Can someone pls explain

The solution is:

the area of this figure is 21.9 ft².

Here, we have,

To find the area of this figure, we must find the area of the 6 x 6 square and subtract the area of a semi-circle with a diameter of 6.

Area square:

6 x 6

36

Area semi-circe:

A = 1/2(πr²)

A = 1/2(6/2)²π

A = 1/2(9π)

A = 14.1

Area shape:

36 - 14.1

21.9

The units are ft², so the answer is 21.9 ft².

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If you flip two coins 68 times, the best prediction for the number of times both coins will land on heads is 17.

If you flip two coins 68 times, the best prediction for the number of times both coins will land on tails is 17.

The possible outcomes when two coins are flipped are;

head - head = HH

tail - tail = TT

Head and tail = HT

Tail and head = TH

The probability of getting two heads = 1/4

If you flip two coins 68 times, the best prediction for the number of times both coins will land on heads is calculated as;

Expected value = (68 flips) x (1/4 probability of getting HH) = 17

The probability of getting two tails = 1/4

Expected value = 68 x 1/4 = 17

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Answer:

I apologize, I am not able to provide visual drawings or diagrams. However, I can still provide a step-by-step guide to solve the problem.

To find the area of each shape, we need to use rectangles to determine the areas of right triangles that are inside the rectangles. Here are the steps:

1. Draw the given shape on geoboard paper.

2. Surround each triangle with a rectangle so that the vertices of the triangle are on the exterior of the rectangle.

3. Identify the right triangles that are inside the rectangles.

4. Use the formula for the area of a triangle, which is A = (base x height) / 2, to find the area of each right triangle.

5. Use the formula for the area of a rectangle, which is A = length x width, to find the area of each rectangle.

6. Add up the areas of the triangles and rectangles to find the total area of the shape.

Remember to label your answers with the correct units (square units).

The sample proportion who said they pray is approximately 0.84, or 84%.

The sample proportion of college students who said they pray can be calculated by dividing the number of students who said they pray (105) by the total number of students in the sample (125).

Sample proportion = Number of students who said they pray / Total number of students in the sample

Sample proportion = 105 / 125

Sample proportion = 0.84

Therefore, the sample proportion who said they pray is approximately 0.84, or 84%.

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The requried area of the shaded shape is 5 square millimeters.

From the figure,
The area of the green shaded area is given by:
The area of a single square is given as = 1 * 1 = 1 square millimeters.
Now there is 5 square in the shaded region, So the area is given as:

= 5 * 1 = 5 square millimeters.

Thus, the requried area of the shaded shape is 5 square millimeters.

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Okay, here are the steps to solve this problem:

Fixed costs per month: $1121

Variable cost per gallon: $7.50

Selling price per gallon: $9.00

Monthly sales (gallons): 1494

Cost of goods sold = Variable cost per gallon * Monthly sales

= $7.50 * 1494 gallons

= $11,105

Gross margin = Revenue - Cost of goods sold

= $9 * 1494 gallons

= $13,446

- $11,105 (Cost of goods sold)

= $2,341

Margin of profit = Gross margin - Fixed costs

= $2,341 - $1121

= $1,220

So the margin of profit if 1494 gallons are produced and sold each month is $1,220.

The answer is:

B $1,220

The length of a side of the square garden is 5.75 feet.

(x+10)(x+5) - x² + (x+13)(x+8) - x² = 700

Simplifying and solving for x, we get:

2x^2 + 46x - 177 = 0

Using the quadratic formula, we can solve for x:

x = (-46 ± ✓46² - 4(2)(-177))) / (2(2))

x = (-46 ± 26) / 4

x = 5.75

The length of a side of the square garden is 5.75 feet.

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Answer:

61 principals

Step-by-step explanation:

189 total - 128 teachers = 61 principals

Using the first two points we can get an exponential model:

[tex]y = (225/23)*(23/15)^x[/tex]

The general exponential equation can be written as:

[tex]y = A*(b)^x[/tex]

We can replace any two values of the table to get the system of eqautions:

[tex]15 = A*(b)\\\\23 = A*(b)^2[/tex]

Taking the quotient between the second and the first equation we get:

[tex]23/15 = (A*b^2)/(A*b)\\\\23/15 = b[/tex]

Replacing that on the first equation we will get:

[tex]15 =A*(23/15)\\15*(15/23) = A\\225/23 = A[/tex]

Then an exponential model is:

[tex]y = (225/23)*(23/15)^x[/tex]

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Answer:

8

Step-by-step explanation:

3x - 10 = x + 2

2x = 12

x = 6

3x - 10 = 3(6) - 10 = 8

The length of each leg of the triangle is 8.

Answer:91.26ft squared

The square root of y is not simplified and can be represented as:

y = √([tex]2^4 \times[/tex] 5) or y = 4√5.

To solve the proportion y/8 = 10/y for y, we can cross-multiply:

y [tex]\times[/tex] y = 8 [tex]\times[/tex]10

This simplifies to:

[tex]y^2[/tex] = 80

To solve for y, we can take the square root of both sides of the equation:

[tex]\sqrt{y^2[/tex] = √80

Since the square root of [tex]y^2[/tex] is simply y, we have:

y = √80

The square root of 80 can be further simplified by breaking it down into its prime factors. Since 80 can be expressed as 2 [tex]\times[/tex]2 [tex]\times[/tex]2 [tex]\times[/tex]2 [tex]\times[/tex]5, we can simplify the square root:

y = [tex]\sqrt(2 \times 2 \times 2 \times 2 \times 5)[/tex]

Therefore, the square root of y is not simplified and can be represented as:

y = [tex]\sqrt{(2^4 \times 5)[/tex] or y = 4√5.

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Answer:

[tex]y = \sqrt{80\\} =4\sqrt{5}[/tex]

Step-by-step explanation:

Based on the given polynomial function, as x approaches positive or negative infinity, the function f(x) = 2x³ - 3x - 4x⁴ + 1 approaches negative infinity.

The end behavior of a polynomial function is determined as follows:

Examine the leading term of the function f(x) = -4x⁴ + 2x³ - 3x + 1

The leading term of the function is -4x⁴.

For large positive values of x, as x approaches positive infinity, the leading term -4x⁴ becomes increasingly negative since x⁴ grows faster than any positive constant.

Therefore, the end behavior of the function as x approaches positive infinity is that f(x) approaches negative infinity.

Similarly, for large negative values of x, as x approaches negative infinity, the leading term -4x⁴ becomes increasingly negative since x⁴ grows faster than any positive constant.

Therefore, the end behavior of the function as x approaches negative infinity is that f(x) approaches negative infinity.

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The amount in this statement, 6 is 30% of 20 is 6.

The amount in the statement "6 is 30% of 20" is 6.

This statement means that if we take 30% of 20, we get 6.

In other words, the amount 6 is 30% of 20.

We can also verify this by calculating 30% of 20:

30% of 20

= (30/100) × 20

= 0.3 × 20

= 6

Hence,  the amount in this statement is 6.

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The value of the parameter p that satisfies the given conditions is 36.

Let the roots of the quadratic equation [tex]3x^2 - 24x + p = 0[/tex] be denoted by α and β, where α is the root that is triple the value of β.

Then we have:

α = 3β

The sum and product of the roots of the quadratic equation are given by:

α + β = 8 (from the coefficient of x in the linear term)

αβ = p/3 (from the constant term)

Substituting α = 3β in the first equation gives:

3β + β = 8

4β = 8

β = 2

Therefore, α = 6.

So the roots of the quadratic equation are α = 6 and β = 2.

The product of the roots is:

αβ = 6 × 2 = 12

From the equation αβ = p/3, we have:

p/3 = 12

p = 36

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Median of the set is 34, as it is the middle value of the ordered set (32, 33, 33, 33, 34, 35, 35, 36, 38).

To find the middle of a bunch of numbers, the initial step is to organize the numbers all together from least to most prominent. For this situation, the arranged set is: 32, 33, 33, 33, 34, 35, 35, 36, 38.

The middle is the center number in the arranged set. On the off chance that there is an odd number of values, the middle is the center worth. On the off chance that there is a considerably number of values, the middle is the normal of the two center qualities.

For this situation, there are nine qualities in the set, which is an odd number. The center worth is the fifth worth, which is 34. Thusly, the middle of the set is B. 34.

To confirm, we can count four qualities before 34 and four qualities after 34 in the arranged set. Since there are an equivalent number of values when the middle, we can infer that 34 is for sure the middle.

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Answer:

24 cakes.

Step-by-step explanation:

6 cups of oil divided by 1/4 cup oil per cake = 24 cakes

6/(1/4) = 24

or 6/(0.25) = 24

She can make 24 cakes with 6 cups of oil.

Answer:

C

Step-by-step explanation:

the expression ! ( factorial ) has the following meaning

n! = n(n - 1)(n - 2) ... × 3 × 2 × 1

Then

4! = 4 × 3 × 2 × 1 = 24

47.17 feet is the height of the building.

We can use the Pythagorean theorem to solve the problem:

Let h be the height of the building.

Then we have a right triangle with legs 20 and h, and a hypotenuse 50.

Using the Pythagorean theorem, we have:

[tex]50^2 = 20^2 + h^2[/tex]

Simplifying and solving for h, we get:

[tex]h = \sqrt{(50^2 - 20^2)[/tex]

h ≈ 47.17 feet (rounded to two decimal places)

Therefore, the height of the building is approximately 47.17 feet.

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If he wants an average of 84, he needs to get at least 93 points.

Remember that the average value between 3 values A, B, and C is:

(A + B + C)/3

Here we know that the first two scores are 76 and 83 points, let's say that the third score is x, if we want to have an average of 84 or more, then we need to solve:

(76 + 83 + x)/3 = 84

159 + x = 252

x = 252 - 159

x = 93

So he needs to get at least 93 points in the next exam.

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The length of gateleg of the table whose leg swings from one corner of the table to the middle of the far side of the table top is 53 inches long.

The shape forms a trapezoid

The length of the parallel side = is 56 in

The length of the base = is 45 in

To the length of the triangle formed  when the base of the gateleg is connected with the middle of the table

The length of the side when connected with the midpoint = 56/2 = 28

The length of gateleg = hypotenuse

Using Pythagorean theorem :

(hypotenuse)² = (base)² + (perpendicular)²

(hypotenuse)² = (45)² + (28)²

(hypotenuse)² = 2025 + 784

(hypotenuse)² = 2809

hypotenuse = 53

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The question is incomplete the complete question is :

Philippa has a gateleg table in her kitchen. The leg swings from one corner of the table to the middle of the far side of the tabletop, as shown in the sketch below.

Note: The figure is not drawn to scale.

How long is the gateleg of the table?

A.) 53 inches

B.) 49 inches

C.) 73 inches

D.) 72 inches

1.It is generally considered best practice for parents to discuss their intentions with their children and heirs to avoid confusion or misunderstandings.

2.As potential heirs, Brennan and Maureen had a responsibility to communicate with their parents about their estate planning and express any concerns or questions they had.

3.I have personally not had experience with a family member's will. However, I believe it is important to approach the topic of writing a will with sensitivity and empathy.

1. While it is understandable that Brennan and Maureen's parents may have wanted to keep their financial affairs private, their lack of communication may have caused confusion and disappointment for their children. Ideally, the parents should have discussed their estate planning with their children and explained the impact of the gifts on their final inheritance.

2. As potential heirs, Brennan and Maureen had a responsibility to communicate with their parents about their estate planning and express any concerns or questions they had. While it can be difficult to broach sensitive topics like death and inheritance, it is important for family members to have open and honest communication to prevent misunderstandings or disputes down the line.

3. It can be a difficult and emotional topic to discuss, but it is important to have open communication to ensure that everyone's wishes are respected and honored. It may be helpful to consult with a lawyer or financial advisor to ensure that the will is properly drafted and that everyone's needs are addressed.

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(a) The given system of equation as an augmented matrix is [tex]\left[\begin{array}{cccc}1&3&0&150\\0&1&0&250\\-1&-1&1&400\end{array}\right][/tex];

(b) For the given augmented matrix, the system of equations is

-5x-6y-4z=400;

    y+z=100;

-3x-3y-2z=150;

A "system-of-equations" is a set of two or more equations which contain multiple variables. The solution to the system of equations is the set of values for the variables that satisfy all the equations in the system.

An "Augmented-Matrix" is a way to represent a system of linear equations in a concise and organized manner. It is obtained by writing the coefficients of the variables and the constants in each equation in a rectangular array, with each row representing an equation.

Part(a) : The system-of-equations is given as :

x  + 3r +0m = 150

0x + r + 0m = 250

-x - r + m = 400,

We see that the first column of the matrix will have 1, 0, -1,

the second-column will have 3, 1, -1 ;

the third-column will have 0, 0, 1.

So, the Augmented Matrix is represented as : [tex]\left[\begin{array}{cccc}1&3&0&150\\0&1&0&250\\-1&-1&1&400\end{array}\right][/tex].

Part(b) :

The augmented-matrix is given as : [tex]\left[\begin{array}{cccc}-5&-6&-4&400\\0&1&1&100\\-3&-3&-2&150\end{array}\right][/tex],

In this matrix, the terms in the "first-column" will be multiplied by variable"x";

the terms in the "second-column" will be multiplied by variable"y"; and

the terms in the "third-column" will be multiplied by variable"z";

The term sin the "fourth-column" represents the output value.

So, "system-of-equation" will be represented as : -5x - 6y - 4z = 400;

 0x + y + z = 100;

-3x - 3y - 2z = 150.

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The statements that complete the function transformations are left, up, stretch and stretch

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

f(x) = (x + 94)²

Also, we have

f(x) = x²

This implies that f(x) = (x + 94)² is obtained by shifting f(x) = x² left by 94 units

Next, we have

f(x) = x² + 94

This implies that f(x) = x² + 94² is obtained by shifting f(x) = x² up by 94 units

Next, we have

f(x) = 94√x from f(x) = √x

This implies that f(x) = 94√x can be obtained from vertically stretching f(x) = √x by a factor of 94

Also, the graph of f(x) = √94x can be obtained from horizontally stretching f(x) = √x by a factor of 1/94

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The actual distance between the two cities is 432 miles.

The figure shows a map of two cities, with a distance between them measured at 4.5 inches.

The scale of the map is given as 1/8 inch to 12 miles.

This means that 1/8 inch on the map represents a distance of 12 miles in real life.

To determine the actual distance between the two cities, we can use the scale provided.

1/8 inch on the map represents 12 miles in real life.

A proportion to find the actual distance between the cities:

1/8 inch on map = 12 miles in real life

4.5 inches on map = x miles in real life

To solve for x, we can cross-multiply and simplify:

1/8 × x = 12 × 4.5

x = 12 × 4.5 × 8

x = 432 miles

Maps with scales can be useful for determining distances, sizes, and proportions of objects in real life.

It allows us to visually represent complex spatial relationships and make measurements without physically being present at the location.

Remember to use the correct scale and make sure to convert units properly in order to accurately determine real-life measurements.

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The area of the composite shape is 125units²

The area of a figure is the number of unit squares that cover the surface of a closed figure.

A composite shape can be defines as a shape created with two or more basic shapes.

The composite shape can be divided into 2 equal squares and a rectangles.

Area of the square = l²

= 5× 5 = 25

For two squares it will be;

25 × 2

= 50 units²

area of the rectangle = l× w

where w is the width

A = 15 × 5

= 75 units²

Therefore the area of the composite shape = 50 + 75 = 125 units²

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If the population in the year 2007 is 111.3 million, then the population in the year 2044 will be 148.37 million.

In order to find the population in the year 2044, we use the population growth formula; which is : P = P₀ × (1 + r)ⁿ;

where P = future population, P₀ = initial population, r = annual growth rate, and n = number of years;

Substituting the values,

We get;

⇒ P = (111.3 million) × (1 + 0.0078)²⁰⁴⁴⁻²⁰⁰⁷;

Simplifying this expression,

We get;

⇒ P = (111.3 million) × (1.0078)³⁷;

⇒ P ≈ 148.37 million;

Therefore, the population in the year 2044 is estimated to be approximately 148.37 million.

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The statement that "the coldest temperature ever recorded on earth was - 89. 2 ° " is True.

The Soviet Union's Vostok Station in Antarctica recorded the coldest temperature ever observed on Earth, measuring at -89.2°C on July 21, 1983 via satellite and weather station data.

This natural occurrence saw a temperature that presents significant risks to animal and human life due to poor insulation available against such extreme colds. Without suitable warming tools, survival is near impossible.

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