If a right triangle has a hypotenuse of length 20 units and one leg of length 16 units, find the length of the other leg. A. 12 B. 656 C. 384 D. 36

As the elevator climbs, the angle of depression to a certain spot on the lobby floor alters. Angle of depression increases.

the arc formed as the line of sight drops from the horizon. The angle of depression is the angle formed when an object is perceived below the observer's height between the horizon and the line of sight of the observer. The depression angle is the angle formed between the line of sight looking down at the object and the horizontal line of sight. If you are on a hill or a building and you are looking down at something, you can tell the slope. To measure these angles, a theodolite or an inclinometer might be employed.

As the elevator climbs, the angle of depression to a certain spot on the lobby floor alters. Angle of the depression increases.

∠x = 65° ≤ ∠XYZ

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If Natalie puts 4 pears in each bag, she will be able to sell a total of 12 bags of pears at the Saturday market.

To represent the number of bags of pears, b, that Natalie sells at the Saturday market, we can use the following equation:

b = total_number_of_pears / pears_per_bag

In this equation, "total_number_of_pears" represents the total quantity of pears Natalie has, and "pears_per_bag" represents the number of pears she puts in each bag.

Given that Natalie has a total of 48 pears, we can substitute the value into the equation:

b = 48 / pears_per_bag

Now, we need to determine the number of pears she puts in each bag. The information provided states that Natalie sells bags of pears, and each bag is sold for $5. However, the specific number of pears per bag is not given. To proceed, we need this information.

Let's assume that Natalie puts 4 pears in each bag. We can substitute this value into the equation:

b = 48 / 4

Simplifying the equation gives:

b = 12

So, if Natalie puts 4 pears in each bag, she will be able to sell a total of 12 bags of pears at the Saturday market.

It's important to note that the specific value of "pears_per_bag" will affect the final result. If Natalie puts a different number of pears in each bag, the equation will yield a different number of bags sold.

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Note that the probabilities are given below.

a) the probability of a randomly selected catch being a mouse caught by Cyd

p(Catching a mount) x p(Cyd made the catch)

= 0.5x .2

= 0.1

b) the   probability of a bird not caught by Cyd is 0.5 x 0.8 = 0.4.

Thus

P(that a catch is a bird) x p(the Cyd didn't make the catch)

= 0.3 x 0.8

=0.24

c) The probability of a randomly selected catch being caught by Greg is 0.45

To calculate, we say

(0.5   x0.45) + (0.3 x 0.45) + (0.2 x .45)

= 0.45.

d)

P (mouse caught by Greg) = (0.45 x 0.5) / 1

= 0.225.

e) P(catch is a mouse caught by Ken and catch is a mouse)

= P(catch is a mouse | catch is made by Ken) x P(catch is made by Ken)

= 0.05 x 0.1

= 0.005

f)

P (catch made by Cyd | catch is a mouse)

= 0.1    x 0.2 / 0.5

= 0.04

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A graph of the given equation is attached below and coordinate of these equations are (2, 3).

There is a large commitment to the use of graphs in teaching and communicating information, both in science and mathematics. An excellent graph or chart may convey information that several pages of text cannot.

Given two equations y − 2x = −1  and 2y − x = 4

first, we calculate the slope of both equation

y - 2x = -1

y = 2x -1  (comparing wit y = mx +c)

the slope of the first equation (m1) = 2

2y - x  = 4

2y = x +4

y = x/2 + 2

Slope of second equation (m2) = 1/2 (comparing wit y = mx +c).

Therefore, the coordinates of these equations are (2, 3) and the graph is attached below.

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The value of a and b is -5/4. The value describes the value of each digit in relation to its position in the number.

(a) Mean Value  = \(\frac{1}{3-1} \int_1^3 f(x)=\frac{1}{2}-\frac{5}{2}=\frac{5}{4}\)

b) \(} \int_3^5 f(x) d x=\int_1^5 f(x) d x-\int_1^3 f(x) d x=10-\frac{5}{2}=\frac{15}{2} \\\)

\(& \left.\int_3^5(2 f(x)+6) d x=2 \int_3^5 f(x) d x+6 \int_3^5 d x=2\left(\frac{15}{2}\right)+6 x\right]_3^5=15+6(2)=27 \\\)

c) \(} f(x)=a x+b \\\)

\(& \left.\int_1^3(a x+b) d x=\frac{a x^2}{2}+b x\right]_{x=1}^3=\frac{9}{2} a+3 b-\frac{a}{2}-b=4 a+2 b=\frac{5}{2} \\\)

Simplifying,

\(\left.\int_1^5(a x+b) d x \cdot \frac{a x^2}{2}+b x\right]_{x=1}^5=\frac{25 a}{2}+5 b-\frac{a}{2}-b=12 a+4 b=10 \\\)

\(4 a+2 b=5 / 2 \stackrel{n-3}{\rightarrow}-12 a-6 b=-15 / 2\)

Then we get,

\(12 a+4 b=10\)

\($ \frac{12 a+4 b=20/2}{ -2 b=5 / 2} b=\frac{-5}{4}\)

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Answer:

29 degrees

Step-by-step explanation:

Note how both triangles are isosceles triangles, which mean two angles will be equivalent. In the triangle with the marked angle measurement, since the total of angles in a triangle is 180, then the measurement of the unmarked angles have a sum of 180-64, which is 116. Then, as stated before, this triangle is isosceles, so the measurement of each unmarked angle is 116/2, which is 58.
Next, notice how the angle below angle x in that triangle shares a line with one of the 58 degree angles. This means that angle is 180-58, which is 122. Now, since the total of angles in a triangle is 180 and the triangle is isosceles, then angle x is (180-122)/2, which is 58/2, or 29 degrees

The equation of the line is y = (3/2)x - 1/2.

The equation of a line is given by:

y = mx + c

where m is the slope of the line and c is the y-intercept.

Example:

The slope of the line y = 2x + 3 is 2.

The slope of a line that passes through (1, 2) and (2, 3) is 1.

We have,

Let's say you need to know the answer about the equation of a line that passes through points (3, 4) and (5, 7).

Now,

The equation of a line.

y = mx + c

The line passes through points (3, 4) and (5, 7).

m = (7 - 4) / (5 - 3)

m = 3/2

Slope = 3/2 _____(1)

Now,

(3, 4) = (x, y)

4 = 3/2 x 3 + c

4 = 9/2 + c

c = 4 - 9/2

c = (8 - 9) / 2

c = -1/2

y-intercept = -1/2 ____(2)

Now,

y = mx + c

From (1) and (2),

y = (3/2)x - 1/2

Thus,

The equation of the line is y = (3/2)x - 1/2.

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The complete question.

Find the equation of a line that [passes through the point (2, 4), and (5, 7).

Answer:  

Identifying Symmetry in Equations Graphs of Equations on a coordinate plane can have symmetry with respect to the X-Axis, Y-Axis, and/or the Origin. Some equations have no symmetry, and some equations have multiple types of symmetry. Each type of symmetry can be determined individually using either graphical or algebraic test methods.

Step-by-step explanation: Hope this helped !

Answer:

Decay rate K = -2.44%

Step-by-step explanation:

From the question, we want to know the decay rate of strontium 90

Mathematically, this is accessible from its decay equation

From the decay equation, we can see that that ;

At = Ao e^-0.0244t

Generally, the decay equation of a radioactive sample can be written as

At = Ao e^-kt

where K represents the decay constant

From the equation, we can see that;

k = 0.0244 which when represented as a percentage is 2.44%

Since it’s a decay we can say that the decay rate is -2.44%

The answer is : -2.44%

This is oddly the funniest question I've seen so far. But never fear, I guess I'm here? :\

Honestly, I'm kinda lost but your answer should be $88.88. Even though it would say $88.88 multiplied by total hours, which is 4 hours and 25 minutes is $377.74, that answer is determined by a thousandth of a number. If you want it the other way, it's 88.8824.

Definitely hope this helped. [Pretty much, the answer is $88.88.]

The cost of labor per hour is $75.

It is required to find the cost of labor per hour.

Arithmetic is the branch of mathematics that deals with the study of numbers using various operations on them. Basic operations of math are addition, subtraction, multiplication and division. These operations are denoted by the given symbols.

Given:

The total amount that the technician charged her is the sum of the cost for the total hours worked and the costs of the parts.

Total charge = cost of total hours worked + cost of parts

$377.75 = $59 +  cost of total hours worked

Cost of total hours worked = $377.75 - $59

Cost of total hours worked = $318.75

In order to determine the cost per hour of labor, divide the total cost of total hours worked by the hours worked.

$318.75 / 4.25 = $75.

Therefore, the cost of labor per hour is $75.

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The approximate lateral area of the cone is equal to 200.96 cm².

Mathematically, the lateral area of a cone can be calculated by using this mathematical expression:

Lateral surface area of a cone, LSA = πrl or πr√(r^2 + h^2)

Where

Mathematically, the area of a circle can be calculated by using this formula:

Area of a circular base = πr²

16π = πr²

Radius, r = √16

Radius, r = 4 cm.

Substituting the given parameters into the lateral area of a cone formula, we have the following;

Lateral surface area of a cone, LSA = πrl = πr4(r)

Lateral surface area of a cone, LSA = 3.14 × 4 × 16

Lateral surface area of a cone, LSA = 200.96 cm².

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Answer:

201 beause you are rounding to the nearest whole number

Step-by-step explanation:

The value of \(b_{1}\) is 69/4h and value of \(b_{2}\) is 43/4h if the area of trapezoid is 14 square units.

Given that area is equal to 1-2(\(b_{1} -b_{2}\))h and area is 14 square units.

We know that area of trapezoid is equal to (a+b)h/2.

We have to put the given equation equal to 14 to get our first equation.

14=1-2(\(b_{1} -b_{2}\))h

14=1-2\(b_{1}\)h+2\(b_{2}\)h

2\(b_{1}\)h-2\(b_{2}\)h=-13------------1

Now put the value of area in the formula of area of trapezoid.

14=\((b_{1} +b_{2})h/2\)

\(b_{1}\)h+\(b_{2}h\)=28-----------------2

Multiply equation 2 by 2 and then subtract 2 from 1

\(2b_{1}h -2b_{2}h -2b_{1}h-2b_{2}h\)=-13-56

-4\(b_{2}h\)=-43

\(b_{2}\)=43/4h

Put the value of \(b_{2}\) in 2 to get the value of \(b_{1}\).

\(b_{1} h+43/4h*h=28\)

\(b_{1}\)=69/4h

Hence The value of \(b_{1}\) is 69/4h and value of \(b_{2}\) is 51/4h if the area of trapezoid is 14 square units.

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Answer: The middle number in a data set when the data are put in order.

Answer and Step-by-step explanation:

To find the median of a set of numbers, you need to find what the number in the center is in a listed group of numbers. I'll use the example of these numbers:

6, 9, 5, 4, 3, 4, 2.5, 8, 0, 1, 5.

First, we need to organize the numbers in numerical order to find the median.

0, 1, 2.5, 3, 4, 4, 5, 5, 6, 8, 9.

It would be the most simple and helpful to cross out each number until we get our center number; the median. (I can't cross the numbers out, so I'll underline them instead.) When crossing out, both sides need to be full of equally crossed out numbers.

0, 1, 2.5, 3, 4, 4, 5, 5, 6, 8, 9.

The number in the center for this example problem is 4. Thus meaning that our median is 4.

Sometimes though, it is not always a whole number. Sometimes you'll have to find the median in between two numbers. For example, let's just say you got stuck between 4 and 5. Then the median for that set of data would be 4.5, because it is still in the middle of the two.

I hope that this helps, let me know if you have any more questions about this topic.

The simplified form of -20/2(7 2/3) is -230/3.

To solve the expression -20/2(7 2/3), we need to follow the order of operations, which states that we should perform the operations inside parentheses first, then any multiplication or division from left to right, and finally any addition or subtraction from left to right.

First, let's convert the mixed number 7 2/3 to an improper fraction.

7 2/3 = (7 * 3 + 2) / 3 = 23/3

Now, let's substitute the value back into the expression:

-20/2 * (23/3)

Next, we simplify the multiplication:

-10 * (23/3)

To multiply a fraction by a whole number, we multiply the numerator by the whole number:

-10 * 23 / 3

Now, we perform the multiplication:

-230 / 3

Therefore, the simplified form of -20/2(7 2/3) is -230/3.

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The steps to sketch the graph of a rational function in the appropriate order is in the order: 1,4,2,3

The steps to sketch the graph of a rational function will be first to find the function's zeros and vertical asymptotes, and plot them on a number line, the second step is to choose test numbers to t the left and right of each of these places, and find the value of the function at each test number., the third step is to use test numbers to find where the function is a positive and where it is negative and the last step is to sketch the function's graph, plotting additional points as guides as negative.

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Place the steps to sketch the graph of a rational function in the appropriate order.

1)find the function's zeros and vertical asymptotes, and plot them on a number line.

2) use test numbers to find where the function is positive and where it is negative.

3) sketch the function's graph, plotting additional points as guides as negative.

4)choose test numbers to t the left and right of each of these places, and find the value of the function at each test number.​

Answer:

Step-by-step explanation:

A ) Let p be the probability of getting affected . Probability of not getting affected be q

p = .3 , q = .7

If n be the member of family , probability that x children will be affected will be given by the expression

p(x) = ⁿCₓ pˣqⁿ⁻ˣ

n = 2 , x=2

p(2) = ²C₂ .3².7²⁻²

= 1 x .09 x 1 = .09

B )

p(1) = ²C₁ .3¹.7²⁻¹

=  2 x .3 x .7

= .42

C ) x = 0

p (0) = ²C₀ .3⁰.7²⁻⁰

=  1 x 1 x .49

= .49

D ) Let A be the probability that older child is affected and B be the probability that younger child is affected

P( A /B ) = P(A∩B) / P(B )

= .09 / .42

= .214

The 9th arrangement will have 36 dots, the 10th arrangement will have 45 dots, and when adding the number of dots in any two consecutive arrangements, the result will be the number of dots in the next arrangement.

To determine the number of dots in the 9th and 10th arrangements, we need to understand the pattern in the given sequence: 1, 3, 6, 10, 15, ...

To find the pattern, we can observe the differences between consecutive terms: 2, 3, 4, 5, ...

We notice that these differences increase by 1 each time. This indicates that the sequence is formed by adding consecutive positive integers to the previous term.

Using this pattern, we can determine the 9th and 10th arrangements as follows:

9th arrangement:

Starting with the 1st arrangement, we add the positive integers consecutively: 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 = 36.

Therefore, the 9th arrangement will have 36 dots.

10th arrangement:

Starting with the 1st arrangement, we add the positive integers consecutively: 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 = 45.

Therefore, the 10th arrangement will have 45 dots.

Now, let's address the observation when we take any two consecutive arrangements and add the number of dots.

If we take the nth arrangement and the (n+1)th arrangement, we can observe that the number of dots in the (n+1)th arrangement will be the sum of the number of dots in the nth arrangement and the number of dots added in the (n+1)th step.

For example, let's consider the 2nd and 3rd arrangements:

2nd arrangement: 3 dots

3rd arrangement: 3 + 3 (adding 2, the next positive integer) = 6 dots

This pattern holds true for any two consecutive arrangements in the sequence.

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To solve this problem, we need to use Charles's law, which states that, at constant pressure, the volume of a sample of gas is directly proportional to its temperature.

The law can be expressed mathematically as:

\(\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{ \frac{V_1}{T_1}=\frac{V_2}{T_2} } \end{gathered}$} }\)

Where:

Now we obtain the data to continue solving:

Now, we will convert the temperatures to Kelvin:

\(\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{T_1=220 \ ^{\circ}C+273=493 \ Kelvin} \end{gathered}$} }\)

\(\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{T_2=40 \ ^{\circ}C+273= 313 \ Kelvin} \end{gathered}$} }\)

Now we solve for V₂:

\(\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{V_2=\frac{V_1T_2}{T_1 } } \end{gathered}$} }\)

Where:

Now, we substitute the values in the formula:

\(\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{V_2=\frac{(0.5 \ L\times313\not{k} )}{493\not{k} } } \end{gathered}$} }\)

\(\boxed{\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{V_2\approx0.32 \ Liters } \end{gathered}$} }}\)

(a). The Tanakas paid a total of $523,906.40 for the townhome.

(b). The Tanakas paid $206,906.40 in interest on their mortgage over the 15-year period.

Simple interest is the type of interest that is calculated on the principal amount only.

It is a fixed percentage of the principal amount that is charged or earned over a certain period of time, without any compounding of interest.

(a) The total amount they ended up paying for the townhome is the sum of the down payment and the total amount of the mortgage payments.

Down payment = $41,000

Total amount of mortgage payments = monthly payment x number of payments = $2675.04 x 12 months/year x 15 years = $482,906.40

Total amount paid = down payment + total amount of mortgage payments = $41,000 + $482,906.40 = $523,906.40

(b) The amount of interest paid on the mortgage can be calculated by subtracting the principal (the amount borrowed) from the total amount paid.

Principal = Total cost of townhome - Down payment = $358,000 - $41,000 = $317,000

Total interest paid = Total amount paid - Principal = $523,906.40 - $317,000 = $206,906.40

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Answer: 0.771 you are welcome

Step-by-step explanation:

b because you have to multiply

Answer:

8x=104

Step-by-step explanation:

The answer above is the question simplified down

Answer:  15 percent

Step-by-step explanation:

A geometric series is one in which there is a constant between two successive numbers in the series.

When there is a constant between the two successive numbers in the series then it is called a geometric series. In other words, every next term is multiplied by that constant term to form a geometric progression.

The sequence in which every next number is the addition of the constant quantity in the series is termed the arithmetic progression

Suppose the series is given as

2,4,8,16,32,64.........

The common difference is defined as the ratio of the next term to the previous term.

From the above series, the common ratio is calculated as,

Common ratio = 4 / 2

Common ratio = 2

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The dimensions of the rectangular box are given as follows:

All the dimensions.

The volume of a rectangular prism, with dimensions length, width and height, is given by the multiplication of these dimensions, according to the equation presented as follows:

Volume = length x width x height.

The box's volume is obtained as follows:

54 x 1³ = 128 x (3/4)³ = 54 cubic inches. (the volume of a cube is the side length cubed)

Hence all the options can be the dimensions of the box, as all the options have a multiplication resulting in 54.

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Answer:

4x = 100, so x = 25

The correct answer is C.