3, which represents the initial height of the ball when it is thrown.

Therefore, the correct answer is (2) the height from which the ball is thrown.

Option (1) cannot be correct, because the maximum height of the ball occurs when the derivative of h(t) is zero, which is not necessarily equal to the constant term in the equation.

Option (3) cannot be correct, because the ball reaches the ground when h(t) = 0, which requires solving a quadratic equation.

Option (4) cannot be correct, because the time it takes for the ball to reach its maximum height is given by the formula t = -b/2a, where a and b are the coefficients of the quadratic equation, and it does not depend on the constant term.

Therefore, option 2 is the correct answer.

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Answer:its b 6,12

Step-by-step explanation:

Answer: Based on the data displayed, Mrs. Cheng's class lost fewer pencils overall as it has a smaller spread in the data compared to Mr. Johnson's class. The box plot of Mrs. Cheng's class has a smaller spread, with a larger interquartile range and smaller range compared to Mr. Johnson's class, indicating that the data is more concentrated and consistent. Additionally, the median value of Mrs. Cheng's class is higher than Mr. Johnson's class, indicating that half of the students in Mrs. Cheng's class lost fewer pencils than half of the students in Mr. Johnson's class. Therefore, the correct answer is "Mrs. Cheng's class; it has a narrow spread in the data".

Step-by-step explanation:

The surface area of the following solids is:

a.54cm².

b. 43.32cm².

c. 21.2cm².

d. The figures b and c are smaller than a.

In contrast to the lateral surface area, which is used to determine the area occupied by the shape's curved surface, the total surface area takes into account all faces of the 3D shape, including both flat and curved surfaces.

The area around the bases is not included. One 3D shape called a sphere has just one round surface and no flat base.

In the given question,

In the 1st figure,

Total surface area = Total surface area of 6 squares.

= 6 × 3²

= 54cm².

In the 2nd figure,

Total surface area = Total surface area of 2 triangles + Total surface area of 3 squares + Total surface area of larger triangle.

= 2 × 1/2 × 3 × 3 + 3 × 3² + 1/2 × 3.96 × 3.7

= 9 + 27 + 7.32

= 43.32cm².

In the 3rd figure,

Total surface area = Total surface area of 4 triangles

= 1/2 × 3 × 3 + 1/2 × 3 × 3 + 1/2 × 4.2 × 3.7 + 1/2 × 3 × 3

= 9 + 7.77 + 4.5

= 21.2cm².

Hence, the figures b and c are smaller than the figure a.

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The volume of Eli's trophy case is 64.4 cubic feet.

Eli's trophy case's length, breadth, and height must be multiplied to determine its volume. The case has the following measurements:

Length = 4 3/5 feet

Width = 2 feet

Height = 3 1/2 feet

We can sum the improper fractions after converting the mixed integers to fractions to arrive at:

Length = 4 3/5 feet = (5*4 + 3)/5 = 23/5 feet

Height = 3 1/2 feet = (2*3 + 1)/2 = 7/2 feet

Now that we have the volume, we can multiply the length, width, and height:

Volume equals length, width, and height

= (23/5) feet x 2 feet x (7/2) feet

= (23 x 2 x 7)/(5 x 2) cubic feet

= (644/10) cubic feet

= 64.4 cubic feet

Eli's trophy case therefore has a 64.4 cubic foot volume.

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