Answer:
20 %
Step-by-step explanation:
four blue shirts, two green shirts, two gray shirts, one white shirt and one red shirt = 10 shirts
P(red) = number of red shirts / total
= 2/10
= 1/5
=20 %
Answer:
10%
Step-by-step explanation:
4 blue
2 green
2 gray
1 white
1 red
4 + 2 + 2 + 1 + 1 = 10
each t-shirt = 10 percent
so 1 red t-shirt = 10%
Find the explicit formula for the geometric sequence. Then find a8.
4, 8, 16, 64, ....
Which Answer is Correct:
A) an = 4 ⋅ rn – 1; 1,024
B) an = a1 ⋅ 2n – 1; 256
C) an = 4 ⋅ 2n – 1; 512
D) an = 2 ⋅ 4n – 1; 512
Answer:
Step-
Honey it c !!!!………!l║.by-step explanation:
The explicit formula for the given "geometric-sequence" is aₙ = 4 × 2ⁿ⁻¹, and the eight term is 512, Option(c) is correct.
To find the explicit formula for a geometric-sequence, we need to find the common ratio between any two consecutive terms.
In this sequence, we can see that each term is obtained by multiplying the previous term by 2. So, the "common-ratio" is 2.
We also know the "first-term" is 4, so we use the formula for the nth term of a geometric sequence which is : aₙ = a₁ × rⁿ⁻¹,
Substituting the values,
We get,
⇒ a₈ = 4 × 2⁽⁸⁻¹⁾
⇒ a₈ = 4 × 2⁷
⇒ a₈ = 512,
Therefore, the correct answer is (c) aₙ = 4 × 2ⁿ⁻¹; 512.
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The given question is incomplete, the complete question is
Find the explicit formula for the geometric sequence. Then find a₈.
4, 8, 16, 32, 64,....
Which Answer is Correct:
(a) aₙ = 4 × rₙ - 1; 1024
(b) aₙ = a₁ × 2ⁿ⁻¹; 256
(c) aₙ = 4 × 2ⁿ⁻¹; 512
(d) aₙ = 2 × 4ⁿ⁻¹; 512
In the derivation of the quadratic formula by completing the square, the equation
- 4ac + b 2
4a?
is created by forming a
perfect square trinomial.
What is the result of applying the square root property of equality to this equation?
Answer:
2nd option is the correct answer.
Step-by-step explanation:
[tex] \because \bigg(x + \frac{b}{2a}\bigg) ^2 = \frac{-4ac+b^2}{4a^2}\\\\
\therefore \bigg(x + \frac{b}{2a}\bigg) ^2 = \frac{b^2-4ac}{4a^2}\\\\
\therefore \bigg(x + \frac{b}{2a}\bigg) = \pm \sqrt {\frac{b^2-4ac}{4a^2}} \\\\
\purple {\boxed {\bold {\therefore x + \frac{b}{2a}= \frac{\pm\sqrt{b^2-4ac}}{2a}}}} \\\\[/tex]
Answer:
B
Step-by-step explanation:
(01.01 LC)
Evaluate the expression
5/7 - 4)2 + 3 + 11.
Answer:
Step-by-step explanation:
[tex](\frac{5}{7}-4)2+3+11=(\frac{5}{7}-\frac{4*7}{7})2+3+11\\\\=(\frac{5}{7}-\frac{28}{7})2+3+11\\\\=(\frac{-23}{7})2+3+11\\\\=\frac{-46}{7}+3+11\\\\=\frac{-46}{7}+14\\\\=\frac{-46}{7}+\frac{14*7}{1*7}\\\\=\frac{-46}{7}+\frac{98}{7}\\\\=\frac{-46+98}{7}\\\\=\frac{52}{7}\\\\=7\frac{3}{7}[/tex]
How do you Convert the decimal into a mixed number 10.5
Answer:
it would be 10 1/2
Step-by-step explanation:
The ten is already a whole number so it would be itself. .5 is in the tenths place so it would be put over ten (5/10). Simplify 5/10 to 1/2 because 5 is half of 10
Answer:
its 10 1/2
Step-by-step explanation:
Please someone help me, i need thier solve please my teacher told me to solve them
Answer:
A. Domain : (-∞, ∞)
B. Function is increasing in the interval (-2, 0) and (2, ∞)
Decreasing in the interval of (-∞, -2) and (0, 2).
Step-by-step explanation:
A. Given function is, y = |2x - 1|
This function is the transformed form of the parent function, y = |x|
Domain of the parent function is { x | x is a set of real numbers}
Therefore, domain of the transformed function will be the same as the domain of the parent function.
Domain of the function = {x | x is a real number}
B. Given function is f(x) = [tex](x^2-4) ^{\frac{2}{3} }[/tex]
Domain of the function : (-∞, ∞)
Critical points of the function are,
⇒ x = 0, ±2
Now we find the three intervals where we have to check the function to be increasing or decreasing.
(-∞ -2), (-2, 0), (0, 2), (2, ∞)
Derivative of the function f(x),
f'(x) = [tex]\frac{4x}{3(x^2-4)^{\frac{1}{3} } }[/tex]
Here, f'(x) < 0 for (-∞, -2)
f'(x) > 0 for (-2, 0)
f'(x) < 0 for (0, 2)
f'(x) > 0 for (2, ∞)
Therefore, given function is increasing in the interval (-2, 0) and (2, ∞)
And it's decreasing in the interval of (-∞, -2), and (0, 2).
This is the question about circle in geometry.
Answer:
A cicle centered in the origin has equation.
[tex]x^2+y^2=r^2\\4^2+1^2=r^2\\r=\sqrt{17}\\ \\\sqrt{5}^2+\sqrt{2}^2\neq \sqrt{17}^2\\ 7\neq 17[/tex]
The point does not lies on the circle
Find the distance between two points (6,−4) and (−4,−4).
Answer:
Step-by-step explanation:
(6, -4) ; (-4,-4)
[tex]Distance=\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1}^{2})}\\\\ =\sqrt{(-4-6)^{2}+(-4-[-4])^{2}} \\\\=\sqrt{(-10)^{2}+(-4+4)^{2}} \\\\=\sqrt{100+0}\\\\ =\sqrt{100}\\\\[/tex]
= 10 units
I put in 6.32 for A but it’s still saying it’s wrong and I need the √ , I only need to answer this right to pass my summer school class someone please help me !
Answer:
Value of blank 1 is 2
Value of blank 2 is 10
Step-by-step explanation:
We are given that a and b are the lengths of legs of right angle in right angled triangle .
b = 3
We are also given that c is the hypotenuse
c = hypotenuse = 7
To find the value of 'a' we will use Pythagoras theorem
[tex]Hypotenuse^2 = perpendicular^2 +base^2\\c^2=a^2+b^2\\7^2=a^2+3^2\\7^2-3^2=a^2\\\sqrt{7^2-3^2}=a\\\sqrt{40}=a\\2\sqrt{10}=a\\[/tex]
Value of blank 1 is 2
Value of blank 2 is 10
How many solutions does the system of nonlinear equations graphed below
have?
Answer: Look at the number of points where the graphs intersect each other...the points where the graphs of the functions cross each other are the solutions to the system.
Upon looking, you should see 4 points where the graphs intersect, so there are 4 solutions to the non-linear system of equations.
Step-by-step explanation:
Answer:
You Should see 4 Points
Step-by-step explanation:
Please Help!!! What is the slope of the line in the graph!!! Braniest will be given!!!
Answer:
m= 1/2
Step-by-step explanation:
Not sure if this is right but I hope this helps :)
Answer:
1/4
Step-by-step explanation:
We can see that two points on the line are (0, 4) and (4, 5). Using the slope formula (y₂ - y₁) / (x₂ - x₁) we get (5 - 4) / (4 - 0) = 1/4.
Given f(x)=3x - 1 and g(x)=-x + 6 find f(-2) + g(5)
Answer:
Step-by-step explanation:
f(-2)= 3(-2) - 1 = -6 - 1 = -7
g(5)= -5 + 6 = 1
-7 + 1 = -6
does anyone know this?
Answer:
6x^2
Step-by-step explanation:
What goes in the box is
2x* 3x
6 x*x
6x^2
i need help please thanks
Answer:
66 units
Step-by-step explanation:
just addition
Answer:
66 units
Step-by-step explanation:
The perimeter of a two dimensional object is all of its sides added together:
6+14+10+17+4+3+8+4=
20+10+17+4+3+8+4=
30+17+4+3+8+4=
47+4+3+8+4=
51+3+8+4=
54+8+4=
62+4=
66 units
Give an example of an absolute value inequality whose answers falls between two values. Give an example of an absolute value inequality whose answers fall outside of two values. What creates the difference? Be specific. *
Answer:
A) Suppose we have an onedimensional situation.
in the 0 of our x-axis, we have a fruit tree, and we want to rest at a distance no bigger than 6 ft of the tree, then all the possible positions of our resting place are:
x ∈(-6ft, 6ft)
we can write this as: IxI < 6ft
b) now we think the opposite situation, we want to rest at least 6ft away from the tree, then we have that:
x ∉ [-6ft, 6ft].
or IxI > 6ft.
So you can see that the difference in those two cases is if we want to be "inside a given range" (for the first case) or "outside a given range" (for the second case).
Inside triangle ABC point O was drawn such that ∠OAB, ∠OBA, ∠OBC, and ∠OCA are all congruent. It is also true that ∠OAC and ∠OCB congruent. Find the angle measures in triangle ABC.
Answer:
m∠A = 60
m∠B = 60
m∠C = 60
Step-by-step explanation:
Please mark Branilest
WILL GIVE BRAINLIEST AND 20 POINTS! Which function is the inverse of f(x) = -5x -4?
Answer:
-1/5x -4/5 = y
Step-by-step explanation:
f(x) = -5x -4
y = -5x-4
Switch x and y
x = -5y -4
Solve for y
Add 4
x+4 = -5y
Divide by -5
-1/5x - 4/5 = -5y/-5
-1/5x -4/5 = y
Answer:
f(x) = -5x - 4
let f(x)= y
y = -5x -4
x = -5y - 4
-5y = x+4
y = - (x +4)/5
The inverse of f(x) is -(x +4)/5
Hope this helps.
A key code must contain 4 numerals. There are 10 numerals available. Using
these numerals, how many different key codes may be created?
O A. 180
O B. 210
O C. 3,060
O D. 5,040
Answer:
C
Step-by-step explanation:
What Am I - using what you know
about triangles, find my missing
measurement and then tell me
my first and last name. First name,
acute, obtuse and righte Last name,
Scalene, isosceles, equilateral.
1) One angle is 82 degrees, the other is
75 degrees, What is my missing angle?
What is
my first and last name?
Find the length and width of a rectangle that has the given perimeter and a maximum area. Perimeter: 392 meters
Answer:
the length is 98 meters and the width 98 meterss
Step-by-step explanation:
We have that the length is l and the width is w, we know that:
P = 2 * w + 2 * l
if we solve for it, we have:
l = P / 2 - w
Now, we know that the area is:
A = l * w
if we replace l, we are left with:
A = (P / 2 - w) * w
A = P * w / 2 - w ^ 2
we derive to know the maximum area and we equal 0 and we have:
A '= P / 2 - 2 * w
0 = P / 2 - 2 * w
w = P / 4
now for him:
l = P / 2 - P / 4
l = P / 4
Therefore, if we replace:
l = 392/4 = 98
w = 392/4 = 98
For the maximum area the length is 98 meters and the width 98 meterss
If f(x) = 2(x)2 + 5 /(x+2)
Answer:
7.07
Step-by-step explanation:
f(x) = 2(x)^2 + 5 sqrt(x+2)
Let x= 0
f(x) = 2(0)^2 + 5 sqrt(0+2)
= 2*0 + 5 sqrt(2)
= 0 + 5 sqrt(2)
= 5 sqrt(2)
= 7.07106
To the nearest hundredth
= 7.07
Find the measure of arc DF (with an explanation of how to solve please!)
Answer:
mDF = 90°
(Assuming arc mCE is 5x + 10)
Step-by-step explanation:
When we have two chords crossing in a circle, there is a property where the angle in the cross point is equal half the sum of the corresponding arcs.
So in this case, we have:
70° = (mCE + mDF)/2
Assuming mCE is 5x + 10, we have:
70 = (5x + 10 + 11x + 2)/2
70 = (16x + 12)/2
70 = 8x + 6
8x = 64
x = 8
So the arc mDF is:
mDF = 11x + 2 = 11 * 8 + 2 = 90°
The measure of arc DF should be 90 degrees.
Calculation of the measure of arc DF:Here we assume arc mCE should be 5x + 10
Since mDF = 90°
Also we know that at the time when two chords should be crossing in a circle so the angle in the cross point should be equivalent to the half the sum of the arcs
So base don this.
[tex]70 = (mCE + mDF)\div 2\\\\70 = (5x + 10 + 11x + 2)\div 2\\\\70 = (16x + 12)\div 2[/tex]
70 = 8x + 6
8x = 64
x = 8
Now the arc mDF is:
mDF = 11x + 2
= 11 (8) + 2
= 90°
Hence, The measure of arc DF should be 90 degrees.
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In the number
23.45, the digit
2 is in the Select...
place.
Answer:
tens place
Step-by-step explanation:
tens ones . tenths hundredths
2 3 . 4 5
The temperature of a city at sunset was -2°F. Overnight, the temperature decreased by 13°F. What was the lowest temperature overnight in that city?
Answer:
the answer is -15°F
1st: draw a number line
2nd: start at -2
3rd: go back 13 spaces toward the negitive
4th: u get your answer= -15°F
The shortest route from London to Cambridge is 60 miles. A lorry is expected to take 1.5 hours to travel this route. The lorry actually travels by a different route which increases the distance by 20%, but it still arrives in 1.5 hours. By how many more mph than the expected speed does the lorry travel?
Answer: 8 miles per hour
Step-by-step explanation:
Speed = distance / time
When diatance is 60 miles
Speed = 60 / 1.5 = 40 miles per hour
When distance is 20% more (72 miles)
Speed = 72 / 1.5 = 48 mph
A triangle on a coordinate plane is translated according to the rule T-8,4(x, y). Which is another way to write this rule?
A (x,y) - (x + 4, y - 8)
B (x,y) - (x - 4, y - 8)
C (x, y) - (x - 8, y + 4)
D (x,y) - (x + 8, y - 4)
Answer:
CStep-by-step explanation:
(x, y) → (x – 8, y + 4)A triangle on a coordinate plane translated according to the rule [tex]T_{-8,4}(x,y)[/tex]can also be written as [tex](x,y)[/tex] → [tex](x-8,y+4)[/tex] according to the translation rule.
What is translation rule ?According to translation rule [tex]T_{a,b}(x,y)[/tex] tells that translation of a point (x,y)
by (a,b) is given by [tex](x,y)[/tex]→[tex](x+a,y+b)[/tex].
How to use translation rule to find the answer?Given that [tex]T_{-8,4}(x,y)[/tex], a=-8 and b=4
Putting in the values given in the question to the translation rule we get
[tex](x,y)[/tex]→[tex](x+(-8),y+(4))[/tex]
[tex](x,y)[/tex]→[tex](x-8,y+4)[/tex]
Hence we get triangle on a coordinate plane translated according to the rule [tex]T_{-8,4}(x,y)[/tex]can also be written as [tex](x,y)[/tex] → [tex](x-8,y+4)[/tex]. Answer C is correct.
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Which of the following is equivalent to RootIndex 5 StartRoot 13 cubed EndRoot? 132 1315 13 Superscript five-thirds 13 Superscript three-fifths
The root index of 5 start root 13 cubed End root is [tex]13^\frac{3}{5}[/tex].
What is root index?If 'n' is a positive integer that is greater than 1, and 'a' is a real number then "n √a = [tex]a^\frac{1}{n}[/tex] where 'n' is root index, 'a' is base and '√' is radical".
According to the question,
5 start root 13 cubed end root can be written in root index form.
If 'n' is a positive integer that is greater than 1, and 'a' is a real number then "n √a = [tex]a^\frac{1}{n}[/tex] where 'n' is root index, 'a' is base and '√' is radical".
= [tex]13^\frac{3}{5}[/tex].
Hence, the root index of 5 start root 13 cubed End root is [tex]13^\frac{3}{5}[/tex].
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Answer: D
Step-by-step explanation:
you're welcome
A die is rolled. Match the events mentioned in the first column with their corresponding probability.
Answer:
Step-by-step explanation:
a number greater than 5 - 1/6
a prime number - 1/2
a number greater than 4 - 1/3
a number less than 6 - 5/6
Simplify this expression
Answer:
17-(- 2 / 5j)
Step-by-step explanation:
16 + (- 5 ) - 2/5j - 4/5 j + 6
\/ \/ \/
11- ( -2/5j ) + 6
From here you over the 6 over to the 11
11+6-(-2/5j)
\/
17-(-2/5j)
It can not be simplified farther I believe
pierre, an art dealer, earns 25% commission of the dollar value of the art pieces that he sells at the bizzell Gallery. Pierre earns $10,800 this month. what is the total dollar value of the art that he sells?
Answer:
$43,200
Step-by-step explanation:
25% is 1/4 of the total dollar value, to find the answer we need to multiply 10,800 by 4 (it is 1/4, and the answer will be equivalent to the 4/4)
10,800 * 4 = 43,200
The total dollar value of the art that he sells is 43200 dollars.
What is percentage ?Percentage is the value per hundredth.We can also convert percentages into decimals by dividing he percentage value by 100.
According to the given question Pierre, an art dealer, earns 25% commission of the dollar value of the art pieces that he sells at the Bizzell Gallery. Pierre earns $10,800.
∴ 25% of the total value is 10800 dollars.
Assuming total value to be x dollars.
So, (25/100)x = 10800
(1/4)x = 10800
x = 10800 × 4
x = 43200 dollars.
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You enjoy reading in your free time and keep every book you have ever read. When you were five, you read 2 books and every year after you tripled the number of books you read. How many books did you have in your bookcase when you were 11 years old?
The total number of books that we had in out bookcase when we were 11 years old was 2,187 books.
What is a geometric sequence and how to find its nth terms?Suppose the initial term of a geometric sequence is [tex]a[/tex]
and the term by which we multiply the previous term to get the next term is [tex]r[/tex]
Then the sequence would look like
[tex]a, ar, ar^2, ar^3, \cdots[/tex]
(till the terms to which it is defined)
Thus, the nth term of such sequence would be
[tex]T_n = ar^{n-1}[/tex] (you can easily predict this formula, as for nth term, the multiple r would've multiplied with initial terms n-1 times).
What is the sum of terms of a geometric sequence?Lets suppose its initial term is [tex]a[/tex] , multiplication factor is [tex]r[/tex]
and let it has total n terms, then, its sum is given as:
[tex]S_n = \dfrac{a(r^n-1)}{r-1}[/tex]
(sum till nth term)
For this case the initial number of books (2) is multiplied by 3 each year.
So we got:
a = 2,
r = 3
Since a = 2 was for age 5, and if we take age 5 at 1st position, then age 11 is at the 7th position.
The number of books we read at each age is a geometric sequence with initial term 2 and multiplication factor 3.
The sum of its term(which would make it geometric series) will give the total number of books we will have.
Since age 11 is at 7th position, so n = 7
Thus, the total number of books we had in the bookcase when we were 11 years old is:
[tex]S_n = \dfrac{a(r^n-1)}{r-1}\\\\S_7 = \dfrac{2((3)^7-1)}{3-1} = 2187[/tex]
We could've derived it without formula as:
Age 5: 2 booksAge 6: [tex]2 \times 3[/tex] booksAge 7: [tex]2 \times 3^2[/tex] booksAge 8: [tex]2 \times 3^3[/tex] booksAge 9: [tex]2 \times 3^4[/tex] booksAge 10: [tex]2 \times 3^5[/tex] booksAge 11: [tex]2 \times 3^6[/tex] booksTheir sum is 2187.
Thus, the number of books that we had in out bookcase when we were 11 years old was 2187 books.
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