a 20-foot ladder leaning against a wall makes a 60 degree angle with the ground. What is the distance between the bottom of the ladder and the base of the wall?
A) 9.3 ft
B) 10 ft
C) 12.4 ft
D) 14 ft
Help please, doing a test rn

The value of an excel formula that will square this number is,

⇒ N²

We have to given that;

A number is stored in cell a1.

Hence, We can formulate;

Type = N² into the empty cell, in which N is a cell reference that contains the numeric value you want to square.

And, We also get;

To display the square of the value in cell A1 into cell B1,

We can type = A1² into cell B1.

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Answer:

The answer is above. Numbers 2 and 3

Negative 4 , negative 6 , negative 8 , negative 10.

An integer is a whole number that can be either positive, negative, or zero. It is not a fraction, decimal, or a percentage. Integers are the basic building blocks of mathematics and are used to represent whole numbers in equations. They are also used in computer programming languages to represent whole numbers.

negative 4 , negative 3 , negative 2 , negative 1,

−4, −5, −6, −7

negative 4 , negative 5 , negative 6 , negative 7,

−4, −2, 0, 2

negative 4 , negative 2 , 0, 2,

−4, −6, −8, −10

negative 4 , negative 6 , negative 8 , negative 10.
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Answer:

6

Step-by-step explanation:

\((3\sqrt{2}) ^{2} + (3\sqrt{2}) ^{2} = 18 + 18 = 36\\\sqrt{36} = 6\)

Answer:

Yes

Step-by-step explanation:

She had more than me

I would help her but she has less than me

The gradient of the curve at point A to 1 is 0.4. The slope of tangent is equivalent to the slope of the curve.

The tangent line to a curve at a point in geometry is the straight line that best approximates (or "clings to") the curve at that point. As the second point approaches the first, it may be considered the limiting position of straight lines passing through the given point and a nearby point of the curve.

The tangent cuts the curve at A.

The coordinate of A is (8,3). The tangent passes through the point (1,0.2).

The slope of the points (x₁, y₁) and (x₂, y₂) is [(y₂ - y₁)/(x₂ - x₁)

The slope of the tangent is (0.2-3)/(1-8) = 0.4.

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Answer:

3/8

Step-by-step explanation:

Answer:

C: 3/8

Step-by-step explanation:

edg2021

There are a total of 16 outcomes, and 6 of them have equal heads and tails. Simplify and its 3/8

The probability that Robert takes one white and one purple sticker is 3/40.

We have,

To calculate the probability of Robert taking one white and one purple sticker, we can use the multiplication rule of probability.

The probability of taking a white sticker from pack A = 6/10.

The probability of taking a purple sticker from pack B = 3/12.

Since the two events are independent, we can multiply these probabilities to get:

P(white from A and purple from B) = (6/10) x (3/12) = 9/120

Simplifying this fraction gives:

P(white and purple) = 3/40

Therefore,

The probability that Robert takes one white and one purple sticker is 3/40.

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A simple linear regression model is appropriate when the response variable is influenced by only one explanatory variable.

A simple linear regression model assumes a linear relationship between the response variable (y) and a single explanatory variable (x).

It is suitable when we want to understand how changes in the explanatory variable affect the response variable.

In the given options, the situation where the response variable y is influenced by one explanatory variable aligns with the requirements of a simple linear regression model.

This means that the relationship between y and x can be adequately described by a straight line.

The model aims to estimate the slope and intercept of this line, allowing us to make predictions and draw conclusions about the impact of the explanatory variable on the response variable.

If the response variable y is influenced by two or more explanatory variables, a multiple linear regression model would be more appropriate.

Multiple linear regression allows for the analysis of the combined effects of multiple predictors on the response variable, accounting for their individual contributions.

Similarly, if the explanatory variable x is influenced by two or more response variables, a different modeling technique, such as multivariate regression, would be more suitable.

Therefore, the situation where the response variable y is influenced by one explanatory variable is the scenario where a simple linear regression model is appropriate.

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The equation of the line tangent to the graph of y = cos(x) at x = π/2 is y = -x + π/2. The correct option is C. y = -x + π/2.

To find the equation of the line tangent to the graph of y = cos(x) at x = π/2, we need to find the derivative of the function and evaluate it at x = π/2. The derivative of y = cos(x) is given by dy/dx = -sin(x).

Now, let's evaluate the derivative at x = π/2:

dy/dx = -sin(π/2) = -1

The derivative gives us the slope of the tangent line at x = π/2. Therefore, the slope of the tangent line is -1.

Now, we have the slope of the tangent line and the point (π/2, cos(π/2)) on the line. Using the point-slope form of a line, y - y1 = m(x - x1), where (x1, y1) is a point on the line, we can write the equation of the tangent line:

y - cos(π/2) = -1(x - π/2)

Since cos(π/2) = 0, the equation simplifies to:

y = -x + π/2

Therefore, the equation of the line tangent to the graph of y = cos(x) at x = π/2 is y = -x + π/2.

Hence, the correct option is C. y = -x + π/2.

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Solving for Cartesian product n(B), we have n(B) = 72 / 24 = 3.

The Cartesian product is a mathematical operation that takes two sets and produces a set of all possible ordered pairs of elements from both sets.

In other words, if A and B are two sets, their Cartesian product (written as A × B) is the set of all possible ordered pairs (a, b) where a is an element of A and b is an element of B.

For example, if A = {1, 2} and B = {3, 4}, then A × B = {(1, 3), (1, 4), (2, 3), (2, 4)}.

By the question.

We know that n (Ax B) represents the number of elements in the set obtained by taking the Cartesian product of sets A and B.

Using the formula for the size of the Cartesian product, we have:

n (Ax B) = n(A) x n(B)

Substituting the given values, we get: 72 = 24 x n(B)

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Answer:

12,342,000,065

Step-by-step explanation:

yeah-ya

The answer is 24π/35 or 2.15 cubic units.

Lets solve this

The solid obtained by rotating the region bounded by y = x^2 and y = 1 about y = 6

To find the volume of the solid, we can use the method of cylindrical shells.

Let's split the region into vertical strips of thickness dx .

The radius of each cylindrical shell is given by the distance between y = 6 and the curve y = x^2.

This distance is given by r = 6 - x^2.

The height of each cylindrical shell is given by the difference between the curves y = 1 and y = x^2.

This difference is given by h = 1 - x^2.

Therefore, the volume of each cylindrical shell is given by:

dV = 2πrh

dx= 2π(6 - x^2)(1 - x^2) dx

To find the total volume of the solid, we need to integrate this expression over the range of x from 0 to 1.

Therefore, the volume of the solid is given by:

V = ∫dV = ∫₀¹ 2π(6 - x²)(1 - x²) dx= 2π ∫₀¹ (6x² - 8x⁴ + 2x⁶) dx= 2π [2x³ - (8/5)x⁵ + (2/7)x⁷]₀¹= 2π [2 - (8/5) + (2/7)] = 24π/35

Therefore, the volume of the solid obtained by rotating the region bounded by y = x^2 and y = 1 about y = 6 is 24π/35 cubic units.

Answer: Volume of the solid is 24π/35 or 2.15 cubic units.

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 To find the x-intercept using the straight-line equation, substitute y=0 and solve for x. To find the y-intercept, substitute x=0 and solve for y.

The equation of a straight line is

y=mx+c

is the gradient and

c

is the height at which the line crosses the y-axis, also known as the y-intercept.

The gradient m is the slope of the line - the amount by which the ycoordinate increases in proportion to the x-coordinate. If you have two points (x1,y1) and (x2,y2) on the line, the gradient ism=y2−y1x2−x1

, we must first work out the gradient using the gradient formula above, and then choose either point to substitute into the straight line equation with this gradient.

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The answers would be z + w = -2 + 3i, z - w = 4 - 7i, and w - z = 4 + 7i after adding and subtracting two complex numbers.

It is defined as the number which can be written as x+iy where x is the real number or real part of the complex number and y is the imaginary part of the complex number and i is the iota which is nothing but a square root of -1.

It is given that:

The complex numbers are:

z = 1 - 2i and w = -3 + 5i

z + w = 1 - 2i - 3 + 5i

z + w = -2 + 3i

z - w = 1 - 2i + 3 - 5i

z - w = 4 - 7i

w - z = 4 + 7i

Thus, the answers would be z + w = -2 + 3i, z - w = 4 - 7i, and w - z = 4 + 7i after adding and subtracting two complex numbers.

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Answer:

3

4

7

Step-by-step explanation:

got it right on edge

The brightness of the Sun as viewed from a distance of 10 AU compared to its brightness on Earth can be determined using the inverse square law. The Sun would appear approximately 1/100th (or 0.01) as bright as it appears from Earth at this distance.

The inverse square law states that the brightness of a light source decreases as the square of the distance from the source increases. In this case, we are comparing the brightness of the Sun on Earth to its brightness when viewed from a distance of 10 AU (astronomical units). Since AU is a unit of distance used to measure distances within the solar system, 1 AU represents the average distance between the Earth and the Sun, approximately 93 million miles or 150 million kilometers.

Using the inverse square law, we can calculate the relative brightness. If we consider the distance from the Sun on Earth as d1 and the distance from the Sun at 10 AU as d2, the brightness ratio (B(d2)/B(d1)) is equal to (d1/d2)^2. Substituting the values, we find that the Sun would appear approximately 1/100th (or 0.01) as bright when viewed from a distance of 10 AU compared to its brightness on Earth. Therefore, the Sun would appear significantly dimmer when observed from such a distance in the solar system.

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The probability that the entire surface can be painted is 0.7486.

The probability formula is:

For instance, when we flip a coin, there are just two possible results:

Z score is given by:

From the Z table:

Therefore, the probability of painting the full surface is 0.7486.

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Answer:

22

Step-by-step explanation:

15+7=22

The value of x or the opposite side has a length of 76 units.

This type of question makes a right-angled triangle that can be solved by Pythagoras's theorem.

In a right-angled triangle, the sum of the squares of the smaller two sides of a right-angle triangle is equal to the square of the largest side.

Given, The larger triangle has hypotenuse (45 + 45) = 90 units and Base is

(24 + 24) = 48 units.

We know

H² = B² + X².

X² = H² - B².

X² = 8100 - 2304.

X² = 5796.

X = 76 units.

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The slope of the line shown in the graph is __2/3__

and the y-intercept of the line is __6___

The general linear equation is written as follows:

y = ax + b

Where a is the slope and b is the y-intercept.

On the graph we can see that the y-intercept is y = 6, then we can write the line as:

y = ax + 6

The line also passes through the point (-9, 0), replacing these values in the line we will get:

0 = a*-9 + 6

9a = 6

a = 6/9

a = 2/3

That is the slope.

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Answer

x=5 y=2

Step-by-step explanation:

Answer:

8th term = 61

Step-by-step explanation:

See attached image

To evaluate \(8^{\frac{2}{3} }\) first find the square of 8 and then take the cube root.

The way of representing huge numbers in terms of powers is known as an exponent. Exponent, then, is the number of times a number has been multiplied by itself.

Depending on the powers they possess, many rules of exponents are given.

Law of Multiplication: Exponents should be added while keeping the base constant when multiplying like bases.

Exponents should be multiplied while bases are kept constant when bases are raised by a power of two or more.

Division Rule: When dividing like bases, maintain the base constant and deduct the exponent of the denominator from the exponent of the numerator.

The given value can be written as:

\(8^{\frac{2}{3} } = \sqrt[3]{8^{2} }\)

Hence, to evaluate \(8^{\frac{2}{3} }\) first find the square of 8 and then take the cube root.

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Answer:

This is the answer

please give me a nice rating

The prooof that the parallelograms ABCD and FBCE are congruent is shown below

Given that

AE || BC, AB || DC and BF || CE

The above means that the above segments are parallel segments

Parallel sides of a parallelogram are equal

This means that

AB = DC and BF = CE

In quadrilateral FBCE, we have

FE = BC

In quadrilateral ABCD, we have

AD = BC

By substitution property, we have

AD = BC = FE

We have proved that two corresponding sides of the two parallelograms are congruent

This means that, the other sides must also be congruent

So, we have

AB = BF = DC = CE

Hence, the parallelograms are congruent

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The outer surface area of the ice coating on a spherical iron ball is decreasing at a rate of approximately 57.636 square centimeters per minute when the outer diameter (ball plus ice) is 146 cm.

To find the rate at which the outer surface area of the ice coating is decreasing, we need to use the concept of related rates. Let's denote the radius of the iron ball as "r" and the thickness of the ice coating as "h." The outer diameter of the ball plus ice is then given as 2r + 2h, which is equal to 146 cm in this case.

We know that the volume of the ice coating is equal to the volume of the spherical shell formed between the outer and inner surfaces of the ice coating. The volume of this shell can be expressed as V = 4/3π((r + h)^3 - r^3).

Since the ice melts at a rate of 39 ml/min, which is equivalent to 39 cm^3/min, we can differentiate the volume equation with respect to time to obtain dV/dt. This represents the rate at which the volume of the ice coating is changing.

To find the rate at which the outer surface area of the ice coating is decreasing, we need to find dA/dt, where A represents the outer surface area. We can relate dA/dt and dV/dt by using the formula for the surface area of a spherical shell: A = 4π(r + h)^2.

By substituting the given values into the equations and differentiating, we can solve for dA/dt. The resulting value will be approximately 57.636 square centimeters per minute, rounded to the nearest thousandth. This indicates the rate at which the outer surface area of the ice coating is decreasing when the outer diameter (ball plus ice) is 146 cm.

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We are given the expression:

We, simply replace the values of solution given and then determine in which it is not a solution, but we can see that when we replace x = 0, we will get:

So, this proves that the function is not an identity.

\(\qquad \qquad \textit{inverse proportional variation} \\\\ \textit{\underline{y} varies inversely with \underline{x}} ~\hspace{6em} \stackrel{\textit{constant of variation}}{y=\cfrac{\stackrel{\downarrow }{k}}{x}~\hfill } \\\\ \textit{\underline{x} varies inversely with }\underline{z^5} ~\hspace{5.5em} \stackrel{\textit{constant of variation}}{x=\cfrac{\stackrel{\downarrow }{k}}{z^5}~\hfill } \\\\[-0.35em] ~\dotfill\)

\(\stackrel{\textit{"y" varies inversely with }x^2}{y = \cfrac{k}{x^2}}\hspace{5em}\textit{we also know that} \begin{cases} x=4\\ y=\frac{11}{4} \end{cases} \\\\\\ \cfrac{11}{4}=\cfrac{k}{4^2}\implies \cfrac{11}{4}=\cfrac{k}{16}\implies \cfrac{(11)(16)}{4}=k\implies 44=k~\hfill \boxed{y=\cfrac{44}{x^2}} \\\\\\ \textit{when x=2, what's "y"?}\qquad y=\cfrac{44}{2^2}\implies y=\cfrac{44}{4}\implies y=11\)

Answer:

y = 11 when x = 2

Step-by-step explanation:

This is indirect proportionality where:

y ∝ \(\frac{1}{x^{2}}\)

This means:

\(y_{1} x_{1}^{2} = y_{2}x_{2}^{2}\)

Substitute the following values in the above equation to solve for \(y_{2}\)

\(y_{1} = \frac{11}{4}\)

\(y_{2} = ?\)

\(x_{1} = 4\)

\(x_{2} = 2\)

= \((\frac{11}{4})(4^{2}) = y_{2}(2^{2})\)

= \((\frac{11}{4})(16) = y_{2}(4)\)

= \(44 = 4y_{2}\)

= \(y_{2} =\frac{44}{4}\)

∴ y = 11

The probability that the last ball taken will be blue is 1.

This is because each time a ball is drawn, it is replaced by a blue one. Therefore, by the time the last ball is drawn, all of the balls in the bag will be blue.

To explain this further, let's look at the process step by step:

1. There are 8 blue and 2 red balls in the bag initially.
2. One ball is drawn and replaced by a blue one. Now there are 9 blue and 1 red ball in the bag.
3. Another ball is drawn and replaced by a blue one. Now there are 10 blue balls in the bag.
4. Since all of the balls in the bag are now blue, the probability of drawing a blue ball on the last draw is 1.

Therefore, the probability that the last ball taken will be blue is 1.

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Answer:

y=2x+4

Step-by-step explanation:

2 is the slope, you can see that with rise over run. 4 is the y intercept

Answer:

y=2x+4

Step-by-step explanation:

Look at the y-axis if the point that touches the y-axis is 4

Then the slope is 2

you go down 2 which is -2 (Since down is negative)

and you go left 1 which is -1 (Since left is negative)

now the equation looks like this:

y=-2/-1x+4

Simplify: (negative and negative cancel each other out making it positive)

y=2x+5