Una heladeria dispone de 20 frutas distintas para elaborar sus malteadas. Si los clientes pueden elegir tres sabores para mezclar, cuantas malteadas de tres sabores distintos puede elegir un cliente en esa heladeria
Answer:
Existen 6840 permitaciones de malteadas de tres sabores distintos que la heladería puede ofrecer.
Step-by-step explanation:
En este caso, el cliente que adquiere una malteada de tres sabores distintos sigue el siguiente procedimiento:
1) El primer sabor sale de cualquiera de las 20 frutas disponibles.
2) El segundo sabor es distinto al primer sabor, es decir, que sale de las 19 frutas restantes.
3) El tercer sabor es distinto al primer sabor y al segundo sabor, es decir, que sale de las 18 frutas restantes.
Puesto que existe una doble conjunción y que puede importar el orden según la preferencia del cliente, se habla matemáticamente de una permutación, definida como:
[tex]n\mathbb{P}k = \frac{n!}{(n-k)!}[/tex] (1)
Donde:
[tex]n[/tex] - Número de sabores disponibles, adimensional.
[tex]k[/tex] - Número de sabores escogidos, adimensional.
Si tenemos que [tex]n = 20[/tex] y [tex]k = 3[/tex], entonces la cantidad de malteadas de tres sabores distintos es:
[tex]n\mathbb{P}k = \frac{20!}{(20-3)!}[/tex]
[tex]n\mathbb{P}k = \frac{20!}{17!}[/tex]
[tex]n\mathbb{P}k = 20\cdot 19\cdot 18[/tex]
[tex]n\mathbb{P}k = 6840[/tex]
Existen 6840 permitaciones de malteadas de tres sabores distintos que la heladería puede ofrecer.
Two life insurance companies determine their premiums using different formulas:
Company A: p= 2a+24
Company B: p= 2.25a+13 where p represents the annual premium, and a represents the client's age. Use the graph to determine the age at which both companies charge the same premium.
Answer:
The age at which both companies charge the same premium is 44 years
Step-by-step explanation:
Graph Solution to System of Equations
One approach to solving systems of equations of two variables is the graph method.
Both equations are plotted in the same grid and we find the intersection point(s) of both graphs. Those are the feasible solutions.
The annual premium p as a function of the client's age a for two companies are given as:
Company A: p= 2a+24
Company B: p= 2.25a+13
The graphs of both functions are shown in the image below.
The red line indicates the formula for Company A and the blue line indicates the formula for Company B.
It can be seen that both lines intersect in the point with approximate coordinates of (44,112).
The age at which both companies charge the same premium is 44 years
Spending $1000 from a savings account paying 4 percent of interest a year means a opportunity cost of how much money a year?
A. $80
B. $40
C. $20
D. $10
-5x - 4x < -9 help me solve it
what is the scientific notation for 92100
Answer:
9.21*10^4
Step-by-step explanation:
Gabby rode her bike 6 miles in 40 minutes. Monica rode her bike 8 miles in 40 minutes. If both girls continue to ride at the same pace, how much further will Monica ride than Gabby at the end of two hours?
Step-by-step explanation:
Gabby will ride for 9 miles and Monica will ride for 12 miles
40×1.5=60 mins
6×1.5=9
8×1.5=12
Kate buys a wheelbarrow priced at $53. Shipping and handling are an additional 30% of the price. How much shipping and handling will Kate pay?
Answer:
$15.90
Step-by-step explanation:
30% of 53 is 15.90
Evaluate the expression
5−2−2+10
= -2
-6
14
2
22
It should be noted that the value of the expression 5 - 2 - 2 + 10 will be 11.
How to illustrate the information?Mathematical operators like addition, subtraction, multiplication, and division are used to create expressions in writing.
You must substitute a number for each variable and carry out the arithmetic operations in order to evaluate an algebraic expression.
For example, x + 6 = 12. Since 6 + 6 equals 12, the variable x in the example above is equal to 6. We can substitute the variables with their values and then evaluate the expression if we know the values of our variables.
Based on the information illustrated, it should be noted that the value of the expression 5 - 2 - 2 + 10 will be 11.
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Which pair of triangles below can be shown to be similar using AA similarity?
350
700
890
67°
7670
249
1640
490
750
820
630
54°
Triangle second and third can be shown to be similar using AA similarity when we take two angles between them.
What is similarity?
In Euclidean geometry, two objects are similar if they have the same shape, or one has the same shape as the mirror image of the other.
How to check similarity of triangle?
In second and third triangle two angles whose measures are 24 degrees and 67 degrees are in both triangles, which is the condition of AA similarity.
To check AA similarity we have to check whether two angles are equal in two triangles to be similar.
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what is the x-coordinate of R' ?
Answer:
3
Step-by-step explanation:
Answer:
12
The x-axis is the horizontal one. The full coordinate is (12, 0), which the x-coordinate (or x-intercept) is 12.
Is the point (4,2) the solution to the system? Why or why not? Explain your reasoning.
2x-y+6
x+y=6
please help me with this :D
Given the quadratic equation: f(x) = x2+4x-21
Identify a, b, and c from your original standard form equation.
a= _____ b= _____ c=_____
PLEASE HURRY
Answer:
f(x)= x²+4x-21
a= 1 b=4 c=-21
from [tex]y=ax^2+bx+c[/tex] and [tex]y=x^2+4x-21[/tex] | Compare the coefficients.
Thus the answer is a = 1, b = 4 and c = -21
The number positioned at point B is...
The payment to a clown for a children's party is directly proportional to the number of
children under 12 at the birthday party. The clown earns $140 at a party that has 10 children attending,
.
How much will the clown earn when 22 children under the age of 12 attend?
If the clown uses 46% of the money earned on his props for the party, and the rest is
profit. What is the profit if only 10 children under the age of 12 attend the party?
Answer:
Step-by-step explanation:
We know he earns $14 per child under 12
So he'll earn 22 times 14 which is $308 earned.
46% of 308 is basically 0.46 X 308=$141.68 spent on props.
He profits $166.32
If only 10 children attend.
He earns 10 times 14= $140
46% of these earnings is for props and 54% is profit so
0.54 X 140=$75.60.
Thus he profits $75.60 if 10 children attended.
The profit will amount to $75.60 when only 10 children under the age of 12 attend the party.
What is the percentage?The percentage is defined as a ratio expressed as a fraction of 100.
We are aware that he receives $14 for each child under the age of 12.
Thus, he will make $308 after multiplying 22 by 14.
In other words, 46% of 308 is 0.46 × 308 or $141.68 spent on props.
He earns $166.32.
If just 10 kids show up.
He makes $10 multiplied by 14 for a total of $140.
Props account for 46% of these revenues, while profits make up 54%, therefore
0.54 × 140=$75.60.
So, if 10 kids showed up, he makes $75.60.
Thus, the profit will amount to $75.60 when only 10 children under the age of 12 attend the party.
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1. Which of the equations below will answer the following question? Check (!) all that apply.
“I think of a number, add 7 and then multiply by 4.
My answer is 80. What was my number?”
1. ¿Cuál de las siguientes ecuaciones responderá a la siguiente pregunta? Marque todo lo que corresponda.
“Pienso en un número, le sumo 7 y luego lo multiplico por 4.
Mi respuesta es 80. ¿Cuál era mi número?”
The correct option is B. 4(x+7) = 80.
Adding 7 to the number then multiplying it with 4 given the result 80 is shown by the equation; 4(x+7) = 80.
What is defined as the mathematical operations?Calculating a value with operands as well as a math operator is referred to as a mathematical "operation." The math operator symbol has predefined rules that must be applied to a given operands and numbers.
Operands are the numbers that are used in an operation. The operands are given different names depending on the type of operation.An operator is a symbol that represents a mathematical operation, such as:+ for addition− for subtraction× for multiplication÷ for division = equal to denotes equivalence, indicating that left hand side value is equal to a right hand side value.Now as per the given question;
Let us assume that the given number is 'x'.
Adding 7 to this number will form; x + 7.
Now, multiplying the number resultant number with 4 gives; 4(x + 7)
Now the number formed is equal to the result 80.
Thus, 4(x + 7) = 80.
Therefore, the equation which correctly represents the given formation is 4(x + 7) = 80.
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The correct question is -
Which of the equations below will answer the following question? Select all that apply. Explain your answers.
I think of a number, add 7 and then multiply by 4. My answer is 80. What was my number?
A. x + 28 = 80
B. 4(x+7) = 80
C. 4x + 7 = 80
D. 4x + 28 = 80
What is the reciprocal of 1 3/4 ?
Answer:
4/7
Step-by-step explanation:
1 3/4 or 7/4
what is 9/10 - 2 3/4 i. the simplest form
−1.85 it says too short so ignore this ssssssndjbdbjddn
An arithmetic sequence has this recursive formula: a1=8 an=an-1-6 what is the explicit formula for this sequence
Answer:
D
Step-by-step explanation:
a p e x
The explicit rule of the sequence is (d) [tex]a_n = 8-6 (n -1)[/tex]
How to determine the explicit formula?The sequence is given as:
a1 = 8
[tex]a_n = a_{n-1} - 6[/tex]
Set n = 2
[tex]a_2 = a_{1} - 6[/tex]
This gives
a2 = 8 - 6
a2 = 2
Calculate the common difference (d)
d = a2 - a1
This gives
d = 2 - 8
Evaluate
a = -6
The explicit formula is then calculated as:
[tex]a_n = a_1 + (n -1)d[/tex]
This gives
[tex]a_n = 8-6 (n -1)[/tex]
Expand
[tex]a_n = 8-6n +6[/tex]
Evaluate the like terms
[tex]a_n = 14-6n[/tex]
Hence, the explicit rule of the sequence is (d) [tex]a_n = 8-6 (n -1)[/tex]
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A company offers a nut mixture with 4 peanuts for every 3 almonds. The company changes the mixture to have 8 peanuts for every 3 almonds, but the number of nuts per container does not change. How many nuts are in the smallest possible container?
Answer:
77 nuts
Step-by-step explanation:
From the above question:
We have ratio
Peanuts : Almonds
The original mixture is given as:
A company offers a nut mixture with 4 peanuts for every 3 almonds.
4 : 3
The sum of the proportion = 7
Hence, there are 7 nuts in the container
The new mixture
The company changes the mixture to have 8 peanuts for every 3 almonds,
8 : 3
Sum of the proportion = 11
We are told : the number of nuts per container does not change.
How many nuts are in the smallest possible container?
To solve this, we use the Lowest Common Multiple principle
We find the L. C. M of 7 and 11
Multiples of 7:
7, 14, 21, 28, 35, 42, 49, 56, 63, 70, 77, 84, 91
Multiples of 11:
11, 22, 33, 44, 55, 66, 77, 88, 99
Therefore,
LCM(7, 11) = 77
Therefore, the number of nuts in the smallest possible container is 77 nuts
When 4x2 + 7x - 5 is subtracted from 9x2 - 2x + 3, the result is
Create two different equations that have infinite solutions to the equations .
Answer:
1. x = y - 2
2. 2y = 2x
Step-by-step explanation:
1. Any number can fit x and y so long as x is 2 lesser than y and y is 2 more than x.
2. x and y can be any number so long as they are the same number.
I'LL GIVE BRAINLIEST TO WHOEVER ANSWERS THE QUESTION CORRECTLY!!!!
Answer:
Reason 3
Step-by-step explanation:
Reason 3 is supposed to be prove
The expression ( x − 12 ) is a factor of x 2 + p x − 48 . What is the value of p ?
Answer:
p = -8
Step-by-step explanation:
Since, (x - 12) is a factor, then;
x - 12 = 0
x = 12
substitute the value of x in the equation
[tex]x^{2}[/tex] + px - 48 = 0
[tex](12)^{2}[/tex] + 12p - 48 = 0
144 + 12p -48
12p = -144 + 48
12p = -96
p = -8
So that,
[tex]x^{2}[/tex] +-8x - 48 = 0
[tex]x^{2}[/tex] -12x + 4X- 48 = 0
([tex]x^{2}[/tex] -12x) + (4X- 48)
X(X - 12) + 4(X - 12)
(X - 12) (X + 4)
Therefore, p = -8 and (X - 12) (X + 4) are factors of the equation.
1/2(x − 2) = 4x − 9/2x − 4 What is the solution?
sorry . I had done it wrong
Jeremiah flies an airplane for 2.7 hours at an average speed of 304.6 miles per hour. How far did Jeremiah fly?
82.242 miles
822.42 miles
8,224.2 miles
82,242 miles
Answer:
b) 822.42
Step-by-step explanation:
Just multiply 2.7 by 304.6 and your answer would be 822.42
Answer:
answer is b
Step-by-step explanation:
Helpppppppppppppppp ill mark you brainlist write in y=mx+b form
Answer:
y=3x+2
Step-by-step explanation:
Answer:
y=3x+2
Step-by-step explanation:
facts: slope is m, and b is y-intercept
y=3x+2
hope this helps!
Plzzzzzzzz help me.
Last winter in the northeast the temperature was 5degrees Fahrenheit at midnight. It dropped 3 degrees every hour for 3hours and then rose 8 degrees every hour after that. What was the temperature at noon?
Answer:
68 [tex]^\circ F[/tex]
Step-by-step explanation:
Initial temperature in the northeast in the midnight = 5 [tex]^\circ F[/tex]
Drop for the next three hours = 3 degrees per hour.
Temperature after the 3 hours = 5 [tex]^\circ F[/tex] - 3 - 3 - 3 = - 4[tex]^\circ F[/tex]
Now, it is given that the temperature is rising 8[tex]^\circ F[/tex] every hour.
3 hours have already passed from the midnight.
Now, there are 9 more hours till noon.
So, the temperature at noon can be found by adding 8 for 9 times in the temperature after 3 hours.
Temperature at noon = - 4 + 8 + 8 .... 9 times
Temperature at noon = - 4 + 9 [tex]\times[/tex] 8 = -4 +72 = 68[tex]^\circ F[/tex]
Therefore, the answer is: 68[tex]^\circ F[/tex]
Juan collected 7,006 sports cards throughout his life. He gave 5,479 sports cards to his friends and a charity. How many sports cards did he keep?
OA 2,473
B.
2.527
OC. 1427
oD. 1527 help sos
Answer:1533
Step-by-step explanation:
7006-5,479=1533
Rick will participate in a walk-thon to raise money for charity. The amount he will raise based on the number of miles he walks is shown in the table, which represents a linear function
Which of these statements are correct? Select all that apply.
Answer: B and E
Step-by-step explanation:
Answer:
b and e
Step-by-step explanation: