Answer:
1/25Step-by-step explanation:
5^-2=1/(5^2)=1/25
For her birthday, Monica can invite 6 of her 15 student friends to join her at a theme park. If she chooses to invite friends at random, what is the probability that friends Tessa,
Guido, Brendan, Faith, Charlotte and Rhianna are chosen?
10 out of 27,358
1 out of 5,005
1 out of 720
1 out of 3,603,600
Answer:
B. 1 out of 5,005
Step-by-step explanation:
Given
Number of Friends = 15
Required
Probability of selecting 6 friends
The first step is to calculate the number of ways 6 friends can be selected
The keyword in the above statement is selection;
This implies combination;
The number of ways is calculated as follows;
[tex]\left[\begin{array}{c}n&r&\end{array}\right] = \frac{n!}{(n-r)!r!}[/tex]
Where n = 15 and r = 6
[tex]\left[\begin{array}{c}n&r&\end{array}\right] = \frac{n!}{(n-r)!r!}[/tex]
becomes
[tex]\left[\begin{array}{c}15&6&\end{array}\right] = \frac{15!}{(15-6)!6!}[/tex]
[tex]\left[\begin{array}{c}15&6&\end{array}\right] = \frac{15!}{9!6!}[/tex]
[tex]\left[\begin{array}{c}15&6&\end{array}\right] = \frac{15 * 14 * 13 * 12 * 11 *10 * 9!}{9! *6 * 5 * 4 * 3 * 2 * 1}[/tex]
[tex]\left[\begin{array}{c}15&6&\end{array}\right] = \frac{15 * 14 * 13 * 12 * 11 *10}{6 * 5 * 4 * 3 * 2 * 1}[/tex]
[tex]\left[\begin{array}{c}15&6&\end{array}\right] = \frac{3603600}{720}[/tex]
[tex]\left[\begin{array}{c}15&6&\end{array}\right] =5005[/tex]
Hence, there are 5005 ways of selecting 6 from 15 friends
Since, there's only one way of selecting the 6 named friends
Then, the probability is 1 out of 5,005
On a winter morning, the temperature before sunrise was -10℉. The temperature then rose by 1℉ each hour for 7 hours before dropping by 2℉ each hour for 3 hours. What was the temperature, in degrees Fahrenheit, after 10 hours?
Answer:
The temperature after 10 hours is -9 ºF.
Step-by-step explanation:
This statement can be translated mathematically as follows. The temperature after 10 hours from sunrise is:
[tex]T = -10\,^{\circ}F + \left(1\,\frac{^{\circ}F}{h} \right)\cdot (7\,h)+ \left(-2\,\frac{^{\circ}F}{h} \right)\cdot (3\,h)[/tex]
[tex]T = -9\,^{\circ}F[/tex]
The temperature after 10 hours is -9 ºF.
Answer:
The answer is in the picture
Step-by-step explanation:
PLZ HURRY How many solutions does this system have? y = 3 x minus 5. y = negative x + 4.
Answer:
one is correct.
Step-by-step explanation:
because it have one solution when you graph it
Answer:
One solution (2.25,1.75)
Step-by-step explanation:
Well first we need to graph the following
[tex]y=3x-5[/tex]
[tex]y=-x+4[/tex]
So look at the image below.
So looking at the image below we can tell that the system only has one solution (2.25,1.75).
What is the Square root of -100
Answer:
[tex]10i[/tex]
Step-by-step explanation:
√(-100)
Use the imaginary number rule [tex]i=\sqrt{-1}[/tex]
√(-1) × √(100)
i × √(10²)
i × 10
= 10i
Answer:
It does not have a square root because it is a minus digit.
Step-by-step explanation:
The square root of one number is the number which is multiplied by itself to form the square number.
But, no negative number has a square root, because
- x - = +
+ x + = +
As you can see, no two same signs multiply together to form a negative.
Hope this helps.
Good Luck
√9pr / (pr)^-3/2 =
A. √3pr
B. 3/pr
C. 3√pr
D. 3pr
E. 3p²r²
Answer:
E
Step-by-step explanation:
=√9pr / (pr)^-3/2
=3√(pr) × (pr)^3/2
= 3p²r²
Answer:
E. 3p²r²
Step-by-step explanation:
√9pr / (pr)^-3/2=
3(pr)^1/2*(pr)^3/2=
3(pr)^(1/2+3/2)=
3(pr)^2=3p^2r^2
Last year Peter spent a total of 8 1/6 hours on community service. Visits to old folks' homes made up 4/7 of the total time. How much time did he spend in visiting old folks homes?
B) This year Peter plans to spend 1 1/5 of his time spent last year on community service.
(i) Find the time he will spend on community service.
(ii) How much more time will he spend this year than last year?
Answer:
A. 4 2/3 hours
B. (i) 9 4/5 hours
(ii) 1 19/30
Step-by-step explanation:
Firstly, to find the number of hours he used in visiting old folks, what we have to do is to multiply the fraction of hours he used by the total number of hours.
Mathematically, that would be;
4/7 * 8 1/6
8 1/6 is same as 49/6
So the number of hours he spent visiting old folks would be ;
49/6 * 4/7 = 14/3 = 4 2/3 hours
B. What we do here is simply multiply the fraction now by what he spent last year.
That would be 1 1/5 * 8 1/6 hours
= 6/5 * 49/6 = 49/5 = 9 4/5 hours
ii) Now we want to know how much more time will be spent this year than last year.
What to do here simply is to subtract the time taken last year from what we have this year
That would be;
49/5 - 49/6 = 49/30 = 1 19/30
436486346349234x98^5/5679ex45+423234723+sqaure root of 34248234824827468246278 If you answer, your are a god.
Answer:
your mom
Step-by-step explanation:
get rekt
Can i have brainliest
Which pair shows equivalent expressions?
Answer:
2(2/5x+2)=4x/5+4
Step-by-step explanation:
2(2/5x+2)=4x/5+4
4x/5 +4=4x/5 +4
ASAP!! Please help me. I will not accept nonsense answers, but will mark as BRAINLIEST if you answer is correctly with solutions.
x-2 is a factor so x = 2 is a root of f(x)
This is because f(x) = (x-2)*g(x) for some polynomial g(x). We don't have to worry about what g(x) is equal to as it doesn't affect the status of the root we're after.
So,
f(x) = 0
(x-2)*g(x) = 0
x-2 = 0 or g(x) = 0
x = 2 or g(x) = 0
This shows how the factor x-2 leads to the root x = 2
Therefore, f(2) = 0
Answer: Choice D
Answer:
F ( 2 ) = 0Last one is the correct option.
Step-by-step explanation:
A root or zero of a polynomial are the value (s) of X that cause the polynomial equal to zero.
y = 0
It is x- intercept. The root is the x-value.
Hope this helps...
Good luck on your assignment..
PLEASE HELP!!!! BRAINLIEST FOR RIGHT ANWSER
Answer:
d.tigers have a great IQR because they were some very heavy tigers.(high outliers)
1. A tank contains 250 litres or weathe
If 96 litre is used, what percentage of the original quantity is left
Answer:
61.6%
Step-by-step explanation:
We know that the tank contains 250 litres and that 96 litres are used. We are trying to find the percentage of the leftover quantity.
First, we need to subtract 250 from 96 litres to get the quantity that is left in the tank in litres. 250-96=154.
Then we need to find the percentage. To find a percentage we need to divide the total minus and the used amount by the total amount and then multiple the whole thing by 100. So in our case, that would be 250-96=154/250*100. Or 154/250*100.
Thus the answer is 61.6%.
Answer:
Step-by-step explanation:
Quantity left in the tank = 250 - 96 = 154 litres
Percentage = [tex]\frac{154}{250}*100\\[/tex]
= 0.616 * 100
= 61.6 %
Tanya can wash a car and vacuum its interior in 22 hours. Pat needs 55hours to do this same job. If Tanya and Pat work together, how many hours will it take them to clean a car?
Answer:
1 hour 26 Minutes
Step-by-step explanation:
Tanya needs 2 hours to do the job.
Pat needs 5 hours to do this same job.
Tanya's rate [tex]=\frac{1}{2}[/tex]
Pat's rate[tex]=\frac{1}{5}[/tex]
Let the number of hours it will take both of them =x
Rate when two of them work together [tex]=\frac{1}{x}[/tex]
Therefore:
[tex]\frac{1}{2}+\frac{1}{5}=\frac{1}{x}\\$Taking lowest common multiple$\\\frac{5+2}{10}=\frac{1}{x}\\\\\frac{7}{10}=\frac{1}{x}\\\\$Cross multiply$\\7x=10\\x=1.43$ hours[/tex]
[tex]0.43 X 60 =25.8 \approx 26$ minutes[/tex]
Therefore: 1.43 hour = 1 hour 26 Minutes
It will take both of them approximately 1 hour 26 minutes to the job.
Which is true about the solution to the system of inequalities shown? y > 3x + 1 y 3x + 1 are solutions. Only values that satisfy y 3x + 1 or y < 3x – 3 are solutions. There are no solutions.
Answer:
The correct option is;
There are no solutions
Step-by-step explanation:
From the graph of the inequality, with the y-intercept = 1 and slope = 3 for the blue shaded inequality
The equation is y > 3x + 1
While that of the other red shaded inequality, the slope is 3 and the y-intercept = -3
The equation is y < 3x - 3
Given that the two inequalities are parallel line that their domains do not overlap, we have that there are no solutions as the y-coordinate values of y > 3x + 1 are always larger for a given x-coordinate value than the y-coordinate value of y < 3x - 3.
Answer:
No solution is correct.
Step-by-step explanation:
I took the test
A truck covers a distance of 150 km at a certain average speed and then covers another 200 km at an average speed which is 20 km per hour more than the first speed. If the truck covers the total distance in 5 hours, find the speed of the truck.
Answer:
Since the speed can't be negative it was 60 km/h for the first stage and 80 km/h on the second stage, averaging 70 km/h for the whole course.
Step-by-step explanation:
The speed of the truck for the first stage of the route is "x" km/h, while on the second one it raises to "x + 20" km/h. The time it takes to complete each stage is shown below:
[tex]t_{stage 1} = \frac{150}{x}\\t_{stage 2} = \frac{200}{x + 20}[/tex]
The sum of these times must be equal to the total time of the trip, therefore:
[tex]t_{stage1} + t_{stage2} = 5[/tex]
[tex]\frac{150}{x} + \frac{200}{x + 20} = 5\\\frac{150*(x + 20) + 200*x}{x(x + 20)} = 5\\150*x + 3000 + 200*x = 5*x*(x + 20)\\5*x^2 + 100*x - 350*x - 3000 = 0\\5*x^2 - 250*x - 3000 = 0\\x^2 - 50*x - 600 = 0\\x_{1,2} = \frac{-(-50) \pm \sqrt{(-50)^2 - 4*1*(-600)}}{2*1}\\x_{1,2} = \frac{50\pm \sqrt{2500 + 2400}}{2}\\x_{1,2} = \frac{50\pm \sqrt{4900}}{2}\\x_{1,2} = \frac{50 \pm 70}{2}\\x_{1} = 60\\x_{2} = -10[/tex]
Since the speed can't be negative it was 60 km/h for the first stage and 80 km/h on the second stage, averaging 70 km/h for the whole course.
Michael has 3 quarters, 2 dimes, and 3 nickels in his pocket. He randomly draws two coins from his pocket, one at a time, and they are both dimes. He says the probability of that occurring is 1 4 because 2 of the 8 coins are dimes. Is he correct
Answer:
No, he is wrong
Step-by-step explanation:
To find that probability, the first thing we need to know is the total number of coins present.
Mathematically, that would be 3 + 2 + 3 = 8
Since there are 8 coins, the probability of selecting a dime is number of dimes/total number of coins = 2/8 = 1/4
The probability we want to work with is that the two selections are dimes, let’s say with replacement.
That means; first selection is a dime and second selection is also a dime
Mathematically in probability, the term and means that we have to multiply our results.
So the probability that both are dimes would be 1/4 * 1/4 = 1/16
And this makes his answer wrong
what is the equation of a circle with the center of (2,3) and crosses through the point (2,1)
Answer: (x - 2)² + (y - 3)² = 4
Step-by-step explanation:
The equation of a circle is: (x - h)² + (y - k)² = r² where
(h, k) is the center of the circler is the radius of the circle.Given: (h, k) = (2, 3) and (x, y) = (2, 1)
Input those values to find r²:
(x - h)² + (y - k)² = r²
(2 - 2)² + (1 - 3)² = r²
0 + 4 = r²
4 = r²
Now input (h, k) = (2, 3) and r² = 4 into the equation of a circle:
(x - h)² + (y - k)² = r²
(x - 2)² + (y - 3)² = 4
Classify the following triangle.Check all that apply
Answer:
B and D
Step-by-step explanation:
=> All of the sides are unequal so it's a scalene triangle.
=> It have a 90 degrees angle, so it is a Right Angled Triangle.
Answer:
B. Scalene
D. Right
Step-by-step explanation:
The triangle is a scalene triangle, because all the three sides have different lengths.
The triangle is a right triangle, because it has an angle of 90 degrees.
Kevin and Emily Johnson pay $1,375 for monthly rent. Emily lost her job and the couple needs a less expensive apartment. They rented a new apartment for $950 per month. If the cost of moving was $275, find their savings the first year if they move to a new apartment.
Step 1) Solve for the amount of money Kevin and Emily used to spend in a year for rent
1375 x 12 = 16500
Step 2) Solve for the amount of money Kevin and Emily spend in a year now for rent
(950 x 12) + 275 = 11675
Step 3) Subtract the new amount of money per year from the old amount of money per year to find the savings in the first year
16500 - 11675 = 4825
Kevin and Emily will save $4,825 the first year if they move to a new apartment.
Hope this helps!! :)
PLS HELP ASAP! A decoration is packed in a box shaped like a cube. The decoration has a volume of 651 cm3. Approximately how much empty space remains in the box?
This question is incomplete.
Find attached to this question the diagram of the cube.
Reference for the attached image: This diagram was obtained from Education Quality and Accountability Office (EQAO) PDF
Answer:
128cm³
Step-by-step explanation:
The diagram of the box shows it has a side length of 9.2cm
Volume of a cube =( Length)³
Volume of a cube =( 9.2cm)³
= 778.688cm³
We are told in the question that the decoration packed in the cube has a volume of 651 cm³.
The amount of empty space remaining in the box is calculated as:
778.688cm³ - 651cm³
= 127.688cm³
Approximately to the nearest whole number = 128cm³
A little help would be nice :')
Answer:
(2,6)
Step-by-step explanation:
x+2y = 14
y = x+4
Substitute x+4 into the first equation for y
x+2(x+4) = 14
Distribute
x+2x+8 = 14
3x+8 = 14
Subtract 8 from each side
3x+8-8 = 14-8
3x = 6
Divide by 3
3x/3 = 6/3
x = 2
Now solve for y
y = x+4
y =2+4
y =6
(2,6)
Answer:
D. (2, 6)
Step-by-step explanation:
Put y as x+4 in the first equation and solve for x.
x + 2(x + 4) = 14
x + 2x + 8 = 14
3x = 14 - 8
3x = 6
x = 2
Put x as 2 in the second equation and solve for y.
y = 2 + 4
y = 6
can someone in here help me with this question I'm stuck and I don't know to do it
Answer:
Substitute -3,-2,-1,0,1,2,3 in d equation given to u at first to complete the table
2/3, 2/8, 2/6 how to do least to greatest?
Answer: 2/8, 2/6, 2/3
Step-by-step explanation:
First, find the LCM of 3, 6, and 8, in this case 24. Then, make the denominator of each fraction 24: 16/24, 6/24, 8/24. Then, simply sort the fractions from least to greatest by their numerators: 6/24, 8/24, 16/24
Hope it helps <3
Graph y=-1/2x^2-1. Identify the vertex of the graph. tell whether it is a minimum or maximum.
Answer:
Graph shown below.
Step-by-step explanation:
The vertex is at (0, -1).
It is a maximum.
What is the shape of the cross section of the figure that is perpendicular to the rectangular base but does not pass through the top vertex? A Rectangular Pyramid. parellogram that is not a rectangle a rectangle a triangle a trapezoid
Answer:
(E)A trapezoid
Step-by-step explanation:
Given the shape which is a rectangular based pyramid.
A cross-section is cut but it does not pass through the top vertex of the pyramid.
The shape formed will have two parallel unequal sides (the base and the top)However, the other two sides will be slant.Therefore, the shape which describes the cross-section will be a trapezoid.
Answer:
The figure is a rectangular pyramid. The cross section is perpendicular to the rectangular base and passes through the top vertex of the figure. A triangle that does not have the same dimensions as one of the faces is formed.
Step-by-step explanation:
Please please urgently helpp❤️
show your work
PLEASE!
Hey there! :)
Answer:
x = 12.
Step-by-step explanation:
Given:
[tex]\frac{3}{5} = \frac{x}{20}[/tex]
Cross multiply to solve for x:
3 · 20 = 5 · x
60 = 5x
Divide by 5:
12 = x.
Answer:
so x=12
Step-by-step explanation:
[tex]\frac{3}{5}=\frac{x}{20}\\ by cross multiplication[/tex]
3×20=5×x
60=5x
dividing 5 on both sides
60/5=5x/5
x=12
i hope this will help you :)
Paula and Karen are playing a game. Paula counts by 4s. Karen counts by 5s. They try to pace the counting so they will say the fist common number together. What is the first number they both say together?
Find the length of the side labeled x. Round intermediate values to the nearest tenth. Use the rounded values to calculate the next value. Round your final answer to the nearest tenth.
Answer:
11.67
Step-by-step explanation:
Data given in the question
∠ADC = 42°
∠BAC = 68°
Let us assume that AC be Y
Now
In ΔACD
tan 42° = AC ÷ CD = Y ÷ x ...............................(i)
In ΔACB
tan 68° = BC ÷ AC = 26 ÷ Y ..........................(ii)
Now take the value of Y from the equation (ii)
Y = 26 ÷ Tan 68° ...................... (iii)
Now place the value of Y in equation (i)
So,
Tan 42° = 26 ÷ tan 68° × X
X = 26 ÷ tan 68° × Tan 42° ......................(iv)
Now placing the values of tan 42° and tan 68° in equation (iv)
So,
X = 26 ÷ 0.900 × 2.475
= 11.67
The tan 42° = 0.900
And, the tan 68° = 2.475
Find the product of the following.
i) –5a2bc, 6ab, 8abc2
ii) –3x2y and (5y – xy)
iii) x2y2z2 and (xy – yz + zx)
iv) (p+6)and (q–7)
v) (2x+7)and(x2 –5x+6) vii) (x + y + 5) and (2x – 2y – 3)
PLEASE I NEED THE ANSWER NOW
Answer:
i) -240[tex]a^{4}b^{3} c^{3}[/tex]
ii) -15x²y² + 3x³y²
iii)x³y³z³ - x²y³z³ + x³y²z³
iv) pq -7p+6q-42
v)9x²-33x +42
vii) 2x² - 2y² + 7x -13y - 15
Step-by-step explanation:
To find product here means to multiply the algebraic expressions together
i) (–5a²bc)×(6ab)×(8abc² )
multiply like terms together
= -240[tex]a^{4}b^{3} c^{3}[/tex]
ii) (–3x²y) ×(5y – xy)
(–3x²y)×(5y) – (–3x²y) ×(xy)
multiply like terms together
multiplication of same sign gives +, while that of opposite sign gives -
= -15x²y² + 3x³y²
iii) (x²y²z²) ×(xy – yz + zx)
(x²y²z²)×(xy) – (yz)× (x²y²z²) + (zx) ×(x²y²z²)
multiply like terms together
multiplication of same sign gives +, while that of opposite sign gives -
= x³y³z³ - x²y³z³ + x³y²z³
iv) (p+6)and (q–7)
p(q–7) +6(q–7)
multiply like terms together
multiplication of same sign gives +, while that of opposite sign gives -
= pq -7p+6q-42
v) (2x+7)and(x² –5x+6)
multiply like terms together
multiplication of same sign gives +, while that of opposite sign gives -
= 2x² -10x+12x+7x²-35x+42
collect like terms
= 9x²-33x +42
vii) (x + y + 5) and (2x – 2y – 3)
multiply like terms together
multiplication of same sign gives +, while that of opposite sign gives -
= 2x²-2xy-3x+2xy-2y²-3y+10x-10y-15
collect like terms
= 2x² - 2y² + 7x -13y - 15
The following are the ages (years) of 5 people in a room: 12, 19, 24, 21, 21 A person enters the room. The mean age of the 6 people is now 25. What is the age of the person who entered the room?
Answer:
53
Step-by-step explanation:
x - the age of the person who entered the room.
(12 + 19 + 24 + 21 + 21 + x)/6 = 25
12 + 19 + 24 + 21 + 21 + x = 150
97 + x = 150
x = 53
Answer:
53
Step-by-step explanation: