(1 point) A rock is thrown into a still pond and causes a circular ripple. If the radius of the ripple is increasing at a rate of 4 feet per second, how fast is the circumference changing when the radius is 18 feet?

The interest expense for West Company in Year 1 is approximately $1,141, calculated using the principal of $38,000, the annual interest rate of 9%, and the time from the loan date to the end of Year 1, which is ⅓ of a year.

The student's question involves calculating the amount of interest expense to be reported on the income statement for West Company in Year 1, given that the company borrowed $38,000 on September 1, Year 1 at an annual interest rate of 9% with an 18-month term. To calculate the interest expense for Year 1, we need to consider the amount of time from the loan initiation date (September 1, Year 1) to the end of Year 1 (December 31, Year 1), which is 4 months or ⅓ of a year.

Interest Expense calculation:

Interest Expense = Principal Amount × Annual Interest Rate × Time in Years

Interest Expense for West's Year 1 = $38,000 × 9% × (⅓)

Interest Expense for West's Year 1 = $38,000 × 0.09 × 0.3333

Interest Expense for West's Year 1 = $1,141 (approximately)

Therefore, the interest expense appearing on West's Year 1 income statement would be approximately $1,141.

Answer:

[tex]3\frac{3}{10} = \frac{33}{10}[/tex]

Step-by-step explanation:

Answer:

Therefore the radius of curvature at A is 432.03 m.

Step-by-step explanation:

Radius of curvature : If an object moves in curvilinear motion, then any point of the motion, the radius of circular arc path which best approximates the curve at that point is called radius of curvature.

Radius of curvature =[tex]\rho = \frac{V^2_p}{a}[/tex]

[tex]V_p[/tex]= velocity

a = acceleration perpendicular to velocity.

Velocity at the point A = [tex]V_A= 100 \ km/h[/tex] [tex]=\frac{100 \ km}{1 \ h}= \frac{100\times 1000 \ m}{3600 \ s}=\frac{250}{9}[/tex] m/s

Velocity at the point C [tex]=V_C=50 \ km/ h=\frac{125}{9} \ m/s[/tex]

The distance between A and B is 120 m.

To find the declaration between the point A and C we use the following formula

[tex]V^2_C=V^2_A+2a_ts[/tex]

[tex]\Rightarrow( \frac{125}{9})^2=(\frac{250}9})^2+2a_t.120[/tex]

⇒[tex]a_t[/tex] = -2.41 m/s²

[tex]a_t[/tex]= tangential acceleration

Given the passengers experience a total acceleration of 3 m/s².

Total acceleration= 3 m/s².

[tex]a = \sqrt{a^2_t+a^2_n[/tex]

[tex]\Rightarrow a^2_n= a^2- a^2_t[/tex]

[tex]\Rightarrow a_n=\sqrt{3^2-(-2.41)^2}[/tex]

       = 1.786 m/s²

Radius of curvature  [tex]\rho_A=\frac{V^2_A}{a_n}[/tex]

                                   [tex]=\frac{(\frac{250}{9})^2}{1.786}[/tex]

                                  = 432.03 m

Therefore the radius of curvature at A is 432.03 m.

Answer:

B

Step-by-step explanation:

The slope is rise over run, meaning it is 3/4. The y-intercept is 2, making the equation y = (3/4)x + 2

Answer:

23, 22, 4, 3, -60

Step-by-step explanation:

f(x)=(x⁴ - 6x¹⁰)²³

f'(x)= 23(x⁴ - 6x¹⁰)²²(4x³ - 60x⁹)

Answer:

m+p-n

Step-by-step explanation:

given that Jerry manages a local car dealership. At the beginning of the month, his lot had m vehicles. During the month his salesman sold n vehicles, and he purchased p vehicles more

We are to find the number of vehicles did the dealership have at the end of the month

At the end of the month the dealer would have

no of vehicles at the start of the month- sales of the vehicle in that month+Purchase of vechicles during that month

No of vehicles at the start of the month = m

Purchase during month                           =p

Total vehicles including purchase         = m+p

LESS: Vehicles sold in the month         =   n

No of vehicles at the end                      = m+p-n

The probability of picking a red marble 3 times in a row  = [tex](\frac{8}{125})[/tex]

Step-by-step explanation:

Here, the total number of red marbles  =  4

The total number of blue marbles  = 6

Now, as the Repetition is allowed.

Let E: The event of picking a red marble

[tex]P(E) = \frac{\textrm{The total number of red marbles}}{\textrm{Total marbles}}[/tex]

So, [tex]P(E) = \frac{4}{10} = \frac{2}{5}[/tex]

Now, as we know after first picking, the chosen red marble is REPLACED in the bowl.

So, again the bowl has 4 red marbles and 10 in total.

⇒P(picking a red marble again)  = 2/5

And similarly for the third time.

So, the probability of picking a red marble 3 times in a row  = [tex](\frac{2}{5}) \times (\frac{2}{5})\times (\frac{2}{5}) = \frac{8}{125}[/tex]

The probability of selecting a red marble on each of the three picks is 2/55.

To determine the probability of selecting a red marble on each of the three picks, we need to consider the number of red and blue marbles in the bowl and the fact that a marble is replaced after each pick.

First, there are 4 red marbles and 6 blue marbles in the bowl. For the first pick, the probability of selecting a red marble is 4/10. After the pick, the bowl will have 5 red marbles and 6 blue marbles.

For the second pick, the probability of selecting a red marble is 5/11. After the pick, the bowl will have 6 red marbles and 6 blue marbles. Finally, for the third pick, the probability of selecting a red marble is 6/12, which simplifies to 1/2.

To find the probability of all three picks being red, we multiply the probabilities of each pick: (4/10) * (5/11) * (1/2) = 2/55.

Therefore, the probability of selecting a red marble on each of the three picks is 2/55.

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Answer:

y = -2x + 4

Step-by-step explanation:

Slope: -2

Intercept: +4

Answer:

(a) [tex]N(t)=10000e^{(\frac{ln5}{10})t }[/tex]

(b) 25,000

(c) 4.3068 min.

Step-by-step explanation:

Rate of change in the number of bacteria is proportional to the number present.

Let N is the population of bacteria.

[tex]\frac{dN}{dt}[/tex] ∝ N ⇒ [tex]\frac{dN}{dt}=kt[/tex] { k = proportionality constant}

initial population No. = 10,000

                          [tex]N(t_{1} )[/tex] = 20,000

         and [tex]N(t_{1}+10 )=100,000[/tex]

(a) For population growth

[tex]N(t)=N_{0}e^{kt}=10000e^{kt}[/tex]

[tex]N(t_1)=10,000e^{kt_1}=20,000[/tex]

[tex]e^{kt}=2[/tex]

[tex]ln(e^{kt_1})=ln(2)[/tex]

[tex]kt_1=ln(2)[/tex]

[tex]t_{1}=\frac{ln2}{k}[/tex] ----------(1)

[tex]N(t_1+t_{10})=100,000[/tex]

[tex]100,000=10,000e^{k(t_1+10)}[/tex]

[tex]10=e^{k(t_1+10)}[/tex]

[tex]ln10=ln[e^{k(t_1+10)}][/tex]

[tex]k(t_1+10)=ln10[/tex]

[tex]k(t_1)=ln10-10k[/tex]

[tex]t_1=\frac{ln10-10k}{k}[/tex] ----------(2)

from equation (1) and (2)

[tex]\frac{ln_2}{k}=\frac{ln10-10k}{k}[/tex]

[tex]ln10-ln2=10k[/tex]

[tex]k=\frac{ln5}{10}[/tex]

so expression will be

[tex]N(t)=10000e^{(\frac{ln5}{10})t }[/tex]

(b) for t = 20

    [tex]N_{(20)}=10,000e\frac{ln5}{10}\times 20[/tex]

             =  [tex]10,000\times e^{2ln5}[/tex]

            = 10,000 × 25

            = 25,000

(c) Since [tex]t_1=\frac{ln2}{k}[/tex]   [from equation (1)]

                  [tex]=\frac{ln2}{\frac{ln5}{10} }[/tex]

                  [tex]=\frac{ln2}{ln5}\times 10[/tex]

                  = 4.3068

                 = 4.3068 min.

Answer:

666.667 feet

Step-by-step explanation:

Slope = -1

Intercept = 10

y = -t + 10

y is the acceleration

Integrate y fornv

v = -t²/2 + 10t + c

At t=0, v=0 so c = 0

v = -t²/2 + 10t

Turns when v = 0,

-t²/2 + 10t = 0

t = 0, 20

Integrate v for s

s = -t³/6 + 5t² + c

At t = 0, s = 10

10 = c

s = -t³/6 + 5t² + 10

s at t=30,

-(30³)/6 + 5(30)² + 10

= 10m

(Back to starting point)

At t = 20,

Displacement in

-(20³)/6 + 5(20)² + 10

= 343.333

Total distance = 2(343.333-10)

= 666.6667

The total distance the car travels in this 30 second interval is 1333.34 units

From the graph, we have the following points

(0, 10) and (10, 0).

Start by calculating the slope (m) of the graph

[tex]m = \frac{y_2 - y_1}{x_2 -x_1}[/tex]

So, we have:

[tex]m = \frac{0 - 10}{10-0}[/tex]

[tex]m =- \frac{10}{10}[/tex]

[tex]m =- 1[/tex]

The equation is then calculated as:

[tex]y = m(x -x_1) + y_1[/tex]

This gives

[tex]y = -1(x -0) + 10[/tex]

[tex]y = -1x+ 10[/tex]

[tex]y = -x+ 10[/tex]

The above equation represents the acceleration (y) as a function of time (x).

Integrate to get the velocity (v)

[tex]v = -\frac{x\²}{2} + 10x + c[/tex]

From the question, we have:

The velocity (v) of the car is 0, when the time (x) is 0.

So, we have:

[tex]0 = -\frac{0\²}{2} + 10(0) + c[/tex]

This gives

[tex]c = 0[/tex]

So, the equation becomes

[tex]v = -\frac{x\²}{2} + 10x + 0[/tex]

[tex]v = -\frac{x\²}{2} + 10x[/tex]

Set v = 0.

So, we have:

[tex]-\frac{x\²}{2} + 10x = 0[/tex]

Multiply through by -2

[tex]x^2 -20x = 0[/tex]

Factorize

[tex]x(x -20) = 0[/tex]

Split

[tex]x = 0\ or\ x -20 = 0[/tex]

Solve for x

[tex]x = 0[/tex] or [tex]x = 20[/tex]  

Integrate velocity (v) to get the displacement (d)

[tex]v = -\frac{x\²}{2} + 10x[/tex]

[tex]d = -\frac{t\³}{6} + 5t\² + c[/tex]

From the question, we have:

The position (d) of the car is 10, when the time (x) is 0.

So, we have:

[tex]-\frac{(0)\³}{6} + 5(0)\² + c = 10[/tex]

[tex]c = 10[/tex]

So, the equation becomes

[tex]d = -\frac{t\³}{6} + 5t\² + 10[/tex]

The position at 30 seconds is:

[tex]d = -\frac{(30)\³}{6} + 5(30)\² + 10[/tex]

[tex]d = 10[/tex]

The position at 20 seconds is:

[tex]d = -\frac{(20)\³}{6} + 5(20)\² + 10[/tex]

[tex]d = 676.667[/tex]

The total distance is then calculated as:

[tex]Total = 2 \times (d_2 -d_1)[/tex]

This gives

[tex]Total = 2 \times (676.667 -10)[/tex]

[tex]Total = 2 \times 666.667[/tex]

[tex]Total = 1333.34[/tex]

Hence, the total distance is 1333.34 units

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Answer:

10%

Step-by-step explanation:

In this question, we are asked to calculate the percentage error in a measurement.

This can be obtained by first getting the error involved. That is calculated by Subtracting the value calculated from the actual value. That is 9.5 - 8.9 = 0.6

The percentage error is thus 0.6/9.5 * 100 = 6%

The value is actually 10% to the nearest tenth of a percent

Answer:

6.3%

Step-by-step explanation:

Answer:

The only x-intercept is x = 1

Step-by-step explanation:

The equation is:

[tex]r(x)=\frac{x-1}{x+4}[/tex]

We can substitute y for r(x), to write in the notation:

[tex]r(x)=\frac{x-1}{x+4}\\y=\frac{x-1}{x+4}[/tex]

To get y-intercept, we put x = 0

and

To get x-intercept, we put y =0

We want to find x-intercepts here, so we substitute 0 into y and solve for x. Shown below:

[tex]y=\frac{x-1}{x+4}\\0=\frac{x-1}{x+4}\\0(x+4)=x-1\\0=x-1\\x=1[/tex]

The only x-intercept is x = 1

Hence correct option is b with 4 colors.

Step by-step explanation:

We are given a graph in which we need to color every vertex or node such that no adjacent vertex or node should have the same color, ex:- If color of node B is blue than it's adjacent vertex A and D must not have the same blue color. Now, Let's start coloring of graph :

Color vertex A as red : Now, it's adjacent vertex as B,C,D,E must not have red color we know this!.

Color vertex B as blue: Now, it's adjacent vertex A and D must not have blue color!

Color vertex C as blue:  Now, it's adjacent vertex A,E and D must not have blue color!

Color vertex D as green:  Now, it's adjacent vertex A,B,C and E must not have green color!

Color vertex E as purple:  Now, it's adjacent vertex C and D must not have purple color!

Hence correct option is b with 4 colors.

Answer:

Option A. 264 ft² ; 4 gallons

Step-by-step explanation:

Given question is incomplete; find the complete question in the attachment.

From the picture attached,

Area of the barn to be painted = Area of the (rectangular base + Triangular top) - Area of the window

Area of the rectangular base = 12 × 18

                                                = 216 ft²

Area of the triangular top = [tex]\frac{1}{2}(\text{Base}\times \text{Height})[/tex]

                                          = [tex]\frac{1}{2}(12)(28-18)[/tex]

                                          = 60 square feet

Area of the window = 3 ft × 4 ft

                                 = 12 ft²

Total area to be painted = 216 + 60 - 12

                                         = 264 ft²

∵ 70 square feet of the barn is covered by the amount of paint = 1 gallon

∴ 1 square feet will be covered by the amount = [tex]\frac{1}{70}[/tex] gallons

∴ 264 square feet will be painted by = [tex]\frac{264}{70}[/tex]

                                                             = 3.77 gallons

                                                             ≈ 4 gallons

Therefore, Option (A). 264 ft²; 4 gallons will be the answer.

Answer:

A) 264 ft2; 4 gallons

Step-by-step explanation:

Right answer on usatestprep

Answer: Option 'D' is true.

Step-by-step explanation:

Since we have given that

Number of points are 7,5,3, and 2 each.

Product of the point values of the removed beads = 147000

So, the possible way is given by

[tex]2^3\times 3\times 5^3\times 7^2=147000[/tex]

Since no other beads is a multiple of 7.

So, there must be two red beads removed.

Hence, Option 'D' is true.

Answer:

A. upside down

Explanation:

Pyramid population, sometimes called afe-gender population is an illustration showing showing various age group distribution. The illustration usually forms the shape of a pyramid, hence its name as the age group increases. It's assumed there are more younger people than older people in a region or country. In this case, the pyramid population is said to be Upside down, because in those regions listed, the number of elderly people is greater than those of the younger people. Population pyramid usually represents the distribution or breakdown of ages and gender of a region at a given point in time.

For a given data set, the equation of the least squares regression line will always pass through the point [tex]\((\bar{x}, \bar{y})\),[/tex] where [tex]\(\bar{x}\)[/tex] is the mean of the x-values and[tex]\(\bar{y}\)[/tex] is the mean of the y-values.

The least squares regression line minimizes the sum of squared differences between the observed y-values and the values predicted by the line. The equation of the line is given byy = mx + b, where m is the slope and bis the y-intercept. The slopem and y-intercept b are determined by formulas involving the means[tex](\(\bar{x}\)[/tex] and [tex]\(\bar{y}\))[/tex]and other statistical measures from the data set.

The specific formulas for the least squares regression line are:

[tex]\[ m = \frac{\sum_{i=1}^{n} (x_i - \bar{x})(y_i - \bar{y})}{\sum_{i=1}^{n} (x_i - \bar{x})^2} \]\[ b = \bar{y} - m\bar{x} \][/tex]

It can be observed from the formulas that when [tex]\(x = \bar{x}\)[/tex], the corresponding y value is[tex]\(\bar{y}\)[/tex]. Therefore, the least squares regression line passes through the point[tex]\((\bar{x}, \bar{y})\)[/tex]. This point represents the centroid of the data set and ensures that the line adequately represents the overall trend of the data.

Question:

It seems there might be some repetition or an incomplete question in your request. Could you please provide more details or clarify your question so that I can assist you accurately? If you have a specific question related to the least squares regression line or any other topic, feel free to provide more context, and I'll do my best to help you.

Answer:

a) 0.00019923%

b) 47.28%

Step-by-step explanation:

a) To find the probability of all sockets in the sample being defective, we can do the following:

The first socket will be in a group where 5 of the 38 sockets are defective, so the probability is 5/38

The second socket will be in a group where 4 of the 37 sockets are defective, as the first one picked is already defective, so the probability is 4/37

Expanding this, we have that the probability of having all 5 sockets defective is: (5/38)*(4/37)*(3/36)*(2/35)*(1/34) = 0.0000019923 = 0.00019923%

b) Following the same logic of (a), the first socket have a chance of 33/38 of not being defective, as we will pick it from a group where 33 of the 38 sockets are not defective. The second socket will have a chance of 32/37, and so on.

The probability will be (33/38)*(32/37)*(31/36)*(30/35)*(29/34) = 0.4728 = 47.28%

Answer:

See explanation

Step-by-step explanation:

The given functions are:

[tex]f(x) = {x}^{2} - 5[/tex]

and

[tex]g(x) = f(x - 7)[/tex]

We substitute x-7, wherever we see x in f(x) to obtain:

[tex]g(x) = {(x - 7)}^{2} - 5[/tex]

This means g(x) is obtained by shifting f(x) 7 units to the right.

Also we can say g(x) is obtained by shifting the parent quadratic function, 7 units left and 5 units down.

You have not provided the options, but I hope this explanation helps you check the correct answers.

Answer:

V = 11.3 ft^3

Step-by-step explanation:

The volume of a cone is given by one third of its base area multiplied by its height:

V = (1/3)*A*h

This cone have a circular base, so the base area is given by

A = pi*r^2, where r is the base radius

The length of a circumference is given by L = 2*pi*r

the base circumference is 5 ft, so we can calculate the base radius:

5 = 2*pi*r -> r = 5/(2*pi)

Using this value, we can calculate A:

A = pi*r^2 = pi * [5/(2*pi)]^2 = pi * 25/(4*pi^2) = 25/(4*pi) = 1.9894

Now, we use the formula to calculate the volume:

V = (1/3)*A*h = (1/3) * 1.9894 * 17 = 11.2735 ft^3

rounding it, we have V = 11.3 ft^3

Answer:

Therefore, we have 36 different treatment groups.

Step-by-step explanation:

We know that the 7 subjects are selected from the 9 that are​ available, and the 7 selected subjects are all treated at the same​ time.

We calculate how many different treatment groups are​ possible.

We get:

[tex]C_7^9=\frac{9!}{7!(9-7)!}=\frac{9\cdot 8\cdot 7!}{7!\cdot 2\cdot 1}= 36[/tex]

Therefore, we have 36 different treatment groups.

Answer:

[tex]\text{Unemployment rate}\approx 7.7\%[/tex]

[tex]\text{Labor force participation rate}\approx 92.9\%[/tex]

Step-by-step explanation:

We have been given that the number of employed persons equals 180 million. The number of unemployed persons equals 15 million, and the number of persons over age 16 in the population equals 210 million. We are asked to find the unemployment rate and the labor force participation rate.

[tex]\text{Unemployment rate}=\frac{\text{Number of unemployed person}}{\text{Labor force}}\times 100\%[/tex]

We know that labor force is equal to employed population plus unemployed population.

[tex]\text{Unemployment rate}=\frac{\text{15 million}}{\text{180 million + 15 million}}\times 100\%[/tex]

[tex]\text{Unemployment rate}=\frac{\text{15 million}}{\text{195 million}}\times 100\%[/tex]

[tex]\text{Unemployment rate}=0.0769230769\times 100\%[/tex]

[tex]\text{Unemployment rate}=7.69230769\%[/tex]

[tex]\text{Unemployment rate}\approx 7.7\%[/tex]

Therefore, the unemployment rate is approximately 7.7%.

[tex]\text{Labor force participation rate}=\frac{\text{Labor force}}{\text{Total eligible population}}\times 100\%[/tex]

[tex]\text{Labor force participation rate}=\frac{\text{195 million}}{\text{210 million}}\times 100\%[/tex]

[tex]\text{Labor force participation rate}=\frac{195}{210}\times 100\%[/tex]

[tex]\text{Labor force participation rate}=0.9285714285714286\times 100\%[/tex]

[tex]\text{Labor force participation rate}=92.85714285714286\%[/tex]

[tex]\text{Labor force participation rate}\approx 92.9\%[/tex]

Therefore, the labor force participation rate is approximately 92.9%.

The unemployment rate is 7.69% and the labor force participation rate is 92.86%.

The unemployment rate can be calculated by dividing the number of unemployed persons by the labor force and multiplying by 100. In this case, the number of unemployed persons is 15 million and the labor force is the sum of employed and unemployed persons, which is 180 million + 15 million.

The labor force participation rate can be calculated by dividing the labor force by the total number of persons over age 16 and multiplying by 100. In this case, the total number of persons over age 16 is 210 million.

Unemployment rate: (15 million / (180 million + 15 million)) x 100 = 7.69%

Labor force participation rate: ((180 million + 15 million) / 210 million) x 100 = 92.86%

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The computer algorithm executes twice as many operations when the input size increases by 1. By using this information and calculating the operations for each input size, we find that it executes 26,624 operations for an input size of 26.

To find out how many operations the computer algorithm executes when it is run with an input of size 26, we can use the given information. The algorithm executes twice as many operations when the input size increases by 1. So, if it executes 7 operations for an input size of 1, it would execute 14 operations for an input size of 2, 28 operations for an input size of 3, and so on.

Since the algorithm executes twice as many operations for each increase in input size, we can see that it follows a pattern of doubling. We can calculate the number of operations for an input size of 26 by doubling the number of operations for an input size of 25. Continuing this calculation, we get:

Input Size 1: 7 operations
Input Size 2: 14 operations
Input Size 3: 28 operations
...

Input Size 25: 13,312 operations
Input Size 26: 26,624 operations

Answer:

a) [tex]\frac{x^{2}}{2352.25} + \frac{y^{2}}{529} = 1[/tex], b) [tex]c = 42.7 ft[/tex], c) [tex]A \approx 3504.447 ft^{2}[/tex]

Step-by-step explanation:

a) An Ellipse centered at origin is modelled by using this formula:

[tex]\frac{x^{2}}{a^2} +\frac{y^2}{b^2}=1[/tex]

Where [tex]a, b[/tex] represents the lengths of horizontal and vertical axis, respectively. Let consider that horizontal axis is parallel and coincident with width of Statuary Hall. So, the measures of each axis are, respectively:

[tex]a = 48.5 ft, b = 23 ft[/tex]  

By substituting known variables, the equation that models the hall is:

[tex]\frac{x^{2}}{2352.25} + \frac{y^{2}}{529} = 1[/tex]

b) The distance between origin and any of the foci is:

[tex]c = \sqrt{a^{2} - b^{2}} \\c = 42.7 ft[/tex]

c) The area of ellipse can determined by applying this formula:

[tex]A = \pi \cdot a \cdot b[/tex]

[tex]A \approx 3504.447 ft^{2}[/tex]

Answer:

B) x=-3(y+3)^2+4

Step-by-step explanation:

Plug quadratic in for proof

Answer:

The answer to your question is Letter C

Step-by-step explanation:

Data

Vertex (4, -3)

Process

From the image, we notice that it is a horizontal parabola that opens to the left.

So, it formula must be          (y - k)² = 4p(x - h)

-Substitute the vertex

                                             (y + 3)² = 4p(x - 4)

Consider 4p = 1

                                             (y + 3)² = x - 4

Solve for x

                                             x = (y + 3)² + 4

Solution

Letter C

Answer:

P ( 2 R , 4 O , 6 G ) = 0.0261

Step-by-step explanation:

Given:

- Red beans = 8

- Orange beans = 6

- Green beans = 9

Find:

What is the probability of reaching into the bag and randomly withdrawing 12 jellybeans such that the number of red ones is 2, the number of orange ones is 4, and the number of green ones is 6?

Solution:

- The question requires the number of selection of 12 jellybeans we can make from total available such that out of those 12 we choose 2 Red, 4 Orange and 6 Green.

- For selection we will use the combinations. So to choose 2 Red from 8; Choose 4 Orange from 6 and 6 green from 9 available. The number of possible outcomes with such condition is:

          Outcomes ( 2 R , 4 O , 6 G ) = 8C2 * 6C4 * 9C6

                                                         = 28*15*84

                                                         = 35280

- The total number of outcomes if we randomly select 12 beans irrespective how many of each color we select from available 23 we have:

          Outcomes ( Select 12 from 23 ) = 23C12

                                                               = 1352078

- Hence, the probability for the case is given by:

P ( 2 R , 4 O , 6 G ) = Outcomes ( 2 R , 4 O , 6 G ) / Outcomes ( Select 12 from 23 )

P ( 2 R , 4 O , 6 G ) = 35280 / 1352078 = 0.0261

Answer:

13) 0

Step-by-step explanation:

Answer:

#13:  0

#14:  -99

Step-by-step explanation:

#13:  g(x) = 2x^3 - 5x^2 + 4x - 1;  x = 1

Step 1:  Substitute 1 for x

2(1)^3 - 5(1)^2 + 4(1) - 1

2(1) - 5(1) + 4 - 1

2 - 5 + 4 - 1

0

Answer:  0

#14:  h(x) = x^4 + 7x^3 + x^2 - 2x - 6;  x = -3

Step 1:  Substitute -3 for x

(-3)^4 + 7(-3)^3 + (-3)^2 - 2(-3) - 6

81 + 7(-27) + 9 + 6 - 6

81 - 189 + 9 + 6 - 6

-99

Answer:  -99

Answer:

The equation representing the scenario is [tex]x+\frac{5}{4}-\frac{3}{4} = \frac{21}{4}[/tex].

Step-by-step explanation:

Given:

Amount of food in the container = [tex]x \ cups[/tex]

Amount of food added in the container = [tex]2\frac12\ cups[/tex]

We will now convert the mixed fraction into Improper fraction by Multiplying the whole number part by the fraction's denominator and then add that to the numerator  and then write the result on top of the denominator.

[tex]2\frac12\ cups[/tex] can be rewritten as [tex]\frac{5}{4}\ cups[/tex]

Amount of food added in the container =  [tex]\frac{5}{4}\ cups[/tex]

Amount of food removed from container to feed dog  = [tex]\frac34 \ cups[/tex]

Amount of food remaining = [tex]5\frac{1}{4} \ cups[/tex]

[tex]5\frac{1}{4} \ cups[/tex] can be Rewritten as = [tex]\frac{21}{4}\ cups[/tex]

Amount of food remaining =  [tex]\frac{21}{4}\ cups[/tex]

We need to write the equation for above scenario.

Solution:

Now we can say that;

Amount of food remaining is equal to Amount of food in the container plus Amount of food added in the container minus Amount of food removed from container to feed dog.

framing in equation form we get;

[tex]x+\frac{5}{4}-\frac{3}{4} = \frac{21}{4}[/tex]

Hence the equation representing the scenario is [tex]x+\frac{5}{4}-\frac{3}{4} = \frac{21}{4}[/tex].

Answer:

The probability of selecting a  person which is  self-employed but not married equals 1/8.

Step-by-step explanation:

Here, the given survey says:

Total number of people surveyed = 248

Number of people married = 156

The number of people are self employed = 70

Now, 25% of people who are married are SELF EMPLOYED.

Now, calculating 25% of 156 , we get:

[tex]\frac{25}{100} \times 156 = 39[/tex]

⇒ out of total 156 married people, 39 are self employed.

So, number of  self employed people but  not married

= Self employed people - Self employed people PLUS  married

=  70  -  39   =  31.

So, the probability that the person selected will be self-employed but not married = [tex]\frac{\textrm{The total number of people self-employed but not married}}{\textrm{Total Number of people}}[/tex] =  [tex]\frac{31}{248} = \frac{1}{8}[/tex]

Hence The probability of selecting a  person which is  self-employed but not married equals 1/8.