In the next Olympics, the United States can enter four athletes in the diving competition. How many different teams of four divers can be selected from a group of nine divers?
a. 36
b. 6,561
c. 126
d. 3,024
Answer:
The correct option is C.
Step-by-step explanation:
From the given information it is clear that the total number of divers in a group is 9.
The number of selected divers is 4.
The total ways to select r items from total n item is
[tex]^nC_r=\frac{n!}{r!(n-r)!}[/tex]
Using this combination formula, the number of different teams of four divers that can be selected from a group of nine divers is
[tex]^9C_4=\frac{9!}{4!(9-4)!}[/tex]
[tex]^9C_4=\frac{9!}{4!5!}[/tex]
[tex]^9C_4=\frac{9\times 8\times 7\times 6\times 5!}{4\times 3\times 2\times 1\times 5!}[/tex]
Cancel out common factors.
[tex]^9C_4=126[/tex]
Therefore the correct option is C.
The correct answer is c. 126 different teams of four divers can be selected from a group of nine divers.
To solve this problem, we use the concept of combinations from combinatorics. A combination is a way of selecting items from a collection, such that the order of selection does not matter. In this case, we want to find out how many different ways we can select 4 divers out of 9 to form a team, and the order in which we select the divers does not matter.
The formula for calculating combinations is given by:
[tex]\[ C(n, k) = \frac{n!}{k!(n-k)!} \][/tex]
For our problem:
[tex]- \( n = 9 \) (the total number of divers)\\ - \( k = 4 \) (the number of divers we want to select for a team)[/tex]
Plugging these values into the formula, we get:
[tex]\[ C(9, 4) = \frac{9!}{4!(9-4)!} \] \[ C(9, 4) = \frac{9!}{4!5!} \] \[ C(9, 4) = \frac{9 \times 8 \times 7 \times 6 \times 5!}{4 \times 3 \times 2 \times 1 \times 5!} \] \[ C(9, 4) = \frac{9 \times 8 \times 7 \times 6}{4 \times 3 \times 2 \times 1} \] \[ C(9, 4) = \frac{3024}{24} \] \[ C(9, 4) = 126 \][/tex]
Therefore, there are 126 different ways to select a team of four divers from a group of nine divers.
Quadrilateral ABCD is similiar to quadrilateral EFGH. The lengths of the three longest sides in quadrilateral ABCD are 20 feet, 18 feet, and 14 feet long. If the two shortest sides of quadrilateral EFGH are 6 feet long and 5 feet long, how long is the 4th side on quadrilateral ABCD
Answer:
35/3 ft = 11 2/3 ft
Step-by-step explanation:
We make a table of the lengths of the sides in descending order of side length. Each line contains two corresponding sides.
Quadrilateral Quadrilateral
ABCD EFGH
Side 1 20 ft ?
Side 2 18 ft ?
Side 3 14 ft 6 ft
Side 4 ? 5 ft
The line corresponding to side 3 is the only line that has the lengths of both corresponding sides.
The ratio of the length of sides in ABCD to EFGH is 14/6 = 7/3.
To find the length of the 4th sides of ABCD, we multiply the length of the 4th side of EFGH by the ratio.
7/3 * 5 ft = 35/3 ft = 11 2/3 ft
What term do you use to describe the amount of three-dimensional space
inside a solid?
A. Volume
B. Perimeter
C. Surface area
D. Lateral area
Answer:
volume
Step-by-step explanation:
volume is measured in cubic
Answer:
A. Volume
Step-by-step explanation:
IN two-dimension space we use to calculate area, perimeter but not volume.
In three-dimensional space we also find Volume, Surface area and lateral surface area only.
In volume we find what amount of substance kept inside that container/solid.
Perimeter is the length of total boundary.
Surface area is total area of each face.
And, In Lateral surface area we find the area of each face except bottom and top face.
Thus, "the amount of three-dimensional space inside a solid" is described by VOLUME.
A triangle contains angles of 95° and 35°. what is the measure of the third angle of the triangle ?
Answer:
50
Step-by-step explanation:
Add up the two known angle measurements:
95+35=130
Subtract this number from 180°:
180-130=50
Write down your answer
95+35+25=180
*The three angles should add up to 180° for the triangle to exist*
I hope that helped
Simplify the expression below.
3 · -8 + 5 - 4 ÷ 2
A-11.5
B-21
C-12.5
S-27
3 · -8 + 5 - 4 ÷ 2
Use PEMDAS
P=parenthesis
E=exponents
M= multiplication
A= addition
S=subtraction
-24+5- 4÷ 2
-19-2
=-21
Answer is B-21
Answer:
B. -21
Step-by-step explanation:
You have to follow PEMDAS
3*-8=-24
So, -24+5-4÷2
-4÷2=-2
So, -24+5-2
Then add and subtract from left to right
-24+5=-19
-19-2=-21
the slope of the line below is -5/-7. write a point slope equation of the line using coordinates of the labeled point
Answer:
B
Step-by-step explanation:
Point slope equation is y-y₁=m(x-x₁) so as long as the x or y is not negative you have to subtract the number hence y-2=-5/7(x-6)
Answer:
B
Step-by-step explanation:
just did it
What is the value of x in the equation 2(x−3)+9=3(x+1)+x?
x = −3
x = −1
x = 0
x = 3
Answer : 0
Step-by-step explanation:
2(x−3)+9=3(x+1)+x
2x-6+9=3x+3+x
3-3=4x-2x
0=2x
x=0
The value of x in the equation 2(x−3)+9=3(x+1)+x is 0 option third x = 0 is correct.
What is a linear equation?It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.
We have a linear equation in one variable:
2(x−3)+9=3(x+1)+x
2x - 6 + 9 = 3x + 3 + x
Combine like terms
2x + 3 = 4x + 3
x = 0
Thus, the value of x in the equation 2(x−3)+9=3(x+1)+x is 0 option third x = 0 is correct.
Learn more about the linear equation here:
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Jeffrey used to be on the phone 3 1/2 times as much as his sister. His parents were angry and told him they would take his his phone away is he did not reduce his time spent on the phone. He cut down to 2/5 of the time he used to be on the phone. How many times as much as his sister is Jeffrey on the phone now?
Answer:
1 2/5 times as much as his sister
Step-by-step explanation:
3 1/2x * 2/5 = 1 2/5x
Violet was carrying around the steps to solve square root of 3x plus 1 = 4. On her way through the Math Factory, Violet dropped them and they mixed with other steps. Put the correct steps in order to solve square root of 3x plus 1 = 4.
A. Subtract 1 from both sides B. Subtract 4 from both sides C. Square root both sides
D. Square both sides E. Divide by 3 from both sides F. Divide by 4 from both sides
Answer:
D
Step-by-step explanation:
solve square root of 3x plus 1 = 4:
D is correct and results in 3x + 1 = 16; after this we subtract 1 from both sides and end up with 3x = 15, or x = 5.
Answer:
To solve this equation we have to first remove the square root from LHS and to remove the square we have to square both sides.
Step-by-step explanation:
The quadratic equation which violet has to solve is given as
[tex]\sqrt{3x+1}=4[/tex]................(1)
Step 1
To solve this equation we have to first remove the square root from LHS and to remove the square we have to square both sides.
After squaring both the sides we got following equation
[tex]3x+1=16[/tex]....(2)
Step 2
now subtract 1 from both sides to remove 1 from LHS
so we will get the following equation
[tex]3x=15[/tex]....(3)
Step 3
Now divide by 3 from both sides to remove 3 from LHS
Therefore,
[tex]x=\frac{15}{3}[/tex]
[tex]x=5[/tex]
An aerial camera is suspended from a blimp and positioned at D. The camera needs to cover 125 meters of ground distance. If the camera hangs 10 meters below the blimp and the blimp attachment is 20 meters in length, at what altitude from D to B should the camera be flown?
A blimp over triangle EDF with height of 10 meters and FE equals 20 meters and triangle ADC with height BD and AC equals 125 meters. Triangles share point D.
A. 31.25 m
B. 62.5 m
C. 150 m
D. 250 m
Answer:
B. 62.5 m
Step-by-step explanation:
∠EDF and ∠ADC are vertical angles, and therefore equal.
EF and AC are parallel, so ∠DEF and ∠DAC are alternate interior angles, as well as ∠DFE and ∠DCA. Therefore, each pair is equal.
From this, we can say ΔDEF and ΔDAC are similar triangles. So we can write a proportion:
10 / 20 = DB / 125
DB = 62.5
Answer:
The correct option is B.
Step-by-step explanation:
Given information: In ΔEDF, FE=20 m and height = 10 m. In ΔADC, AC=125 m.
From the given information, we conclude that AC║EF.
In ΔEDF and ΔADC,
[tex]\angle E=\angle A[/tex] (Alternate interior angles)
[tex]\angle EDF=\angle ADC[/tex] (Vertically opposite angle)
By AA rule of similarity,
[tex]\triangle EDF\sim \triangle ADC[/tex]
The corresponding sides of two similar triangles are similar. So in ΔEDF and ΔADC,
[tex]\frac{base}{height}=\frac{FE}{h}=\frac{AC}{DB}[/tex]
[tex]\frac{20}{10}=\frac{125}{DB}[/tex]
[tex]2=\frac{125}{DB}[/tex]
On cross multiplication, we get
[tex]2DB=125[/tex]
Divide both sides by 2.
[tex]\frac{2DB}{2}=\frac{125}{2}[/tex]
[tex]DB=62.5[/tex]
Therefore the correct option is B.
A group of college students is volunteering for Homes for the Community during their spring break. They are putting the finishing touches on a house they built. Working alone, Wade can paint a certain room in 5 hours. Rhonda can paint the same room in 6 hours. How long will it take them working together to paint the room? Round your answer to the nearest hundredth if necessary.
Answer: 2.72 hours
Step-by-step explanation:
Let's call [tex]t_1[/tex] while it takes Wade to paint the room
Let's call [tex]t_2[/tex] while it takes Rhonda to paint the same room.
Then we know that:
[tex]t_1 = 5\ hours\\t_2 = 6\ hours[/tex].
Let's call it t as it takes Rhonda and Wade to paint the same room working together.
Now we use the following formula to calculate t.
[tex]\frac{1}{t}=\frac{1}{t_1}+\frac{1}{t_2}[/tex]
[tex]\frac{1}{t}=\frac{1}{5}+\frac{1}{6}[/tex]
[tex]\frac{1}{t}=\frac{11}{30}[/tex]
[tex]t=\frac{30}{11}[/tex]
[tex]t=2.72\ hours[/tex]
If they work together they will be able to paint the room in 2.72 hours
Answer: 2.73 hours
Step-by-step explanation:
What number comes next in the series? 31, 1031, 402, 16, ____
Answer:
Another person already answered this question. Their name is writersparadise. I give all credit to him/her for this answer.
Step-by-step explanation:
There could be many answers for this question. In general, the number that comes after 16 is a number with 8 as the sum of its digits.
Explanation:
1st number 31 – Sum of digits is 3 + 1 = 4
2nd number 1031 – Sum of digits is 1 + 0 + 3 + 1 = 5
3rd number 402 – Sum of digits is 4 + 0 + 2 = 6
4th number 16 – Sum of digits is 1 + 6 = 7
Therefore, the missing number could be the single digit number 8 or any of the two-digit numbers 17, 26, 35, 44, 53, 62, 71 or 80. It could also be a bigger number with the digits of any of the given two-digit numbers and 0 for the other digits such as 260 or 7001.
Read more on Brainly.in - https://brainly.in/question/3032926#readmore
Solve the system of equations.
y= 6x-27
y= 4x - 17
a. (-5, 3)
b. (-3, -5)
C. (5, 3)
d. No solution
Answer:
C. (5, 3)Step-by-step explanation:
[tex]\left\{\begin{array}{ccc}y=6x-27&(1)\\y=4x-17&(2)\end{array}\right\\\\\text{Substitute (1) to (2):}\\\\6x-27=4x-17\qquad\text{add 27 to both sides}\\6x=4x+10\qquad\text{subtract}\ 4x\ \text{From both sides}\\2x=10\qquad\text{divide both sides by 2}\\x=5\\\\\text{Put it to (2):}\\\\y=4(5)-17\\y=20-17\\y=3[/tex]
Which similarity postulate or theorem can be used to verify that the two
triangles shown below are similar?
How many real and complex roots exists for a polynomial?
Step-by-step explanation:
whenever a complex number is a root of a polynomial with real coefficients, its complex conjugate is also a root of that polynomial. as an example, we'll find the roots of the polynomial..
x^5 - x^4 + x^3 - x^2 - 12x + 12.
the fifth-degree polynomial does indeed have five roots; three real, and two complex.
3 units
V13 units
2 units
In this right triangle, the length of the hypotenuse, BC, is units:
Answer:
[tex]\large\boxed{BC=\sqrt{13}}[/tex]
Step-by-step explanation:
[tex]\text{If}\ a\leq b\leq c\ \text{are lengths of sides of a right triangle, then}\\\\a^2+b^2=c^2.\\\\\text{We have:}\ 2<3<\sqrt{13}\\\\\text{Substitute:}\\\\2^2+3^2=(\sqrt{13})^2\qquad\text{use}\ (\sqrt{a})^2=a\\4+9=13\\13=13\qquad\bold{CORRECT}\\\\\text{The hypotenuse is the longest side of a right triangle.}\\\text{Therefore}\ BC=\sqrt{13}[/tex]
A hummingbird lives in a nest that is 3 meters high in a tree. The hummingbird flies 5 meters to get from the nest to a flower on the ground. How far is the flower from the base of the tree
Answer: 4 meters.
Step-by-step explanation: You need to set up the Pythagorean Theorem, which is a^2 + b^2 = c^2. The c is the hypotenuse. A is 3 because it is the height. We are trying to find b, the distance from the flower to the tree. C is 5.
Plug in the numbers.
3^2 + b^2 = 5^2.
Simplify.
9 + b^2 = 25.
Isolate b by subtracting 9 from each side.
B^2 =16.
Square root each side.
B = 4.
The flower is 4 meters away from the base of the tree.
Complete the equation of the line through (6,-6) and (8,8).
Use exact numbers.
y=?
Answer:
7x-48
Step-by-step explanation:
if Q(-3,4), R(-2,-1),T(3,1),W(3,5) is a quadrilateral and Q'(-27,36) is the image of Q under a dilation centered at the origin, find W'
Answer:
W'(27,45)
Step-by-step explanation:
First we must fnd the scale factor of the dilation and then multiply the coordinates of W(3,5) by the scale factor.
Let k be the scale factor of the dilation centered at the origin.
The mapping for a dilation by a scale factor k is
[tex](x,y)\to (kx,ky)[/tex]
[tex]Q( - 3,4)\to Q'( - 3k,4k)[/tex]
But we were given the coordinates of the image, which is
Q'(-27,36)
Comparing coordinates:
[tex]4k = 36[/tex]
[tex] \implies \: k = 9[/tex]
We could compare the first coordinates too and get the same result.
The image of W(3,5) is given by:
[tex]W(3,5) \to \: W'(3 \times 9,5 \times 9)[/tex]
[tex]W(3,5) \to \: W'(27,45)[/tex]
For Cynthia's third lab report, she calculated the mass of an object as it slid down an inclined plane. She got the following three masses.
1.20 kg
0.91 kg
1.08 kg
The true mass of the object is 1 kg.
Cynthia's percent error was [blank]−−−−−−%.
Enter your answer as the number that correctly fills in the blank, rounded to two decimal places, like this: 42.53
Answer:
Percent error: 6.00%
Step-by-step explanation:
We find the mean of the three masses
Mean = 1.20 + 0.91 + 1.08 / 3
Mean = 1.06 kg
The experimental value of mass is = 1.06 kg
The actual value of mass = 1 kg
The percent error is: (experimental value - actual value/actual value)*100
Percent error : (1.06 - 1 / 1)*100
Percent error: 6.00%
Answer:
6.33
Step-by-step explanation:
1. Find the average:
1.20+0.91+1.08 = 3.19
3.19/3 = 1.06333... (aka the Average)
2. Subtract the average by the True mass:
1.06333... - 1 (the True Mass) = 0.06333...
3. Divide answer by the True mass:
[Because when you divide it by the True Mass it's still 0.06333...]
4. Multiply by 100 (to get the percentage)
0.06333 * 100 = 6.333...
5. In result 6.33% is the correct answer.
What is the mean of 108,305,252,113,191
Answer:
193.8
Step-by-step explanation:
Mean is the average. Find the average by dividing the sum of all numbers by the amount of numbers.
108+305+252+113+191
divided by 5
108+305+252+113+191= 969
969/5= 193.8
Final answer:
The mean of 108, 305, 252, 113, and 191 is 193.8.
Explanation:
To find the mean of a set of numbers, you need to add up all the numbers in the set and then divide the sum by the total number of values.
In this case, we have the numbers 108, 305, 252, 113, and 191.
To find the sum, you add these numbers together:
108 + 305 + 252 + 113 + 191 = 969.
Next, you divide this sum by the total number of values, which is 5 in this case.
So, the mean is 969 ÷ 5 = 193.8.
This is the average value of the set of numbers provided.
ANSWER QUICK PLEASE
Use the grouping method to factor:
Answer:
B. [tex](x^2 + 5)(x + 1)[/tex]
Step-by-step explanation:
Hello!
We can group the first two terms and the last two terms and factor each group.
Factor by Grouping[tex]x^3 + x^2 + 5x + 5[/tex][tex](x^3 + x^2)+ (5x + 5)[/tex][tex]x^2(x + 1) + 5(x + 1)[/tex]Now we can combine the like factors:
[tex](x^2 + 5)(x + 1)[/tex]The answer is Option B.
Let f(x) = (4x^2 - 11)^3 and g(x) = 4x^2- 11.
Given that f(x) = (hºg)(x), find h(x).
Enter the correct answer.
Answer:
[tex]\large\boxed{h(x)=x^3}[/tex]
Step-by-step explanation:
[tex]f(x)=(4x^2-11)^3\\\\f(x)=(h\circ g)(x)=h\bigg(g(x)\bigg)\to\text{exchange x to}\ g(x)=4x^2-11\\\\f(x)=(\underbrace{4x^2-11}_{g(x)})^3=\bigg(g(x)\bigg)^3=h\bigg(g(x)\bigg)\\\\\text{Therefore}\ h(x)=x^3[/tex]
Answer:
the person on top is correct
Step-by-step explanation:
In the triangle below, what is the measure of R?
Answer:
30
Step-by-step explanation:
the slope in decimal form ?
Answer:
2
Step-by-step explanation:
Look at two points on the graph that are easy to read.
(0, 0) and (1, 2) are on the graph and are easy to read.
slope = (y2 - y1)/(x2 - x1) = (2 - 0)/(1 - 0) = 2/1 = 2
Answer:
-2
Step-by-step explanation:
Let's get two coordinate points and plug into the slope equation.
(1,2) and (.5,1)
[tex](y_{2} - y_{1}) / (x_{2} - x_{1} )[/tex]
(1-2) / (.5 - 1)
1 / (-.5)
-2
what is 4/2 ÷ 2 +(3^2 - 1)
Answer:
9
Step-by-step explanation:
Good ol' PEMDAS
First things first, we simplify what is in the parentheses.
4/2 ÷ 2 + (3² - 1)
4/2 ÷ 2 + (9 - 1)
4/2 ÷ 2 + 8
Next we do division. Because there are two instances of division, we work left-to-right. Note that a fraction such as 4/2 is division itself.
4/2 ÷ 2 + 8
2 ÷ 2 + 8
1 + 8
Lastly, it just solving the addition.
1 + 8 = 9
the answer would be 9
Solve |y-2|<10
——————————
[tex]|y-2|<10\\y-2<10 \wedge y-2>-10\\y<12 \wedge y>-8\\y\in(-8,12)[/tex]
1. Which equation represents a linear function?
A. y = x - 4
B. y = x + 4
C. x = (y - 2)2
D. y = x + 7
Answer:
A, B, D are equations representing a linear function
Step-by-step explanation:
All linear functions have an equation like the following: y=mx+b, where m is the slope and b is an offset.
A. y=x-4, m=1 and b=-4
B. y=x+4, m=1 and b=4
D. y=x+7, m=1 and b=7
The third eq dont behave like a linear function since there is quadratic term on one side of the equation, this is not a linear function
4 middle school questions
Answer:
884. D
885. C ( changed my answer)
886. B
887.A
For number 844, the diameter if the fan is 12 inches. To find Circumference, multiply the radius by two and then pi. The radius of the fan is 6, multiplied by 2 is 12, and multiplied by pi gives 12 times pi.
885 says half of the area gives the circumference. So we can write a formula, (pi*r^2)/2=2*pi*r. If the radius were 4, this would make the equation true. So the answer is 4.
886. Circumference=2*pi*r
r=6.78
2*pi*6.78
13.56*pi
887.
3*3=9
13-3=10
10*23=230
230+9=239 units squared
Answer:
884.D
885.C
886.B
887.A
Step-by-step explanation:
I just multiplied
Which of the following statements best describes a linear pair
Answer:
B) A linear pairs consists of supplementary angles
Step-by-step explanation:
First let's see the definition of linear pair.
The two adjacent angles add up to 180° (supplementary) is called linear pair.
Example:
If ∠A and ∠B said to be linear pair, then they must be adjacent angles and add up to 180 degrees.
∠A + ∠B = 180°
From the definition, we can find the answer.
A) in correct because complementary angles add up to 90 degrees.
B) Correct (A linear pair consists of supplementary angles)
C) In correct because the pair consists of adjacent angles
D) In correct because vertical angles is nothing but 90°