9514 1404 393
Answer:
118
Step-by-step explanation:
Oganesson is the heaviest element ever created. It is a "super-heavy" noble gas with a half-life less than 1 millisecond. Its atomic number is 118.
Nadia is ordering cheesecake at a restaurant, and the server tells her that she can have up to five toppings: caramel, whipped cream, butterscotch sauce, strawberries, and hot fudge. Since she cannot decide how many of the toppings she wants, she tells the server to surprise her. If the server randomly chooses which toppings to add, what is the probability that Nadia gets just caramel, butterscotch sauce, strawberries, and hot fudge
Answer:
The probability that Nadia gets just caramel, butterscotch sauce, strawberries, and hot fudge is P = 1/32 = 0.03125
Step-by-step explanation:
There are up to 5 toppings, such that the toppings are:
caramel
whipped cream
butterscotch sauce
strawberries
hot fudge
We want to find the probability that, If the server randomly chooses which toppings to add, she gets just caramel, butterscotch sauce, strawberries, and hot fudge.
First, we need to find the total number of possible combinations.
let's separate them in number of toppings.
0 toppins:
Here is one combination.
1 topping:
here we have one topping and 5 options, so there are 5 different combinations of 1 topping.
2 toppings.
Assuming that each topping can be used only once, for the first topping we have 5 options.
And for the second topping we have 4 options (because one is already used)
The total number of combinations is equal to the product between the number of options for each topping, so here we have:
c = 4*5 = 20 combinations.
But we are counting the permutations, which is equal to n! (where n is the number of toppings, in this case is n = 2), this means that we are differentiating in the case where the first topping is caramel and the second is whipped cream, and the case where the first topping is whipped cream and the second is caramel, to avoid this, we should divide by the number of permutations.
Then the number of different combinations is:
c' = 20/2! = 10
3 toppings.
similarly to the previous case.
for the first topping there are 5 options
for the second there are 4 options
for the third there are 3 options
the total number of different combinations is:
c' = (5*4*3)/(3!) = (5*4*3)/(3*2) = 10
4 toppings:
We can think of this as "the topping that we do not use", so there are only 5 possible toppings to not use, then there are 5 different combinations with 4 toppings.
5 toppings:
Similar to the first case, here is only one combination with 5 toppings.
So the total number of different combinations is:
C = 1 + 5 + 10 + 10 + 5 + 1 = 32
There are 32 different combinations.
And we want to find the probability of getting one particular combination (all of them have the same probability)
Then the probability is the quotient between one and the total number of different combinations.
p = 1/32
The probability that Nadia gets just caramel, butterscotch sauce, strawberries, and hot fudge is P = 1/32 = 0.03125
In the figure, m is parallel to n and m <4 = 125 degrees. Find the measures of the other angles.
Answer:
m<1 = 55°
m<2 = 125°
m<3 = 55°
m<5 = 55°
m<6 = 125°
m<7 = 55°
m<8 = 125°
Step-by-step explanation:
m<4 = 125° (given)
✔️m<8 = m<4 (alternate exterior angles are congruent)
m<8 = 125° (substitution)
✔️m<1 = 180° - m<8 (supplementary angles/linear pair)
m<1 = 180° - 125° (substitution)
m<1 = 55°
✔️m<2 = m<8 (vertical angles are congruent)
m<2 = 125° (substitution)
✔️m<7 = m<1 (vertical angles are congruent)
m<7 = 55° (Substitution)
✔️m<3 = m<7 (alternate interior angles are congruent)
m<3 = 55° (substitution)
✔️m<5 = m<3 (vertical angles are congruent)
m<5 = 55°
✔️m<6 = m<4 (vertical angles)
m<6 = 125°
A dinner mint costs 85¢ and a toffee costs 73¢. What is the cost of both sweets rounded to the nearest dollar?
Answer:
85 rounded to the nearest dollar would be $1. 73 rounded to the nearest dollar would also be $1
Step-by-step explanation:
I NEED HELP ON C,E,F,G PLEASE ASAP!!!!
if "-3<" x/5 < "-1" what is the value of x
Answer:
-15 < x < -5
Step-by-step explanation:
-3 < x/5 < -1
Multiply all sides by 5
-3*5 < x/5 *5 < -1*5
-15 < x < -5
X ^2 + 2x + y’ + 6y = 15
Step-by-step explanation:
x^2+2x+7y=15
7y=15-x^2-2x
y=15/7-1/7x^2-2/7x , x ∈ all real numbers
Chen rode his skateboard 3/3/4 miles in 34 of an hour.
What was his average speed in miles per hour?
_[blank]_ miles per hour
Answer:
5 miles per hour
Step-by-step explanation:
3¾ ÷ ¾ =
15/4 ÷ ¾ =
15/4 x 4/3 =
15/3 = 5
Two equal positive charges are placed x m apart. The equipotential lines are at 100 V interval. The work required to move a third charge, q = -e, from the +100 V line to b is:______
Answer:
+200 J
Step-by-step explanation:
The equally positive charges plates are placed at point x. Exponential lines are 100 V interval and therefore the charges on the potential line is positive. The potential for line c is +200 V which indicates that work required to move the third line is +200 J.
Find f(2) given f(x) = -3x^2 + 2x+11
Answer:
Answer:f(2)=-3(2)^2+2*2+11
Answer:f(2)=-3(2)^2+2*2+11 =-3*4+4+11
Answer:f(2)=-3(2)^2+2*2+11 =-3*4+4+11 =-12+4+11
Answer:f(2)=-3(2)^2+2*2+11 =-3*4+4+11 =-12+4+11 =3
hence, f(2)=3
A farmer weighs a dozen chicken eggs. The heaviest egg is 56 g.
Step-by-step explanation:
hi
what is your question?
Step-by-step explanation:
please tell full questions
how to work this fraction 4/11+5/22+3/44
Answer:
29/44
Step-by-step explanation:
[tex]\frac{4}{11} +\frac{5}{22} +\frac{3}{44} =\\[/tex]
-find the common denominator
[tex]\frac{4*4}{4*11} + \frac{2*5}{2*22} +\frac{3}{44} =[/tex]
[tex]\frac{16}{44} +\frac{10}{44} +\frac{3}{44} =[/tex]
-add the fractions and solve
[tex]\frac{16+10+3}{44} =[/tex]
[tex]\frac{29}{44}[/tex]
Find the area of a triangle as a mixed number.
Answer:
I believe the answer is 4 37/50!
Select the statement that best justifies the conclusion based on the given information.
a. Definition of bisector.
b. Definition of midpoint.
c. If two lines intersect, then their intersection is exactly one point.
d. Through any two different points, exactly one line exists.
9514 1404 393
Answer:
a. Definition of bisector.
Step-by-step explanation:
Line l is a line through the midpoint M. We can conclude it is a bisector, because, by definition, a bisector is a line through the midpoint.
The conclusion is justified by the definition of a bisector.
Question 27 of 58
Select the equation that represents the problem. Let x represent the unknown
number.
Mr. Jefferson bought 336 markers for his class. The
markers came in packs of 12. How many packs did he
buy?
A. 336 - x= 12
B. 12x= 336
O C. 336x= 12
O D. x + 12 = 336
SUBMIT
Answer:
B.
Step-by-step explanation:
The answer is B.
A hotel has 210 units. All rooms are occupied when the hotel charges $90 per day for a room. For every increase of x dollars in the daily room rate, there are x rooms vacant. Each occupied room costs $24 per day to service and maintain. What should the hotel charge per day in order to maximize daily profit
Answer: [tex]\$162[/tex]
Step-by-step explanation:
Given
There are 210 units of hotel
Each room charge $90 when fully occupied
occupied room charges is $24 per day
Suppose x rooms are vacant, so, there 210-x occupied
Daily expense on maintenance[tex]=(210-x)\times 24[/tex]
Earning from 210-x rooms[tex]=(210-x)(90+x)[/tex]
Profit(P)=Earning - Expense
[tex]\Rightarrow P=(210-x)(90+x)-(210-x)24\\\Rightarrow P=21,600+210x-90x-x^2-5040+24x\\\Rightarrow P=-x^2+144x+16,560\\[/tex]
To get the maximum profit, determine the derivative of P w.r.t. x and equate it to zero
[tex]\Rightarrow \dfrac{dP}{dx}=-2x+144\\\\\Rightarrow -2x+144=0\\\\\Rightarrow x=72[/tex]
Charges for maximum profit is [tex]90+72=\$162[/tex]
Number of occupied rooms are [tex]210-72=138[/tex]
The hotel charge per day will be $162 in order to maximize daily profit.
Given that, Hotel has 210 units
Let us consider that x rooms are vacant.
Total occupied rooms = [tex](210-x)[/tex]
Since, Each occupied room costs $24 per day to service and maintain
So, Total expense = [tex]24*(210-x)=5040-24x[/tex]
Since, For all rooms are occupied when the hotel charges $90 per day for a room. For every increase of x dollars in the daily room rate, there are x rooms vacant.
So, Total earing = [tex](210-x)*(90+x)=-x^{2} +120x+21600[/tex]
Profit = Total earning - Total expense
[tex]P=-x^{2} +120x+21600-5040+24x\\\\P=-x^{2} +144x+16560[/tex]
In order to maximize profit, Differentiate profit expression with respect to x.
[tex]\frac{dP}{dx}=\frac{d}{dx}(-x^{2} +144x+16560) \\\\\frac{dP}{dx}=-2x+144=0\\\\\\x=\frac{144}{2}=72[/tex]
Thus, Hotel charges per day for maximum profit = [tex]90+x=90+72=162[/tex]
Learn more:
https://brainly.com/question/19578119
Which one is the intersection point of
f(x) = x3 + 3x and
g(x) = x2 + 3
A) (0,0)
B) (0,3)
C) (1,4)
D) (-1,4)
I URGENTLY NEED HELP PLEASE , I WOULD ALSO MARK AS BRAINLIEST!!
Answer: C) (1,4)
Step-by-step explanation:
The intersection point is where f(x) = g(x)
x³ + 3x = x² + 3
x³ - x² +3x - 3 = 0
A. (0, 0) → x = 0 → (0)³ - (0)² +3(0) - 3 = -3 ≠ 0B. (0, 3) → x = 0 → (0)³ - (0)² +3(0) - 3 = -3 ≠ 0C. (1, 4) → x = 1 → (1)³ - (1)² +3(1) - 3 = 0 + 0 = 0D. (-1, 4) → x = -1 → (-1)³ - (-1)² +3(-1) - 3 = 0 - 3 - 3 = -6 ≠ 0Verify that the function satisfies the three hypotheses of Rolle's Theorem on the given interval. Then find all numbers c that satisfy the conclusion of Rolle's Theorem. (Enter your answers as a comma-separated list.) F(x) = sin(x/2) , [π/2,3π/2]
Answer:
The numbers 3(pi)/2, 5(pi)/2 satisfy the conclusion of Rolle's Theorem
Step-by-step explanation:
1. The function must be continuous.
Trigonometric functions are continuous.
2. It must be true that f(a) = f(b) = 0
For this case sin(pi) = sin(3pi) = 0
3. Therefore by Rolle's Theorem, there exist a point, x, such that f(x) = 0
For this case f(x) = cos(x)
And cos(x) = 0 at x = 3(pi)/2,5(pi)/2
Question 5 plz show steps
Answer:
C
Step-by-step explanation:
If there is a maximum of 4,000 hours of labor available per month and 300 ping-pong balls (x1) or 125 wiffle balls (x2) can be produced per hour of labor, which of the following constraints reflects this situation?
a. 300x1 + 125x2 > = 4,000
b. 300x1 + 125x2 < = 4,000
c. 425(x1 + x2) < = 4,000
d. 300x1 + 125x2 = 4,000
Answer:
b. 300x1 + 125x2 < = 4,000
Step-by-step explanation:
Maximum of 4,000 hours
This means that the the total amount of labor has to be of at most 4,000, that is:
[tex]T \leq 4000[/tex]
300 ping-pong balls (x1) or 125 wiffle balls (x2) can be produced per hour of labor
The total amount of labor is:
[tex]T = 300x1 + 125x2[/tex]
Uniting the two equations:
[tex]T \leq 4000[/tex]
[tex]300x1 + 125x2 \leq 4000[/tex]
And thus the correct answer is given by option b.
what number increased by 130% is 69
Answer:
The number is 30.
Step-by-step explanation:
Let the number be x
so
x + (130% of x) = 69
x + 13x/10 = 69
or, (10x + 13x)/10 = 69
or, 23x = 690
or, x = 690/23
so, x = 30
Answer: 30
Step-by-step explanation:
its correct on rsm
guys help me I really need your help
Answer:
a x^2/2 is a polynomial because the power of x is 2 which is a positive whole number but 2/x^2 is not a polynomial because the power of x is -2 which is negative whole number.
b.in
[tex] \sqrt{2 x} [/tex]
the power if x will be
[tex]x {}^{ \frac{1}{2} } [/tex]
which is not a whole number so it is not a polynomial.
but in
[tex] \sqrt{2} x[/tex]
the power if x is a positive whole number.so it is a polynomial.
c.the greatest power of variable of the term is called degree of polynomial
Abigail buys two cartons of strawberries. One carton has 191919 berries and the other carton has 262626 berries. She wants to divide the berries into bags so there are exactly 666 berries in each bag.
How many bags will have 666 berries?
Answer:
682
Step-by-step explanation:
191,919 + 262,626
454545 ÷ 666 = 682.5
Thus meaning 682 bags will have 666 berries and one bag will have 333 berries.
Describe domain and range of the graph.
30 is what percent of 44?
Answer:
68.18
Step-by-step explanation:
→ Set up an equation
[tex]\frac{44x}{100} =30[/tex]
→ Times both sides by 100
44x = 3000
→ Divide both sides by 44
68.18
Given the following coordinates complete the glide reflection transformation.
A(−1,−3)
B(−4,−1)
C(−6,−4)
Transformation: Reflection over the x-axis and a translation of shifting right 10 units.
Given:
The vertices of a triangle are A(−1,−3) , B(−4,−1) and C(−6,−4).
Transformation: Reflection over the x-axis and a translation of shifting right 10 units.
To find:
The image after glide reflection transformation.
Solution:
The vertices of a triangle are A(−1,−3) , B(−4,−1) and C(−6,−4).
If a figure is reflected over the x-axis, then
[tex](x,y)\to (x,-y)[/tex]
Using this, we get
[tex]A(-1,-3)\to A'(-1,3)[/tex]
[tex]B(-4,-1)\to B'(-4,1)[/tex]
[tex]C(-6,-4)\to C'(-6,4)[/tex]
If a figure is shifting 10 units right, then
[tex](x,y)\to (x+10,y)[/tex]
Using this we get
[tex]A'(-1,3)\to A''(-1+10,3)[/tex]
[tex]A'(-1,3)\to A''(9,3)[/tex]
Similarly,
[tex]B'(-4,1)\to B''(-4+10,1)[/tex]
[tex]B'-4,1)\to B''(6,1)[/tex]
And,
[tex]C'(-6,-4)\to C''(-6+10,4)[/tex]
[tex]C'(-6,-4)\to C''(4,4)[/tex]
Therefore, the vertices of the image are A''(9,3), B''(6,1) and C''(4,4).
Does the function ƒ(x) = (1∕2) + 25 represent exponential growth, decay, or neither?
A) Exponential growth
B) Impossible to determine with the information given.
C) Neither
D) Exponential decay
Answer:
A) Exponential growth
Step-by-step explanation:
HELP! NO SCAMS PLZ, i need to know how to write the proportion.
Answer:
Terry misappropriately represented the ratio on the left-hand side. Instead of 16/4, he wrote 4/16.
4+z/y = 36/18
Step-by-step explanation:
a) Since both triangles are similar triangles, then the ratio of their similar sides is equal to a constant k. Therefore:
16/4 = 18/y
Note that the arrangement depends on which of the triangles sides cones first.
Terry misappropriately represented the ratio on the left-hand side. Instead of 16/4, he wrote 4/16.
b) Same rule in (a) applies to the sum as well. Hence;
4+z/y = 16+20/18
4+z/y = 36/18
15. On Sports Day, Mike runs 100 metres in 13.89 seconds and Neal runs the same distance in 13.01 seconds. Who is the FASTER runner?
Answer:
Neal
Step-by-step explanation:
13.01 < 13.89
Find the area of a circle with a radius of 6 ft. Round off your answer to one decimal point. (The formula for the area of a circle is A = ar?)
Answer:
Using 3.14 for pi A = 113.0 ft^2
Using the pi button A = 113.1 ft^2
Step-by-step explanation:
The area of a circle is given by
A = pi r^2
A = pi ( 6)^2
A = 36 pi
Using 3.14 for an approximation for pi
A = 36(3.14) = 113.04
To 1 decimal
113.0
Using the pi button
A = 113.0973355
A = 113.1
From the picture, two cylindrical glasses of the same capacity. Find the diameter length (X) of a small glass of water.
8
12
14
10
Answer:
12
Step-by-step explanation:
πr²h=πr²h
π(4.5)²*10=π(x/2)²4.9
