Answers
ANSWER:
AC = 3√ 17
α = 75.96°
Θ = 14.04°
STEP-BY-STEP EXPLANATION:
We can calculate the length of side AC by means of the Pythagorean theorem, just like this:
[tex]\begin{gathered} c^2=a^2+b^2 \\ \text{ in this case:} \\ (AC)^2=3^2+12^2 \\ (AC)^2=9+144 \\ AC=\sqrt[]{153} \\ AC=3\sqrt[]{17} \end{gathered}[/tex]We can calculate the angles by applying the following trigonometric ratios:
[tex]\begin{gathered} \sin \alpha=\frac{12}{3\sqrt[]{17}} \\ \alpha=\arcsin \mleft(\frac{12}{3\sqrt{17}}\mright) \\ \alpha=75.96 \\ \\ \sin \theta=\frac{3}{3\sqrt[]{17}} \\ \theta=\arcsin \mleft(\frac{3}{3\sqrt{17}}\mright) \\ \theta=14.04 \end{gathered}[/tex]Related Questions
3.2 x 104 bacteria are measured to be in a dirt sample that weighs 1 gram. Usescientific notation to express the number of bacteria that would be in a sampleweighing 21 grams.
Answers
The number of bacteria that weighs 1 gram are,
[tex]3.2\times10^4[/tex]Determine the number of bacteria in a sample that weighs 21 grams.
[tex]\begin{gathered} 21\cdot3.2\times10^4=67.2\times10^4 \\ =6.72\times10^5 \end{gathered}[/tex]So answer is,
[tex]6.72\times10^5[/tex]A) how many of these voters plan to vote for the library? B) how many voters are not planning to vote for the library?
Answers
Answer:
Explanation:
From the information given, 3
4. Sales tax in a certain state is 5%. If the sales tax on a new boat was $400, what was the selling price of the boat?
Answers
Sales tax percentage = 5% = 5/100 = 0.05 (decimal form)
Sales tax amount = $400
Multiply the selling price of the boat (x) by the sales tax percentage in decimal form. That expression must be equal to 400.
0.05x = 400
Solve for x:
x = 400/ 0.05
x= $8,000
Choose a student in grades 9 to 12 at random and ask if he or she is studying a language other than English. Here isthe distribution of the students:
Answers
Solution:
a) 0.38
b)0.36
c)0.33
Analysis:
a)Studying a language other than English: In this case, we add all probabilities of the chart, except None (Because that is people don't study a la
Find the volume of cylinder with r=25.5 ft and height=45ft use 3.14 for pi. Round the answer to the nearest hundredth
Answers
The Volume of a Cylinder
Given a cylinder of base radius r and height h, its volume is calculated as follows:
[tex]V=\pi r^2h[/tex]We have a cylinder with dimensions r = 25.5 ft and h = 45 ft. Substituting the values in the formula:
[tex]V=\pi\cdot25.5^2\cdot45[/tex]Using π = 3.14:
[tex]\begin{gathered} V=3.14\cdot650.25ft^2\cdot45ft \\ V=91,880.325ft^3 \end{gathered}[/tex]Rounding to the nearest hundredth:
V = 91,880.33 cubic ft
b. Solve the system of linear equations y = x + 2 and y = 3x – 4 by graphing.
Answers
To find the solution we need to graph both lines on the plane. To do this we need to find two points for each line.
First we graph the line y=x+2. To find a point we give x a value, whichever value we like, and then find y.
Let x=0, then:
[tex]\begin{gathered} y=0+2 \\ y=2 \end{gathered}[/tex]Then we have the point (0,2).
Let x=1, then:
[tex]\begin{gathered} y=1+2 \\ y=3 \end{gathered}[/tex]Then we have the point (1,3).
Then we plot this points in the plane and join them with a line:
Now let's plot eh second line, y=3x-4.
Let x=0, then:
[tex]\begin{gathered} y=3(0)-4 \\ y=-4 \end{gathered}[/tex]So we have the points (0,-4).
Let x=1, then:
[tex]\begin{gathered} y=3(1)-4 \\ y=3-4 \\ y=-1 \end{gathered}[/tex]so we have the point (1,-1).
Now we plot this points and join them with a line:
Once we have both lines graph in the plane the solution is the intersection of the lines. Looking at the graph we conclude that the solution of the system is x=3 and y=5.
Write an equation that expresses the following relationship.u varies jointly with p and d and inversely with wIn your equation, use k as the constant of proportionality.
Answers
Answer:
[tex]u=k\cdot\frac{p\cdot d}{w}[/tex]Explanation:
If a varies jointly with b, we write the equation
a = kb
If a varies inversely with b, we write the equation
a = k/b
So, if u varies jointly with p and d and inversely with w, the equation is
[tex]u=k\cdot\frac{p\cdot d}{w}[/tex]The maintenance department at the main campus of a large state university receives daily requests to replace fluorescent lightbulbs. The distribution of the number of daily requests is bell-shaped and has a mean of 37 and a standard deviation of 10. iS Using the 68-95-99.7 rule, what is the approximate percentage of lightbulb replacement requests numbering between 37 and 67?
Answers
Answer: 49.85%
Explanation:
From the information given,
mean = 37
standard deviation = 10
The 68-95-99.7 rule states that 68% of the data fall within 1 standard deviation of the mean. 95% of the data fall within 2 standard deviations of the mean and 99.7% of the data fall within 3 standard deviations of the mean. Thus,
1 standard deviation to the left of the mean = 37 - 10 = 27
1 standard deviation to the right of the mean = 37 + 10 = 47
3 standard deviation to the left of the mean = 37 - 3(10) = 37 - 30 = 7
3 standard deviations to the right of the mean = 37 + 3(10) = 37 + 30 = 67
We can see that the percentage of lightbulb replacement requests numbering between 37 and 67 falls within 3 standard deviations to the right of the mean. This is just half of the area covered by 99.7%. Thus
The percentage of lightbulb replacement requests numbering between 37 and 67
= 99.7/2 = 49.85%
Arc Length Formula:: Cx = degree measure of arcC-circumferenceDirections: Find each arc length. Round to the nearest hundredth.10. If EB = 15 cm, find the length of CD. 11. IF NR = 8 ft, find the length of NMP.DC12. IF VS = 12 m, find the length of UT.13. If JH = 21 in, fnd the length of KJG.12759DBS14. If FG = 27 yd, find the length of FED.15. If WS = 4.5 mm, find the length of TS.4780128317.62
Answers
Arc length formula:
[tex]\begin{gathered} \text{Arc length=}\frac{x}{360}\cdot C \\ \\ C=2\pi r \\ r=\text{radius} \end{gathered}[/tex]____________________________
10. r= 15cm
Angle CED is supplementary with angle BEC (add up to 180°)
[tex]\begin{gathered} m\angle\text{CED}+m\angle\text{BEC}=180 \\ \\ m\angle CED=180-m\angle BEC \\ m\angle CED=180-68 \\ m\angle CED=112 \end{gathered}[/tex]Then, arc CD is:
[tex]\begin{gathered} CD=\frac{112}{360}\cdot2\pi(15\operatorname{cm}) \\ \\ CD\approx29.32\operatorname{cm} \end{gathered}[/tex]___________________________________________________
11. r=8ft
The measure of central angle MRQ is equal to the measure of the given arc MQ (162°) and this angle and angle NRP are vertical angles (have the same measure) then, angle MRN and QRP (also vertical angles) need to add up 360° with the other angles, use it to find the measure of angle MRN:
[tex]\begin{gathered} m\angle NRP+m\angle NRP+m\angle MRN+m\angle QRP=360 \\ \\ 2m\angle NRP+2m\angle MRN=360 \\ 2(162)+2m\angle MRN=360 \\ 324+2m\angle MRN=360 \\ 2m\angle MRN=360-324 \\ m\angle MRN=\frac{36}{2} \\ \\ m\angle MRN=18 \end{gathered}[/tex]The angle for arc NMP is equal to the sum of angle MRP (180°) and angle MRN (18°).
Then, the length of arc NMP is:
[tex]\begin{gathered} \text{NMP}=\frac{180+18}{360}\cdot2\pi(8ft) \\ \\ \text{NMP}=27.65ft \end{gathered}[/tex]___________________________
find the area of each. use your calculator's value of pi. round your answer to the nearest tenth.
Answers
We are asked to find the area of the given circle.
Recall that the area of a circle is given by
[tex]A=\pi r^2[/tex]Where π is a constant and r is the radius of the circle.
From the figure, we see that the diameter is 22 km
Recall that the radius is half of the diameter.
So, the radius of the circle is
[tex]r=\frac{D}{2}=\frac{22}{2}=11\: km[/tex]So, the area of the circle is
[tex]A=\pi r^2=\pi(11)^2=\pi\cdot121=380.1\: km^2[/tex]Therefore, the area of the circle is 380.1 square km (rounded to the nearest tenth)
Calculate the determinant of this 2x2 matrix. Provide the numerical answer. 2 -14 - 5
Answers
In order to find the determinant we just multiply the diagonals
Then we substract the second result to the first:
[tex]\begin{gathered} \begin{bmatrix}{2} & {-1} & {} \\ {4} & {-5} & {} \\ & {} & {}\end{bmatrix}=2\cdot(-5)-4\cdot(-1) \\ =-10-\mleft(-4\mright)=-10+4 \\ =-6 \end{gathered}[/tex]Answer: the determinant of this 2x2 matrix is -6Solve the equation-3 + a = 13a = ???
Answers
ANSWER
a = 16
EXPLANATION
To solve for a we have to add 3 on both sides of the equation:
[tex]\begin{gathered} -3+3+a=13+3 \\ a=16 \end{gathered}[/tex][tex] log_{2 }(x - 6) + log_{2}(x - 4) = log_{2}(x) [/tex]x=8,3x=8No solution
Answers
Answer:
x=8,3
Explanation:
Given the expression:
[tex]\log _2\mleft(x-6\mright)+log_2\mleft(x-4\mright)=log_2\mleft(x\mright)[/tex]Applying the addition law of logarithm:
[tex]\log _2(x-6)(x-4)=log_2x[/tex]Next, cancel the logarithm operator on both sides:
[tex]\begin{gathered} (x-6)(x-4)=x \\ x^2-4x-6x+24=x \\ x^2-10x-x+24=0 \\ x^2-11x+24=0 \end{gathered}[/tex]We solve the resulting quadratic equation:
[tex]\begin{gathered} x^2-8x-3x+24=0 \\ x(x-8)-3(x-8)=0 \\ (x-3)(x-8)=0 \\ x-3=0\text{ or }x-8=0 \\ x=3\text{ or }x=8 \end{gathered}[/tex]The value of x is 3 or 8.
The bacteria in a dish triples every hour. At the start of the experiment therewere 400 bacteria in the dish. When the students checked again there were32,400 bacteria. How much time had passed? (Write your equation and solve forx; y= a • bx).
Answers
Given
The bacteria in a dish triples every hour. At the start of the experiment there
were 400 bacteria in the dish. When the students checked again there were
32,400 bacteria. How much time had passed? (Write your equation and solve for
x; y= a • bx)
Solution
If y varies directly with x and y = 48 when x = -4, write the equation that represents this direct variation relationship12 345
Answers
Answer
The equation that represents the direct variation relationship between y and x is
y = -12x
Explanation
We are told that y varies directly with x.
y = 48 when x = -4.
We are then told to write the equation that represents this direct variation relationship.
In mathematical terms, y varies directly with x is written as
y ∝ x
If we introduce a constant of variation, k, we can then write this relationship as
y = kx
To now fully write this relationship, we need to solve for k.
y = 48 when x = -4.
y = kx
48 = k × -4
48 = -4k
-4k = 48
Divide both sides by -4
(-4k/-4) = (48/-4)
k = -12
We can then put in the value of k obtained
y = kx
y = -12x
The equation given is
3y = 10x
Recall that variation is represented as
y ∝ x
And written as
y = kx
So, we can convert 3y = 10x into this form and establish the direct variation and obtain the value of k.
3y = 10x
Divide both sides by 3
(3y/3) = (10x/3)
y = (10x/3)
which is similar to y = kx
k = (10/3)
So, option A is correct.
Hope this Helps!!!
6. If you start with 200 MNM's and eat 15 every minute and your friend starts with300 MnM's but eats 25 every minute. When will you have the same number asyour friend? How much longer will it take you to finish your MnM's? At 10minutes you both will have 50 left. You will finish 1 min and 20 seconds after yourfriend.
Answers
Given:
The initial number of MNMs I have, x=200.
The number of MNM's eat by me every minute, p=15.
The initial number of MNMs my friend have, y=300.
The number of MNM's eat by friend every minute, q=25.
Let n be the number of minutes after which both will have the same number of MNM. Then, the amount of MNM remaining with me after n minutes is,
[tex]x-pn[/tex]The amount of MNM remaining with my friend after n minutes is,
[tex]y-qn[/tex]Equate the above expressions and substitute the values to find the number of minutes n.
[tex]\begin{gathered} x-pn=y-qn \\ 200-15n=300-25n \\ 25n-15n=300-200 \\ 10n=100 \\ n=\frac{100}{10} \\ n=10 \end{gathered}[/tex]Therefore, I will have the same number as my friend after 10 minutes.
The number of minutes taken by me to finish 200 MNM's is,
[tex]\begin{gathered} m=\frac{x}{p} \\ =\frac{200}{15} \\ =13\frac{5}{15} \\ =13\frac{1}{3}\text{minutes} \\ =13\text{minute}+\frac{1}{3}\min utes\times\frac{60\text{ seconds}}{1\text{ minute}} \\ =13\text{ minutes +20 seconds} \end{gathered}[/tex]So, I will take 13 minutes 20 seconds to finish the MNM's.
The number of minutes taken by my friend to finish 300 MNM's is,
[tex]\begin{gathered} k=\frac{y}{q} \\ =\frac{300}{25} \\ =12\text{ minutes} \end{gathered}[/tex]So, the friend will take 12 minutes to finish the MNM's.
So, I will finish
A student sketched some art on an 8-inch x 10-inch piece of paper. She wants to resize it to fit a 4-inch x 6 inchframe (as shown below).What percent of the original sketch was still able to be included in the frame?
Answers
So,
The area of art can be found multiplying:
8in * 10in = 80in²
And, the area of the frame, can be also found multiplying the dimentions:
4in * 6in = 24in².
If we divide, we'll obtain a ratio between the area of the frame and the area of the art as follows:
[tex]\frac{24}{80}=0.3[/tex]And, 0.3*100% = 30%.
So,30 percent of the original sketch was still able to be included in the frame.
Hello,May I please request for help on the word problem number 37, please?
Answers
As the last stand-up comic of the evening is granted. The combination of schedules is made with the other 5 performers.
To find how many ways you can order 5 performers you multiply 5x4x3x2x1 (or factorial 5: 5!)
[tex]5!=5\times4\times3\times2\times1=120[/tex]Then, there are 120 different ways to schedule the appearancesWalnuts make up half of the nuts in this nut bread:
It has exactly 2 pecans
The number of walnuts is double the number of pecans.
Write an equation to show how many of each nut this nut bread contains.
Answers
The equation to show how many of each nut this nut bread contains is w = 2p and there are 4 walnuts.
What is an equation?A mathematical equation is the statement that illustrates that the variables given. In this case, two or more components are taken into consideration to describe the scenario.
The number of walnuts is double the number of pecans. This can be illustrated as:
w = 2p
Therefore, the number of buts will be:
w = 2p
w = 2(2)
w = 4
Therefore, ther are 4 walnuts
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1) After the rise in popularity of the Croc shoe, a competitor brand will launch in January called “Srocs.” The company spends $9 to manufacture each pair of Sroc shoes. They also spend $8,000 on their Sroc-making machine and $4,000 on ads. One of the founders wants to sell each pair for $49 because that is the retail price for Crocs, but the other founder says they should sell the Srocs for $39.Write an equation for the company’s costs:Determine which price option you would choose and why.How much of the product must be sold to break even (using your chosen selling price)?
Answers
Company's costs:
Sroc's making machine = $8000
Ads = $4000
For each manufactured pair of Sroc shoes = $9
We add them to find the cost equation in terms of x manufactured pair of Srocs:
[tex]\begin{gathered} C(x)=8000+4000+9x \\ \\ \Rightarrow C(x)=9x+12000 \end{gathered}[/tex]There are two options for the selling price:
[tex]\begin{gathered} P_1(x)=49x \\ P_2(x)=39x \end{gathered}[/tex]We use each of them to find out how many Srocs we need to sell in order to have a null profit:
[tex]\begin{gathered} 49x=9x+12000 \\ 40x=12000 \\ x=300 \end{gathered}[/tex][tex]\begin{gathered} 39x=9x+12000 \\ 30x=12000 \\ x=400 \end{gathered}[/tex]As we can see, we need to sell only 100 pairs of Srocs more to recover the investment. Therefore, we choose the selling price P₂:
[tex]\text{ Selling price: \$39}[/tex]Finally, we have already found how much of the product must be sold to break even:
[tex]\text{ Answer: 400 pairs of Srocs}[/tex]For the data values 69, 54, 27, 43, 69, 56, the mean is 53.
Answers
From the table given,
To find the x - mean,
By the summation of all the x - mean
The value of x - mean is
[tex]x-\operatorname{mean}=16+1-26-10+16=-3[/tex]Hence, the value of x - mean is -3
To find the (x - mean)²
By the summation of all the values of (x - mean)²
The value of (x - mean)² is
[tex](x-\operatorname{mean})^2=256+1+676+100+256=1289[/tex]Hence, the value of (x - mean)² is 1289
Write the equation for a parabola with a focus at (1,2) and a directrix at y=6
Answers
Solution:
Given:
[tex]\begin{gathered} focus=(1,2) \\ directrix,y=6 \end{gathered}[/tex]Step 1:
The equation of a parabola is given below as
[tex]\begin{gathered} y=\frac{1}{4(f-k)}(x-h)^2+k \\ (h,f)=focus \\ h=1,f=2 \end{gathered}[/tex]Step 2:
The distance from the focus to the vertex is equal to the distance from the vertex to the directrix:
[tex]\begin{gathered} f-k=k-6 \\ 2-k=k-6 \\ 2k=2+6 \\ 2k=8 \\ \frac{2k}{2}=\frac{8}{2} \\ k=4 \end{gathered}[/tex]Step 3:
Substitute the values in the general equation of a parabola, we will have
[tex]\begin{gathered} y=\frac{1}{4(f-k)}(x-h)^{2}+k \\ y=\frac{1}{4(2-4)}(x-1)^2+4 \\ y=-\frac{1}{8}(x-1)^2+4 \\ \end{gathered}[/tex]By expanding, we will have
[tex]\begin{gathered} y=-\frac{1}{8}(x-1)^{2}+4 \\ y=-\frac{1}{8}(x-1)(x-1)+4 \\ y=-\frac{1}{8}(x^2-x-x+1)+4 \\ y=-\frac{1}{8}(x^2-2x+1)+4 \\ y=-\frac{x^2}{8}+\frac{x}{4}-\frac{1}{8}+4 \\ y=-\frac{x^2}{8}+\frac{x}{4}-\frac{1+32}{8} \\ y=-\frac{x^2}{8}+\frac{x}{4}+\frac{31}{8} \end{gathered}[/tex]Hence,
The final answer is
[tex]\begin{gathered} \Rightarrow y=-\frac{x^{2}}{8}+\frac{x}{4}+\frac{31}{8}(standard\text{ }form) \\ \Rightarrow y=-\frac{1}{8}(x-1)^2+4(vertex\text{ }form) \end{gathered}[/tex]find the circumstances of the circle. use 3.14 for pi.
Answers
Given:
The radius of the circiel is 4.2 in.
The value of π is 3.14.
The objective is to find the circumference of the circle.
The formula to find the circumference of the circle is,
[tex]\begin{gathered} C=2\cdot\pi\cdot r \\ =2\cdot3.14\cdot4.2 \\ =26.376\text{ inches} \end{gathered}[/tex]Hence, the circumference of the circle is 26.376 inches.
Write 5.8% as a fraction in lowest terms.
Answers
Answer:
[tex]5.8\text{ \%}\rightarrow\frac{29}{500}[/tex]Explanation: We have to write 5.8% In fraction in lowest terms:
This percent number essentially is:
[tex]5.8\text{ \%=}\frac{5.8}{100}[/tex]Therefore we can write it as:
[tex]\frac{5.8}{100}=\frac{5.8\times10}{100\times10}=\frac{58}{1000}[/tex]In lowest terms, this would be:
[tex]\frac{58}{1000}=\frac{29}{500}[/tex]3
Drag each tile to the correct box.
Place the parallelograms in order from least area to greatest area.
3 cm
4 cm
6 cm
3 cm
4 cm
5 cm
4 cm
3 cm
----
4 cm
Submit Test
}
Answers
The least area of the parallelogram will be 12cm² and the greatest area will be 20cm².
What will be the area of the parallelogram?The area of a parallelogram is simply calculated thus:
= Base × Height
The least area will be:
= Base × Heights
= 3cm × 4cm
= 12cm²
The greatest area of the parallelogram will be:
= Base × Height
= 4cm × 5cm
= 20cm²
Note that the figures are gotten from the. information given.
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Which of the following steps were applied to ABC obtain A’BC’?
Answers
Given,
The diagram of the triangle ABC and A'B'C' is shown in the question.
Required:
The translation of triangle from ABC to A'B'C'.
Here,
The coordinates of the point A is (2,5).
The coordinates of the point A' is (5,7)
The translation of the triangle is,
[tex](x,y)\rightarrow(x+3,y+2)[/tex]Hence, shifted 3 units right and 2 units up.
Write an equation or inequality and solve:32 is at most the quotient of a number g and 8
Answers
The quotient of a number g and 8 can be written as:
[tex]\frac{g}{8}[/tex]Since it is given that 32 is at most( this quotient, then it follows that:
[tex]32\le\frac{g}{8}[/tex]Next, solve the resulting inequality:
[tex]\begin{gathered} 32\le\frac{g}{8} \\ \text{Swap the sides of the inequality and change the sign:} \\ \frac{g}{8}\ge32 \end{gathered}[/tex]Multiply both sides of the inequality by 8. Note that the sign will not change since you are multiplying a positive number:
[tex]\begin{gathered} \Rightarrow8\times\frac{g}{8}\ge8\times32 \\ \Rightarrow g\ge256 \end{gathered}[/tex]Hence, the inequality is:
[tex]32\le\frac{g}{8}[/tex]The solution is:
[tex]g\ge256[/tex]Add or subtract the fractions. Write the answer in simplified form.-2/13+(-1/13)
Answers
1) To add or subtract fractions, let's firstly check the denominators
In this case, the denominator is the same.
The plus before the bracket does not change the sign.
[tex]\begin{gathered} -\frac{2}{13}+(-\frac{1}{13}) \\ \frac{-2-1}{13} \\ \\ \frac{-3}{13} \end{gathered}[/tex]That is why we get to -3/13 as a result.
This probability distribution shows thetypical grade distribution for a Geometrycourse with 35 students.GradeEnter a decimal rounded to the nearest hundredth.Enter
Answers
Explanation:
The total number of students is
[tex]n(S)=35[/tex]Concept:
To figure out the probability that a student earns grade A,B or C
Will be calculated below as
[tex]P(A,BorC)=P(A)+P(B)+P(C)[/tex]The Probability of A is
[tex]P(A)=\frac{n(A)}{n(S)}=\frac{5}{35}[/tex]The probabaility of B is
[tex]P(B)=\frac{n(B)}{n(S)}=\frac{10}{35}[/tex]The probabaility of C is
[tex]P(B)=\frac{n(B)}{n(S)}=\frac{15}{35}[/tex]Hence,
By substituting the values in the concept, we will have
[tex]\begin{gathered} P(A,BorC)=P(A)+P(B)+P(C) \\ P(A,BorC)=\frac{5}{35}+\frac{10}{35}+\frac{15}{35}=\frac{30}{35} \\ P(A,BorC)=0.857 \\ P(A,BorC)\approx0.86(nearest\text{ }hundredth) \end{gathered}[/tex]Hence,
The final answer is
[tex]0.86[/tex]A COMPUTER OPERATOR MUST SELECT FOUR JOBS AMOUNG 10 AVAILABLE JOB WAITING TO BE COMPLETED. HOW MANY DIFFERENT ARRANGMENTS CAN BE MADE?
Answers
This is a problem based on permutations. We must select four jobs among ten jobs and see how many arrangments can be made.
The formula for the number of permutations is:
[tex]P(n,r)=\frac{n!}{(n-r)!}.[/tex]Where:
• n = total number of jobs = 10,
,• r = number of jobs to be selected = 4.
Replacing these data in the formula above, we get:
[tex]P(10,4)=\frac{10!}{(10-4)!}=\frac{10!}{6!}=\frac{10\cdot9\cdot8\cdot7\cdot6!}{6!}=10\cdot9\cdot8\cdot7=5040.[/tex]Answer5040
