A committee must be formed with 5 teachers and 4 students. If there are 6 teachers to choose from, and 15 students, how many different ways could the committee be made?

Answers

Answer 1

There are 6 teachers and 15 students to choose from

To form a committee of 5 teachers and 4 students

The combination rule will be applied

From 6 teachers, The number of ways 5 teachers can be selected is

[tex]^6C_5[/tex]

From 15 students, the number of ways 4 students can be selected is

[tex]^{15}C_{4^{}}[/tex]

Therefore, the total number of ways a committee of 5 teachers and 4 students can be formed from 6 teachers and 15 students is

[tex]^6C_5\times^{15}C_{4^{}}[/tex]

Simplifying this gives

[tex]^6C_5\times^{15}C_{4^{}}=\frac{6!}{(6-5)!\times5!}\times\frac{15!}{(15-4)!\times4!}[/tex]

This further gives

[tex]\begin{gathered} ^6C_5\times^{15}C_{4^{}}=\frac{6!}{1!\times5!}\times\frac{15!}{11!\times4!} \\ ^6C_5\times^{15}C_{4^{}}=\frac{6\times5!}{1\times5!}\times\frac{15\times14\times13\times12\times11!}{11!\times4\times3\times2\times1} \end{gathered}[/tex]

Cancel out common factors

[tex]\begin{gathered} ^6C_5\times^{15}C_{4^{}}=6\times\frac{15\times14\times13\times12}{4\times3\times2\times1} \\ ^6C_5\times^{15}C_{4^{}}=6\times\frac{32760}{24} \\ ^6C_5\times^{15}C_{4^{}}=6\times1365 \\ ^6C_5\times^{15}C_{4^{}}=8190 \end{gathered}[/tex]

Therefore, the number of ways the committee can be formed is 8190 ways


Related Questions

Suppose that the probability that you will win a contest is 0.0002, what is theprobability that you will not win the contest? Leave your answer as a decimal and donot round or estimate your answer.

Answers

Answer:

0.9998

Explanation:

The probability that you will not win the contest can be calculated as 1 less the probability that you will win a contest, so

1 - 0.0002 = 0.9998

Therefore, the answer is 0.9998

can you please solve this practice problem for me I need assistance

Answers

The missing angle in the triangle of the left is:

51 + 74 + x = 180

x = 180 - 51 - 74

x = 55°

The missing angle in the triangle of the right is:

55 + 74 + x = 180

x = 180 - 55 - 74

x = 51°

Then, both triangles are similar. This means that their corresponding sides are in proportion. These sides are:

35 in

A child has an empty box that measures 4 inches by 6 inches by 3 inches. View the figure.What is the length of the longest pencil that will fit into the box, given that the length of the pencil must be a whole number of inches? Do not round until your final answer.

Answers

Solution

For this case we can do the following:

We can find the value of s on this way:

[tex]s=\sqrt[]{6^2+4^2}=\sqrt[]{52}=7.21[/tex]

And solving for r we got:

[tex]r=\sqrt[]{6^2+3^2}=\sqrt[]{45}=6.71[/tex]

Then the answer for this case would be:

[tex]\sqrt[]{52}=7.21[/tex]

which describes the solution of the inequality y>-15? a) solid vertical line through (0,-15) with shading to the left of the line. b) dashed vertical line through (0,-15) with shading to the left of line. c) solid horizontal line through (0,-15) with shaing below line. d) dashed horizontal line through (0,-15) with shaing above line.

Answers

The solution to the inequality y > - 15 is all values of y greater than -15. This means the number -15 itself is not included; therefore, the line is a dashed line that passes through (0, -15). Furthermore, the > sign implies that the shaded region is found above the dashed line. Hence, the solution to our inequality is a dashed horizontal line through (0, -15), with shading above the line.

8+7t=22 in verbal sentence

Answers

Eight plus Seven times t equals twenty-two

Explanation

Step 1

Let

a number= t

seven times a number= 7t

the sum of eigth and seven times a number=8+7t

the sum of eigth and seven times a number equals twenty-two=8+7t=22

or,in other words

Eight plus Seven times t equals twenty-two

I hope this helps you

I inserted a picture of the question Check all that apply

Answers

Recall that the line equation is of the form

[tex]y=mx+c\ldots\ldots\text{.}(1)[/tex]

The points lie in the line are (2,5) and (-2,-5).

Setting x=2 and y=5 in the equa

Figure A is a scale image of Figure B.27Figure AFigure B4535What is the value of x?

Answers

Answer:

x = 21

Explanation:

Figure A is a scaled version of figure B. This means that the ratio between any two sides must be the same for both figures.

It follows then

[tex]\frac{27}{45}=\frac{x}{35}[/tex]

which just means that the ratio f sides 27 with 45 must be the same as the ratio between side x and 35. Why? Because these two sides are the same across the two figures and therefore their size with respect to each other must not change.

Now to find the value of x, we simply need to solve for x.

We do this by multipying both sides by 35:

[tex]undefined[/tex]

4. Driving on the highway, you can safely drive 65 miles per hour. How far can you drive in ‘h’ hours? What is the domain of the function which defines this situation?A) 65B) the number of hours you driveC) the distance you driveD)the amount of gas you use

Answers

Answer:

[tex]\text{ The number of hours you drive.}[/tex]

Step-by-step explanation:

For distance, we can apply the following equation:

[tex]\begin{gathered} d=s*h \\ where, \\ s=\text{ speed} \\ h=\text{ hours} \end{gathered}[/tex]

Since we know that we can safely drive 65 miles per hour, the domain will be defined by the number of hours you drive:

[tex]d=65h[/tex]

the pie chart below shows how the annual budget for general Manufacturers Incorporated is divided by department. use this chart to answer the questions

Answers

You can read a pie chart as follows

Looking at the given pie chart.

The budget for Research is arounf 1/6

The budget for Engineering is around 2/6

The budget for Support is around 1/8

The budget for media and marketing are 1/16 each

The budget for sales is around 3/16

a) The department that has one eight of the budget is Support.

b) The budgets for sales and marketing together add up to

[tex]\frac{3}{16}+\frac{1}{16}=\frac{4}{16}=\frac{1}{4}[/tex]

Multiply it by 100 to express it as a percentage

[tex]\frac{1}{4}\cdot100=25[/tex]

25% of the budget correpsonds to sales and marketing

c) The budget for media looks around one third the budget for research, to determine the percentage of budget that corresponds to media, divide the budget of research by 3

[tex]\frac{18}{3}=6[/tex]

The budget for media is 6%

what is the slope intercept form of the line passing through the point (2,1) and having a slope of 4?

Answers

The equation of a line has the form:

[tex]y=mx+b[/tex]

if the slope is equal to 4 then we know that: m = 4 and now we can replace the slope and the coordinate ( 2,1 ) to find b so:

[tex]\begin{gathered} 1=4(2)+b \\ 1-8=b \\ -7=b \end{gathered}[/tex]

So the final equation will be:

[tex]y=4x-7[/tex]

Earth's Moon is 384,400 km from Earth. What is the correct way to write this distance in scientific notation? O A. 3.844 x 105 km OB. 38.44 x 10-4 km O C. 38.44 x 104 km O D. 3.844 x 10-5 km SUBMIT

Answers

To do this, move the decimal in such a way that there is a non-zero digit to the left of the decimal point. The number of decimal places you shift will be the exponent by 10. If the decimal is shifted to the right the exponent will be negative. If the decimal is shifted to the left, the exponent will be positive.

So, in this case, you have

Therefore, the correct way to write this distance in scientific notation is

[tex]3.844\times10^5[/tex]

And the correct answer is

[tex]undefined[/tex]

All of the following ratios are equivalent except 8 to 12 15/102/36:9

Answers

False

1) Let's examine those ratios, and simplify them whenever possible:

[tex]\begin{gathered} \frac{15}{10}=\frac{3}{2} \\ \frac{2}{3} \\ \frac{6}{9}=\frac{2}{3} \\ \frac{8}{12}=\frac{2}{3} \end{gathered}[/tex]

2) Simplifying those ratios, all the following but 15/10 are equivalent to 8/12

3) So this is a false statement to say that all of those are equivalent except 8 to 12.

is this equation no solution, one solution, or infinitely may solutions

Answers

Given:

[tex]\begin{gathered} x+4y=8\ldots\ldots\ldots\ldots(1) \\ y=-\frac{1}{4}x+2\ldots\ldots\ldots\ldots(2) \end{gathered}[/tex]

To solve for x and y:

Substitute the equation (2) in (1) we get,

[tex]\begin{gathered} x+4(-\frac{1}{4}x+2)=8 \\ x-x+8=8 \\ 8=8 \end{gathered}[/tex]

Therefore, the given system has infinitely many solutions.

tom has a rectangular prism - shaped suitcase that measures 9 inches by 9 inches by 24 inches. he needs a second suitcase that has the same volume but smaller surface than his current suitcase. which suitcase size would fit Toms needs

Answers

ANSWER:

18 inches by 9 inches by 12 inches

EXPLANATION:

The volume of Tom's rectangular prism-shaped suitcase which measures 9 inches by 9 inches by 24 inches is;

[tex]\begin{gathered} Volume=l*w*h \\ \\ =9*9*24 \\ \\ =1944\text{ }square\text{ }inches \end{gathered}[/tex]

So the volume of Tom's suitcase is 1944 cubic inches

The surface area will be;

[tex]\begin{gathered} SA=2(lw+wh+hl) \\ \\ =2(9*9+9*24+24*9) \\ \\ =2(81+216+216) \\ \\ =2(513) \\ \\ =1026\text{ }square\text{ }inches \end{gathered}[/tex]

So the volume of the suitcase is 1026 square inches

*Let's go ahead and determine the volume and surface area of a suitcase that measures 18 inches by 18 inches by 6 inches;

[tex]\begin{gathered} Volume=l*w*h \\ \\ =18*18*6 \\ \\ =1944\text{ cubic inches} \end{gathered}[/tex][tex]\begin{gathered} Surface\text{ }Area=2(18*18+18*6+6*18) \\ \\ =2(324+108+108) \\ \\ =2(540) \\ \\ =1080\text{ square inches} \end{gathered}[/tex]

We can see that the suitcase that measures 18 inches by 18 inches by 6 inches has the same volume as the first one but a higher surface area which doesn't fit Tom's needs

*Let's go ahead and determine the volume of a suitcase that measures 12 inches by 10 inches by 9 inches;

[tex]\begin{gathered} Volume=12*10*9 \\ \\ =1080\text{ cubic inches} \end{gathered}[/tex]

We can see that the suitcase that measures 12 inches by 10 inches by 9 inches has a different volume from the first one which doesn't fit Tom's needs.

Let's go ahead and determine the volume of a suitcase that measures 16 inches by 5 inches by 9 inches;

[tex]\begin{gathered} Volume=16*5*9 \\ \\ =720\text{ cubic inches} \end{gathered}[/tex]

We can see that the suitcase that measures 16 inches by 5 inches by 9 inches has a different volume from the first one which doesn't fit Tom's needs.

*Let's go ahead and determine the volume and surface area of a suitcase that measures 18 inches by 9 inches by 12 inches;

[tex]\begin{gathered} Volume=l*w*h \\ \\ =18*9*12 \\ \\ =1944\text{ cubic inches} \end{gathered}[/tex][tex]\begin{gathered} Surface\text{ }Area=2(18*9+9*12+12*18) \\ \\ =2(162+108+216) \\ \\ =2(486) \\ \\ =972\text{ square inches} \end{gathered}[/tex]

We can see that the suitcase that measures 18 inches by 9 inches by 12 inches has the same volume as the first one and s smaller surface area which fits Tom's needs

PLEASE ITS URGENT I NEED HELP!!! I BEG YOU GUYS PLEEAASEEE THANKS..

Answers

[tex]b,c\text{ and d}[/tex]

Explanation

remember some properties of the exponents

[tex]\begin{gathered} a^m\cdot a^n=a^{m+n} \\ (a^m)^n=a^{m\cdot n} \\ a^{-m}=\frac{1}{a^m} \end{gathered}[/tex]

then, to solve this solve each option and compare

Step 1

[tex]6^{-5}\cdot6^2[/tex]

solve

[tex]\begin{gathered} 6^{-5}\cdot6^2=6^{-5+2}=6^{-3} \\ \end{gathered}[/tex]

so, this is not an answer

Step 2

[tex](\frac{1}{6^2})^5[/tex]

solve

[tex]\begin{gathered} (\frac{1}{6^2})^5=(6^{-2})^5=6^{(-2\cdot5)}=6^{-10} \\ \end{gathered}[/tex]

so, this is an answer

Step 3

[tex]\begin{gathered} (6^{-5})^2 \\ \text{solve} \\ (6^{-5})^2=6^{-5\cdot2}=6^{-10} \end{gathered}[/tex]

so, this is an answer

Step 4

[tex]\begin{gathered} \frac{6^{-3}}{6^7} \\ \text{solve} \\ \frac{6^{-3}}{6^7}=\frac{1}{6^3\cdot6^7}=\frac{1}{6^{3+7}}=\frac{1}{6^{10}}=6^{-10} \end{gathered}[/tex]

so, this is an answer

Step 5

[tex]\begin{gathered} \frac{6^5\cdot6^{-3}}{6^{-8}} \\ \text{solve} \\ \frac{6^5\cdot6^{-3}}{6^{-8}}=\frac{6^{5-3}}{6^{-8}}=\frac{6^2}{6^{-8}}=6^2\cdot\frac{1}{6^{-8}}=6^2\cdot6^8=6^{10} \end{gathered}[/tex]

so, this is not an answer

I hope this helps you

Answer the questions below about the quadratic function.g(×)=2×^2-12×+19Does the function have a minimum or maximum? minimum or maximum what is the functions minimum or maximum value?Where does the minimum or maximum value occur?x=?

Answers

Given the function:

[tex]g(x)=2x^2-12x+19[/tex]

Let's determine if the function has a minimum or maximum.

The minimum and maximum of a function are the smallest and largest value of a function in a given range or domain

The given function has a minimum.

Apply the general equation of a quadratic function:

[tex]y=ax^2+bx+c[/tex]

To find the minimum value, apply the formula:

[tex]x=-\frac{b}{2a}[/tex]

Where:

b = -12

a = 2

Thus, we have:

[tex]\begin{gathered} x=-\frac{-12}{2(2)} \\ \\ x=-\frac{-12}{4} \\ \\ x=3 \end{gathered}[/tex]

To find the function's minimum value, find f(3).

Substitute 3 for x in the function and evaluate:

[tex]\begin{gathered} f(x)=2x^2-12x+19 \\ \\ f(3)=2(3)^2-12(3)+19 \\ \\ f(3)=2(9)-36+19 \\ \\ f(3)=18-36+19 \\ \\ f(3)=1 \end{gathered}[/tex]

Therefore, the function's minimum value is 1

Therefore, the functions minimum value occurs at:

x = 3

ANSWER:

• The function has a minimum

• Minimum value: 1

• The minimum occurs at: x = 3

Eliana drove her car 81 km and used 9 liters of fuel. She wants to know how many kilometres she can drive on 22 liters of fuel. She assumes her car will continue consuming fuel at the same rate. How far can Eliana drive on 22 liters of fuel? What if Eliana plans to drive from Dubai to Abu Dhabi via Sheikh Zayed Bin Sultan which is 139.4 km? How many liters of fuel does she need?

Answers

Eliana can drive 198 km with 22 liters of fuel.

If Eliana plans to drive from Dubai to Abu Dhabi via Sheikh Zayed Bin Sultan which is 139.4 km then she would need 15.5 liters of fuel

In this question, we have been given Eliana drove her car 81 km and used 9 liters of fuel.

81 km=9 liters

9 km= 1 liter

She wants to know the distance she can drive on 22 liters of fuel. She assumes her car will continue consuming fuel at the same rate.

By unitary method,

22 liters = 22 × 9 km

              = 198 km

Also, given that  if Eliana plans to drive from Dubai to Abu Dhabi via Sheikh Zayed Bin Sultan which is 139.4 km.

We need to find the amount of fuel she would need.

Let 139.4 km = x liters

By unitary method,

x = 139.4 / 9

x = 15.5 liters

Therefore, Eliana can drive 198 km with 22 liters of fuel.

If Eliana plans to drive from Dubai to Abu Dhabi via Sheikh Zayed Bin Sultan which is 139.4 km then she would need 15.5 liters of fuel

Learn more about Unitary method here:

https://brainly.com/question/22056199

#SPJ1

rewrite using a single exponent. 9 4, 9 4

Answers

We need to represent the product of two exponents as one single exponent. To do that we need to calculate their product, when the bases are equal we can conserve the base and add the exponents. We will do this below:

[tex]9^49^4=9^{4+4}=9^8[/tex]

Find the volume of the figure. Round to the nearest hundredths place if necessary.

Answers

The volume of a Pyramid

Given a pyramid of base area A and height H, the volume is calculated as:

[tex]V=\frac{A\cdot H}{3}[/tex]

The base of this pyramid is a right triangle, with a hypotenuse of c=19.3 mm and one leg of a=16.8 mm. The other leg can be calculated by using the Pythagora's Theorem:

[tex]c^2=a^2+b^2[/tex]

Solving for b:

[tex]b^{}=\sqrt[]{c^2-a^2}=\sqrt[]{19.3^2-16.8^2}=9.5\operatorname{mm}[/tex]

The area of the base is the semi-product of the legs:

[tex]A=\frac{16.8\cdot9.5}{2}=79.8\operatorname{mm}^2[/tex]

Now the volume of the pyramid:

[tex]V=\frac{79.8\operatorname{mm}\cdot12\operatorname{mm}}{3}=319.2\operatorname{mm}^3[/tex]

The volume of the figure is 319.2 cubic millimeters

In the triangle below, if B = 69°, A = 32°, c = 5.7, use the Law of Sines to find a. Round your answer to the nearest hundredth.

Answers

We know that the interior angles have to add to 180°, then we have that:

[tex]\begin{gathered} C=180-69-32 \\ C=79 \end{gathered}[/tex]

Hence angle C=79°.

Now that we know the angle C we can use the law of sines to find a; the law of sines states that:

[tex]\frac{\sin A}{a}=\frac{\sin B}{b}=\frac{\sin C}{c}[/tex]

From this we have the equation:

[tex]\frac{\sin A}{a}=\frac{\sin C}{c}[/tex]

Plugging the values given and solving for a we have:

[tex]\begin{gathered} \frac{\sin32}{a}=\frac{\sin 79}{5.7} \\ a=(5.7)\frac{\sin 32}{\sin 79} \\ a=3.08 \end{gathered}[/tex]

Therefore a=3.08

The first three terms of a sequence are given. Round to the nearest thousandth (ifnecessary).15, 18, 108/5. find the 8th term

Answers

SOLUTION

The following is a geometric series

We will use the formula

[tex]T_n=ar^{n-1}[/tex]

Where Tn is the nth term of the series,

n is the number of terms = 8,

a is the first term = 15

And r is the common ratio = 1.2 (to find r, divide the second term, 18 by the first term which is 15

Now let's solve

[tex]\begin{gathered} T_n=ar^{n-1} \\ T_8=15\times1.2^{8-1} \\ T_8=15\times1.2^7 \\ T_8=15\times3.583 \\ T_8=53.748 \end{gathered}[/tex]

So the 8th term = 53.748

find the values of x and y that maximize the objective function c = 3x + 4y for the graph

Answers

Answer:  The correct answer is x=0 and y=4 or (0,4) per the graph

Step-by-step explanation:

To find the maximum value, we must test each point using the equation:

Check for (0,4):

C=3x+4y

C=3(0)+4(4)

C=16

Check for (2,2):

C=3(2)+4(2)

C=6+8

C=14

Check for (4,0):

C=3(4)+4(0)

C=12

Answer:

Step-by-step explanation:

On the graph below, what is the length of side AB? B ...

Answers

The distance between two points in the plane is:

[tex]d(P,Q)=\sqrt[]{(x_2-x_1)^2+(y_2}-y_1)^2[/tex]

The points A and B have coordinates A(5,3) and B(5,6). Then the distance between them is:

[tex]\begin{gathered} d(A,B)=\sqrt[]{(5-5)^2+(6-3)^2} \\ =\sqrt[]{(3)^2} \\ =\sqrt[]{9} \\ =3 \end{gathered}[/tex]

Therefore, the length of the side AB is 3 units.

The angle of depression from the top of a sheer cliff to point A on the ground is 35º. If point A is280 feet from the base of the cliff, how tall is the cliff? Round the answer to the nearest tenth of afoot.

Answers

In this case, to calculate the tall of the cliff, consider the distance from the base of the cliff to the point A, as a hypotenuse of a right triangle.

The tall of the clift is given by:

h = 280 sin(35)

h = 280(0.573)

h = 160.60

Hence, the tal of the clift is 160.60 feet

cabrinha run 3/10 mile each day for 6 days how many miles did she run in off

Answers

3/10 mile per day for 6 days.

To find how many miles did she run multiply the miles per day by 6days:

[tex]\frac{3\text{mile}}{10\text{day}}\cdot6\text{days}=\frac{18}{10}\text{mile}=\frac{9}{5}\text{mile}[/tex]Then, in 6 days she run 9/5 mile

If the 10 letters are {aa,aa,aa,aa,bb,bb,cc,cc RR,RR} are available and all 10 of them are to be selected without replacement,what is the number of different permutations?

Answers

In order to calculate the number of permutations, first we start with the factorial of the number of letters.

There are 10 letters, so we start with the factorial of 10.

Then, we need to check the number of repetitions. Each repetition will be a factorial in the denominator:

[tex]x=\frac{10!}{a!\cdot b!\operatorname{\cdot}...}[/tex]

We have four repetitions of aa, two repetitions of bb, two repetitions of cc and two repetitions of RR, therefore the final expression for the number of permutations is:

[tex]x=\frac{10!}{4!2!2!2!}[/tex]

Calculating this expression, we have:

[tex]x=\frac{10\operatorname{\cdot}9\operatorname{\cdot}8\operatorname{\cdot}7\operatorname{\cdot}6\operatorname{\cdot}5\operatorname{\cdot}4!}{4!\operatorname{\cdot}2\operatorname{\cdot}2\operatorname{\cdot}2}=\frac{10\operatorname{\cdot}9\operatorname{\cdot}8\operatorname{\cdot}7\operatorname{\cdot}6\operatorname{\cdot}5}{8}=18900[/tex]

Therefore there are 18900 permutations.

mrs Middleton makes a solution to Clean her windows she uses 2:1 ratio for every two cups of water she uses one cup of vinagar if ms middleton uses a gallon of water how mant cups of vinagara. 12 cups b. 2 quartz c. 2 pints d. 1 gallon

Answers

To answer this question we have to find (among the options) the amount that represents half the amount of water used.

Since the ratio of water to vinegar is 2:1, half of the amount of water will be used of vinegar.

In this case we have to find the answer that represents half a gallon.

That answer is 2 quarts. 2 guarts are 0.5 gallons, it means they are half the amount of water used.

It means that the answer is b. 2 quarts.

Scientists are conducting an experiment with a gas in a sealed container. The mass of the gas is measured and the scientists realize that the gas is leaking over time in a linear way. Eight minutes since the experiment started the gas had a mass of 302.4 grams. Seventeen minutes since the experiment started the gas had a mass of 226.8 gramsLet x be the number of minutes that have passed since the experiment started and let y be the mass of the gas in grams at that moment. Use a linear equation to model the weight of the gas over time.a) This lines slope-intercept equation is [ ] b) 39 minutes after the experiment started, there would be [ ] grams of gas left. c) if a linear model continues to be accurate, [ ] minutes since the experiment started all gas in the container will be gone.

Answers

Here, we want to model an experiment linearlly

From the question, we have it that;

The coordinates are written as;

(number of minutes, mass of gas)

So, what we have to do know is to set up the two given points

These are the points;

(8,302.4) and (17,226.8)

Now, using these two points, we can model the equation

We start by getting the slope of the line that passes through these two points

To do this, we shall use the slope equation

We have this as;

[tex]\begin{gathered} \text{slope m = }\frac{y_2-y_1}{x_2-x_1} \\ \\ (x_1,y_1)\text{ = (8,302.4)} \\ (x_2,y_2)\text{ = (17,226.8)} \\ \text{substituting these values;} \\ m\text{ = }\frac{226.8-302.4}{17-8}\text{ = }\frac{-75.6}{9}\text{ = -8.4} \end{gathered}[/tex]

The general equation representing a linear model is ;

[tex]\begin{gathered} y\text{ = mx + b} \\ m\text{ is slope} \\ b\text{ is y-intercept} \\ y\text{ = -8.4x + b} \end{gathered}[/tex]

To get the y-intercept so as to write the complete equation, we use any of the two points and substitute its coordinates

Let us substitute the coordinates of the first point

[tex]\begin{gathered} 302.4\text{ = -8.4(8) + b} \\ 302.4\text{ = -67.2 + b} \\ b\text{ = 67.2 + 302.4} \\ b\text{ = 369.6 } \end{gathered}[/tex]

a) Thus, we have the complete linear model as;

[tex]y\text{ = -8.4x + 369.6}[/tex]

b) To get this, we simply substitute the value of x given into the linear model

[tex]\begin{gathered} y\text{ = -8.4(39) + 369.6} \\ y\text{ = -327.6 + 369.6} \\ y\text{ = 42} \end{gathered}[/tex]

39 minutes after the experiment started, there would be 42 grams

c) If all the gas is gone, then the value of y will br zero at this point

To get the corresponding x-value which is the time, we have it that;

[tex]\begin{gathered} 0\text{ = -8.4x +369.6} \\ 8.4x=\text{ 369.6} \\ x\text{ = }\frac{369.6}{8.4} \\ x\text{ = 44} \end{gathered}[/tex]

In 44 minutes, all the gas in the container will be gone

I need to double check 15 I got answer B

Answers

We will have that the area of one sector of the circle will be:

[tex]A=(\frac{45}{360})\pi(20in)^2\Rightarrow A=\frac{25\pi}{2}in^2[/tex]

So, the solution is option B.

The following are the annual salaries of 15 chief executive offers of major companies. The salaries are written in thousands of dollars.

Answers

The original data is:

405, 1108, 84, 315, 495, 609, 362, 428, 224, 338, 700, 790, 814, 767, 633

To find the required percentiles, we need to sort the dataset from lowest to highest.

84, 224, 315, 338, 362, 405, 428, 495, 609, 633, 700, 767, 790, 814, 1108

The total number of data is 15.

a) The 25th percentile is the element located at the position:

25/100 * 15 = 3.75

Rounding down, the position is 3, so the 25th perc

Other Questions
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