[tex]\bf 8~~,~~\stackrel{8-2}{6}~~,~~\stackrel{6-2}{4}~~,~~\stackrel{4-2}{2}~~,~~\stackrel{2-2}{0}[/tex]
so, as you can see, the common difference is then -2, and the first term is clearly 8, thus
[tex]\bf n^{th}\textit{ term of an arithmetic sequence}\\\\a_n=a_1+(n-1)d\qquad\begin{cases}n=n^{th}\ term\\a_1=\textit{first term's value}\\d=\textit{common difference}\\[-0.5em]\hrulefill\\a_1=8\\d=-2\\n=14\end{cases}\\\\\\a_{14}=8+(14-1)(-2)\implies a_{14}=8-26\implies a_{14}=-18[/tex]
Final answer:
The explicit formula for the given arithmetic sequence is an = 10 - 2n. By applying this formula, we find that the 14th term of the sequence (a14) is -18.
Explanation:
The sequence given is 8, 6, 4, 2, 0, ... and it is decreasing by 2 every term. This is an arithmetic sequence where each term is 2 less than the previous term. To write an explicit formula for an arithmetic sequence, we use the formula an = a1 + (n - 1)d, where an is the nth term, a1 is the first term, d is the common difference, and n is the term number.
For this sequence, a1 = 8 and d = -2. Substituting these values into the formula, we get an = 8 + (n - 1)(-2). Simplifying this, the explicit formula for the nth term is an = 10 - 2n. To find the 14th term, a14, we substitute n = 14 into the formula: a14 = 10 - 2(14) = 10 - 28 = -18. Therefore, the 14th term of the sequence is -18.
30 POINTS HELP PLEASE the letter z illustrates alternate interior angles. which letter illustrates corresponding angles
x
n
t
f
(if you were to draw this letters and use the angles inside them)
With the help of the definition of alternate angle and corresponding angle, the result obtained is The letter 'F' illustrates corresponding angle Fourth option is correct
What is alternate angle and corresponding angle?
At first we need to understood what is angle, parallel lines and transversal Angle When two straight lines intersect, an angle is formed. The point of intersection is called the vertex of the angle and the lines are called the arms of the angle. Parallel lines Two lines are said to be parallel if on extending them indefinitely, they will never intersect Transversal is a line that intersects two or more parallel lines Alternate angle The angle formed on the opposite side of transversal is called alternate angle. Corresponding angles are those angles formed on same side of transversal when a transversal intersect two or more parallel lines
Here,
The letter 'F' illustrates corresponding angle
Fourth option is correct
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whats the meadian
3 4 6 3 3 5 4 2 0 1 4 3 5 3 6 4 2 2 5 1
The median is the number that is halfway into the set. To find the median, the numbers should be arranged in order from least to greatest. After arranging these numbers find the middlemost number in the set which is th median.
3 Is the median.
The median in a series of numbers represents the middle value when the numbers are arranged in ascending order. If the number of observations is even, as in this case, the median is the average of the two middle numbers. Therefore, the median of the given set of numbers is 3.
Explanation:The question is about finding the median of a given set of numbers. The median is the middle value in a set of numbers when the numbers are arranged in ascending or descending order. If the set has an even number of observations, the median is the average of the two middle numbers.
1. Firstly, arrange the set of numbers in ascending order: 0, 1, 1, 2, 2, 2, 3, 3, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 6, 6.
2. Since we have an even number of observations (20), we need to find the average of the 10th and 11th numbers. Those numbers are 3 and 3.
3. Average of 3 and 3 is 3.
So, the median of the given set of numbers is 3.
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divide sh.6300 in the ratio 3:4. how much is each share?
3 : 4 = 2700 : 3600
sum the parts of the ratio : 3 + 4 = 7
divide 6300 by 7 to obtain 1 part
[tex]\frac{6300}{7}[/tex] = 900 ← 1 part
3 parts = 3 × 900 = 2700
4 parts = 4 × 900 = 3600
note that 2700 + 3600 = 6300
I need to know how to solve these simple interest word problems step by step.
1. What is the new balance of your account after 8 months if you earn 2.7% on your balance of $13,132?
(by the way, I’ve tried .66 and .67 for time and it doesn’t give us our answer apparently :/)
2. Last Year you earned $273.47 in interest for your online savings account. If your starting balance was $8,546, what was your interest rate?
Answer:
$236.38
3.20%
Step-by-step explanation:
Simple interest = PNR/100 where P = Principal = 13132/-
N = 8 months = 8/12 years and r = 2.7%
Hence simple interest = 13132 (8/12)(2.7/100)
= 236.376
= 236.38 dollars
-----------------------------------------------------
2) On the same notation, here PNR/100 = 8546(1)(R)/100=273.47
Solving
R = 273.47(100)/8546 = 3.19999
= 3.20% apprxy.
-------------------------------
Question 12 please , thank you in advance.
I think It is C but not sure
Scotty and Tyler are training for a pizza-eating contest. They are trying to eat 6 pizzas in total. So far, Scotty has eaten 2 3/4 pizzas and Tyler has eaten 1 7/8 pizzas. How much more pizza do they have left to eat?
Answer:
They are left with [tex]1\frac{3}{8}[/tex] pizza to eat.
Step-by-step explanation:
Scotty and Tyler are trying to eat 6 pizzas in total.
Sotty has eaten = [tex]2\frac{3}{4}[/tex] Pizzas
Tyler has eaten = [tex]1\frac{7}{8}[/tex] Pizzas
Total pizza eaten by them = [tex]2\frac{3}{4}[/tex] Pizzas + [tex]1\frac{7}{8}[/tex] Pizzas
= [tex]\frac{11}{4}[/tex] + [tex]\frac{15}{8}[/tex]
= [tex]\frac{37}{8}[/tex]
Total pizza was eaten = [tex]4\frac{5}{8}[/tex]
Pizza have left to eat = 6 - [tex]4\frac{5}{8}[/tex]
= 6 - [tex]\frac{37}{8}[/tex]
= [tex]\frac{11}{8}[/tex]
= [tex]1\frac{3}{8}[/tex]
They are left with [tex]1\frac{3}{8}[/tex] pizza to eat.
Adding and subtracting integers
[tex] - 6 - 9 = [/tex]
[tex]10 -5 = [/tex]
[tex] - 1 - 12 = [/tex]
[tex]9 - 13 = [/tex]
[tex] - 2 - ( - 7) = [/tex]
[tex]11 - ( - 3) = [/tex]
[tex] - 5 - ( - 5) = [/tex]
[tex]4 - 12 = [/tex]
[tex]4 - 12 = [/tex]
[tex]15 - 8 = [/tex]
1) -15
2) 5
3) -13
4) -4
5) 5
6) 14
7) 0
8) -8
9) -8
10) 7
These are very easy, when subtracting a negative from a positive think of it as just plain subtraction. When adding a negative to a positive, again, think of it as subtraction. When subtracting two negatives it's basically addition but you final answer should have a negative sign.
Hope I could help! :)
Can 11/154 be simplified
Yes, if it exists, and reduce our fraction by dividing both numerator and denominator by it. GCF = 11, and get our simplified answer
Answer:no
Step-by-step explanation:
¯\_(ツ)_/¯
I think it’s pretty annoying that I need help on this...[I should know this but I don’t :( ] Can anyone help me on this I would really appreciate it. Thanks
The first one would be 1 since you're dividing and whenever you divide exponents you're supposed to subtract them. And the second one is also the first one since it's basically the work shown for how you got your first answer.
The Atlantic Ocean borders 14 of the 50 states in the United States . What present of the 50 staates border the Atlantic Ocean
I got 28%. I divided 14 by 50 to get 0.28. The problem can then be multiplied by 100 to get 28.
Which of the following illustrates the Law of Syllogism?
The answer is letter A.
Answer:
A.If[tex](p\implies q)\;and \;(q\implies r)[/tex],then [tex]p\implies r[/tex].
Step-by-step explanation:
We have to find the which statement illustrate the law of syllogism.
Law of syllogism: Premise: if p then q
Premise:If q then r.
Conclusion:If p then r.
It is like transitive property of equality.
A.If[tex](p\implies q)\;and \;(q\implies r)[/tex],then [tex]p\implies r[/tex].
It is true by definition of law of syllogism.
B.If[tex](p\implies q)\;and \;(q\implies p)[/tex],then [tex]p\implies r[/tex].
It is not true by definition of syllogism.
C.If[tex](p\implies q)\;and \;(p\implies r)[/tex],then [tex]q\implies r[/tex]
It is not true by definition of syllogism.
D.If[tex]p\implies r)\;and \;(q\implies r)[/tex],then [tex]p\implies r[/tex].
It is not true by definition of law of syllogism.
Answer:A
Patricia has saved $625. She is starting a part-time job that pays her $350 a week, and she plans to save all of the money she earns. Which algebraic expression can be used to represent Patricia's total savings after x weeks?
A: 975x
B: 350x+625
C: 625x+350
D: 350(625+x)
B Should be your answer!
Answer:
B. [tex]350x+625[/tex].
Step-by-step explanation:
Let x represent number of weeks.
We have been given that Patricia is starting a part-time job that pays her $350 a week. So the amount saved after x weeks would be [tex]350x[/tex].
We are also told that Patricia has saved $625. So total amount saved by Patricia after x weeks would be [tex]350x+625[/tex].
Therefore, the expression [tex]350x+625[/tex] represent Patricia's total savings after x weeks and option B is the correct choice.
the sum of six and four times d is the same as d minus nine
According to question
6 + 4 d = d - 9
4d - d = -9 - 6
3d = - 15
d = -15/3
d = -5
Someone give me a short history summary of the summary 17th amendment (government)
The 17th Amendment came about during the Progressive Era. During this time in American history, reformers were pushing to clean up health standards, improve moral standards, elevate American education and fight corruption in state and local governments. The push for popular election of Senators became part of that campaign.
Leading the way for this reform was the populist William Jennings Bryan. Bryan, who would later become Secretary of State, served as a representative of the House of Representatives. Bryan also ran for president, although he lost to William McKinley. Bryan was highly critical of the Senate's perceived corruption and ineffectiveness. Consequently, he actively campaigned for the passing of the 17th Amendment.
In addition to Williams Jennings Bryan, the yellow journalist William Randolph Hearst published in Cosmopolitan magazine a series of articles criticizing the way in which the Senate conducted business. This helped gain popular support for the new constitutional amendment.
A patient in the emergency room is monitored for heart rate, oxygenation level, etc. The nurse notices that the heart beat averages 80 but drops to 60 beats every other minute and then spikes to 120. The cardiologists have asked the nurses to notify them if this happens, as that pattern is indicative of heart attacks. The nurse calls the doctor.
Is the nurse using inductive or deductive reasoning?
The nurse is using Deductive reasoning.
Deductive reasoning is a valid form of proof. Here, a person makes conclusions based on previously known facts. It is process of reasoning from one or more statements to reach a logically certain conclusion. If all the parameters are true and the terms are clear then the conclusion reached is necessarily true.
In the image, shape DEFG is similar to shape WXYZ . Find the measure of side YZ.
DDFG:
Length: 18
Width: 24
WXYZ:
Legnth: 30
Width: YZ (unknown)
It is 40 because 24/40= 0.6 and 18/30= 0.6 so yeah its 40
Answer:
40
Step-by-step explanation:
We know that DEFG is similar to WXYZ. This means we can set up a proportion to find the length of the unknown side (let x be the unknown side):
18/30 = 24/x
Cross multiplying,
18(x) = 30(24)
18x = 720
Divide both sides by 18:
18x/18 = 720/18
x = 40
Which ordered pairs are solutions to the inequality 2x+y>−4?
Select each correct answer.
(5, −12)
(−3, 0)
(−1, −1)
(0, 1)
(4, −12)
if ∠2 and ∠3 are supplementary angles, then ∠2 and ∠3 form a linear pair true or false
Answer:
True ,if they are adjacent and share a vertex and one side
as part of his workout Jamal does two sets of 25 push-ups. if he does this 10 times each month, how many push ups does he do each month? write equation to show your work.
Answer:
Step-25×2=50
50×10=500by-step explanation:
In a geometric sequence the ratio between consecutive terms is
if the terms of a geometric sequence are
[tex]a_{1}[/tex], [tex]a_{2}[/tex], [tex]a_{3}[/tex], [tex]a_{4}[/tex], .....
then the common ratio r = [tex]\frac{a_{4} }{a_{3} }[/tex] = [tex]\frac{a_{3} }{a_{2} }[/tex] = [tex]\frac{a_{2} }{a_{1} }[/tex]
Answer:
In a geometric sequence the ratio between consecutive terms is constant.
Step-by-step explanation:
A geometric sequence is that sequence where the ratio between two consecutive terms is constant.
This ratio is called the common ratio.
For example:
Lets take an example :
1,6,36,216,1296,.....
To find the common ration we divide the second term by first term.
[tex]\frac{6}{1} =\frac{216}{36} =6[/tex]
Here, the common ratio is 6.
a company rents out 15 food. booths and 20 games booths at the county fair.the fee for a food booths is 100 plus 5 per day the. fee for game booths is 50 plus 7per day the fair lests for d day and all the booths are rented for the entire time write and simplify and expression for the amount in dollars that the company is paid
Answer:
2500 + 215d
Step-by-step explanation:
Total revenue from all booths is the sum of the revenue from the food booths and from the games booths. The food booth revenue for each booth is 100 + 5d, where d is the number of days the fair lasts. There are 15 food booths, so the total revenue from them is ...
... (food booth revenue) = 15(100 +5d)
The games booth revenue for each booth is 50 + 7d, where d is the number of days the fair lasts. There are 20 games booths, so the total revenue from them is ...
... (games booth revenue) = 20(50 +7d)
Then the total revenue is
... total revenue = (food booth revenue) + (games booth revenue)
... = 15(100 +5d) + 20(50 +7d) . . . . . . use the expression for revenue from each
... = 1500 +75d + 1000 +140d . . . . . . eliminate parentheses
... = 2500 + 215d . . . . . . . . . . . . . . . . collect terms
0.85 3/5 0.15 7/10 in order from least to greatest
0.85=0.85
3/5=0.60
0.15=0.15
7/10=0.70
L-G
0.15, 3/5, 7/10, 0.85
To order the numbers from least to greatest, convert the fractions to decimals and compare. The ascending order is 0.15, 0.6, 0.7, and 0.85.
Explanation:
To order the given numbers from least to greatest, we can convert all the fractions to decimals.
0.85 is already a decimal.3/5 = 0.60.15 is already a decimal.7/10 = 0.7The numbers in ascending order are: 0.15, 0.6, 0.7, 0.85.
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The round tree school district has 101,687 students. The Samson school district has 173,245 students. Round to the nearest ten thousand to estimate how many students attend both school district
100,000 at round tree, 170,000 at Samson. both would be 270,000
a jar of juice contains 8 fluid ounces. about how many milliliters of juice does the jar hold? (1 fluid ounce is approximately 29.6 milliliters.)
A:237 ml
B:3.7 ml
C:37.9 ml
D:250 ml
please show work thank you!
Write an equation representing what you already know:
x=29.6
x represents fluid ounces. One fluid ounce is 29.6 mL.
You want to find 8 fluid ounces.
8x=8*29.6
x=236.8
Round to the nearest whole number.
x=237
Answer:
A
Step-by-step explanation:
in a school the ratio of boys to girls 6/5. what is the probability of choosing a girl from a class of 22?
the ratio 6/5 means for every 6 boys there are 5 girls.
Add the ratio: 6+5 = 11
Divide class total by 11: 22/11 = 2
Multiply each ratio number by 2 to find the number of boys and the number of girls:
6 x 2 = 12 boys
5 x 2 = 10 girls.
10 out of the 22 kids are girls.
The probability of picking a girl would be 10/22, which reduces to 5/11
Wich inequality statement best represents the graph ?
SERIOUS ANSWERS ONLY!
The answer is f(x) ≥ 2x^2 + 4x
Hope this helps!
Answer: a) f(x) ≤ -2x^2 + 4x
Step-by-step explanation:
In the graph you can see that the "hands" of the quadratic function go up, this means that the principal constant (the one that multiplicates the square term) is positive:
this is:
for a function f(x) = a*x^2+ b*x + c
if a is positive, the hands will go upside, if a is negative, the hands will go downside.
we also can see that the shaded area is upside the curve, so we are looking for f(x) > something.
Then we can discard the third option because we have f > -2*x^2..
the remaining options are:
a) f(x) ≤ -2x^2 + 4x or f(x) ≥ 2x^2 - 4x
b) f(x) ≥ 2x^2 + 4x
first, you can see that in the second function both terms have the same sign, so there can be only one x-intercept, but in the graph, we can see two x-intercepts, so we can also discard option b.
The remaining option, and the correct one, is option a.
A spacecraft travels 7,500,000 miles in one year. Express the distance in scientific notation.
A) 7.5 x 106
B) 7.5 x 10−7
C) 7.5 x 108
D) 75 x 106
Answer:
The answer is A
Step-by-step explanation:
The distance of 7,500,000 miles expressed in scientific notation is 7.5 × 10⁶, which corresponds to option A) 7.5 × 10⁶.
The spacecraft travels 7,500,000 miles in one year. To express this distance in scientific notation, we need to convert it into the form of a × 10ⁿ, where a is a number between 1 and 10, and n is an integer.
To find the correct form, we can manipulate the original number. We move the decimal point 6 places to the left (since there are six zeros in the million), which gives us 7.5. Thus we can write 7,500,000 as 7.5 × 10⁶. So, the correct answer is A) 7.5 × 10⁶.
If the equation y = (x - 6)(x + 12) is graphed in the xy-plane, what is the x-coordinate of the parabola’s vertex? Also please show the steps. :)
First write the function [tex]y=(x+12)(x-6)[/tex] in standard form [tex]y=ax^2+bx+c:[/tex]
[tex]y=x^2-6x+12x-72,\\\\y=x^2+6x-72.[/tex]
Find the x-coordinate according to the rule
[tex]x_{vertex}=-\dfrac{b}{2a}.[/tex]
Thus,
[tex]x_{vertex}=-\dfrac{6}{2\cdot 1}=-3.[/tex]
Now find the y-coordinate of the vertex substituting x=-3 into the parabola equation:
[tex]y_{vertex}=(-3)^2+6\cdot (-3)-72=9-18-72=-81.[/tex]
Answer: the x-coordinate if the vertex is -3.
The x-coordinate of the parabola’s vertex is 3
How to determine the x-coordinate of the parabola’s vertex?from the question, we have the following parameters that can be used in our computation:
y = (x - 6)(x + 12)
When expanded, we have
y = x² - 6x + 12x - 72
So, we have
y = x² + 6x - 72
the x-coordinate of the parabola’s vertex is calculated as
x = -b/2a
So, we have
x = -6/2* 1
Evaluate
x = -3
Hence, the x-coordinate of the parabola’s vertex is 3
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Ms Chavez bought 20 eggs at a market.she will use %30 of these eggs to make cookies. How many eggs will Ms Chavez use to make cookies
20 divided by 1/3 = 6 2/3, therefore Ms Chavez used 6 and two thirds of eggs.
Final answer:
Ms. Chavez will use 6 eggs to make cookies.
Explanation:
Ms. Chavez bought 20 eggs at the market. She will use 30% of these eggs to make cookies.
To find out how many eggs Ms. Chavez will use to make cookies, we can multiply the total number of eggs by the percentage used:
Number of eggs used = 20 × 0.30
Number of eggs used = 6
Therefore, Ms. Chavez will use 6 eggs to make cookies.
Evaluate.
6^2+(3⋅4)−2^4
Enter your answer in the box.
To evaluate the given expression, we follow the order of operations (PEMDAS) and calculate the exponentials first. Next, we perform the multiplication and addition/subtraction operations from left to right to find the final result. Following the order of operations (PEMDAS), the expression 6^2+(3⋅4)−2^4 simplifies to 32.
Explanation:To evaluate the given expression, we need to follow the order of operations, which is PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction).
First, let's calculate the exponentials:
6^2 = 6 * 6 = 36
2^4 = 2 * 2 * 2 * 2 = 16
Next, let's perform the multiplication and addition/subtraction operations from left to right:
3 * 4 = 12
36 + 12 - 16 = 48 - 16 = 32
Therefore, the result of the given expression is 32.
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