Answer:
[tex]Domain = \{-3,0,2,1,6,3\}[/tex]
[tex]Range = \{4,6,-2,-3,-7,2\}[/tex]
Step-by-step explanation:
Given
[tex]\{(- 3,4), (0,6), (2, - 2), (1, - 3), (6, - 7), (3, 2)\}[/tex]
Required
The domain and range
A function is represented as:
[tex]Function = \{(x_1,y_1),(x_2,y_2),....(x_n,y_n)\}[/tex]
Where
[tex]x \to[/tex] domain
[tex]y \to[/tex] range
So, we have:
[tex]Domain = \{-3,0,2,1,6,3\}[/tex]
[tex]Range = \{4,6,-2,-3,-7,2\}[/tex]
Map Reading. A map is drawn so that every 3.3 inches on the map corresponds to an actual distance of 120
miles. If the actual distance between the two cities is 440 miles, how far apărt are they on the map?
The two cities are
inches apart on the map.
50 students in a class were asked at the beginning of the week what they did at the weekend. 18 read their books, while 28 watched films, and 7 neither read their books nor watched films. How many students both read their books and watched films?
Answer:
so 3 people both read their books and watched films.
Step-by-step explanation:
n(U) = 50
n(A) = 18 ( read books)
n(B) = 28 ( watched films)
n(A U B) with a line at the top = 7
so
Finding n(AUB)
n( A U B) with a line at the top = n(A) + n(B) - n( A n B)
7 = 50-n(A U B)
or, n( A U B) = 50 - 7
so, n(A U B) = 43
Then
n( A U B) = n(A)+n(B)-n(A n B)
43 = 18 + 28 - n( A n B)
or, 43 = 46 - n(A n B)
or, n(A n B) = 46 - 43
so, n(A n B) = 3
True or false?
A function assigns each value of the independent variable to exactly one
value of the dependent variable.
A. True
B. False
SUB
Answer:
This statement would be true.
Step-by-step explanation:
Find the first five terms of the sequence..
Answer:
The Next fiver tems are - 2, -2,-8,-12,-16
Step-by-step explanation:
Answer:
2,-6,2,-6,2
Step-by-step explanation:
a1 = 2
an = -an-1 -4
Let n =2
a2 = -a1 -4 = -2-4 = -6
Let n=3
a3 = -a2 -4 = - (-6) -4 = +6 -4 = 2
Let n = 4
a4 = -a3 -4 = -2 -4 = -6
Let n=5
a5 = -a4 -4 = -(-6) -4 = +6-4 = 2
1. Write the polynomial function that models the given situation.A rectangle has a length of 12 units and a width of 11 units. Squares of x by x units are cut out of each corner, and then the sides are folded up to create an open box. Express the volume V of the box as a polynomial function in terms of x.
2. Write the polynomial function that models the given situation. A square has sides of 24 units. Squares x + 1 by x + 1 units are cut out of each corner, and then the sides are folded up to create an open box. Express the volume V of the box as a function in terms of x.
3. Write the polynomial function that models the given situation. A cylinder has a radius of x + 6 units and a height 3 units more than the radius. Express the volume V of the cylinder as a polynomial function in terms of x.
Answer:
1. (12 - 2x)(11 - 2x)x
2. 4(11 - 2x)²(x + 1)
3. π(x³ + 15x² + 63x + 81)
Step-by-step explanation:
1. Write the polynomial function that models the given situation.
A rectangle has a length of 12 units and a width of 11 units. Squares of x by x units are cut out of each corner, and then the sides are folded up to create an open box. Express the volume V of the box as a polynomial function in terms of x.
Since the length of the rectangle is 12 units and its width 11 units and squares of x by x units are cut from its corners, it implies that a length x is cut from each side. So, the length of the open box is L = 12 - 2x and its width is w = 11 - 2x.
Since the cut corners of the rectangle are folded, the side x which is cut represents the height of the open box, h. so, h = x
So, the volume of the open box V = LWh = (12 - 2x)(11 - 2x)x
2. Write the polynomial function that models the given situation. A square has sides of 24 units. Squares x + 1 by x + 1 units are cut out of each corner, and then the sides are folded up to create an open box. Express the volume V of the box as a function in terms of x.
Since the square has sides of 24 units and squares of x + 1 by x + 1 units are cut from its corners, it implies that a length x + 1 is cut from each corner and the length 2(x + 1) is cut from each side. So, the length of side open box is L = 24 - 2(x + 1) = 24 - 2x - 2 = 24 - 2 - 2x = 22 - 2x = 2(11 - x)
Since the cut corners of the square are folded, the side x + 1 which is cut represents the height of the open box, h. so, h = x + 1
Since the area of the base of the pen box is a square, its area is L² = [2(11 - 2x)]²
So, the volume of the open box V = L²h = [2(11 - 2x)]²(x + 1) = 4(11 - 2x)²(x + 1)
3. Write the polynomial function that models the given situation. A cylinder has a radius of x + 6 units and a height 3 units more than the radius. Express the volume V of the cylinder as a polynomial function in terms of x.
The volume of a cylinder is V = πr²h where r = radius and h = height of cylinder.
Given that r = x + 6 and h is 3 units more than r, h = r + 3 = x + 6 + 3 = x + 9
So, V = πr²h
V = π(x + 3)²(x + 9)
V = π(x² + 6x + 9)(x + 9)
V = π(x³ + 6x² + 9x + 9x² + 54x + 81)
V = π(x³ + 15x² + 63x + 81)
50T Q12 A man wants to buy bags of gravel to cover his driveway. He decides to work out the area of his driveway. 1 bag of gravel covers 14m2 3m Sketch of driveway Not to scale 3m 8m 6m What is the area of his driveway? How many bags of gravel must he buy?
Answer:
hi amki nai patajjdkfkejd
write the greatest and smallest four digit number by using 7,8,0,9 digit
2. In a 100m race, Luke was 2m ahead of Azam. Chandra was 3m behind Luke, Maggie was 7m ahead of Chandra. Luke was 5m behind Darren. Who was in the first place?
Answer:
luke won
Step-by-step explanation:
he is 2 meters ahead of azam witch is in 2dn place
please help me with geometry
Answer:
A. If the side lengths are the same, then a triangle is not scalene.
Step-by-step explanation:
A triangle can be defined as a two-dimensional shape that comprises three (3) sides, three (3) vertices and three (3) angles.
Simply stated, any polygon with three (3) lengths of sides is a triangle.
In Geometry, a triangle is considered to be the most important shape.
Generally, there are three (3) main types of triangle based on the length of their sides and these include;
I. Equilateral triangle: it has all of its three (3) sides and interior angles equal.
II. Isosceles triangle: it has two (2) of its sides equal in length and two (2) equal angles.
III. Scalene triangle: it has all of its three (3) sides and interior angles different in length and size respectively.
Which number is divisible by 5? 99 45 83 94
Answer:
45
Step-by-step explanation:
because 5•9=45 so yeah that's the answer
Hallar el noveno término de la progresión aritmética 8, 13, 18,…
Answer:18
Step-by-step explanation:
divide 111001 by 1101
Based on the fact that you asked this three times and got the same answer three times, I suspect the interpretation made by the users that posted those answers was incorrect, and that you meant to ask about dividing in base 2.
We have
111001₂ = 1×2⁵ + 1×2⁴ + 1×2³ + 1×2⁰ = 57
1101₂ = 1×2³ + 1×2² + 1×2⁰ = 13
and 57/13 = (4×13 + 5)/13 = 4 + 5/13.
4 = 2² is already a power of 2, so we have
111001₂/1101₂ = 1×2² + 5/13
we just need to convert 5/13. To do this, we look for consecutive negative powers of 2 that 5/13 falls between, then expand 5/13 as the sum of the smaller power of 2 and some remainder term. For instance,
• 1/4 < 5/13 < 1/2, and
5/13 - 1/4 = (20 - 13)/52= 7/52
so that
5/13 = 1/4 + 7/52
or
5/13 = 1×2 ⁻² + 7/52
Then a partial conversion into base 2 gives us
111001₂/1101₂ = 1×2² + 1×2 ⁻² + 7/52
111001₂/1101₂ = 100.01₂ + 7/52
Continuing in this fashion, we find
• 1/8 < 7/52 < 1/4, and
7/52 = 1/8 + 1/104
==> 111001₂/1101₂ = 100.011₂ + 1/104
• 1/128 < 1/104 < 1/64, and
1/104 = 1/128 + 3/1664
==> 111001₂/1101₂ = 100.0110001₂ + 3/1664
• 1/1024 < 3/1664 < 1/512, and
3/1664 = 1/1024 + 11/13312
==> 111001₂/1101₂ = 100.0110001001₂ + 11/13312
• 1/2048 < 11/13312 < 1/1024, and
11/13312 = 1/2048 + 9/26624
==> 111001₂/1101₂ = 100.01100010011₂ + 9/26624
• 1/4096 < 9/26624 < 1/2048, and
9/26624 = 1/4096 + 5/53248
==> 111001₂/1101₂ = 100.011000100111₂ + 5/53248
and so on.
It turns out that this pattern repeats, so that
[tex]\displaystyle \frac{111001_2}{1101_2} = 100.\overline{011000100111}_2[/tex]
SAT scores are normally distributed with a mean of 1,500 and a standard deviation of 300. An administrator at a college is interested in estimating the average SAT score of first-year students. If the administrator would like to limit the margin of error of the 88% confidence interval to 15 points, how many students should the administrator sample? Make sure to give a whole number answer.
Answer:
The administrator should sample 968 students.
Step-by-step explanation:
We have to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1 - 0.88}{2} = 0.06[/tex]
Now, we have to find z in the Z-table as such z has a p-value of [tex]1 - \alpha[/tex].
That is z with a p-value of [tex]1 - 0.06 = 0.94[/tex], so Z = 1.555.
Now, find the margin of error M as such
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.
Standard deviation of 300.
This means that [tex]n = 300[/tex]
If the administrator would like to limit the margin of error of the 88% confidence interval to 15 points, how many students should the administrator sample?
This is n for which M = 15. So
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
[tex]15 = 1.555\frac{300}{\sqrt{n}}[/tex]
[tex]15\sqrt{n} = 300*1.555[/tex]
Dividing both sides by 15
[tex]\sqrt{n} = 20*1.555[/tex]
[tex](\sqrt{n})^2 = (20*1.555)^2[/tex]
[tex]n = 967.2[/tex]
Rounding up:
The administrator should sample 968 students.
how many feet is 2 1/2 miles
Answer:
13200 ft
Step-by-step explanation:
1 mi = 5280 ft
5280 ft x 2.5 = 13200 ft
If my answer is incorrect, pls correct me!
If you like my answer and explanation, mark me as brainliest!
-Chetan K
I need help ASAP please
Answer:
5:10
6 (-2,0)
7 (-5,6)
8 (5,3)
9 No, ab=8 CD=6
Step-by-step explanation:
Write the ratio as a fraction in simplest form, with whole numbers in the numerator and denominator. 2.1yd : 1.4yd
9514 1404 393
Answer:
3/2
Step-by-step explanation:
Multiplying numerator and denominator by 10 will convert the ratio to a ratio of whole numbers. Then dividing by the common factor of 7 will reduce it to simplest form.
[tex]\dfrac{2.1\text{ yd}}{1.4\text{ yd}}=\dfrac{2.1\times10}{1.4\times10}=\dfrac{21}{14}=\dfrac{3\times7}{2\times7}=\boxed{\dfrac{3}{2}}[/tex]
Solve for Y equals -2 over 3x minus 1
Answer:
y=-\frac{2}{3}\approx -0.666666667
I purchased a new Apple iPad on Amazon for $249.00. The tax rate is 8.625%. What is the total purchase price of the iPad?
Answer:
270.47625
Step-by-step explanation:
249 is the original price
(249/100) · 8.625 = 21.47625 the tax total
249 + 21.47625 = 270.47625
Factor 64a^3 -8b^3 Explain all steps.
Answer:
[tex]8(2a- b)(4a^2+ 2ab+ b^2)[/tex]
Step-by-step explanation:
factor out the 8
then you have the sum/difference of cubes..
look that up SOAP: same opposite, always a plus
[tex]64a^3 -8b^3\\8(8a^3 -b^3)[/tex]
[tex]8(2a- b)(4a^2+ 2ab+ b^2)[/tex]
a. 6
b. 10
c. 7
d. 9
Answer:
6
Step-by-step explanation:
21-20 = 1
20-18 =2
18 -15 = 3
15-11 = 4
We are subtracting 1 more each time
11-5 = 6
In a geometric sequence, t4 = 8 and t7 = 216. Find the value of t2
Question 14 plz show ALL STEPS ASAP
Answer:
8/9
Step-by-step explanation:
Let the geometric series have the first term=a and common ratio=r. ATQ, ar^3=8 and ar^6=216. r^3=27. r=3. a=8/3^3=8/27. t2=ar=8/9
This graph represents which expression?
Answer:
x >7
Step-by-step explanation:
There is an open circle at 7, which means it cannot equal 7. The line goes to the right
x >7
write 6x10x10x10x10 with an expont
Answer:
6x10^4
Step-by-step explanation:
Destiny just received two separate gifts from her great-great-grandmother.
The first gift is a box of 18 chocolate candy bars, and the second gift is a pack of 12 cookies.
Destiny wants to use all of the chocolate candy bars and cookies to make identical snack bags for her cousins.
What is the greatest number of snack bags that Destiny can make?
Answer:
Destiny will be able to create 12 identical snack bags.
Step-by-step explanation:
Given that a snack bag will be 1 chocolate candy bar, and 1 cookie, we have to subtract 1 chocolate for every cookie she has, and that will leave us with 6 chocolate bars left. The equation for this is 18 - 12 = 6.
3(6x+3)=63 How to do it
(07.03. 07.04 MC)
Part A: The area of a square is (4x2 + 20x + 25) square units. Determine the length of each side of the square by factoring the area expression completely. Show
your work (5 points)
Part B: The area of a rectangle is (4x2 - 9y2) square units. Determine the dimensions of the rectangle by factoring the area expression completely. Show your work
(5 points)
Answer:
A) 4x^2+20x+25=(2x)^2+2*(2x)*5+5^2=(2x+5)^2
Area=(side)^2, side=sqrt(area)=sqrt((2x+5)^2)=2x+5
B) 4x^2-9y^2=(2x-3y)(2x+3y), these are the dimensions of the rectangle
A) The length of each side of the square is (2x + 5).
B) The dimensions of the rectangle are (2x - 3y) and (2x + 3y).
Used the concept of a quadratic equation that states,
An algebraic equation with the second degree of the variable is called a Quadratic equation.
Given that,
Part A: The area of a square is [tex](4x^2 + 20x + 25)[/tex] square units.
Part B: The area of a rectangle is [tex](4x^2 - 9y^2)[/tex] square units.
A) Now the length of each side of the square is calculated by factoring the area expression completely,
[tex](4x^2 + 20x + 25)[/tex]
[tex]4x^2 + (10 + 10)x + 25[/tex]
[tex]4x^2 + 10x + 10x + 25[/tex]
[tex]2x (x + 5) + 5(2x + 5)[/tex]
[tex](2x + 5) (2x+5)[/tex]
Hence the length of each side of the square is (2x + 5).
B) the dimensions of the rectangle are calculated by factoring the area expression completely,
[tex](4x^2 - 9y^2)[/tex]
[tex](2x)^2 - (3y)^2[/tex]
[tex](2x - 3y) (2x + 3y)[/tex]
Therefore, the dimensions of the rectangle are (2x - 3y) and (2x + 3y).
To learn more about the rectangle visit:
https://brainly.com/question/2607596
#SPJ4
PLEASE HELP
Solve the equation for y. Identify the slope and y-intercept then graph the equation.
2y-3x=10
Y=
M=
B=
Please Include a picture of the graph and show your work if you can
Hey there! I'm happy to help!
Here is our equation.
[tex]2y-3x=10[/tex]
Let's add 3x to both sides.
[tex]2y=3x+10[/tex]
Divide both sides by 2.
[tex]y=\frac{3}{2}x+5[/tex]
Here is slope intercept form.
[tex]y=mx+b\\m=slope\\b=y-intercept[/tex]
So, we can just find those two things in the equation, and here are our answers.
[tex]y=\frac{3}{2}x+5\\m=\frac{3}{2}\\b=5[/tex]
The graph is down below. If our y-intercept is 5, then one of our points is (0,5). You can then plug a random x-value into the formula to find another point and then draw the line going through the two points.
[tex]y=\frac{3}{2}(2)+5\\y=3+5\\y=8\\(2,8)[/tex]
Have a wonderful day and keep on learning! :D
Please help I’m really stuck!!
Step 1: Solve for one variable
---I will be using the first equation and solving for a.
a + c = 405
a = 405 - c
Step 2: Substitute into the other equation
---Now that we have a value for a, we can substitute that value into the second equation. Then, we can solve for c.
12a + 5c = 3950
12(405 - c) + 5c = 3950
4860 - 12c + 5c = 3950
-12c + 5c = -910
-7c = -910
c = 130
Step 3: Plug back into the first equation
---We now know one variable, which means we can plug back into our first equation and solve for the other.
a = 405 - c
a = 405 - 130
a = 275
Answer: 275 adults, 130 children
Hope this helps!
help
What is 5 added to 3 4?
6. 12
Answer:
8.4
Step-by-step explanation:
jjdijendjndoendidnie
The distribution of sample means uses
to measure how much distance
is expected on average between a sample mean and the population mean.
re
o the standard error of M
none of these
the standard deviation of the sample
the standard deviation of the population
< Previous
Next
Answer:
A: the standard error of the mean
Step-by-step explanation:
The most frequently used measure to determine how much difference there is between population mean and sample mean is by calculating the standard deviation of the sampling distribution of the mean. This standard deviation is also referred to as the sew Station.