Write the equation of the line that passes through the point (- 6, 1) and has a slope of 1/2 in slope-intercept form

Answer:

\(53010000\)

Step-by-step explanation:

\(5.301 \times {10}^{7} \\ \\ 5301 \times {10}^{ - 3} \times {10}^{7} \\ \\ 5301 \times {10}^{ - 3 + 7} \\ \\ = 5301 \times {10}^{4} \\ \\ = 53010000 \)

Answer: Please check the explanation.

Step-by-step explanation: To solve this problem, first you need to do the equation, 10 to the 7th power, which is 10000000. Then you need to multiply 10000000 by 5.301, which is 53010000. Hope this helped!

Answer:

(9,12) I think  

Step-by-step explanation:

Answer:

10/12 also 5/6

Step-by-step explanation:

Answer:

10/12 or the simplified version 5/6

Step-by-step explanation:

you have to multiply 2/3 by the reciprocal of 4/5 which is 5/4

so you write down 2/3 times 5/4 (just multiply across so it's 2x5 over 3x4)

2x5=10 and 3x4=12

10 is the numerator and 12 is the denominator

simplify if the problem calls for it by dividing the top and bottom numbers by 2

Answer:

1135.28

Step-by-step explanation:

1102 * (1.02) = 1124.04

1124 * (1.01) = 1135.28

Your final regular expression is "[123abc]+". This expression will match any sequence of the specified digits and lowercase letters (1, 2, 3, a, b, and c) within a text string.

To write a regular expression that matches all the digits 1, 2, and 3, and the lowercase letters a, b, and c within a text string, follow these steps:
Start the regular expression with an opening square bracket "[", which indicates the start of a character class.
List the digits you want to match, in this case, 1, 2, and 3, followed by the lowercase letters a, b, and c. So the expression inside the character class would be "123abc".
Close the character class with a closing square bracket "]". Your regular expression should now look like "[123abc]".
To match one or more occurrences of these characters, add a "+" sign after the closing square bracket. This makes the expression "[123abc]+".
Now, your final regular expression is "[123abc]+". This expression will match any sequence of the specified digits and lowercase letters (1, 2, 3, a, b, and c) within a text string.

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Set A is more widely dispersed than Set B based on the coefficient of variation.

The coefficient of variation (CV) is a measure of relative variability, which is used to compare the dispersion of data sets with different means. It is calculated as the ratio of the standard deviation to the mean, expressed as a percentage.

Let's calculate the coefficient of variation for each set of numbers:

Set A:

Mean of Set A = (2+3+1+4+5+6+7+25+9+8) / 10 = 7

Standard Deviation of Set A = √[(2-7)² + (3-7)² + (1-7)² + (4-7)² + (5-7)² + (6-7)² + (7-7)² + (25-7)² + (9-7)² + (8-7)²] / √10 ≈ 7.156

Coefficient of Variation for Set A = (7.156 / 7) * 100 ≈ 102.23%

Set B:

Mean of Set B = (32+45+40+38+47+50+43+36+44+35) / 10 = 40

Standard Deviation of Set B = √[(32-40)² + (45-40)² + (40-40)² + (38-40)² + (47-40)² + (50-40)² + (43-40)² + (36-40)² + (44-40)² + (35-40)²] / √10 ≈ 5.09

Coefficient of Variation for Set B = (5.09 / 40) * 100 ≈ 12.72%

Comparing the coefficient of variation for Set A (102.23%) and Set B (12.72%), we can see that Set A has a much higher coefficient of variation, indicating greater dispersion or variability compared to Set B.

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Using the order of operations, the expression can be simplified as  

9 + 1.34 + 62.88 = 73.22

The order of operations instructs us on how to solve steps in multi-step expressions. Any operations contained within parenthesis or brackets are first solved. After that, we handle any exponents. Third, we perform all division and multiplication operations from left to right. Fourth, all addition and subtraction problems are solved from left to right.

Remember PEMDAS when simplifying multi-step expressions, i.e.:

P (Parentheses)

E (Exponents, Powers and Square Roots)

MD (Multiplication and Division, left-to-right)

AS (Addition and Subtraction, left-to-right)

The expression given in the problem is:  9 + 1.34 + 1 2 (3.50 +1.74)

Apply the above operation order:

Step 1: solve the addition inside the parenthesis

9 + 1.34 + 1 2 (3.50 +1.74)  =  9 + 1.34 + 1 2 (5.24)

Step 2: Multiply the result by 12

9 + 1.34 + 1 2 (5.24) = 9 + 1.34 + 62.88

Step 3: Apply addition from left to right

9 + 1.34 + 62.88 = 73.22

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The transformations that result in similar triangles are dilations, rotations, reflections, and translations.

A transformation that conserves the shape, but not necessarily the size, of a figure is called a similarity transformation. Rotation, reflection, and translation are rigid motions, which means they preserve both size and shape, on the other hand, dilation only ensures that the shape is preserved. As the rigid motions are congruence transformations, all congruent figures are also similar.

A similarity transformation is a dilation or a combination of rigid motions and dilations. Two geometric figures are similar if and only if there is a similarity transformation that maps one of the figures onto the other. Similar figures have the same shape but necessarily not the same size.

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Answer:

They will deliver on the same day again 21 days later

Step-by-step explanation:

Multiples of 3 and 7

3: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30

7: 7, 14, 21, 28, 35, 42, 49

They will deliver on the same day again 21 days later

Answer:690

Step-by-step explanation:

690

Answer:  $3,261.

Step-by-step explanation:

The answer is $3,261. Jayden would have more money in his account than Camden because his account pays a higher interest rate and is compounded continuously, which allows more frequent compounding of interest. This means that Jayden's account accumulates more interest than Camden's account over time.

Integer represents the change in the height of the elevator, in meters, every second is 25200.

The speed at which an object's location changes in any direction. The distance travelled in relation to the time it took to travel that distance is how speed is defined. Since speed simply has a direction and no magnitude, it is a scalar quantity.

Given Data

The main elevator in the Willis Tower descends 420 meters in 60 seconds.

Distance = 420meters

Time = 60 seconds

Speed = distance (time)

Speed = 420(60)

Speed = 25200

Integer represents the change in the height of the elevator, in meters, every second is 25200.

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Answer:

22

Step-by-step explanation:

The centroid divides a median in two parts that have this ratio = 1/3 and 2/3

In particular the part between the vertex and the centroid is 2/3 of the median.

So we have:

XN = (33 * 2)/3 = 22

The correct answer is: Yes, relation Q is a function,because there is exactly one y-value for every x-value.

To determine whether the given relation Q is a function, we need to check if each x-value is associated with a unique y-value. If there is any x-value that corresponds to multiple y-values, then the relation is not a function.

Let's examine the ordered pairs in relation Q: (3, -2), (-3, 1), (-2, -2), (1, -3).

We can see that each x-value in Q is associated with a unique y-value:

For x = 3, the y-value is -2.

For x = -3, the y-value is 1.

For x = -2, the y-value is -2.

For x = 1, the y-value is -3.

Since each x-value is paired with a unique y-value in relation Q, we can conclude that Q is a function.

In a function, every input (x-value) maps to a single output (y-value). If there were any repeated x-values with different y-values in the relation, it would indicate a violation of this rule and Q would not be a function. However, in this case, all the x-values have distinct y-values, satisfying the criteria for a function.

It's worth noting that we can also visualize this relation on a coordinate plane and check if there are any vertical lines that intersect the graph at more than one point. If there are no such lines, it confirms that the relation is a function.

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A gas station is open 365 day a year, 24 hours a day. If the gas station served 40,000 cups of coffee last year, then it served an average of 5 cups of coffee per hour.

The problem can be solved using the average value approach.

Average value = total amount or sum of data / number of data

In the given problem,

total amount = total coffee served last year

total amount = 40,000

number of data = number of hours in a year

number of data = 365 day/year x 24 hours/day = 8760 hours

Hence,

Average value = total amount or sum of data / number of data

                         = 40000 / 8760

                         = 4,6 ≈ 5 (round to the nearest whole cup)

Hence, the average coffee served is 5 cups per hour.

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First derisive the equation for C

\(\\ \sf\longmapsto F=\dfrac{9}{5}C+32\)

\(\\ \sf\longmapsto C+32=\dfrac{5}{9}F\)

\(\\ \sf\longmapsto C=\dfrac{5}{9}F-32\)

\(\\ \sf\longmapsto C=\dfrac{5}{9}101-32\)

\(\\ \sf\longmapsto C=\dfrac{505}{9}-32\)

\(\\ \sf\longmapsto C=56.1-32\)

\(\\ \sf\longmapsto C=24.1°C\)

Answer:

The answer is 660

Step-by-step explanation:

30×2200÷100= 660

Answer:

660

Step-by-step explanation:

to know 30%

2200÷10×3=660

The most appropriate translation of the English sentence. the amount of time spent driving (which depends on the speed of the car) is 5 hours. is time(speed) = 5, making option C the right choice.

The time spent by a body covering a certain distance at a certain speed is given as time = distance/speed.

In the question, we are asked to translate the English sentence, :"the amount of time spent driving (which depends on the speed of the car) is 5 hours".

In the given sentence, the time spent driving is given to be 5 hours, depending on the speed of the car.

Thus, the time can be shown as a function of speed with a value of 5.

Thus, the translation can be, time(speed) = 5.

Thus, the most appropriate translation of the English sentence. the amount of time spent driving (which depends on the speed of the car) is 5 hours. is time(speed) = 5, making option C the right choice.

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The provided question is incomplete. The complete question is:

"Choose the most appropriate translation of the English sentence. the amount of time spent driving (which depends on the speed of the car) is 5 hours.

a. speed(time) = 5

b. time(5) = 50 mph

c. time(speed) = 5

d. time(speed) > 0"

Answer

he diameter of the circle is 22 units.

x² + y² - 16x + 12y = 21    

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The rate of change of output with respect to skilled workers when 18 skilled workers and 31 unskilled workers are employed is 427.94.

Given, the function is z = f(x, y)

= 14500x + 4000y + 15x²y - 11x³

Where, z = the weekly # of pounds of acetate fiber

X = the # of skilled workers at the planty = the # of unskilled workers at the plant

(a) We are given the values of skilled workers and unskilled workers, we need to calculate the number of pounds of fiber that can be produced.

Put x = 18

and y = 31 in the given function

z = f(x, y)

= 14500x + 4000y + 15x²y - 11x³z

= 14500 (18) + 4000 (31) + 15 (18)² (31) - 11 (18)³

= 261180 lbs

Hence, the weekly number of pounds of fiber that can be produced with 18 skilled workers and 31 unskilled workers is 261180 lbs.

(b) We need to find an expression (fx) for the rate of change of output with respect to the number of skilled workers.

Differentiate the given function with respect to x.

z = f(x, y)

= 14500x + 4000y + 15x²y - 11x³∂z/∂x

= 14500 + 30xy - 33x²

= 14500 + 30y (x - 11x²/30y)fx

= ∂z/∂x = 14500 + 30y (x - 11x²/30y)

Hence, the expression (fx) for the rate of change of output with respect to the number of skilled workers is fx = 14500 + 30y (x - 11x²/30y).

(c) We need to find an expression (fy) for the rate of change of output with respect to the number of unskilled workers.

Differentiate the given function with respect to y.z

= f(x, y)

= 14500x + 4000y + 15x²y - 11x³∂z/∂y

= 4000 + 15x²

= 15 (x² + 267)fy

= ∂z/∂y

= 15 (x² + 267)

Hence, the expression (fy) for the rate of change of output with respect to the number of unskilled workers is fy = 15 (x² + 267).

(d) We need to find the rate of change of output with respect to skilled workers when 18 skilled workers and 31 unskilled workers are employed.

Put x = 18 and

y = 31 in the expression of fx.

fx = 14500 + 30y (x - 11x²/30y)

= 14500 + 30 (31) (18) - 11 (18)² / 31

= 14500 + 16740 - 12762/31

= 427.94

Hence, the rate of change of output with respect to skilled workers when 18 skilled workers and 31 unskilled workers are employed is 427.94.

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Step-by-step explanation:

96/8=__________ will be the answer

Lines AC and BD intersect at point O. The measure ∠AOB is 54° and is less than measure of either of its adjacent angles: ∠AOD and ∠BOC. Then the measure of ∠AOB=54°, ∠COD=126°, ∠AOD=63°, and ∠BOC=63° .

Since lines AC and BD intersect at point O, we know that angles ∠AOD and ∠BOC are opposite angles and therefore congruent. Similarly, angles ∠COB and ∠DOA are opposite angles and congruent. Let's start with finding the measure of ∠COD. Since angles ∠COB and ∠DOA are congruent, we can find the measure of ∠COD by subtracting the measure of ∠AOB from 180° (since ∠COB and ∠DOA together form a straight line and therefore add up to 180°).
∠COD = 180° - 54° = 126°
Now, let's find the measure of ∠AOD and ∠BOC. We know that ∠AOB is less than either of its adjacent angles, so that means that both ∠AOD and ∠BOC are greater than 54°. Since angles ∠COB and ∠DOA together add up to 180°, we can subtract the measure of ∠AOB from 180° to find the total measure of angles ∠AOD and ∠BOC together.
180° - 54° = 126°
Since ∠AOD and ∠BOC are congruent, we can divide 126° by 2 to find the measure of each angle.
∠AOD = ∠BOC = 63°
So to summarize:
- ∠AOB = 54°
- ∠COD = 126°
- ∠AOD = ∠BOC = 63°

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With reference to graph a, at a price of $10, total revenue equals $400.

By multiplying the total number of items and services sold by their prices, total revenue—the sum of all sales—is determined. The extra money made from selling one more unit of an item or service is known as marginal revenue. The term "revenue" refers to the sum of money that a business makes from the sale of goods and services during the course of its operations. Total earnings or the profit a corporation makes are other names for revenue. The business of the corporation affects the revenue formula. For instance, a product sale is computed by multiplying the total number of product sales by the average price at which the goods are sold.

Given

With reference to graph a, at a price of $10,

total revenue equals:

$400

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The correct option is statement 1 and statement 4. The letter y is a variable and the number 9 is a constant

Mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

The given the expression y + 9. The terms will be noted as:-

E = y + 9

Here y is the variable and 9 is a constant term in the given expression.

Therefore, the correct option is statement 1 and statement 4. The letter y is a variable and the number 9 is a constant.

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Step-by-step explanation:

We can estimate 320/11 by using 320/10, which is 32.

Making it divide by 10 is easier as compared to 11.

Answer:

117.3 in^3

Step-by-step explanation:

Volume of cone=π(r^2)h/3=π·42·7/3≈117.3 in^3

Answer:

117.3in³

Step-by-step explanation:

πr²\(\frac{h}{3}\)

3.14x4²x\(\frac{7}{3}\)= 117.29

117.29 to nearest 10th= 117.3in³

Answer:

-2,3

Step-by-step explanation:

There are 37 numbers from 1 to 37, inclusive.

The probability of choosing a number that is a multiple of 3 is approximately 0.324 or 32.4%.

How to find and what is probability?

To count the number of multiples of 3, we can first find the smallest multiple of 3 that is greater than or equal to 1, which is 3.

Then we can find the largest multiple of 3 that is less than or equal to 37, which is 36. We can then count the multiples of 3 by counting in increments of 3 from 3 to 36: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36. There are 12 such numbers.

Therefore, the probability of choosing a number that is a multiple of 3 is:

P(multiple of 3) = number of multiples of 3 / total number of numbers

P(multiple of 3) = 12/37

So the probability of choosing a number that is a multiple of 3 is approximately 0.324 or 32.4%.

Probability is a measure of the likelihood or chance of an event occurring. It is expressed as a number between 0 and 1, where 0 represents an impossible event and 1 represents a certain event.

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Answer:

The answer is

Step-by-step explanation:

The distance between two points is found by using the formula

\( \sqrt{ {(x1 - x2)}^{2} + {(y1 - y2)}^{2} } \)

Where (x1 , y1) and ( x2 , y2) are the points

The distance between (-6, -2) and (0, -1) is

\( \sqrt{ {( - 6 - 0)}^{2} + {( - 2 + 1)}^{2} } \\ \\ = \sqrt{ {( - 6})^{2} + {( - 1)}^{2} } \\ \\ = \sqrt{36 + 1} \\ \\ = \sqrt{37} \: units\)

Hope this helps you

Answer: √37 units

hope that helped!

Answer:

8

Step-by-step explanation:

0.20 x 40 = 8

Therefore, 20% of 40 is 8

The total number of engineering students is 176 approximately among the 750 students enrolled in the college by using the proportionate formula.

It is mentioned here that a college has 19 students of engineering for every 81 students who got enrolled.

Therefore the ratio of engineering students to total number of students is as follows:

No. of engineering students = 19

Total number of students = 81

Ratio = \(\frac{19}{81}\)

Now if the total number of students that the college has is 750 then the number of engineering students can be found by using the proportionate formula as the ratio of the engineering to the total students will remain same.

Total number of students = 750

Let the number of engineering students be y

Ratio = \(\frac{y}{750}\)

Comparing it with the above ratio and using the proportionate formula,

\(\frac{19}{81} = \frac{y}{750}\)

⇒ y = \(\frac{19*750}{81}\)

⇒ y = 175.925

So approximately 176 were the engineering students among 750 students enrolled.

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