1. Find the 15th term of the arithmetic senquence 26, 13, 0, -13, ...
2. Find the first term of the arithmetic sequence if the 8th term is 67.
3. Find the 23rd term of the arithmetic sequence 5, 11, 17,....
4. What is the common difference of the arithmetic sequence whose first term is 10 7th term is 28?
5. Find the term of the sequence whose 200th term is 893 and common difference is 7,
Answers
Answer:
To find the
n
t
h
term, we use the formula
x
n
=
a
+
d
(
n
−
1
)
, where
n
is the term you are looking for,
a
is the
1
s
t
term and
d
is the difference between terms (it does not vary)
From the arithmetic sequence
−
3
,
4
,
11
,
18
...
, we can see that
a
=
−
3
and
d
=
7
You can find
d
by subtracting a number by its precedent
⇒
d
=
4
−
(
−
3
)
=
7
or
d
=
11
−
4
=
7
and so on! It's always going to be the same value.
So,
x
15
=
−
3
+
7
(
15
−
1
)
=
−
3
+
7
(
14
)
=
−
3
+
98
=
95
Another way to do this since it's "only" the
15
t
h
term is by hands or calculator. They already gave you the four terms, which will help you find the difference "
d
". Use only the first term "
−
3
" and add 7 until you reach the
15
t
h
term.
⇒
−
3
+
7
+
7
+
7
+
7
+
7
+
7
+
7
+
7
+
7
+
7
+
7
+
7
+
7
+
7
=
95
Step-by-step explanation:
Related Questions
Graph the solution of the inequality.
3.5
Answers
Answer:
x>14
Step-by-step explanation:
since 14/4 = 3.5 your X value should be greater than 14. You would graph the point anywhere to the right of 14
Answer: x>14
Step-by-step explanation:
isolate x
3.5<x/4
14<x
x>14
open circle x>14
Alberto started out bench pressing 60 pounds. He then added 5 pounds every week. Determine whether the situation is linear or nonlinear, and proportional or nonproportional
Answers
Answer
linear
nonproportional
Step-by-step explanation:
Since for each equal change in time (1 week), there is an equal change in weight (5 lb), the situation is linear.
At time zero, the first week, the weight was not zero. It was 60 lb, so it is not proportional.
Answer:
linear
nonproportional
a fair bet is a: wager entered into with honesty and concern for the welfare of the other party. gamble that provides net gains to all participants so there is no loser. wager entered into when the rules are clear to all participants. gamble that, on average, will leave a person with the same amount of money.
Answers
Answer:gamble that,on average,will leave a person with the same amount of money.
Step-by-step explanation:
someone please help me with this problem
Answers
Answer:
A and E
Step-by-step explanation:
If you add all the perimeters and the half circles, it would make 40 + 20π. And you can get this in two ways. A and E
Answer:
The correct answer is A and E.
Step-by-step explanation:
The perimeter of this shape is 10 + 10 + \(\frac{20\pi }{2}\) + 10 + 10 + \(\frac{20\pi }{2}\) = 10 + 10 + \(10\pi\) + 10 + 10 + \(10\pi\) = 40 + \(20\pi\).
Solve the following:
1 - .008 =
Answers
Answer:
0.992
Step-by-step explanation:
do you not have a calculator
Answer:
0.992
Step-by-step explanation:
1 - 0.008 = 0.992
limx^2-9/x-3 even though the limit can be found using the theorem, limits of rational functions at infinity and horizontal asymptotes of rational functions, use rule to find the limit.
Answers
The solution of the given problem , there is no horizontal asymptote.
\($lim_{x \to 3} \frac{x^2 - 9}{x - 3}$\)
By factorizing the numerator as difference of squares, we can write it as,
\($lim_{x \to 3} \frac{(x + 3)(x - 3)}{(x - 3)}$\)
Canceling out the common term, we get,
\($lim_{x \to 3} (x + 3)$\)
As the value of x approaches 3, the value of (x+3) also approaches 6. Hence, the limit of the given expression is 6.
We could also have found the limit using the theorem - Limits of rational functions at infinity and horizontal asymptotes of rational functions. For this, we would have needed to check the degree of the numerator and denominator.
The degree of the numerator is 2, and the degree of the denominator is 1. Hence, as x approaches infinity, the function approaches infinity. Similarly, as x approaches negative infinity, the function also approaches infinity. Thus, there is no horizontal asymptote.
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This scatter plot shows the amount of tips earned and hours worked. Choose the statement that is best supported by the data in the scatter plot. Question 10 options: The data shows a non-linear association between the number of hours worked and tips earned.
The data shows no apparent association between the number of hours worked and tips earned.
The data shows a positive linear association between the number of hours worked and tips earned.
The data shows a negative linear association between the number of hours worked and tips earned.
Answers
“There is a positive linear association between the number of hours worked and tips earned.”
The data plotted on the scatter plot reveals there is a positive linear association between the number of hours worked and tips earned. (Option C).
Recall:
A scatter plot shows an association between two variables, either positively associated or negatively associated.If one variable increases as the other variable increases, it means the association is positive, and vice versa.The association is linear if the trend line appears to be straight.The scatter plot given shows a trend line of the data. It also shows that as time worked increases, tips earned also increases. This shows a positive linear association between tips earned and time worked. (Option C).
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Which expression correctly represents 10 less than a number cubed?
Answers
Sorry I can’t see pic
Brainliest is appreciated
Answer:
a
Step-by-step explanation:
\(c^{3} - 10\)
On a map 1 cm = 50 mi. On the map, Grand Canyon is 4 cm from Phoenix. What is the actual distance?
Answers
Answer:
200
Step-by-step explanation:
1cm=50m
1*4=50*4
4=200 miles
How do you tell if a pair of equations are parallel perpendicular or neither?
Answers
Two non-vertical lines in the same plane are said to be parallel if they have the same slope. No two parallel lines will ever cross. A set of non-vertical lines within the same plane are considered to be perpendicular if they meet at a right angle.
Perpendicular lines and parallel lines both meet at 90 degrees, although parallel lines never do. Lines are perpendicular if the slope of one line is equal to the reciprocal of the second line's negative slope.
Lines that have the same slope are therefore said to be parallel, and if the slope of one line is equal to the negative reciprocal of the slope of the other, the two lines are said to be perpendicular; otherwise, they are just intersecting lines.
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What is the length of line ED?
Answers
Answer:
ED = 8
Step-by-step explanation:
2x+4 = (3/2)x+6
2x = (3/2)x+2
(1/2)x = 2
x = 4
ED = 4+4 = 8
Henry bonnacio deposited $1,000 in a new savings account at first national bank. He made no other deposits or withdrawals. After 6 months the interest was computed at an annual rate of 6 1/2 percent . How much simple interest did his money earn
Answers
Henry's money earned a simple interest of $32.50 over 6 months.
Henry Bonnacio deposited $1,000 in a new savings account at First National Bank with an annual interest rate of 6 1/2 percent. To calculate the simple interest earned on his deposit, we can use the formula:
Simple Interest = (Principal * Rate * Time) / 100
In this case, the principal is $1,000, and the rate is 6 1/2 percent, or 6.5% in decimal form. However, the interest is computed after 6 months, so we need to adjust the time accordingly.
Since the rate is annual, we divide it by 12 to get the monthly rate, and then multiply it by 6 (months) for the actual time:
Rate per month = 6.5% / 12 = 0.0054167
Time = 6 months
Now we can calculate the simple interest:
Simple Interest = (1000 * 0.0054167 * 6) / 100 = 32.50
Therefore, Henry's money earned a simple interest of $32.50 over 6 months.
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e(xy)=e(x)e(y) proof
Answers
The equation e(xy) = e(x)e(y) holds true and can be proven by utilizing the properties of exponential functions.
To prove the equation e(xy) = e(x)e(y), we start with the left-hand side (LHS) of the equation, which is e(xy). The exponential function e(x) can be defined as the infinite series: e(x) = 1 + x/1! + x^2/2! + x^3/3! + ...
Now, substituting xy for x in the exponential function, we have e(xy) = 1 + (xy)/1! + (xy)^2/2! + (xy)^3/3! + ...
Next, let's consider the right-hand side (RHS) of the equation, which is e(x)e(y). Using the definition of the exponential function, we have e(x)e(y) = (1 + x/1! + x^2/2! + x^3/3! + ...)(1 + y/1! + y^2/2! + y^3/3! + ...).
Expanding this expression, we obtain e(x)e(y) = 1 + (x+y)/1! + (x^2+2xy+y^2)/2! + (x^3+3x^2y+3xy^2+y^3)/3! + ...
Comparing the expressions for e(xy) and e(x)e(y), we can see that both are equal. Therefore, the equation e(xy) = e(x)e(y) is proven.
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An arts academy requires there to be 5 teachers for every 115 students and 3 tutors for every . How many students does the academy have per teacher? Per tutor? How many tutors does the academy need if it has 77 students ?
Answers
Answer:
1.23
2. Question incomplete
3. Needs Question 2 to Answer
Step-by-step explanation:
1. 115÷5=23
Write an equation of the trend line in slope intercept form
Answers
Answer:
the answer for this question you have id number 8
What is the line segment BC?.
Answers
The length of BC is 10cm, in the given triangle.
What is are of the triangle?
The territory included by a triangle's sides is referred to as its area. Depending on the length of the sides and the internal angles, a triangle's area changes from one triangle to another. Square units like m2, cm2, and in2 are used to express the area of a triangle.
BR = 3 cm, let's say AR = 4 cm, and AC = 11 cm.
Since tangents to an exterior point are always equal, we can conclude that BR = BP = 3 cm.
4 cm if AQ = AR
QC=AC-AQ=11 – 4 = 7 cm
Q = P = 7 cm
It follows that BC = BP+PC = 3 + 7 = 10 cm.
BC, therefore, has a length of 10 cm.
Therefore, BC is 10 cm long.
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What is the area of GPH? in square yards
Answers
Answer:Therefore, the required area of the sector GPH is about 50.24 yd.
Step-by-step explanation:its ez
Select the correct answer.The product of two integers is 72. One number is two less than five times the other.Which of the following equations could be used to find one of the numbers?
Answers
Solution:
Let the two integers be x and y;
\(\begin{gathered} xy=72 \\ \\ y=5x-2 \end{gathered}\)Thus;
\(\begin{gathered} x(5x-2)=72 \\ \\ 5x^2-2x=72 \end{gathered}\)CORRECT OPTION: B
The jenkins family drinks 3/4 of a gallon of orange juice every 3 days. How many orange juice do they drink per day?
Answers
Answer:
1/4
Step-by-step explanation:
3/4 divided by 3=1/4
i’ll give you brainlest but please help answer this
Answers
Answer:
X=9
Step-by-step explanation:
X/ Y=X/Y
3/18=x/54
next is simple math
X=9
x = 9.
I hope this helped!
I Would appreciate it if you gave me a Thanks and a brainliest (:
pls solve this 4 a branliest
Answers
Answer:
B
Step-by-step explanation:
It says she thought half which equals to 1/2 or 0.5
26. In the figure F is a point on AE. FC and BE meet at D. Given that
AB=BF FE and ZABF = LDFE.
(n) Prove that AFBD-AAEB.
(4 marks)
Suppose that ZABF = LEBC,
(b) Prove that AFBD-AFCB,
(3 marks)
(e) If AB // FC, write down a triangle that is congruent to AFBD.
(1 mark)
Answers
Part #1: find the solution of the inequality.\(10 \geqslant p - 4\)Part #2: describe the solution
Answers
Part 2
The solution is described as p is less than or equal or equal to 14
sample variance and standard deviation are considered biased estimates of population variance and standard deviation because they tend to:
Answers
Sample variance and standard deviation are considered biased estimates of population variance and standard deviation because they tend to underestimate the true population variance and standard deviation.
The reason for this is that the sample variance and standard deviation are based on a sample of the population, not the entire population. The sample may not accurately represent the entire population, and thus the sample variance and standard deviation may not accurately reflect the true population variance and standard deviation. To correct for this bias, a correction factor is usually added to the sample variance calculation. For example, when estimating the population variance from a sample of size n, the sample variance is divided by (n-1) instead of n. This correction factor helps to provide a more accurate estimate of the population variance. Similarly, the sample standard deviation is calculated as the square root of the sample variance, and the correction factor is also applied to the sample standard deviation calculation. This corrected sample standard deviation is known as the unbiased sample standard deviation.
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Complete Question
sample variance and standard deviation are considered biased estimates of population variance and standard deviation because they tend to: What?
C. The painting American Gothic by
Grant Wood is rectangular in shape
and measures 29"in height and 25"
in width. A reproduction is made
where each dimension is some
fraction of the original dimension. If
the reproduction has 1/9 of the
original area, what is the width of
the reproduced piece?
Answers
the width of the reproduced piece is 2.78 inches.
Now, we first need to find the original area of the painting.
Since, The original area is,
= 29 inches x 25 inches
= 725 square inches
Now. we know that the reproduction has 1/9 of the original area, which means that the area of the reproduction is:
= 725 square inches / 9
= 80.56 square inches
Hence, for the width of the reproduced piece, we need to find the width of a rectangle whose area is 80.56 square inches, given that the height is 29 inches which remains constant in the reproduction.
Hence, We can use the formula for the area of a rectangle,
Area = length x width
In this case, we know the area is, 80.56 square inches)
and the length is, 29 inches
Thus, we can solve for the width:
80.56 square inches = 29 inches x width
width = 2.78 inches
Thus, the width of the reproduced piece is 2.78 inches.
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The bar graph below gives the distribution of the most popular colors for cars and light trucks sold globally in 2010.
Answers
The given distribution of the most popular car colors for 2010 is presented in a bar graph. This type of plot effectively displays the categorical data and their corresponding percentages. Therefore, the appropriate plot for representing the given data is the bar graph provided initially.
Now let's consider the options:
a) A time series plot: A time series plot is used to visualize data over a specific period of time. Since the given data represents the distribution of car colors for a single year (2010), a time series plot is not appropriate in this case. Therefore, option a) is not suitable.
b) A pie chart: A pie chart is commonly used to represent parts of a whole. In this case, the data is already presented in a bar graph, which effectively displays the proportions of each car color. Although a pie chart can also represent proportions, it may not provide the same level of clarity as the bar graph. Therefore, option b) is not necessary.
c) A histogram: A histogram is used to visualize the distribution of continuous or discrete data across intervals or bins. In this case, the data is categorical, representing specific car colors and their corresponding percentages. Therefore, a histogram is not appropriate.
d) All of the above: Since options a) and c) are not suitable for representing the given data, the correct answer is not d) "All of the above."
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The bar graph below gives the distribution of the most popular colors for cars and light trucks sold globally in 2010. Most popular car colors (2010) CE 20 15 Percent 10 Silver Black While Blue Gray Red Color Brown Other Which of the following kinds of plots would also be appropriate for these data? a) a time series plot b) a pie chart a histogram. a) a time series plot b) a pie chart. c) a histogram. d) All of the above
When using the negative exponent properties, why is it important to know if any of the variables is equal to 0?
Answers
Answer:
Because that give you something like this \(\frac{a}{0}\) who is undefined.
Step-by-step explanation:
When you raise something to a negative exponent give you:
\(a^{-b} = \frac{1}{a^b}\)
Then if \(a\) is equal to 0 is considerate undefined because whatever number raising 0 is equal to 0.
This video explain why you can't divide by zero if you want a deepest answer: 'Why can't you divide by zero? - TED-Ed'
(i) if b=250, what is the largest rate of increase in the number of frogs in the pond? explain your reasoning, and indicate units of measure.
Answers
The units of measure for the rate of increase would be frogs per unit of time
(The largest rate of increase in the number of frogs in the pond would be when the growth rate is at its maximum. This can be determined by finding the derivative of the growth function and setting it equal to zero to find the maximum point.
Since we are not given a specific growth function, we cannot accurately determine the largest rate of increase. However, we can say that the largest rate of increase would occur at the point where the derivative of the growth function is at its maximum. The units of measure for the rate of increase would be frogs per unit of time (e.g. frogs per day or frogs per week).
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Work out the value of
5^8 x 5^-2 /
5^4
Answers
Answer:
the answer is 25
Step-by-step explanation:
After simplifying the expression the final value of the expression is given by 25
What are exponents?Exponent is a mathematical operation, written as an. Here the expression an involves two numbers, the base 'a and the exponent or power 'n'. Exponents are used to simplify algebraic expressions.
Given here : The expression 5⁸×5⁻² / 5⁴
We know from the law of exponents, for any non-zero term a,
\(a^m.a^n=a^{m+n}\)
Thus simplifying the expression we get
5⁸×5⁻² / 5⁴
=5⁸⁻² /5⁴
=5⁶⁻⁴
=5²
=25
Hence, The value of the expression is 25
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A flange is to be machined at a diameter of 6.77 cm ± 0.01 cm. The process standard deviation is 0.005 cm. What is the process capability ratio? A. 0.67. B. 1.01. C. 0.87. D. 0,34.
Answers
The process capability ratio is approximately 0.67 (option A).
To calculate the process capability ratio, we need to use the following formula:
Process Capability Ratio = (Upper Specification Limit - Lower Specification Limit) / (6 * Process Standard Deviation)
Given the following values:
Upper Specification Limit = Diameter + Tolerance = 6.77 cm + 0.01 cm = 6.78 cm
Lower Specification Limit = Diameter - Tolerance = 6.77 cm - 0.01 cm = 6.76 cm
Process Standard Deviation = 0.005 cm
Plugging these values into the formula, we have:
Process Capability Ratio = (6.78 cm - 6.76 cm) / (6 * 0.005 cm)
Process Capability Ratio = 0.02 cm / 0.03 cm
Process Capability Ratio ≈ 0.67
Therefore, the process capability ratio is approximately 0.67. The correct answer is A) 0.67.
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