Answer:
1109
Step-by-step explanation:
you can subtract the terms to see the difference between them
-11-(-27)=16
The sequence is increasing by 16
you can plug that 16 in the formula for d
a_n=a_1+(n-1)d
a_n=a_1+(n-1)16
n represents the term you want to find in this case the 72nd
a sub 1 is the first term of the sequence in this case -27
a_72=-27+(72-1)16
a_72=-27+(71)16
a_72=-27+1136
a_72=1109
The 72nd term of the given arithmetic sequence is 1109.
What is an arithmetic sequence?A sequence in which the difference between any two consecutive terms is the same is known as an arithmetic sequence.
The given arithmetic sequence is -27, -11, 5...
The common difference of the arithmetic sequence is:
d = -11 - (-27)
d = 16
The nth term of an arithmetic sequence is:
aₙ = a₁ + (n-1)d
= -27 + (n-1)16
= -27 +16n -16
= 16n - 43
To find the 72nd term, substitute n = 72 into the above equation:
a₇₂ = 16(72) -43
a₇₂ = 1109
Hence, the 72nd term of the given arithmetic sequence is 1109.
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factor as the product of two binomials x^2-100
Answer:
(x+10)(x-10)
Step-by-step explanation:
See the explanation on your other problems;
Quickly:
x^2 = x timex x
-100 = 10 x -10
(x+10)(x-10)
Can you please help out
Lou’s gross annual income is $41,028. He is paid biweekly and has 4% deducted from his paychecks for his 401(k). His employer matches his deduction, up to 3%.
How much is deposited into Lou’s 401(k) each payday?
Answer:
Amount deposited into Lou's 401(k) each payday is $119.665
Step-by-step explanation:
Here we have gross income annual $41028
Payment frequency = Every two weeks
Number of payments (Pay days per annum) = 12 × 2 = 24 payments annually
Amount payed on pay day = $41028/24 = $1709.5
Amount deducted from Lou's paycheck on payday = 4% of Pay = 0.04×$1709.5
∴ Amount deducted from Lou's paycheck on payday = $68.38
Amount employer matches = 3% of pay = 0.03 × $1709.5 = $51.285
Therefore, amount deposited into Lou's 401(k) each payday = $68.38 + $51.285
Amount deposited into Lou's 401(k) each payday = $119.665.
Answer:
$110.46
Step-by-step explanation:
Consider the complex number z = -7 + 5i.
The real part of the complex number is _____.
(-2, 5i, 5, or 7)
The imaginary part of the complex number is _____.
(-2, 5i, 5, or 7)
Answer:
-7 is the real part
5i is the imaginary part
Step-by-step explanation:
z = -7 + 5i
i is the imaginary number
-7 is the real part
5i is the imaginary part
Answer:
The real part of the complex number is -7
The imaginary part of the complex number is 5
What is the inverse operation for addition?
multiplication
subtraction
division
addition
Answer: Subtraction
Adding is the opposite of Subtraction
Multiplication is the opposite of Division
Sal recorded the number of crackers in each snack-sized package he opened.
Number of Crackers in Each Package
5
6
7
8
+
9
10
+
11
+
12
+
13
+
14
+
15
Which statement must be true according to the box plot?
O
O
O
O
The data is symmetric, and the lowest number of crackers in a package was 7.
The data is symmetric, and the lowest number of crackers in a package was 8.
The data is skewed, and the lowest number of crackers in a package was 7.
The data is skewed, and the lowest number of crackers in a package was 8.
The statement must be true according to the box plot if the data is skewed, and the lowest number of crackers in a package was 7. Option C is correct.
What is a number line?A number line is drawn with numbers equally spaced or sections running the length of it.
Here, we have,
A number line should be drawn horizontally and can be extended in any direction indefinitely.
The number line shows the number of crackers lies between 7 and 13. Which is numerically as 7,8,9,10,11,12,13.The number of the digit on the number line skewed is 7.
Hence statement must be true according to the box plot if the data is skewed, and the lowest number of crackers in a package was 7. Option C is correct.
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You are a plumber, and you are repairing a toilet leak. The job should take 0.9 hours. About how many minutes will it
take to complete the job?
O 0.015
O 5.4
O 54
O 67
O 540
Answer:
54
Step-by-step explanation:
multiply 60 by 0.9 and you get 54..?
Answer:
54
Step-by-step explanation:
0.1 is 10% of 1 and was subtracted off so we subtract 10% off 60 so 60 x 10% = 6
60 - 6 = 54
Hope this helps can I have brainliest
Compare and contrast alternate interior angles and
alternate exterior angles.
Answer:
if lines are parralel then corresponding angles are congruent and alternate exterior angles are congruent. if lines are parralel, them same side interior angles are suplementary and same side exterior angles are suplementary
Answer:
When two lines are crossed by another line (called the Transversal): Alternate Exterior Angles are a pair of angles on the outer side of each of those two lines but on opposite sides of the transversal. In this example, these are two pairs of Alternate Exterior Angles: a and h.
Step-by-step explanation:
HELP ON A TEST
Factor the expression: 4x^2 - 121 (x^2 means x squared)
Henry is a high school basketball player. In a particular game, he made some free
throws (worth one point each) and some two point shots. Henry made a total of 9
shots altogether and scored a total of 16 points. Determine the number of free throws
Henry made and the number of two point shots he made.
Answer:
7 two point shots and 2 free throws
Step-by-step explanation:
There is a relationship between the variables, because as the number of apples increases, the weight of the apples
Answer:
There is a relationship between the variables, because as the number of apples increases, the weight of the apples also increases.
Step-by-step explanation:
Answer:the answer is: increases
Step-by-step explanation:
P(t) = 21,000 (4/7)^t/3
Answer:
3
Step-by-step explanation:
Hannah invested $4000 in a savings account that that earned 2% interest compounded quarterly. she determined that if she does not withdraw or deposit any more money, the value of the account at the end of 3 years will be $4244.83.what error did Hannah make in her calculations? what will her account balance be after 3 years
Answer:
Her account balance after 3 years is $4,246.71
Step-by-step explanation:
In this question, we are tasked with calculating what Hannah's account balance will be after 3 years and the error she made in her calculations
Mathematically, to calculate the account balance after 3 years, we use the formula for the compound interest as follows.
Mathematically, the amount A earned on a compound interest is calculated as
A = P[tex](1+r/n)^{nt}[/tex]
where A is the account balance after the number of years which is what we want to know
P is the initial amount invested which is $4000
r is the interest rate which is 2%(2/100 = 0.02) according to the question
n is the number of times interest is compounded per year which is 4(quarterly means every 3 months)
t is the number of years which is 3
We plug the values into the question;
A = 4000(1 + 0.02/4)^(3)(4)
A = 4000(1+0.005)^12
A = 4000(1.005)^12
A = $4,246.71
P.S ; I do not see Hannah's calculation and as such I cannot spot where she made the error in her calculations
Final answer:
Hannah made a calculation error; the correct balance after 3 years at 2% interest compounded quarterly on a $4000 investment is approximately $4248.71.
Explanation:
The student has incorrectly calculated the future value of a $4000 investment at 2% interest, compounded quarterly. The accurate calculation involves using the compound interest formula:
P = P0 (1 + r/n)nt
Where:
P is the future value of the investment.
P0 is the principal amount ($4000).
r is the annual interest rate (2%, or 0.02).
n is the number of times interest is compounded per year (4, since it is quarterly).
t is the time the money is invested for (3 years).
Plugging in the values we get:
P = $4000 (1 + 0.02/4)4*3
After solving, we get P = $4000 * (1 + 0.005)12 ≈ $4000 * 1.061677812
Hence, the account balance after 3 years would be approximately $4248.71, not $4244.83 as Hannah initially thought.
Write the ordered pair that represents yzThen find the magnitude of yz.
Y(5,0), Z(7,6)
Answer: (2,6) ; 2sqrt10 units
Step-by-step explanation:
How does the mean absolute deviation (MAD) of the data in set 1 compare to the mean absolute deviation of the data in set 2?
Set 1: 82, 80, 90
Set 2: 82, 80, 60, 90
The MAD of set 1 is 6 less than the MAD of set 2.
The MAD of set 1 is 5 less than the MAD of set 2.
The MAD of set 1 is 5 more than the MAD of set 2.
The MAD of set 1 is 6 more than the MAD of set 2.
Answer:
The answer is The MAD of set 1 is 5 less than the MAD of set 2.
Step-by-step explanation:
HELP ME!!!!!!!!!The potatoes beth brought weighed 3 kilograms and 420 grams. Her onions weighed 1,050 grams less than the potatoes. How much did the onions and potatoes weigh together
The required total weight of the potato and onion is given as 5.79 Kg.
As given in the question, the potatoes beth brought weighed 3 kilograms and 420 grams. Her onions weighed 1,050 grams less than the potatoes.
The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
Here,
Weight of the potatoes = 3 + 0.420 = 3.420 Kg
Weight of the onion = weight of potato - 1.050
Weight of onion = 3.420 - 1.050
weight of onion = 2.370 Kg
Total weight = 3.42 + 2.37 = 5.79 Kg
Thus, the required total weight of the potato and onion is given as 5.79 Kg.
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I need help with this
Answer:
Step-by-step explanation:
Fill in the blanks:
a. range
b. median
c. mode
d. mean
1. mean: 5+3+2+6+5+2+5= 15+4+6+3= 28/7= 4
median: 2,2,3,5,5,5,6: 5
mode: 5
range: 6-2= 4
2. 24+12+10+15+10+22+12= 105/7= 15 mean
10,10,12,12,15,22,24: 12 is the median
mode: 10, 12
range: 24-10= 14
3. 14+9+20+5+17+13= 78/6= 13 is the mean
5,9,13,14,17,20: 13+14= 27/2= 13.5 median
no mode
20-5= 15 the range
4. 21+15+16+25+13+18= 108/6= 18 is the mean
median: 13,15,16,18,21,25: 16+18= 34/2= 17
no mode
range: 25-13= 12
5. 10+12+17+18+20+25+31= 133/7= 19 mean
median: 18
mode: none
range: 31-10=21
6. 40+43+46+48+52+53= 282/6= 47
median: 46+48= 94/2 = 47
mode: none
range: 53-40= 13
7. 8+9+10+15+28= 70/5= 14 mean
median: 10
mode: none
range: 28-8= 20
8. 22+32+33+58+85= 230/5= 46 mean
median: 33
mode: none
range: 85-22= 63
9. 17+18+20+24+30+35= 144/6= 24 mean
median: 24+20= 44/2= 22
mode: none
range: 35-17= 18
10. 116+120+125+125+130+140= 756/6=126: mean
median: 125+125= 250/2= 125
mode: 125
range: 140-116= 24
Bella spent 4/7 of her money on a dictionary and 3 identical books. She spent 1/6 of the remainder on a journal that cost $7. a) How much did she spend on the dictionary and 3 books? b) If 3/8 of the cost of the dictionary was the same as 1/2 of the total cost of 3 books, how much did each book cost?
a) 9.33$
b) 1.33$
Step-by-step explanation:
a)
To solve the problem, let's call
[tex]m[/tex] = the money that Bella has at the beginning
[tex]d=[/tex] the price of a dictionary
[tex]b=[/tex] the price of one book
[tex]j=\$7[/tex] the price of the journal
Here, Bella spent 4/7 of her money to buy a dictionary and 3 books, so
[tex]\frac{4}{7}m=d+3b[/tex] (1)
Then she spent 1/6 of the remainder (which is [tex]\frac{3}{7}m[/tex]) to buy the journal so
[tex]\frac{3}{7}m=j=7[/tex] (2)
So from this second equation we can find m, the money that she has at the beginning:
[tex]m=\frac{7}{3}\cdot 7 =\frac{49}{3}=\$16.3[/tex]
So the amount that she spent for the dictionary + the 3 books is
[tex]\frac{4}{7}m = \frac{4}{7}\cdot \frac{49}{3}=\frac{28}{3}=\$9.33[/tex]
b)
Here, we are told that
3/8 of the cost of the dictionary was the same as 1/2 of the total cost of 3 books
Which can be rewritten as an equation as follows:
[tex]\frac{3}{8}d=\frac{1}{2}(3b)[/tex]
This means that we can rewrite the cost of the dictionary by re-arranging this equation as:
[tex]d=\frac{8}{3}\cdot \frac{1}{2}(3b) =4b[/tex]
Substituting into eq.(1) of part a),
[tex]\frac{4}{7}m=4b+3b\\\frac{4}{7}m=7b[/tex]
And from this, we can find b, the cost of each book:
[tex]b=\frac{1}{7}\cdot \frac{4}{7}m=\frac{4}{49}\cdot \frac{49}{3}=\frac{4}{3}=\$1.33[/tex]
a. She spent on the dictionary and 3 books is $8.
b. The cost of each book is $2.
a) First, let's find out how much Bella spent on the dictionary and 3 books.
Given that Bella spent 4/7 of her money on the dictionary and 3 identical books, this means she spent 1 - 4/7 = 3/7 of her money on other items.
Next, she spent 1/6 of the remaining money on a journal, which cost $7. So, 1/6 * 3/7 * Total money = $7.
To find the total money she had, we'll multiply $7 by 6/1 * 7/3 = $14.
Now, let's find out how much she spent on the dictionary and 3 books. She spent 4/7 * $14 = $8 on them.
b) Now, let's find out how much each book costs.
Given that 3/8 of the cost of the dictionary is the same as 1/2 of the total cost of 3 books, we set up the equation:
(3/8) * Cost of Dictionary = (1/2) * Total cost of 3 books.
Let's denote the cost of each book as x.
So, (3/8) * Cost of Dictionary = (1/2) * 3x.
To solve for x, first find the cost of the dictionary. From part a, we know the cost of the dictionary is $8.
Substitute $8 into the equation: (3/8) * 8 = (1/2) * 3x.
Simplify: 3 = (3/2) * x.
Now, isolate x: x = 3 * 2/3 = $2.
Therefore, each book costs $2.
A circle has a circumference of 10\blue{10} 10 start color #6495ed, 10, end color #6495ed . It has an arc of length 92\dfrac{9}{2} 2 9 start fraction, 9, divided by, 2, end fraction . What is the central angle of the arc, in degrees? ∘^\circ ∘ degrees
Answer:
[tex]\theta=162^0[/tex]
Step-by-step explanation:
[tex]\text{Circumference of a circle}=2\pi r[/tex]
Circumference of the Circle =10
[tex]\text{If the length of an arc}=\dfrac{9}{2}[/tex]
[tex]\text{Length of an arc}=\dfrac{\theta}{360}X2\pi r[/tex]
Therefore:
[tex]\dfrac{9}{2}=\dfrac{\theta}{360}X10\\\dfrac{\theta}{360}=\dfrac{9}{2}\div 10\\\dfrac{\theta}{360}=\dfrac{9}{20}\\$Cross Multiply\\20\theta=9X360\\\theta=(9X360)\div 20\\\theta=162^0[/tex]
The central angle of the arc is 162 degrees.
The suns diameter is about 860,000 miles. It's diameter is about 8000 miles. Estimate how many times larger the sun's diameter is than earth's diameter
Answer:
The Sun's diameter is [tex]1.075\times 10^2[/tex] times the Earth's diameter.
Step-by-step explanation:
We are given the following in the question:
Sun's diameter = 860,000 miles
Earth's diameter = 8000 miles
Comparison of Sun's and Earth's diameter:
[tex]\dfrac{\text{Sun's Diameter}}{\text{Earth's Diameter}}\\\\=\dfrac{860000}{8000}\\\\=\dfrac{8.6\times 10^{5}}{8\times 10^3}\\\\=1.075\times 10^2[/tex]
Thus, the Sun's diameter is [tex]1.075\times 10^2[/tex] times the Earth's diameter.
If given x=3 and x= -5
write a quadratic equation
Lou had r rocks in his collection. He separated his rocks into 3 equal piles. He now has 12 rocks in each pile. Which equation represents this situation?
Answer:
[tex]r[/tex] [tex]\div[/tex] 3 = 12
Step-by-step explanation:
Given:
Lou had r rocks in his collection.
He separated his rocks into 3 equal piles.
He now has 12 rocks in each pile.
Question asked:
Which equation represents this situation?
Solution:
Total number of rocks = [tex]r[/tex]
He separated in number of piles = 3
Each pile contains = 12 rocks
The equation will be :-
[tex]r[/tex] [tex]\div[/tex] 3 = 12
Therefore, equation which represents this situation is [tex]r[/tex] [tex]\div[/tex] 3 = 12
Solve the system of equations
x + 3y = 5
-x + 6y = 4
A) x = 1, y = 2
B) x = 2, y = 1
C) x = 1, y = 1
D) x = 0, y = 2
Answer:
B) x = 2, y = 1
Step-by-step explanation:
Add the two equations to eliminate the x-variable.
(x +3y) +(-x +6y) = (5) +(4)
9y = 9 . . . . . . .simplify
y = 1 . . . . . . . . divide by 9
You can substitute this value into either equation to find x.
x + 3(1) = 5
x = 2 . . . . . . . . subtract 3
The solution is (x, y) = (2, 1).
Answer:
B) x=2, y=1
Step-by-step explanation:
x+3y=5
-x+6y=4
solve the equation
x=5-3y
-x+6y=4
substitute the value of x into an equation
-1(5-3y)+6y=4
multiply numbers in parenthesis by -1
-5-3y+6y=4
put -5 as positive and add 5 to 4 and put -3y as positive and add to 6y.
9y=9
divide both sides by 9
y=1
substitute the value of y into an equation
x=5-3•1
multiply 3 to 1
x= 5-3
subtract 5 to 3
x=2
------------
x=2
y=1
------------
Have three witches each holding a broom and a spoon. Witches say witch plus witch plus witch =45. Three brooms say broom plus broom plus a broom =21 and three spoons say spoon plus spoon plus spoon = 12 then final question is a plain witch plus broom x spoon equal a ? What's answer?
Answer:
32
Step-by-step explanation:
witch plus witch plus witch = 45 ⇒ witch = 45/3 = 15
broom plus broom plus a broom = 21 ⇒ broom = 21/3 = 7
spoon plus spoon plus spoon = 12 ⇒ spoon = 12/3 = 4
__
If we assume each witch on first line refers to a "loaded" witch that includes a broom and a spoon, then a "plain" witch is ...
plain witch = witch - broom - spoon = 15 -7 -4 = 4
and the final total of interest is ...
plain witch plus broom x spoon = 4 + 7 × 4 = 4 +28 = 32
PLEASE HELP!!!Hannah conducts an investigation to determine if adding fertilizer to the soil helps tomato plants grow taller. She puts 20 tomato plants in individual pots and adds an equal amount of soil to each pot. All 20 plants are the same height at the beginning of the investigation. She adds the same amount of fertilizer to the soil of 10 pots. Hannah measures the height of each plant once a day for 15 days. The presence of fertilizer in the soil is the . The height of the tomato plants is the . The pots without fertilizer are the .
Answer:
1. independent variable
2. dependent variable
3. control group
Step-by-step explanation:
Independent variables are the factors in the experiment that are being modified to discover some sort of result.
Dependent variables are those that change because of the independent variable; they're also the ones that are measured in the experiment.
The control group is a group that undergoes the same exact procedure as the experimental group(s) do, but without the independent variable; it is to make sure that the different results aren't due to environmental factors.
Here, because Hannah is changing the amount of fertilizer in the plants (none or a specific amount), the presence of fertilizer is the independent variable. Since the heights of the plants will likely change due to the presence of fertilizer, height is the dependent variable. And, finally, the pots without fertilizer undergo the same procedure but without the independent variable, or the fertilizer, so it's the control group.
Hope this helps!
Answer:
The presence of fertilizer in the soil is the independent variable
The height of the tomato plants is the dependent variable
The pots without fertilizer form the control group
Step-by-step explanation:
She has divided the pots into 2 groups of 10 each:
1) experimental group
2) control group
She can decide the amount of fertiliser so that's an independent variable
What's she's observing are the heights which she can't control so heights is the dependent variable
Gustavo and Aiden are walking due west through the forest when they happen upon an angry grizzly bear. Gustavo runs away 23^\circ23 ∘ 23, degrees north of east for 300 \,\text{m}300m300, start text, m, end text, and Aiden runs away 33^\circ33 ∘ 33, degrees south of east for 250 \,\text{m}250m250, start text, m, end text. How far are Gustavo and Aiden away from each other?
Answer:
They are 261.96 meters apart.
Step-by-step explanation:
From the question, considering a North, East, South and west pole, Gustavo ran 23° above the east horizontal, while Aiden ran 33° below the east horizontal.
Thus, the total angle between them is 23 + 33 = 56°.
Therefore, let the distance between them be c and we can calculate that using the cosine law. Thus,
c² = a² + b² – 2ab cos θ
Where a and b are distances travelled respectively by Gustavo and Aiden. While θ is the angle between them.
Thus,
c² = 300² + 250²– 2(300) (250)cos 56
c² = 90000 + 62500 - 83878.9355
c² = 68621.0645
c = √68621.0645
c = 261.96 m
They are 261.96 meters apart.
Answer:
56 degrees
Step-by-step explanation:
Khan academy
Can someone please help me ASAP
1.6 is 8% of what?
Answer:
20%
Step-by-step explanation:
1.6:8*100 =
(1.6*100):8 =
160:8 = 20
Now we have: 1.6 is what percent of 8 = 20
Question: 1.6 is what percent of 8?
Percentage solution with steps:
Step 1: We make the assumption that 8 is 100% since it is our output value.
Step 2: We next represent the value we seek with $x$.
Step 3: From step 1, it follows that $100\%=8$.
Step 4: In the same vein, $x\%=1.6$.
Step 5: This gives us a pair of simple equations:
$100\%=8(1)$.
$x\%=1.6(2)$.
Step 6: By simply dividing equation 1 by equation 2 and taking note of the fact that both the LHS
(left hand side) of both equations have the same unit (%); we have
{100\%}{x}={8}{1.6}
Step 7: Taking the inverse (or reciprocal) of both sides yields
{100\%}={1.6}{8}
x=20
Therefore, $1.6$ is $20 of $8$.
Daniel is given the following information to construct a triangle. Determine what type of triangle will be constructed
80 degrees,40 degrees, and 40 degrees
A. an acute triangle
B.no triangle
C.A right angle
D. obtuse triangle
Answer:
An acute triangle
Step-by-step explanation:
All of the angles are less than 90 degrees
With the given angles of 80, 40, and 40 degrees, a triangle can be constructed because they sum up to 180 degrees. Since all the angles are less than 90 degrees, the triangle formed will be an acute triangle (option A).
The question is to determine what type of triangle will be constructed using the given angles of 80 degrees, 40 degrees, and 40 degrees. The sum of the angles in any triangle must equal 180 degrees. Given the angles provided, if we add them up (80 + 40 + 40), we get exactly 180 degrees. This confirms that a triangle can indeed be constructed with these angles.
Furthermore, since all the given angles are less than 90 degrees, this means each angle is acute. Therefore, a triangle with all acute angles is known as an acute triangle (option A). Hence, the triangle that will be constructed with the given angles is an acute triangle.
fractions that are equivent to 4/12
Answer:
1/3 2/6
Step-by-step explanation:
Answer:
2/6 and 1/3
Step-by-step explanation:
Which expression is equivalent to StartFraction b Superscript negative 2 Baseline Over a b Superscript negative 3 Baseline EndFraction? Assume a not-equals 0, b not-equals 0.
Given:
The given expression is [tex]\frac{b^{-2}}{a b^{-3}}[/tex]
Let us assume that [tex]a \neq 0, b \neq 0[/tex]
We need to determine an expression that is equivalent to the expression [tex]\frac{b^{-2}}{a b^{-3}}[/tex]
Equivalent expression:
The equivalent expression can be determined by solving the given expression.
Hence, applying the exponent rule, [tex]\frac{x^{a}}{x^{b}}=x^{a-b}[/tex]
Thus, we get;
[tex]\frac{b^{-2}}{a b^{-3}}=\frac{b^{-2-(-3)}}{a}[/tex]
Subtracting the numbers, we get;
[tex]\frac{b^{-2}}{a b^{-3}}=\frac{b}{a}[/tex]
Thus, the equivalent expression is [tex]\frac{b}{a}[/tex]
Hence, Option D is the correct answer.
Answer:
d
Step-by-step explanation: