Answer:
9
Step-by-step explanation:
given
10x + 3y = 2
then
10x + 3y + 7
= 2 + 7
= 9
I need help plsssss select the correct way to write the expanded form of 0.68 with decimals. group of answer choices 0 x 1 + 6 x 0.1 + 8 x 0.01 0 x 1 + 6 x 0.01 + 8 x 0.001 0 + 6 + 8 0 x 1 + 6 x 0.1 + 8 x 0.001
The expanded form of 0.68 is written as 0 x 1 + 6 x 0.1 + 8 x 0.01.
To express decimal numbers in their expanded form simply means writing each number according to its place value. It can be done by multiplying each digit of the decimal by its place value and adding it all together.
Given the decimal 0.68 or sixty eight hundredths in words, first, multiply the digit 0 by its place value, which is 1.
0 x 1
Multiply the digit 6 by its place value, which is 0.1.
6 x 0.1
Multiply the digit 8 by its place value, which is 0.01.
8 x 0.01
Add it all together.
0 x 1 + 6 x 0.1 + 8 x 0.01
Hence, the expanded for of the decimal 0.68 is written as 0 x 1 + 6 x 0.1 + 8 x 0.01.
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what is the mean, median, and mode of the following data set? 27, 31, 33, 33, 35, 45
Answer: mean = 34
median = 33
mode = 33
Step-by-step explanation:
To figure out the mean you add every number and divide them by the number of values you added together so 27 + 31 + 33 + 33 + 35 + 45 = 204 then we would divide that by 6 = 34
To find the median you put all the numbers into order so which it already is meaning now you find the number in the middle which is 33 and 33 if there were two more values you would have to find the mean of them, but in this case its 33
The mode is the number which appears the most which is 33 as it appeared more than 2 times.
Please Help, Consider the following sets in the universal set U, which is the set of all elements of the three given sets below. List the elements of the sets being described.
B = {d, o, I, e} I = {p, i, n, a, y} J = {p, i, n, o, y}
The results of the operations between the sets are given as follows:
1. U = {a, d, e, i, l, o, n, p, y}
2. E ∪ I = {d, o, l, e, p, i, n, a, y}.
3. E ∩ I = ∅.
4. J' = {d, a, l, e}
5. I ∪ J = {p, i, n, a, y, o}
6. (J ∩ I) ∪ E = {p,i,n,y,d,o,l,e}
7. E = {p, i, n, a, y}
8. I' ∪ J = {p, i, n, y, d, o, l, e}
9. (E ∪ I) ∩ (I ∪ J) = {p, i, n, a, y, o}
10. (J ∪ I)' = {d, l, e}
What is the universal set?The universal set is the set that contains all elements that belong to at least one of the sets E, I and J, hence:
U = {a, d, e, i, l, o, n, p, y}
What is the union operation?The union operation between two sets is the set of elements that belong to at least one of the sets.
Hence, in item 2, we have that:
E ∪ I = {d, o, l, e, p, i, n, a, y}
In item 5, we have that:
I ∪ J = {p, i, n, a, y, o}
What is the negation operation?The negation operation of a set X is the set that contains all elements that belong to the universe U but do not belong to X.
Hence, for item 4, we have that:
J' = {d, a, l, e}
For item 7, we have that:
E = {p, i, n, a, y}
Item 8 involves a negation then a union, hence:
I' = {d,o,l,e}
I' ∪ J = {p, i, n, y, d, o, l, e}
Item 10 involves an union then a negation, just different precedence of 8, hence:
I ∪ J = J ∪ I = {p, i, n, a, y, o}
(J ∪ I)' = {d, l, e}
What is the intersection operation?The union operation between two sets is the set of elements that belong to both of the sets.
Hence, in item 3, we have that:
E ∩ I = ∅ (no element belongs to both sets).
For item 6, we have an intersection then an union, hence:
J ∩ I = {p,i,n,y}
(J ∩ I) ∪ E = {p,i,n,y,d,o,l,e}
For item 9, we have the intersection of two unions, hence:
E ∪ I = {d, o, l, e, p, i, n, a, y}
I ∪ J = {p, i, n, a, y, o}
(E ∪ I) ∩ (I ∪ J) = {p, i, n, a, y, o}
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Find the 17 th term of each sequence. a₁₈ = -9, d = -11
The 17 th term of each sequence. a₁₈ = -9, d = -11 is [tex]a_{17}[/tex] = -185.
What is a sequence?a₁₈ = -9, d = -11 is
[tex]a_{17}[/tex] = -9 + (16)(-11)
[tex]a_{17}[/tex] = -185.
succession: the doing of one thing after another. A list of books is presented in alphabetical order. a succession of sonnets that is continuous or connected. a later event, outcome, or repercussion; something that happens after.
A series of numbers is an ordered list. The three dots signify moving forward in the set pattern. Each digit in the sequence is referred to as a word. The first term in the list is 1, followed by the second by 3, the third by 5, and so on.
Arithmetic sequences, geometric sequences, quadratic sequences, and special sequences are the four primary categories of distinct sequences you need to be familiar with.
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1/16 to the power of 2
Answer: 0.00390625
Step-by-step explanation:
Answer:
The answer is 1/256 :)
Step-by-step explanation:
This one is actually quite simple! All you need to do is multiply 1/16 by 1/16! 1 x 1 is 1 of course, and 16 x 16 is 256. I've attached an image to help break it down even further. (credit to cymath.com)
Hope this helps!
Kelly’s car travels 26 1/4 miles on 5/8 gallon of gas how much Can the car go per gallon
Answer:
42 miles per gallon
Step-by-step explanation:
First, Convert it into a decimal to make it easier, 26.25 miles on .625 gallon. Now we Divide the two numbers 26.25 ÷ .625 = 42.
Hope this helps :D
When radioactive substances decay, the amount remaining will form a geometric sequence when measured over constant intervals of time. The table shows the amount of Np-240, a radioactive isotope of Neptunium, initially and after 2 hours. What are the amounts left after 1 hour, 3 hours, and 4 hours?
The amounts left after: 1 hour = 642g, 3 hours = 160.6g, 4 hours = 80.3g, as calculated by the formula of radioactive decay.
What is radioactive decay?The process of radioactive decay is how an unstable atomic nucleus loses energy through radiation. A substance that has unstable nuclei is regarded as radioactive.Alpha, beta, and gamma decay are three of the most prevalent types of decay, and they all entail the emission of one or more particles.The formula so used: A = [tex]\frac{-dN}{dt}[/tex]
=> N = A ([tex]e^{-kt}[/tex]), where:
N = amount left after the decay.A = initial amountk = constantt = time taken by the decayNow,
AS shown in the table (refer to the image attached), for k:
=> 322 = 1284[tex]e^{-2k}[/tex]
=> [tex]\frac{322}{1284}[/tex] = [tex]e^{-2k}[/tex]
=> 0.25 = [tex]e^{-2k}[/tex]
Taking natural logarithm on both sides.
=> ln(0.25) = ln([tex]e^{-2k}[/tex])
=> ln(0.25) = (-2k) ln(e)
As ln (e) = 1,
=> ln (0.25) = -2k
=> -1.386 = -2k
=> k = 0.693
Now, for t = 1 and k = 0.693, in the original formula, we get:
=> N = 1284 ([tex]e^{-0.693(1)}[/tex])
=> N = 1284 (0.5)
=> N = 642
For t = 3 and k = 0.693, in the original formula, we get:
=> N = 1284 ([tex]e^{-0.693(3)}[/tex])
=> N = 1284 (0.125)
=> N = 160.6g
For t = 4 and k = 0.693, in the original formula, we get:
=> N = 1284 ([tex]e^{-0.693(4)}[/tex])
=> N = 1284(0.0625)
=> N = 80.3g
Thus, The amounts left after: 1 hour = 642g, 3 hours = 160.6g, 4 hours = 80.3g, as calculated by the formula of radioactive decay.
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b. Explain how your answer to part (a) relates to the explicit formula a n = a+(n-1) d
My answer to part (a) relates to the explicit formula in an n = n+6 n a= n+6 n.
a= n+6 n
Step-by-step explanation:
n=an−1−5
Step 1: Flip the equation.
an−6=n
Step 2: Add 6 to both sides.
an−6+6=n+6
an=n+6
Step 3: Divide both sides by n.
an n = n+6 n a= n+6 n
What is explicit formula?An arithmetic sequence has the explicit formula a = a + (n - 1)d, and each term of the sequence may be computed without knowing the values of the previous terms. The nth term of an arithmetic, geometric, or harmonic series is usually the explicit formula.
The formal equations for L-functions in mathematics are Riemann's zeta function and links between sums over an L-complex function's number zeroes and sums over prime powers.
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Find the sum of each finite series. Σ¹° n = 1 (3 n-4)
The sum of the given finite series is 125
The given finite series is:
[tex]\sum\limits^{10}_{n=1} {(3n-4)}[/tex]
Use the properties of sum operator:
[tex]\sum\limits^{10}_{n=1} {(3n-4)}=\sum\limits^{10}_{n=1} {3n}-\sum\limits^{10}_{n=1} {4}[/tex]
Calculate each term on the right side:
[tex]\sum\limits^{10}_{n=1} {4}=4+4+...+4=10\times4=40[/tex]
[tex]\sum\limits^{10}_{n=1} {3n}=3\sum\limits^{10}_{n=1} {n}[/tex]
= 3.(1 + 2 + 3 + ... + 10)
The series in the brackets is an arithmetic series with :
the first term: a(1) = 1
the last term: a(10) = 10
the common difference: d = 2 - 1 = 1
Use the sum formula for arithmetic series:
S(n) = n/2 [a(1) + a(n)]
S(10) = 10/2 [1 + 10]
=5 . 11 = 55
Therefore,
[tex]\sum\limits^{10}_{n=1} {3n}=3\times{55}=165[/tex]
Combine the sum:
[tex]\sum\limits^{10}_{n=1} {3n}-\sum\limits^{10}_{n=1} {4}=165-40[/tex]
= 125
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Solve each equation for y .
-10 y=5 x
y = -x/2 is the value of y in the equation -10 y=5 x
⇒ -10 y=5 x
⇒ y = -5x/10
⇒ y = -x/2
How to solve an equation?To solve linear equations, utilize the steps that are provided below.
Remove parentheses from each side of the equation and combine similar terms to make it simpler.To separate the variable term on one side of the equation, use addition or subtraction.To find the variable, use division or multiplication.The common denominator can be multiplied by each side of the equation to eliminate fractions.Lets take an example of solve z for 7z – (3z – 4) = 12
Here is no multiplication or division, so this will be easy to solve
⇒ 7z – (3z – 4) = 12
⇒ 7z – 3z + 4 = 12
⇒ 4z = 12 – 4
⇒ 4z = 8
⇒ z = 8/4
⇒ z = 2
See, that was so simple, using the mentioned methods, every linear equation can be solved easily.
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In this problem, you will explore changing dimensions in circles.
f. If the scale factor from ®A to ®B is 1/3 , and the circumference of ®A is 12 inches, what is the circumference of ®B ?
The circumference of ®B is 36 units.
What is scale factor?A scale factor in math is the ratio between corresponding measurements of an object and a representation of that object.
Now it is given that,
The scale factor from ®A to ®B = 1/3
⇒Ks = 1/3
∵ Ks = A/B
By comparison we get,
A = 1
and B = 3
Thus, circumference (CA) of ®A = 12
⇒ Since scale factor for A = 1
⇒ 2πr = 12
⇒ r = 6/π
Now, circumference (CB) of ®B = 2πr = 2π* 6/π
⇒ circumference (CB) of ®B = 12
Since scale factor for B = 3
⇒ circumference (CB) of ®B = 3 * 12
⇒ circumference (CB) of ®B = 36 units.
Thus, the circumference of ®B is 36 units.
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The expressions c - e, where c
stands for the money collected and e
stands for the expenses, is used to find
the profit from a basketball concession.
If $500 was collected and expenses
were $150, find the profit for the
concession.
The profit of the concession is $350.
What specifically are expressions?A group of numbers or variables combined with the operations +, -, ×, or ÷ form an expression.While algebraic expressions include variables, numbers, and mathematical operators, arithmetic expressions only contain numbers and mathematical operators.Any mathematical statement that includes numbers, variables, and an arithmetic operation between them is known as an expression or algebraic expression. In the expression 4m + 5, for instance, the terms 4m and 5 are separated from the variable m by the arithmetic sign +.So, c - e:
Substitute the values in the expression:
c - e500 - 150$350Therefore, the profit of the concession is $350.
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solve each equation.c heck your solution
x(x + 3)=0
Answer: x= negative 3
Step-by-step explanation:
Answer:
-3
Step-by-step explanation:
-3(-3+3)=0
-3(0)=0
0=0
Type the correct answer in the box.
What trigonometric expression can be used to find the value of x? Replace a and b with the correct values.
25 x
12
√0
(0) 101
0.
04
=
< >
S 2
X
a B
AU
8 9
Q
4
sin cos tan sin
tan-1
csc sec cot log log In
COS
=
ZAN
2
•
U
Σ
Answer:
x ≈ 25.73
Step-by-step explanation:
using the tangent ratio in the right triangle
tan25° = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{12}{x}[/tex] ( multiply both sides by x )
x × tan25° = 12 ( divide both sides by tan25° )
x = [tex]\frac{12}{tan25}[/tex] ≈ 25.73 ( to 2 dec. places )
The value of the line segment in the right-angle triangle 'x' will be 25.75 units.
What is a right-angle triangle?It's a form of a triangle with one 90-degree angle that follows Pythagoras' theorem and can be solved using the trigonometry function.
Trigonometric functions examine the interaction between the dimensions and angles of a triangular form.
The measure of the length 'x' is calculated by the tangent of angle 25°. The tangent of an angle is the ratio of the perpendicular to the base of the right-angle triangle. Then we have
tan 25° = 12 / x
x = 12 / tan 25°
x = 12 / 0.466
x = 25.75 units
The value of the line segment in the right-angle triangle 'x' will be 25.75 units.
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which of the following is an example of a rational number between 7 and 8?
The six rational number between 7 and 8 are 7.5 ,7.75, 7.875 , 7. 9375 ,7.9675 and 7.98375
what do i do when my algebra has something like this 9x+45=15x+3/7x im used to having constants and variables on both sides
Answer:
x = 2 11/12
Step-by-step explanation:
First of all, on the right you have to combine 15x+3/7x which equals 15 3/7x.
9x + 45 = 15 3/7x
-9x -9x Next step is to subtract 9x from both sides.
45 = 15 3/7x
/ /
15 3/7 15 3/7 Third step is to divide 15 3/7 on both sides to leave x
by itself.
35/12 = 2 11/12 = x
x = 2 11/12
Write in point-slope form an equation of the line through each pair of points. (7,11) and (13,17)
The equation of the line in point-slope form, which passes through the pair of points located at (7 , 11) and (13 , 17), is y - 11 = (x - 7).
The equation of a line can be expressed in three different forms: standard form, slope-intercept form, and point-slope form.
The standard form of an equation of a line is expressed as ax + by = c, where a and b, if all possible must be integers, are the coefficients of variable x and y, respectively, and c is a constant. Meanwhile, slope-intercept form is given by the formula y = mx + b, where m is the slope of the line and b is the y- intercept. On the other hand, given the slope m and a point on the line (x , y), we can express the equation in point-slope form, (y - y1) = m(x - x1).
Getting the slope of the two points: (7 , 11) and (13 , 17).
m = (y2 - y1)/(x2 - x1)
m = (17 - 11)/(13 - 7)
m = 6/6
m = 1
Using the point slope form, plug in the values of the slope and one point to set up the equation.
(y - y1) = m(x - x1)
where m = 1 and (x1 , y1) = (7 , 11)
(y - 11) = 1(x - 7)
y - 11 = (x - 7)
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Do the following side lengths form a right triangle?
51, 68, 85
Answer:
Yes
Step-by-step explanation:
We can check using pythagoras theorem, setting a and b equal to the shorter sides.
[tex]51^2+68^2=85^2\\2601+4624=7225\\7225[/tex]
d at ( − 6 , − 3 ) (−6,−3) on the coordinate plane. Point K K is reflected over the y y-axis
the reflection of coordinates ( -6, -3 ) on y-axis has coordinates ( 6, -3 ).
The reflection transformation can be with respect to x-axis and y-axis. When a point is reflected about the x-axis, the x-coordinates stay the same and y-coordinates are transformed and written with their opposite signs.
For example, the reflection of the point with coordinates (x, y) across x-axis is (x, -y).
When a point is reflected about the y-axis, the y-coordinates stay the same and the x-coordinates are transformed and written with their opposite signs.
For example, the reflection of the point (x, y) across y-axis is (-x, y).
As we can see that the point with coordinates ( -6, -3 ) lies in the third quadrant and thus the reflection of this point on y-axis lies in fourth quadrant. We know that in fourth quadrant the x coordinate is positive and y coordinate is negative.
By changing the signs according to the above rules, we get
from ( -6, -3 ) to ( 6, -3 ).
Therefore, we can conclude that the reflection of coordinates ( -6, -3 ) on y-axis has coordinates ( 6, -3 ).
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Find the sum of each finite series. Σ⁴ n=1 2ⁿ
A sequence is a geometric sequence if all the numbers of a list are found by multiplying the preceding term by the common ratio r of that sequence. Sigma notation can represent the sum of a finite number of terms (although higher mathematics will tell you how it works for infinite numbers as well).
Now the given problem is,
calculate ∑ n=1, 4, 2n
∑n=1 , 4 , 2n
Since the bounds are finite, the number of terms is finite as well, and we just calculate the sum by summing up the terms.
(∑n=1 4 ,2n) = (2+4+8+16) (∑n=1 4, 2n) = (2+4+8+16)
(∑n=1 4 ,2n) = (30) (∑n=1 4, 2n) = (30)
Hence,
∑n=1 4, 2n=30 ∑n=1 4, 2n=30
Answer:
∑n=1 4, 2n=30
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What is the simplest form of [tex]\sqrt) 3025[/tex]
Answer:
55
Step-by-step explanation:
[tex]\sqrt{3025} =55^2\\\sqrt{55^2}\\\sqrt{55^2}=55\\=55[/tex]
Hope this helps.
Easton drove 224 miles in 8 hours. On average, how fast did he drive in miles per hour? Express your answer in simplest form.
Answer: 28 miles per hour
Step-by-step explanation:
224 miles / 8 hours=
224/8= 28 miles per hour
what is the value of 7 -(-4)
the elevator starts on floor 12 it goes down 8 floors then it goes up 14 floors what floor does it end on?
6 4 0,409, 210
onas period
ones
The number name for this number is six hundred forty million, four hundred
nine thousand, two hundred ten.
1Expanded form is a way to write a number as the sum of each
digit multiplied by its place value. Fill in the blanks to write the
number in expanded form.
The expansion of 6 4 0,409, 210 is given below with the solution.
What does "expanded form" mean?The division of numbers into groups according to place value, such as ones, tens, hundreds, thousands, ten thousand, and so on, results in the expanded form of the number. The expanded version of the number is the one that is represented by the sum of each digit times its place value.
6 4 0,409, 210 = 6 × 10,00,00,000 + 4 × 100,00,000 + 0 × 10,00,000 + 4 × 100,000 + 0 × 10,000 + 9 × 1000 + 2 × 100 + 1 ×10 + 1 × 0
A number is displayed in expanded form according to the place values of its digits.
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Write an equation of a parabola with vertex at the origin and the given focus. (0,6)
Answer:
27273763hebvrhejwj27222
a web music store offers two versions of a popular song. The size of the standard version is 2.6 megabytes (NB). The size of the high-quality version is 4.7
Yesterday, the high-quailty version was downloaded three times as often as the standard version. The total size downloaded for the two versions was 4509
How many downloads of the standard version were there?
The downloads of the standard version are 1127.25.
What are expressions?In mathematics, an expression is a sentence that contains at least two numbers or variables and at least one mathematical operation. This math operation can be addition, subtraction, multiplication, or division. An expression has the following structure: The expression is (Number/variable, Math Operator, Number/variable).So, let the download of the standard version be 'x'.
Then, automatically the download of the high-quality version becomes '3x'.
Now,
3x + x = 45094x = 4509x = 4509/4x = 1127.25 (downloads of the standard version)Then, downloads of the high-quality version: 1127.25 × 3 = 3,381.75Therefore, the downloads of the standard version are 1127.25.
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I'm more sophisticated than my little sister. I save my money in a bank account that pays
me 3% interest on the money in the account at the end of each month. (If I take my money
out before the end of the month, I don't earn any interest for the month.) I started the
account with $50 that I got for my birthday. How much money will I have in the account at
the end of 10 months? How many months will it take to have at least $100? Justify your
answer with a mathematical model of the problem situation.
The amount of money after 10 months will be $67.2. The number of months (n) that it takes to have at least $100 will be 2 years or 24 months.
What is compound interest?A loan or deposit's interest is computed using the starting principle and the interest payments from the ago decade as compound interest.
We know that the compound interest is given as
[tex]\rm A = P \left (1 + r \right ) ^{t}[/tex]
Where A is the amount, P is the initial amount, r is the rate of interest, and t is the number of months.
I keep my savings in a bank account that, at the end of each month, gives me 3% interest on the balance. (If I withdraw my funds before the end of the month, I forfeit the interest I would have accrued.) I opened the account using the $50 I received as a birthday gift.
The amount of money after 10 months will be
A = 50 (1 + 0.03)¹⁰
A = 50(1.03)¹⁰
A = 50 x 1.344
A = $67.2
The number of months (n) that it takes to have at least $100 will be
100 = 50 (1.03)ⁿ
2 = (1.03)ⁿ
n ln 1.03 = ln 2
n = ln 2 / ln 1.03
n = 23.5 ≈ 24 months or 2 years
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PLEASE HELP ANSWER I CANT FIND ANSWERS ANYWHERE THIS IS MY LAST HOPE PLS
which expression is equivalent to 1/3 + (3/4+3/4)
1/3 + (3/4 +3/4)
1/3 (3/4+2/3
3/4 - 2/3 + 1/3
(1/3+3/4) +2/3
question 2
Which property explains why these two expressions are equal?
(w+ 2/3) + 5 = w + (2/3 + 5)
A)
associative
B)
commutative
C)
distributive
D)
transverse
Which property is BEST to use when combining
3/5 +1/4 +2/5?
additive inverse property
distributive property
commutative property of addition
identity property of addition
Answer For Question 2: Associative property. The associative property says that even if you rearrange the parenthesis () the result will still be the same. And that is what is happening in question 2
Answer For Question 3: Commutative property of addition. This is the BEST choice because you will first want to add 3/5 + 2/5. And since the Commutative property says that no matter the order of the addends, you can add what ever you think is the best choice.
Here are some answers. I couldn't really understand Question 1 so i didn't want to give you an incorrect answer. Also are the pictures questions too? Im not too sure but here you go hope this helps you in some way
Rex and Samir participated in a walkathon. Rex walked for 1 2/3 hours, and Samir walked for 3 1/3 hours. complete the comparison. Samir walked _____ times ad many hours as Rex walked.
Samir walked 2 times as many hours as Rex walked.
What is ratio?A ratio can be defined as the comparison of two or more numbers on the basis of their sizes in relation to each other.
It also indicates how many times one number contains another.
Given that;
Rex walked = 1 2/3 hours = 5/ 3 hoursSamir walked = 3 1/3 = 10/ 3 hoursTo determine the ratio, we have to divide Samir's walking hours by Rex's working hours
= 10/ 3 ÷ 5/ 3
Take the inverse of the divisor and multiply
= 10/ 3 × 3/ 5
= 2 hours
Thus, Samir walked 2 times as many hours as Rex walked.
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