Find the common factor of all the terms of the polynomial 16x² - 14x.

The population of McKinney after 2 years with an average growth rate of 8.4% will be approximately 210,099.76.

To calculate the population of McKinney after 2 years with an average growth rate of 8.4%, we can use the formula for compound interest:

[tex]P = P_0 * (1 + r/100)^t[/tex]

Where P0 is the initial population, r is the growth rate, and t is the number of years. In this case, P0 = 180,000, r = 8.4, and t = 2. Plugging these values into the formula, we get:

[tex]P = 180,000 * (1 + 8.4/100)^2[/tex]

[tex]P = 180,000 * 1.084^2[/tex]

[tex]P = 180,000 * 1.174996[/tex]

[tex]P = 210,099.76[/tex]

So, the population of McKinney after 2 years with an average growth rate of 8.4% will be approximately 210,099.76.

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The complete question is :

The population of McKinney is about 180,000. The population is increasing at an average rate of 8.4% . It's population after 2 years will be.

Answer:

0.609

Step-by-step explanation:

convert to a fraction then convert to a decimal by dividing the numerator and denominator :)

It would take Tracy and Dave approximately 4.8 hours to complete the task together. So, the correct option is C.

To solve this problem, we can use the formula:

time = work / rate

where work is the amount of work to be done (in this case, collecting signal strength data from each house), and rate is the rate at which the work is being done.

Let's start by finding Tracy's and Dave's individual rates:

Tracy's rate: 1 job / 8 hours = 0.125 jobs per hour

Dave's rate: 1 job / 12 hours = 0.0833 jobs per hour

Now, let's find their combined rate when they work together:

Combined rate = Tracy's rate + Dave's rate

Combined rate = 0.125 + 0.0833

Combined rate = 0.2083 jobs per hour

Finally, we can use the formula time = work / rate to find how long it would take them to complete the task together:

time = 1 job / 0.2083 jobs per hour

time ≈ 4.8 hours

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Answer:

?

Step-by-step explanation:

The given Expression simplifies to -8.1069556e+27

BODMAS stands for Bracket, Of, Division, Multiplication, Addition, and Subtraction. A mathematical expression's order of execution is explained using the BODMAS.

Given an equation to solve,

6234653928 + 294292342 - 424624642 x 16515615615165161 x 1156 + 6466456

Let us consider this Expression as A + B - C * D * E + F, with the corresponding terms being equal

By, the BODMAS rule,

First step: Multiply C, D, E. Let this be G

Now, the equation will look like this: A + B - G + F

Second step: We can add and subtract according to the signs now

On solving, the expression simplifies to -8.1069556e+27

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The lower quartile for the given data is -2, since it is the 25th percentile and is the value that lies at the 25th position when the data is sorted in ascending order.

1. Sort the data in ascending order: -4, -2, 1, 1, 6, 8, 12, 15

2. Calculate the 25th percentile: 25th percentile = (n + 1) * 0.25 = (8 + 1) * 0.25 = 2.25

3. The 25th percentile is between the 2nd and 3rd values, which are -2 and 1 respectively.

4. The lower quartile is -2.

The lower quartile (also known as the 25th percentile) is the value that lies at the 25th position when the data is sorted in ascending order. To find the lower quartile of the given set of data (1, 8, 1, -4, 12, -2, 15, 6), the data needs to be sorted in ascending order. This gives us the following data: -4, -2, 1, 1, 6, 8, 12, 15. Now, to calculate the 25th percentile, we use the formula (n + 1) * 0.25, where n is the number of data points. In this case, n = 8, so the 25th percentile = (8 + 1) * 0.25 = 2.25. This means the 25th percentile is between the 2nd and 3rd values, which are -2 and 1 respectively. Therefore, the lower quartile for the given data is -2.

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Answer:

0.2115

Step-by-step explanation:

probability the first lefty is the second person:

1. the first person must be right handed (1-13% = 0.87)

2. the second person must be left handed (0.13)

both must happen, so this is 0.87 * 0.13

probability the first lefty is the third person:

1. the first person must be right handed (0.87)

2. the second person must be right handed (0.87)

3. the third person must be left handed (0.13)

all must happen, so this is 0.87 * 0.87 * 0.13

either the second or third person must be left handed, so we add this to get

0.87 * 0.13 + 0.87 * 0.87 * 0.13 = 0.2115

The area of field hockey is larger by 3162.85 [tex]m^2[/tex].

The amount of unit squares that cover an enclosed figure's surface is its area. Square units like [tex]cm^2[/tex] and [tex]m^2[/tex] are used to measure area. A shape's area is a two-dimensional measurement. The space inside the perimeter or boundaries of a closed shape is known as the "area."

The hockey surface given here is in rectangular shape, so,

Area = length x breadth

Area of the hockey surface at a community centre is,

= 61 m x 30.5 m

=1860.5 [tex]m^2[/tex]

Area of field hockey played at outdoors,

= 91.5 m x 54.9 m

= 5023.35    [tex]m^2[/tex]

Clearly, we can see that area of field hockey is larger.

Difference between both the areas = 5023.35 -1860.5 = 3162.85 [tex]m^2[/tex].

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With the help of given table of data of travelling time to work for 50 people, the estimated mean travelling time is 24.8 minutes.

To estimate the mean travelling time from the given frequency table, we can use the midpoint method, where we calculate the midpoint of each class interval and multiply it by the frequency of that interval. We then sum up the products and divide by the total frequency to get the estimate of the mean travelling time. The midpoint of each interval can be calculated as the average of the lower and upper bounds of the interval. Using this method, we get:

Class interval 0 < t < 10 | 10 < t < 20 |  20 < t < 30 | 30 < t < 40 |  40 < t < 50

Midpoint (m)    5                     15               25                 35                  45

Frequency (f)    5                    15               13                  10                   7

Midpoint x Frequency 25      225            325               350               315

Total | | 50 | 1240

To estimate the mean travelling time, we can now calculate the sum of the products of the midpoint and frequency for each interval, which is 1240. We then divide this by the total frequency, which is 50. Therefore, the estimate of the mean travelling time for these 50 people is: Mean  travelling time = Sum of (midpoint x frequency) / Total frequency

Mean travelling time = 1240 / 50 = 24.8

Thus, the estimated mean travelling time is 24.8 minutes.

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Complete Question

The table shows the travelling time to work of 50 people.

-Travelling time (t)  in minutes- -Frequency-

0 <t<10                                           5

10 < t < 20                                     15  

20 < t < 30                                    13

30 < t < 40                                    10

40 < t < 50                                    7

Calculate an estimate of the mean travelling time

Answer:

S∞ = 96

Step-by-step explanation:

An objective tally of the results of a probability experiment is called a random variable. It gives a number to each potential result of the experiment, and its values are decided by chance.

How something is to Happen is known as its probability. We can discuss the probabilities of various outcomes—how likely they are—when we aren't sure how a particular event will turn out. Statistics defines series of events subject to probability.

Always between 0 and 1 are the possible outcomes. Probability = Number of favourable outcomes / Total number of outcomes is how the general probability formula is written. Alternatively, P(A) = f / N.

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Answer:

8 to 2

Step-by-step explanation:

because u have 8 cocca and 2 sugar

Answer:

A ratio of 5 parts water to 1 part fertilizer for watering plants. This ratio ensures that the plants receive the proper amount of nutrients without being over-fertilized, which can harm their growth.

A ratio of 5 parts rest to 1 part exercise for a healthy lifestyle. This ratio helps to maintain a healthy balance between rest and physical activity, allowing for proper recovery and growth. It also ensures that a person does not over-exercise and become exhausted, which can lead to injury or burnout.

Answer:

According to Kepler's third law, what is the orbital period of this asteroid in terms of Earth years? A certain asteroid is approximately 50 AU from the Sun.

The value of x/y is 37/35, if a square with side length x is inscribed in a right triangle and a square with side length y is inscribed in another right triangle.

Note that triangle ABC and triangle FBE are similar,(by AAA)

As [tex]\angle B[/tex] is common in both, and [tex]\angle F= \angle A[/tex] as they both are 90°

so, the [tex]\angle C[/tex] will also be equal to [tex]\angle E[/tex]

so [tex]\frac{BF}{FR} = \frac{AB}{AC}[/tex]

This can be written as [tex]\frac{4-x}{x} = \frac{4}{3}[/tex]

solving: 12 - 3x = 4x

7x = 12 or x = 12/7

Similarly, triangle A'B'C' and triangle RB'Q are similar,

so RB' = [tex]\frac{4}{3}y[/tex] and C'S= [tex]\frac{3}{4}y[/tex]

Thus, C'B' = C'S+ SR+ RB'

or  [tex]\frac{4}{3}y + y + \frac{3}{4} = 5[/tex]

solving y = 60/37

Now, x/y = [tex]\frac{12}{7} \times \frac{37}{60}[/tex] = 37/35

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The measure of the missing angle α is 62 degrees.

The sum of angles on the straight line adds up to 180 degrees.

From the diagram;

Since the sum of angles on a straight line adds up to 180 degrees.

Angle 1 + Angle 2 + Angle 3 = 180

Plug in the values

118 + α = 180

Subtract 118 from both sides

118 - 118 + α = 180 - 118

α = 180 - 118

α = 62°

Therefore, the value of angle α is 62 degrees.

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Answer:

Step-by-step explanation:

Let's say that after the break, the group of friends watches m minutes of the movie.

We know that they watched 42 minutes before the break, so the total time they have watched before and after the break is 42 + m minutes.

Since the movie is 115 minutes long, the inequality that represents the number of minutes they will watch after the break is:

42 + m < 115

So, the inequality that represents the number of minutes, m, they will watch after the break is:

m < 115 - 42 = 73

This means that m has to be less than 73 for the group of friends to finish watching the movie.

Left and right multiplying a positive semi-definite matrix by another matrix will always result in a positive semi-definite matrix.

Positive semi-definite matrices are important in many areas of mathematics and science, including linear algebra, optimization, and physics.

Let A be a positive semi-definite matrix, and let B be an arbitrary matrix. We want to determine whether AB and BA are also positive semi-definite matrices.

First, let's consider AB. To show that AB is positive semi-definite, we need to show that for any non-zero column vector x, xT(AB)x ≥ 0. We can expand this expression as:

xT(AB)x = (xTA)Bx = yTBy

where y = Ax. Since A is positive semi-definite, we know that yTy ≥ 0 for any vector y. Therefore, we have shown that xT(AB)x ≥ 0 for any non-zero column vector x, and hence AB is positive semi-definite.

Next, let's consider BA. To show that BA is positive semi-definite, we need to show that for any non-zero column vector x, xT(BA)x ≥ 0. We can expand this expression as:

xT(BA)x = (xTB)Ax = zTAz

where z = Bx. Since A is positive semi-definite, we know that zTAz ≥ 0 for any vector z. Therefore, we have shown that xT(BA)x ≥ 0 for any non-zero column vector x, and hence BA is also positive semi-definite.

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An irrational number is created by adding two rational numbers, according to the answer to the given question. If the oppositely irrational numbers a and b.

Rational numbers are those that may be written as a ratio (or fraction) of two integers. A fraction with a non-zero denominator is said to be rational.

A few instances of rational numbers are 1/2, 1/5, and 3/4. A rational number, “0,” can also be stated in a number of different ways, such as 0/1, 0/2, and 0/3. But 1/0, 2/0, 3/0, and so forth.

The number seven makes sense. A rational number is produced when two integers are split. To get the rational number 7, divide the whole number 7 by the whole number 1. Since 7 can be obtained by dividing two integers, it is referred to as a rational number.

Two rational integers added together yield an irrational number. Ab is irrational if and only if a and b are mutually exclusive irrational numbers.

Therefore, a = 2 and b = ab = 2 is an irrational number.

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Answer:

The equation is:

8x + 4 = 68

and the solution is:

x = 8

Step-by-step explanation:

The equation is:

8 time x and 4 is 68

8x+4 = 68

Solve:

8x + 4 - 4 =  68 - 4

8x + 0 = 64

8x = 64

x = 64/8

x = 8

Check:

8*8 + 4 = 68

Factor the polynomial by factoring out the greatest common factor, 7x2 + 5 - x = 6x2 + 10

x = -5

Soultion:

→ 7 × 2 + 5 - x = 6 × 2 + 10

Multiply.

→ 14 + 5 - x = 12 + 10.

Combine like terms.

→ 19 - x = 24

Isolate x (I'm going to add x and subtract 24 from both sides to avoid changing signs)

Answer

→ = x = -5

Answer:

x-8

Step-by-step explanation:

the answer is  x-8                                                             correct answer x-8

Answer:

170 feet per second

Step-by-step explanation:

To answer the question you need to find the unit rate. To find the unit rate divide the denominator with the numerator in a way that the denominator becomes 1.

5,100/30 = 170

The skydiver falls at a rate of 170 feet per second before opening the parachute.

Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications.

For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.

We have to given that;

It takes a skydiver 30 seconds to fall 5,100 feet before opening the parachute.

Hence, Height for this is,

⇒ 5100 / 30

⇒ 170 feet per second

Thus, the skydiver falls at a rate of 170 feet per second before opening the parachute.

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We solved the given inequality and found the values of x lie in the interval   ( -∞ , 4). This is graphed and shown on the number line as below.

What is meant by inequality?

A relationship that compares two numbers or other mathematical expressions in an unequal way is known as an inequality. It is most frequently used to compare the sizes of two numbers on the number line.

Given inequality is:

11x + 6 < 9x + 10

Solving,

11x - 9x < 10 - 6

2x < 4

x < 4

The values of x is in the interval : ( -∞ , 4)

The above inequality is shown below on the number line as well as on the graph.

We can see that all the values to the left of 4 but not including 4 can be taken as the value of x.

Therefore we solved the given inequality which is graphed and shown on the number line.

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Sipho earned R33.15 in simple interest.

The balance of the account at the end of the first 30 days was R2 133.15.

a. To calculate the simple interest earned by Sipho, we need to calculate the total amount deposited and the interest earned on that amount.

Total amount deposited = R600 + R1 000 + R500 = R2 100

Interest earned = R2 100 x 4.5% x 30/365 = R33.15 (rounded to the nearest cent)

Therefore, Sipho earned R33.15 in simple interest.

b. The balance of the account at the end of the first 30 days can be calculated by adding the total amount deposited and the interest earned to the initial deposit:

Balance = R600 + R1 000 + R500 + R33.15 = R2 133.15

Therefore, the balance of the account at the end of the first 30 days was R2 133.15.

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Keenan has placed his solar panel at an optimal angle.

The cosine law is a mathematical relationship between the sides and angles of a triangle. The cosine law states that:

cos(C) = (a² + b² - c²) / 2ab

where a, b, and c are the lengths of the sides of the triangle and C is the measure of one of the angles. This law can be used to find unknown side lengths or angle measures in a triangle when given the other values.

Check the attached image for labelling.

The angle we are trying to calculate is labelled C.

cos (C) = (20² + 18² - 19²) / (2*20*18)

cos (C) = 363/720

C = cos⁻¹(363/720)

C = 59.72°

Since the angle obtained is between 58° and 60°. Thus, Keenan has placed his solar panel at an optimal angle.

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Complete Question

Check the attached image for complete question

Answer:44

Step-by-step explanation:44444444

Answer:

The perimeter of △ABC is 144 cm.

------------------------------

Since points C and D are on the perpendicular bisector of AB, we have:

Find the length of AC using Pythagorean:

Find the perimeter of ΔABC:

The variable gets eliminated, then the equation has no solution.

In other words, the collection of all feasible values for the parameters that satisfy the specified mathematical equation is the convenient storage of the bunch of equations.

The equation is given below.

(10x - 4) + ( -7 + x) = (10x + 2) + (-4 + x)

Simplify the equation, then we have

(10x - 4) + ( -7 + x) = (10x + 2) + (-4 + x)

10x - 4 - 7 + x = 10x + 2 - 4 + x

11x - 11 = 11x - 2

11x - 11x = 9

The variable gets eliminated, then the equation has no solution.

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The correct equation is given below.

(10x - 4) + ( -7 + x) = (10x + 2) + (-4 + x)