the top of a 13 foot ladder, leaning against a vertical wall, is slipping down the wall at the rate of 5 feet per second. how fast is the bottom of the ladder sliding along the ground away from the wall when the bottom of the ladder is 12 feet away from the base of the wall? answer: ft/s.

Answer:

92.14

Hope this helps!

Step-by-step explanation:

To find the area of the figure, you need to find the area of the rectangle and the semi-circle.

13 × 6 = 78, the area of the rectangle is 78.

The area of the semi-circle can be found using the formula \(\frac{\pi r^{2} }{2}\), the diameter is 6 so the radius is 3.

\(\frac{\pi 3^{2} }{2} =\frac{\pi 9}{2} =\frac{9\pi }{2} = \frac{28.27433...}{2} = 14.1371...\)

14.137 + 78 = 92.137 or 92.14.

To calculate the number of possibilities for the Almeida family ordering 3 specialty pizzas from the menu of 15 different options, the appropriate method to use is the combination formula.

The combination formula calculates the number of ways to choose a subset of items from a larger set without considering the order in which they are chosen. In this case, the Almeida family wants to order 3 pizzas out of 15 options, and the order in which they choose the pizzas does not matter.

The formula for combinations is given by:

C(n, r) = n! / (r! * (n - r)!)

where n is the total number of options, and r is the number of choices.

Therefore, the calculation for the number of possibilities for the Almeida family can be done using the combination formula as:

=C(15, 3) = 15! / (3! * (15 - 3)!)

= (15 * 14 * 13 * 12!) / (3! * 12!)

= (15 * 14 * 13) / (3 * 2 * 1)

= 455

the number of possibilities for the Almeida family  is 455.

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A scientific calculator is typically used for pre-calculus.

This type of calculator is designed to handle more advanced mathematical functions, such as trigonometry, logarithms, and exponents, which are commonly used in pre-calculus.

It is important to have a scientific calculator for pre-calculus because it allows you to easily solve more complex equations and perform calculations quickly and accurately.

Additionally, many scientific calculators have graphing capabilities, which can be useful for visualizing equations and understanding how they behave. Overall, a scientific calculator is an essential tool for pre-calculus and can help you succeed in the course.

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The variation between the sample means is small.

The variation between the sample means provides insight into the spread or dispersion of the data. In this case, if the variation between the sample means is small, it indicates that the mean name lengths across the seven samples are relatively similar and close together. This suggests that there is not much variability or difference in the average name lengths among the different samples of students. Therefore, the variation between the sample means is small, indicating a certain level of consistency in the mean name length across the samples.

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So the answer is 1.3 after rounding to 10.

The probability that the team wins the match is 1/9.

Here the odds against winning are given to be 8 to 1. It is also said that they lose more than they win.

The above statement indicates that out of every 8 + 1

= 9 matches, the team has a probability of losing 8 matches and winning one match

Probability

= no. of observations for the favorable event / Total number of observations

Here we need to find the probability of winning.

Let A be the event that the team wins the match.

As we can see the total number of observations is 9 matches.

Therefore, n = 9

n(A) = 1

Hence, P(A)

= n(A)/n

= 1/9

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There are 15 / 2 ways to distribute 11 identical candies between 4 children such that each child receives at least 2 candies.

If we give child A four candies and so we were left with 9 candies.

In addition, we will take child A away from consideration to ensure he received exactly four candies, and thus we were left with 9 dots and 2 slashes, separating the 4 remaining distinct children.

So the possible ways are:  (11 + 4 / 2) = (15 / 2).

Problem-solving is the act of defining a problem; determining the purpose of the trouble; figuring out, prioritizing, and selecting alternatives for an answer; and imposing a solution.

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Answer:

18%

Step-by-step explanation:

5500y=6500

y=6500/5500

y=1.18

1.18*100=118%

118%-100%=18%

nAnswer:

bStep-by-step explanation:

Answer:

its 5

Step-by-step explanation:

I know this because you just need to find the opposite integer and then that make s a zero pair and then you get 5

Answer:

Step-by-step explanation:

  Number               Estimate using a single digit and power of 10  

23,898,497                      2 × 10⁷          

0.000136                          1 × 10⁻⁴

26,857                              3 × 10⁴

0.0302                             3 × 10⁻²

Answer:

yes

Step-by-step explanation:

it was just rotated not dilated

The area of triangle ΔEFG changes after rotation and dilation.

The scale factor is a type of measurement which is used to increase or decrease the size of an object keeping its shape as the same. It can be determined by taking the ratio of the new and the original dimension of the object.

Suppose the scale factor is k for the dilation of triangle.

Now, new dimensions of ΔE'F'G' is k times the dimension of ΔEFG.

Area of triangle ΔEFG = 1/2 × b × h

Then, triangle area for ΔE'F'G' = 1/2 × kb × kh = k²(1/2 × b × h)

Thus, the area becomes k² times.

Hence, the given triangles ΔEFG and ΔE'F'G' do not have the same area.

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Step-by-step explanation:

(a)

100% = 450

1% = 100%/100 = 450/100 = 4.5

232 are his many % ? as many as 1% fit in :

232 / 4.5 = 51.55555555... % ≈ 51.56%

(b)

100% = 122

1% = 122/100 = 1.22

35 are

35 / 1.22 = 28.68852459... % ≈ 28.69%

Answer:

1 f

2 t

3f

4 t

hope its right

answer:

30 > 4x + 2 and 6 books

step-by-step explanation:

30 > 4x + 2

30 > 4x + 2

28 > 4x

7 > x

well, since the y-intercept is at -5, or namely when the line hits the y-axis is at -5, that's when x = 0, so the point is really (0 , -5), and we also know another point on the line, that is (-1 ,6), to get the equation of any straight line, we simply need two points off of it, so let's use those two

\(\stackrel{y-intercept}{(\stackrel{x_1}{0}~,~\stackrel{y_1}{-5})}\qquad (\stackrel{x_2}{-1}~,~\stackrel{y_2}{6}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{6}-\stackrel{y1}{(-5)}}}{\underset{run} {\underset{x_2}{-1}-\underset{x_1}{0}}} \implies \cfrac{6 +5}{-1} \implies \cfrac{ 11 }{ -1 } \implies - 11\)

\(\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-5)}=\stackrel{m}{- 11}(x-\stackrel{x_1}{0}) \implies y +5 = - 11 ( x -0) \\\\\\ y+5=-11x\implies {\Large \begin{array}{llll} y=-11x-5 \end{array}}\)

The domain for the given function is {-1, 2, 33, 32}.

A function's or relation's domain is the set of all possible independent values that the relation can take. It is the sum of all possible inputs.

A function's or relation's range is the set of all possible dependent values that the relation can produce from the domain values. It is the sum of all possible outputs.

When dealing with sets of ordered pairs, we simply divide the pairs into x- and y-coordinates. The domain is formed by the x-coordinates, which are independent values. The y-coordinates are the dependent values, i.e. they define the range.The domain in the set of ordered pairs {(a,b); (c,d); (e,f); (g,h)} is the set of the first number in each pair (those are the x-coordinates): {a,c,e,g}. The range is the set of all the pairs with the second number (the y-coordinates): {b,d,f,h}.

Given,

The set of ordered pair =   {(-1,5) , (2,3), (33,6), (32,7)}

then,

the Domain = {-1, 2, 33, 32}

Range = {5, 3, 6, 7}

Thus, the domain for the given function is {-1, 2, 33, 32}

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Answer:

what is the difference between 880 and 580

Answer:

x×2/5=3/20

x=3/8

this is your answer hope it will help you dear

\(\huge\boxed{\sf{Hello\:there!}}\)

How to Write the Word Sentence as an Equation?

That's easy!

Let's say the number is x.

x multiplied by \(\displaystyle\frac{2}{5}\) is \(\displaystyle\frac{3}{20}\)

\(\displaystyle\frac{2}{5} x=\frac{3}{20}\)

Notice that we write the number before the variable.

Now, let's solve.

Step number 1:

Divide both sides by \(\displaystyle\frac{2}{5}\).

Wait, how do we divide fractions?

\(\bigstar\) We take the fraction that we divide by and flop it over.

\(\bigstar\) Then, we multiply the first fraction times the one that we flopped over.

\(\displaystyle\frac{2}{5} x=\frac{3}{20} \\x=\displaystyle\frac{3}{20} :\frac{2}{5}\)

\(x=\displaystyle\frac{3}{20}*\frac{5}{2}\)

Now, all we have to do is multiply 3 by 5 and 20 by 2:

\(x=\displaystyle\frac{15}{40}\)

Simplify by dividing the numerator and the denominator by 5:

\(\displaystyle\frac{3}{8}\)

\(\huge\boxed{\sf{Answer:{\boxed{\bf{\frac{3}{8} }}}}}]\)

Hope it helps! Enjoy your day!

Feel free to ask if you have any doubts.

\(\star\star\) The crown would be greatly appreciated ;)

~Just a determined gal

\(\bf{erutaNtneliS\)

So the probability, rounded to the nearest thousandth, of getting at least 2 fours in 5 rolls of a fair die is 0.194.

A probability is a number that expresses the possibility or likelihood that a specific event will take place. Probabilities can be stated as proportions with a range of 0 to 1, or as percentages with a range of 0% to 100%.

The probability of getting at least 2 fours is the sum of the probabilities of getting exactly 2, 3, 4, or 5 fours:

P(X ≥ 2) = P(X=2) + P(X=3) + P(X=4) + P(X=5)

Using the binomial formula, we can calculate each of these probabilities:

P(X=k) = (n choose k) p^k (1-p)^(n-k)

where (n choose k) is the binomial coefficient, which represents the number of ways to choose k items from n distinct items.

P(X=2) = (5 choose 2) (1/6)² (5/6)³ = 0.1608

P(X=3) = (5 choose 3) (1/6)³ (5/6)² = 0.0322

P(X=4) = (5 choose 4) (1/6)⁴ (5/6)¹ = 0.0013

P(X=5) = (5 choose 5) (1/6)⁵ (5/6)⁰ = 0.00003

Therefore,

P(X ≥ 2) = 0.1608 + 0.0322 + 0.0013 + 0.00003 = 0.1943

So the probability, rounded to the nearest thousandth, of getting at least 2 fours in 5 rolls of a fair die is 0.194.

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Answer:

\(\displaystyle{P(x)=x^3-x^2}\)

Step-by-step explanation:

Given the zeros of 0, 0, 1. We can write the polynomial in form of x-intersects:

\(\displaystyle{P(x) = (x-x_1)(x-x_2)(x-x_3)}\)

Hence:

\(\displaystyle{P(x)=(x-0)(x-0)(x-1)}\)

Which can be simplified to:

\(\displaystyle{P(x)=x\cdot x \cdot (x-1)}\\\\\displaystyle{P(x)=x^2(x-1)}\)

Convert to the standard form by distributing x²:

\(\displaystyle{P(x)=x^2\cdot x - x^2 \cdot 1}\\\\\displaystyle{P(x)=x^3-x^2}\)

The wind chill at 20 mph is -5 degrees Fahrenheit.

Wind chill is the perceived decrease in air temperature felt by the body on exposed skin due to the flow of air. Wind chill is always lower than the actual air temperature and is most relevant in cold weather.

The wind chill is calculated by taking the temperature and wind speed into account. The formula for calculating wind chill is as follows:

Wind chill (W) = 35.74 + 0.6215T – 35.75(V^0.16) + 0.4275T(V^0.16)

Where T is the temperature in Fahrenheit, and V is the wind speed in miles per hour.

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The sampling distributions reach a normal distribution as sample sizes increase.

For the given statement in the question-

As sample sizes grow larger, sampling distributions reach a normal distribution.

The mean of the sampling distribution equals the population mean (µ) (with "infinite" numbers of the successive random samples).

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The production level that would minimize the average cost per item of making x items is x = 12

We have Cx = x3 - 24x2 + 30,000x

divide through the equation by x, this would give us

c = x² - 24x + 30,000

we have to take the first derivative of this

so we would have

2x - 24= 0

From the equation above we have

2x = 24

divide through by 2

x = 24/2

x = 12

The production level that would minimize the average cost per item of making x items is x = 12

Complete question

Suppose c(x) = x3 - 24x2 + 30,000x is the cost of manufacturing x items. Find a production level that will minimize the average cost per item of making x items.

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Answer:

-38 is an integer

Step-by-step explanation:

An integer is a whole-valued positive or negative number or 0. They are generated from the set of counting numbers 1, 2, 3,… and the operation of subtraction. So -38 is an integer.

hope this this helps

:)

Answer:

Probably 80* (* means degrees for me) i might be wrong

Step-by-step explanation:

So if m<1 = 50* and m<2 = 65, then there might be a pattern.

50 + 15 = 65. So if 65 + 15 = 80, then 80* MIGHT be the answer.

Answer:

f(3)= 12

Step-by-step explanation:

if f(1)= 4 then f(3)= 12

The patient is recieving nearly 35.5 miligrams of the drugs for  per kilogram per 24 hours.

First, we need to convert the child's weight from pounds to kilograms:

99 lbs / 2.205 = 44.9 kg

Next, we calculate the recommended dose for this weight:

40 mg/kg/24h x 44.9 kg = 1796 mg/24h

Since the recommended dose is divided into four equal doses, each dose should be:

1796 mg/24h ÷ 4 doses = 449 mg/dose

However, the physician ordered 400 mg every 6 hours, which is not the same as 449 mg every 6 hours. To calculate the actual dose per kilogram per 24 hours, we need to convert the ordered dose to the recommended dose:

400 mg/dose x 4 doses = 1600 mg/24h

Then, we divide the actual dose by the child's weight in kilograms:

1600 mg/24h ÷ 44.9 kg = 35.6 mg/kg/24h

Therefore, the patient is receiving 35.6 mg/kg/24h, which is slightly lower than the recommended dose of 40 mg/kg/24h.

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y=375+25x

not sure if this is correct