Recursive form of sequence is given by f(n) = f(n-1) - 3
What is function?
Function, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable.
here, we have,
The explicit form of sequence is given as
f(n) = −3n + 2
So nth term is given by
f(n) = −3n + 2
(n-1)th term is given by
f(n-1) = −3(n-1) + 2
We have
f(n) - f(n-1) = −3n + 2 - (−3(n-1) + 2)
f(n) - f(n-1) = −3n + 2 +3(n-1) - 2
f(n) - f(n-1) = −3n + 2 +3n -3 - 2
f(n) - f(n-1) = -3
f(n) = f(n-1) - 3
Recursive form of sequence is given by f(n) = f(n-1) - 3
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b) The sum of the age of two sisters is 20 years. If one of them is 4 years younger than other, find their age.
Step-by-step explanation:
is mentioned above.. If you get some knowledge or liked it.please rate the answer
Please help!!!!!!!!!!!
Answer:
A
Step-by-step explanation:
P = 4 pi I r^2 solve for I Divide both sides by 4 pi r^2
to get
I = P / (4 pi r^2)
Are zeros at the end of a number significant if the number contains a decimal point?
The zeros at the end of a number can be significant if it contains decimal point only if the digit next to or at the end of the number (of decimal point) is a significant number.
Significant numbers of a given number are those digits that can convey the meaning of the number or what it stands for (measures as) according to its accuracy.
All non-zero numbers are significant numbers irrespective of the fact where they are positioned, that is they can be positioned before or after a decimal (also before or after a zero).
All zeros are not significant numbers and whetehr they are to be called significant numbers or depend on the fact where they are positioned and whether they convey any meaning (or value ) of the number. If the zeros are between two non zero significant digits then zero is also considered as a significant number.
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HELPPP PLEASEEE
what is the slope of the line that contains the points ( -3 -7/2) and (2,-4)?
Answer:
-1/10
Step-by-step explanation:
Slope:[tex]\sf (-3 , \frac{-7}{2}) \ ; \ x_1 = -3 ; \ ; y_1=\frac{-7}{2}[/tex]
[tex]\sf (2 , -4) ; \ x_2 = 2 \ ; \ y_2 = -4[/tex]
[tex]\sf \boxed{slope = \dfrac{y_2-y_1}{x_2-x_1}}[/tex]
[tex]= \dfrac{-4-[-\frac{7}{2}]}{2-[-3]}\\\\\\= \dfrac{-4+ \frac{7}{2}}{2+3}\\\\[/tex]
[tex]\sf = \dfrac{ \frac{-4*2}{1*2}+ \frac{7}{2}}{5}\\\\\\= \dfrac{ \frac{-8+7}{2}}{5}\\\\\\= \dfrac{ \dfrac{-1}{2}}{5}\\\\= \dfrac{-1}{2*5}\\\\\\= \dfrac{-1}{10}[/tex]
Question 4(Multiple Choice Worth 2 points)
(Effects of Changes in Data MC)
The average high temperatures in degrees for a city are listed.
58, 61, 71, 77, 91, 100, 105, 102, 95, 82, 66, 57
help fast
If a value of 50° is added to the data, how does the median change?
The median decreases to 77°.
The median decreases to 65.2°.
The median stays at 82°.
The median stays at 79.5°.
Answer: I'm no expert but i would have to say the median would decrease to 77 degrees
Step-by-step explanation: The median is not going to stay the same when you have a lot of high numbers and with a bunch of high numbers the median is going to be close to 77 degrees than to 65.2 degrees
Find the surface area of the curved surfaces
Answer:
155.744
Step-by-step explanation:
What is the volume area of a cylinder with base radius 2 and height 6?
Answer:
75.4
Step-by-step explanation:
Volume of cylinder=πr2h
=π·22·6≈75.39822
are all isosceles triangles similar
Answer:
Step-by-step explanation:
isosceles triangles are all similar in that they have 2 sides that are equal.
however, the angles can differ and so they are not all similar in that term
Three times a number is 14.1.
Choose the equation that represents the statement and the value of a that makes the statement true.
OA. 2-3=14.1;z = 17.1
OB. +3=14.1;z = 11.1
OC. 3r = 14.1;z = 4.7
OD. = 3;x=42.3
Answer:
option C
Step-by-step explanation:
let 'r' equal 'a number'
let 'is' mean 'equals'
3r = 14.1
I need some help on this question please, thank you.
Answer:
37cm^2
Step-by-step explanation:
Area of rectangle = Length × Width
This shape needs to be split then you simply work out the area of each shape and add it.
Shape 1: 3cm × 5cm = 15cm^2
Shape 2: 2cm × 11cm = 22cm^2
Now add them together: 15cm^2 + 22cm^2 = 37cm^2
when we talk about measures of center, we look to the shape of the distribution to decide whether to use the mean or median. when do you think we should use the mean? (pick all that apply)
When the distribution is essentially symmetric or bell-shaped, with no extreme outliers, the mean is a useful measure of the center to employ. This is so because the mean can be impacted by extreme values, which can drive it away from the distribution's center, and is sensitive to the values of all the observations in the data set.
What is mean?In statistics, in addition to the mode and median, the mean is one of the measures of central tendency. Simply put, the mean is the average of the values in the given set. It indicates that values in a particular data set are distributed equally. The three most frequently used measures of central tendency are the mean, median, and mode. Assuming that the data is regularly distributed and that the mean is a suitable measure of center, the mean is often chosen when doing specific statistical procedures, such as linear regression and hypothesis testing.
The median, however, might be a better indicator of the center to utilize if the distribution is skewed or contains severe outliers. In these situations, the median better captures the distribution's midpoint and is less vulnerable to high extremes.
Which center measure to choose ultimately comes down to the specifics of the data collection and the objectives of the investigation.
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Which type of triangle can be constructed with a 50° angle between two 8-inch sides? A. Equilateral B. Isosceles C. Scalene D. Obtuse.
The correct option is (C) Isosceles. An Isosceles triangle can be constructed with a 50° angle between two 8-inch sides.
This is because isosceles triangle having two sides that are equal in length, and have 50° angle, which is acute angle, that is less than 90°. This state that the remaining angle in the triangle must also be acute triangle, as the sum of all angles in a triangle must equal 180°.
This means that the remaining angle must be 80° (i.e. 180 - 50 = 80). An isosceles triangle is triangle consisting of two sides of equal length and two angles of equal measure. The two equal sides that make up the isosceles triangle are referred to as the base and the remaining side is height or altitude.
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what is 120 kilos in pounds
The required value of 120 kilos which is same as 120 kilograms is equal to ( 264.55 ) pounds ( round up to two decimals ) .
Kilos is short form of kilogram.Kilograms and pounds both are the standard units of mass.
One kilogram = 2.20462 pounds
We need to convert 120 kilograms into pounds :
⇒ 120 kilograms = ( 120 × 2.20462 ) pounds
⇒ 120 kilograms = ( 264.5544 ) pounds
⇒ 120kilograms = ( 264.55 ) pounds ( round up to two decimals )
Therefore, the value of the 120 kilograms is equal to ( 266.55 ) pounds ( round up to two decimals ) using converting factor.
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How to write 42 in Roman Numerals?
The roman numerals of 42 is XLII
Roman numerals are a number system that originated in ancient Rome and remained the standard numbering system throughout Europe until the late Middle Ages. Numbers are written using combinations of letters from the Latin alphabet, each letter has a fixed integer value, and only the following seven are used in modern style:
I V X L C D M
1 5 10 50 100 500 1000
The use of Roman numerals continued long after the fall of the Roman Empire. From the 14th century onwards, Roman numerals were replaced by Arabic numerals. However, this process was gradual and the use of Roman numerals continues to this day in some applications.
The roman numerals of 42 is
42 = 40 +2
for 40 = 50-10 = XL
and for 2 II
so for 42 = XLII
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What would the location of the 83 percentile be for a data set with 40 observations? Click the answer you think is right. 33.20 34.03 40.00 32.00
The location of the 83rd percentile for a data set with 40 observations would be 34.03.
What is data?Data is the collection of data term that is organized and formatted in a specific way it's typically contains fact observation or statistics that are collected through a process of measurement or research data set can be used to answer question and help make informed decision they can be used in a variety of ways such as to identify trends on cover patterns and make prediction.
A percentile is a value on a scale of one hundred that indicates the percentage of a distribution that is equal to or below it. For example, the 83rd percentile for a data set with 40 observations would indicate that 83% of the observations in the data set are equal to or less than 34.03. To calculate the location of a given percentile, the formula is (p/100) * n, where p is the given percentile and n is the total number of observations. Therefore, for a data set with 40 observations and an 83rd percentile, the formula would be (83/100) * 40 = 33.2, which would be rounded up to 34.03.
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The 8 students in the Environmental Club represent 5% of the students in the seventh grade. How many students are in the seventh grade?
There are 160 students in the seventh grade.
What is number?Number is a mathematical entity used to represent a computer magnitude it can be symbol or a combination of simple you should in order to take quantity such as the two, five, seven, three or eight number are used to verify the context including counting measuring and computing.
To calculate the number of students in the seventh grade, you must divide the number of students in the Environmental Club by the percentage they represent. The answer is 8 divided by 0.05, which equals 160. Therefore, there are 160 students in the seventh grade.
The Environmental Club provides students with an opportunity to learn more about the natural environment and how to help protect it. The club members work together to come up with ideas to promote environmental awareness and action in their school and community. They plan activities such as tree-planting, trash clean-ups, and educational presentations. The club also participates in activities like field trips to local parks and nature preserves.
By joining the Environmental Club, students can gain a better understanding of their local environment and how to protect it. This can help them become more aware of their actions and how they can make a difference in the world. They can also develop leadership and communication skills, as well as an understanding of the importance of teamwork. Furthermore, they can make friendships and connections with other students who share the same values and interests.
Overall, the Environmental Club is an important part of the school community and provides great benefits to its members. It allows students to gain knowledge, build skills, and make a positive difference in their communities.
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Rasheed has four and one-sixth cups of berries. He uses one and three-fourths cups of berries to make a milkshake. He then uses one and one-half cups of berries. After he makes his milkshake and muffins, how many cups of berries will Rasheed have left?
eleven-twelfths cups
one and five-twelfths cups
one and nine-eighteenths cups
one and sixteen twenty-fourths cups
Answer:
11 /16
Step-by-step explanation:
The factor theorem can help use determine if a factor is a [blank] of a polynomial
If and only if f(a) = 0, a polynomial f(x) has a factor (x-a). It's one of the techniques for factoring a polynomial.
A polynomial is an equation made up of coefficients and in determinates that uses only the addition, subtraction, multiplication, and powers of positive-integer variables.
The factor theorem can help us determine if a factor is a "root" or "zero" of a polynomial. In other words, if we have a polynomial function, the factor theorem allows us to check if a particular value (usually represented by the variable x) is a solution to the polynomial equation, which means that when we plug in that value for x, the resulting output of the polynomial function will be zero. If it is, then we know that (x - a) is a factor of the polynomial, where "a" is the solution we found.
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The local supermarket had a sale on canned green beans. The green beans sold for 3!cans for $1. 25. One can of green beans usually sells for 50 cents. Find the percent of increase of decrease
The sale price of the green beans represents a decrease of 16.67% compared to the original price of the beans.
To find the percent increase or decrease in the price of a can of green beans during the sale, we need to compare the sale price with the original price.
During the sale, the green beans were sold at a rate of 3 cans for $1.25, or approximately 41.67 cents per can:
Sale price per can = $1.25 / 3 = $0.4167 ≈ 41.67 cents
The original price of a can of green beans was 50 cents.
To find the percent increase or decrease in the price, we can use the following formula:
Percent increase or decrease = ((New value - Old value) / Old value) x 100%
Substituting the values, we get:
Percent increase or decrease = ((0.4167 - 0.5) / 0.5) x 100%
Percent increase or decrease = (-0.0833 / 0.5) x 100%
Percent increase or decrease = -16.67%
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For a project in her Geometry class, Aria uses a mirror on the ground to measure the height of her school building. She walks a distance of 11.45 meters from the school, then places a mirror on flat on the ground, marked with an X at the center. She then steps 1.25 meters to the other side of the mirror, until she can see the top of the school clearly marked in the X. Her partner measures the distance from her eyes to the ground to be 1.15 meters. How tall is the school? Round your answer to the nearest hundredth of a meter.
Answer = 10.53m
The height of the school building is approximately 9.69 meters or 10.53 meters (rounded to the nearest hundredth).
What is trigonometry?
Trigonometry is a branch of mathematics that deals with the studies of relationships between angles and sides of triangles.
Let's denote the height of the school building as "h".
From the given information, we can draw a right triangle with the mirror on the ground, the top of the school building, and Aria's eyes as the vertices. The distance from Aria to the mirror is 1.25 meters, and the distance from the mirror to the school building is the unknown height "h". The distance from Aria's eyes to the mirror is 1.15 meters.
We can use similar triangles to set up an equation to solve for "h".
In the smaller triangle formed by Aria's eyes, the mirror, and the point directly below the top of the school building, we can see that:
h/1.25 = (h + 1.15)/11.45
This equation comes from the fact that the ratios of corresponding sides in similar triangles are equal.
Simplifying this equation gives us:
1.45h = 14.06875
Dividing both sides by 1.45 gives us:
h ≈ 9.6931
Hence, The height of the school building is approximately 9.69 meters or 10.53 meters (rounded to the nearest hundredth).
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I will give 5 star and a star for the right answer
Answer:
2.6
Step-by-step explanation:
I think the formula is 6x=14
what is the result of 6022 x 1023 ?
The value of (6022*1023) will be = 61,60,506
As per question,
We need to find the value of (6022*1023)
For finding the value of given expression, we will use the identity of multiplication.
So, applying the multiplication identity:
We can write the above as:
6022*1023 = (6000+22) * (1000+23)
As we know,
(a+b)*(c+d) = ac+ad+bc+bd
So, applying the identity in above expression,
We will get,
6022*1023 = (6000+22) * (1000+23)
=(6000*1000)+(6000*23)+(22*1000)+(22*23)
=(6000000+138000+22000+506)
=61,60,506
Multiplication is a way of calculating the product of two or more integers in mathematics. It is one of the most fundamental mathematical operations that we utilise every day.
Multiplication is the process of taking one integer and multiplying it by a certain number of times. 5 multiplied by 4 is 5 + 5 + 5 + 5 = 20. We took the number 5 and multiplied it by four. This is why multiplication is often known as "times".
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The second angle of the triangle is 25 degrees larger than the first, while the third angle of the triangle is 3 times the second. How big is the first angle? Remember, the sum of the angles in any triangle is 180 degrees.
Answer: look at the image for the answer and the explanation
Step-by-step explanation:
Answer: 16 degrees
Step-by-step explanation:
What is the expected temperature on Febuary 15?
The expected temperature in Peoria Illionis on february 15 is 22.028≈22 degrees farenheit.
Atmospheric Temperature:A measure of the temperature at high elevations in the Earth's atmosphere is called the atmospheric temperature. Many factors, such as incoming solar radiation, humidity, and altitude, affect it.
The average daily temperature in Peoria Illionis can be predicted by given formula ,
[tex]T=50-28cos[\frac{2\pi (x-31)}{365} ][/tex]
where , x is the number of day in year.
February 15 is (31+15)th day of the year
therefore, February 15 1s 46th day of the year.
now in the given formula,
[tex]T=50-28cos[\frac{2\pi (x-31)}{365} ]\\\\T=50-28cos[\frac{2\pi (46-31)}{365} ]\\\\T=50-28cos[\frac{2\pi (15)}{365} ]\\\\T=50-28cos[\frac{30\pi}{365} ]\\\\T=50-28cos[0.258]\\\\T=50-28(0.999)\\\\T=50-27.972\\\\T=22.028[/tex]
So , the expected temperature on february 15 is 22.028≈22 degrees farenheit.
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4^3 = X X = 64
fill in the blanks
Answer: The answer will be 8^2
Step-by-step explanation: We know,
4^3 = 4*4*4 = 64 which is also equivalent to next in series 4*4 =8 and 3-1 =2
i.e. 8^2= 64
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Jen left the house at 10:03. She went to the post office, returned books to the library, and bought groceries at the store. Jen was running errands for 59 minutes. What time was it when she returned home?
Jen returned home was 11:02. Below, you will learn how to solve the problem.
When Jen left the house, it was 10:03, she was running errands for 59 minutes. To find out what time it was when she returned home, we need to add the 59 minutes to the time she left the house.
First, we need to convert the time she left the house to minutes, 10:03 is equal to 603 minutes (10 hours x 60 minutes per hour + 3 minutes).
Next, we add the 59 minutes she was running errands to the 603 minutes:
603 minutes + 59 minutes = 662 minutes
Finally, we convert the 662 minutes back to hours and minutes:
662 minutes ÷ 60 minutes per hour = 11 hours with 2 minutes remaining
So, the time when Jen returned home was 11:02.
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explain why lagrange multipliers fail to solve the problem
The Lagrange multipliers fail to solve the problem because g = 0 at the coordinates (x, y) = (0, 1) where f reaches its minimum on g = 0,
The Italian mathematician Joseph-Louis Lagrange is honoured by having his multiplier method named after him. In order to apply the derivative test of an unconstrained problem to a constrained problem, it is necessary to convert it into a different form.
Moreover, this technique is frequently employed in mathematical optimization. When a function of the form f(x, y, and z) is subject to equality constraints of the form g(x, y, and z) = k or g(x, y, and z) = 0, one useful technique is the method of Lagrange's multipliers. This means that it depends on the values of the desired variable exactly satisfying the terms of one or more equations.
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Please help me for 30 points!!.
By adding the fractions and getting 5/6, we conclude that the correct option is B.
How Mariana could share the crackers left?We know that Mariana has 5/6 of the crackers left, so we only need to select the option where both fractions add upt o 5/6.
When both fractions have the same denominator like:
a/b and c/b
The sum is:
a/b + c/b = (a + c)/b
Then the correct option is the second one:
3/6 + 2/6 = (3 + 2)/6 =5/6
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what is 42 in base 5?
42 in base 5 is written as 132.
In mathematics, we often use different number systems, also known as bases, to represent numbers. The most commonly used number system is the decimal system, which is base 10. However, there are many other number systems, such as base 2, base 5, base 8, and so on. Each base system has its own set of digits that are used to represent numbers. In this explanation, we will focus on base 5 and how to convert the number 42 to base 5.
To convert a number to a different base system, we need to first understand the concept of place value. Place value is the value of a digit based on its position in a number. In the number 42, the digit 4 is in the tens place and has a value of 40 (4 x 10). The digit 2 is in the ones place and has a value of 2.
In base 5, we only have 5 digits to work with: 0, 1, 2, 3, and 4.
To convert the number 42 to base 5, we need to divide 42 by 5 and record the remainder.
We then divide the quotient by 5 again and record the remainder, and so on, until the quotient is 0.
42 ÷ 5 = 8 remainder 2
8 ÷ 5 = 1 remainder 3
1 ÷ 5 = 0 remainder 1
To convert these remainders into the corresponding digits in base 5, we simply read them from bottom to top. Therefore, 42 in base 5 is written as 132.
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4-(-7)+(-2)=?
SHOW STEP BY STEP HOW U GOT THE ANSWER PLEASE
Answer: x should be equal to 9 (please correct me if i'm wrong)
Step-by-step explanation: Let's say the answer for this problem is equal to x
4 -(-7) + (-2) = x
4 + 7 + (-2) = x
11 + (-2) = x
9 = x