The sequence 7, 5, 2, 1, then the
( i ) . The general term d = 2
( ii ) . The next three terms are, [tex]a_{5} =3 ,a_{6} = 5 ,a_{7} = 7[/tex]
( iii ) . The 25th term [tex]a_{25}[/tex] = 55
The sequence is,
⇒ 7, 5, 2, 1
[tex]a_{1} ,a_{n+1} ,a_{n+2} ,a_{n+3} = 7 , 5 , 2 , 1[/tex]
( i ) . The general term,
Let us assume general term = d
We can use this formula,
d = [tex]a_{n+1} -a_{n}[/tex]
where,
[tex]a_{n+1} = 5\\a_{n} = 7[/tex]
d = 7 - 5
d = 2
So,
The general term d = 2
( ii ) . The next three terms, [tex]a_{5} ,a_{6} ,a_{7}[/tex]
We can use this formula,
[tex]a_{n+1} =a_{n} +d[/tex]
[tex]a_{5} =a_{4} +d ;\\a_{6} = a_{5} +d ;\\a_{7} = a_{6} +d[/tex]
[tex]a_{5} = 1+2\\a_{5} = 3[/tex]
[tex]a_{6} = 3+2\\a_{6} = 5[/tex]
[tex]a_{7} = 5+2\\a_{7} = 7[/tex]
So,
The next three terms are, [tex]a_{5} =3 ,a_{6} = 5 ,a_{7} = 7[/tex]
( iii ) . The 25th term
We can find nth term,
We can use this formula,
[tex]a_{n} =a_{1} +(n-1)d[/tex]
[tex]a_{n} = 7+(n-1)2[/tex]
[tex]a_{n} =7+2n-2\\a_{n} = 2n+5[/tex]
Then, 25th term is,
We can substitute n = 25
[tex]a_{25} = 2(25)+5\\a_{25} =50 + 5\\a_{25} = 55[/tex]
So,
The 25th term [tex]a_{25}[/tex] = 55
Therefore,
( i ) . The general term d = 2
( ii ) . The next three terms are, [tex]a_{5} =3 ,a_{6} = 5 ,a_{7} = 7[/tex]
( iii ) . The 25th term [tex]a_{25}[/tex] = 55
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Dante buys candy that costs $7 per pound. He will spend at least $42 on candy. What are the possible numbers of pounds he will buy? Use p for the number of pounds Dante will buy. Write your answer as an inequality solved for p
Answer:
p [tex]\geq[/tex] 6
Step-by-step explanation:
If one pound costs $7 and he's going to spend at least $42, then he will buy at least as many pounds as what costs $42.
42 divided by 7 equals 6, so he will buy at least 6 pounds of candy.
Solve the following...
4x+10=-26
Answer:
x = -9
Step-by-step explanation:
the goal is to get x by itself, so subtract 10 from both sides: 4x=-36
divide both sides by 4: x = -9
|-----4x+10=-26 |
|ANSWER= x=-9-------|
happy fall!
explanation ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
When we have questions like this, and the x is just THROWN in there, we have to "combine our like terms."
STEP ONE ✨: "How do we do that..if one is on the other side?"
We have to make it disappear. +10-10 equals zero, right? right! So do that!
4x+10=-26
-10
But what we do to one side, we do to the other! Subtract 10 from the numbers on the equal side.
4x+10=-26
-10 -10
-26-10
4x=-36
STEP TWO : What do we do when a number has an X beside it?
Since this number is being multiplied to the x, we have to DIVIDE the 4x by 4, so we just get the x alone. It always works like this. Don't doubt yourself!!
4x=-36
/4 /4
-36/4=-9
x=-9!
----------------
i hope this helped! || much love! <33
(Laws of Exponents with Integer Exponents LC) Simplify (34)−1. one over three raised to the fourth power one over three raised to the power of negative four −34 33
The simplified value of (3⁴)⁻¹ is 1/(3⁴) , which means one over three raised to the fourth power , the correct option is (a) .
In the question ,
the expression is given as (3⁴)⁻¹ ,
the rule of law of exponents states that a⁻ⁿ = 1/aⁿ .
Using the above mentioned law of indices , the expression (3⁴)⁻¹ can be written as ,
(3⁴)⁻¹ = 3⁻⁴ = 1/3⁴
which can be expressed in words as one over three raised to the fourth power .
Therefore , the simplified value of (3⁴)⁻¹ is 1/(3⁴) , which means one over three raised to the fourth power , the correct option is (a) .
The given question is incomplete , the complete question is
The Simplified value of (3⁴)⁻¹ is
(a) one over three raised to the fourth power
(b) one over three raised to the power of negative four
(c) −3 to the power of 4
(d) 3 to the power of 3
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URGENT!! ILL GIVE
BRAINLIEST! AND 100 POINTS
The answer is not D
Answer:
b
Step-by-step explanation:
The area and perimeter
Answer:
N/A
Step-by-step explanation:
the area and perimeter for what exactly?
Three consecutive positive odd integers such that 5 times the square of the
middle integer exceeds the product of the other two by 488.
By letting the smallest integer equal x, set up and solve a quadratic equation
to find the middle integer.
A solution by trial and improvement will not be accepted.
An analogous equation can be created by factoring a quadratic equation. 5x^2 = (x-2) * (x+2) + 488 can give integers 9, 11,13.
What is a quadratic equation?In algebra, quadratic equation (from Latin quadratus 'square') is any equation that can be rearranged in standard form as
[tex]{ax^{2}+bx+c=0}[/tex]
where a 0 and x denotes an unknown and a, b, and c denote known numbers, Since there is no ax2 term, the equation is linear (and not quadratic) if a = 0 (and b 0). The coefficients of the equation, denoted by the numbers a, b, and c, are the quadratic coefficient, linear coefficient, and constant or free term, respectively.
The roots or zeros of the expression on the left-hand side of the equation are the values of x that fulfill the equation. There can only be two solutions to a quadratic problem. One claims that a problem is a double root if there is just one solution. There are either two real solutions, one real double root, two complex solutions that are complex conjugates of one another, or two real solutions if all the coefficients are real values. If complex roots are included, a quadratic equation will always have two roots; a double root counts as two. An analogous equation can be created by factoring a quadratic equation.
According to the formula, if 5x2 = x2 - 4 + 488, then 5x2 = x2 + 484.
For 4x2 = 484, subtract x2 from each side, resulting in x2 = 121.
For x = 11, square root each side.
TEST: 5*121 = 9*13 + 488, so 605 is equal to 117 plus 488.
The middle odd number, x, is equal to 11.
The figures are 9, 11, and 13.
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Determine the angle of rotation
Answer: b
Step-by-step explanation:
:)
your pulse reflects the rate at which your heart beats. a healthy resting pulse rate in adults is between 60 and 100 beats per minute. in which of these two settings is a binomial distribution more likely to be at least approximately correct? explain your answer. (a) you select at random 10 times in the next 24-hour period to take your pulse. you then go about your usual activities, including exercising and sleep. the random variable ???? is the number of measurements that are less than 100 beats per minute. (b) a nurse instructs an adult patient to take his resting pulse 10 times over the next few days. a resting pulse requires resting for at least 10 minutes before taking the pulse. the random variable ???? is the number of measurements that are less than 100 beats per minute.
The situation in which the binomial distribution can be approximated to the normal distribution is given by:
(b) a nurse instructs an adult patient to take his resting pulse 10 times over the next few days. a resting pulse requires resting for at least 10 minutes before taking the pulse. the random variable ???? is the number of measurements that are less than 100 beats per minute.
What is the binomial distribution formula?The formula for the probability of x successes is:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The parameters are given by:
n is the number of trials of the experiment.p is the probability of a success on a single trial of the experiment.The binomial distribution can be approximated to the normal distribution if there are at least 10 failures and 10 successes on the experiment, that is:
np ≥ 10, n(1 - p) ≥ 10.
Meaning that a large number of trials is usually required for the approximation.
In the context of this problem, to achieve the large number of trials needed for the approximation, multiple days are needed to take the observations, hence option b is correct.
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I need help..........
Answer:
y=1.34x-3.22
Step-by-step explanation:
y=mx+b
find m/ gradient:
[tex]m = \frac{-3.94 - 2.4}{-4.75 - 0}[/tex]
∴[tex]m=1.34[/tex]
find b/ y-intercept:
sub (2.4,0)
0= 1.34 (2.4) +b
b=0-3.216
b= -3.216
∴ b=-3.22(2.d.p)
linear equation:
∴1.34x-3.22
what is the maximum number of balls of clay of radius 2 that can completely fit inside a cube of side length 7 assuming the balls can be reshaped but not compressed before they are packed in the cube?
Answer:
Number of balls of clay: 10
Step-by-step explanation:
The volume of the cube is [tex]$V_{\text{cube}}=7^3=343,$[/tex]
and the volume of a clay ball is: [tex]$V_{\text{ball}}=\frac43\cdot\pi\cdot2^3=\frac{32}{3}\pi.$[/tex]
Since the balls can be reshaped but not compressed, the maximum number of balls that can completely fit inside a cube is
[tex]\[\left\lfloor\frac{V_{\text{cube}}}{V_{\text{ball}}}\right\rfloor=\left\lfloor\frac{343}{\frac{32\pi}{3} }\right\rfloor.\][/tex]
Approximating with [tex]$\pi\approx3.14[/tex]
We have:
[tex]\[\left\lfloor\frac{V_{\text{cube}}}{V_{\text{ball}}}\right\rfloor=10.23565228[/tex]
We simplify to get:
[tex]\[\left\lfloor\frac{V_{\text{cube}}}{V_{\text{ball}}}\right\rfloor\approx10[/tex]
So:
[tex]\boxed{number\ of\ balls = 10}.$[/tex]
answer these 2 questions for a cookie
Answer:
1. C
2. D
5. C
Step-by-step explanation:
Answer:
C as j is a variable
D
C as 13+9+1.9= 23.9
pls mark as brainliest
True value received an invoice dated may 08, 2020. the invoice had a $5,800 balance that included $800 freight. terms were 3/10, 2/30, n/60. true value pays the invoice on may 22. what amount does true value pay?
True value received an invoice dated may 08, 2020. the invoice had a $5,800 balance that included $800 freight true value pays the invoice on may 22. then true value pay amount is $4900
Invoice dated 08/may/2020. Amounting to $5,800 which includes $800 freight.
Terms:
3/10 ; 2/30 ; n/60
The term 3/10 means that True value can avail of 3% discount if it pays within 10 days from date of issuance. The 10th day would be 18/may/2020
The term 2/30 means that True value can avail of 2% discount if it pays from the 11th day up to the 30th day from the date of issuance.
may 22 is beyond the 10th day but within the 30 days discount period. True Value can avail of the 2% discount.
5,800 - 800 = 5,000 The freight can't be subjected to discount thus it is deducted from the total invoice amount.
5,000 * 2% = 100
5,000 - 100 = 4900 amount True Value has to pay.
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How much hours does it take the robot to complete one task
Answer:
0.41
Step-by-step explanation:
Select the correct answer from each drop down-menu.
Which are the best definitions for theorem, conjecture, and axiom?
A statement that is assumed to be true without proof is a(n)
. A statement that has been shown to be true by vigorous application of logic is a(n)
. A(n)
is a statement that is believed to be true but hasn't been proven.
A statement that is assumed to be true without proof is a(n) Theorem
A statement that has been shown to be true by vigorous application of logic is a(n) ---> Conjecture
A(n) Axiom is a statement that is believed to be true but hasn't been proven.
What's the big difference between a definition and a theorem?A definition is both a precise and a general statement of the significance of a mathematical term.
It does this by laying down all of the characteristics of the word together with the structures that need to be true.
This is how the meaning of the word is defined. A mathematical assertion that can be demonstrated using logically sound mathematical reasoning is called a theorem.
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HELP!!!! HELP HELP HELP HELP
The matchings are:
3x - y = -5 ⇒ table C.
x - 3y = 12 ⇒ table A.
3x - y = -2 ⇒ table D.
2x - 3y = 9 ⇒ table B.
How to match each equation to the correspondent table?The first equation we have is:
3x - y = -5
Evaluating in x = 0, we have:
3*0 - y = - 5
y = 5
So we have the point (0, 5).
Evaluating in x = -2 we get:
3*-2 - y = -5
6 + y = 5
y = 5 - 6 = -1
So we have the point (-2, -1)
The only table with that point is table C, so we conclude that it is the correct option.
2) The second equation is:
x - 3y = 12
Evaluating in x = 0 we get:
0 - 3y = 12
y = 12/-3 = -4
So we have the point (0, -4)
if x = 3 we have:
3 - 3*y = 12
-3*y = 12 - 3 = 9
y = 9/-3 = -3
So we have the point (3, -3)
The only table with these two points is table A, so that is the correct one.
3) The next equation is:
3x - y = -2
The tables left are B and D.
Now, let's evalaute this equation in x = 3.
3*3 - y = -2
9 - y = -2
9 + 2 = y
11 = y
So we have the point (3, 11)
Notice that on table B,the value associated to x = 3 is y = -1, so we discard table B, and we conclude that this equation relates to table D.
Trivially, the last equation:
2x - 3y = 9
Matches table B.
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Kaj needs to order some new supplies for the restaurant where she works. The restaurant needs at least 736 knives. There are currently 155 knives. If each set on sale contains 12 knives, what is the minimum number of sets of knives Kaj should buy?
Please hurry! :D
Answer:
736 - 155 = 581.
581 divided by 12 is 48.416.
that means the minimum number of sets of knives Kaj should buy is 49.
Step-by-step explanation:
A match-seller arranges his matchboxes in a
triangular pattern as shown in Fig. 18.4. He
continues until there are 11 matchboxes in
the bottom row of the triangle. How many
matchboxes are in the complete pattern?
MATO
MATCHES
MATCHES
Fig. 18.4
MATCHES
MATCHES
MATCHES
MATCHES
MATCHES
MATCHES
MATCHES
MATCHES
Using the properties of an arithmetic sequence we can conclude that the total number of match boxes is 66.
There is a consistent distinction between the words in a sequence of numbers known as a "arithmetic progression" or "arithmetic sequence" (AP).
In an arithmetic series, the space between subsequent terms is constant. The numbers 3, 5, 7, and 9 come to mind. because there is always a two-term difference between two succeeding terms, it is arithmetic.We know that the bottom row of the pyramid has 11 matchboxes .
As we can see in the figure that the each succeeding step has one matchbox less.
Therefore the number of matchboxes in each row is in an AP.
Therefore the AP has a common difference of -1 and the first term is 11
The last term of the AP is 1.
Therefore
aₙ = a + (n-1)d
or, 1 = 11 + (n-1)(-1)
or, n = 11
We know that the sum of all terms of an AP is given by
S=n/2{2a+(n-1)d}
or, S = 11/2 {2×11 + (10)(-1)}
or, S = 66
Therefore from the arithmetic progression we calculate that the total number of match boxes is 66.
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Disclaimer: The missing diagram is attached below.
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Which of the following situations can be modeled by the equation?
answer = a
formula; a(1 + r)^x
a = the initial amount - 7.71 [answer cannot be b or d]
! i think it's a as the decay factor is < 1, therefore, 100-.933333
The subtraction of 8 from a number is 2. What is the number?
Answer:6
Step-by-step explanation:
8-6 = 2
Answer:
10
Step-by-step explanation:
Let the number be equal to y
y-8=2y=8+2y=10if u know this please help
Answer:
alternate angles and corresponding angles.
and vertical opposite angles
Step-by-step explanation:
#G o o g l e
Name the reciprocal that you will use to multiply
(Equations in picture)
I only need the reciprocals
Answer: 9/4 and -2/1 (or -2)
Step-by-step explanation: Reciprocals are just the fraction flipped
Fav Sport
volleyball (12)
Basketball (18)
Ping Pong (8)
Softball (10)
Football (24)
(#s in brackets are the frequencies of their individual sports)
It should be noted that the angle sector for each sport will be:
volleyball (12) = 60°
Basketball (18) = 90°
Ping Pong (8) = 40°
Softball (10) = 50°
Football (24) = 120°
How to illustrate the information?From the information given, the following can be illustrated:
volleyball (12) = 12/72 × 360° = 60°
Basketball (18)= 18/72 × 360° = 90°
Ping Pong (8) = 8/72 × 360° = 40°
Softball (10) = 10/72 × 360° = 50°
Football (24) = 24/72 × 360° = 120°
Total = 72
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Evaluate the expression when a = 2 and x = -4.
2a-x
The expression when a = 2 and x = -4, given 2a-x. The value will be 8.
What are mathematical operations?In mathematics, an operation is a function that transforms zero or more arguments or operands into a clearly defined output value. The number of operands in the operation determines how difficult it is.
Unary operations (i.e., operations of arity 1), which include additive inverse and multiplicative inverse, as well as binary operations (i.e., operations of arity 2), which include addition and multiplication, are the operations that are most frequently studied. The nullary operation, also referred to as a zero-arity operation, is a constant. The mixed product is an example of a ternary operation, also referred to as an operation of arity 3.
The arity is typically assumed to be limited. Even yet, infinitary operations are occasionally taken into account, in which case the "typical" operations of finite dimensionality are referred to as finiteary operations.
Similar to an operation, but with partial function in place of a function, is the definition of a partial operation.
Since, a= 2 and x= -4, then,
2(2)-(-4)= 8
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Evaluate m + (n-1)^2 if m = 3 and n = -4
Answer:
Step-by-step explanation:Answer: using identity[(a+b)(a-b) = a^2 - b^2]. (m+n)(m-n) = m^2 - n^2. m^2 - n^2 = (3)^2 - (4)^2 = -7.
What is the value of r in the equation 6(1 + 2r) - 3(1 - 8r) = 75?
Answer:
2
Step-by-step explanation:
[tex]6(1+2r)-3(1-8r)=75 \\ \\ 6+12r-3+24r=75 \\ \\ 3+36r=75 \\ \\ 36r=72 \\ \\ r=2[/tex]
Thực hiện phép tính -7x^2(3x-4y)
Answer: -21x^3 + 28x^2 y
Ella walks to the art store at 2mph, but returns home at 4 mph. If her total walking time is 1/2 an hour, how far away is the art store? Express your answer as a fraction.
The distance of art store from Ella's house is 2/3 miles or 0.67 miles.
It is a question of time, speed and distance.
It is given in the question that Ella walks to the art store at 2mph, but returns home at 4 mph.
Also, the total time taken by Ella to cover the journey is 1/2 an hour.
We have to find the distance of art store from Ella's house.
Let the distance from Ella's house to art store be d miles.
We know that,
Speed = distance/time
Time = distance/speed
Hence, we can write,
time = d/2 (walking to the art store from from)
Also,
time = d/4 (walking to home from the art store)
Hence,
d/2 + d/4 = 1/2
3d/4 = 1/2
d = 2/3 miles or 0.67 miles.
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Could you guys help a sista out? I’m struggling
4. Mrs. Sparks is a 9th grade Algebra 1 teacher. She teaches three
Algebra 1 courses and all the classes recently took a chapter exam.
Below are the scores.
Class 1
45
68
77
90
90
95
100
100
86
90
50
55
Class 2
64
65
70
40
100
87
84
88
90
90
95
80
Class 3
70
75
75
90
100
80
55
65
76
80
88
99
a. Find the mean, median, mode and range of Class 1.
b. Find the mean, median, mode and range of Class 2.
c. Find the mean, median, mode and range of Class 3.
d. Find the standard deviation of Class 1.
e. Find the standard deviation of Class 2.
f. Find the standard deviation of Class 3.
g. Which class had a higher standard deviation and what does that mean?
h. In your opinion, which class did better on the exam? Explain your answer.
The mean of Class 1 is 78.83.
The median of Class 1 is 88
The mode of Class 1 is 90
The mean of Class 2 is 79.42
The median of Class 2 is 85.50
The mode of Class 2 is 90
The mean of Class 3 is 79.42
The median of Class 3 is 78
The mode of Class 3 are 75 and 80
The standard deviation of Class 1 is 18.81
The standard deviation of Class 2 is 16.15
The standard deviation of Class 3 is 12.70.
The class that had the higher standard deviation is class 1.
The class that did better on the exam is class 3 because it has the higher mean and the lowest standard deviation.
What is the mean, median and mode?Mean is the average of a set of numbers.
Mean = sum of numbers / total number
Mean of Class 1 = (45 + 50 + 55 + 68 + 77 + 86 + 90 + 90 + 90 + 95 + 100 + 100) / 12 = 78.83
Mean of Class 2 = (40 + 64 + 65 + 70 + 80 + 84 + 87 + 88 + 90 + 90 + 95 + 100) / 12 = 79.42
Mean of Class 3 = (55 + 65 + 70 + 75 + 75 + 76 + 80 + 80 + 88 + 90 + 99 + 100) / 12 = 79.42
Median is the number that is at the center of the dataset that is arranged in either ascending or descending order.
Median of Class 1 = (86 + 90) / 2 = 88
Median of Class 2 = (84 + 87) / 2 = 85.50
Median of Class 3 = (76 + 80) / 2 = 78
Mode is the number that occurs most frequently in a dataset.
Standard deviation is used to calculate the average variation of a dataset.
Standard deviation = [tex]\sqrt{\frac{(x - u)^{2} }{n} }[/tex]
Where:
x = number in the dataset u = mean n = total numbers in the dataset.Standard deviation of Class 1 = 18.81
Standard deviation of Class 2 = 16.15
Standard deviation of Class 3 = 12.70
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Answer:
Down below!
Step-by-step explanation:
A.
The mean 78.83.
The median 88
The mode 90
The range 55
B.
The mean 79.42
The median 85.50
The mode 90
The range 60
C.
The mean 79.42
The median 78
The mode 75 and 80
The range 45
D. 18.81
E. 16.15
F. 12.70
G. The class that had the higher standard deviation is class 1.
H. The class that did better on the exam is class 3 because it has the higher mean and the lowest standard deviation.
How many sheets of metal are in a stack 4.00 in. high if each sheet is 0.0146 in. thick?
The number of metal sheets in the stack is
(Round to the nearest whole number as needed.)
The number of metal sheets in the stack is 274 metal sheets
Ratio and proportionFractions are written as a ratio of two integers. For instance a/b is a fraction.
Given the following parameters
Height of metal sheet = 4.00in
Height of each sheet= 0.0146 in
Number of metal sheet = height of metal sheet/height of each sheet
Substitute
Number of metal sheet = 4.00/0.0146
Number of metal sheet = 274 metal sheets
This gives the required number of sheets
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