Answer:
1800
Step-by-step explanation:
c = 2a;
b = 2d;
c + 2d = a + 2b
2a + b = a + 2b
a = b
a = b
c = 2a
d = b/2
Assume a = 100.
b = 100
c = 200
d = 50
This cannot be, but we can continue.
Add them: 100 + 100 + 200 + 50 = 450
The total must be an even multiple of 450.
The total can be 900, 1800, 2700, etc.
Answer: 1800
La duración de las llamadas telefónicas de larga distancia realizadas desde una central telefónica tiene distribución normal con media de 130 segundos y desviación estándar de 30 segundos. Si en un día cualquiera se realizaron 500 llamadas telefónicas desde esta central, ¿cuál es la probabilidad que la duración total de estas llamadas supere las 18 horas? Considere independencia en la duración de las llamadas.
El valor de la probabilidad es: ______ (escriba su respuesta con tres decimales)
The probability that the total duration of the 500 calls is greater than 18 hours, using the normal distribution, is of:
0.618 = 61.8%.
Normal Probability DistributionThe z-score of a measure X of a variable that has mean symbolized by [tex]\mu[/tex] and standard deviation symbolized by [tex]\sigma[/tex] is obtained by the rule presented as follows:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score represents how many standard deviations the measure X is above or below the mean of the distribution, depending if the obtained z-score is positive or negative.Using the z-score table, the p-value associated with the calculated z-score is found, and it represents the percentile of the measure X in the distribution.By the Central Limit Theorem, for n instances of a normal variable, the mean is of [tex]\mu n[/tex] and the standard deviation is of [tex]\sigma\sqrt{500}[/tex]Hence, for the total duration of the 500 calls, in seconds, the mean and the standard deviation are given as follows:
[tex]\mu = 500 \times 130 = 65000, \sigma = 30\sqrt{500} = 670.82[/tex]
Each hour has 3600 seconds, hence the number of seconds in 18 hours is given as follows:
3600 x 18 = 64800.
The probability that the total time is greater than 18 hours is one subtracted by the p-value of Z when X = 64800, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
Z = (64800 - 65000)/670.82
Z = -0.3.
Z = -0.3 has a p-value of 0.382.
1 - 0.382 = 0.618 = 61.8% probability.
TranslationThe problem says that:
Telephone calls are normally distributed with mean of 130 seconds and standard deviation of 30 seconds.A sample of 500 calls is taken.The problem asks for the probability that the total duration of these calls is greater than 18 hours.Calls are independent.More can be learned about the normal distribution at https://brainly.com/question/25800303
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Sandra can knit 36 rows on a scarf in 18 minutes. How many rows can she knit in 25 minutes?
This calls for applying rates:
18 minutes = 36 rows
1 minute = 36/18 = 2 rows
25 minutes = 2 x 25 = 50 rows
The answer is 50 rows in 25 minutes. I hope this helps!
alpha beta square +alpha square beta quadratic equation
β=-α is the solution for alpha beta square +alpha square beta quadratic equation
What is quadratic equation?A quadratic equation is a second-order polynomial equation in a single variable x , ax2+bx+c=0. with a ≠ 0 .
alpha beta square +alpha square beta quadratic equation
αβ²+βα²
αβ(β+α)
αβ=0
and
β+α=0
β=-α
Hence β=-α is the solution for alpha beta square +alpha square beta quadratic equation
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Pleas help congruent, triangles, and classifying and solving for sides/angels
8. The value of x is 9.
9. The value of x is 6.
What are congruent triangles?Two triangles are congruent if all the corresponding sides and corresponding angle are equal.
8.
In the given triangle ∠A=(3x-4)°, ∠B=(13x+2)° and ∠C=(5x-7)°
The sum of all three angles of a triangle is 180°,
Implies that,
∠A+∠B+∠C=180°
3x-4+13x+2+5x-7=180
21x-9=180
21x=189
x=9
9.
In the given triangle, ∠A=(7x+1)°, ∠B=(19x-18)° and ∠C=(10x-9)°
The sum of all three angles of a triangle is 180°,
Implies that,
∠A+∠B+∠C=180°
7x+1+19x-18+10x-9=180
36x-26=180
36x=216
x=6
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Someone please help…
Answer:
(x-5),(y+2)
Step-by-step explanation:
The penguins at the zoo eat 2 5/8 pounds of fish each day. The zookeeper bought 5 1/4 pounds of fish. How many days will the fish last?
In Aurora’s candy box, of the candies are strawberry flavored and are chocolate flavored.
What is the fraction of strawberry and chocolate flavored candies that Aurora has in her box?
The fraction of strawberry and chocolate flavored candies that Aurora has in her box is 5/4
How to calculate the fraction?From the information illustrated, 30 of the candies are strawberry flavored and 24 are chocolate flavored.
Therefore, to get the fraction, we have to divide them. This will be illustrated as:
= Number of strawberry candies / Number of chocolate candies
= 30 / 24
= 5/4
The fraction is 5/4.
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Complete question
In Aurora’s candy box, 30 of the candies are strawberry flavored and 24 are chocolate flavored. What is the fraction of strawberry and chocolate flavored candies that Aurora has in her box?
Y is inversely proportional to the square of x. If Y = 5 when x = 3, then Y=1 4/5
, when x is.
[tex]\qquad \qquad \textit{inverse proportional variation} \\\\ \textit{\underline{y} varies inversely with \underline{x}} ~\hspace{6em} \stackrel{\textit{constant of variation}}{y=\cfrac{\stackrel{\downarrow }{k}}{x}~\hfill } \\\\ \textit{\underline{x} varies inversely with }\underline{z^5} ~\hspace{5.5em} \stackrel{\textit{constant of variation}}{x=\cfrac{\stackrel{\downarrow }{k}}{z^5}~\hfill } \\\\[-0.35em] ~\dotfill[/tex]
[tex]\stackrel{\textit{"y" varies inversely to }x^2}{y=\cfrac{k}{x^2}}\hspace{5em}\textit{we also know that} \begin{cases} y=5\\ x=3 \end{cases} \\\\\\ 5=\cfrac{k}{(3)^2}\implies 5=\cfrac{k}{9}\implies 45=k\hspace{5em}\boxed{y=\cfrac{45}{x^2}} \\\\\\ when~y=1\frac{4}{5}\textit{ what is "x"?}\implies 1\frac{4}{5}=\cfrac{45}{x^2}\implies \cfrac{9}{5}=\cfrac{45}{x^2} \implies 9x^2=(5)(45) \\\\\\ x^2=\cfrac{(5)(45)}{9}\implies x^2=25\implies x=\sqrt{25}\implies {\Large \begin{array}{llll} x=5 \end{array}}[/tex]
y= -x+8
y= 2x+5
solve the following systems..
Answer:
x = 1
y = 7
Step-by-step explanation:
y = -x + 8
-y= -2x - 5 (Switch the signs of y = 2x + 5)
0= - 3x + 3 (Subtract both equations)
3x = 3 (Add 3x on both sides)
x = 1 (Divide by 3 on both sides)
y = -1 + 8 (Plug x as 1 in the equation y = -x + 8)
y = 7 (Simplify)
Leading to the answer
x = 1
y = 7
(x³ + 2x² - 8x+6) ÷ (x² +9)
Answer:
this should help
Step-by-step explanation:
it is step by step on screenshots I have above
Complete the table representing a linear function.
Answer:
x y
1 0
2 10
5 40
10 90
Step-by-step explanation:
In a linear function, every time x is increased by 1, y is increased by a set amount. The only two complete rows in the table are when x = 1 and x = 5. x is increased four times in that interval while y has increased by 40(40 - 0). This means that every time x increases by 1, y increases by 10(40/4).
Therefore, when x is 2, y will be 10.
To get to ninety, 10 will needed to be added to 0(when x=1) 9 times. 1 + 9 is 10, so x = 10 when y = 90.
Answer:
Step-by-step explanation:
(1,0) (5,40)
Using these coordinates we find the line equation y=mx+b:
[tex]\displaystyle\\m=\frac{y_2-y_1}{x_2-x_1} \\\\x_1=1\ \ \ \ \ x_2=5\ \ \ \ \ y_1=0\ \ \ \ y_2=40\\\\m=\frac{40-0}{5-1} \\\\m=\frac{40}{4} \\\\m=10\\\\Thus,\ y=10x+b \ \ \ \ (1)\\[/tex]
We substitute the value of coordinate (1,0) into equation (1):
[tex]0=10(1)+b\\\\0=10+b\\\\-10=b\\\\Thus, \ b=-10\\\\Hence,\\\\ y=10x-10\\\\x=2\\\\y=10(2)-10\\\\y=20-10\\\\y=10\\\\Thus,(2,10)\\\\y=90\\\\90=10x-10\\\\100=10x[/tex]
Divide both parts of the equation by 10:
[tex]10=x\\\\Thus, (10,90)[/tex]
x | y
-----------------
1 | 0
------------------
2 | 10
------------------
5 | 40
------------------
10 | 90
Please help!
You are playing a game where you must spin a spinner that is numbered 1–8 on equal parts. What is the probability that you would get an odd number twice in a row?
25%
50%
12.5%
6.25%
The probability that your would get an odd number twice when the rolling is 1-8 is 12.5%
Probability is the chance of occurrence of an even (E) Over a period of time. That is, it is the extent to which an event is likely to occur, measured by the ratio of the favorable cases to the whole number of cases possible.
How to get the probability of the spinning?
From the analysis, the spinning is done twice from numbers 1-8
this means that in ever row, each number appears double.
The sample size is 8x8=64
1,1 1,2 1,3 1,4 1,5 1,6 1,7 1,8
2,1 2,2 2,3 2,4 2,5 2,6 2,7 2,8
3,1 3,2 3,3 3,4 3,5 3,6 3,7 3,8
4,1 4,2 4,3 4,4 4,5 4,6 4,7 4,8
5,1 5,2 5,3 5,4 5,5 5,6 5,7 5,8
6,1 6,2 6,3 6,4 6,5 6,6 6,7 6,8
7,1 7,2 7,3 7,4 7,5 7,6 7,7 , 7,8
8,1 8,2 8,3 ,,8,4 ,,, 8,5 ,,8,6 8,7,,, 8,8
The required outcome is 8
These outcomes are
1,1 2,2 3,3 4,4 5,5 6,6 7,7 8,8=8 outcomes
Probability of and event is
P=[tex]\frac{number of required outcome}{number of possible outcome}[/tex]
P(E)=[tex]\frac{8}{64}[/tex]
P(E)=[tex]\frac{1}{8}[/tex]
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Answer: 25%
Step-by-step explanation:
You have 4/8 chances of getting an odd number on the spinner, which equals 1/2, or 50%. Now if you are going to get another odd number, you have an additional 1/2 (half your chances) or 50% of a chance of getting it after you get the first odd number. This means you must mutliply these chances. 1/2x1/2 which is 1/4 = 25%
bala had 240 cards and tom had 780 cards. after tom gave some cards to bala, bala had twice as many cards as tom. how many cards did tom give to bala?
The answer is tom will give 440 cards to Bala, using arithmetic operation.
What is the arithmetic operation?
The four fundamental operations of arithmetic are addition, subtraction, multiplication, and division of two or more quantities. Included in them is the study of numbers, especially the order of operations, which is important for all other areas of mathematics, including algebra, data management, and geometry. The rules of arithmetic operations are required in order to answer the problem.
The total number of cards is 780+240 = 1020.
If in the end Bala will have twice as many cards as Tom then I would divide the 1020 by 3 which equals 340.
So Bala will have 2*340 = 680 cards
Tom will have 340 cards.
Now Bala will need (680-240) = 440 more cards.
Hence Tom will give 440 cards to Bala.
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what would the correct number line be for this compound inequality? 3x - 5 > or -2x _< -10
The correct number line that shows the solution to the compound inequality is given by:
Number Line A.
What is a compound inequality?A compound inequality is an inequality that is composed by multiple conditions.
Then these conditions are related with one of two operations, listed as follows:
and operation: the values need to respect all the conditions of the compound inequality.or operation: the values need to respect at least one of the conditions of the compound inequality.In this problem, the compound inequality is given as follows:
3x - 5 > 1 or -2x ≤ -10.
The solutions to the first condition are given as follows:
3x > 6
x > 2.
The solutions to the second condition are given as follows:
2x ≥ 10
x ≥ 5.
The interval of values that is the union of these solutions is given by:
x > 2.
Hence number line A is the solution to the inequality.
Missing InformationThe complete problem is given by the image shown at the end of the answer.
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4a² + 4ab-3b² = (2a+3b)(_)
Complete the factoring
Answer:
(2a + 3b)(2a - b)
Step-by-step explanation:
4a² + 4ab - 3b²
consider the factors of the product of the coefficient of a² and b² which sum to give the coefficient of the ab- term.
product = 4 × - 3 = - 12 and sum = 4
the factors are + 6 and - 2
use these factors to split the ab- term
= 4a² + 6ab - 2ab - 3b² ( factor the first/second and third/fourth terms )
= 2a(2a + 3b) - b(2a + 3b) ← factor out (2a + 3b) from each term
= (2a + 3b)(2a - b)
When the inequality. y> x + 1 is graphed, the shade is below the line and the line is dashed.
False
True
فے
The inequality y > x+1 graphed is false.
Given,
In the question:
When the inequality y > x +1 is graphed,
The shade is below the line and the line is dashed.
Check the above information is true or false.
Now, According to the question:
The inequality is given as:
y > x +1
The graph is:
∴The shade is below the line and the line is dashed
The answer is false.
Hence, The inequality y > x+1 graphed is false.
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The vaule of 5-a is 20 greather than the vaule of 6a-1
The value of a when the value of 5-a is 20 greater than the vaule of 6a-1 is -2.
What is an inequality?Inequalities are created through the connection of two expressions. It should be noted that the expressions in an inequality aren't always equal. Inequalities implies that the expressions are not equal. They are denoted by the symbols ≥ < > ≤.
Since the value of 5-a is 20 greater than the vaule of 6a-1. This will be:
5 - a > 6a - 1 + 20
Collect like terms
-a - 6a > - 1 + 20 - 5
-7a > 14
Divide
a > 14 / -7
a > -2
Therefore, a is greater than -2.
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6 eggs in 7 months Remember to write your answer with the unit rate per something. Round to the hundredths place if necessary. PLS HELP
The unit rate which correctly corresponds to.the given rate; 6 eggs in 7 months is; 0.86 eggs per month.
What is a unit rate?A unit rate as the name implies is one in which case a given quantity is expressed in terms of one unit of the other quantity.
Such units are expressed as; a per b.
On this note, since the given rate is; 6 eggs in 7 months.
It follows that the rate can be expressed as;
6 eggs / 7 months
= 6/7 eggs per month.
= 0.85714 eggs per month.
And ultimately, when rounded to the nearest hundredth; we have; 0.86 eggs per month.
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A square has a side length of 4x+1
What is the perimeter of the square and area of the square?
I’ll give points + brainalist
Answer:
16x+4
Step-by-step explanation:
Perimeter= side+side+side+side or 4(side)
Plug in side length
Perimeter= 4(4x+1)
Perimeter=16x+4
It can't be further simplified
The exponential model A=302.5e^0.0211 describes the population, A, of a country in millions, t years after 2003. Use the model to determine the population of the country in 2003.
The population of the country in 2003 is 302.5 million
How to determine the population of the country in 2003.From the question, we have the following parameters that can be used in our computation:
Exponential model, A = 302.5e^0.0211t
Where i is the number of years after 2003
In the year 2003, the value of t is 0
i.e. 0 years after 2003
So, we have
A = 302.5e^(0.0211 * 0)
Evaluate the products
A = 302.5 * 1
So, we have the following result
A = 302.5
Hence, the population is 302.5 million
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Griffin wants to go hiking, but the weather is not cooperating. Right now, there is 2 inches of snow on the ground and snow is falling at a rate of 0.25 in/hr. (a) Write the linear equation that represents the represents the total amount of snow, y, after x amount of hours. (b) How much snow will be on the ground after 4 hours? You must use your equation above to solve, and you must show all of your work. (c) If Griffin does not want to be hiking when there is 6 inches of snow on the ground, how long does he have to complete his hike? Do you think he will finish his hike in time? You must use your equation above to solve, and you must show all of your work.
a) The linear function is:
y = 2 + 0.25x.
b) The amount of snow on the ground after 4 hours will be of 3 inches.
c) The time that he has to complete the hike is of 16 hours, which is enough to finish the hike, as they don't take this long.
What is a linear function?The slope-intercept representation of a linear function is presented by the rule as follows:
y = mx + b
The coefficients of the function and their meaning are described as follows:
m is the slope of the function, representing the unit rate of change of the output y by the input x.b is the y-intercept of the function, which is the numeric value of the output y when the input x assumes a value of zero.In this problem, the values of these coefficients are given as follows:
b = 2, which is the initial amount of snow on the ground.m = 0.25, which is the hourly rate of snow.Hence the equation is:
y = 2 + 0.25x.
After four hours, the amount of snow on the ground will be of:
y = 2 + 0.25(4) = 2 + 1 = 3 inches.
The time until the amount reaches 6 inches is of:
2 + 0.25x = 6
0.25x = 4
x/4 = 4
x = 16 hours.
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(9t²-t-6)(9t² +9t - 1)
Help!
Answer:
we can't give an answer if there's not explanation of which "t" is
Need answers for these questions.
The future value of $8904.56 compounded semi annually is $13,468.95 The interest earned is approximately $4,564.39
The future value of $8904.56 compounded continuously is $66,185.90.
The interest earned is approximately $57,281.34.
What are the future values and the interests?When an investment is compounded semi annually, it means that both the amount that was invested and the interest that has already been earned increases in value twice in a year.
The formula for calculating future value:
FV = P (1 + r)^nm
Where:
FV = Future value P = Present value R = semi annual interest rate = annual interest rate / number of compounding = 6% / 2 = 3%m = number of compoundingN = number of yearsFV = 8904.56 x 1.03^(7 x 2) = $13,468.95
Interest = future value - amount invested
$13,468.95 - $8904.56 = $4,564.39
When an amount is compounded continusoly, it increases in value infinitely over the investment time horizon.
The formula for calculating future value when there is continuous compounding is : A x e^r x N
Where:
A= amount e = 2.7182818 N = number of years r = interest rateFV = 8904.56 x e^0.06 x 7 = $66,185.90
Interest = future value - amount invested
$66,185.90 - 8904.56 = $57,281.34
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solve for x in the simplest form
Answer:
x= 12/5
Step-by-step explanation:
Distribute the fraction and solve for x.
19. Barney divides a rectangle into fourths.
Show two ways he could do this. That’s the space or something in the picture
Answer:
slice it in the middle in the top and bottom or do it corner to corner.
Step-by-step explanation:
1. have 2 braincells
2. put them toghether and think.
The annual fundraising goal of a is $100,000. So far $46,088 has been raised. How much more money is needed to reach the goal? What???
If annual fundraising goal of a is $100,000 and so far $46,088 has been raised, then they have to raise $53912 to reach the goal
The goal of the annual fund raising = $100000
The raised amount = $46088
The amount of money needed to reach the goal = The goal of the annual fund raising - The raised amount
Here we have to use the subtraction
Substitute the values in the equation
The amount of money needed to reach the goal = 100000 - 46088
= $53912
Hence, if annual fundraising goal of a is $100,000 and so far $46,088 has been raised, then they have to raise $53912 to reach the goal
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Given: x-5> -10.
Choose the solution set.
The solution set. for the given inequality : x-5> -10. is (-5, ∞]
An inequality is a relationship that shows a non-equal comparison between two numbers or mathematical expressions.
We need to find the solution set for x-5> -10.
x - 5 > - 10
x > -10 + 5
x > -5
The solution set = (-5, ∞]
Therefore, the solution set. for the given inequality : x-5> -10. is (-5, ∞]
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Stanley thinks of a positive number, n, which is less than 1. He adds this number to its reciprocal and gets 2.05. Work out the value of n. Give your answer as a fraction in its simplest form.
The value of n is given by either 4/5 or 16/25.
Given that the positive number is n which is n<1.
Reciprocal of the number is = 1/n
Addition of the number and the reciprocal is 2.05.
So the suitable equation for this,
n + 1/n = 2.05
[tex]n^2+1=\frac{41}{20}n\\20n^2-41n+20=0\\n=\frac{41\pm\sqrt{1681-1600}}{40}=\frac{41\pm9}{40}=\frac{50}{40},\frac{32}{50}=\frac{4}{5},\frac{16}{25}[/tex]
So the number can be either 4/5 or 16/25.
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Based on the graph, how many distinct real number
solutions does the equation x³ + 6x² + 12x +8=0
have?
O no real number solutions
O one real number solution
O two real number solutions
O three real number solutions
Because the graph only intercepts the x-axis only once, the equation has only one solution. The correct option is the second one.
How many solutions the equation has?Here we want to see, based on a graph, how many solutions does the cubic equation:
x³ + 6x² + 12x +8 = 0
The graph of the function:
g(x) = x³ + 6x² + 12x +8
Can be seen below, the number of real solutions that the equation:
x³ + 6x² + 12x +8 = 0
has, will depend on how many times the graph intercepts the x-axis.
We can see that there is only one intercept, so there is one real solution.
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raise u to the 10th power, then double the result
u raised to the 10th power, then the result doubled gives 2u¹⁰
How to write an algebraic expression?An algebraic expression is an expression that is made up of variables and constants, along with algebraic operations like addition, subtraction, multiplication, exponent, etc.
Given: raise u to the 10th power, then double the result
Step 1: Raising u to the 10th power implies: u¹⁰
Step 2: Doubling the result means multiplying what you obtained in step 1 by 2, that is, 2 × u¹⁰ = 2u¹⁰
Therefore, raising u to the 10th power and then doubling the result gives 2u¹⁰
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