write an equation for the function graphed.

Answer:

The completely factored form of 15a³bc³ – 6a²b²c³ is 3a²bc³ × (5a - 2b).

Answer:

[tex]3a^{2} bc^{3} ( 5a - 2b)[/tex]

Step-by-step explanation:

[tex]15a^{3} bc^{3} - 6a^{2} b^{2} c^{3}[/tex]

[tex]3a^{2} bc^{3} ( 5a - 2b)[/tex]

Speed of bicycle in miles per hour will be 12.85 mi/h.

What is the definition of speed?

The following is the definition of speed:

The rate at which the position of an item changes in any direction.

The ratio of distance travelled to time spent travelling is described as speed. Speed is a scalar number since it has just one direction and no magnitude.

Formula for Speed

The speed formula is as follows:

s=d/t

Where,

s denotes the speed in metres per second, d the distance travelled in metres, and t the time in seconds.

Now,

Given Diameter=18 inch

then distance covered by cycle in 4 rotation in one second =4*π*diameter

=4*22/7*18

=226.28

Then Speed=226.28 in/s

As 1 mike=63360 inch and 1 hour= 3600 seconds

then Speed in miles/hour=226.28*3600/63360

=12.85 mi/h

hence,

          Speed of bicycle in miles per hour will be 12.85 mi/h.

To know more about speed visit the link

https://brainly.com/question/7359669?referrer=searchResults

#SPJ1

a ) Construction of stem and leaf display of the data is:

For n = 129 and with splint unit = 0.1, the stem and splint map of the given data on Shower- inflow rate( L/ min) is as follows

a stem-and-leaf display of the data.

   Stems                                                Leaves

       2                                                       28

       3                                                1344567789

       4                                                 01356889

       5                                          00001114455666789

       6                              0000122223344456667789999

       7                                     00012233455555668

       8                                                02233448

       9                                         012233335666788

      10                                             2344455688

      11                                                2335999

      12                                                     17

      13                                                      9

      14                                                     36

      15                                                  0035

      16                                                  None

      17                                                  None

      18                                                     3

b) From brume and splint map we note that minimal Shower inflow rate is2.2 whereas outside is18.3 L/ mim. farther typical or representative rate is7.0 L/min.

c) The display of data on steam and leaf chart shows that data is positively skewed means concentration of data on left side or lower value side is high as compared to other side.

d) Distribution is not symmetric rather very clear positive skew ness is observed through steam and leaf chart. Even distribution is Unimodal.

e) From steam and leaf chart is indicative to conclude that the highest observation 18.3 is outlier.

A stem and splint plot, also known as a stem and splint illustration, is a way to arrange data so that it's simple to see how constantly colorful feathers of values do. It's a graph that displays ordered numerical data. A stem and a splint are divided into each piece of data.

Learn more about Stem and Leaf display:

https://brainly.com/question/30189491

#SPJ4

Complete question:

The accompanying data set consists of observations on shower-flow rate (L/min) for a sample of n = 129 houses:

4.6 12.1 7.1 7.0 4.0 9.2 6.7 6.9 11.5 5.1

11.2 10.5 14.3 8.0 8.8 6.4 5.1 5.6 9.6 7.5

7.5 6.2 5.8 2.8 3.4 10.4 9.8 6.6 3.7 6.4

8.3 6.5 7.6 9.3 9.2 7.3 5.0 6.3 13.9 6.2

5.4 4.8 7.5 6.0 6.9 10.8 7.5 6.6 5.0 3.3

7.6 3.9 11.9 2.2 15.0 7.2 6.1 15.3 18.3 7.2

5.4 5.5 4.3 9.0 12.7 11.3 7.4 5.0 3.5 8.2

8.4 7.3 10.3 11.9 6.0 5.6 9.5 9.3 10.4 9.7

5.1 6.7 10.2 6.2 8.4 7.0 4.8 5.6 10.5 14.6

10.8 15.5 7.5 6.4 3.4 5.5 6.6 5.9 15.0 9.6

7.8 7.0 6.9 4.1 3.6 11.9 3.7 5.7 6.8 11.3

9.3 9.6 10.4 9.3 6.9 9.8 9.1 10.6 4.5 6.2

8.3 3.1 4.9 5.0 6.0 8.2 6.3 3.8 6.0

(a) Construct a stem-and-leaf display of the data. (Enter numbers from smallest to largest separated by spaces. Enter NONE for stems with no values.)

Stems Leaves

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

(b) What is a typical, or representative, flow rate?

L/min

(c) Does the display appear to be highly concentrated or spread out?

highly concentrated, except for a few values on the positive sidehighly concentrated in the middle highly concentrated, except for a few values on the negative sidespread out

(d) Does the distribution of values appear to be reasonably symmetric? If not, how would you describe the departure from symmetry?

Yes, the distribution appears to be reasonably symmetric.No, the data are skewed to the right, or positively skewed. No, the data are skewed to the left, or negatively skewed.No, the distribution of the values appears to be bimodal.

(e) Would you describe any observation as being far from the rest of the data (an outlier)?

Yes, the value 2.2 appears to be an outlier.Yes, the value 15.5 appears to be an outlier. Yes, the value 18.3 appears to be an outlier.No, none of the observations appear to be an outlier.

Bro Use SOH CAH TOA and you check through to now whether u use Cos, Sine or tan

Using the a pair of adjacent angles, we will see that:

Z° = 137°

When we have an intersection between two lines, we know that any pair of adjacent angles (they share a side) are congruent angles, thus, their measures add up to 180°.

Then here we can write a linear equation for z.

z + 43 = 180

Solving that for z, we will get:

z = 180 - 43

z = 137

That is the measure of the angle.

Learn more about congruent angles by reading:

https://brainly.com/question/14791175

#SPJ1

The radius of the circle is 7.8 cm.

What is a circle?

All points in a plane that are at a specific distance from a specific point, the center, form a circle. In other words, it is the curve that a moving point in a plane draws to keep its distance from a specific point constant.

Given that the area of a circle is 192 cm².

The area of a circle is πr², where r is the radius of the circle.

Assume that the radius of the circle is r.

Therefore,

πr² = 192

Divide both sides by π:

r² = 192/π

r² = 61.115

r = 7.817

r  ≈ 7.8 cm

To learn more about the circumference of a circle, click on the

https://brainly.com/question/12158384

#SPJ1

Answer: 821

Step-by-step explanation: The nearest tenth is the first digit after the decimal point.

The area of the kite is 0.08 metres squared.

A kite is a quadrilateral. Therefore, the window has the shape of a kite. The square metres of glass that will be used to construct the kite can be calculated as follows:

The area of a kite is half the products of the diagonals of the kite.

Therefore,

area of the kite = 1 / 2 pq

where

Therefore,

p = 20 + 20 = 40 cm

q = 25 + 15 = 40 cm

Hence,

area of the kite = 1 / 2 × 40 × 40

area of the kite = 1600  /2

area of the kite = 800 cm²

area of the kite = 0.08 m²

learn more on area here: brainly.com/question/23718948

#SPJ1

Answer:

W =1 1/4Step-by-step explanation: Let W = what. W - 1/2 = 3/4. Add 1/2 to each side. W -1/2 +1/2 = 3/4+1/2. W = 3/4+1/2.

Step-by-step explanation:

Answer:

(a) To determine the mean and standard deviation of Y, we need to find the expected value and standard deviation of the number of defects that can be sold by Company F. Since the number of defects that can be sold is equal to X if X is less than or equal to 2, and equal to 2 if X is greater than 2, we can use the following formula to find the expected value of Y:

E(Y) = P(X = 0) × 0 + P(X = 1) × 1 + P(X = 2) × 2 + P(X > 2) × 2

E(Y) = 0.58 × 0 + 0.23 × 1 + 0.11 × 2 + 0.03 × 2

E(Y) = 0.23 + 0.22 + 0.03

E(Y) = 0.48

To find the standard deviation of Y, we can use the following formula:

Var(Y) = P(X = 0) × (0 - E(Y))^2 + P(X = 1) × (1 - E(Y))^2 + P(X = 2) × (2 - E(Y))^2 + P(X > 2) × (2 - E(Y))^2

Var(Y) = 0.58 × (0 - 0.48)^2 + 0.23 × (1 - 0.48)^2 + 0.11 × (2 - 0.48)^2 + 0.03 × (2 - 0.48)^2

Var(Y) = 0.58 × 0.2304 + 0.23 × 0.1024 + 0.11 × 0.0304 + 0.03 × 0.0304

Var(Y) = 0.1333

The standard deviation of Y is the square root of the variance:

StdDev(Y) = √Var(Y)

StdDev(Y) = √0.1333

StdDev(Y) = 0.3663

So, the mean and standard deviation of Y are 0.48 and 0.3663, respectively.

(c) To find the mean and standard deviation of the selling price for the fat quarters sold by Company G, we need to find the expected value and standard deviation of the price, taking into account the discount for each defect. We can use the following formula to find the expected value of the price:

E(Price) = $5.00 - $1.50 × E(Defects)

E(Price) = $5.00 - $1.50 × 0.40

E(Price) = $5.00 - $0.60

E(Price) = $4.40

To find the standard deviation of the price, we can use the following formula:

StdDev(Price) = $1.50 × StdDev(Defects)

StdDev(Price) = $1.50 × 0.66

StdDev(Price) = $0.99

So, the mean and standard deviation of the selling price for the fat quarters sold by Company G are $4.40 and $0.99, respectively.

Answer:

To find the coordinates of A′ and B′ after a dilation with a scale factor of 2 and with the center of dilation at the origin (0, 0), we need to apply the dilation formula:

(x', y') = (2 * (x - 0) + 0, 2 * (y - 0) + 0) = (2x, 2y)

For point A, the original coordinates are (-4, 1), so we substitute these values into the dilation formula:

(x', y') = (2 * (-4 - 0) + 0, 2 * (1 - 0) + 0) = (-8, 2)

So, after the dilation, the new coordinates of point A are (-8, 2).

For point B, the original coordinates are (-1, 3), so we substitute these values into the dilation formula:

(x', y') = (2 * (-1 - 0) + 0, 2 * (3 - 0) + 0) = (-2, 6)

So, after the dilation, the new coordinates of point B are (-2, 6).

Answer:

Step-by-step explanation:

Step 1: Understanding the Dilation

A dilation with a scale factor of 2 and a center of dilation at the origin is a transformation that enlarges or shrinks an object by a factor of 2, with the origin (0, 0) as the center of the dilation.

Step 2: Using the Formula

To find the coordinates of the dilated points, we use the formula:

(x', y') = (2 * x, 2 * y)

Where (x, y) are the original coordinates of the points, and (x', y') are the coordinates of the dilated points.

Step 3: Finding the Coordinates of A′

We are given that the original coordinates of point A are (-4, 1), so we substitute these values into the formula:

A′ = (2 * -4, 2 * 1) = (-8, 2)

Step 4: Finding the Coordinates of B′

We are given that the original coordinates of point B are (-1, 3), so we substitute these values into the formula:

B′ = (2 * -1, 2 * 3) = (-2, 6)

Step 5: Conclusion

So, after a dilation with a scale factor of 2 and a center of dilation at the origin, the new coordinates of A′ and B′ are (-8, 2) and (-2, 6) respectively.

-1/10 should be subtracted from 1/2 to get 4/10.

A fraction is of the form → (x/y).

For example, we can write fractions as → 2/3.

Fractions and ratios represent the same aspect. We can write -

2 : 3 = 2/3

4 : 7 = 4/7

Given is to solve the expression -

(1/2) - ? = 4/10

We can write the expression as -

(1/2) - (x) = (4/10)

(x) = 4/10 - 1/2

(x) = 4/10 - 5/10

(x) = -1/10

Therefore, -1/10 should be subtracted from 1/2 to get 4/10.

To solve more questions on subtracting fractions, visit the link below

https://brainly.com/question/30489902

#SPJ9

{Question in English -

What fraction subtracted from 1/2 equals 4/10?}

Answer:

Step-by-step explanation:

The number of ways to arrange the letters in "HEDGEHOG" is 8!/(2!3!). The exclamation mark (!) means factorial, which is the product of all positive integers up to that number. For example, 5! = 5 x 4 x 3 x 2 x 1 = 120.

In this case, we have two H's and three E's, so we have to divide the total number of arrangements by the number of arrangements of H's and the number of arrangements of E's to avoid overcounting.

The total number of arrangements of the eight letters is 8!:

8! = 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 = 40320

The number of arrangements of H's is 2!:

2! = 2 x 1 = 2

The number of arrangements of E's is 3!:

3! = 3 x 2 x 1 = 6

So the number of arrangements of the letters in "HEDGEHOG" that avoid overcounting is:

40320 / (2 x 6) = 40320 / 12 = 3360.

Therefore, there are 3360 ways to arrange the letters in "HEDGEHOG".

The graph of the quadratic function y = -2x² + 1 is given by the image presented at the end of the answer.

The parent quadratic function is given as follows:

y = x².

The transformed quadratic function is given as follows:

y = -2x² + 1.

The transformations are given as follows:

More can be learned about quadratic functions at https://brainly.com/question/1214333

#SPJ1

The area of the given composite figure with a side length of 14mm and an edge length of 8mm is 158.2 mm².

What is a composite figure?

A two-dimensional figure built up of fundamental two-dimensional shapes like triangles, rectangles, circles, semicircles, etc. is known as a composite shape or composite figure. A variety of forms that we encounter every day are composite figures that can be created from two or more fundamental figures.

The figure is given below.

From the figure, we can see that the sides of a triangle at the top and bottom are the same.

So the triangle cut from the bottom is placed at the top of the figure.

When the cut triangle is placed back at the bottom, we get a rectangle of length 14 mm and breadth 11.3 mm, as given below.

So the area of the given composite figure is the same as the area of the rectangle.

The area of the rectangle = length * breadth = 14 * 11.3 = 158.2 mm²

Therefore the area of the given composite figure is 158.2 mm².

To learn more about composite figures, follow the link.

https://brainly.com/question/21135654

#SPJ1

Answer:

x+1/x

Step-by-step explanation:

The future value is 6,495,554.308.

What has compounded annually?

The interest charged on a loan or deposit is known as compound interest. It is the idea that we use the most frequently on a daily basis. Compound interest is calculated for an amount based on both the principal and cumulative interest. The main distinction between compound and simple interest is this.

Compound interest can be calculated in math in a variety of ways depending on the circumstances. To make the calculations simpler, we can use the compound interest formula. We need to know the amount and the principal in order to calculate compound interest. The distinction is between the amount and the principal.

Given that  $12,000 is invested in a project at 7% for 9 years.

The formula of compound interest is

A = P(1+r/n)^nt

A = amount

P = principal

r = rate of interest

t = time

n =  number of compound interest per annum

For the given problem:

P =12,000, r = 7%, t = 9, n = 365:

The amount after 9 years will be:

A = 12,000(1+0.07/365)^(365×9)

A = 6,495,554.308

To learn more about compounded daily, click on the below link:

https://brainly.com/question/29293818

#SPJ1

The measure of sinx from the trigonometry is 7/25

Given the following trigonometry

tan x = 7/24

Since tan theta = opposite/adjacent

Determine the hypotenuse

h^2 = 7^2 + 24^2

h^2 = 49 + 576
h^2 = 625

h = 25

The value of sin x will be given as:

sinx = opposite/hypotenuse

sinx = 7/25

Hence the exact value of sinx where sinx>0 is 7/25

Learn more on trigonometry here: https://brainly.com/question/24349828

#SPJ1

[tex]~~~~~~ \textit{Simple Interest Earned Amount} \\\\ A=P(1+rt)\qquad \begin{cases} A=\textit{accumulated amount}\dotfill & \pounds 17160\\ P=\textit{original amount deposited}\dotfill & \pounds 11000\\ r=rate\to r\%\to \frac{r}{100}\\ t=years\dotfill &16 \end{cases}[/tex]

[tex]17160 = 11000[1+(\frac{r}{100})(16)] \implies \cfrac{17160}{11000}=1+\cfrac{16r}{100}\implies \cfrac{39}{25}=1+\cfrac{4r}{25} \\\\\\ \cfrac{39}{25}=\cfrac{25+4r}{25}\implies 39=25+4r\implies 14=4r\implies \cfrac{14}{4}=r\implies \stackrel{\%\qquad }{\boxed{3.5=r}}[/tex]

The amount after 35% off on a 85 dollar item will be $55.25

Percentage is a way to express a number as a fraction of hundred. It is often used to represent proportions  and  ratios in a more convenient and understandable form, especially in financial  statistical and financial  contexts. For example, 50% means 50 per 100, or half of a given quantity. It is denoted using the symbol "%".

To find the sale price of an item that has a discount, you can use the following formula:

Sale price = Original price - (Discount percent × Original price)

In this case, the discount is 35% off of an $85 item. So we have:

Discount percent = 35%

Original price = $85

Substituting these values into the formula, we get:

Sale price = $85 - (35% × $85)

Sale price = $85 - $29.75

Sale price = $55.25

Therefore, the sale price of the item after a 35% discount is $55.25.

To know more about Percentage check:

https://brainly.com/question/29306119

#SPJ1

The volume of the rectangular prism is 140 cubic meters

The volume of a figure is a measure of the amount of space it occupies in three-dimensional space. It is a scalar quantity, meaning that it is a single numerical value with no direction.

The volume of a rectangular prism is given by the formula V = l * w * h, where l is the length, w is the width, and h is the height.

This problem is a two rectangular prism joined together.

The volume can be calculated as;

V = l * w * h

v = (4 * 7 * 3) + (2 * 7 * 4)

v = 140m³

Learn more on volume of a rectangular prism here;

https://brainly.com/question/23665595

#SPJ1

The value of each variable in the quadrilateral can be found such that :

Angle 107 degrees and z degrees will add up to 180 degrees which means that the value of z is:

= 180 - 107

= 73 degrees

Using this value of z as 73 degrees, we can then solve for y because the sum of the interior angles of a quadrilateral need to add up to 360 degrees.

The value of y variable  is therefore:

= 360 - 83 - 103 - 73

= 101 degrees

Find out more on angles at https://brainly.com/question/25716982

#SPJ1

Answer:

the IQR is the best measure which equals 16

Step-by-step explanation:

the 2nd option is not correct because, while the range is 45, there are only two out of eleven data items above 45, which is not representative of the majority of the data

the 3rd option is incorrect because the IQR does not equal 45, it's 16

the 4th option is incorrect because the range does not equal 16, it's 45

Answer:

Step-by-step explanation:

Let me explain each step in more detail.

Step 1: Calculate the Z-score

The Z-score is a measure of how many standard deviations a value is from the mean. To calculate the Z-score, we use the following formula:

Z = (x - μ) / σ

Where:

x = 9.8 ounces (the value we want to examine)

μ = 10.2 ounces (the mean of the distribution)

σ = 0.12 ounces (the standard deviation of the distribution)

Plugging in the values, we get:

Z = (9.8 - 10.2) / 0.12 = -3.33

This Z-score tells us that 9.8 ounces is 3.33 standard deviations below the mean of 10.2 ounces.

Step 2: Look up the cumulative probability from a Z-table

A Z-table is a table that lists the cumulative probabilities for various Z-scores. The cumulative probability tells us the probability of getting a value less than or equal to a certain Z-score. To use the Z-table, we need to know the Z-score and whether we want the cumulative probability to the left (for values less than) or to the right (for values greater than). In this case, we want the cumulative probability to the left because we want to find the probability of getting a weight less than or equal to 9.8 ounces.

The cumulative probability for a Z-score of -3.33 is approximately 0.0004. This means that there is a 0.0004 (or 0.04%) chance of getting a weight of 9.8 ounces or less in a bag of chips.

Step 3: Interpret the results

Since the cumulative probability is very small, it is highly unlikely that a bag of chips would contain 9.8 ounces or less of chips. Therefore, we can conclude that it is unusual for a bag of chips to contain 9.8 ounces or less.

If my answer met your requirements, please rate it AWESOME BRAINLY ANSWER.

The meaning of 5 = f(I) is that the 5% have an income of $6000

The average rate is that %0.054 per thousand of dollars

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

The graph

The equation is given as

5 = f(I)

This means that:

We find x when f(I) = 5

Using the graph, we have

x = 6

This means that the income is $6000

This is calculated as

Rate = (f(x2) - f(x1))/(x2 - x1)

Substitute the known values in the above equation, so, we have the following representation

Rate = (1.8 - 4.5)/(10 - 60)

Evaluate

Rate = 0.054

Read more about average rate at

https://brainly.com/question/17131025

#SPJ1

Percentages are:

Middle school

Spring = 75%    Winter = 25%

High school

Spring = 40%     Winter = 60%

What is the percentage?

A percentage is a figure or ratio stated as a fraction of 100 in mathematics. Frequently, it is indicated with the per cent sign, "%".  A percentage is a number without dimensions and without a standard measurement.

Given,

Middle school

Number of students preferring spring = 93

Number of students preferring winter = 31

High school

Number of students preferring spring = 36

Number of students preferring winter = 54

Total  number of middle school students =  93 + 31 = 124

Percentage of middle school students who prefer spring =  [tex]\frac{93}{124} * 100[/tex]

                                                                                     = 75%

Percentage of middle school students who prefer winter = [tex]\frac{31}{124} * 100[/tex] = 25%

Total number of high school students = 36+54 = 90

Percentage of high school students who prefer spring = [tex]\frac{36}{90} * 100[/tex]

                                                                                             =  40%

Percentage of high school students who prefer winter = [tex]\frac{54}{90} *100[/tex]

                                                                                            = 60%

Therefore the above is the percentage of students who prefer spring and winter.

To learn more about percentages, follow the link.

https://brainly.com/question/24877689

#SPJ1

The solution to the inequality are the region in the shaded area

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

y < 3x+3

3x-y ≤ 4

Represent properly

y < 3x + 3

3x - y ≤ 4

Next, we make a plot of the system to determine the solution

The shaded area in the plot represent the solution to the inequality

In this case, one of the coordinates in the shaded area has a coordinate of (0.2, 2)

Read more about inequality at

brainly.com/question/25275758

#SPJ1

Answer: To find the total weight of 400 apples, we need to multiply the number of apples by their weight. Each apple weighs 1/4 pound, so 400 apples weigh 400 * (1/4) = 100 pounds.

Since each bag should weigh 5 pounds, we can divide the total weight of apples (100 pounds) by 5 to find the number of bags: 100 / 5 = 20 bags.

So, the answer is 20 bags.

Step-by-step explanation:

Answer:

The company must make $450.

If the company must pay $300, then you will take 300, and since they want to make a profit, which means 1500 dollars more once they pay the 300, the you will add that to 300.

300 + 150 = 450

Now to find how many weeks it will take, you will divide 450 by 60:

450/60 = 7.5

It will take 7 1/2 (or round it to 8)weeks to gain $450, which is enough money to pay the bank $300, and make a profit of $150.

Step-by-step explanation:

Hope it helps! =D

Ans:-

[tex] \: [/tex]

Solution:-

[tex] \: [/tex]

[tex] \: [/tex]

[tex] \: [/tex]

[tex] \: [/tex]

hope it helps! :)

Answer:

z = -37/50

Step-by-step explanation:

Now we have to,

→ Find the required value of z.

The equation is,

→ 51z - 21 = z - 58

Then the value of z will be,

→ 51z - 21 = z - 58

→ 51z = z - 58 + 21

→ 51z = z - 37

→ 51z - z = -37

→ 50z = -37

→ [ z = -37/50 ]

Hence, value of z is -37/50.