Sylvia designed a frame for a rectangular garden plot to put in her backyard. The design, along with its outer dimensions,Garden Plot Frame911in.Sylvia has several wooden boards she will use to make the frame. Each board is 12 feet long, 6 inches wide, and 2 inches thick. Based on the design, what is the minimumnumber of boards Sylvia will need, and how many feet of the boards will remain after she makes the frame?O She needs 4 boards and will have 6 feet left overShe needs 4 boards and will have 10 feet left overShe needs 6 boards and will have 30 feet left over.O She needs 6 boards and will have 34 feet left over

Altitude is in a polygon, a perpendicular segment from a vertex to the opposite side or to the line containing the opposite side.

In geometry, the hypotenuse is the longest side of a right-angled triangle, opposite to the right angle. It is also the side that connects the two other sides, which are called the adjacent and opposite sides.

One of the key properties of the geometric mean is that it is always less than or equal to the arithmetic mean (the regular average) of the same set of numbers, except when all the numbers are equal.

The geometric mean is used in various fields such as finance, economics, biology, and physics. It is particularly useful in situations where values are subject to compounding or exponential growth, and where small changes in values can have a significant impact over time.

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Answer:

if x=4, the answer is -2.

Step-by-step explanation:

4x3-(3+4)2

12-7x2

12-14

= -2

i hope this helps :)

Hey there!

Anything powered to the 1st is that number….. just like anything powered the zero is 0.

Anyway, let’s answer your question.

14^1

= 14 * 1

= 14

Therefore, your answer should be:

14

Good luck on your assignment & enjoy your day!

~Amphitrite1040:)

Answer:

14

Powers in math are exponents that raise a given value to its power. As a simple rundown, when you raise something to an exponent, you are multiplying that value by itself as many times as the exponent declares.

For instance, if you were to raise 2 to the 2nd power (2²), this would mean that you are multiplying 2 two times: \(2\times2=4\)

To solve, raise 14 to the 1st power:

\(14^1 = 14 \times 1\)

\(14\)

The final answer is 14.

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Answer:

\(\displaystyle g=\frac{4\pi^2l}{T^2}\)

Step-by-step explanation:

Equation Solving

Given the equation

\(\displaystyle l=\frac{gT^2}{4\pi^2}\)

It's required to solve it for g. Let's swap sides of the equation:

\(\displaystyle \frac{gT^2}{4\pi^2}=l\)

Multiply by \(4\pi^2\) to remove the denominator:

\(\displaystyle gT^2=4\pi^2l\)

Divide by \(T^2\)

\(\boxed{\displaystyle g=\frac{4\pi^2l}{T^2}}\)

Answer:

16.86 ft/s

Step-by-step explanation:

Given that,

Angular speed of a carousel, \(\omega=14\ rev/min\)

The diameter of the carousel, d = 23 feet

We need to find the speed of the carousel and jump on.

\(\omega=14\ rev/min=1.46\ rad/s\)

Radius, r = 11.5 feet

Let v is the velocity. So,

\(v=r\omega\\\\=11.5\times 1.46\\\\=16.79\ ft/s\)

Hernce, the correct option is (d) "16.86 ft/s"

Answer: 0.8

Step-by-step explanation:

The formula to find area of a parallelogram is A = bh. This means that area = base x height. You can manipulate this formula to what height equals instead of the area. To do that, you can divide b on both sides. This would make the equation h = A/b.

Now that you know how to find what height equals, first find the base of the parallelogram. To find b, multiply 6 x 5. 6 x 5 = 30. This means that your base is 30.

Take the information given to you in the problem about the area. The area is given to you. We know that the area is 24 squared units. Remember what the equation to find height is. It's h = A/b. Substitute the variables for your numbers. h = 24/30.

24/30 = 0.8.

This means that your height is 0.8. This would be 8/10 in fraction form, but you can simplify it further to 4/5.

Hope it helps. Good luck!

The conclusion is option A, we cannot reject the null hypothesis.

An assumption or concept is given as a hypothesis for the purpose of debating it and testing if it might be true.

The null hypothesis cannot  be rejected for the entire population if your sample is not sufficiently incompatible with it, which can be determined if your P value is small enough.

Therefore, we can not reject the hypothesis.

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Answer:

Yea i definitly just lost brain cells

Step-by-step explanation:

Answer:

0

Step-by-step explanation:

x < 4 means all numbers less than 4, excluding 4 itself.

4.5 > 4.

5 > 4.

so 0 is the solution

Answer:

4

Step-by-step explanation:

interval notation ( negative infinity, 4)

Answer:

numero uno, ok

Step-by-step explanation:

Answer:

The triangles are similar.

Explanation:

Similar triangles have 3 pairs of congruent angles. In this diagram, we can see that the triangles WXP and WYZ share angle W, which is congruent to itself; therefore, they have at least 1 pair of congruent angles. We are given that angle X is congruent to angle Y, so that is a second pair of congruent angles. Finally, we know that angle P is congruent to angle Z because if two pairs of corresponding angles are congruent, then the third pair must also be congruent because the measures of the interior angles of both triangles have to add to 180°.

Answer:

26/52 or 1/2

Step-by-step explanation:

There are 13 cards per suit therefore there must be 26

Answer:

Step-by-step explanation:

13/52

Answer: 6.8622 ; 8.1778

Step-by-step explanation:

Given the data:

2 6 7 8 9 9 9 10 10 10 10 9 4 5 6 6 8 7 9 10 9

6 5 7 6 8 4 2 10 9 9 10 10 9 8 7 5 9 9 3 6 2 9

7 10 7 9 9 9 9

Assume a confidence interval of 95%

Using calculator :

The mean of the distribution (m) = 7.52

Standard deviation (s) = 2.314

Sample size),

Obtaining the t score ;

Degree of freedom (df) = (n-1) = 50 - 1 = 49

t(1-α/2), 49 = t(0.025, 49) = 2.01 ( t distribution table)

Margin of Error :

2.01 * s/√n = 2.01 * 2.314/7.0710678

Margin of Error (E) = 0.6578

Confidence interval:

(Mean - E) ≤μ≤ (mean + E)

(7.52 - 0.6578) ≤μ≤ (7.52 + 0.6578)

6.8622 ≤μ≤ 8.1778

The greatest distance, in feet, a person could be from the lamp and be detected is: B. 12 ft

The equation (x+16)² + (y-13)² = 36 describes a circle with center (-16,13) and radius 6. The motion detector on the lamp post can detect motion within this circle.

To find the greatest distance a person could be from the lamp and still be detected, we need to find the diameter of the circle, which is equal to twice the radius. Therefore, the greatest distance a person could be from the lamp and still be detected is 2(6) = 12 feet.

Therefore, the correct answer is B) 12 ft.

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The volume of the sphere is approximately 3431.82 cubic miles.

To find the volume of a sphere, we need the radius of the sphere. The length of a great circle is the circumference of the sphere, which is related to the radius by the formula C = 2πr, where C is the circumference and r is the radius.

In this case, we are given that the length of the great circle is 60 miles. We can use this information to find the radius of the sphere.

C = 2πr

60 = 2πr

Divide both sides of the equation by 2π:

r = 60 / (2π)

r = 30 / π

Now that we have the radius, we can use the formula for the volume of a sphere:

V = (4/3)πr³

V = (4/3)π(30/π)³

V = (4/3)π(27000/π³)

V = (4/3)π(27000/π³)

V = (4/3)π(27000/π³)

V = (4/3)(27000/π²)

V = (4/3)(27000/9.87) (approximating π to 3.14)

V ≈ 3431.82 cubic miles

Therefore, the volume of the sphere is approximately 3431.82 cubic miles.

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Question

You are given the great circle of a sphere is a length of 60 miles. What is the volume of the sphere?

Step-by-step explanation:

35:12

40:17

45:22

50:27

55:32

The value of df, when x = π/4 and dx = 1/24, is (-5π - 5√2)/(96√2).

To find the derivative of the function f(x) = -5cos(x) + xtan(x), we'll use the sum and product rules of differentiation. Let's start by finding df/dx.

Apply the product rule:

Let u(x) = -5cos(x) and v(x) = xtan(x).

Then, the product rule states that (uv)' = u'v + uv'.

Derivative of u(x):

u'(x) = d/dx[-5cos(x)] = -5 * d/dx[cos(x)] = 5sin(x) [Using the chain rule]

Derivative of v(x):

v'(x) = d/dx[xtan(x)] = x * d/dx[tan(x)] + tan(x) * d/dx[x] [Using the product rule]

= x * sec^2(x) + tan(x) [Using the derivative of tan(x) = sec^2(x)]

Applying the product rule:

(uv)' = (5sin(x))(xtan(x)) + (-5cos(x))(x * sec^2(x) + tan(x))

= 5xsin(x)tan(x) - 5xcos(x)sec^2(x) - 5cos(x)tan(x)

Simplify the expression:

df/dx = 5xsin(x)tan(x) - 5xcos(x)sec^2(x) - 5cos(x)tan(x)

Now, we need to evaluate df/dx at x = π/4 and dx = 1/24.

Substitute x = π/4 into the derivative expression:

df/dx = 5(π/4)sin(π/4)tan(π/4) - 5(π/4)cos(π/4)sec^2(π/4) - 5cos(π/4)tan(π/4)

Simplify the trigonometric values:

sin(π/4) = cos(π/4) = 1/√2

tan(π/4) = 1

sec(π/4) = √2

Substituting these values:

df/dx = 5(π/4)(1/√2)(1)(1) - 5(π/4)(1/√2)(√2)^2 - 5(1/√2)(1)

Simplifying further:

df/dx = 5(π/4)(1/√2) - 5(π/4)(1/√2)(2) - 5(1/√2)

= (5π/4√2) - (10π/4√2) - (5/√2)

= (5π - 10π - 5√2)/(4√2)

= (-5π - 5√2)/(4√2)

= (-5π - 5√2)/(4√2)

Now, to evaluate df/dx when dx = 1/24, we'll multiply the derivative by the given value:

df = (-5π - 5√2)/(4√2) * (1/24)

= (-5π - 5√2)/(96√2)

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Answer:

84 she will give 84

Step-by-step explanation:

the first thing you need to do is put 2184 in to a chart for dividing then just divide until you get the product your looking for in this problem the answer would be 84

Answer:

28°

Step-by-step explanation:

x+85°+67°=180°(being sum of all interior angle of triangle)

x+152°=180°

x=180°-152°

x=28°

Answer:

where is the figure or picture

The median of the given data set is 26.

In statistics and probability theory, the median is the value separating the higher half from the lower half of a data sample, a population, or a probability distribution. For a data set, it may be thought of as "the middle" value.

Given the data set, we need to find the median.

So, let's arrange the numbers from smallest to largest in order to find the median.

\(\sf 15,20,22,26,28,35,36.\)

\(\text{Median}=\sf 26\)

Therefore, the median of the data set is 26.

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Answer:

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

Find the difference of the initial and used amounts:

The domain of the relation of the graph representing a relation where x represents the independent variable and y represents the dependent variable is {−4, −2, 0, 3, 5}.

The domain of a relation is the set of all possible input values (independent variable) for which the relation is defined.

Looking at the given points, the x-coordinates are -4, -2, 0, 3, and 5. So, the possible input values are -4, -2, 0, 3, and 5.

Therefore, the domain of the relation is {−4, −2, 0, 3, 5}.

Hence, the correct option is {−4, −2, 0, 3, 5}.

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Answer:

Step-by-step explanation:

y - 3 = -(x + 2)

y - 3 = -x - 2

y = -x + 1

The functions for this problem are classified as follows:

a) q(x) is an odd function.

b) r(x) is an even function.

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Answer:

14xz+2x−22y+5z

Step-by-step explanation:

Combine like terms

Answer:

(4, 1 )

Step-by-step explanation:

Given the 2 equations

2x + 3y = 11 → (1)

x - 3y = 1 → (2)

Adding (1) and (2) term by term will eliminate the term in y

3x = 12 ( divide both sides by 3 )

x = 4

Substitute x = 4 into either of the 2 equations and evaluate for y

Substituting into (1)

2(4) + 3y = 11

8 + 3y = 11 ( subtract 8 from both sides )

3y = 3 ( divide both sides by 3 )

y = 1

Solution is (4, 1 )

Answer:

Step-by-step explanation:

For step explanation:

1. write the problem

2. distinguishing the neg sign

3. distributing 3

4. moving like terms next to each other through commutative property

5.  Combining like terms

6. getting rid of parentheses