Fill in the following values for a 45-45-90 triangle Leg Leg Hypotenuse 5 А B C С D 32 Fill in the following values for a 30-60-90 triangle Short Leg Long Leg Hypotenuse 6 E H 20 G
Answers
First Part 45-45-90 Triangle
first triangle
where the two angles different to 90° are same, the measure of the legsof the triangle are the same
then
[tex]A=5[/tex]and to calculate B or the hypotenuse we use pythagoras
[tex]a^2+b^2=h^2[/tex]where a and b are legs and h the hypotenuse
replacing
[tex]\begin{gathered} 5^2+5^2=h^2 \\ 25+25=h^2 \\ 50=h^2 \\ h=\sqrt[]{50} \\ h=5\sqrt[]{2} \end{gathered}[/tex]the hypotenuse or B is
[tex]B=5\sqrt[]{2}[/tex]Second triangle
legs of the triangle have the same value then if we apply pythagoras
[tex]a^2+b^2=h^2[/tex]and replace the legs with the same value(a)
[tex]\begin{gathered} a^2+a^2=h^2 \\ 2a^2=h^2 \end{gathered}[/tex]we can replace the hypotenuse and solve a
[tex]\begin{gathered} 2a^2=(3\sqrt[]{2})^2 \\ 2a^2=18 \\ a^2=\frac{18}{2} \\ \\ a=\sqrt[]{9} \\ a=3 \end{gathered}[/tex]value of each leg is 3 units, then
[tex]C=D=3[/tex]Second part 30-60-90 triangle
First triangle
we use trigonometric ratios to solve, for example I can use tangent for the angle 60 to find E
[tex]\tan (\alpha)=\frac{O}{A}[/tex]where alpha is the angle, O the oppiste side of the angle and A the adjacet side of the angle
using angle 60°
[tex]\begin{gathered} \tan (60)=\frac{E}{6} \\ \\ E=6\tan (60) \\ \\ E=6\sqrt[]{3} \end{gathered}[/tex]now using sine we calculate F or the hypotenuse
[tex]\sin (\alpha)=\frac{O}{H}[/tex]where alpha is the angle, O the opposite side from the angle and H the hypotenuse
using angle 60°
[tex]\begin{gathered} \sin (60)=\frac{E}{F} \\ \\ F=\frac{E}{\sin (60)} \\ \\ F=\frac{6\sqrt[]{3}}{\sin (60)} \\ \\ F=12 \end{gathered}[/tex]Second triangle
we use sine with 60° to find H
[tex]\begin{gathered} \sin (\alpha)=\frac{O}{h} \\ \\ \sin (60)=\frac{H}{20} \\ \\ H=20\sin (60) \\ H=10\sqrt[]{3} \end{gathered}[/tex]use cosine with 60° to find G
[tex]\begin{gathered} \cos (\alpha)=\frac{A}{h} \\ \\ \cos (60)=\frac{G}{20} \\ \\ G=20\cos (60) \\ \\ G=10 \end{gathered}[/tex]Final Values
[tex]\begin{gathered} A=5 \\ B=5\sqrt[]{2} \\ C=3 \\ D=3 \\ E=6\sqrt[]{3} \\ F=12 \\ G=10 \\ H=10\sqrt[]{3} \end{gathered}[/tex]
Related Questions
what is the equation for the line that passes through the given point and is parallel to the graph of y=3x-2; (3,2)
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A kitche sa tabletop that is a rectangle 24 in long and 18 in wide.Rita is an interior designer and wants to cover the tabletop in small tiles.She knows the area each bag of tiles covers, but only in square centimeters.(a) Find the area of the tabletop in square centimeters. Do notround intermediate computations and round your finalanswer to two decimal places. Use the table of conversionfacts, as needed.cm(b) The designer wants to cover the tabletop with tiles. Shedoesn't have any to begin with and she can't buy partialbags of tiles. Each bag of tiles covers 260 cm². How manywhole bags of tiles does the designer need to buy tocompletely cover the tabletop?bags(c) If each bag of tiles costs $3.76, how much will she need tospend on tile? Write your answer to the nearest cent.ExplanationCheckConversion facts for length2.54 centimeters (cm)= 30.48 centimeters (cm)≈ 0.91 meters (m)1 inch (in)1 foot (ft)1 yard (yd)1 mile (mi)XNote that means "is approximately equal to".For this problem, treat as if it were = .1.61 kilometers (km)5?I need help with this math problem.
Answers
Given: a tabletop that is a rectangle 24 in long and 18 in wide.
Find: (a) the area of the tabletop in square centimeters
(b) The designer wants to cover the tabletop with tiles. She doesn't have any to begin with and she can't buy partial bags of tiles. Each bag of tiles covers 260 cm². number of bags of tiles does the designer need to buy to completely cover the tabletop
(c)If each bag of tiles costs $3.76, how much will she need to spend on tiles.
Explanation: (a)
[tex]1\text{ inch= 2.54cm}[/tex]so the length of the tabletop in cm will be
[tex]24\times2.54=60.96cm[/tex]and the breadth of the tabletop in cm will be
[tex]18\times2.54=45.72cm[/tex]the area of the tabletop will be
[tex]\begin{gathered} l\times b \\ =60.96\times45.72 \\ =2787.09cm^2 \end{gathered}[/tex](b) The designer wants to cover the tabletop with tiles and she can't buy partial bags of tiles. Each bag of tiles covers 260 cm² so the numbe rof bags designer needs to buy to cover the tabletop is
[tex]\begin{gathered} \frac{2787.09}{260} \\ =10.71 \end{gathered}[/tex]it means that designer needs to buy 11 bags of tiles to cover the tabletop.
(c) If each bag of tiles costs $3.76.the the total cost will be equal to
[tex]3.76\times11=41.36\text{ \$}[/tex]-7 x -10 y equals -83 4x - 10 y equals 16
Answers
Answer:
Subtract to eliminate y.
Step by step explanation:
[tex]\begin{gathered} -7x-10y=-83 \\ 4x-10y=16 \end{gathered}[/tex]Since we have the same negative coefficient for y, we can subtract them to eliminate y.
-10-(-10)=0.
Using the z score formula use the information below to find the value of
Answers
Explanation
Given that
[tex]\begin{gathered} z=-4.80 \\ x=23.55 \\ \mu=32.67 \end{gathered}[/tex]Using the z-score formula;
[tex]\begin{gathered} z=\frac{x-\mu}{\sigma} \\ -4.80=\frac{23.55-32.67}{\sigma} \\ -4.80\sigma=-9.12 \\ \sigma=\frac{-9.12}{-4.80} \\ \sigma=1.9 \end{gathered}[/tex]Answer: 1.9
I need help it says identity the equivalent expression for the expression above
Answers
Given:
Expression is
[tex]=\frac{m^{\frac{1}{3}}}{m^{\frac{1}{5}}}[/tex]Required:
Equivalent expression for the given expression.
Explanation:
We will use
[tex]\frac{x^a}{x^b}=x^{a-b}[/tex]So,
[tex]\begin{gathered} \frac{m^{\frac{1}{3}}}{m^{^{\frac{1}{5}}}}=m^{\frac{1}{3}-\frac{1}{5}} \\ =m^{\frac{2}{15}} \end{gathered}[/tex]Answer:
Hence, 1st option is correct.
Zoe and Marsden are working with expressions with rational exponents. Zoe believes V2+ V8 is equivalent to 2.21. Marsden believes v2 + V8 is equivalent to 3.21. Use the properties of exponents to decide who is correct. Write the correct answer in the space provided.
Answers
Explanation
the properties of exponents
[tex]\begin{gathered} \sqrt[n]{a}=a^{\frac{1}{n}} \\ \sqrt[n]{a^{n^{}}b^n}\text{ = ab} \\ \sqrt[]{ab}=\sqrt[]{a}\cdot\sqrt[]{b} \end{gathered}[/tex]Step 1
Zoe believes
[tex]\sqrt[]{2}+\sqrt[]{8\text{ }}=\text{ 2.21}[/tex]Marsden Believes
[tex]\sqrt[]{2}+\sqrt[]{8}=3.21[/tex]Step 2
[tex]\sqrt[]{8}=\sqrt[]{4}\cdot\sqrt[]{2}=\text{ 2}\sqrt[]{2}[/tex]then
[tex]\begin{gathered} \sqrt[]{2}+\sqrt[]{8}=\text{ }\sqrt[]{2}+2\sqrt[]{2}=3\sqrt[]{2} \\ \text{also } \\ \sqrt[]{2}=\text{ 1.4142} \\ so, \\ \sqrt[]{2}+\sqrt[]{8}=3\sqrt[]{2}=3\cdot1.4142=4.24 \end{gathered}[/tex]then
[tex]\sqrt[]{2}+\sqrt[]{8}=3\sqrt[]{2}=3\cdot1.4142=4.24[/tex]I hope this helps you
Graph the parabola.y=1/4x^2-1Plot five points on the parabola: the vertex, two points to the left of the vertex, and two points to the right of the vertex. Then click on the graph-a-function button
Answers
This is basic parabola of the form:
[tex]y=ax^2-b[/tex]So, this one is shifted 1 units down.
The vertex is at (0, -1).
To take 2 points to the left of vertex, we find coordinates for x = -2 and x = -4.
To take 2 points to the right of vertex, we find coordinates for x = 2 and x = 4.
Let's find it:
[tex]\begin{gathered} \text{When x = -2,} \\ y=\frac{1}{4}x^2-1 \\ y=\frac{1}{4}(-2)^2^{}-1 \\ y=0 \\ When\text{ x = -4,} \\ y=\frac{1}{4}x^2-1 \\ y=\frac{1}{4}(-4)^2-1 \\ y=3 \\ \text{When x = 2,} \\ y=\frac{1}{4}x^2-1 \\ y=\frac{1}{4}(2)^2-1 \\ y=0 \\ \text{When x= 4,} \\ y=\frac{1}{4}x^2-1 \\ y=\frac{1}{4}(4)^2-1 \\ y=3 \end{gathered}[/tex]So, the 4 coordinates are:
(-2,0), (-4,3), (2,0), (4,3)
The graph:
Given h(x) = 5x – 3 and m(x)= -2x^2 what (h o m)(-1)=
Answers
Let's begin by listing out the information given to us:
[tex]\begin{gathered} h\mleft(x\mright)=5x-3 \\ m\mleft(x\mright)=-2x^2 \\ \mleft(h^om\mright)\mleft(x\mright)=5(-2x^2)-3 \\ (h^om)(1)=-10x^2-3=-10(-1^3)-3 \\ (h^om)(1)=10-3=7 \\ (h^om)(1)=7 \end{gathered}[/tex]Choose whether the number given in specific notation is representing a large or small number.
Answers
Given:
[tex]\begin{gathered} a)1.2\times10^3 \\ b)7.5\times10^^{-4} \end{gathered}[/tex]To find:
The number given in a specific notation is representing a large or small number.
Explanation:
a) It can be written as,
[tex]\begin{gathered} 1.2\times10^3=1.2\times1000 \\ =1200 \end{gathered}[/tex]So, it is a large number.
b) It can be written as,
[tex]\begin{gathered} 7.5\times10^{-4}=7.5\times\frac{1}{10^4} \\ =\frac{7.5}{10000} \\ =0.00075 \end{gathered}[/tex]So, it is a small number.
Final answer:
a) Large
b) Small
Evaluate 2g - 4, if the value of g=5
Answers
Put g=5 in 2g-4.
[tex]\begin{gathered} 2g-4=2\times5-4 \\ =10-4 \\ =6 \end{gathered}[/tex]The value is 6.
Sam bought a stereo that listed for $795. He saved 20% of the originalcost by buying it at a sale and paying cash. How much did he pay for thestereo?a. $159b. $636c. $63.60d. $795
Answers
Given:
a.) Sam bought a stereo that was listed for $795.
b.) He saved 20% of the original cost by buying it at a sale and paying cash.
We will be using the following formula:
[tex]\text{ Discounted price = Original Price x (}\frac{100\text{\% - \% Discount}}{100})[/tex]We get,
[tex]\text{ Discounted price = Original Price x (}\frac{100\text{\% - \% Discount}}{100})[/tex][tex]\text{= 795 x (}\frac{100\text{\% - 20\%}}{100})[/tex][tex]\text{ = 795 x (}\frac{80}{100})[/tex][tex]\text{ = 795 x 0.80}[/tex][tex]\text{ Discounted Price = \$}636.00[/tex]Therefore, Sam paid $636 for the stereo.
The answer is letter B.
Which of the functions is an exponential function? F(x)=-3x^-1F(x)=-3(2)^2F(x)=-3(1)^xF(x)=-3x^2
Answers
For this problem we recall the definition of an exponential function:
[tex]\begin{gathered} f(x)\text{ is an exponential function if } \\ f(x)=a\cdot b^{kx} \\ \text{Where a}\ne0,\text{ k}\ne0\text{ and b}\ne1 \end{gathered}[/tex]Answer: F(x)= - 3 (2)^x
shania traveled 310 miles in 5 hours. if she remain at a constant rate , how many miles can she travel in 1 hour
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Can someone help me with these geometry questions sorry it’s a two parter.
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In this problem, we are trying to choose between using a permutation and a combination.
The main difference between the two is the order.
In a combination, order doesn't matter, but it does matter in a permutation. Since the coach is choosing people based on how they performed, this will be a permutation.
For the first box on your screen, you should drag and drop the "P" variable for permutation.
Next, we need to apply the permutation formula:
[tex]_nP_r=\frac{n!}{(n-r)!}[/tex]I'm assuming there are a total of 14 players on the team? So we will let
[tex]\begin{gathered} n=14 \\ r=3 \end{gathered}[/tex]Where n represents the total number of players, and r represents the number of people being chosen based on performance. Then we have:
[tex]\frac{14!}{(14-3)!}=\frac{14!}{11!}[/tex]You can drag the 14! to the numerator and the 11! to the denominator.
Finally, we need to simplify to get the final answer. We can always use a calculator, but I'll show the steps for simplifying here:
[tex]\begin{gathered} \text{ Rewrite}14! \\ \frac{14\cdot13\cdot12\cdot11!}{11!} \end{gathered}[/tex][tex]\begin{gathered} \text{ Cancel the }11! \\ \\ \frac{14\cdot13\cdot12\cdot\cancel{11!}}{\cancel{11!}} \end{gathered}[/tex]Multiply the remaining values:
[tex]14\cdot13\cdot12=2184[/tex]The coach has 2184 ways to choose a player.
Solve for x. -2x+5≤10
Answers
Answer:
x≥-2.5
Explanation:
Given the inequality:
[tex]-2x+5\le10[/tex]Step 1: Subtract 5 from both sides of the inequality
[tex]\begin{gathered} -2x+5-5\le10-5 \\ -2x\le5 \end{gathered}[/tex]Step 2: Divide both sides by -2.
Note: Since we divide by a negative number, the inequality sign is reversed.
[tex]\begin{gathered} -\frac{2x}{-2}\ge\frac{5}{-2} \\ x\ge-\frac{5}{2} \\ x\ge-2.5 \end{gathered}[/tex]The solution to the inequality is x≥-2.5.
A composite figure is shown. 10 ft А 6 ft - 10 ft तो 12 ft B C 12 ft 4 ft Determine whether each statement about the composite figure is correct. Choose True or False for each statement. a. The area of region B is the same as the area of region C. True False b. The area of region A is double the area of region C. True False C. The area of the composite figure is 180 square feet. True False True False d. The sum of the areas of regions B and C is less than the area of region A.
Answers
ANSWERS
a. True
b. False
c. True
d. False
EXPLANATION
a. Regions B and C are both rectangles with the same side lengths. Therefore, they are congruent rectangles, so the areas must be the same.
b. For this item we have to find the areas of region A and C.
Region A is a trapezoid. The area is:
[tex]A_A=\frac{(10+18)}{2}\times6=84ft^2[/tex]The area of region C is:
[tex]A_C=12ft\times4ft=48ft^2[/tex]Two times the area of region C is 96ft², so this statement is false.
c. In the previous item we found the area of regions A and C. From item a we know that the area of region C is the same area of region B. The area of the figure is:
[tex]A=A_A+A_B+A_C=84+48+48=180ft^2[/tex]This statement is true.
d. Since regions B and C have the same area, saying 'the sum of the areas of regions B and C' is the same as saying 'double the area of region C'. From item b, we know that the sum of areas B and C is 96ft², and area A is 84ft².
Area A is less than the sum of areas B and C. Therefore this statement is false.
Given the function g(x) =x^2 +9x+18, determine the average rate of change of the function over the interval -8_
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The given function is:
[tex]undefined[/tex]Angles P and Q are supplementary and m
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Given: P &Q are supplementary. Therefore P+Q = 180 degress
P = 180 - Q
If m
then m +30 = p
m + 30 = 180 - Q
m = 150 - Q
m - 150< -Q
m + 150 > Q
m>q = 150
Find x and y without a calculator! No Desmos! Make sure that this one is on your work that you are uploading.
Answers
Given:
Given the system of equations:
[tex]\begin{gathered} y=4x \\ 2x+3y=-28 \end{gathered}[/tex]Required: Values of x and y
Explanation:
Substitute 4x for y into the equation 2x + 3y = -28.
[tex]\begin{gathered} 2x+3\cdot4x=-28 \\ 14x=-28 \\ x=-2 \end{gathered}[/tex]Plug the obtained value of y into y = 4x.
[tex]\begin{gathered} y=4(-2) \\ =-8 \end{gathered}[/tex]Solution is (x, y) = (-2, -8).
Final Answer: Solution is (-2, -8).
What is the equation of the circle whose diameter is the segment with endpoints (4,3) and (20,-9).
Answers
The standard equation of a circle is expressed according to the equation
[tex](x-a)^2+(y-b)^2=r^2[/tex]where;
(a, b) is the coordinate of the centre of the circle
r is the radius of the circle;
Get the diameter of the circle;
[tex]\begin{gathered} D=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2} \\ D=\sqrt[]{(20-4)^2+(-9-3)^2} \\ D=\sqrt[]{16^2+(-12)^2} \\ D=\sqrt[]{256+144} \\ D=\sqrt[]{400} \\ D=20\text{units} \end{gathered}[/tex]For the radius of the circle;
[tex]\begin{gathered} r=\frac{D}{2} \\ r=\frac{20}{2} \\ r=10\text{units} \end{gathered}[/tex]Get the centre of the circle. Note that the centre will be the midpoint of the given endpoints as shown;
[tex]\begin{gathered} (a,b)=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}) \\ (a,b)=(\frac{4+20}{2},\frac{3-9}{2}) \\ (a,b)=(\frac{24}{2},-\frac{6}{2}) \\ (a,b)=(12,-3) \end{gathered}[/tex]Substitute the centre (12, 3) and the radius 10 units into the equation of the circle above to have:
[tex]\begin{gathered} (x-12)^2+(y-(-3))^2=10^2 \\ (x-12)^2+(y+3)=100 \end{gathered}[/tex]This gives the equation of the circle whose diameter is the segment with endpoints (4,3) and (20,-9).
Suppose sin(A) 2/5 Use the trig identity sin(A) + cos(A) = 1 and the trig identity tan(A)= sin(A)/cos(A) to find can(A) in quadrant I. Round to ten thousandth.
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Trigonometric identity is tanθ ≅ 0.4364
[tex]$\sin A=\frac{2}{5}$[/tex]
[tex]$\cos ^2 A=1-\sin ^2 A=\frac{21}{25}$[/tex]
[tex]$\cos A=\frac{\sqrt{21}}{5}$[/tex]
[tex]$\tan A=\frac{\sin A}{\cos A}=\frac{\left(\frac{2}{5}\right)}{\left(\frac{\sqrt{21}}{5}\right)}=\frac{2}{\sqrt{21}} \cong 0.4364$[/tex]
Sine, cosine, tangent, cosecant, secant, and cotangent are the functions. All of these trigonometric ratios are defined using the sides of a right triangle, specifically the adjacent, opposite, and hypotenuse sides.
The even-odd identities relate the value of a trigonometric function at a given angle to the value of the function at the opposite angle. tan ( − θ ) = − tan θ tan ( − θ ) = − tan θ cot ( − θ ) = − cot θ cot ( − θ ) = − cot θ sin ( − θ ) = − sin θ sin ( − θ ) = − sin θ csc ( − θ ) = − csc θ csc ( − θ ) = − csc θ
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XIXIXI
Name:
amount paid (in dollars)
Movie Mania Tickets
ty
72
63
54
45
36
27
10 00
18
9
0
CINEMA
ADMIT ONE
12345
ADMIT ONE
nyum
Movie Ticket Sales
12345
2 4 6
8
# of tickets
72=6=12
X
10
Perfect Picture Tickets
Only $65.50 for 5 tickets!
65÷5=13
# of tickets
Date:
Fantastic Flicks Tickets
3
6
9
12
amount paid (in dollars)
38.25
76.50
114.75
153
Periods:
The Big Screen
Which movie theater is the cheapest?
Pertert Picture
Which movie theater is the most expensive?
Movie mania
What is the constant of proportionality (slope) of each option?
movie minin. = 12
Perfect Pictures (3
·Fantastic Flick5= 12.75
The Big screen= 12.90
Write an equation to represent all four options.
12345
CINEMA
ADMIT ONE
y = 12.90x
NEMA
ADMIT ONE
12345
12.75
Answers
1. The cheapest movie theatre is Fantastic Flicks.
2. The most expensive movie theatre is Movie Mania.
3. The slopes for the ticket prices for Movie Mania, Perfect Picture, The Big Screen, and Fantastic Flicks are 13.5, 13.1, 12.9, and 12.75.
4. The equation to represent all the four options is (y - 13.5x)*(y - 13.1x)*(y - 12.9x)*(y - 12.75x) = 0.
We have four movie theaters. The names of the movie theatres are Movie Mania, Perfect Picture, The Big Screen, and Fantastic Flicks. We need to calculate the slopes for each option. Let the slopes for Movie Mania, Perfect Picture, The Big Screen, and Fantastic Flicks be m1, m2, m3, and m4, respectively.
m1 = 27/2 = 13.5
m2 = 65.5/5 = 13.1
m3 = 12.9
m4 = 153/12 = 12.75
The equations for the price of tickets for each theatre are given below.
E1 : y = 13.5x
E2 : y = 13.1x
E3 : y = 12.9x
E4 : y = 12.75x
The theatre with the minimum slope is the cheapest. The theatre with the maximum slope is the most expensive.
The equation to represent all four options is the product of all the other equations.
(y - 13.5x)*(y - 13.1x)*(y - 12.9x)*(y - 12.75x) = 0
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A warren of bunnies is growing at 14% per month.a. Find the approximate doubling time.b. If the warren is currently at a population of 400 bunnies, use the approximate doubling time to find the size of the warren in 2 years.c. Find the exact doubling time. Round to 2 decimal places.d. If the warren is currently at a population of 400 bunnies, use the exact doubling time to find the size of the warren in 2 years. e. What is the relative error caused by using the approximate doubling time instead of the exact doubling time? Round to 2 decimal places.
Answers
If a warren of bunnies is growing at 14% per month then the approximate doubling time is 5 months.
A warren of bunnies is growing at 14% per month
r = 14% = 0.14
Let the initial population of bunnies be N
Then the final population of bunnies = 2N
N(1 + r)ˣ = 2N
here x is time in months
(1 + 0.14)ˣ = ln 2
x ln 0.14 = ln 2
x = 5.29 months
b) doubling time = 5months
number of cycle = 24/5
population = 400(2)²⁴/⁵
= 11143
c) exact doubling time is 5.29 months
Therefore, if a warren of bunnies is growing at 14% per month then the approximate doubling time is 5 months.
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which expression below has the same value as 9[tex] {9}^{6} [/tex]
Answers
Given data:
The given number is 9^6.
The given number can be written as,
[tex]9^6=9\times9\times9\times9\times9\times9[/tex]Thus, second option is correct.
What is - 4 - 2y= - x in standard form ?
Answers
The standard form is
[tex]Ax+By=C[/tex]We have
[tex]-4-2y=-x[/tex][tex]x-2y-4=0[/tex][tex]x-2y=4[/tex]The standard form is
[tex]x-2y=4[/tex]ANSWER
can someone help me find the valu of X &Y?
Answers
Given that the triangle ABC and DEF are similar, therefore its corresponding sides must be proportional,
[tex]\begin{gathered} \frac{AB}{DE}=\frac{BC}{EF}=\frac{AC}{DF} \\ \frac{4}{6}=\frac{10}{y}=\frac{x}{12} \end{gathered}[/tex]Comparing the first and third terms,
[tex]\begin{gathered} \frac{4}{6}=\frac{x}{12} \\ x=\frac{4}{6}\times12 \\ x=4\times2 \\ x=8 \end{gathered}[/tex]Comparing the first and second terms,
[tex]\begin{gathered} \frac{4}{6}=\frac{10}{y} \\ y=\frac{6}{4}\times10 \\ y=3\times5 \\ y=15 \end{gathered}[/tex]Thus, the values of 'x' and 'y' are 8 and 15, respectively.
give the following five-number summary, find the interquartile range. 29, 37, 50, 66, 94
Answers
we have the data set
29, 37, 50, 66, 94
step 1
Order the data from least to greatest
so
29, 37, 50, 66, 94
step 2
Find the median
29, 37, 50, 66, 94
the median is 50
step 3
Calculate the median of both the lower and upper half of the data
29, 37, 50, 66, 94
the lower half ------> (29+37)/2=33
upper half -------> (66+94)/2=80
step 4
The IQR is the difference between the upper and lower medians
so
80-33=47
the answer is 47A certain virus infects one in every 300 people. A test used to detect the virus in a person is positive 80% of the time if the person has the virus and 10% of the time if the person does not have the virus. (This 10% result is called a false positive.) Let A be the event "the person is infected" and B be the event "the person tests positive". DRAW A TREE DIAGRAM IN YOUR NOTES AND USE IT TO HELP YOU SOLVE THIS PROBLEM. Find the probability that a person has the virus given that they have tested positive; i.e. find P(AIB). Give your answer as a decimal number and include at least 3 or more non-zero digits. P(AIB)=
Answers
In the tree, the first branch will be person has virus or person doesn't have the virus.
P(virus) = 1/300
P(not virus) = 299/300
Now,
Then we branch out from each option. These branches would be positive or negative.
If they have virus:
P(positive) = 0.8
P(negative) = 0.2
If don't have virus:
P(positive) = 0.1
P(negative) = 0.9
Now, solving the question of probability that a person has the virus given that they have tested positive:
We find:
P(A|B)
P(has virus | positive test) = P(positive and has virus) / P(positive test)
P(positive and has virus) = 4/5 * 1/300 = 4/1500
P(positive test) = 1/300 * 4/5 + 1/10 * 299/300
= (4/1500)+(299/3000)
=(8/3000) + (299/3000) = 307/3000
= 0.10233
So,
P(positive and has virus) / P(positive test) = 4/1500 divided by 299/3000 = 0.02675
Verify my answer an explanation on how to do this
Answers
Given:
In the California Community Colleges an undergraduate student survey was taken that compares the class of the student to their opinion on whether or not they favor or oppose same sex marriages . The following data is a summary of the survey taken by questioning 500 undergraduate students.
Required:
If a student from the survey is selected at random , then we need to find the probability that the student favors same sex marriages , given that the student is not a Senior
Explanation:
Here we need the probability in which students are in the favor of sex marrige but noe senior
[tex]276-53=223[/tex]so 223 students are in the favors sex marrige but not seniors
so the probability is
Final answer:
[tex]\frac{223}{500}[/tex]What is the quotient and the remainder of 491÷3
Answers
To find the quotient of 491 by 3,
We have to divide 491 by 3
So,
[tex]\frac{491}{3}=163.66[/tex]Answer : 163.66