What is the nth term for 2,7,14,23,34,47
The expression [tex]s(n) = 2 + \sum\limits_{i = 2}^{n} [5 + 2 \cdot (i - 2)][/tex] represents the n-th element of the series.
How to derive the expression of a arithmetic sum-like sequence
In this question we find a sequence with a progressive difference between any two consecutive terms, whose definition is shown below:
s(1) = a
[tex]s(n) = a + \sum\limits_{i = 2}^{n} [b + r \cdot (i - 2)][/tex]
Where:
a - Value of the first element of the sequence.b - Difference between the first and second elements of the sequence. r - Increase for the difference between two consecutive elements of the sequence.First, determine value of the first element of the sequence:
a = 2
Second, find the difference between the first and second elements of the sequence:
b = 7 - 2
b = 5
Third, determine the increase for the difference between two consecutive elements of the sequence:
r = 2
The formula for the n-th term is [tex]s(n) = 2 + \sum\limits_{i = 2}^{n} [5 + 2 \cdot (i - 2)][/tex].
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Graph the step function. (5 points - 1 point for each part of the graph)
Answer:
Step-by-step explanation:
Find the z value such that 97% of the standard normal curve lies between −z and z. (Round your answer to two decimal places.)
The positive value of Z is 2.17.
What do you mean by normal distribution?
A data collection with a normal distribution is put up so that the majority of the values cluster in the middle of the range and the remaining values taper off symmetrically in either direction. Because of its flared appearance, a normal distribution's graphic representation is occasionally referred to as a bell curve. The specific shape may change depending on how the population is distributed, but the peak and curve are always symmetrical and in the centre.
The information can be represented in the standard normal curve below:
It is given that 97% of the standard normal curve lies between −z and z.
The area in between is 0.97 meaning that one side is (0.97)/2 = 0.485
In addition, the region not shaded is the level of significance represented by (1-0.97)/2 = 0.03/2 = 0.015
From the Z-Score table (0 to Z table), this probability corresponds to the Z value of Z= 2.17 and -2.17
Thus the positive value of Z is 2.17.
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An x-ray machine for animal cot 125,000. If the loan i for 10 year, and the interet paid i $65,625, what i the interet rate on the loan?
The interest rate on loan is 5.25%.
What is principal amount?
The loan amount that the lender gives to the borrower is referred to as the primary amount. Additionally, it is the factor the lender uses to calculate interest.
What is simple interest?
Simple interest is a method to calculate the amount of interest charged on a sum at a given rate and for a given period of time. The formula to calculate simple interest is I=P.r.t
Given, Principal amount=$125,000, time=10years, Interest=$65,625.
Let r be the rate of interest, on applying simplest interest formula
I=P.r.t
Where P=principal amount, r=rate, t=time.
I=125,000 x r x10
65,625=125,000 x r x10
r=[tex]\frac{65,625}{125,000(10)}[/tex]
r=0.0525
r=5.25%
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State the coordinates of the point.
Answer:
Step-by-step explanation:
B
Answer 0,4
Answer:
(-5,-1)
Step-by-step explanation:
Start at the orginal. This is (0,0), the middle of the graph. From that point you move 5 spaces left. That is the -5 in the answer. Then from that point, you move one space down. That is the -1 in the answer.
11) -8x + 2x-16 <-5x+7x
An isosceles triangle has a perimeter of 30cm. If the area is 7.8cm long. Find the length of the equal sides
The length of the equal sides is 11.1cm
From the question, we have
perimeter = 30 cm
base = 7.8 cm
perimeter = sum of all sides
30=7.8+x+x
30-7.8=2x
x = 22.2/2 =11.1cm
Addition:
The phrase "the addition" refers to combining two or more numbers. Adding two numbers is indicated by the plus sign (+), therefore adding three is written as three plus three. Additionally, the number of times the plus symbol (+) is used is up to you. For example, 3 + 3 + 3 + 3. Mathematical addition is a crucial component of the learning curriculum for kids. In primary school, students learn simple addition sums such as one-digit facts, Math addition sums, and double-digit Math addition sums. One of the most fundamental and interesting Math concepts for elementary school children is addition sums. Math is a fascinating subject, and children first learn basic mathematical concepts like adding numbers in their early years.
Complete question: An isosceles triangle has a perimeter of 30 cm. If the base is 7.8 cm long, find the length of the equal sides.
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3. What is m ∠ E?
(x + 10)
E
(4x - 35)°
Using the corresponding angle theorem, the value of m∠E is 155.
In the given question we have to find the value of m∠E.
As we know that,
According to the corresponding angle theorem, if a transversal meets two parallel lines, the corresponding angles must be congruent.
So from the figure
4x−35=x+10
Add 35 on both side we get
4x=x+10+35
4x=x+45
Subtract on both side
4x−x=x+45−x
3x=45
Divide by 3 on both side we get
x=15
So the value of x+10
=15+10
=25
As we know that value the angle of straight line is 180.
So m∠E+25=180
Subtract 25 on both side we get
m∠E=180−25
m∠E=155
Hence, the value of m∠E is 155.
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PLEASSEEEEEE HELP MEEEE
determine the percentage of gross domestic product that went toward healthcare in 2009 using the given function
does this underestimate or overestimate the percent displayed by the graph
cording to the model when will 18.4% of domestic gross product go towards healthcare around to nearest year
The percentage in 2009, calculated from the logarithmic function is given as follows:
16.5%.
Which underestimates the graphed amount by 0.4%.
According to the model, the year in which 18.4% of the domestic gross product will go towards healthcare is:
2020.
What is the function?The logarithmic function in the context of this problem is given as follows:
f(x) = 1.2ln(x) + 15.2.
In which x is the number of years since 2006.
2009 is three years after 2006, hence the percentage is obtained as follows:
f(3) = 1.2ln(3) + 15.2 = 16.5%.
The percentage on the graph is given by:
16.9%.
Hence the function underestimates the graphed amount by 0.4%.
The year in which 18.4% of the domestic gross product will go towards healthcare is x for which f(x) = 18.4, hence:
18.4 = 1.2ln(x) + 15.2.
1.2ln(x) = 3.2
ln(x) = 3.2/1.2
ln(x) = 2.67.
ln and the exponential are inverse functions, hence:
x = e^2.67 = 14.4.
2006 + 14 = 2020.
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$1200, 3.5%, 2 years
The simple interest would be $84.
What is simple interest?
Calculating the interest on a loan using simple interest is quick and simple. Simple interest is calculated by dividing the principle by the daily interest rate and the number of days between installments.
A quick and simple way to figure out interest on money is to use the simple interest technique, which adds interest at the same rate for each time cycle and always to the initial principal amount. Any bank where we deposit our funds will pay us interest on our investment. One of the different types of interest charged by banks is simple interest.
Interest = (Principle x Rate x Time in years)/100
= (1200 x 3.5 x 2)/100
= 84
The simple interest would be $84.
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f(x)= -x
r(x)= f(1/4x)
describe the transformation pls help!!
The sequence of transformations applied to function f(x) to produce function r(x) is a reflection across the y-axis and dilation by a scale factor of 1/4.
What is a reflection?A reflection can be defined as a type of transformation which moves every point of the object by producing a flipped but mirror image of the geometric figure.
In Geometry, a reflection across the y-axis (y = x) of a graph is given by this transformation rule (x, y) → (-x, y). This ultimately implies that, function f(x) = -x would be transformed to function r as follows:
f(x) = -(-x)
r(x) = x
By applying a dilation with a scale factor of 1/4 to function r, we have:
r(x) = (1/4 × x) → r(x) = f(1/4x)
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an individual was making blankets for a few friends. the individual used 6.3 feet of fabric for one blanket. if the individual makes 4 blankets, how many feet of fabric will the individual have used to make 4 blankets (round to the nearest whole number)?
Answer:
25
Step-by-step explanation:
6.3= 1 blanket
to find 4 blankets you multiply 6.3 by 4
6.3x4=25.2
to the nearest whole number
25
square root of 81 divided by 3
Answer: Yes
Step-by-step explanation: Can this help , 81 ÷ 3 is 27 which is one of the factors in the 3 multiplications
300 large pretzels cost $171. What is the unit price per pretzel?
Answer:
The unit price per pretzel is 57 cents (fifty-seven cents) each!
Step-by-step explanation:
Step One: Divide
Since the price is 171 dollars for 300 large pretzels, and you want to find the price of each pretzel, divide the price by the amount of pretzels.
171 / 300 = 0.57
Step Two: Convert
The answer is 0.57, but since you want to know the unit price, you need to convert it to dollars, and that's simple.
0.57 of a dollar is 57 cents.
Step Three: Get your Answer
Your answer is 57 cents per pretzel! You can double-check this by multiplying 0.57 by 300, getting 171.
Hope my answer helped you!
The bookstore sold 40 biographies and
100 mysteries. Find the ratio of biographies
to mysteries sold
Answer:
2 : 5 or 2/5
Step-by-step explanation:
The ratio is 40 : 100, which can simplify into 2 : 5.
How can i tell that there's multiple solutions?
Answer:
C. infinitely many solutionsStep-by-step explanation:
We can tell that an equation has multiple/ infinitely many solutions if we try to solve it and get a variable or a number equal to itself.
Let's solve the given equation and see what we'll get :-
[tex]\sf 15-10b-6=-10b+9[/tex]
Add 10b to both sides:-
[tex]\sf 15-10b-6+10b=-10b+9+10b[/tex]
Simplify:-
[tex]\sf 15-6=9[/tex]
Subtract:-
[tex]\sf 15-6=9[/tex]
[tex]\sf 9=9[/tex]
As we can see, both sides ended up equal, therefore, this equation has infinitely many solutions!
______________________Hope this helps!
Have a great day!
In a game the average score was 40
Jim's score was 5/2 of the average.
What was Jim's score?
In the game where average score was 40 , then Jim's score was 100 .
In the question ,
it is given that ,
the average score in the game was 40 .
and also given that the Jim's score was 5/2 of the average .
So , the Jim's score can be calculated using the equation .
Jim's score = (5/2) × (Average score of the game)
Substituting the value of average in the equation ,
we get,
Jim's Score = (5/2) × 40
= 5 × 20
= 100
Jim's score is 100 .
Therefore , The Jim's score in the game where average score was 40 is 100 .
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Consider the line y = 5/7x+1.
Find the equation of the line that is parallel to this line and passes through the point (-5, 6).
Find the equation of the line that is perpendicular to this line and passes through the point (-5, 6).
Note that the ALEKS graphing calculator may be helpful in checking your answer.
Equation of parallel line:
Equation of perpendicular line:
П
X√√
0=0
$
keeping in mind that parallel lines have exactly the same slope, let's check for the slope of the equation above
[tex]y = \stackrel{\stackrel{m}{\downarrow }}{\cfrac{5}{7}}x+1\qquad \impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}[/tex]
so for the parallel line we're really lookikng for the equation of aline whose slope is 5/7 and that it passes through (-5 , 6)
[tex](\stackrel{x_1}{-5}~,~\stackrel{y_1}{6})\hspace{10em} \stackrel{slope}{m} ~=~ \cfrac{5}{7} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{6}=\stackrel{m}{ \cfrac{5}{7}}(x-\stackrel{x_1}{(-5)}) \implies y -6= \cfrac{5}{7} (x +5) \\\\\\ y-6=\cfrac{5}{7}x+\cfrac{25}{7}\implies y=\cfrac{5}{7}x+\cfrac{25}{7}+6\implies {\Large \begin{array}{llll} y=\cfrac{5}{7}x+\cfrac{67}{7} \end{array}}[/tex]
now, keeping in mind that perpendicular lines have negative reciprocal slopes
[tex]\stackrel{~\hspace{5em}\textit{perpendicular lines have \underline{negative reciprocal} slopes}~\hspace{5em}} {\stackrel{slope}{\cfrac{5}{7}} ~\hfill \stackrel{reciprocal}{\cfrac{7}{5}} ~\hfill \stackrel{negative~reciprocal}{-\cfrac{7}{5}}}[/tex]
so for the perpendicular line we're really looking for the equation of a line whose slope is -7/5 and that it passes through (-5 , 6)
[tex](\stackrel{x_1}{-5}~,~\stackrel{y_1}{6})\hspace{10em} \stackrel{slope}{m} ~=~ - \cfrac{7}{5} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{6}=\stackrel{m}{- \cfrac{7}{5}}(x-\stackrel{x_1}{(-5)}) \implies y -6= -\cfrac{7}{5} (x +5) \\\\\\ y-6=-\cfrac{7}{5}x-7\implies {\Large \begin{array}{llll} y=-\cfrac{7}{5}x-1 \end{array}}[/tex]
Which set of ordered pairs shows the result of a dilation by a factor of 2 around the origin?
The set of ordered pairs that represent dilation factor of 2 is
a. A' (2, 12) B' (12, 12) C' (2, 4)
How to find the coordinates of the imageDilation is a method of transformation which uses a scale factor. The scale factor determines if the dilation is magnification or shrinking
|0 < r < 1| is shrinking
|r > 1| is magnification
The transformation rule for dilation is as follows
(x, y) for a scale factor of r → (rx, ry)
From the graph the coordinates are read and following the given transformation rule we have
preimage image
A (1, 6) → (1 * 2, 6 * 2) → A' (2, 12)
B (6, 6) → (6 * 2, 6 * 2) → B' (12, 12)
C (1, 2) → (1 * 2, 2 * 2) → C' (2, 4)
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1.7 × 4= with a rounded answer
I need to know (basically what the picture shows)
The coterminal angle is 299°, lies in the IV quadrant and the reference angle is 61°.
Coterminal angles: are angles in standard position (angles with the initial side on the
positive x-axis) that have a common terminal side. For example, the angles 30°, –330°
and 390° are all coterminal.
For angle 659°,
coterminal angle = 659 - 360
= 299°
For quadrant,
299/90 = 3.32
After truncating it's equal to 3.
Therefore, it lies in the IV quadrant.
A reference angle is the size of the smallest acute angle, t, formed by the terminal side of the angle t and the horizontal axis.
659 = 2*360-61
Therefore, the reference angle is 61°.
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CHALLENGE btw it hard
Answer:
25%
Step-by-step explanation:
Lets find how many people were at the pool at the 4th week.
1060 - 110 + 145 - 247 =
848
Use percent error formula,
[tex]\frac{v_a-v_e }{v_e}[/tex]
Actual - Estimate over Estimate
Actual (1st week): 1060
Estimate (4th week): 848
Plug into formula.
[tex]\frac{1060-848}{848}[/tex]
Simplify.
[tex]\frac{212}{848}[/tex]
Divide.
0.25
Multiply by 100 and write with a percentage sign.
0.25*100 = 25
25%
Answer:
The percent decrease is 20%
Step-by-step explanation:
First week : 1060 people
Second week: 1060 - 110 = 950 people
Third week : 950 + 145 = 1095 people
Fourth week: 1095 - 247 = 848 people
Make 1060 the whole (100%), we need to figure out 848 percent
848 x
1060 100
848 x 100 = 84800
84800 divided by 1060 = 20
From 1060 people to 848 people is a 20% decrease
(22-23)
-Jeva
7
#7 of 9 -
Ms. Smith opened a bank account to save money. The balance of the account is modeled by the function
f(x) = 4,000 (1.06)*, where x is the number of years since the account is opened. According to the function,
what is happening to the balance of the account each year?
A The balance of the account increases by 1.06% each year.
B The balance of the account decreases by 6% each year.
C The balance of the account decreases by 1.06% each year.
D The balance of the account increases by 6% each year.
<6)
The changes in his account is that (d) The balance of the account increases by 6% each year.
How to determine the occurrence in his account?The function of the account balance is given as
f(x) = 4,000 (1.06)*
The above function is an exponential growth function
Such that the growth factor (b) is the number in bracket
This is represented as
b = 1.06
The percentage growth rate (r) is calculated as:
r = b - 1
Substitute known values
r = 1.06 - 1
Evaluate the difference
r = 0.06
Express as percentage
r = 6%
This implies that the balance increases by 6% each year.
So, the true statement is (d)
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Frank' beak grow by 0. 25 inche per year and Alice' grow by 0. 40 inche per year. Write an equation to repreent the length of each penguin' beak in x year
Frank equation is : 0.25x + 1.95 = y
Alice equation is : 0.4x + 1.5 = y
This question is incomplete and actual question is
Frank and Alice are penguins. At birth, Frank’s beak was 1.95 inches long, while Alice’s was 1.50 inches long. Frank’s beak grows by 0.25 inches per year and Alice’s grows by 0.40 inches per year. Write an equation to represent the length of each penguin’s beak in x years.
Given that
Frank’s beak was 1.95 inches long and Frank’s beak grows by 0.25 inches per year
let y be the total long
equation is 0.25x + 1.95 = y
while Alice’s was 1.50 inches long and Alice’s grows by 0.40 inches per year
equation is 0.4x + 1.5 = y
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The sum of two numbers is 2. The difference between 8 and twice the smaller number is two less than four times the large number. Find the numbers.
Answer:
larger number = 3
smaller number = -1
Step-by-step explanation:
x = larger number
y = smaller number
x+y=2
8-2y=4x-2 ---> 10 = 4x+2y
10 = 4x+2y
5=2x+y
y = 5-2x
2x=5-y
x+5-2x = 2
-x+5=2
-x=-3
x=3
3+y=2
y=-1
Wich rule best represents the dilation applied to circle I to create circle II?
Answer:
Step-by-step explanation:
F 3/8x 3/8y
98. XYZ Corporation hired 6 people as
summer workers. Of these 6 people, 3 will
be hired as permanent employees in the
fall. If 2 of the 6 people are male, how
many of the possible groups of 3 people
hired in the fall will include only 1 male?
E. 4
F. 6
G. 12
H. 24
Answer:
G. 12
Step-by-step explanation:
You want the number of ways 1 male and 2 females can be chosen from a group of 2 males and 4 females.
MalesFrom a group of 2 males, there are 2 ways that 1 male can be chosen. (He can be one, or the other.
FemalesFrom a group of 4 females, there can be 4C2 = 4!/(2!(2!)) = 4·3/2 = 6 ways that 2 females can be chosen.
Possible groupsThe total number of possible groups is the product of the numbers of groups of males and of females:
possible groups = 2 · 6 = 12
G. There are 12 possible groups of 3 people.
__
Additional comment
If the males are {a, b} and the females are {A, B, C, D}, the 12 possible groups are ...
aAB aAC aAD aBC aBD aCD bAB bAC bAD bBC bBD bCD
<95141404393>
For a certain population of penguins, the distribution of weight is approximately normal with mean 15. 1 kilograms (kg ) and standard deviation 2. 2 kg. Approximately what percent of the penguins from the population have a weight between 13. 0 kg and 16. 5 kg ?.
56.78% of the penguins in the population have a weight between 13.0 kg and 16.5 kg, according to the usual distribution.
Given,
The mean of the population, μ = 15.1 kg
Standard deviation, σ = 2.2 kg
We have to find the percent of the penguins from the population have a weight between 13. 0 kg and 16. 5 kg;
Here,
z score = x - μ / σ
The z-score calculates how far the measure deviates from the mean by standard deviation.The p-value for this z-score, which is the percentile of X, can be obtained by looking at the z-score table.The ratio of the p-value of Z when X = 16.5 minus the p-value of Z when X = 13 indicates the percentage of penguins in the population whose weight is between 13.0 kg and 16.5 kg.
x = 16.5
z score = x - μ / σ
z = (16.5 - 15.1) / 2.2 = 0.64
Z = 0.64 has a p-value of 0.7389.
x = 13
z score = x - μ / σ
z = (13 - 15.1) / 2.2 = -0.95
Z = -0.95 has a p-value of 0.1711.
0.7389 - 0.1711 = 0.5678.
0.5678 = 56.78% of the penguins from the population have a weight between 13.0 kg and 16.5 kg.
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16 = -7v - 8 + 3v Solve for v.
Simplify your answer as much as possible.
To solve for v, isolate the variable by dividing each side by factors that don't contain the variable.
Solve for v.
[tex]16=-7v-8+3v[/tex][tex]v = -6[/tex] ← Our SolutionHope this helps!
the power of a test is measured by its capability of a) rejecting a null hypothesis that is true. b) not rejecting a null hypothesis that is true. c) rejecting a null hypothesis that is false. d) not rejecting a null hypothesis that is false.
The power of a test is measured by its capability of rejecting a null hypothesis that is false, so option C is the correct answer
what is power with respect to probability?
Power is defined as the probability of correctly rejecting the false null hypothesis. It is the measure of the capability of rejecting a null hypothesis that is false.
Power = P[ rejecting a null hypothesis that is false.]
So, option C is correct, the power of a test is measured by its capability of rejecting a null hypothesis that is false
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