The formula for combination is
nCr = n!/(n - r)!r!
C represents the number of combinations
n represents the total number of objects to choose from
r represents the number of items selscted from n
From the information given,
n = 8 and r = 3
8C3 = 8!/(8 - 3)!3!
= 8! /5!3!
= 8 * 7 * 6 * 5 * 4 * 3!/5 * 4 * 3 * 2 * 1 * 3!
The 3! cancels out. It becomes
8 * 7 * 6 * 5 * 4 /5 * 4 * 3 * 2 * 1
= 6720/120
= 56
The answer is 56
There’s a few more questions like this I been stuck on
Problem N 9
we have that
m by addition angles postulate
substitute given values
164=(13x+4)+(10x-1)
solve for x
164=23x+3
23x=164-3
23x=161
x=7
Find out the measure of angle SQR
msubstitute the value of x
mm
compare the elevation of death valley and westmorland using< or >
Answer:
If D represent the elevation of Death valley , California and W represent the elevation of Westmorland, California.
So, we would have;
[tex]DWhich means that;the elevation of Death valley < the elevation of Westmorland
Explanation:
Given that the elevation of Death valley , California is -282 feet
[tex]D=-282[/tex]And the elevation of Westmorland, California is -157 feet;
[tex]W=-157[/tex]And we know that -282 ft is less than -157 ft.
[tex]-282<-157[/tex]Therefore, the elevation of Death valley , California is less than the elevation of Westmorland, California.
So, if D represent the elevation of Death valley , California and W represent the elevation of Westmorland, California.
So, we would have;
[tex]DWhich means that;the elevation of Death valley < the elevation of Westmorland
Patrick has a swimming pool that needs to be drained. His pool holds9,644.6 gallons of water and will need to drain completely in 8 hours.What is the change in the water level per hour for Patrick's swimmingpool? Round your answer to the nearest hundredth.
Explanation
We are asked to find the change in the water level per hour for Patrick's swimming
We have to use the formula
[tex]change\text{ in water level per hour=}\frac{Volume\text{ of water}}{Time\text{ taken to drain}}[/tex]Thus
[tex]change\text{ in water level per hour=}\frac{9644.6}{8}=1205.575\text{ gallons per hour}[/tex]Note: The rate will be negative because we are draining
Therefore, the change in water level will be -1205.58 gallons per hour
Can you help me with this? The approximate area of the circle is (Blank) square feet. (Use 22/7 as an approximation for pi) The approximate circumference of the circle is (Blank) feet. Use 22/7 as an approximation for pi
Let's begin by listing out the given information:
What is the probability of choosing a recheck at first and then choosing a red card with a replacement
Since there are 25 cards in the deck
Since there are 4 jacks on it 2 red and 2 black
Since the probability of an event = outcomes of events/total outcomes
Then for the first card
There are 2 red jacks for a total of 52 cards
[tex]P(r.j)=\frac{2}{52}=\frac{1}{26}[/tex]For the second card with NO replacement
Since there are 26 red cards in the deck
Since we took out one of them for the first card, then
There are 25 red cards
Since the total is less by 1 because of the first card, then
There are 51 cards
[tex]P(r)=\frac{25}{51}[/tex]Since and in probability means multiply, then
[tex]P(r.j&r)=\frac{1}{26}\times\frac{25}{51}=\frac{25}{1326}[/tex]The answer is the 3rd choice 25/1326
Select all statements that must be true.
(Select all that apply)
Students selecting B are likely mistaking the range for
the IQR. Students selecting C are likely mistaking the
median for the IQR. Students selecting D are likely
mistaking the mean for the median. It may be possible
that the mean is 3.6 goals per game, but cannot be
determined from the box plot alone. Students selecting
F are likely mistaking Q1 for the minimum.
A. The interquartile range (IQR) is 1.2 goals per game.
B. The interquartile range (IQR) is 3.2 goals per game.
C. The interquartile range (IQR) is 3.6 goals per game.
The average goals scored per game are calculated for
20 soccer tournaments. The 20 averages are used to
create this box plot.
O O OOO
D. The mean is 3.6 goals per game.
E. The median is 3.6 goals per game.
E The minimum is 2.8 goals per game.
H
G. The maximum is 5.6 goals per game.
2
2.4 2.8 3.2 3.6
4
4.4
4.8
5.2 5.6
6
Average Number of Goals per
Game
The maximum = 5.6 goals per game
median = 3.6 goals per game
Interquartile range (IQR ) = 1.2 goals per games
Explanation:To solve this question, we need an illustration that identifies the part of the box and whiskers plot:
The minimum on the box and whiskers = 2.4 goals per game
The maximum = 5.6 goals per game
The median = the line in between the box
median = M on the image
median = 3.6 goals per game
upper quartile = Q3 = 4
lower quartile = Q1 = 2.8
The interquartile range = IQR
[tex]\begin{gathered} \text{IQR = Q}_3-Q_1 \\ \text{IQR = }4\text{ - 2.8} \\ \text{IQR = 1.2} \end{gathered}[/tex]Interquartile range (IQR ) = 1.2 goals per games
[tex]\begin{gathered} \text{Mean = average of the data set} \\ \text{Mean = }\frac{su\text{m of the numbers}}{nu\text{mber of the data set}} \\ \text{Mean = }\frac{2.4\text{ + }2.8+3.6+4+5.6}{5} \\ \text{Mean = 18.4/5} \\ \text{Mean = 3.68} \end{gathered}[/tex]The mean is 3.68 goals per game
Solve the following system of linear equations using elimination. -3x + 3y=-3 2x-y=0
The system of equations is
[tex]\begin{gathered} -3x+3y=-3\Rightarrow(1) \\ 2x-y=0\Rightarrow(2) \end{gathered}[/tex]Since all terms in equation 1 can divide by 3, then
Divide each term in equation 1 by 3
[tex]\begin{gathered} \frac{-3x}{3}+\frac{3y}{3}=\frac{-3}{3} \\ -x+y=-1\Rightarrow(3) \end{gathered}[/tex]Add equations (2) and (3) to eliminate y
[tex]\begin{gathered} (2x-x)+(-y+y)=(0-1) \\ x+0=-1 \\ x=-1 \end{gathered}[/tex]Substitute x by -1 in equation (2) to find y
[tex]\begin{gathered} 2(-1)-y=0 \\ -2-y=0 \end{gathered}[/tex]Add y to both sides
[tex]\begin{gathered} -2-y+y=0+y \\ -2+0=y \\ -2=y \\ y=-2 \end{gathered}[/tex]The solution of the given system of equations is (-1, -2)
Which represents the inverse of the function f(x) = 4x?h(x) = x + 4Oh(x) = X-4Oh(x) = 2xh(x) =17 1x
f(x) = 4x
To find the inverse of a function, you have to replace every x with an y, as follows:
f(x) = 4y
then, replace f(x) with an x,
x = 4y
and now, isolate y,
x/4 = y
Finally, replace y whit h(x),
h(x) = 1/4x
Could someone help me out please I don’t know how to
As per given by the question,
There are given that ,
[tex]4y^2+y-9,\text{ when y=-3}[/tex]Now,
There are given y=-3.
So,
Substitute the value -3 instead of y in given equation,
Then,
From the equation,
[tex]4y^2+y-9[/tex]Put the value of y in given equation,
[tex]4y^2+y-9=4(-3)^2+(-3)-9[/tex]Now, solve the above equation,
[tex]\begin{gathered} 4y^2+y-9=4(-3)^2+(-3)-9 \\ =4(9)-3-9 \\ =36-3-9 \\ =36-12 \\ =24 \end{gathered}[/tex]Hence, the value of given equation is 24.
How many kg of water are in a 132 kg person ?
Answer:
[tex]88kg\text{ of water}[/tex]Explanation:
Here, we want to get the number of kg of water in a 132 kg person
From the question, there is a direct variation between kg of water in the human body and the mass of the body
Let the mass be m and the amount of water be w
By direct variation, with k as the proportionality constant, we have it that:
[tex]w\text{ = }km[/tex]From the question, a 72 kg mass boy has 48 kg of water
Mathematically, we have it that:
[tex]\begin{gathered} 48\text{ = k }\times72 \\ k\text{ = }\frac{48}{72} \\ \end{gathered}[/tex]Now, we want to get the kg of water in a 132 kg person
What we have to do here is to have k as 48/72 and solve for w
Mathematically, we have that as:
[tex]\begin{gathered} w\text{ = }\frac{48}{72}\times132 \\ \\ w\text{ = 88 }kg \end{gathered}[/tex]The cube root of our varies inversely with the square of S which to equations model this relationship?
The question states as follows;
"The cube root of r varies inversely with the square of s."
The general form of an inverse relationship is shown below;
[tex]y=\frac{k}{x}[/tex]Substituting the variables, we would now have;
[tex]\sqrt[3]{r}=\frac{k}{s^2}[/tex]Therefore, the third option is correct.
Also;
[tex]\begin{gathered} \sqrt[3]{r}=\frac{k}{s^2} \\ \text{Observe that}_{} \\ \sqrt[3]{r}=r^{\frac{1}{3}} \end{gathered}[/tex]Therefore, we can alo have the expression;
[tex]\begin{gathered} r^{\frac{1}{3}}=\frac{k}{s^2} \\ \text{Cross multiply, and we'll have;} \\ s^2r^{\frac{1}{3}}=k \end{gathered}[/tex]The fifth option is also correct.
ANSWER:
The third and fifth options are both correct models of the inverse relationship given.
16x^2 + 56x + 49 Is this a special product? If yes, what type
Let's check if the given equation is a special product.
[tex]16x^2+56x+49[/tex]Let,
a = 1st term coefficien
b = 2nd term coefficient
c = constant
We get,
a = 16
b = 56
c = 49
Let's check, you can use this method to check if it is a perfect square binomial:
[tex]\begin{gathered} \text{ 2(}\sqrt[]{a}\text{ x }\sqrt[]{c})\text{ = b ;} \\ (a+c)^2\text{ if b is positive} \\ (a-c)^2\text{ if b is negative} \end{gathered}[/tex][tex]\begin{gathered} 2(\sqrt[]{16}\text{ x }\sqrt[]{49})\text{ = 56} \\ 2(4\text{ x 7) = 56 ; since b is positive, a and c are positive} \\ 2(28)\text{ = 56} \\ 56\text{ = 56} \end{gathered}[/tex]Therefore, the equation is a special product. It is a square of a binomial.
The answer is YES, it is a special product. It is a Square of a Binomial (x + y)².
can you help pls with
Answer:
C. 3.5=3.50
Explanation:
Given the statements below:
[tex]\begin{gathered} A.$0.43>0.5$ \\ B.$0.65<0.56$ \\ C.3.5=3.50 \\ D$.2.45>2.54$ \\ E.$0.4<0.04$ \end{gathered}[/tex]The only true statement out of the given options is:
[tex]3.5=3.50[/tex]The correct choice is C.
According to psychologist IQs are normally distributed with a mean of 100 and a standard deviation of 19. What’s the percentage of the population has IQs above 154?
In order to solve this problem, we will calculate the z-score of the given data.
To do this, we use the formula,
[tex]z=\frac{x-\mu}{\sigma}[/tex]We plug in the given data:
[tex]z=\frac{154-100}{19}\approx2.8421[/tex]With this z-score, we can consult a z-score probability table or use an online resource. However, this will give us
[tex]P(z<2.8421)[/tex]but we are interested in itbeing greater than it, so we must calculate
[tex]1-P(z<2.8421)=1-0.99776=0.00224[/tex]So, the percentage of the population that has an IQ above 154 is 0.224%.
A new song has gone viral on the Internet. The website hosting the song uses the function f(t)=500t^2 to represent the number of daily hits over time, where t is time in days. Use the function to predict the day on which the number of daily hits reaches 1,000,000. Show your work.
We will have the following:
[tex]\begin{gathered} 1000000=500t^2\Rightarrow t^2=2000 \\ \\ \Rightarrow t=\sqrt{2000}\Rightarrow t=20\sqrt{5} \\ \\ \Rightarrow t=44.72135955... \end{gathered}[/tex]So, on day 44 it will reach 1 000 000.
Use the number line to answer the question. Each tick represents 1.Which point is located at 2?PQSnone of the above
Given that each tick represents 1. The numbers on the right of 0 are positiv and on the left of 0 are negative. SInce 2 is positive, 2 lies on the right side of 0.
Since each tick represents 1, the first tick represents 0+1 = 1.
Now, the second tick represents 0 + 2 = 2. The second tick on the right of 0 denoted as S.
The correct option is S.
What are inequalites, and a example of one.
Inequalities are relationships like equalities, what makes it different from equalitites is that on both sides are different expressions that allows to comparate them without been equal, for this we have 4 types
≤ less or equal than
≥ greater or equal to
< less than
> greater than
some examples are:
[tex]\begin{gathered} 3x-3<50 \\ 5x-45>33x \\ x^2-15x<34 \end{gathered}[/tex]Another difference between inequalities and equalities is that in equalities we obtain 1,2 or 3 solutions accronding to the degree of the equation, in inequalities we can obtain infinite number of solutions.
What is the volume of this cone? Use 3.14 and round your answer to the nearest hundredth. 38 mm cubic millimeters
ANSWER
[tex]V=7179.09\operatorname{mm}[/tex]EXPLANATION
We are given the height of the cone as 19 mm and the diameter of its base as 38 mm.
The volume of a cone is given as:
[tex]V=\frac{1}{3}\pi\cdot r^2h[/tex]where r =radius; h = height
The diameter of a circle (the base of a cone) is twice the radius. Therefore:
[tex]\begin{gathered} D=2r \\ r=\frac{D}{2} \\ r=\frac{38}{2} \\ r=19\operatorname{mm} \end{gathered}[/tex]Therefore, the volume of the cone is:
[tex]\begin{gathered} V=\frac{1}{3}\cdot3.14\cdot19^2\cdot19 \\ V=7179.09\operatorname{mm}^3 \end{gathered}[/tex]Question 4 If the vertices of ABC are A(-3,5), B(2,4). and C(-1,2), then ABC is classified as
To be able to classify the triangle you have to plot it
You can calculate the length of the sides as follows:
[tex]\begin{gathered} AC=\sqrt[]{(-1+3)^2+(5-2)^2} \\ AC=\sqrt[]{13} \end{gathered}[/tex][tex]\begin{gathered} AB=\sqrt[]{(5-4)^2+(2+3)^2} \\ AB=\sqrt[]{26} \end{gathered}[/tex][tex]\begin{gathered} BC=\sqrt[]{(2+1)^2+(4-2)^2} \\ BC=\sqrt[]{13} \end{gathered}[/tex]Sides AC and BC are equal.
You can classify this triangle as an isosceles triangle
Suzan collected 560 milliliters of rainwater on Saturday. She collected 3.5 liters of rainwater on Sunday.How many total milliliters of rainwater did Suzan collect on Saturday and Sunday?A.910B.4,060C.4,600D.9,100
It's easy to see that to obtain the total of milliliters of rainwater that Suzan collected on Saturday and Sunday is the sum of the milliliters that Suzan collected each day.
The problem that we need to be careful about is the units. So we need to pass all the numbers to milliliters, we already have one in this unit then we just need to transform one:
[tex]3.5L\ast\frac{1000mL}{1L}=3500mL[/tex]Now we can use the sum as:
[tex]mL\text{ total=}3500mL+560mL=4060mL[/tex]Then the correct answer is B, 4060 mL.
What is the surface area of the following figure?
Answer:
surface area of cube = 37.5 units
Step-by-step explanation:
Find the area of one side of the cube with the formula sidexside:
2.5 x 2.5 = 6.25 units
now multiple the area of one side by the number of sides of the cube which is 6 sides:
6.25 x 6 = 37.5 units
A parallelogram has a height of 7 meters and an area of 35 square meters. what would the sum of the bases be for a trapezoid with the same height and area as the parallelogram?
The height of trapezoid is h = 7 m.
The area of trapezoid is A = 35 m^2.
The formula for the area of trapezoid is,
[tex]A=\frac{a+b}{2}\cdot h[/tex]Here, a and b are length of bases of trapezoid.
Substitute the values in the formula to obtain the sum of bases of trapezoid.
[tex]\begin{gathered} 35=\frac{a+b}{2}\cdot7 \\ \frac{a+b}{2}=\frac{35}{7} \\ a+b=5\cdot2 \\ =10 \end{gathered}[/tex]So sum of bases of trapezoid is equal to 10 meters.
what digit is in the
EXPLANATION
Rounding 9177 to the nearest hundred give us the following number:
9,200
3. A doctor sees between 7 and 12 patients each day. On Mondays and Tuesdays.the appointment times are 15 minutes. On Wednesdays and Thursdays, they are30 minutes. On Fridays, they are one hour long. The doctor works for no morethan 8 hours a day. Here are some inequalities that represent this situation,0.25 Sy 51YS0S 12Y S83a. What does each variable represent?Your anowar3b. What does the expression xy in the last inequality mean in thissituation?
Solution
We have the following inequalities:
0.25 <= y<= 1, 7 <= x<= 12, xy <= 8
And we can conclude this:
Part a
the variable y represents the appointment time in hours and x the number of patients by the doctor
Part b
the expression xy is the time in hours that spends with a patient
What percent of 40 is 17?
In general, we can calculate what percent of y is x using the equation:
[tex]P=\frac{x}{y}\cdot100\text{\%}[/tex]In our problem, we identify:
[tex]\begin{gathered} x=17 \\ y=40 \end{gathered}[/tex]The percentage is:
[tex]\begin{gathered} P=\frac{17}{40}\cdot100\text{\%}=\frac{17\cdot5}{2}\text{ \%} \\ \Rightarrow P=42.5\text{\%} \end{gathered}[/tex]please help me solve. The answer I have is incorrect which is 527.5
527.8 m³
1) Let's find out the Volume of the biggest cylinder then subtract from it the smaller one.
Big Cylinder Volume:
[tex]\begin{gathered} V=\pi\cdot r^2\cdot h \\ V=\pi\cdot9^2\cdot3 \\ V=243\pi\approx763.4m^3 \end{gathered}[/tex]The Small one:
[tex]\begin{gathered} V=\pi\cdot5^2\cdot3 \\ V=75\pi m^3 \end{gathered}[/tex]Subtracting 75π from 243π we have:
V=243π -75π =168π approximately 527.7875658 to the nearest tenth: 527.8 m³
Hi, could you please help me understand why I got some of the answers wrong?
For the figure in the right up
The two triangles have 2 equal angles and one equal side
Then it should be AAS
Triangle AOC is congruent to triangle BOC
You must write the name of the triangles with equal angles
Since < AOC = < BOC ------- Given
Since Since OC = OC ------- common side
By using the AAS theorem of congruency
Then triangle AOC is congruent to triangle BOC
For the figure in the right down
Since OX // YC, then
Since
Since OC = CB ------- Given
Then by using the AAS theorem of congruency
Triangle XCO is congruent to triangle YBC
what will the deposit have to be if you want to have 12000 in an account that will earn 8.55% compounded weekly at the end of 5 years
Given:
The expected deposit =?
This is also referred to the principal
r = rate = 8.55%
t = time = 5years
n = we
Write the phrase as an algebraic expression: a number divided by 2
Answer:
x/2
Explanation:
Let the number = x
If the number is divided by 2, then an algebraic expression to represent the phrase is:
[tex]\frac{x}{2}[/tex]It can also be written in the form:
[tex]x\div2[/tex]You randomly select one card from a 52-card deck. Find the probability of selecting a black eight or a black king.
The theoretical probability is defined as the ratio of the number of favourable outcomes to the number of possible outcomes.
We have only two black eights on the deck and two black kings on the deck, therefore, the amount of favourable outcomes is equal to their sum, which is 4. The total amount of possible outcomes are the amount of cards, 52. The probability of selecting a black eight or a black king is:
[tex]P=\frac{4}{52}=\frac{1}{13}[/tex]