The domain and the range of the ordered pairs in interval notations are as follows: 1) Domain = [0,4], Range = [1,5] ; (2) Domain [-1,-4], Range =[0,-3]
Domain and Range of a set of Ordered pairsThe domain of a function is the collection of all conceivable values that may be used as inputs, or alternatively, it is the whole array of possible values for independent variables.
The range of a function is the set of every possible value for the dependent variable's outcomes, or the whole set of all possible values when the domain is substituted.
In a set of ordered pairs (x,y), the domain (input) refers to all the x-values and the range refers to all the y-values.
From the points on the graph given:
(0,1) (1,2) (2,3) (3,4) (4,5)
Domain: (0, 1, 2, 3, 4)
In interval notation: = [0,4]Range: (1, 2, 3, 4, 5)
In interval notation: = [1, 5](-1,0) (-2,-1) (-3,-2) (-4,-3)
Domain: ( -1, -2, -3, -4)
In interval notation: = [-1, -4]Range: (0, -1, -2, -3)
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Caleb observed the costumes that people wore to a costume party. The themes of the costumes and the number of people who wore them are shown in the following table.
Costume Theme Superhero Decades Scary TV & Movie Characters Animals Career
Number of People 128 96 72 52 24 28
A circle graph was drawn from the data in the table. What percentage would be on the Decades slice of the circle graph?
24%
26.7%
86.4%
96%
Answer:
(a) 24%
Step-by-step explanation:
You want the percentage of people in the Decades slice of a circle graph if it represents 96 people. The other slices represent 128, 72, 52, 24, and 28 people.
PercentThe fraction in the second category is the ratio of the number in that category to the total number. The percent is the fraction multiplied by 100%.
96/(128 +96 +72 +52 +24 +28) × 100% = 96/400 × 100% = 24%
The Decades slice of the circle would be 24%, choice A.
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I need the modulus of: I 9+40i I
I = absolute value
The required modulus is 41 .
Complex Numbers:A real and imaginary number combo with the formula a + bi , where
a and b are real numbers, and
i is the "unit imaginary number" √(−1)
a and b may also have zero values.
We are aware that complex numbers are made up of both actual and fictitious numbers.
The imaginary part, y, is multiplied by I the square root of -1, and the real part, x.
Modulus of x+iy = [tex]\sqrt{x^2 +y^2}[/tex]
Here, 9 and 40 are substituted for x and y.
i.e. 9+40i
We square the coefficients, add them, and then find the square root to obtain the modulus.
|9+40i| =[tex]\sqrt{9^2 +40^2} =\sqrt{81+1600} =\sqrt{1681}[/tex][tex]=41[/tex]
By long division method we find that
|9+40i| =41
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Que es el crecimiento exponencial?
The concept of exponential growth function is discussed below.
What is exponential function?An exponential function is of the form -
y = A(B)ˣ
Given is to explain exponential growth.
Exponential growth of a quantity happens if the rate of instantaneous change is directly proportional to the quantity itself. The general exponential function is -
y = A(B)ˣ
More specifically -
[tex]$f(x)=a(1+r)^{x}[/tex]
where -
f(x) = exponential growth function
{a} = initial amount
{r} = growth rate
{x} = number of time intervals
Therefore, the concept of exponential growth function is discussed above.
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{Question in english -
What is exponential growth?}
Hannah has to make 168 gallons of punch for a big party. The punch is made of soda and fruit drink. The cost of the soda is $1.57 per gallon and the cost of the fruit drink is $2.41 per gallon. Hannah's budget requires that the punch cost $1.66 per gallon. How many gallons of soda and how many gallons of fruit drink does she need?
Gallons of soda =
Gallons of fruit punch =
The number of gallons of fruit drink is 118 gallons and the number of gallons of soda is 150 gallons.
How much fruit drink and soda does he need?The system of equations that represents the question is:
f + s = 168 equation 1
2.41f + 1.57s = (1.66 x 168)
2.41f + 1.57s = 278.88 equation 2
Where:
f = number of gallons of fruit drink s = number of gallons of sodaThe elimination method would be used to determine the required values
Multiply equation 1 by 2.41
2.41f + 2.41s = 404.88 equation 3
Subtract equation 2 from equation 3
126 = 0.84s
s = 126 / 0.84
s = 150
Substitute for s in equation 1
f + 150 = 168
f = 168 - 150
f - 118 gallons
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Please help me!! Quiz due 11:59pm - Match each scatterplot shown below with one of the four specified correlations
You randomly draw once from this deck of cards.
4 6
1 6 9 4
8
1
1
2 6 7
What is the probability of not drawing an even number? Write your
answer as a fraction.
9
5
Answer:why not
Step-by-step explanation:that sa prrety nice ask
Answer: 5/8
Step-by-step explanation:
The probability of not drawing an even number can be calculated by finding the number of odd numbers in the deck and dividing by the total number of cards. In this deck, there are 5 odd numbers: 1, 1, 1, 7, and 9. The total number of cards is 8. Therefore, the probability of not drawing an even number is 5/8. The answer is written as a fraction as 5/8.
A rectangular garden 12 feet by 16 feet has a stone path along the perimeter with the same width, w. The area of the garden and path is 420 square feet.
The correct equation to find the width, w, of the stone path would be: Option B. (2w+12) (2w+16) = 420
This is because the area of the garden and path is equal to the area of the rectangle with dimensions (12+2w) and (16+2w). Therefore, we can set up the equation:
(12+2w)(16+2w) = 420
Expanding and simplifying, we get:
4w² + 56w - 204 = 0
Dividing by 4, we get:
w² + 14w - 51 = 0
Factoring, we get:
(w+17)(w-3) = 0
Since the width of the path cannot be negative, the only valid solution is w = 3.
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Complete question is in the image attached
Select the correct answer.
of a group of 500 people, 60 are fit enough to climb Mount Shasta in California. The group has 300 women and 200 men. 12% of the men are fit
to climb the mountain. What is the probability that a person picked at random from the group is a male or is fit to climb Mount Shasta?
OA
OC
OD.
Answer as a fraction
Answer:
As a fraction, the probability that a person picked at random from the group is a male or is fit to climb Mount Shasta is 12/100.
Step-by-step explanation:
Let the number of fit men is x.
Now,
we know
x = 12% of 200 men
x = [tex]\frac{12}{100}[/tex] ×200
x = 0.12 × 200
= 24 men.
Given,
The 60 people are fit to climb the Mount Shasta ,24 of them are men,
so there must be
60 - 24 = 36 women who are fit to climb the mountain.
The probability of a person picked at random from the group is a male or is fit to climb Mount Shasta is the sum total of the probability of picking a fit male and the probability of picking a fit female is,
P(male or fit) = P(male and fit) + P(female and fit)
P(male or fit) = P(male) × P(fit | male) + P(female) × P(fit | female)
P(male or fit) = ([tex]\frac{200}{500}[/tex]) ×([tex]\frac{24}{200}[/tex]) + ([tex]\frac{300}{500}[/tex]) × ([tex]\frac{36}{300}[/tex])
=.4 × .12 + .6 × .12
= 0.048 + 0.072
=.12
So,
P(male or fit) ≈ 0.12
As a fraction, the probability that a person picked at random from the group is a male or is fit to climb Mount Shasta is 12/100.
Which of the following is the midsegment for A ACE?
A. AC
B. BC
C. DB
D. CE
Explanation:
Points B and D are midpoints of segments AC and CE respectively. This is because of the tickmarks indicating congruent segment pieces (AB = BC and CD = DE)
Joining the midpoints together forms a midsegment. The midsegment is half as long as the side parallel to it. This means BD is half as long as AE. Flip things around to say that AE is twice as long as BD.
Suppose that x and y vary inversely, and x = 10 when y = 8. Write the function that models the inverse variation.
If x and y vary inversely, we can write their relationship then the function that models the inverse variation is y = 80/x.
What is Function?
In mathematics, a function is a rule or mapping that associates each input value (also called the independent variable) with a unique output value (also called the dependent variable). Functions are often represented using an equation, formula, or a graph, and are used to model real-world phenomena and solve problems in various fields such as science, engineering, economics, and more.
They can take different forms and have different properties, such as being linear, quadratic, exponential, periodic, or more complex. Some common notation used to represent functions includes f(x), y = f(x), or simply y.
If x and y vary inversely, we can write their relationship as:
x * y = k
where k is a constant of proportionality. We can use the given initial values of x and y to solve for k:
10 * 8 = k
k = 80
Therefore, the function that models the inverse variation is:
x * y = 80
or
y = 80/x
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A cupcake shop makes 25 dozen
cupcakes every 2 days. At this rate, how
many cupcakes does the shop make in
five days?
A. 600
B. 650
C. 750
D. 900
I got a bit confused with this pls help.
Answer:
The correct answer is c. 750
Step-by-step explanation:
if the shops makes 25 dozen in two days that makes it 300 cupcakes In two days because 1 dozen is 12 cupcakes, so you will see that they make 50 dozen in 4 days which is 600 then you know he/she is going to make half of the 25 dozen on the 5th day so you will take half of 300 which is 150 and add it all together, so will get 300+300+150= 750 as your answer.
e 1.5 Checkpoint: Rational and irrational numbers SNE
Select all the numbers that are irrational.
√55
36
39
√40
L
√√49
√55 and √40 are the irrational numbers.
What is Number system?A number system is defined as a system of writing to express numbers.
A rational number is the one which can be represented in the form of P/Q where P and Q are integers and Q ≠ 0.
But an irrational number cannot be written in the form of simple fractions.
√55 is an irrational number
√40 is an irrational number
√49 value is 7 which is a natural number
Hence, √55 and √40 are the irrational numbers.
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Interpret the scatter plot based on the shape of the distribution.
Answer: Looks like a positive correlation with an outlier in the lower left.
Step-by-step explanation:
help me with this please i need help because i dont get it <33
Answer:
C
Step-by-step explanation:
consider the coordinates of the same points on both figures
top left vertex of figure P (- 8, 8 )
top left vertex of figure Q (- 4, 4 )
note that both coordinates from Q are half the coordinates of P
then to obtain Q from P multiply each coordinate by [tex]\frac{1}{2}[/tex] , that is
(x, y ) → ([tex]\frac{1}{2}[/tex] x , [tex]\frac{1}{2}[/tex] y )
why is this graph not a function?
The graph is not a function because it fails the vertical line test
How to determine why it is a not functionFrom the question, we have the following parameters that can be used in our computation:
The graph (added as an attachment)
The given graph when represented as an equation, is a circle equation
As a general rule, we have
Circle equations are not functions and they do not represent a function on a graph
This is so because they do not pass the vertical line test
Hence, the graph is not a function
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In ΔGHI, i = 800 cm, m m∠G=26° and m m∠H=122°. Find the length of h, to the nearest 10th of a centimeter.
Answer:
For the nearest 10th of a centimeter, the value of h is 460 cm
Step-by-step explanation:
To find length of h we can use Law of Sines . The Law states that for a triangle with sides a, b, and c and angles A, B, and C opposite to those sides, the following equation holds:
a/sin A = b/sin B = c/sin C
In ΔGHI, let h be the length of the side opposite angle H, and let i be the length of the side opposite angle I.
Now:
h/sin 122° = i/sin 26°
We can find h by cross multiplying:
h = i * sin 122° / sin 26°
=459.9
Here,
h = 459.9 cm
By taking approximation we get 460 cm
Answer:
This answer is actually 1280.3
Step-by-step explanation:
The length of each side of an equilateral triangle having an area of square root of 243sq.cm is
Answer:
[tex]\textrm{Each side = 23.6893 cm}\\\\\\\textrm{Rounded to 2 decimal places = 23.69 cm}\\\\\textrm{Rounded to 1 decimal place = 23.7 cm}[/tex]
You can choose the level of precision as desired from the above
Step-by-step explanation:
The area of an equilateral triangle of side a
is
[tex]A = \dfrac{(a^2 \sqrt{3})}{4}[/tex]
We are given A = 243
Plugging in values we get
[tex]243 = \dfrac{a^2\sqrt{3}}{4}[/tex]
Switch sides so [tex]a^2[/tex] term is on the left
[tex]\dfrac{a^2\sqrt{3}}{4} = 243[/tex]
Multiply by 4 both sides to get rid of the denominator:
[tex]\dfrac{a^2\sqrt{3}}{4} \times 4 = 243 \times 4\\\\a^2\sqrt{3} = 972\\\\[/tex]
Divide by [tex]\sqrt{3}[/tex] both sides:
[tex]a^2 = \dfrac{972}{\sqrt{3}}\\\\a^2 = 561.18446\\\\a = \pm \sqrt{561.18446}\\\\[/tex]
Taking only positive square root:
[tex]a = \sqrt{561.18446}\\\\a = 23.6893\\\\[/tex]
help please!!!!!!!!!!
Answer:
5x(8-1)=(5x10)-(5x4)
ASAPPPPPPPPPPPPPPPPPPPPPPPPPPPPP
Answer:
48ft²
Step-by-step explanation:
Visualize the trapezoid as consisting of a rectangle with two triangles on either side. To find its total area, find the area of each and add them up.
Note that the formula for the area of a square is (base*height) and the formula for the area of a triangle is (0.5*base*height). The bottom of the trapezoid is 15ft and the top is 9ft, which makes the combined bases of the two triangles 15-9=6ft, meaning each triangle's base is 3ft.
Area of left triangle = 0.5*3*4 = 6ft²
Area of square = 4*9 = 36ft²
Area of right triangle = 0.5*3*4 = 6ft²
Therefore the total area is: 6ft² + 36ft² + 6ft² = 48ft²
Answer:
48ft?
Visualize the trapezoid as consisting of
a rectangle with two triangles on either
side. To find its total area, find the area of
each and add them up.
If possible factor. Find LCD. Multiply both sides by LCD. Solve show all work.
The lowest common denominator of the fraction is 6
What is LCDThe lowest common denominator (LCD) is the smallest common multiple of the denominators of a set of fractions. It is used to add or subtract fractions with different denominators.
The LCD of a set of fractions is the smallest number that is divisible by all the denominators in the set. When all the denominators are divided into the LCD, each fraction has an equivalent fraction with the same value and a denominator equal to the LCD.
In the fraction given;
x / 3 + x / 2 = 20
The lowest common denominator is 6
Using 6, we can divide through each of the fraction.
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The cost for shipping a package that weighs x pounds from Boise
to Los Angeles is shown at the right. How much more does
Shipping Central charge than Globe Delivery?
Shipping Central charges $0.51 more than Globe Delivery for any given weight of the package.
How to calculate this?The cost for shipping a package that weighs x pounds from Boise to Los Angeles is shown below.
Company Cost ($)
Shipping Central 3x+3.50
Globe Delivery 2x + 2.99
To determine the amount more Shipping Central charges than Globe Delivery, you can subtract the cost function for Globe Delivery from the cost function for Shipping Central.
The difference between the two cost functions is:
3x + 3.50 - (2x + 2.99) = x + 0.51 = $0.51 + x
This means that, for any given weight of the package, Shipping Central charges $0.51 more than Globe Delivery.
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or problems 2-7, find the slope of the line.
1.
1.
-10
-10
2 PRACTICE
y
y
10
10
3.
y
10
H
5.
-10-
y
10
2
+
10
Copyright ©Great Minds PBC
The slope of the line in graph 2 is equal to 1.
The slope of the line in graph 3 is equal to 1/2.
The slope of the line in graph 4 is equal to 3/4.
The slope of the line in graph 5 is equal to 3.
How to calculate the slope of a line?In Mathematics, the slope of any straight line can be determined by using this mathematical equation;
Slope (m) = (Change in y-axis, Δy)/(Change in x-axis, Δx)
Slope (m) = (y₂ - y₁)/(x₂ - x₁)
Substituting the given data points into the slope formula, we have the following;
Slope, m = (7 - 2)/(7 - 2)
Slope, m = 5/5
Slope, m = 1.
For the line in graph 3 with the given data points, we have:
Slope, m = (3 + 2)/(6 + 4)
Slope, m = 5/10
Slope, m = 1/2.
For the line in graph 4 with the given data points, we have:
Slope, m = (6 - 0)/(8 - 0)
Slope, m = 6/8
Slope, m = 3/4.
For the line in graph 5 with the given data points, we have:
Slope, m = (6 - 0)/(2 - 0)
Slope, m = 6/2
Slope, m = 3.
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The triangles are similar. What is the missing length?
8
18
72
16
The answer is B. 18
When solving similar triangles, you must set up a proportion. We do not know what the other two lengths are for side AB, but we can still solve another way. For side AC, we can set up a proportion of 33/44. We're going to take AM and put that over the total. The total length of side AB is 24, and we're going to use x for AL.
33/44 = x/24
Once finished solving the proportion, you are left with 18
The missing length of triangle is 18.
What exactly is a triangle?
Triangles are polygons in geometry that have three sides and three vertices. This is a two-dimensional figure with three straight sides. A triangle is a three-sided polygon. A triangle's three angles added together equals 180°. A single plane contains the triangle. The triangle is classified into six forms based on its sides and angles.
A triangle is categorised into three categories based on its sides, namely:
Scalene Triangle - Each side has a distinct length.Isosceles Triangle - A triangle with two sides of equal length and one side of a different length.Equilateral Triangle - A triangle has three sides that are of the same length.A triangle is categorised into three categories based on its angles, namely:
Acute Angle Triangle - A triangle with all of its angles smaller than 90°.Obtuse Angle Triangle - A triangle with one of its angles larger than 90°.Triangle with a Right Angle - A triangle with one of its angles equal to 90°.Now,
As these triangles are similar that means
we can find the proportion of sides from given sides and
from that find x.
So, here AC/AM=AL/AB
44/33=24/x
AL=24*33/44
AL=18
Hence,
The missing length AL of triangle is 18.
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Out of a random sample of 300 voters, it was found that 172 voters are in favor of Issue #1.
Out of a total of 75,000 voters, how many do you predict will vote against Issue #1?
It is predicted that ___
voters are against Issue #1.
A- 30,000
B- 32,000
C- 43,000
D- 60,000
Answer:
B)32000
Step-by-step explanation:
Out of 300, 172 are in favor, and 142/300 is simplfieid as 43/75
43/75 is equal to 43,000/75000
Subtract 75000 by 43000
The difference is 32,000.
32,000 voters are against the Issue.
Describe a single transformation of △ABC that is a composition of the following pair of transformations:
T<−5,−3>(ABC) followed by T<−4,−2> (A'B'C).
A. T<−1,−5>(ABC)
B. T<−9,−5>(ABC)
C. T<−9,−1>(ABC)
D. T<−1,−1>(ABC)
The required overall translation is T<−9,−5>(ABC). The correct answer would be option B.
What is a transformation?A point is transformed when it is moved from where it was originally to a new location. Translation, rotation, reflection, and dilation are examples of different transformations.
Starting with triangle ABC, we first apply the transformation T<−5,−3>, which means each vertex of the triangle is shifted 5 units to the left and 3 units down. So the triangle becomes A'B'C'.
Next, we apply the transformation T<−4,−2> to triangle A'B'C', meaning that each vertex is shifted 4 units to the left and 2 units down.
To find the overall effect of these two transformations, we can think of the second transformation as shifting the entire triangle produced by the first transformation.
In other words, we're combining the effects of the two transformations by adding the translations together.
So, the overall translation is T<−5 + −4, −3 + −2> = T<−9,−5>,
Thus, the correct answer would be option B: T<−9,−5>(ABC).
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Sami is 5 feet 8 inches tall and his younger sister is 4 feet 11 inches tall. How many inches taller is sami than his sister?.
The number of inches Sami is taller to his younger sister as per their respective given heights is equal to 9 inches.
Height of Sami in feet and inches is equal to 5 feet 8 inches
Height of Sami's younger sister is equal to 4 feet 11 inches
Convert all height into inches we get,
1 feet = 12inches
5 feet = 5 × 12 inches
= 60 inches
4 feet = 4 × 12 inches
= 48 inches
Number of inches Sami's is taller than his younger sister is equal to
= ( 5 feet 8 inches ) - ( 4 feet 11 inches )
= ( 60 + 8 ) inches - ( 48 + 11 ) inches
= 68 inches - 59 inches
= 9 inches
Therefore, the number of inches Sami is taller than his younger sister is equal to 9 inches.
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An angler catches a fish that weighs 20 kg. The fish’s bones make up approximately 10% of the fish’s total weight. What is the weight of the fish meat, not including the bones, in pounds? Round to the nearest tenth if necessary.
44.0
40.0
39.6
4.4
4.0
Answer: approximately 40lbs.
Step-by-step explanation:
First, you multiply 20kg to 10%, or 0.10.
20(0.10)=2kg
Then you minus the 2kg from the initial weight
20kg
-2kg
18kg
1 kg is approximately 2.20462262 lbs., so you need to convert your kg to lbs
18kg * 2.20462262 lb/kg = 39.68320716 which is rounded up to approximately 40lbs
Hope that helps!
A woman has a total of $7,000 to invest. She invests part of the money in an account that pays 10% per year and the rest in an account that pays 11 per year. If the interest earned in the first year is $730 , how much did she invest in each account
The investments are $ 4000 and $ 3000 in the respective accounts
What is Algebra ?The mathematical field of algebra assists in the depiction of problems or conditions as mathematical statements. It involves variables like x, y, z, and mathematical operations like addition, subtraction, multiplication, and division to form a meaningful mathematical expression.
In the given question,
x = amount invested at 10 %
( 7000 - x ) = amount invested at 11 %
The total interest was $730 :
.10 (x) + .11 (7000-x) = 730
0.1 x + 770 - 0.11 x = 730
0.01 x = 40
x = 4000
Therefore, the amount invested in an account that pays 10 % per year is $ 4000.
Hence , the amount invested in an account that pays 11 % per year is
= ( 7000 - x ) = 7000 - 4000 = $ 3000.
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Please I could really use some help
Answer:
-1/2
Step-by-step explanation:
cos(-360+60)=-1/2
[tex]\cos(\alpha - \beta)= \cos(\alpha)\cos(\beta) + \sin(\alpha)\sin(\beta) \\\\[-0.35em] ~\dotfill\\\\ -300\implies 30-330\hspace{5em}\cos(-300^o)\implies \cos(30^o-330^o) \\\\\\ \cos(30^o-330^o)\implies \cos(30^o)\cos(330^o)+\sin(30^o)\sin(330^o) \\\\\\ \cfrac{\sqrt{3}}{2}\cdot \cfrac{\sqrt{3}}{2}~~ + ~~\cfrac{1}{2}\cdot \cfrac{-1}{2}\implies \cfrac{3}{4}~~ + ~~\cfrac{-1}{4}\implies \cfrac{3}{4}-\cfrac{1}{4}\implies \cfrac{2}{4}\implies \boxed{\cfrac{1}{2}}[/tex]
LMNO is a parallelogram. If NM = x + 37 and OL = 5x + 9 find the value of x.
The value for the variable x in the parallelogram is equal to 7.
How to evaluate for the variable x in the parallelogramThe parallelogram LMNO have two pairs of parallel sides hence LO = MN and LM = ON.
We shall evaluate for variable x as follows:
5x + 9 = x + 37
5x - x = 37 - 9 {collect like terms}
4x = 28
x = 28/4 {divide through by 4}
x = 7
Therefore, the value for the variable x in the parallelogram is equal to 7.
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The value of the variable x is 7
How to determine the valueIt is important to note that the opposite sides of a parallelogram are congruent or equal in length.
Then, for the parallelogram LMNO
NM is parallel to OL
Now, substitute the values, we get;
NM = OL
x + 37 = 5x + 9
collect like terms
x - 5x = 9 - 37
subtract the like terms
-4x = -28
Make 'x' the subject
x = 7
Hence, the value is 7
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