the lengths of the right sides of a right triangle were 12 cm and 16 cm The first side is increasing at a rate of 2 cm/sec and the second side is decreasing at a rate of 1 cm/sec so that the triangle keeps its shape Find the rate of change of the area of the triangle after two seconds have passed

The time it took Aniya to do cartwheels, which can travel at 0.5 mph for a total distance of 0.1 miles, is 12 minutes.

The distance, time, and average speed formulas are based on distance equals to time multiplied by the average speed.

Conversely, the total time taken to cover a certain distance is equal to distance divided by the average speed.

Total distance traveled doing cartwheels = 0.1 miles

Average speed = 0.5 mph

Time = Distance/Average speed

= 0.1/0.5

= 0.2 hours

1 hour = 60 minutes

= 12 minutes (0.2 x 60)

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Answer: If the service rate is 6 customers per hour, the mean service time can be calculated as 1/6 = 0.1 hours or 6 minutes. The negative exponential distribution is commonly used to model the service time distribution in queuing theory. The cumulative distribution function (CDF) of the negative exponential distribution is given by:

F(x) = 1 - e^(-λx)

where λ = 1/μ, where μ is the mean service time (in this case, μ = 0.1 hours or 6 minutes).

So, the probability that the service time will be less than or equal to 6 minutes can be calculated as:

F(6) = 1 - e^(-0.1 * 6) = 1 - e^(-0.6) ≈ 0.5488

So, the answer is approximately 0.549, which is closest to option (b).

Step-by-step explanation:

The probability that the thread length of a randomly selected bolt is farther than 2. 5 standard deviations from its mean value is 0.62%.

If the thread length of bolts is normally distributed, then we can use the concept of probability to determine the probability that the thread length of a randomly selected bolt is farther than 2.5 standard deviations from its mean value.

This can be calculated using the area under the normal curve.

Specifically, the area to the right of 2.5 standard deviations is 0.0062, meaning that there is only a 0.0062 probability (or 0.62%) that the thread length of a randomly selected bolt is farther than 2.5 standard deviations from its mean value

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Check the picture below.

[tex]~~~~~~\textit{initial velocity in feet} \\\\ h(t) = -16t^2+v_ot+h_o \quad \begin{cases} v_o=\textit{initial velocity}&16~\frac{ft}{s}\\ \qquad \textit{of the object}\\ h_o=\textit{initial height}&192~ft\\ \qquad \textit{of the object}\\ h=\textit{object's height}&h\\ \qquad \textit{at "t" seconds} \end{cases} \\\\\\ h(t)=-16t^2+16t+192\hspace{5em}f(x)=-16x^2+16x+192[/tex]

now, keeping in mind that x-axis is the seconds, however a parabola could go into the 2nd, 3rd and 4th Quadrants, but for this case, we only need it in the 1st Quadrant, because the seconds are positive, it begins at 0 seconds and goes up, then down and hits the ground later on when f(x) = 0, hmmm when is that?

[tex]\stackrel{f(x)}{0}=\stackrel{ \textit{hits the ground} }{-16x^2+16x+192}\implies 0=-16() \\\\\\ 0=x^2-x-12\implies 0=(x+3)(x-4)\implies x= \begin{cases} -3 ~~ \bigotimes\\\\ ~~ 4 ~~ \checkmark \end{cases}[/tex]

now, both values are valid for "x", however for this specific case, we can't have negative seconds, so the negative value won't work.  So the appropriate domain or values for "x" are from 0 to 4, the object went up and down in 4 seconds flat.

C) 2.5 kHz, C) 15, A) 101010, D) CA35, A) (A), A) XOR, B) Exclusive OR, A)True, A) (A + B)C, B) Variable complements can be eliminated by using Karnaugh maps.

K-maps, commonly referred to as Karnaugh maps, are visual tools for simplifying digital circuits and Boolean algebraic formulas. In order to make Boolean functions simpler for use in digital electronics, Maurice Karnaugh first presented them in 1953. K-maps are used to consolidate terms with similar values and get rid of extraneous terms in the truth table of a Boolean function. With a grid of cells corresponding to all conceivable combinations of binary input values, the map is a two-dimensional representation of a truth table. Depending on the truth value of the relevant word in the truth table, the cells in the grid are either filled with 0s or 1s.

The fundamental benefit of employing Karnaugh maps is that they give the Boolean expression a visual representation, making it simpler to spot patterns and understand the expression. They can also be used to check the accuracy of the final expression and find flaws in digital circuits. Karnaugh maps can be used to quickly and effectively simplify complicated digital circuits, which cuts down on the time and effort needed for circuit design.

Karnaugh maps are perfect for designing and optimizing digital circuits because they may be used to simplify big or complex Boolean statements. For more effective and efficient results, they can be combined with other digital design tools, such as logic gates.

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The perimeter of the square is 40m

The formula for calculating the area of a square is given as;

A =  a²

Given that;

Substitute the value

100 = a²

Find the square root of both sides

a = 10m

The formula for the perimeter of a square is expressed as;

Perimeter = 4a

Substitute the value into the formula;

Perimeter = 4(10)

expand the bracket

Perimeter = 40 m

Hence, the value is  40 m

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Answer:

Step-by-step explanation:

14

The number of children who ordered hamburgers from class A = ( 5/6 )A , where A is the total number of students in the class A

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the number of students in class A = A

Let the number of students in class B = B

Let the number of students in class C = C

Now , the equation will be

The number of students who ordered hamburgers is = ( 5/6 )A

The number of students who ordered hot dogs is = ( 2/4 )B

The number of students who ordered hot dogs is = ( 1/2 )B

The number of students who ordered chicken wings is = ( 1/2 )C

Hence , the number of students who ordered hamburgers , hot dogs and chicken wings are ( 5/6 )A , ( 1/2 )B and ( 1/2 )C respectively

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The number of sheets that can be cut from 22 1/8 inches would be 4 25/38

To solve this, I would first have to convert the values to decimals

4 3/4in = 4.75 inches

22 1/8 = 22.125

To get the full length that can be cut from the 22.125, we would have to divide. That is;

22.125 / 4.75

= 4.657

4 25/38

The number of full sheet that can be cut from this would be 4 25/38

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The probability of getting at least one defective disk in a lot of 50 is 0.2217.

Probability refers to potential. A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events. The degree to which something is likely to happen is basically what probability means. You will understand the potential outcomes for a random experiment using this fundamental theory of probability, which is also applied to the probability distribution.

Given that,

P (defective disc) = 0.005

P (non-defective) = 1 - 0.005 = 0.995

Now,

P(Getting one defective) = 1 - P(getting 50 non -defective)

= 1 - (0.995)^(50)

= 1- 0.7783

= 0.2217

Hence, the probability of getting at least one defective disk in a lot of 50 is 0.2217.

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Answer:

72 inches

Step-by-step explanation:

What we know:

1 yard = 3 feet

3 feet = 36 inches

If 1 yard equals 3 feet, which equals 36 inches, then we can multiply 1 yard, 3 feet, and 36 inches by 2.

1 yard * 2 = 2 yards

3 feet * 2 = 6 feet

36 inches * 2 = 72 inches.

So, the answer is 72 inches.

Using Hamilton's method of apportioning, 21 salespeople can be assigned in the table in the following order:

2, 5, 6, 8.

The approach that now bears his name was first proposed by Alexander Hamilton. Congress endorsed his approach in 1791, but President Washington rejected it. Later, in 1852, it became widely used until 1911. He starts by calculating the precise number of items that each group needs.

Since in the interested question it's about salesperson assigned, we’ll use the language of shift and hours, so we can determine how many salespersons each shift should get.

Now total no. of customers given = 125 + 305 + 439 + 515

                                                        = 1375

Now total no of salesperson available = 21.

So, the divisor = 1375/21

                        = 65.47

Now using Hamilton's method when we divide the average customers per shift by the divisor, we get the no. of salesperson assigned.

So, the salesperson assigned are:

Morning = 125/65.47

              = 2

Midday = 305/65.47

             = 5

Afternoon = 430/65.47

                 = 6

Evening = 515/65.47

               = 8 (Decimals rounded according to Hamilton's principle)

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Answer:

yes it will fit;  there would be 35.2 sf remaining

Step-by-step explanation:

Find the dimensions of the table in inches:

2.5/5 = x/6

x = 3 in

2.5/5 = x/8

x = 4 in

Scaled table area = (3 in)(4 in) = 12 in²

Scaled room area = (4 in)(5.2 in) = 20.8 in²

12 < 20.8, Therefore, the table would fit.

How much room is left over:

Find the room dimensions in feet.

2.5/5 = 4/x

x = 8 ft

2.5/5 = 5.2/x

x = 10.4 ft

Room area = (8)(10.4) = 83.2 sf

Table area = (8)(6) = 48 sf

83.2 - 48 = 35.2 sf space would remain

Answer: 15a

Step-by-step explanation: 6 + 9 = 15, 6a + 9 = 15a

The height of the building is 92.52 ft

What is a right-angle triangle?

It is a triangle in which one of the angles is 90 degrees and the other two are sharp angles. The sides of a right-angled triangle are known as the hypotenuse, perpendicular, and base.

Using law of sines:

first angle A:

sum of all angles in a triangle = 180 degree

A+B+C = 180

A+90+55 = 180

=> A+145 =180

=> A= 180 - 145 = 35 degrees

Use:

AB= c, BC=a

(sin A)/a = (sin C)/c

=> (sin 35)/40= (sin 55)/c

=> -0.4281/40= -0.99/c

=> 0.0107 = 0.99/c

=> c= 0.99/0.0107 = 92.52 ft

The height of the building is 92.52 ft

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Answer:

Below

Step-by-step explanation:

Volume of a cylinder = area of end X height =  pi r^2 * h

  r = 4 in    h = 10 in

volume = pi (4)^2 * 10 =    160 pi in^3      or    ~  503 in^3

Answer:

160π in.³

Step-by-step explanation:

Get the circle area then multiply for the height. In the end, devide the result by 3,14 (π).

π* . r²                                  50,24 . 10*
π* . 4²                                 502,40 in.³ (cylinder volume)
50,24 (circle area)            

obs: 502,4 leads you to a non-comma π result, considering π as 3,14. If you round, the correct way will be transforming into 502. But 502/3,14 is equal to 159,87..., infinite non-repetitive numbers.

Result in π = 160π* in.³

r - circle radius

10* - height

π* - 3,14 (Used that way)

The side lengths of rectangle B, given that they are proportional to rectangle A would be :

To find proportionality, the dimensions of Rectangle B which correspond to Rectangle A, need to be divisible by, or be able to divide Rectangle A's dimensions without leaving a remainder.

The side lengths of 3 cm and 1. 75 cm are proportional because:

= Dimensions A / Dimensions of B

= 6 / 3 :  3. 5 / 1. 75

= 2 : 2

The side lengths of 5. 25 and 9 cm are also proportional because :

= 9 / 3 : 5 . 25 / 1 . 75

= 3 : 3

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The rest of the question is:

What could be the side lengths of rectangle B?

A. 3cm and 1.75cm

B. 5cm and 2.5cm

C.7 cm and 7cm

D. 12cm and 5 cm

E. 5.25cm and 9cm

Therefore , the solution of the given problem of linear equation comes out to be the decision variables x1, x2, x3, and x4 must be non-negative.

The formula y=mx+b is used to draw a simple regression graph. The inclination is B, and the y-intercept is m. It is frequently referred to as a "simple algorithm incorporating many factors" even though the section before it includes independent parts. Bivariate linear equations only contain two variables. Application problems with linear equations have no known answers. Y=mx+b, also known as mx+b, provides a number of straightforward equations.

Here,

To solve this linear programming problem, we can use the following decision variables:

Let x1 = number of pancakes

Let x2 = number of eggs

Let x3 = number of sausage patties

Let x4 = number of slices of toast

The objective function is to minimize cost:

Minimize Z = 0.5x1 + 0.2x2 + 0.3x3 + 0.1x4

Subject to the following constraints:

Calories: 120x1 + 90x2 + 280x3 + 70x4 >= 420

Iron: 1.2x1 + 1.8x2 + 2.4x3 + 0.8x4 >= 5

Calcium: 10x1 + 20x2 + 90x3 + 20x4 >= 400

Protein: 3x1 + 6x2 + 9x3 + 3x4 >= 20

Fiber: 2x1 + 0.5x2 + 1x3 + 1x4 >= 12

Fat: 2x1 + 6x2 + 20x3 + 1.5x4 <= 20

Cholesterol: 50x1 + 190x2 + 60x3 + 0x4 <= 30

The decision variables x1, x2, x3, and x4 must be non-negative.

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Therefore , the solution of the given problem of standard deviation comes out to be the typical distance between the observed and predicted foot lengths is 1.61 centimeters.

Variance is a measure of difference used in statistics. The average variance between the data and indeed the mean is calculated using the mathematical formula of that figure. By comparing each data point's value to the mean, it incorporates all data points into its computations, unlike some other number measures of variability.

Here,

D. The typical distance between the observed and predicted foot lengths is 1.61 centimeters.

The standard deviation of the residuals measures the typical distance between the observed values and the predicted values (based on the regression line).

In this case, the regression analysis is for foot length and arm span, and the standard deviation of the residuals tells us about the typical distance between the observed foot lengths and the predicted foot lengths based on the regression line.

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Answer:

y=-7/2x-9/2

Step-by-step explanation:

The inverse operations are (b) and (c)

From the question, we have the following parameters that can be used in our computation:

m/4-18= -10

Operation 1: Option (B)

Add 18 to both sides of the equation, and then multiply through by 4

Using the above as a guide, we have the following:

m/4 = 8

m = 32

Operation 2: Option (C)

Multiply each side by 4 and then add 72

Using the above as a guide, we have the following:

m - 72 = -40

m = 32

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The limit when we approach x = 3 from the right side is:

[tex]\lim_{x \to 3^+} f(x) = 4[/tex]

Here we have the graph of a function f(x), and we want to find the value of the limit:

[tex]\lim_{x \to 3^+} f(x)[/tex]

That would be the value of f(x) as it approaches x from the right side, in this case, will be the value on the graph when we go from right to left.

We can see an open circle at y = 4

Then we can conclude that the value of the limit when we approach x  = 3 from the positive side is:

[tex]\lim_{x \to 3^+} f(x) = 4[/tex]

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Answer:

2.15 * 10⁶

Step-by-step explanation:

1,000,000= 1 * 10⁶

2,150,000= 2.15 * 10⁶

Answer:

The grouped frequency distribution for the data is shown below.

A grouped frequency distribution is a way of summarizing and organizing raw data into a more manageable and meaningful form. The data is divided into intervals or "classes", and the number of data points that fall into each class is counted and recorded as the frequency of that class. This allows for easier interpretation and comparison of the data, as well as identifying patterns or trends. The grouped frequency distribution is commonly displayed in a table or a histogram.

Given that,

79, 85, 71, 83, 78, 67, 70, 87, 81, 86, 74, 67, 68, 76, 66, 72, 76, 80

Now, arranging the given data in ascending order,

66, 67, 67, 68, 70, 71, 72, 74, 76, 76, 78, 79, 80, 81, 83, 85, 86, 87

The grouped frequency distribution for the data:

Test Scores                   Frequency

65.5 - 71.5                        6

71.5 - 77.5                         4

77.5 - 83.5                        5

83.5 - 89.5                        3

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The HCF of the numbers is 1078

From the question, we have the following parameters that can be used in our computation:

183260 and 2900898

Next, we factorize each number

This is represented as

183260 = 1078 * 170

2900898 = 1078 * 2691

The common factor above is

Comon factor = 1078

Hence. the HCF is 1078

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The ordered pairs that represent the linear function is Option A, B and C.

A linear function in mathematics is one that has either one or two variables and no exponents. It is a function with a straight line as its graph. If the function has more variables, they should all be constants or known variables in order for the function to continue to function as a linear function.

To determine which ordered pairs represent a linear function we use the equation of slope.

The slope is given as:

m = (y2 - y1) / (x2 - x1)

Option A:

m = (5 - 8) / (-4 + 8) = -3 / 4

m = (2 - 5) / (0 + 4) = -3/ 4

The slopes between the consecutive points are same hence option A represents a linear equation.

Similarly, for option B:

m = (1 + 2) / (2 + 1) = 1

m = (4 - 1) / (5 - 2) = 1

Option B is correct.

Option C:

m = (5 - 8) / (1 + 2) = -3 / 3 = -1

m = (2 - 5)/ (4 - 1) = -1

Option C is correct.

Option D:

m = (1- 0)/ (1 + 1) = 1/2

m = (5 - 1) / (7 - 1) = 4 / 6 = 2/3

Option D is incorrect.

Hence, the ordered pairs that represent the linear function is Option A, B and C.

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