Use the following figure and information to complete the proof. Given: m∠4=m∠2m∠5=m∠3m∠DBE=180∘ Prove: m∠1+m∠2+m∠3=180∘ Parallel lines m & n. Triangle A B C with A & C on n & B on m. A is to the left of C with angle 2 at A & angle 3 is at C. B is above A & C with angles 4 3 & 5 at C from left to right.© 2019 StrongMind. Created using GeoGebra. Match each numbered statement in the proof to its correct reason.
Answers
Explanation:
The given information is
m∠4 = m∠2
m∠5 = m∠3
m∠DBE = 180
The angle addition postulate says that the angle that the sum of the angles 4, 1, and 5 is equal to the angle DBE, so we can write the following equation
m∠4 + m∠1 + m∠5 = m∠DBE
But, we know that m∠DBE = 180, so by transitivity, we get:
m∠4 + m∠1 + m∠5 = 180
Then, we also know that m∠4 = m∠2 and m∠5 = m∠3, so we can substitute the angles to get
m∠2 + m∠1 + m∠3 = 180
Therefore, we can change the order by the commutative property to get
m∠1 + m∠2 + m∠3 = 180
Answer:
So, the answer is
Related Questions
What additional piece of information is needed to show that ABC ≅ XYZ by AAS?
There are two triangles, triangle ABC and triangle XYZ. Side BC is congruent to side YZ and angle ABC is congruent to angle XYZ.
Answers
There are several congruence criteria between triangles. The case of your figure, the congruence must be given by the equality of the sides BC and ZY.
If we have an equal side on both sides, we need 2 angles at the end of that segment to be equal to each other. Your exercise shows that angle B and angle Y are equal.
So for them to be congruent, the angle C and the Z need to be equal.
Then the answer would be the letter C.
The first thing we have to do is identify all the angles, as shown in the figure. Triangles also show lines in yellow (single and double) in both triangles and this notation means that those sides are the same length. In other words, both triangles are isoceles.
What information can we get:
- By opposite vertices we know that R1 = R2=R
- The angles of the isosceles triangles are equal at their ends, that is: P=Q and S=R2=R
We also know that the internal sum of the angles of the triangles gives 180º. This gives us 2 more equations
[tex]\begin{gathered} S+R+44º=180º \\ Q+R+P=180º \end{gathered}[/tex]We replace the equalities taken from the isosceles triangles
[tex]\begin{gathered} S+S+44º=180º \\ 2S=180º-44º \\ S=\frac{136º}{2} \\ S=68º=R \\ P+S+P=180º \\ 2P+68º=180º \\ P=\frac{112º}{2} \\ P=56º=Q \end{gathered}[/tex]A cab company charges a $11 boarding fee and a meter rate of $2 per mile. The equation is y = 2x + 11 where x represents the number of miles to your destination. If you traveled 5 miles to your destination, how much would your total cab fee be?
Answers
Answer: 2(5) + 11= 21$
Step-by-step explanation:
help meeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee please
Answers
Answer:
Equation of the vertical asymptote is x = 0
Graph B is the correct graph
Step-by-step explanation:
The easiest way to answer this question would be to graph the function instead of attempting to solve for it algebraically which can also be done
The attached graph shows the function g(x) = -9/x
What is an asymptote?
In simple terms, an asymptote is a line that a curve approaches, as it heads towards infinity:
From the figure it is seen that the vertical asymptote occurs at x = 0 and the horizontal asymptote at y = 0
That's because at x = 0, the line almost touches but not quite the y-axis and is in a vertical direction both up and down
polynomials - mixed practicesimplify the polynomials write your answer in standard form please make the minimum of step thank you!
Answers
The given expression is
[tex](4x+1)(x+8)[/tex]We have to use the distributive property
[tex](4x+1)(x+8)=4x\cdot x+4x\cdot8+1\cdot x+1\cdot8=4x^2+32x+x+8[/tex]Then, we reduce like terms.
[tex]4x^2+33x+8[/tex]Hence, the final expression is[tex]4x^2+33x+8[/tex]According to data released in 2016, 69% of students in the United States enroll in college directly after high school graduation. Suppose a sample of 178 recent high school graduates israndomly selected. After ventying the conditons for the Central Limit Theorem are met. find the probability that at most 67 % enrolled in college directiy after high school graduaton
Answers
Given
students enroll = 69%
n = 178
Find
probability that at most 67 % enrolled in college directiy after high school graduation
Explanation
Let p be the proportion of students in the united states enroll directly after high school graduation.
p = 69% = 0.69
q = 1 - p = 1 - 0.69 = 0.31
n = 178
we have to find
[tex]\begin{gathered} P(p\leq0.67)=P(\frac{\hat{p}-p}{\sqrt{\frac{p(1-p)}{n}}}\leq\frac{0.67-0.69}{\sqrt{\frac{0.69\times0.31}{178}}}) \\ \\ P(p\leq0.67)=P(Z\leq-0.58) \\ P(p\leq0.67)=0.280 \end{gathered}[/tex]Final Answer
probability that at most 67 % enrolled in college directiy after high school graduation = 0.280
Question 811pA ship is travelling due north with a speed of 12 km hr-1 relative to the water.The current in the water is flowing at 1.1 km hr-1 to the east. Determine themagnitude of the velocity of the ship.
Answers
We have the following excerpt for the analysis:
" A ship is travelling due north with a speed of 12 km/hr relative to the water. The current in the water is flowing at 1.1 km/hr to the east. Determine the magnitude and the velocity of the ship "
We will investigate the application for the concept of relative velocity. The following variables can be extracted from the given excerpt:
[tex]\begin{gathered} V_{sw}\text{ = 12 }\frac{\operatorname{km}}{hr}\ldots\text{ due north} \\ \\ V_w\text{ = }1.1\text{ }\frac{\operatorname{km}}{hr}\ldots\text{ due east} \end{gathered}[/tex]In such cases of application we seek help by formulating a velocity triangle. We need to determine the direction and magnitude of ship's velocity that it must traverse in and by the effect of current due east the ship starts to move north.
We can go ahead and express the above information graphically in form a velocity triangle as follows:
Think of the above velocity triangle as such:
" The ship initital moves with a velocity ( Vs ) which is unknown at a certain angle. During the course the current of the water ( Vw ) pushes the ship nose from east side towards north. With the effect of the current the ship "seems" to be moving due north ( Vsw ) "
The above triangle is represented as a right angled triangle. We will recall the properties and the application of pythagoream theorem that only applies to right angle triangle as follows:
[tex]H^2=P^2+B^2[/tex]Where,
[tex]H=V_s,P=V_w,B=V_{sw}[/tex]We will plug in the respective quantities in the pythagorean theorem relation expressed above:
[tex]\begin{gathered} (V_s)\text{ = }\sqrt[]{(V_w)^2+(V_{sw})^2} \\ \\ (V_s)\text{ = }\sqrt[]{(1.1)^2+(12_{})^2} \\ \\ (V_s)\text{ = }\sqrt[]{(145.21)} \\ \\ (V_s)\text{ = 12.05 }\frac{\operatorname{km}}{hr}\ldots Answer \end{gathered}[/tex]
Nancy has 120,000 in a bank savings account. The bank pays 4% simple interest a year. How much will his money earn after two years? How much money will he have after two years?
Answers
Given:
Principal (P) = $120,000
Interest Rate (r) = 4% annually or 0.04 annually
Time in years (t) = 2
Find: interest and the accumulated value after 2 years
Solution:
Since this is simple interest, the formula for getting the simple interest of a principal amount is:
[tex]Interest=Principal\times Rate\times Time[/tex]Since we already identified the principal, rate, and time in the given information, let's plug them into the formula.
[tex]Interest=120,000\times0.04\times2[/tex]Then, multiply the three of them.
[tex]Interest=9,600[/tex]The interest is $9, 600.
Therefore, after 2 years, Nancy will earn $9, 600 in his bank account.
Since Nancy already has $120,000 and he earned $9, 600, then Nancy will have a total of $129, 600 in his bank account after 2 years.
[tex]\begin{gathered} A=Principal+Interest \\ A=120,000+9,600 \\ A=129,600 \end{gathered}[/tex]In the long run, which plan has the higher payout?
Plan A
Payout P(Payout)
-$5000
0.67
$55,000
0.09
$95,000
0.24
Payout
Plan B
- $30,000
$35,000
$65,000
P(Payout)
0.15
0.44
0.41
Answers
The most appropriate choice for expectation will be given by-
Plan B has a higher payout
What is expectation?
At first it is important to know about probability of an event.
Probability gives us the information about how likely an event is going to occur
Probability is calculated by Number of favourable outcomes divided by the total number of outcomes.
Probality of any event is greater than or equal to zero and less than or equal to 1.
Probability of sure event is 1 and probability of unsure event is 0.
Here,
For planout A
Expected value of plan A = [tex]-5000 \times 0.67 + 55000 \times 0.09 + 95000 \times 0.24\\[/tex]
= $24400
For planout B
Expected value of plan A = [tex]-30000 \times 0.15 + 35000 \times 0.44 + 65000 \times 0.41\\[/tex]
= $37550
Plan B has a higher payout
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A ball is thrown from an initial height of 3 feet with an initial upward velocity of 29 s. The ball's heighth (in feet) after seconds to given by the following:H=3+29t-16t^2Find all values of for which the ball's height is 15 feetRound your answer(s) to the nearest hundredth(if there is more than one answer, use the "of" button)
Answers
The height of the ball at time t is modeled by
[tex]H(t)=3+29t-16t^2[/tex]To find the values of t for which the height is 15 feet, let us solve the equation
[tex]\begin{gathered} H(t)=15 \\ 3+29t-16t^2=15 \\ 16t^2-29t+12=0 \\ x=\frac{29\pm\sqrt[]{73}}{32} \\ =0.64,1.17 \end{gathered}[/tex]So, at t=0.6 sec and =1.173 sec, the height of the ball is 15 feet (Rounding off to the nearest hundredth)
$55,000 at 16% compounded annually for 2 years.
Answers
Explanation:
The question wants us to find the amount that will be obtained when $55,000 at 16% is compounded annually for 2 years
To do so, we will use the formula below
[tex]\begin{gathered} A=P(1+\frac{r}{100})^t \\ \text{where} \\ r=16\text{ \%=0.16} \\ t=2 \\ P=55,000 \end{gathered}[/tex]Thus, we will have
[tex]\begin{gathered} A=55000(1+0.16)^2 \\ A=55000(1.16)^2 \\ A=55000\times1.3456 \\ A=74008 \end{gathered}[/tex]Thus, the amount will be $74,008
Mr. Jones has a box of t-shirts to distribute to his students for Field Day. There are 30 red and 60 blue t- shirts in the box. If the first student chooses a t-shirt without looking , what is the probability that she will choose a blue t- shirt?
Answers
Given:
Number of blue t-shirst, B=60.
Number of red t-shirs, R=30.
The number of total t-shirts is,
[tex]\begin{gathered} T=B+R \\ T=60+30 \\ T=90 \end{gathered}[/tex]The probabilty of choosing a blue t-shirt is,
[tex]\begin{gathered} P(B)=\frac{B}{T} \\ =\frac{60}{90} \\ =\frac{2}{3} \end{gathered}[/tex]Therefore, the probabilty of choosing a blue t-shirt is 2/3.
Is y is proportional to x?What’s the constant of proportionality (k)?K = y/xWhat’s the equation that represents the table?
Answers
For two numbers to be proportional, they must verify:
[tex]y=kx[/tex]"y is proportional to x"
In this case, to verify this, we nedd to calculate if each value of y can be founded by multiplying x by a constant k.
If y = kx is true, then:
[tex]k=\frac{y}{x}[/tex]And if k is the same for al pairs (x, y) then the relationship is proportional.
Using the table we do:
[tex]\begin{gathered} k=\frac{2}{12}=\frac{1}{6} \\ k=\frac{3}{18}=\frac{1}{6} \\ k=\frac{4}{24}=\frac{1}{6} \\ k=\frac{5}{30}=\frac{1}{6} \end{gathered}[/tex]Since k is the same for all pair of values, y is proportional to x.
Also we have already calculated k = 1/6
And the equation that represents the table is:
[tex]y=\frac{1}{6}\cdot x[/tex]A smaller number and a larger number add up to 8 and have a difference of 6. (Let X be the larger number and Y be the smaller number) A. 2x=8 x-y=6 B. 2x+2y=8 x-y=6 C. x+y=8 x-y=6D. x+y+8=0 x-y+6=0Which one is it A, B, C or D
Answers
Answer
Option C is correct.
x + y = 8
x - y = 6
Explanation
The larger number is x
The smaller number is y
The two numbers sum up to give 8
x + y = 8
The two numbers have a difference of 6
x - y = 6
Hope this Helps!!!
From the image sent, we can tell that the total ounces of solution is 28 ounces.
x + y = 28
Then, the second equation will be formed using the pure acid content
0.07x + 0.14y = 0.12 (28) = 3.36
So, the two equations are
x + y = 28
0.07x + 0.14y = 3.36
We can then solve this simultaneous equation and obtain that
x = 8 ounces, y = 20 ounces
Hope this Helps!!!
Two piecewise functions are shown below. What is the value of 6f * (- 2) + 3g * (1) ?
Answers
To find the value of f(-2), we replace x = -2 into the second piece of the function. Then, we operate.
[tex]\begin{gathered} f(-2)=\frac{1}{3}(-2)^3 \\ f(-2)=\frac{1}{3}(-8) \\ f(-2)=-\frac{8}{3} \end{gathered}[/tex]Second partTo find the value of g(1), we replace x = 1 into the first piece of the function. Then, we operate.
[tex]\begin{gathered} g(1)=2|1-1|+3 \\ g(1)=2|0|+3 \\ g(1)=2\cdot0+3 \\ g(1)=0+3 \\ g(1)=3 \end{gathered}[/tex]Finally, we find the value of the given expression:
[tex]\begin{gathered} 6f(-2)+3g(1)=6\cdot-\frac{8}{3}+3\cdot3 \\ 6f(-2)+3g(1)=-\frac{6\cdot8}{3}+9 \\ 6f(-2)+3g(1)=-\frac{48}{3}+9 \\ 6f(-2)+3g(1)=-16+9 \\ 6f(-2)+3g(1)=-7 \end{gathered}[/tex]Help needed! please help math
PLEASEEE!!!
Answers
t = 4.738 * 10³ would take the rocket to travel the speed.
What is speed, for instance?
Speed is a way to gauge how rapidly something is happening, moving, or moving swiftly. The speed of a car being driven at 45 mph serves as an illustration. A person cleaning a room in 10 minutes is an illustration of speed.Speed indicates how quickly something or someone is moving. If you know how far something has traveled and how long it took to get there, you can calculate its average speed. Speed is calculated as follows: speed = distance * time.d = 1.701 * 10⁸
s= 3.59 * 10⁴
s = d/t
t = d/s
t = 1.701 * 10⁸/3.59 * 10⁴
t = 0.4738 * 10⁸⁻⁴
t = 0.4738 * 10⁴
t = 4.738 * 10³
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6. An apartment building contains 12 units consisting
of one- and two-bedroom apartments that rent for
$360 and $450 per month, respectively. When all
units are rented, the total monthly rental is $4,950.
What is the number of two-bedroom apartments?
a) 3
b) 4
c) 5
d) 6
e) 7
* also comment your name and grade ( so I can be impressed- it doesn't have to be your real name)
Answers
Using a system of equations, the number of two-bedroom apartments is e) 7.
What is an equation?An equation is a mathematical statement that shows that two expressions are equal.
Equations are written with the equation symbol (=) to show that they enjoy equivalent relationships.
The total number of units in the apartment building = 12
Let one-bedroom apartments = x
Let two-bedroom apartments = y
x + y = 12 ...equation 1
x = 12 - y ... equation 2
The cost of one-bedroom apartments = $360 per unit
The cost of two-bedroom apartments = $450 per unit
The total monthly rental = $4,950
Let 4,950 = 360x + 450y ... equation 3
Substitute x = 12 - y in equation 2 in equation 3:
360 (12 - y) + 450y = 4,950
4,320 - 360y + 450y = 4,950
4,320 + 90y = 4,950
90y = 4950 - 4,320
90y = 630
y = 7
In equation 2, x = 12 - y
x = 12 - 7
x = 5
Check Total Monthly Rental:360x + 450y = 4,950
360(5) + 450(7) = 4,950
1,800 + 3,150 = 4,950
4,950 = 4,950
Thus, based on equivalent values, the number of two-bedroom apartments is 7, while the number of one-bedroom apartments is 5, giving a total of 12.
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The frequency F of a fire truck siren heard by a stationary observer is given below, where ± v represents the velocity of the accelerating fire truck in meters per second (see figure). (Round your answers to 3 decimal places).
Answers
In order to calculate the rate of change, we can use the following derivatives:
[tex]\begin{gathered} u=\frac{1}{a+x} \\ \frac{du}{dx}=-\frac{1}{(a+x)^2} \\ \\ u=\frac{1}{a-x} \\ \frac{du}{dx}=\frac{1}{(a-x)^2} \end{gathered}[/tex]So, calculating the rate of change in each case, we have:
a)
[tex]\begin{gathered} F=\frac{130600}{321-x} \\ \frac{dF}{dx}=\frac{130600}{(321-x)^2}=\frac{130600}{(321-25)^2}=\frac{130600}{296^2}=\frac{130600}{87616}=1.491 \end{gathered}[/tex]b)
[tex]\begin{gathered} F=\frac{130600}{321+x} \\ \frac{dF}{dx}=-\frac{130600}{(321+x)^2}=-\frac{130600}{(321+25)^2}=-\frac{130600}{346^2}=-\frac{130600}{119716}=-1.091 \end{gathered}[/tex]Which fraction that is not equivalent to the other fractions.
Answers
Simplify each fraction as follows:
[tex]\begin{gathered} \frac{4}{12}=\frac{4\times1}{4\times3}=\frac{1}{3} \\ \frac{2}{5}=\frac{2}{5} \\ \frac{3}{9}=\frac{3\times1}{3\times3}=\frac{1}{3} \\ \frac{1}{3}=\frac{1}{3} \end{gathered}[/tex]As seen above, the three fractions 4/12,3/9 and 1/3 are equivalent.
The fraction 2/5 is not equivalent to the other three.
Hence 2/5 does not belong and is not equivalent to the other three given fractions.
What is the value of the expression (5)³?
Answers
Answer:
125
Step-by-step explanation:
since 5^3=5*5*5then 5^3=125
Find the distance between the two points.
(1,−7) and (17,−19)
Answers
The distance between the two points is 20.
Here the two points are (1.-7) and (17, -19)
The formula for the distance between the two points is:
distance = [tex]\sqrt{(x_{2} -x_{1} )^{2} +( y_{2}- y_{1} )^{2} }[/tex]
So here
([tex]x_{1} , y_{1}[/tex]) = (1.-7)
([tex]x_{2} ,y_{2}[/tex]) = (17, -19)
distance = [tex]\sqrt{(17 - 1)^{2} + ( -19-(-7))^{2} }[/tex]
= [tex]\sqrt{16^{2} + 12^{2} }[/tex]
= [tex]\sqrt{256 + 144}[/tex]
= √400
= 20
Therefore the distance between the two points is 20.
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kaitlin, john and carlos sent a total of 109 text messages during the weekend. kaitlin sent 7 more messages than carlos. John 4 times as many messages as carlos How many messages did they each send?number of text messages kaitlin sent=number of text messages john sent =number of text messages carlos sent =
Answers
let k be Kaitlin, j be John and c be Carlos. We get that
[tex]\begin{gathered} k+j+c=109 \\ k=c+7 \\ j=4c \end{gathered}[/tex]so we get that
[tex]\begin{gathered} c+7+4c+c=109 \\ 6c=109-7=102 \\ c=\frac{102}{6}=17 \end{gathered}[/tex]so carlos sent 17 messages. Kaitlin sent 24 and John 68
Find the area between the curve
y
=
x
3
, the axis of
y
and the lines
y
=
1
and
y
=
8
Answers
Answer:
(d) 11 1/4 units²
Step-by-step explanation:
You want the area bounded by the x-axis, the lines y=1 and y=8, and the curve y=x^3.
AreaSince the y-axis is one bound it works well to use a differential of area that is (x2 -x1)dy, where x1 = 0, and x2 = ∛y. The limits of the integration will be the boundary lines y=1 and y=8. The power rule is used for integration.
[tex]\displaystyle A=\int_{1}^{8}{y^{\frac{1}{3}}}\,dy=\left.\dfrac{3}{4}y^{\frac{4}{3}}\right|_{1}^8=\dfrac{3}{4}(16-1)=\dfrac{45}{4}=\boxed{11\dfrac{1}{4}\text{ units}^2}[/tex]
__
Additional comment
The given curve is y=x³. Solving for x, we find x=∛y. This is the boundary curve we used for integration.
The attachment also shows the integral over x. For that, the region is divided into two parts: a rectangle to the left of x=1, and the region bounded on the bottom by y=x³ to the right of x=1. The x-value corresponding to y=8 is x=2, so that is the limit of integration for the part of the region to the right of x=1.
Decide whether there is enough information to prove that mln. If so, state the theroem you would use.#O No, there is not enough information.O Yes. Alternate Interior Angles ConverseO Yes. Alternate Exterior Angles ConverseOYes. Consecutive Interior Angles ConverseO Yes. Corresponding Angles Converse
Answers
Explanation
The converse of alternate interior angles theorem states that if two lines are intersected by a transversal forming congruent alternate interior angles, then the lines are parallel.
For the given question, we can then conclude that
Line m and n are parallel because of the Alternate Interior Angles Converse
Therefore, the answer is
A number is selected at random from the set 2, 4, 6, 8, 10. Which event, by definition, covers the entire sample space of this experiment? A. The number is greater than 2. B. The number is not divisible by 5. C. The number is even and less than 12. D. The number is neither prime nor composite. E. The square root of the number is less than 3.
Answers
Answer:
The number is even and less than 12
Step-by-step explanation:
all of these numbers fit into this category
Answer: Numbers that are even or less than 12
Step-by-step explanation:
. In a recent year, the U.S. Postal Service handled approximately 0.459 of the world's card and letter mail volume. Write this decimal as a percent.
Answers
The percentage of of the given decimal value is 45.9%
Decimal to PercentageTo solve this problem, we have to express the decimal value into a percentage and this can be done by simply multiplying the ratio of world's card to letter mail volume by 100.
To change a fraction to a percentage, you can divide the numerator by the denominator which will give us a decimal number then multiply the result by 100. Alternatively, you can multiply the numerator by 100 first then divide the result by the denominator of the fraction.
Mathematically, this can be achieved by
[tex]0.459 * 100[/tex]
Solving this, we would have
[tex]0.459 * 100 = 45.9\%[/tex]
The percentage of world's card to letter mail volume is 45.9%
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Help please my last tutor got it wrong thank you
Answers
In order to solve this, the first thing we have to do is to determine the value of g(-2), this is possible by evaluating -2 for x in g(x), like this:
g(-2) = 3(-2)²= 3×4 = 12
Now that we know the value of g(-2), we can determine the value of f(g(-2)) by evaluating g(-2) = 12 in f(x), like this:
f(g(-2)) = f(12) = 5(g(-2)) + 3 = 5(12) + 3 = 60 + 3 = 63
Then, f(g(-2)) = 63
Evaluate each expression for the given value of the variable. #8
Answers
8.
You evaluate the expression given the value of n.
The expression is:
[tex]4(n-1)^2[/tex]We want the value of this expression, GIVEN that n is 6.
So, let's substitute 6 into n and find out the answer. Shown below:
[tex]\begin{gathered} 4(n-1)^2 \\ =4(6-1)^2 \\ =4(5)^2 \\ =4\times25 \\ =100 \end{gathered}[/tex]the question is in the pic! Also, you have to give the answer in simplified, decimalized, and percentaged form!!
Answers
The total number of pieces in the domino is 28.
a)
The number of pieces that have an odd number of dots is 12, so the probability of choosing a piece with an odd number of dots is:
[tex]P=\frac{12}{28}=\frac{3}{7}=\text{0}.4286=42.86\text{\%}[/tex]b)
The number of pieces that have 2 dots is 2, so:
[tex]P=\frac{2}{28}=\frac{1}{14}=0.0714=7.14\text{\%}[/tex]c)
The number of pieces that don't have 7 dots is 25, so:
[tex]P=\frac{25}{28}=0.8929=89.29\text{\%}[/tex]d)
The number of pieces that have at most 8 dots is 22, so:
[tex]P=\frac{22}{28}=\frac{11}{14}=0.7857=78.57\text{\%}[/tex]e)
The number of pieces that have more than 10 dots is 2, so:
[tex]P=\frac{2}{28}=\frac{1}{14}=0.0714=7.14\text{\%}[/tex]f)
The number of pieces that have a number of dots multiple of 4 is 7, so:
[tex]P=\frac{7}{28}=\frac{1}{4}=0.25=25\text{\%}[/tex]A civil air patrol unit of fifteen members includes three officers. In how many ways can three members be selected for a search and rescue mission such that at least one officer is included
Answers
The three members be can selected in 455 ways.
What in mathematics is a combination?
Combinations are mathematical operations that count the number of potential configurations for a set of elements when the order of the selection is irrelevant. You can choose the components of combos in any order. Permutations and combinations can be mixed up.
The officers can be selected in 15C3 ways.
15c3
=15!/(15-3)! . 3!
After calculating get that,
= 5 x 7 x 13
=455
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"The surface area of a sphere is 205 in^2. If its radius is tripled, what will be the new surface area of the sphere? " If you could help explain how to solve this that would be great! Thank you!
Answers
Question:
The surface area of a sphere is 205 in^2. If its radius is tripled, what will be the new surface area of the sphere?
Solution:
The surface area of a sphere is given by the following formula:
[tex]SA=4\pi r^2[/tex]where r is the radius of the sphere. Now, if the surface area of the sphere is 205 in^2, by the above equation we have that:
[tex]205=4\pi r^2[/tex]solving for r^2, we get:
[tex]r^2\text{ = }\frac{205}{4\pi}[/tex]and solving for r, we get:
[tex]r\text{ = }\sqrt[]{\frac{205}{4\pi}}\text{ = 4.03}[/tex]this means that the radius of the sphere with a surface area of 205 in^2 is 4.03. Then, if this radius is tripled, we get a new radius of
r = 3 x 4.03 = 12.09
then, replacing this new value in the first equation (surface area), we get:
[tex]SA=4\pi(12.09)^2\text{ = 1836.80}[/tex]Then, we can conclude that the correct answer is:
[tex]SA=\text{ 1836.80}[/tex]