Answer:
n = 4
Step-by-step explanation:
36 = 13n - 4n
<=> 36 = (13-4).n
<=> 36 = 9n
<=> n = 36 / 9
<=> n = 4
What is the solution to this equation?
Answer:
x = -7/2
Step-by-step explanation:
(1/4) ^ (x+1) = 32
Rewriting 32 as 2^5 and 1/4 and 2^-2
2^-2 ^ (x+1) = 2^5
We know that a^b^c = a^ ( b*c)
2 ^ (-2x-2) = 2 ^ 5
Since the bases are the same, the exponents have to be the same
-2x-2 = 5
Add 2 to each side
-2x = 7
Divide by -2
x = -7/2
Laurissa rolls two number cubes, each with the numbers 1 through 6. Laurissa adds the numbers that appear on the roll Which two sums have an equal chance of occurring?
Answer:
2 and 12;
4 and 10;
5 and 9
6 and 8
Step-by-step explanation:
Given
Roll of two number cubes
Required
Determine the sums which have equal chance
Represent the sample space of both number cubes with S1 and S2
[tex]S_1 = \{1,2,3,4,5,6\}[/tex]
[tex]S_2 = \{1,2,3,4,5,6\}[/tex]
Next, get the outcome of roll two number cubes
Outcome = [tex](1,1)(1,2)(1,3)(1,4)(1,5)(1,6)\ (2,1)(2,2)(2,3)(2,4)(2,5)(2,6)\ (3,1)(3,2)(3,3)(3,4)(3,5)(3,6)[/tex][tex](4,1)(4,2)(4,3)(4,4)(4,5)(4,6)\ (5,1)(5,2)(5,3)(5,4)(5,5)(5,6)\ (6,1)(6,2)(6,3)(6,4)(6,5)(6,6)[/tex]
Next, get the sample space;[tex]S = \{2,3,4,5,6,7, 3,4,5,6,7,8, 4,5,6,7,8,9, 5,6,7,8,9,10, 6,7,8,9,10,11, 7,8,9,10,11,12\}[/tex]
Reorder from lowest to highest[tex]S = \{2,3,3,4,4,4,5,5,5,5,6,6,6,6,6,7,7,7,7,7,7,8,8,8,8,8,9,9,9,9,10,10,10,11,11,12 \}[/tex]
Next, form a frequency table
Sum -- Frequency
2 ---- -- 1
3 ---- -- 2
4 ---- -- 3
5 ---- -- 4
6 ---- -- 5
7 ---- -- 6
8 ----- -- 5
9 - ------ 4
10 --- -- 3
11 --- ---- 2
12 ------ 1
From the above table, we can now determine the two sums that have equal probability;
The two sums that have equal probability have the same frequency;
Hence;
2 and 12 have the same chance of occurring
4 and 10 have the same chance of occurring
5 and 9 have the same chance of occurring
6 and 8 have the same chance of occurring
Answer:
5 and 8
Step-by-step explanation:
Find the value of x in the equation below. 12+x = 16.7
Answer:
[tex] \boxed{ \bold{ \huge{ \boxed{ \sf{x = 4.7}}}}}[/tex]
Step-by-step explanation:
[tex] \sf{12 + x = 16.7}[/tex]
Move 12 to right hand side and change it's sign
[tex] \dashrightarrow{ \sf{x = 16.7 - 12}}[/tex]
Subtract 12 from 16.7
[tex] \dashrightarrow{ \sf{4.7}}[/tex]
Hope I helped!
Best regards!
Answer:
[tex]\huge\boxed{\sf x = 4.7}[/tex]
Step-by-step explanation:
12 + x = 16.7
Subtracting 12 to both sides
x = 16.7 - 12
x = 4.7
Isabel need to cut a square piece of wood with the area of 70 in.² approximate the size of the square round to the nearest 10th of a inch
Answer:
8.4 in by 8.4 in
Step-by-step explanation:
The area of a square is the side length squared.
Let s be the side length:
s^2 = 70
s = \sqrt(70) = 8.4 in
82, 77, 72, 67, 62 ....... The recursive pattern in the sequence above is latex-_ (be sure to show if it is positive or negative). The 4th term in the sequence is . An explicit formula that I can use to write for this sequence is latex-_ . The value of the 100th term is .
Answer:
a. It is a negative pattern
b. Fourth term is 67
c. Explicit formula is Tn = 87 - 5n where n is the number of the term.
d. The value of the 100th term is -413
Step-by-step explanation:
1.Firstly, we want to know if the pattern is positive or negative.
Looking at the pattern, we can see our first term as 82, second as 77, third as 72.
What this show is that the pattern is decreasing as we move on from one term to another. So we can say it is a negative recursive pattern.
2. We are asked which term is the 4th.
This is quite obvious from the spelt out pattern.
82 77 72 67
1....2......3.....4
67 is the fourth term.
3. We want an explicit formula for the sequence.
What this question is asking us is a formula such that we can use at any point in time to calculate the value of the term at that point.
Firstly we have the first term as 82.
We need the common difference.
Mathematically this is the second term minus the first term which is same as the third term minus the second term.
That would be; 77-82 = 72-77 = -5
Mathematically the nth term of an arithmetic sequence is;
Tn = a + (n-1) d
Where in this case a is 82 and d is -5
Substituting these values, we have;
Tn = 82 + (n-1)-5
Tn = 82 -5n + 5
Tn = 82 + 5 -5n
Tn = 87 -5n
Where Tn is the term we are looking for while n is the number of the term.
4. Value of the 100th term
Simply substitute the value of 100 for n in the explicit formula.
That would be;
87 -5(100) = 87-500 = -413
1. The subsets of the real numbers can be represented in a Venn diagram as shown. To which subsets of real numbers does 12 belong? A) Integers and Whole Numbers only B) Rational Numbers, Integers, and Whole Numbers C) Rational Numbers and Integers only D) Irrational Numbers, Integers, and Whole Numbers 2. Which statement BEST describes the relationship between whole numbers and natural numbers shown in the diagram? A) The diagram shows that whole numbers are a subset of natural numbers, because all whole numbers are natural numbers. B) The diagram shows that natural numbers are a subset of whole numbers, because all natural numbers are whole numbers. C) The diagram shows that whole numbers are a subset of natural numbers, because some whole numbers are not natural numbers. D) The diagram shows that natural numbers are a subset of whole numbers, because all whole numbers and natural numbers have no numbers in common.
1. C) Rational Numbers and Integers only
2. D) The diagram shows that natural numbers are a subset of whole numbers, because all whole numbers and natural numbers have no numbers in c.
In mathematics, a rational number is a number such as −3/7 that can be expressed as the quotient or fraction p/q of two integers, a numerator p and a non-zero denominator q. Every integer is a rational number: for example, 5 = 5/1
what is repeating .67 as a fraction?
Answer:
67-100
Step-by-step explanation:
This is the answer because the . is ones the 6 is tens and the 7 is the hundreds
Find the distance between the two points. (-6,-10) & (-2,-10)
Answer:
The answer is 4 unitsStep-by-step explanation:
The distance between two points can be found by using the formula
[tex]d = \sqrt{( {x1 - x2})^{2} + ({y1 - y2})^{2} } \\ [/tex]where
(x1 , y1) and (x2 , y2) are the points
From the question the points are
(-6,-10) & (-2,-10)
The distance between them is
[tex]d= \sqrt{ ({ - 6 + 2})^{2} + ({ - 10 + 10})^{2} } \\ = \sqrt{ ({ - 4})^{2} + 0} \\ = \sqrt{16} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: [/tex]We have the final answer as
4 unitsHope this helps you
Solve in fraction form.
3
Angela has 7 cups of rice and she buys another 2 cup. How much rice does Angela have in all?
Answer:
Hey there!
Angela will have 7+2, or 9 cups of rice.
Let me know if this helps :)
Answer:
7/2
Step-by-step explanation:
Name the sets of numbers to which
3/5
belongs
Answer:
Fractions , Rational numbers ,Real numbers
Step-by-step explanation:
-3/5 is arguably a real number
Match the statement to the property it shows.
If MN = XY, and XY = AB, then MN = AB.
If AB = CD, then CD = AB.
Segment CD is congruent to segment CD.
Answer:
If MN = XY, and XY = AB, then MN = AB. Transitive Property
If AB = CD, then CD = AB. Symmetric Property
Segment CD is congruent to segment CD. Reflexive Property
Step-by-step explanation:
Transitive property states that for all reall numbers a, b, and c, if a = b, b = c, then a = c.
Symmetric Property states that for all real numbers a and b, if a = b, then b = a.
Reflexive Property states that for every real number a, a=a
1. Transitive property
2. Symmetric property
3. Reflexive property
What are equivalence properties ?The equivalence properties are Reflexive property, Symmetric property & Transitive property.
Reflexive Property : For every real number a, a=a
Symmetric Property : For real numbers a & b, if a=b then b=a
Transitive Property : For real numbers a, b, c, if a=b & b=c then a=c
What are the perfect matches ?1. If MN = XY, and XY = AB, then MN = AB ⇒ Transitive property
2. If AB = CD, then CD = AB ⇒ Symmetric property
3. Segment CD is congruent to segment CD ⇒ Reflexive property
Learn more about equivalence properties here :
https://brainly.com/question/2273381
#SPJ2
What is this answer ?
Answer:
its a bit cut off can u add the whole screen pls
Step-by-step explanation:
Answer:
KL NM
Step-by-step explanation:
that is the answer
In a rectangular field of dimensions 20m x 15m , a triangular park is constructed. If the
dimensions of the park are 5m, 7m and 8m respectively, find the cost of levelling the
remaining field at the rate of Rs 100 per m
m?
Answer:
My answer is 28,250Rs.
Area of a triangle=1/2b×h.
1/2×7×5=17.5.
Area of a rectangle=l×b.
20×15=300.
Area of rectangle-Area of the triangle=300-17.5=282.5m^2.
If 1m^2=100Rs.
then 282.5m^2=282.5×100=28,250Rs.
6. Write 1.12 repeating as a mixed number.
Answer:
3
1 -----
25
Step-by-step explanation:
The length of a rectangle is 2 m more than twice its width. Find the length and width of the rectangle, if its perimeter is 28 m.
Please use algebra.
Answer:
Length is 10
Width is 8
Step-by-step explanation:
The formula for the perimeter of a rectangle is:
[tex]P=2l+2w[/tex]
We are told that the length l is 2 more than twice the width w. In other words:
[tex]l=2+2w[/tex]
Also, we are given that the perimeter is 28. Therefore:
[tex]P=2l+2w\\28=2(2+2w)+2w[/tex]
Distribute:
[tex]28=4+4w+2w[/tex]
Combine like terms:
[tex]28=4+6w[/tex]
Subtract 4 from both sides:
[tex]6w=24[/tex]
Divide by 6:
[tex]w=4[/tex]
So, the width is 4.
And the length is 2 more than twice the width. Thus:
[tex]l=2+2(4)\\l=2+8=10[/tex]
The length is 10.
And we are done :)
Chocolate and peanut butter cookies are randomly chosen from a cookie jar and placed onto a plate. The first plate had four chocolate chip cookies and one peanut butter cookie. A second plate was prepared with 2 chocolate cookies and p peanut butter cookies. If the probability of drawing a chocolate cookie from each plate is 8/25, how many peanut butter cookies, P, are on the second plate?
Answer:
Step-by-step explanation:
-6=-2+w solve the equation
Answer:
w = -4
Step-by-step explanation:
Answer:
w = -4
Step-by-step explanation:
[tex]-6=-2+w\\[/tex]
Switch sides
[tex]-2+w=-6[/tex]
Add 2 to both sides
[tex]-2+w+2=-6+2[/tex]
Simplify
[tex]w=-4[/tex]
The second side of a triangular deck is 3 feet longer than the shortest side, and the third side is3 feet shorter than twice the length of the shortest side. If the perimeter of the deck is 52 feet, what are the lengths of the three sides?
Answer:
13, 16, 23
Step-by-step explanation:
The first side is x.
The second side is x + 3
The third side is 2x - 3
(x) + (x +3) + (2x - 3) = 4x
4x = 52
x = 13
4√2 + √2 with work
8√3 - 4√3 with work
2√3 x √32 with work
Step-by-step explanation:
4√2 + √2 = 5√2 we add 4 and the invisible 1 in front of √2, the common root stays same
8√3 - 4√3 = 4√3 subtract 4 from 8 the common root stays same
2√3 x √32 ➡ 2√3 x 4√3 too add the expressions we first need to make the roots common then add 4 and 2
Answer:
1. [tex]5\sqrt{2}[/tex]
2. [tex]4\sqrt{3}[/tex]
3. [tex]8\sqrt{6}[/tex]
Step-by-step explanation:
Number 1:
We can treat [tex]\sqrt{2}[/tex] as a variable in which we are multiplying 4 by. Let's call [tex]\sqrt{2}[/tex] x.
This makes our expression [tex]4x + x[/tex]. Combining like terms, we get [tex]5x[/tex]. This means that [tex]4\sqrt{2} + \sqrt{2} = 5\sqrt{2}[/tex].
Number 2:
Again, we can use the same logic as we did in number 1. Let's treat [tex]\sqrt{3}[/tex] as a variable y.
[tex]8y-4y[/tex]
Subtracting a y term from a y term will equal the difference between the coefficients times y. So it's [tex]4y[/tex]. This means that [tex]8\sqrt{3}-4\sqrt{3}=4\sqrt{3}[/tex]
Number 3:
When we multiply radicals, we want to put the radicals in [tex]\sqrt{x}[/tex] form.
[tex]\sqrt{32}[/tex] is already in this form.
However [tex]2\sqrt{3}[/tex] is not.
[tex]2\sqrt{3}[/tex] is the same thing as [tex]\sqrt{3\cdot2^2} = \sqrt{3\cdot4} = \sqrt{12}[/tex].
Now we multiply these radicals by multiply the term inside the square root sign
[tex]\sqrt{32}\cdot\sqrt{12}=\sqrt{32\cdot12} =\sqrt{384}[/tex]
384 is divisible by 64, so:
[tex]\sqrt{384} = \sqrt{64\cdot6} = 8\sqrt{6}[/tex]
Hope this helped!
Pick any number and add 5 to it. Find the sum of the new number and the original number. Add 5 to the sum. Divide the new sum by 2 and subtract the original number from the quotient. What is the final number?
Answer: The final number is 5
Step-by-step explanation:
Picked number: 10
STEP are all according to what you stated
10+5=15 (first sentence)
15+10=25 (second sentence)
25+5=30 (third sentence)
30÷2-10=5 (fourth sentence)
The final number is 5.
An instructional video is 1.8 minutes long. How long is the video in seconds? How long is it in hours?
Answer:
108 seconds and 0.03 hours
4.32x+1=17.8929 Sole for x
Answer:
x = 3.91039
Step-by-step explanation:
Order of Operations: BPEMDAS
Step 1: Write out equation
4.32x + 1 = 17.8929
Step 2: Subtract 1 on both sides
4.32x = 16.8929
Step 3: Divide both sides by 4.32
x = 3.91039
Which words represent SUBTRACTION
less than
sum
difference
total
Answer:
I think it's sum and difference
Answer:
less than and difference
Step-by-step explanation:
The sum of two numbers is 180. If one number is 40% more than the other, find the numbers
Answer:
We have 2 values to work with, both in terms of x. the first value is just x, our first number. The second value is 40% higher than the original.
x + (x + .4x) = 180
x + 1.4x = 180
2.4x = 180
x = 180/2.4
x = 75 1.4(75) = 105
Check:
75 * .4 = 30
75 + 30 = 105
Answer:
75, 105
Step-by-step explanation:
Let's let the two numbers be a and b.
The sum of them is 180. Thus:
[tex]a+b=180[/tex]
One of the number is 40% more than the other. In other words, let's let a be the bigger number:
[tex]a=1.4b[/tex]
Substitute this into the first equation:
[tex]1.4b+b=180[/tex]
Combine like terms:
[tex]2.4b=180[/tex]
Divide everything by 2.4:
[tex]b=75[/tex]
So, b is 75.
And their sum is 180. Thus, a is 180-75 or 105.
And we're done!
What is the approximate value of this square root?
Answer:
12.1
Step-by-step explanation:
To approximate this value, we simply need to know some perfect squares. We know that the value 144 is the perfect square of 12. And we know the value 169 is the perfect square of 13.
Note, that our value, 146 is far closer to 144 than to 169, so we know that we will be close to 12 as our approximation.
The distance from 144 to 146 is 2, while the distance from 169 to 146 is 23.
A rough fractional approximation can be found with 2/23 approximately 0.08.
For the solution then, our approximation of sqrt(146) ~= 12.08 ~= 12.1
Cheers.
Sebastien hand-crafts circular braided rugs. The graph shows the prices of various sizes of his rugs. A customer ordered 3 identical rugs for a total of $1,350. Use the graph to determine the radius of each rug in the order. (Enter numerical answer only). Please help.
The correct answer is 6 ft
Explanation:
It is known the customer bought 3 identical rugs, which means the size and radio of each rug was the same. Moreover, the total this customer paid for the rugs was $1350, which is equivalent to $450 for each rug as $1350 ÷ 3 = $450.
Besides this, the black line in the graph shows at $450 (between 400 and 500 in the y-axis) the rugs have a ratio of 6 feet, which is shown in the x-axis as these two values intersect or align to form the black line. This means a carpet with a radius of 6ft costs $450, and therefore each of the rugs the customer bought had a radius of 6ft.
10k4 ⋅ (−9k3) how to solve this
Answer:
The product of the terms in the given expression is -90k⁷
Step-by-step explanation:
10k⁴ · (-9k³)
When we multiply exponents, then we are going to add the exponential together. So, we will add 4 and 3 together which is 7. Since our base numbers are different, then we also multiply them together. So, we will multiply 10 by -9 which is -90.
-90k⁷
What is the meaning of the
word arch"
8(7x-2)=96 What is X
Answer:
x = 2
Step-by-step explanation:
8(7x-2)=96
7x-2 = 96 : 8
7x-2 = 12
7x = 12 +2
7x = 14
x = 14 : 7
x = 2
Answer:
x=2Step-by-step explanation:
[tex]8\left(7x-2\right)=96\\\\\mathrm{Divide\:both\:sides\:by\:}8\\\frac{8\left(7x-2\right)}{8}=\frac{96}{8}\\\\Simplify\\7x-2=12\\\\Add\:2\:to\:both\:sides\\7x-2+2=12+2\\\\Simplify\\7x=14\\\\\mathrm{Divide\:both\:sides\:by\:}7\\\frac{7x}{7}=\frac{14}{7}\\\\Simplify\\x=2[/tex]
Which is the better buy, 6 bagels for $3.29 or 8 bagels for $4.15? Justify your answer by giving the cost per bagel for each offer in order to get full credit.
Answer: The better buy would be 8 bagels for $4.15
explanation: If you were to buy 6 bagels for $3.29, It would be about $.54 per bagel. but if you were to buy 8 bagels for $4.15, it is about about $.52 per bagel which makes it a better deal.