In exercise 1:
Situation: The account holder saves $30 each month
The first three terms of the sequence are: $120, $150, $180.
In exercise 2:
Situation: The account earns 25% interest each month.
The first three terms of the sequence are: $120, $150, $187.50.
What is a sequence?A sequence in mathematics is described as an enumerated collection of objects in which repetitions are allowed and order matters.
Explaining exercise 1:
In this exercise, the account balance for each month should form an arithmetic sequence with a common difference of $30
February 1 balance: $150
March 1 balance: $180
Hence, we have the first three terms of the sequence as: $120, $150, $180.
Explaining exercise 2:
In this exercise, the account balance for each month should form a geometric sequence with a common ratio of 1.25.
The account earns 25% interest each month is the situation here.
February 1 balance: $150
March 1 balance: $187.50
The first three terms of the sequence are: $120, $150, $187.50.
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Prove the following,in a semigroup:
By induction, we can conclude that in a semigroup, all products of x1, x2, ...... xn (in that order) are equal.
What is semigroup?A semigroup is a mathematical structure consisting of a set of elements along with an associative binary operation. The operation must be associative, meaning that the result of the operation is independent of the order of the operands.
We can prove this by induction. Let S be a semigroup and x1, x2, x3, ..., xn be the elements of S.
Base Case: When n = 2, then the product of x1 and x2 is x1x2.
Inductive Step: Assume that the product of x1, x2, ..., xn (in that order) is equal. Then we can prove that the product of x1, x2, ..., xn+1 (in that order) is also equal.
Let a be the product of x1, x2, ..., xn (in that order). Then a = x1x2x3....xn.
Now the product of x1, x2, ..., xn+1 (in that order) is a x xn+1. Since S is a semigroup, a x xn+1 = x1x2x3....xn x xn+1.
Since the product of x1, x2, ..., xn (in that order) is equal, a = x1x2x3....xn. Therefore, the product of x1, x2, ..., xn+1 (in that order) is also equal.
By induction, we can conclude that in a semigroup, all products of x1, x2, ...... xn (in that order) are equal.
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1. Write down the first five multiples of:
a) 3
b) 9
c) 14
Answer:
a)3,6,9,12,15
b)9,18,27,36,45
c)14,28,42,56,70
Step-by-step explanation:
multiply each of it with 1,2,3,4 and 5 :)
Answer:
3-3,6,9,12,15
9-9,18,27,36.45
14-14,28,42,56.70
which equation has an infinite number of solutions?
The equation 8(x-9)=6(2x-12)-4x (option C) has an infinite number of solutions.
How to check for infinite number of solutions?Let's simplify the given equation and solve for x:
8(x-9) = 6(2x-12) - 4x
8x - 72 = 12x - 72 - 4x // Distributing 6
8x - 72 = 8x - 72 // Simplifying
We can see that both sides of the equation are equal, and there is no variable 'x' present. This means that the equation is an identity and it will hold true for any value of x.
Therefore, this equation has an infinite number of solutions, since any value of x will satisfy the equation.
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*THESE ARE 4 SIMPLE GEOMETRY QUESTIONS!!*
Hello please help! I dont know a single thing about geometry and i need your help!
Very appreciated!
1. B.
2. C.
3. A.
4. C.
if 8 cookies are shared between 4 people how many cookies would each person get
2
you divide 8 with 4 and the answer is 2
Please I need assistance please help
The length of the diagonal of the television screen is equal to 56 cm to the nearest centimeter using the Pythagoras rule.
What is the Pythagoras rule?The Pythagoras rule states that in a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
we shall represent the length of the diagonal with the letter x so by Pythagoras rule we can write:
x² = 34² + 45²
x² = 1156 + 2025
x² = 3181
x = √3181 {take square root of both sides}
x = 56.4004
Therefore, the length of the diagonal of the television screen is equal to 56 cm to the nearest centimeter using the Pythagoras rule.
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Which of the following represent dividing 72 by 6?
a. 72 ÷ 6
b. 7/2
c. 6÷72
d. 7/2
a and d
a and c
b and c
Cb and d
Answer:
Step-by-step explanation:
The answer to your question is a.
Write an equation of the line that passes through a pair of points:
ú
T
-3 -2 -1
a.
y=x+3
b. y=x-3
5.
4+
3+
2+
1+
7
-1
-2+
-3
4
1 2,
3
5 X
c.
d.
y = -x + 2
y = -x-2
The equation of the given line is expressed as:
y = x - 3
What is the equation of the line?The formula for the equation of a line in slope intercept form is:
y = mx + c
where:
m is slope
c is y-intercept
The formula for the equation of a line between two coordinates is:
(y - y1)/(x - x1) = (y2 - y1)/(x2 - x1)
The pair of coordinate points marked are:
(4, 1) and (5, 2)
Thus, the equation of the line is:
(y - 1)/(x - 4) = (2 - 1)/(5 - 4)
y - 1 = x - 4
y = x - 3
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Help please! I need help with my hw!
The area of the shaded portion in the image of right triangle attached is solved to be 401.85 square millimeters
How to find the area of the shaded portionThe area of the shaded portion is solved by subtracting the area of the smaller triangle from the area of the bigger triangle
The area of a triangle is solved using the formula
= 0.5 base * height
Information given in the problem
base1 = 24.8
base2 = 15.9
height1 = 34.2 mm
height2 = 21.9
where
base1 and height1 are for the bigger triangle while
base2 and height2 is for smaller triangle
area of shaded portion = 0.5(24.8 * 34.2) - 0.5(15.9 * 21.9)
area of shaded portion = 418.95 - 174.105
area of shaded portion =401.845
area of shaded portion = 401.85 square millimeters
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How to write 0.03 + 8 + 0.2 + 50 in word form
Answer:
Fifty eight and twenty-three hundredths
Step-by-step explanation:
A smart tablet manufacturer test 1 out of every 25screens for flaws out of 125 tablets tested 2 had defective screens how many defective screens should the manufacturer expect out of 45000 smart tablets
Answer:
720
Explanation:
[tex]2:125[/tex]
[tex]x:45000[/tex]
to go from 125 to 45000 we need to multiply by 360
that's why we will multiply 2 with 360 to balance both ratios
when we do that we get 720
2:125
[tex]\bold{720:45000}[/tex]
Answer:
720
Step-by-step explanation:
Given the function of(x) = 2√x +√x³, find f'(3). Express your answer as a
single fraction in simplest radical form.
Answer:
Here is the answer for the following question:
probability problem algebra 2 please help
The probability that the alumni member is male and did not attend graduate school is (546-206)/1214, or 83.09%.
What is probability?Probability is a measure of how likely an event is to happen. It is expressed as a number between 0 and 1, where 0 means that the event is impossible and 1 means that the event is certain. Probability is used to describe the likelihood of something happening and to make decisions when dealing with uncertain situations. Probability theory is the mathematics of predicting the outcomes of events when the exact outcome is unknown.
In conclusion, the probability that the alumni member is female is 8.55%, that the alumni member is male is 16.91%, that the alumni member is female and went on to graduate school is 8.55%, that the alumni member is male and went on to graduate school is 16.91%, that the alumni member is female and did not attend graduate school is 79.60%, and that the alumni member is male and did not attend graduate school is 83.09%.
The probability that the alumni member is female is 104/1214, or 8.55%. The probability that the alumni member is male is 206/1214, or 16.91%. The probability that the alumni member is female and went on to graduate school is 104/1214, or 8.55%. The probability that the alumni member is male and went on to graduate school is 206/1214, or 16.91%. Finally, the probability that the alumni member is female and did not attend graduate school is (668-104)/1214, or 79.60%.
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Tina used 10 1/2 yards of yarn to make three yarn dolls. She used 3 1/2 yards of yarn for the first doll and 4 1/8yards for the second doll. How much yarn did Tina use for the third doll?
Answer:
To find how much yarn Tina used for the third doll, we can subtract the total amount of yarn used for the first two dolls from the total amount of yarn used.
Total amount of yarn used = 10 1/2 yards
Amount used for first doll = 3 1/2 yards
Amount used for second doll = 4 1/8 yards
To add 3 1/2 and 4 1/8, we need to find a common denominator:
3 1/2 = 7/2
4 1/8 = 33/8
Common denominator = 8
So, 3 1/2 = 28/8 and 4 1/8 = 33/8
Total amount used for first two dolls = 28/8 + 33/8 = 61/8
Subtracting the total amount used for the first two dolls from the total amount of yarn used:
10 1/2 - 61/8 = 84/8 - 61/8 = 23/8
Therefore, Tina used 23/8 yards of yarn for the third doll.
Below is the relative-frequency table of the probability distribution for the discrete random variable X, with X = "the number of cars owned by families in New York."
x P(X = x)
0 0.03
1 0.31
2 0.43
3 0.14
4 0.09
If the expected value is 1.95, what is the standard deviation?
0.93
0.99
0.96
Answer: To calculate the standard deviation of a discrete random variable, we need to know the expected value and the variance. The variance of a discrete random variable X is given by:
Var(X) = Σ [ (x - E(X))^2 * P(X = x) ]
where the summation is taken over all possible values of X, and E(X) is the expected value of X.
We are given that the expected value of X is 1.95. Using the formula for the variance and the probabilities given in the table, we can calculate the variance as follows:
Var(X) = (0 - 1.95)^2 * 0.03 + (1 - 1.95)^2 * 0.31 + (2 - 1.95)^2 * 0.43 + (3 - 1.95)^2 * 0.14 + (4 - 1.95)^2 * 0.09
Var(X) = 1.1429
To find the standard deviation, we take the square root of the variance:
SD(X) = sqrt(Var(X))
SD(X) = sqrt(1.1429)
SD(X) ≈ 1.07
Therefore, the standard deviation of the number of cars owned by families in New York is approximately 1.07. None of the options given match this value exactly, but 0.99 is the closest.
Step-by-step explanation:
Which statement is in-correct
The statement "The Poisson distribution is always skewed right" is incorrect. Option A
What is Poisson distribution?The Poisson distribution is a discrete probability distribution that is used to model the probability of a given number of events occurring in a fixed interval of time or space, assuming that the events occur independently and at a constant rate.
The key features of the Poisson distribution include:
The distribution is discrete, meaning that it only takes on integer values.The distribution is defined by a single parameter, lambda (λ), which represents the expected number of events that will occur in the interval.The distribution is skewed right, with a long tail on the right-hand side.The mean and variance of the distribution are both equal to λ.The statement "The Poisson distribution is always skewed right" is incorrect.
The Poisson distribution can be skewed left, right, or approximately symmetric depending on the value of its parameter lambda. If lambda is small, the distribution will be skewed right. If lambda is large, the distribution will be approximately symmetric.
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|a-b|-|c+d| if a=-5, b=4. c=1, d=-3
please help soon!
Answer:-7
Step-by-step explanation:
|-5 - 4| = -9
|1 + -3|= -2
|-9 - -2| = -7
Answer:
Step-by-step explanation:
[tex]|a-b|-|c+d|=|-5-4|-|1+(-3)|=|-9|-|-2|=9-2=7[/tex]
Absolute value is just the distance from 0 and therefore is always positive.
Match the name of the sampling method descriptions given.
Situations:
1. ask all the students in your math class
2. choosing every 5th person on a list
3. pulling 50 names from a hat
4. randomly select two tables in the cafeteria and survey all the people at those two tables
5. dividing the population by Gender, and choosing 30 people of each gender
Sampling Method:
a. Simple Random
b. Convenience
c. Cluster
d. Systematic
e. Stratified
Enquire οf each pupil in yοur math class. --> b. Cοnvenience
chοοsing every 5th persοn οn a list --> d. Systematic
pulling 50 names frοm a hat --> a. Simple Randοm
Chοοse twο cafeteria tables at randοm, then pοll every patrοn at thοse twο tables. --> e. Stratified
selecting 30 individuals frοm each gender after dividing the pοpulatiοn intο genders. --> c. Cluster
What is the sampling methοd?Samples can be categοrized intο:
Cοnvenient: Sample taken frοm a pοοl that is easily accessible.
Put all the pοssibilities intο a hat, and draw sοme οf them at randοm.
Every kth cοmpοnent is taken in a systematic manner. If yοu wanted tο survey anything οn the street, fοr instance, yοu may interview every fifth persοn.
Cluster: This pοpulatiοn is brοken dοwn intο grοups, οr clusters, and each cluster's cοnstituents are surveyed.
Further divides the peοple intο several grοups. After that, thοugh, just a small percentage οf the grοup gets quizzed.
Thus, cοrrect match οf the sampling methοd are:
enquire οf each pupil in yοur math class. --> b. Cοnvenience
chοοsing every 5th persοn οn a list --> d. Systematic
pulling 50 names frοm a hat --> a. Simple Randοm
Chοοse twο cafeteria tables at randοm, then pοll every patrοn at thοse twο tables. --> e. Stratified
selecting 30 individuals frοm each gender after dividing the pοpulatiοn intο genders. --> c. Cluster
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The diameter of a circle is 33 cm. Find its area to the nearest whole number.
Answer:
Step-by-step explanation:
The answer is not 855.3^2cm
A standardized exam's scores are normally distributed. In a recent year, the mean test score was 1534 and the standard deviation was 310. The test scores of four students selected at random are 1940, 1280, 2260, and 1420. Find the z-scores that correspond to each value and determine whether any of the values are unusual.
The first student Z-score= 1.31, the second student= -0.82, the third student = 2.35, the fourth student = -0.37. None of these scores are unusual.
Describe Z-score?In statistics, a Z-score (also known as a standard score) is a measure of how many standard deviations a data point is from the mean of a population or sample. The Z-score is calculated by subtracting the mean from the data point and then dividing by the standard deviation.
A Z-score of 0 indicates that the data point is equal to the mean, while positive Z-scores indicate that the data point is above the mean and negative Z-scores indicate that the data point is below the mean.
Z-scores are often used in statistics to standardize data so that it can be compared across different populations or samples. Z-scores can also be used to identify outliers, which are data points that are unusually far from the mean and may skew the analysis of the data.
To find the z-score for each student, we use the formula:
z = (x - μ) / σ
where x is the student's score, μ is the mean test score, and σ is the standard deviation.
For the first student with a score of 1940:
z = (1940 - 1534) / 310
z = 1.31
For the second student with a score of 1280:
z = (1280 - 1534) / 310
z = -0.82
For the third student with a score of 2260:
z = (2260 - 1534) / 310
z = 2.35
For the fourth student with a score of 1420:
z = (1420 - 1534) / 310
z = -0.37
To determine if any of these values are unusual, we can use the rule of thumb that considers any z-score greater than 3 or less than -3 to be unusual.
None of the z-scores calculated above are greater than 3 or less than -3, so we can conclude that none of these scores are unusual.
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To use the method of triangulation you need measurement from at least three locations
The given statement is false. The solution has been obtained by using the concept of triangulation.
What is triangulation?
Based on the principles of trigonometry, triangulation is a technique used to locate a fixed point. According to these principles, it is possible to compute the other two sides and angle of a triangle if just one side and two angles of the triangle are known.
We are given a statement that to use the method of triangulation you need measurement from at least three locations.
The statement is false because for this, we need only two points.
Hence, the given statement is false.
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Question: To use the method of triangulation, you need measurements from at least three other locations.
A.True
B.False
Cuantos minutos tardará en llenarse un depósito de 10.080 litros de capacidad si recibe agua por 3 grifos diferentes que arrojan 60 litros, 70 litros, 80 litros cada minuto?
Answer:
El tanque tardará aproximadamente 48 minutos en llenarse.
Step-by-step explanation:
Podemos encontrar la tasa de llenado del depósito sumando las tasas de flujo de los tres grifos:
Tasa de llenado = 60 + 70 + 80 = 210 litros/minuto
Luego, podemos usar la fórmula:
Tiempo = Volumen / Tasa de llenado
Donde el volumen es 10.080 litros y la tasa de llenado es 210 litros/minuto. Sustituyendo estos valores, obtenemos:
Tiempo = 10.080 / 210 ≈ 48 minutos
Por lo tanto, tardará alrededor de 48 minutos en llenarse el depósito de capacidad 10.080 litros si recibe agua por tres grifos diferentes que arrojan 60 litros, 70 litros, 80 litros cada minuto.
¡Espero que esto ayude! Lo siento si no es así. ¡Si necesitas más ayuda, pregúntame! :]
Which two consecutive numbers that this number comes between? 2 3/10 + 4 1/2
Two consecutive number between [tex]2 \frac{3}{10}[/tex] and [tex]4 \frac{1}{2}$[/tex] are 3 and 4.
What is a Composite Number?Composite number are those number which follow a particular sequence whether it is normal, even, odd or any other sequence. AP) is the best method to identify whether the number are consecutive or not.
So here, we can write as [tex]\frac{23}{10}=2.3[/t[/tex] ex] and we can write [tex]\frac{1}{2}[/tex] as [tex]frac| {9}{2}=4.5[/tex]
So, two composite number are 3 and 4.
Arithmetic Progression, (AP) A sequence can called in as AP when the difference between them are common which means the each previous is differ from its preceding one by a constant quantity.
[tex]a_n=a_1+(n-1) * d[/tex] where, [tex]a_1=[/tex] first termed= common difference [tex]a_n=[/tex] term in the sequence
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determine the total amount of money that was utilized on fuel in june 2022.
The Consumer Price Index (CPI) for All Urban Consumers grew by 9.1%. The all items index rose 9.1%, the largest annual increase since the year that ended in November 1981.
What is Consumer Price Index?A consumer price index can be defined as a measure of a market basket of goods and services that households have purchased at a weighted average price. The measured CPI fluctuates(differs) to reflect changes in prices over time.
The CPI is one of the most widely(popularly) used indicators of inflation and deflation.
[tex]Annual\ CPI = \frac{Value\ of Basket\ in \ Current \Year}{Value\ of Basket\ in \ Prior\ Year} *100[/tex]
[tex]Inflation\ Rate = \frac{New \ CPI - Prior\ CPI}{Prior\ CPI} *100[/tex]
It is one of the most used methods for measuring inflation and reveals the state and trajectory of the economy.
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HURRY I WILL GIVE BRAINLIEST TO WHO ANSWERS FIRST
Raymond was riding a zip-cable from the top of a viewing post. The cable is 55 yards long. The viewing post is 44 yards high and forms a right angle with the ground, as shown in the picture below.
Given this information, how far is the bottom of the cable from the base of the viewing post?
Answer: i am pretty sure it is 33
Step-by-step explanation:
determine the length of a plot of land 16 m wide and whose area is 336 m².
Answer:
21
Step-by-step explanation:
The equation to find the area of a space is length x width. Divide the total area by the width to find the length.
1
A number x is multiplied by 4, and 2
is added to it; the result is less than 82.
Find the range of values of x.
Based on the given statement, the range of values of x is the values that do not exceed 82
How to determine the range of values of x.From the question, we have the following parameters that can be used in our computation:
A number x is multiplied by 4, and 2 is added to it; the result is less than 82.Using the above as a guide, we have the following:
The output of the operation cannot exceed 82
The range is teh set of the output values
This means that the range is all set of real values less than or equal to 82
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Answer:
Step-by-step explanation
Kids under 16 must be accompanied by an adult. Which inequality describes the age, a, of a kid accompanied?
Group of answer choices
x ≤ 16
x < 16
x > 16
x ≥ 16
Answer:
x < 16
Step-by-step explanation:
What is -2, 3 reflected over the y- axis?????
I NEED THE ANSWER ASAP
Answer:
2, 3
Step-by-step explanation:
When a point is reflected over the y-axis, the x-coordinate changes sign while the y-coordinate remains the same. Therefore, if you reflect the point (-2, 3) over the y-axis, it will become (2, 3).
(Sorry, I tried to provide a picture but I could not.)
A triangle has the measures of two of its interior angles 48° and 65°, the third interior angle is unknown. What is the value of the exterior angle corresponding to the interior angle whose value is unknown?
a) 123°
b) 131°
c) 113°
d) 128°
e) 118°
Answer:
c) 113°
Step-by-step explanation:
Exterior angle is equal to the sum or the "remote" interior angles, that is the two angles that are not just next to the exterior angle. See image.
So the answer, quickly:
exterior angle
= 65° + 48°
= 113°
This is why:
(skip if you don't care)
The three angles in a triangle add up to 180° But also, a linear pair of angles also add up to 180°
So
x + 65° + 48° = 180°
x + y = 180°
y = 65° + 48°
See image.