The 7th term of the Arithmetic Progression (AP) is found using the common difference formula.
What is the sequence of AP arithmetic progression?In Arithmetic Progression, the difference between the two arithmetical orders is just a constant value (AP). Arithmetic Sequence is another name for it.
We'd come across the few key phrases in AP that were denoted as:
The first term (a)Common difference (d)Term nth (an)The total of first n terms (Sn)As shown below, the AP can also be described in terms of common differences.
The following is the formula for determining an AP's n-th term: an = a + (n − 1) × dThe arithmetic progression sum is as follows: Sn = n/2[2a + (n − 1) × d].Common difference 'd' of an AP: d = a2 - a1 = a3 - a2 = a4 - a3 = ...... = an - an-1.Now, according the given condition in the question.
Let the 5th term is defined by 'a₅'.
Let the 6th term is defined by 'a₆'.
Let the 7th term is defined by 'a₇'.
The common difference of the can be calculated as;
d = a₆ - a₅
Now, for the second case, it could be written as;
d = a₇ - a₆
So,
a₇ = d + a₆.
Therefor, the 7th term of an AP can be computed by adding the common difference to the 6th term of an AP.
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PLEASE ANSWER FAST Estimate 4001 + 283 + 97 =
Answer:
4400
Step-by-step explanation:
4001→4000 (you need to round the number to the nearest thousand)
283→300 (you need to round the number to the nearest hundred)
97→100 (you need to round the number to the nearest ten, in this case 100)
4000+300+100= 4400
Hope this helps! :)
How do i solve this?[tex]2(-15)-\sqrt[3]{18(-15)-1061}[/tex]
- 40.18 is the solution of this function .
What does a math cube root mean?
The factor we multiply by itself three times to obtain a number is its cube root. 3 cube root of, end cubic root is the symbol for the cube root. The opposite of cubing an integer is to get its cube root.Finding a number that, when multiplied twice by itself, equals the original number is necessary in order to compute the square root of any number. Similar to this, we must discover a number that, when multiplied three times by itself, equals the original number in order to find the cube root of any number.[tex]2( -15) - \sqrt[3]{18( -15 ) - 1061}[/tex]
= [tex]2 ( -15 ) - \sqrt[3]{3 - 1061}[/tex]
= [tex]-30 - \sqrt[3]{ - 1058}[/tex]
= - 30 - 10.18
= - 40.18
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(3x^5+8x^3-10x^2)-(-12x^5+4x^3+14x^2)
Answer:x
2
(
15
x
3
+
4
x
−
24
)
Step-by-step explanation:
Evaluate. Remember Order of
Operations! (PEMDAS)
-8 × 2² - (-40+ 6) = [?]
Answer:
The answer is 2
Step-by-step explanation:
Your friend gave you a free parking pass to a baseball game. Unfortunately, the parking spot number was smudged on the ticket. You know the parking spot was 7 spaces away from your friend's spot. If your friend's parking spot is number 19 in the same row, write and solve and absolute value equation to determine your possible parking spot number(s)? (use \displaystyle xx as the variable to represent the parking spot)
The possible parking spot numbers can be either 12th spot or 26th spot.
What are inequalities ?
When two values are compared , an inequality represents whether one is greater than, less than, or not equal to the other.
It is given that the parking spot was smudged on the ticket.
Let's assume the possible parking spot numbers can be given by x which is represented by an inequality.
Your parking spot is 7 spaces away from your friend's spot which is number 19 in the same row. So , the possible parking spot numbers can be given by ;
19 - 7 ≤ x ≤ 19 + 7
12 ≤ x ≤ 26
Therefore , the possible parking spot numbers can be either 12th spot or 26th spot.
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I can’t seem to figure out how to properly insert (r) and (t) after 2 and 3.
Answer:
7
Step-by-step explanation:
(2t+3r) divide 4
so if r=2 and t=11 the new equation will be :
(2times11 + 3times 2) divide 4
(22+6) divide 4
= 28 divide 4 = 7
Every item in the Just a Dollar store is priced
$
1.00
. When Jack opens the store, there is
$
125.00
in the cash register. When he counts the money in the cash register at the end of the day, the total is
$
935.00
. If the sales tax rate is
8
%
, how many items were sold that day?
750 items were sold that day
How to calculate the number of items sold ?The first step is to calculate the total revenue
Total revenue= 935 - 125
= 810
Therefore the number of items sold can be calculated as follows
810= 1x + 8/100
810= 1x + 0.08x
810= 1.08x
x= 810/1.08
x= 750
Hence 750 items were sold that day
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what is 49/200 equal to explain
Answer:
0.245
Step-by-step explanation:
Divide both the numerator and denominator by 2.
49/200 will be 24.5/100
If you divide a number by 100, you move the decimal place 2 digits to the left. 24.5/100 will become 0.245
samantha is using a wooden strip 7/8 yard long to make a picture frame.If she cuts off a piece that is 3/4 long, which fraction best represents the porportion that is left lf the original strip?
The portion of wooden strip that is left from the original strip is 1/4
How to calculate the amount of the original strip left ?Samantha is using a wooden strip that measures 7/8 yard
Samantha cuts off a piece of the wood that is 3/4 long
The fraction that represents the proportion of the original strip that is left can be calculated as follows
7/8 - 3/4
The LCM of both fractions is 8
7 - 6/8
= 2/8
convert to the lowest term
1/4
Hence the proportion of the original wooden strip that remains is 1/4
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A die is rolled. If the number rolled is greater than 2 , find the probability that it is a 6 .
According to the question, when die is rolled check the number is greater than two and it should be [tex]6[/tex].
The total number of outcomes : [tex]n(E)= {1,2,3,4,5,6}[/tex]
And getting a number greater than [tex]2[/tex] [tex]= {3,4,5,6}[/tex]
Finally, getting a number as [tex]6 = {6}[/tex]
Therefore, the probability can be written as:
[tex]P(E) = \frac{1}{6}[/tex]
Hence, the calculated probability is [tex]\frac{1}{6} .[/tex]
What is Probability?
The term probability means the study of the occurrence or the outcomes of the event. It is the measurement of the events that occurred during events. And many uncertain events cannot be measured.
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Write an explicit formula for each sequence. Then generate the first five terms. a₁ =1024, r=0.5
The formula of the given geometric sequence is: a(n) = 1024 . (0.5)ⁿ⁻¹ and the first five terms are: 1024, 512, 256, 128, and 64.
The formula of the n-th term of a geometric sequence is:
a(n) = a₁ . r^(n-1)
Where:
a₁ is the first term
r is the ratio = a(n)/a(n-1)
Parameters given in the problem:
a₁ =1024, r=0.5
Plug these parameters into the formula, then we get the explicit formula of the n-th term:
a(n) = 1024 . (0.5)ⁿ⁻¹
The first 5 terms:
a₁ = 1024
a(2) = 1024 . (0.5)²⁻¹
= 1024 . (0.5)¹ = 512
a(3) = 1024 . (0.5)³⁻¹
= 1024 . (0.5)² = 256
a(4) = 1024 . (0.5)⁴⁻¹
= 11024 . (0.5)³ = 128
a(5) = 1024 . (0.5)⁵⁻¹
= 1024 . (0.5)⁴ = 64
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PLEASE HELP!!! Given the function defined by f(x)=6x-3, find f(-4.6). Simplify.
Please help on geometry step by step im trying to learn
Answer:
m∠FQR = 23°
Step-by-step explanation:
Since m∠KQF = 90°, it's a complementary angle and is equal to 90°
Step 1: Write the equation. Since The whole angle equals 90° add everything together to equal 90°
(3x - 23)° + (2/3x + 3)° = 90
3x - 23 + (2/3)x + 3 = 90
Combine like terms
multiply the denominator by 3. (3 × 3) = 9 + 2 = 11
(11/3)x - 20 = 90
+ 20 +20
(11/3)x = 110
÷(11/3) ÷(11/3)
x = 30°
Step 2: Find m∠FQR
m∠FQR = ((2/3)x + 3))
(2/3)(30) + 3
20 + 3 = 23
m∠FQR = 23°
I hope this helps!
Answer:
Step-by-step explanation:
(2/3x+3) + (3x-23)=90
(2/3+3)x -20 =90
11/3x =90 + 20
x= 110 * 3/11 =30
FQR = 2/3x+3= 2/3 (30) +3 = 20 +3 =23
Carla puts $625 into a savings account at an annual interest rate of 2.5%. If she does not withdraw or deposit any money, what is the interest that Carla will earn at the end of 6 months?
The formula is I=prt
Given the principal and annual interest rate, the interest that Carla will earn at the end of 6 months is $7.81.
What is the interest that Carla will earn at the end of 6 months?Simple interest is simply a method to determine the amount of interest charged on a sum at a given rate and for a given period of time.
It is expressed as;
I = prt
Given the data in the question;
Principal P = $625Annual interest r = 2.5% = 2.5/100 = 0.025Time period t = 6 months = 6/12 = 0.5 yearsInterest I = ?Plug the given values into the formula above and solve for I.
I = p × r × t
I = $625 × 0.025 × 0.5
I = $7.81
Given the principal and annual interest rate, the interest that Carla will earn at the end of 6 months is $7.81.
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Write these propositions using p and q and logical connectives (including negations). (a) you do not drive over 65 miles per hour. (b) you drive over 65 miles per hour, but you do not get a speeding ticket. (c) you will get a speeding ticket if you drive over 65 miles per hour
Writing the propositions using p and q with logical connectives, including negations, in each of the statement will give;
(a) you do not drive over 65 miles per hour-
¬ p
(b) you drive over 65 miles per hour, but you do not get a speeding ticket
p ∨ ¬ q
(c) you will get a speeding ticket if you drive over 65 miles per hour-
p → q
We are to represent each statement using letters; p and q
The letters p and q are then connected with the logical connectives symbols; example negation, conjunction, disjunction and implication symbols.
Thus, each statement given in the question is logically written as;
(a) ¬ p
(b) p ∨ ¬ q
(c) p → q
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Which number line model shows the subtraction −3−6?
Answer:
C.
-3-6=-9
Step-by-step explanation:
-3-6=-9
C. The blue arrow goes to negative 3. Then the red arrow goes from negative 3 to negative 9.
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3/4 h -12= 8 5/8 pls answer with a detailed explanation
The value of h based on the information illustrated is 24 1/2.
How to calculate the value?It should be noted that the fraction given is illustrated as:
3/4h - 12 = 8 5/8
Add 12 to both sides
3/4h - 12 + 12 = 8 5/8 + 12
3/4h = 20 5/8
Multiply both side by 4/3
3/4h × 4/3 = 20 5/8 × 4/3
h = 165/8 × 4/3
h = 27 1/2
Therefore, the value of h is 24 1/2.
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Every year, the number of birds in a bird sanctuary increases by 3 percent. In 1997, there were 175 birds in the sanctuary. Using this data, predict the number of birds in the sanctuary in 2020.
There are 190 more birds than expected at the refuge.
The information provided in the question indicates that there are 3 percent more birds than there were previously. The sanctuary houses 175 birds, which may be pictured as follows:
There are 175 birds in all.
According to the inquiry, it is rising by 3%.
Number of birds = (175)(3%) = 5.25 at this point.
As a result, given the data, the anticipated enhanced data is as follows:
Added birds is 175 + 5 + 5 + 5 = 190.
190 more birds are therefore expected in the refuge.
How much is a percentage?The final computed numbers should be divided by the total value and then multiplied by 100 to obtain the percentage.
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What is the simplified answer to 5.3. √2 ? 8√2 2/2 15√2
The simplified answer to 5.3. √2 will be 7.495.
How to calculate the value?It should be noted that we are to find the simplified answer to 5.3. √2 .
This means that we have to multiply them. This will be:
= 5.3 × ✓2
= 5.3 × 1.1414
= 7.495
Note that the options given aren't complete.
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Zachary purchased a computer for $1,100 on a payment plan. Two months after he purchased the computer, his balance was $870. Six months after he purchased the computer, his balance was $410. What is an equation that models the balance y after x months?
Answer:
y = 1100 - 115x
Step-by-step explanation:
Let the monthly payment be $p
In two months Zach would have paid 2p dollars
Balance would be 1100 - 2p = y
We know after 2 months, balance y was actually 870
Substituting y = 870 we get
1100 - 2p = 870
Subtract 1100 on both sides
1100 - 1100 - 2p = 870 -1100
==> -2p = - 230
Divide by -2 on both sides
-2p/-2 = -230/-2
p = 115 which represents the monthly payment .
So the balance y after m months is given by the equation
y = 1100 - 115x
We can verify by plugging in the values for the second scenario
For 6 months
y = 1100 - 115 x 6 = 1100 - 690 = $410 which agrees with the given value so our equation is consistent
Arrange the numbers Least to Greatest1/2, -1/4, 7.2, 121, 1-41, -1.8, 9.1
The numbers in the order of least to greatest is :
₋1.8 , ₋1/4 , 1/2 , 1.41 , 7.2 , 9.1 , 121
Given, the numbers are in decimal and fraction form.
1/2 , -1/4 , 7.2 , 121 , 1.41 , -1.8 , 9.1
we need to convert the fractions and then arrange the numbers in the ascending order.
Writing the numbers in an ordered list according to their values means arranging them from least to greatest. The smallest number should be put on the left, followed by the next smallest number, which should be written directly to its right.
for 1/2:
1/2 = 0.5
for ₋1/4:
₋1/4 = 0.25
now arrange the numbers according to the least to greatest form.
we have numbers:
0.5 , 0.25 , 7.2 , 121 , 1.41 , ₋1.8 , 9.1
least to greatest form:
₋1.8 , 0.25 , 0.5 , 1.41 , 9.1 , 121
i.e , ₋1.8 , 1/4 , 1/2 , 1.41 , 9.1 , 121
Hence we get the required form.
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Find the next term in each sequence. 2,4,8,16, . . . . . .
Answer:2,4,8,16,32,64,128,256,512,1024,2048,4096
Step-by-step explanation:
You just mutiply the number with 2
Identify the segment bisector of JK
The length of JM is
Given that point M bisects segment JK, the numerical length of segment JK and segment JM are 80 and 40 respectively.
What is the numerical value of JK and JM?Given the data in the question;
Point M bisects segment JK.Segment JM = 7x + 5Segment MK = 8xA bisector divides a line or angle into two equal halves.
Hence
Segment JM = Segment MK
7x + 5 = 8x
Solve for x
8x - 7x = 5
x = 5
Now, numerical value of segment JM will be;
Segment JM = 7x + 5 = 7(5) + 5 = 35 + 5 = 40
Segment JK = (7x + 5) + 8x = 7(5) + 5 + 8(5) = 80
Given that point M bisects segment JK, the numerical length of segment JK and segment JM are 80 and 40 respectively.
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Lo5(x2-9)=0 pls help me my assignments is too hard so i learned that you can help me thanks
The final answer is the combination of both solutions x = 3,− 3.
What are quadratic in math?
A quadratic in mathematics is a particular kind of problem that involves squaring, or multiplying a variable by itself. This terminology comes from the fact that a square's area equals the product of its side length and itself. Quadratum, the Latin word meaning square, is where the word "quadratic" originates.Use the quadratic formula to find the solutions
x = - b + √b² - 4ac / 2a
Substitute the values
a = 1, b = 0, and c = − 9 into the quadratic formula and solve for x.
x = 0 + √ 0² - 4 . ( 1 . 9 ) / 2. 1
Simplify
The final answer is the combination of both solutions.
x = 3,− 3
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How can I solve this?
Answer:
Mean: 160
Median: 150
Mode: none
Range: 105
Standard deviation: 35.3
Step-by-step explanation:
Given:
Mean = 320Median = 300Mode = noneRange = 210Standard deviation = 70.6If each value in the data set is multiplied by a constant value, the mean, median, mode, range, and standard deviation will all be scaled by the same amount.
Therefore, if each value in the data set is multiplied by 0.5:
Mean: 320 × 0.5 = 160Median: 300 × 0.5 = 150Mode: none × 0.5 = noneRange: 210 × 0.5 = 105Standard deviation: 70.6 × 0.5 = 35.3Proof
Data set: {1, 2, 3, 4, 5}
[tex]\sf Mean\:\mu =\dfrac{\sum x_i}{n}= \dfrac{1+2+3+4+5}{5} = 3[/tex]
[tex]\sf Median = 3[/tex]
[tex]\sf Mode = none[/tex]
[tex]\sf Range = 5-1=4[/tex]
[tex]\sf Standard\:deviation\:\sigma=\sqrt{\dfrac{\sum (x_i-\mu)^2}{n}}=\sqrt{\dfrac{10}{5}}=\sqrt{2}[/tex]
If we multiply each value by 0.5, the new data set is:
{0.5, 1, 1.5, 2, 2.5}
[tex]\sf Mean\:\mu =\dfrac{\sum x_i}{n}= \dfrac{0.5+1+1.5+2+2.5}{5} = 1.5[/tex]
[tex]\sf Median = 1.5[/tex]
[tex]\sf Mode = none[/tex]
[tex]\sf Range = 2.5-0.5=2[/tex]
[tex]\sf Standard\:deviation\:\sigma=\sqrt{\dfrac{\sum (x_i-\mu)^2}{n}}=\sqrt{\dfrac{2.5}{5}}=\dfrac{\sqrt{2}}{2}[/tex]
Therefore, if each value in the data set is multiplied by 0.5, the mean, median, mode, range, and standard deviation are all scaled by the same amount.
Determine whether each sequence is arithmetic, geometric, or neither. Then find the tenth term. -5,15,-45,135,-405,. . . .
The sequence -5,15,-45,135,-405,. . . . is a geometric sequence and its 10th term is a(10) = 98,415
To determine whether a sequence is an arithmetic or geometric one, we need to check the relation between two consecutive terms.
In an arithmetic sequence, the nth term is obtained by adding the (n-1)th term with a constant, called a common difference (d).The given sequence is:
-5,15,-45,135,-405,....
In this sequence:
a(1) = -5
a(2) = 15
a(3) = -45
and so on.
Notice that:
15 = -5 . (-3) ⇒ a(2) = a(1) . (-3)
-45 = 15 . (-3) ⇒ a(3) = a(2) . (-3)
Since the n-th term is obtained by multiplying the (n-1)-th term by a constant, r = -3, hence, the given sequence is a geometric sequence.
The formula for the nth term in a geometric sequence is given by:
a(n) = a(1) . rⁿ⁻¹
Substitute n = 10, r = -3, and a(1) = -5
a(10) = (-5) . (-3)¹⁰⁻¹
a(10) = (-5) . (-3)⁹
= 98,415
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Determine whether each sequence is arithmetic. If so, identify the common difference and find the 32 nd term of the sequence. 2,4,7,10, . . . . .
The given sequence 2, 4, 7, 10, … is not an Arithmetic sequence.
The sequence we are provided is 2, 4, 7, 10, …
Here, [tex] a_{1}[/tex] = 2, [tex] a_{2}[/tex] = 4 and [tex] a_{3}[/tex] = 7.
A sequence is considered as an Arithmetic sequence if their difference is equal. Represented as -
[tex] a_{2}[/tex] - [tex] a_{1}[/tex] = [tex] a_{3}[/tex] - [tex] a_{2}[/tex] = [tex] a_{4}[/tex] - [tex] a_{3}[/tex] and so on
Now, in the given sequence
⇒[tex] a_{2}[/tex] - [tex] a_{1}[/tex] = 4 - 2
[tex] a_{2}[/tex] - [tex] a_{1}[/tex] = 2
⇒ [tex] a_{3}[/tex] - [tex] a_{2}[/tex] = 7 - 4
[tex] a_{3}[/tex] - [tex] a_{2}[/tex] = 3
⇒ [tex] a_{4}[/tex] - [tex] a_{3}[/tex] = 10 - 7
[tex] a_{4}[/tex] - [tex] a_{3}[/tex] = 3
Since, the difference between the given sequence of terms are not same.
∴ The given sequence 2, 4, 7, 10, … is not an Arithmetic sequence.
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h(x) = -4x - 3, find h(2).
Answer:
-11.
Step-by-step explanation:
h(x) = -4x - 3, find h(2).
Replace the x by 2:
h(2) = -4(2) - 3
= -8 - 3
= -11.
PLEASE HELP! The value of x is 6 numbers away from –1 on a number line. Which numbers could be the value of x?
On a number line, the value of x is six places away from zero. Any of the following numbers, from 1 to 5, could serve as the x.
When X is 6 numbers away from -1, it has a value of 5.
The values from -1 after 6 is -1,0,1,2,3,4,5 so 5 is the 6th number from -1
A number line is a straight line with numbers spaced at equal segments or intervals in mathematics.
A number line is often shown horizontally and can be extended indefinitely in any direction.
Moving from left to right causes the numbers on the number line to climb, whilst moving from right to left causes them to fall.
On a number line, both positive and negative integers can be shown.
Comparing numbers is made simpler by writing them on a number line. The number line's leftmost numerals are smaller than its right most digits.
A number line can be used to do addition, subtraction, and multiplication. We always move to the right, to the left, or by skipping a count while adding, subtracting, or multiplying.
Hence, x could be any one of the following Numbers: 5, 4, 3, 2, or 1.
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Kate cut a 100-foot rope into two pieces.one piece was 5 feet longer than 4 times the length of the other. Find the length of each piece
Answer:
81 feet & 19 feet
Step-by-step explanation:
