At the park there a pool shaped like a circle. A - shaped path goes around the pool. Its inner diameter is 18 yd and its outer diameter is 28 yd. 28 yd We are going to give a new layer of coating to the pathIf one gallon of coating can cover 8v * d ^ 2 how many gallons of coating we need? Note that coating comes only by the , so the number of gallons must be a whole number(Use the value 3.14 for )

Answer:

n = \(5\frac{4}{5}\)

Step-by-step explanation:

You obviously have to solve for n

Answer:

1.5

Step-by-step explanation:

The height is 1.5 because to find the volume of a rectangular prism, you do length x width x height. Without height, you multiply length x width (6x2) and divide that by the volume (18 divided by 12 = 1.5)

Answer:

7.65 ft apart (to nearest hundredth)

Step-by-step explanation:

The A frame creates an isosceles triangle with equal legs of 10 ft and a vertex of 45°.  To find how far apart the footings should be, we need to find the base of the triangle.

To find the base, use the cosine rule:

\(c^2=a^2+b^2-2ab \cos(C)\)

where:

So for this triangle:

Substitute these values into the formula and solve for c:

\(c^2=10^2+10^2-2(10)(10) \cos(45)\)

\(\implies c^2=200-200\cos(45)\)

\(\implies c=\sqrt{200-200\cos(45)}\)

\(\implies c=7.653668647...\)

Therefore, the footings should be 7.65 ft apart (to nearest hundredth)

Answer:

  7.65 ft

Step-by-step explanation:

The distance can be figured using the Law of Cosines, or it can be figured by considering half of the isosceles A-frame to be a right triangle. We choose the latter.

__

An altitude of the A-frame bisects the vertex angle so that the angle of interest in our right triangle is 22.5°. Then half the distance between the footings will be given by ...

  Sin = Opposite/Hypotenuse

  Opposite = Hypotenuse × Sin

  half-distance = (10 ft)·sin(22.5°)

  footing spacing = 2 × half-distance = (20 ft)sin(22.5°) ≈ 7.654 ft

The footings for each A-frame should be about 7.65 feet apart.

Answer:

1244 DCD

Step-by-step explanation:

The post-neonatal mortality rate for the year is 1.1×10⁻⁷.

The post-neonatal mortality rate in a year is applicable when the death day lies between 28 and 364. First, divide the number of post-neonatal deaths by the number of live births. Then multiply the obtained value by 1000 to get the post-neonatal mortality rate.

It is known that 1 billion units = 10⁹ units. So, 20 billion live births will be 20×10⁹ live births. Also, the number of post-neonatal deaths is 2200.

So, use the formula, post-neonatal mortality rate = (the number of post-neonatal deaths)/(the number of live births).

post-neonatal mortality rate = 2200/(20×10⁹)

= 110×10⁻⁹

= 1.1×10⁻⁷

Therefore, the obtained answer is 1.1×10⁻⁷.

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The line or points has a slope value of -1

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

The slope of -3 up to positive 3

For a start, we represent the above parameters using an ordered pair

The ordered pair is represented as

(x, y) = (-3, 3)

The slope of the point is then calculated using the following slope formula

Slope = (y₂ - y₁)/(x₂ - x₁)

Where

(x, y) = (-3, 3) and (0, 0)

The coordinate (0, 0) represents the origin

Substitute the known values in the above equation

So, we have the following equation

Slope = (3 - 0)/(-3 - 0)

Evaluate the difference

So, we have the following equation

Slope = (3)/(-3)

Evaluate the quotient

So, we have the following equation

Slope = -1

Hence, the slope is -1

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You invested $3000 at 3% annual interest rate, and the remaining amount of $4000 - $3000 = $1000 was invested at 4% annual interest rate.

Let's assume you invested an amount, x, at 3% annual interest rate. This means the amount invested at 4% annual interest rate would be $4000 - x.

To calculate the interest earned from the investment at 3%, we multiply x by 3% (0.03). Similarly, the interest earned from the investment at 4% is calculated by multiplying ($4000 - x) by 4% (0.04).

According to the given information, the total interest earned from both investments is $130. So we can set up the equation:

0.03x + 0.04($4000 - x) = $130

Simplifying the equation:

0.03x + 0.04($4000 - x) = $130

0.03x + $160 - 0.04x = $130

-0.01x = $130 - $160

-0.01x = -$30

x = -$30 / -0.01

x = $3000

Therefore, you invested $3000 at 3% annual interest rate, and the remaining amount of $4000 - $3000 = $1000 was invested at 4% annual interest rate.

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Answer:

9

Step-by-step explanation:

\(\frac{12}{4}+3(2) \\ \\ =3+6 \\ \\ =9\)

Answer:

Answer is 9.

Step-by-step explanation:

If x is 12, then do 12 divided by 4, and you get 3. If y is 2, then di 3 times 2, which is 6. 3 plus 6 is 9.

A set of numbers that can represent the side lengths, in centimeters, of a right triangle is any set that satisfies the Pythagorean theorem, where the square of the hypotenuse's length is equal to the sum of the squares of the other two sides.

A right triangle is a type of triangle that contains a 90-degree angle. According to the Pythagorean theorem, in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

Let's consider a set of numbers that could represent the side lengths of a right triangle in centimeters.

One possible set could be 3 cm, 4 cm, and 5 cm.

To verify if this set forms a right triangle, we can apply the Pythagorean theorem.

Squaring the length of the shortest side, 3 cm, gives us 9. Squaring the length of the other side, 4 cm, gives us 16.

Adding these two values together gives us 25.

Finally, squaring the length of the hypotenuse, 5 cm, also gives us 25. Since both values are equal, this set of side lengths satisfies the Pythagorean theorem, and hence forms a right triangle.

It's worth mentioning that the set of side lengths forming a right triangle is not limited to just 3 cm, 4 cm, and 5 cm.

There are infinitely many such sets that can be generated by using different combinations of positive integers that satisfy the Pythagorean theorem.

These sets are known as Pythagorean triples.

Some other examples include 5 cm, 12 cm, and 13 cm, or 8 cm, 15 cm, and 17 cm.

In summary, a right triangle can have various sets of side lengths in centimeters, as long as they satisfy the Pythagorean theorem, where the square of the hypotenuse's length is equal to the sum of the squares of the other two sides.

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Answer:

85

Step-by-step explanation:

im new↑∵∴∵∴∞

Answer:

4x² + 22x - 12

Step-by-step explanation:

A = bh/2

A = (4x - 2)(2x + 12)/2

A = (8x² + 48x - 4x - 24)/2

A = (8x² + 44x - 24)/2

A = 4x² + 22x - 12

Lets look through all 4 options.

A)

They rise upward to the right.

This is true, they are both increasing.

B)

Line x-1 starts on the x axis.  We assume that the area shown is the domain.

However, x+2 starts on the y axis.

False

C)

The distance of the starting point of each line from the origin is 2.

True.

D)  Steepness refers to slope.  They both have a slope of 1.  For one x they rise one y.  True.

Options A, C, and D are true

Hope this helps,

Jeron

:- )

Answer:

The order of operations will allow you to solve this problem the right way. The order is this: Parenthesis, Exponents, Multiplication and Division, and finally Addition and Subtraction. Always perform the operations inside a parenthesis first, then do exponents. After that, do all the multiplication and division from left to right, and lastly do all the addition and subtraction from left to right.

(11+33-4^2) /(8-4) =

1 . (11+33) = 44

2 . (44 - 4^2) = 28

3 . (8-4) = 4

4 . 28/4 = 7

Answer:

96,000

Step-by-step explanation:

To round to the nearest thousand, we need to look at the digit in the hundreds place, which is 6. Since 6 > 5, we know that we need to round up (because 6 is closer to 10 than it is to 0). Currently, the number is 95 thousand so when rounding up, the answer will be 96,000.

Answer:

361

Step-by-step explanation:

Answer:

75% of 250 is 187.5

Step-by-step explanation:

To determine the 75% of 250 use this formula

= n % of n

= n/100×n

= answer

Solution:-

75% of 250

→75% × 250

→75/100 ×250

→375/2

→187.5

Answer:

volume of the triangular prism

\( (\frac{1}{2} \times 10 \times 10) \times 25 \\ 1250 {cm}^{3} \)

Answer:

Step-by-step explanation:

BY: \(ζBenjamin\)

The maximum revenue possible in this situation is 15625/A dollars, where A is the coefficient in the quadratic equation.

To find the maximum revenue possible in this situation, we can use the concept of vertex or the vertex form of a quadratic equation.

The revenue equation is given by R = -Ax^2 + 250x, where A is a constant coefficient.

The maximum revenue occurs at the vertex of the parabolic curve represented by the equation. The x-coordinate of the vertex can be found using the formula x = -b / (2a), where a and b are the coefficients of the quadratic equation.

In this case, a = -A and b = 250. Plugging in these values, we get:

x = -250 / (2 * (-A))

= 125 / A

To find the maximum revenue, we substitute this value of x into the revenue equation:

R = -A * (125 / A)^2 + 250 * (125 / A)

= -A * (15625 / A^2) + (31250 / A)

= -15625 / A + 31250 / A

= 15625 / A

The maximum revenue is given by 15625 / A. The value of A is not specified in the question, so we cannot determine the exact maximum revenue without knowing the value of A. However, we can say that the maximum revenue increases as A decreases.

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The equation of the line in slope-intercept form is y = (3/5)x + 2. This form allows us to easily identify the slope and y-intercept of the line and to graph it on a coordinate plane.

To write the equation of a line in slope-intercept form, we use the formula:y = mx + b

where:

- y represents the dependent variable (the vertical axis)

- x represents the independent variable (the horizontal axis)

- m represents the slope of the line

- b represents the y-intercept, the point where the line intersects the y-axis.

In this case, we are given the slope as 3/5 and the y-intercept as 2. Plugging these values into the formula, we get:

y = (3/5)x + 2

This equation represents a line with a slope of 3/5, indicating that for every 5 units we move horizontally (along the x-axis), the line moves 3 units vertically (along the y-axis). The y-intercept of 2 tells us that the line intersects the y-axis at the point (0, 2).

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Answer:

30=6j

j=5

hope it helps .......

Answer:

1.2

Step-by-step explanation:

\(\frac{3x2}{5}\) = \(\frac{6}{5}\) = 1.2

Answer: 6/5

Step-by-step explanation:

Answer:

Option B,  two variables are measured and two groups are compared

Step-by-step explanation:

In a correlation study relationship between two variable is established.

The two variables represents two group.

For instance correlation study is conducted to determine the relationship between two variables X and Y

X and Y are variable

While X represents the group "number of cars passing through a lane"

Y represents the group "width of the road".

Hence, Option B is correct  

In 2021 a 30-second commercial during the Super Bowl cost $5.6 million and the CPI was approximately 271.4. Assuming that price changes are simply due to inflation, when the CPI was 33.4 the estimated cost of a 30-second commercial during the first Super Bowl in 1967 would be approximately $68,900.

To calculate the cost of the 30-second commercial during the first Super Bowl in 1967, we can use the concept of inflation and the Consumer Price Index (CPI).

The CPI measures the average price change of a basket of goods and services over time. By comparing the CPI values of two different years, we can estimate the relative increase in prices due to inflation.

Given data:

Cost of a 30-second commercial in 2021 = $5.6 million

CPI in 2021 = 271.4

CPI in 1967 = 33.4

To calculate the cost in 1967, we need to adjust the 2021 cost for inflation using the CPI ratio:

Cost in 1967 = (Cost in 2021) * (CPI in 1967 / CPI in 2021)

Cost in 1967 = ($5.6 million) * (33.4 / 271.4)

Cost in 1967 ≈ $0.689 million

To round the cost to the nearest hundred dollars, we can multiply the cost by 100 and round it to the nearest whole number:

Cost in 1967 ≈ $68,900

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Answer:

Answer: $125.00

Step-by-step explanation:

Work:

¾ + ½= 1 ¼  

60 * 1 ¼= 75

75/3= 25

25 * $5.00= $125

Answer:

1.  Vertical shrink by a factor of ¹/₅

2.  Right 5

3.  Up 5

Step-by-step explanation:

Transformations of Graphs (functions) is the process by which a function is moved or resized to produce a variation of the original (parent) function.

Transformations

For a > 0

\(f(x+a) \implies f(x) \: \textsf{translated}\:a\:\textsf{units left}\)

\(f(x-a) \implies f(x) \: \textsf{translated}\:a\:\textsf{units right}\)

\(f(x)+a \implies f(x) \: \textsf{translated}\:a\:\textsf{units up}\)

\(f(x)-a \implies f(x) \: \textsf{translated}\:a\:\textsf{units down}\)

\(y=a\:f(x) \implies f(x) \: \textsf{stretched parallel to the y-axis (vertically) by a factor of}\:a\)

\(y=f(ax) \implies f(x) \: \textsf{stretched parallel to the x-axis (horizontally) by a factor of} \: \dfrac{1}{a}\)

\(y=-f(x) \implies f(x) \: \textsf{reflected in the} \: x \textsf{-axis}\)

\(y=f(-x) \implies f(x) \: \textsf{reflected in the} \: y \textsf{-axis}\)

Identify the transformations that take the parent function to the given function.

Question 1

\(\textsf{Parent function}: \quad f(x)=x^3\)

\(\textsf{Given function}: \quad f(x)=\dfrac{1}{5}x^3\)

Comparing the parent function with the given function, we can see that the parent function has been multiplied by ¹/₅.

Therefore, the transformation is:

\(y=\dfrac{1}{5}\:f(x) \implies f(x) \: \textsf{stretched parallel to the y-axis (vertically) by a factor of}\:\dfrac{1}{5}\)

As 0 < a < 1, the transformation visually is a compression in the y-direction, so we can also say:  Vertical shrink by a factor of ¹/₅

Question 2

\(\textsf{Parent function}: \quad f(x)=x^3\)

\(\textsf{Given function}: \quad f(x)=(x-5)^3\)

Comparing the parent function with the given function, we can see that 5 has been subtracted from the x-value of the parent function.

Therefore, the transformation is:

\(f(x-5) \implies f(x) \: \textsf{translated}\:5\:\textsf{units right}\)

Question 3

\(\textsf{Parent function}: \quad f(x)=x^3\)

\(\textsf{Given function}: \quad f(x)=x^3+5\)

Comparing the parent function with the given function, we can see that  5 has been added to the parent function.

Therefore, the transformation is:

\(f(x)+5 \implies f(x) \: \textsf{translated}\:5\:\textsf{units up}\)

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Answer:

1) Vertical shrink by a factor of 1/5

2) Right 5

3) Up 5

Explanation:

Given main function: f(x) = x³

1.) f(x) = 1/5 (x³)

Comparing with a(f(x)) which gives vertical stretch or compression.

Here the function f(x) has been shrinked vertically by a factor of 1/5

2.) f(x) = (x - 5)³

Comparing with f(x - c) which gives horizontal translation c units right.

Here the function f(x) has been shifted 5 units to the right.

3.) f(x)= x³ + 5​

Comparing it with f(x) + d which gives vertical translation d units up.

Here the function f(x) has been moved 5 units up.

Answer:

8/27

Explanation:

First, determine the common ratio of the geometric sequence:

The nth term of any geometric sequence is obtained using the formula:

Thus, the 8th term will be:

The exact value of the eighth term of the geometric sequence is 8/27.

As per the matrix, the three linearly independent eigenvectors are 0, 0.05 and 1.

Now let's consider the given matrix A. We are asked to find three linearly independent eigenvectors and their corresponding eigenvalues. Linearly independent eigenvectors are important because they allow us to represent any vector in the space as a linear combination of these eigenvectors.

The first eigenvector v1 is -1, and it corresponds to the eigenvalue λ1 = 0. To check if this is indeed an eigenvector, we multiply it by A and check if the resulting vector is a scalar multiple of v1. In this case, Av1 = 0v1, which means that v1 is indeed an eigenvector with eigenvalue λ1 = 0.

The second eigenvector v2 is also -1, and it corresponds to the eigenvalue λ2 = 0. Again, we multiply it by A and check if the resulting vector is a scalar multiple of v2. Av2 = 0v2, which means that v2 is an eigenvector with eigenvalue λ2 = 0.

The third eigenvector v3 is 0, and it corresponds to the eigenvalue λ3 = 1. We repeat the same process and check if Av3 is a scalar multiple of v3. In this case, Av3 = 0.05v3, which satisfies the given condition of having all entries with absolute value smaller than 0.05. Therefore, v3 is an eigenvector with eigenvalue λ3 = 1.

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