A 11 foot ladder is placed against a building. If the base of the ladder is 7 feet away from the building, how far up the building will the ladder reach? Round the answer to the nearest tenth.

The three consecutive multiples of 3 are 15, 18 and 21

First, let's determine three successive multiples of 3:

The subsequent two would be "x+3" and "x+6" if we call the initial number "x".

Since we are aware that the third number (x+6) is one more than the first two numbers (x + x+3), we can write the following equation:

2/3(x + x+3) = (x+6) + 1

Simplifying this equation, we get:

2/3(2x+3) = x+7

Multiplying both sides by 3, we get:

2(2x+3) = 3(x+7)

Expanding and simplifying, we get:

4x + 6 = 3x + 21

Subtracting 3x and 6 from both sides, we get:

x = 15

Therefore, the three consecutive multiples of 3 are 15, 18 and 21

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Answer:

B; There is only one (x,y) solution and y is negative

Step-by-step explanation:

First, I graphed the two equations. Attached is an image of the equations graphed. Next, I looked for overlapping points. Wherever the two points overlap, there is a solution. When looking at the graph, we can see the lines overlap at only one point, (0,-1). Since y is negative, the answer must be B; there is only one (x,y) solution and y is negative.

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answer: the range is 41.

to find the range of this data set, we first need to find the minimum and maximum values - which are 59 and 100.

then we subtract the minimum from the maximum.

59 - 100 = 41.

Answer: First, calculate the total value of the shares after the price fall to $80:

value = 200 shares * $80/share = $16,000

Then, calculate the amount of money borrowed:

borrowed = $14,000 / (1 - margin requirement)

= $14,000 / (1 - 0.20)

= $14,000 / 0.80

= $17,500

Finally, calculate the percentage return on investment:

return = (value - borrowed) / borrowed * 100%

= ($16,000 - $17,500) / $17,500 * 100%

= -6.06%

The return on investment is -6.06%, meaning that the investment lost 6.06% of its value.

Step-by-step explanation:

As per the error function, \(\int e^{-5t^2} dt\) is a erf(bx) | = 0

To illustrate this concept, let us consider the integral ∫ e^(-5t²) dt with limits of integration from 0 to x. We can rewrite this integral in terms of the error function by making the substitution u = √5t, which gives us du/dt = √5 and dt = du/√5. Thus, the integral becomes ∫ (e^-u²) (du/√5), with limits of integration from 0 to √(5x²).

Next, we can express the integrand as e^(-u²) = (2/√π) ∫ e^(-v²) dv, which follows from the standard result that ∫ e^(-x²) dx = √π/2. Substituting this expression into our integral, we obtain:

∫ (e^-u²) (du/√5) = (2/√(5π)) ∫ ∫ e^(-v²) du dv,

with limits of integration from 0 to √5x and 0 to u, respectively. Interchanging the order of integration, we get:

∫ (e^-u²) (du/√5) = (2/√(5π)) ∫ ∫ e^(-v²) dv du

= (2/√(5π)) ∫ e^(-v²) (u=0 to u=√5x) dv

= (2/√π) ∫ e^(-5x²) dx.

Therefore, we have shown that the integral ∫ e^(-5t²) dt with limits of integration from 0 to x can be expressed as:

| (2/√π) ∫ e^(-5x²) dx = a erf(bx) |,

where a = √(2/π) and b = 1/√5. Here, erf(bx) denotes the error function evaluated at the argument bx.

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The sum of angles in a triangle is givento be 180 degrees.

This means that:

We're given the values of y and z in the question. We can substitute these into the equation above:

We can solve it as shown below:

ANSWER

Six (6) confidence intervals or hypothesis tests would need to be done to make significant statements for each pair-wise comparison.

In an ANOVA F test, the null hypothesis is that the means of all the treatments are equal, and the alternative hypothesis is that at least two of the means are different. If the null hypothesis is rejected at the 5% significance level, this means that the differences between the means are statistically significant and the treatments can be considered different.

Since there are four treatments, there are 6 possible pairs of treatments. These tests would determine whether the means of each pair of treatments are significantly different from each other.

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Answer:

B

Step-by-step explanation:

By using the fraction strip, if you think about it:

Pretend to color in 5/6 on the yellow side, and do the same to the 1/12 part, instead pretend to shade in 5/12. If you see how much remaining you have, you get 5/12.

Answer:

37

Step-by-step explanation:

Before we find quartile, we have to arrange the data set in order first from least to greatest which this problem has already arranged the data for us.

Next, proceed with the calculation. The formula for finding position of quartile is:

\(\displaystyle{Q_r = \dfrac{r(N+1)}{4}}\)

Where \(\displaystyle{Q_r}\) means the rth quartile, N means number of data set. Since we want to find the third quartile, substitute r = 3 and there are 11 data so substitute N = 11:

\(\displaystyle{Q_3 = \dfrac{3(11+1)}{4}}\\\\\displaystyle{Q_3 = \dfrac{3(12)}{4}}\\\\\displaystyle{Q_3 = 3\cdot 3}\\\\\displaystyle{Q_3 = 9}\)

So the position of third quartile is at 9th position which is 37.

Henceforth, the third quartile is 37.

Answer:

37.

Step-by-step explanation:

The data is in ascending order, which is what we need to get the answer.

As there are 11 numbers the 9th number is the upper(third)  quartile.

The median ( middle) number is 29 and the upper quartile is the middle number of the 5 numbers to the right of the median.

It is 37.

Answer:

number is 5

Step-by-step explanation:

let the number be n, then

30 subtracted from 14 times the number is

14n - 30

the result is 20 more than 4 times the number, that is

4n + 20

the equation is then

14n - 30 = 4n + 20 ( subtract 4n from both sides )

10n - 30 = 20 ( add 30 to both sides )

10n = 50 ( divide both sides by 10 )

n = 5

the number is then 5

The value of the car after 3 years is $79, 000

To determine the value, we have to use the formula;

Value = Initial value × (1 - Depreciation rate)ⁿ

Substitute the values given, we get;

Remaining value after 3 years = $100,000 × (1 - 0.10)³

Expand the bracket, we get;

Value after 3 years = $100,000 × (0.90)³

Find the cube value and substitute, we have;

Value after 3 years = $100,000 × 0.729

Multiply the values, we have;

Value after 3 years = $72,900

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To be able to verify the statement, let's first recall the formula in getting the area of a rectangle:

Answer:

approximately 28.26 square feet

Step-by-step explanation:

The formula for the area of a circle is A = pi(r)^2. So, the radius is half of the diameter, meaning it's 3 feet. Then we square it to get 9, and multiply by pi, or 3.14. This leads us to the approximated answer of 28.26 square feet.

The area is:

28.27 square feet

Work/explanation:

Since the tabletop is circular, we use the formula for a circle's area, which is: \(\bf{A=\pi r^2}\).

We have the diameter, and to find the radius, we divide the diameter by 2, which gives us 6 ÷ 2 = 3 feet, so the radius of the tabletop is 3 feet.

Now, here's a diagram for you;

\(\setlength{\unitlength}{1cm}\begin{picture}(0,0)\thicklines\qbezier(2.3,0)(2.121,2.121)(0,2.3)\qbezier(-2.3,0)(-2.121,2.121)(0,2.3)\qbezier(-2.3,0)(-2.121,-2.121)(0,-2.3)\qbezier(2.3,0)(2.121,-2.121)(-0,-2.3)\put(0,0){\line(1,0){2.3}}\put(0.5,0.3){\bf\large 3\ ft}\end{picture}\)

Plug in the data:

\(\sf{A=\pi\times3^2}\)

\(\sf{A=\pi\times9}\)

\(\sf{A=28.27\:ft^2}\)

Answer:

12x+y

Step-by-step explanation:

12 times a number x

12x

Plus y

12x+y

Answer:

its B

Step-by-step explanation:

Answer:

n = -3

Step-by-step explanation:

slope = 10 = (7 - n) / (9 - 8) = (7 - n) / 1

7 - n = 10

-n = 10 - 7 = 3

n = 3/-1 = -3

The corner shop has 15 cartons of 600 mL milk.

Let the number of milk cartons be y.

The number of bottles of milk is double the number of cartons of milk.

Now,

There are 84 liters of milk in total.

The shop has an equal number of 1 liter and 600mL cartons of milk and doubles the number of 2-liter bottles.

Therefore, the equation for the total liter of milk will be:

y × 600mL + y × 1 L + 2y × 2 L = 84 L

y × 0.6 L + y × 1 L + 2y × 2 L = 84 L

0.6y + y + 4y = 84

5.6y = 84

Dividing each side of the equation by 5.6,

( 5.6y/ 5.6 ) = ( 84/ 5.6 )

y = 15

Therefore, there are 15 cartons of milk of 600 mL.

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Answer:

Surface Area

Step-by-step explanation:

You are calculating the measurements for the surface of the prism. The interior is volume.

Answer:

Surface Area

Step-by-step explanation:

Answer:

SNSPEUE is the

code

The volume of the given cylinder is 84.8 cm³.

Given: Radius of cylinder, r = 3cm Height of cylinder, h = 3cm

Formula used: Volume of cylinder = πr²hπ is a constant and is approximately equal to 3.14.

Volume of cylinder = πr²h= 3.14 x 3² x 3= 84.78 cm³ (rounded to the nearest tenth)= 84.8 cm³

Therefore, the volume of the given cylinder is 84.8 cm³.

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Answer:

tan(F)

Step-by-step explanation:

This is an isoceles triangle, both sides are the same so both the angles are the same as well. The sine and cosine of angles D and F are going to be the exact same because of the same sides. The only one that would be different would be the tangent of F or D.

The question is an illustration of an isosceles right triangle

The function that is not equal to cos(F) is tan(F)

From the figure, we can see that the triangle is an isosceles right triangle

This means that:

cos(F) = sin(F) = cos(D) = sin(D)

The odd option from the list of given option is tan(F)

Hence, the function that is not equal to cos(F) is tan(F)

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Using the information in the given diagram, the value of the missing angle is: m∠1 = 75°

The transverse line theorem states that If two parallel lines are cut by a transversal, then corresponding angles are congruent. Two lines cut by a transversal are parallel IF AND ONLY IF corresponding angles are congruent.

Now, when we draw a horizontal line parallel to lines a and b and directly cutting across the vertex of angle 1, we can see that angle 1 will be composed of two angles.

Now, for the transverse line theorem we can say that:

Angle 1 will be composed of two angles namely:

48 degrees and (180 - 153) degrees.

Thus:

m∠1 = 48° + 27°

m∠1 = 75°

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Answer:

36

Step-by-step explanation:

36 u think you need to multiply it by 2

Answer:

495

Step-by-step explanation:

using the definition

n\(C_{r}\) = \(\frac{n!}{r!(n-r)!}\)

where n! = n(n - 1)(n - 2) ... × 3 × 2 × 1

then

12\(C_{4}\)

= \(\frac{12!}{4!(12-4)!}\)

= \(\frac{12!}{4!(8!)}\)

cancel 8! on numerator/ denominator

= \(\frac{12(11)(10)(9)}{4!}\)

= \(\frac{11880}{4(3)(2)(1)}\)

= \(\frac{11880}{24}\)

= 495

The symbolic representation for the argument is that Jeri drew a polygon with exactly three sides will be : Δ ABC has been drawn.

A polygon is a plane figure with at least three straight sides and angles, typically five or more.

In this case, the symbolic representation for this argument is that Jeri drew a polygon with exactly three sides.

That is Δ ABC has been drawn.

Therefore, the symbolic representation for the argument is that Jeri drew a polygon with exactly three sides will be : Δ ABC has been drawn.

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Using the expected value, it is found that the mean of the distribution equals $0.1.

The probabilities of each outcome are:

Thus, the mean is given by:

\(E(Y) = 0.0000001(1000000) + 0.9999999(0) = 0.1\)

Thus showing that the expected value is $0.1.

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