The probability is 0.1429.
The probability that the first person chosen is a boy is 5/7. The probability that the second is a boy is 4/6; the third, 3/5; and the fourth, 2/4. Both the numerator and denominator decrease every time, because you lose a boy to choose from and you lose a student to choose from as well. This gives us:
5/7(4/6)(3/5)(2/4) = 120/840 = 0.1429.
The probability that everyone in the group is a girl is 2/7.
What is probability?Probability sampling is defined as a sampling technique in which the researcher chooses samples from a larger population using a method based on the theory of probability.
Total number of students in a class = 7
Number of boys students = 2
Number of girls students = 5
The probability that everyone in the group is a girl is;
[tex]\rm Probability =\dfrac{Total \ number \ of \ girls}{Total \ number \ of \ boys}\\\\Probability=\dfrac{2}{7}[/tex]
Hence, the probability that everyone in the group is a girl is 2/7.
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HELP HELP HELP HELO HELP HELP HELP
This function is Exponential
Reason: Exponential graphs tend to get very big quickly, and though they start out smaller than polynomial functions or vice versa
Hope that helps!
I need help with the working
Answer:
288 cm^3.
Step-by-step explanation:
The volume of each small square = 2*2*2 = 8 cm^3
Each rectangular length of end 2*2 is made up of 12/2 = 6 squares.
There are 6 of these rectangular lengths.
So the volume = 6 * 6 * 8 cm^3
288 cm^3.
Write the equation in standard form for the circle with center (0, -5) and radius 2
The standard equation for a circle is '[tex](x-h)^2+(y-k)^2=r^2[/tex]
(h,k): coordinate for the center of the circle --> (0,-5)r: radius --> 2--> Standard form:
[tex](x - )^2 +(y-(-5))^2=2^2\\x^2+(y+5)^2=4[/tex]
Hope that helps!
Answer:
x^2 + (y + 5)^2 = 4.
Step-by-step explanation:
Standard form is (x - a)^2 + (y - b)^2 = r^2
- where (a, b) is the center and radius = r.
So our equation is:
(x - 0)^2 + (y - (-5))^2 = 2^2
x^2 + (y + 5)^2 = 4.
Is -2 a whole number or irrational number?
Answer:
It is neither.
Step-by-step explanation:
A whole number is all numbers is 0, 1, 2, 3, 4.... you get it
An irrational number is a number that cannot be written as a fraction and -2 can be written as -2/1
Swimming Pool On a certain hot summer's day, 163 people used
the public swimming pool. The daily prices are $1.25 for children
and $2.00 for adults. The receipts for admission totaled $257.00.
How many children and how many adults swam at the public pool
that day?
There were
children at the public pool.
Use the spinner to answer the question. It is divided into 8 congruent sections. Orange, Blue, Pink, Brown, Purple, Red, Bronze, Black. Determine whether the statement is true or false. After 96 spins, Tiffany would expect the spinner to land on a color section beginning with the letter "B" roughly 48 times.
Using proportions, it is found that the statement that Tiffany would expect the spinner to land on a color section beginning with the letter "B" roughly 48 times is True.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three.
In this problem, out of 8 sections, 4(Blue, Brown, Bronze and Black) begin with letter "B". We want to find the equivalent amount out of 98 trials. Hence, the rule of three is:
8 trials - 4 start with "B".
96 trials - n start with "B".
Applying cross multiplication:
8n = 4 x 96
n = 0.5 x 96
n = 48.
Hence, the statement is True.
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A 15-meter by 23-meter garden is divided into two sections. Two sidewalks run along the diagonal of the square section and along the diagonal of the smaller rectangular section. A rectangle is shown. The length of the top and bottom sides is 23 meters. The length of the left and right sides is 15 meters. A vertical line is drawn from the top to bottom side to split the shape into a square and a rectangle. Lines are drawn from the bottom left point to the top of the vertical line and from the bottom right point to the top of the vertical line. What is the approximate sum of the lengths of the two sidewalks, shown as dotted lines? 21. 2 m 27. 5 m 32. 5 m 38. 2 m.
Approximate sum of the lengths of the two sidewalks, shown as dotted lines in the figure of rectangle garden is 38.2 meters.
What is Pythagoras theorem?Pythagoras theorem says that in a right angle triangle the square of hypotenuse side is equal to the sum of square of other two legs of right angle triangle.
A 15-meter by 23-meter garden is divided into two sections. In this rectangle,
Two sidewalks run along the diagonal of the square section and along the diagonal of the smaller rectangular section. The length of the top and bottom sides is 23 meters. The length of the left and right sides is 15 meters.Here, a vertical line is drawn from the top to bottom side to split the shape into a square and a rectangle. The length of the left side of the square will be 15 long. Thus, the lenght of its diagonal is,
[tex]d_1=15\sqrt{2}\\d_1=21.213\rm\; m[/tex]
The length of the sidewalk in smaller rectangle in the right side of figure is,
[tex]d_2=\sqrt{15^2+8^2}\\d_2=17\rm\; m[/tex]
Sum of the lengths of the two sidewalks using the pythagoras theorem is,
[tex]S=21.2+17\\S=38.2\rm\;m[/tex]
Thus, approximate sum of the lengths of the two sidewalks, shown as dotted lines in the figure of rectangle garden is 38.2 meters.
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Answer:
D 38.2
Step-by-step explanation:
E2020
Find the solution of the system of equations.
-
5x – 4y = -9
10x– 7y = -22
Answer:
x = -5
y = -4
Step-by-step explanation:
5x - 4y = -9
10x - 8y = -18
10x - 7y = -22
-y = 4
y = -4
Substitue y into any equation
5x - (-16) = -9
5x = -25
x = -5
What is the best first step in solving the equation 3 +[tex]3\sqrt[6]{x}[/tex] = 5?
[tex]3+3\sqrt[6]{x}~~ = ~~5\implies \stackrel{\textit{1st step,-3 to both sides}}{3\sqrt[6]{x}~~ = ~~2}\implies \sqrt[6]{x}=\cfrac{2}{3} \\\\\\ (\sqrt[6]{x})^6=\left( \cfrac{2}{3} \right)^6\implies x=\cfrac{2^6}{3^6}\implies x=\cfrac{64}{729}[/tex]
Find the area of the regular polygon. Give the answer to the nearest tenth.
Square with a radius of 13 m.
Answer:
338 m^2
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Which inequality can be used to find how many $1.25 snack packs can be purchased for $10.00?
Answer:
1.25s [tex]\leq[/tex] 10.00
Step-by-step explanation:
Let's snack = s
Note:
[tex]\leq[/tex] ⇒ Less than or equal to
[tex]\geq[/tex] ⇒ Greater than or equal to
< ⇒ Less than
> ⇒ Greater than
Since we are trying to find how many $1.25 snack packs can be purchased for $10.00.. Thus, that less than or equal to $10.00 which also means we use [tex]\leq[/tex].
Thus the equation is 1.25s [tex]\leq[/tex] 10.00
`lenvy`
Answer:
8 snacks can be purchased
Step-by-step explanation:
10.00/1.25=8
Write the log equation as an exponential equation. You do not need to solve for x.
In (3x + 2) = 3x
[tex]\ln(3x+2) = 3x\\\\\implies \log_e (3x+2) = 3x\\\\\implies e^{3x} = 3x+2[/tex]
-5x - 2y = 12 and 3x +2y = 8 using elimination as an ordered pair
Answer:
(-10, 19)
Step-by-step explanation:
Hey there!
In order to find the value of x and y, you need to make a system of equations
Now the question says to use elimination
The elimination method is when you make two values the same and then eliminate them with the proper sign: addition, subtraction, etc.
In this case, the step of making equal values is already done for us since there is 2y in both equations
[tex]-5x-2y=12\\3x+2y=8\\\\-2x=20\\x=-10\\[/tex]
What was done was called elimination
I added both equations together and when you add -2y and 2y, they eliminate each other
Now when you simplify the system, you get that x is equal to -10
Now we can substitute this value into the first or second equation
I am going to do the first equation
[tex]-5(-10)-2y=12\\50-2y=12\\-2y=-38\\y=19[/tex]
So after substituting the x value in the equation, we got the y value
Which is 19
So the solution to this system of equations is:
(-10, 19)
i need help with this hard question
Answer:
Bottom left = 8
Top right = 15
Middle right = 25
Step-by-step explanation:
Total = 40
3 + 5 = 8
40 / 8 = 5
1 part = 5
5 x 3 = 15
5² = 25
Kim says that 1/4 x 12 is the same as dividing 12 by 4 do you agree with Kim? explain your answer.
Answer:
yes i do
Step-by-step explanation:
1/4 x 12= 3
12 divided by 4 = 3
A pool company offers a pool with dimensions x and 2x. They also include a 3 foot deck around the entire pool.
1. Write an equation to represent the area of the pool and deck combined.
2. If someone wants a 10ft wide pool (x = 10) how many square feet must they have available in their back yard?
Answer:
1) area = (x + 3)(2x + 3) ft²
2) 299 ft²
Step-by-step explanation:
Question 1
Area of a rectangle = width x length
Given:
width = x + 3length = 2x + 3⇒ area = (x + 3)(2x + 3) ft²
Question 2
If x = 10:
⇒ area = (10 + 3)(2(10) + 3)
= 13 · 23
= 299 ft²
#1
New dimensions=x+3 and 2x+3ftSo
Area:-
Length ×Breadth(x+3)(2x+3)x(2x+3)+3(2x+3)2x^2+3x+6x+92x^2+9x+9ft^2#2
Put x=10
2(10)^2+9(10)+92(100)+90+9200+99299ft^2Helppp Please!!!!!!!!
Answer:
Emma began her journey at 7:30 a.m., at 8 a.m. she was 20 miles away, she stayed for an hour and a half, she left at 10 a.m., she was 7.5 miles from her house at 11:45, she traveled 80 miles total
Step-by-step explanation:
please let me know what you don't understand here. because this is really simple.
the distance from home is increasing and then decreasing when she is traveling.
the rate of distance per time would give us even the speed with which she was traveling.
when there is no change in the distance over time, that means she was "stationary" - either at home or at her grandmother's place.
so, let's answer the questions :
(a)
movement started at 7:30am (that is when she began her journey).
(b)
20 miles
you pick 8am on the time scale and move straight up until you hit the curve. and then you check what value is at that point all the way to the left on the distance scale : 20.
(c)
from 8:30am to 10am = 1.5 hours.
we see this by the interval on the time scale for which the curve is totally flat (a horizontal line) = no change in distance from home during that time.
(d)
at 10am
that is when the curve indicates the begin of a change in the distance to home.
(e)
7.5 miles.
this is the point marked by a star on the graph.
down on the time scale this point shows 11:45am, and on the left side in the distance scale it shows 7.5 miles (the middle between 5 and 10 miles).
so, at that time she was still 7.5 miles away from home.
(f)
she traveled 40 miles to her grandmother (the left part of the curve from 0 distance until it turns flat), and then 40 miles back home (the right part of the curve from 40 distance all the way down to 0).
so, in total she traveled
40 + 40 = 80 miles
State the domain and range and determine if it's a function?
if we do a vertical line test on that graph, we'll find that a vertical line will pass by and hit the line only once on its way down, only once meaning the graph is the graph of a function.
Rangewell, is really how high and low it goes or namely over the y-axis.
well, it goes up up up to 3 then U-turns and back down it goes, now the graph has arrowheads, meaning the graph keeps on going towards infinity, vertically as well as horizontally since it's a parabola, so the range will be
[3 , +∞)Domainwell, is simply how left and right it goes or namely over the x-axis.
judging from the arrowheads it moves from infinity to infinity, so
(-∞ , +∞).573,297.88 rounded to the nearest 10
Answer:
573,300.00 to the nearest 10
Step-by-step explanation:
A rectangular yard measures 12 feet by 10 feet. Find the cost of installing a fence around the yard if the fence costs
$3.10 per foot
Answer:
$372
Step-by-step explanation:
12 × 10 = 120
1 foot = $3.10
120 feet = ?
120 feet × $3.10
= $372
$372÷ 1 foot = $372
4) What is the slope of the line joining (7, 8) and (17, 13)
slope is = (13 - 8) / (17 - 7) = 5/10 = 1/2 or 0,5
slope for A (xa ; ya) and B (xb ; yb) = (yb - ya) / (xb - xa)
bellamy is building a gate to put on a fence. the gates measurements are 7 feet by 7 feet a diagonal wooden brace is going to be attached to keep the gate rigid what is the length of wood bellany needs to cut for the brace leave your answer in simplified radical form
The length of the diagonal is the hypotenuse of the fence
The length of the wood is [tex]7\sqrt{ 2[/tex] yards
How to determine the length of the wood?The dimensions of the fence are:
7 ft by 7 ft
The length (L) of the diagonal is calculated using:
[tex]L = \sqrt{a^2 + b^2[/tex]
This gives
[tex]L = \sqrt{7^2 + 7^2[/tex]
Express as products
[tex]L = \sqrt{7^2 * 2[/tex]
Express as radical
[tex]L = 7\sqrt{ 2[/tex]
Hence, the length of the wood is [tex]7\sqrt{ 2[/tex] yards
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Find the simple interest earned to the nearest cent for each principal, interest rate, and time 1,050, 4.6%, two years
Answer:
The interest earned is $96.60
Step-by-step explanation:
Since we are working the a simple interest problem, we will use the formula
[tex]I=Prt[/tex],
Where P represents the principal, r represents the rate as a decimal, and t represents the time in years. First, we need to change the 4.6% into a decimal by dividing by 100:
[tex]4.6\div 100 = 0.046[/tex]
From our given information and our decimal rate, we have:
[tex]P=1050\\r=0.046\\t=2[/tex]
Substituting these into our equation, we get:
[tex]I=1050(0.046)(2)\\I=96.6[/tex]
We write that as $96.60 in context of the problem.
Answer:
principle (p)=RS 1,050
Rate(R)=4.6
time(T)=2years
we know that
I=P×R×I/100
=1050×4.6×2/100
=9660/100
=96.6
therefore the earned simple interest is RS.96.6
does anyone know the answer to this question?
Answer:
c = 2.5 , d = - 3
Step-by-step explanation:
f(x) = cx + d
f(4) = 7 ( substitute x = 4 into the equation and equate to 7 )
f(10) = 22 ( substitute x = 10 into the equation and equate to 22 )
4c + d = 7 → (1)
10c + d = 22 → (2)
subtract (1) from (2) term by term to eliminate d
(10c - 4c) + (d - d) = 22 - 7 , that is
6c = 15 ( divide both sides by 6 )
c = 2.5
substitute c = 2.5 into (1) and solve for d
4(2.5) + d = 7
10 + d = 7 ( subtract 10 from both sides )
d = - 3
Answer:
c = 2.5
d = - 3
Step-by-step explanation:
f(x) = cx + d
f(4) = 7
f(10) = 22
4c + d = 7
10c + d = 22
(10c - 4c) + (d - d) = 22 - 7
6c = 15
--- ----
6 6
c = 2.5
4(2.5) + d = 7
10 + d = 7
-10 -10
d = - 3
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SOLVE THIS SYSTEM OF EQUATIONS BY USING THE ELIMINATION METHOD.
3x + 2y = 6
-3x + y + 12
the ordered pair of solutions is written in the format (x, y)
([x], [y])
[tex]3x + 2y = 6[/tex]
[tex] - 3x + y = 12[/tex]
Add the systems:[tex]3x - 3x + 2y + y = 6 + 12[/tex]
[tex]3y = 18[/tex]
[tex]y = \frac{18}{3} = 6[/tex]
Replace y=6 in any equation:[tex]3x + 2y = 6[/tex]
[tex]3x + 2(6) = 6[/tex]
[tex]3x + 12 = 6[/tex]
[tex]3x = 6 - 12[/tex]
[tex]3x = - 6[/tex]
[tex]x = \frac{ - 6}{3} = - 2[/tex]
Pair: ( -2 , 6 )How many degrees are in 25π18?
Answer:
[tex]\displaystyle 250°[/tex]
Explanation:
When converting from radians to degrees, multiply one hundred eighty by the radian measure, then divide it pi:
[tex]\displaystyle \boxed{250°} = 1\frac{7}{18}\pi[\frac{180}{\pi}][/tex]
I am joyous to assist you at any time.
A bag contains 40 red and green marbles. The number of green marbles, g, is 9 times the number of red marbles, r.
How many red marbles are in the bag?
Answer:
4 red marbles
Step-by-step explanation:
r is the number of red marbles then green marbles is 9r , so
r + 9r = 40
10r = 40 ( divide both sides by 10 )
r = 4
there are 4 red marbles
Jill always buys the same kind of shampoo in an 11.5-ounce bottle. She is at the store buying more and sees that the bottle is now bigger and has 20% more for the same price. How many ounces of shampoo are in the new bottle.
Step-by-step explanation:
100% = 11.5
20% more means 120%
120% = 100%×1.2 = 11.5×1.2 = 13.8 ounces
This year Heather watched 20 movies. She thought that 9 of them were very good. Of the movies she watched, what percentage did she rate as very good?
Answer:
45%
Step-by-step explanation:
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The exponential function f(x) has a positive coefficient, a base of 0.6, and a horizontal asymptote at y = 3. If g(x) = 2(x - 3), which statement is true? A. The function f(x) represents exponential growth, and the function g(x) represents exponential decay. B. The function f(x) represents exponential decay, and the function g(x) represents exponential growth. C. The functions f(x) and g(x) both represent exponential growth. D. The functions f(x) and g(x) both represent exponential decay.
Answer:i don’t know the answer the answer but it’s f
Step-by-step explanation: