Answer:
See below
Step-by-step explanation:
Q1. if a counting number is selected at random from a set of whole number less than or equal to 20 find the probability of getting:
Counting numbers are Natural numbers: [tex]\mathbb{N}[/tex]
Also, we have Whole numbers. Despite not having an official symbol, I usually denote the set as [tex]\mathbb{Z}_{\ge 0}[/tex]
Whole numbers less than or equal to 20: [tex]A\leq 20, A \subset \mathbb{Z}_{\ge 0} \\\implies A=\{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20\}[/tex]
A. Prime numbers
From the set A, the prime numbers are 2, 3, 5, 7, 11, 13, 17, 19.
Once we have 21 numbers in total and 8 prime numbers, the probability is:
[tex]$P=\frac{8}{21} \approx 40\%$[/tex]
B. Composite numbers
From the set A, the composite numbers are 4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20.
Once we have 21 numbers in total and 11 composite numbers, the probability is:
[tex]$P=\frac{11}{21} \approx 52\%$[/tex]
C. Divisible by three
From the set A, the numbers divisible by three are 3, 6, 9, 12, 15, 18.
Once we have 21 numbers in total and 6 numbers divisible by three, the probability is:
[tex]$P=\frac{6}{21} \approx 30\%$[/tex]
D. Square of 2
From the set A, the numbers square of 2 are 0, 1, 4, 9, 16.
[tex]\sqrt{0} =0[/tex]
[tex]\sqrt{1} =1[/tex]
[tex]\sqrt{4} =2[/tex]
[tex]\sqrt{9} =3[/tex]
[tex]\sqrt{16} =4[/tex]
Once we have 21 numbers in total and 5 numbers square of 2 , the probability is:
[tex]$P=\frac{5}{21} \approx 24\%$[/tex]
Q2. The opposite angle of acyclic quadrilaterals is in the ratio of 2:3. Find the degree measure of each opposite angle?
Once they're opposite, they add up to 180º
[tex]2x+3x=180 \implies 5x=180 \implies x=36[/tex]
The first angle is 72º
The second angle is 108º
Q3. what is the solution set of 9x-4<13x-7 (domain, x e z) ?
[tex]x \in \mathbb{Z}\\[/tex]
[tex]$x>\frac{3}{4} $[/tex]
[tex]$x\in \left(\frac{3}{4},\infty \right)$[/tex]
Q4. if three fourth of a number is one tenths, what is the number?
[tex]$\frac{3}{4} x =\frac{1}{10} \implies 3x=\frac{4}{10} \implies \boxed{x = \frac{2}{15}} $[/tex]
Q5. which one is the equation of the line passing through the origin and having a slope 4?
[tex]y=mx+b[/tex]
[tex]m: \text{slope}[/tex]
[tex]b: \text{y-intercept}[/tex]
B. Y= 4x
To find the distance between (17,3) and (17,−5), Marcia used the following equation. Is Marcia correct? Explain. D=|3−(−5)|=8
Answer:
Step-by-step explanation:
The formula for finding the distance between two points is expressed as shown
D = √(x₂-x₁)²+(y₂-y₁)²
Given the coordinate (17,3) and (17,−5), from the coordinates x₁ = 17, y₁ = 3, x₂ = 17 and y₂ = -5.Substituting the values given into the formula;
D = √(17-17)²+(-5-3)²
D = √0²+(-8)²
D = √64
D = 8
According to the result gotten, it can concluded that Marcia is correct although she didn't use the right expression to calculate her distance. She should have taken the square root of the sum of the square of difference in the coordinates axis according to the formula used.
Your school is 4 miles east and 1 mine south of your apartment there is a park 3 miles east and 4 miles south of your apartment estimate the distance between the park and your school
The estimated distance between the park and your school is 5 miles.
Here,
To estimate the distance between the park and your school, we can use the Pythagorean theorem, as the distance forms a right-angled triangle with the school, apartment, and park as its vertices.
Let's label the points as follows:
S = School
A = Apartment
P = Park
Given:
School (S) is 4 miles east and 1 mile south of the apartment (A).
Park (P) is 3 miles east and 4 miles south of the apartment (A).
Now, we have two right-angled triangles:
The triangle formed by S, A, and P. This is the triangle for which we want to estimate the distance between the school and the park.
The triangle formed by A, S, and P.
Since both triangles share the side AS (4 miles east), we can use the Pythagorean theorem for the triangle ASP to find the distance between the school and the park.
The Pythagorean theorem states that for a right-angled triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
In this case, let's represent the distance between the school and the park as d (the hypotenuse), and the other two sides as 3 miles (east) and 4 miles (south).
Using the Pythagorean theorem:
[tex]d^2 = 3^2 + 4^2\\d^2 = 9 + 16\\d^2 = 25\\[/tex]
Now, take the square root of both sides to find d:
d = √25
d = 5
So, the estimated distance between the park and your school is 5 miles.
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Determine for each x-value whether it is in the domain of f or not. -
Answer:
-7 is in our domain.
0 is in our domain
7 is not in our domain.
Step-by-step explanation:
So we have the rational function:
[tex]f(x)=\frac{x}{x-7}[/tex]
The domain restrictions of rational functions are the zeros of the denominator. In other words, the domain of rational functions are always all real numbers except for the zeros of the denominator.
So, solve for the denominator by setting it to 0:
[tex]x-7=0[/tex]
Add 7 to both sides:
[tex]x=7[/tex]
So, our domain is all real numbers except for 7.
(When x=7, we have 7/0, which is undefined.)
Therefore:
-7 is in our domain.
0 is in our domain
7 is not in our domain.
Answer:
the picture has it all!
whatever equals zero is not the domain and whatever doesnt equal zero is the domain!
hope i helped :)
Solve the following three equations.
Equation #1 60 = 6(6 – 2n)
Equation #2 5x + 7 + 3x = -8 + 3x
Equation #3 3(1 + 4v) – 2(5v- 3) = 25
and add explanation please.
Answer:
#1 : -2=n
#2: x=-3
#3: v=8
Step-by-step explanation:
the pictures are the explination
i hope they help
sorry if they dont
im a bad explainer
A bakery sold a total of 500 cupcakes in a day, and 200 of them were mocha flavored. What percentage of cupcakes sold that day were mocha flavored?
Answer:
20%
Step-by-step explanation:
200 mocha flavored cupcakes of the 500 cupcakes were sold. (200/500).
Reduce to 2/5. Then multiply 20/20 to 2/5 and get 20/100.
20% cupcakes were mocha flavored.
The logic behind me rewriting the fraction to 20/100 was because 200/500 could easily be divided be 100 and 5.
Answer:40%
Step-by-step explanation: 200/500=?/100
2/5 x 20/20= 40/100
40%
A floor 5 m by 20 m is covered by square tiles of side 20 cm. How many tiles are needed
Answer:
number of tiles needed = 2500 pieces
Step-by-step explanation:
Floor area = 5m x 20m = 100 m²
area of 1 square tile = 20cm x 20cm = 400 cm² ---- convert to m²
400 cm² x [tex]\frac{1 m^{2} }{100^2 cm^2}[/tex] = 0.04 m²
To get the number of tiles required to cover the floor area 5x20 = 100 m²
just divide it by the area of tile.
so Number of tile req'd = 100 / 0.04 = 2500
therefore,
the number of tiles needed = 2500 pieces
Slove the question please
Answer:
24m
Step-by-step explanation:
factor the equation to get 6x4m which gets you 24m
Answer: option 3. 24m
Step-by-step explanation:
concept to know: (a+b)²=a²+2ab+b²
(a-b)²=a²-2ab+b²
(2m+3)²-(2m-3)²
=(4m²+12m+9)-(4m²-12m+9) ⇔ Use the formula mentioned above
=4m²+12m+9-4m²+12m-9 ⇔ take off parentheses
=4m²-4m²+12m+12m+9-9 ⇔ move the like term together
=24m ⇔ combine like term
Hope this helps!! :)
Please let me know if you have any question
Simplify 10 3 × 10 3 leaving your answer in index form.
Answer:
10^3×10^3
is 100000000 which is 10^7 in index form.
3e - 19-7e + 10 simplified?
Answer:
Answer:-4e-9
[tex]3e - 19 - 7e + 10[/tex]
Start by combining like terms. I put like terms in parentheses so you can see them, but they are not needed.
[tex] = (3e - 7e) + ( - 19 + 10)[/tex]
[tex] = - 4e - 9[/tex]
That's it.
1. FIND THE EQUATION OF THE LINE THAT PASSES THROUGH THE GIVEN POINT (1,2) AND (-1,5)
2. WHAT IS THE EQUATION OF A LINE THAT PASSES THROUGH POINTS (-0.72, 1.42) and (4.22, 5.83)
Please help :(
Answer:
slope: (y₂ - y₁) / (x₂ - x₁)
(5 - 2) / (-1 - 1) = 3/-2 = -3/2
y = -3/2x + b
5 = -3/2(-1) + b
5 = 3/2 + b
b = 3.5
y = -3/2x - 7/2
(5.83 - 1.42) / (4.22 + 0.72) = 4.41/4.94
y = 4.41/4.94x + b
5.83 = (4.41/4.94)(4.22) + b
5.83 = 3.76724696 + b
b = 2.06275304
y = 4.41/4.94x + 2.06
(the numbers are really wacky so i hope thats right, so sorry if it isn't)
jndxihdhwquihxois2njknz'oqwjskzlnzljx
Answer:
Yjtccjtchtcychy
Step-by-step explanation:
Can someone help? I don’t really understand what reflect over line y=x means :)
Answer: (-3,7)
Step-by-step explanation:
Flip the signs
A random sample of 1,500 couples was asked the question, "How many children presently reside in your household?" Number of Children Frequency 0 325 1 212 2 660 3 151 4 68 5 or more 84 What number of children occurred the least frequently? Calculate this percent. (2 points) a 0, 21.67% b 0, 11.75% c 5 or more, 5.6% d 4, 4.53%
Answer: d. 4, 4.53%
Step-by-step explanation:
Given table :
Number of Children Frequency
0 325
1 212
2 660
3 151
4 68 ← Least frequency
5 or more 84
Total = 1500
or Sample size of couples = 1500
The number of children occurred the least frequently = 4 [Minimum frequency is 68 at number of children=4]
Percentage =[tex]\dfrac{least\ frequency}{Total}\times100[/tex]
[tex]\dfrac{68}{1500}\times100=4.53\%[/tex]
Hence, the correct answer is d. 4, 4.53%
Solve for the linear equation 3x+2+x=x+5 please show work
Answer:
3x +2 +X = X+5
4x + 2 = X + 5
3x = 3
X = 1
Step-by-step explanation:
brain list me plzzz I need it
x = 1
Step-by-step explanation:3x + 2 + x = x + 5
3x + x - x = 5 - 2
3x = 3
x = 3 : 3
x = 1
Write an inequality for Five dollars less than two times Chris' pay is at most
$124
Answer: 2x -5 less than or equal to 124
While on beach vacation, tasha makes scale drawing of points of intererest between priers on her drawing 2 cm represents 15 MI the priers are 12 cm apart on tashas drawing. What is the actual distnace between 2 priers
Answer:
Actual distance between the 2 priers = 90 MI
Step-by-step explanation:
Ratio of Scaled drawing to actual dimension = 2 : 15
2 cm represents 15MI
2cm ≡ 15 MI
∴ 1 cm ≡ (15/2) MI
1 cm ≡ 7.5 MI
scaled distance of priers in drawing = 12cm
∴ 12 cm ≡ 7.5 × 12
= 90 MI
∴ Actual distance between the 2 priers = 90 MI
Cynthia Besch wants to buy a rug for a room that is 21 ft wide and 34 ft long. She wants to leave
a uniform strip of floor around the rug. She can afford to buy 338 square feet of carpeting. What
dimensions should the rug have?
Answer:
Dimensions of the rug = 13 ft × 26 ft
Step-by-step explanation:
Dimensions of the room = 21 ft × 34 ft
Area of the room = 21 × 34 = 714 ft²
Cynthia wants to leave a uniform strip of floor around the rug.
Let the width of the rug = x ft
Then the dimensions of the rug will be = (21- 2x)ft × (34 - 2x)ft
Area of the rug = (21 - 2x)×(34 - 2x) square feet
338 = (21 - 2x)×(34 - 2x)
338 = 714 - 68x - 42x + 4x²
4x² - 110x + 714 - 338 = 0
4x² - 110x + 376 = 0
2x² - 55x + 188 = 0
2x² - 47x - 8x + 188 = 0
x(2x - 47) - 8(x - 47) = 0
(x - 4)(2x - 47) = 0
x = 4, [tex]\frac{47}{2}[/tex]
For x = 23.5 area of the rug will be negative.
Therefore, x = 4 ft will be the width of the rug.
Dimensions of the rug will be 13 ft × 26 ft.
Which of the following statements are true about this graph? Check all that apply. The three points do not form a straight line. The three points form a straight line. The graph passes through the origin. The graph does not pass through the origin. The graph shows a proportional relationship. The graph does not a show a proportional relationship.
Answer:
B,D,F
Step-by-step explanation:
I got it correct on edge
The area of an 13-cm-wide rectangle is 286 cm^2. What is its length?
20 points and brainliest to whoever has the correct answer in the next 2 hours
Answer:
L = 22 cm
Step-by-step explanation:
Area of a triangle = L x W
where W = 13 cm
Area = 286 cm²
A = L x W
286 = L x 13
L = 286 / 13
L = 22 cm
proof:
286 = 22 x 13
286 = 286 --- ok
by selling a camera for $2400, ron loses 4%.At what price should he sell it to gain 12%.
Answer: $ 2800
Step-by-step explanation:
2400 is 96% of the initial price of camera which is 2400/0.96 =$2500
Now to gain 12% profit the camera should be sold at 2500+ .12*2500=$2800
Rodney rented a machine for $70.00 to make popcorn at a school event. In addition to the machine rental cost, the popcorn supplies cost him $0.15 per bag sold. Rodney sold popcorn for $1.00 per bag how much profit did rodney make if he sold 200 bags of popcorn
Answer:
170
Step-by-step explanation:
The amount of profit Rodney made when he sold 200 bags of popcorn is given by A = $ 100
What is an Equation?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the equation is
Let the amount for renting the machine be = $ 70
The amount per bag for packing popcorn = $ 0.15 per bag
The sale price of the popcorn per bag = $ 1.00
And ,
The total number of bags sold by Rodney = 200 bags
So , the total profit made by Rodney A is calculated from the equation ,
Total amount made by Rodney = total number of bags sold by Rodney x sale price of the popcorn per bag
Substituting the values in the equation , we get
Total amount made by Rodney = 200 x 1
Total amount made by Rodney = $ 200
Now , the cost per bag is deducted from the total amount made by Rodney
So ,
Total amount made by Rodney after deduction of bag cost = ( Total amount made by Rodney - amount per bag for packing popcorn x 200 )
Substituting the values in the equation , we get
Total amount made by Rodney after deduction of bag cost =
= 200 - ( 0.15 x 200 )
= 200 - 30
= $ 170
Now , the cost of renting the machine should also be deducted from the remaining amount to calculate the profit earned by Rodney
So , The profit earned by Rodney A = 170 - amount for renting the machine
The profit earned by Rodney A = $ 170 - $ 70
The profit earned by Rodney A = $ 100
Therefore , the value of A is $ 100
Hence , The amount of profit Rodney made when he sold 200 bags of popcorn is given by A = $ 100
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what is the sum?
[tex] \frac{2}{ {x}^{2} } + \frac{4}{ {x}^{2} } [/tex]
Answer:
6/x^2
Step-by-step explanation:
Simplify the following:
2/x^2 + 4/x^2
2/x^2 + 4/x^2 = (2 + 4)/x^2:
(2 + 4)/x^2
2 + 4 = 6:
Answer: 6/x^2
Answer:
6/x²
Step-by-step explanation:
[tex]\frac{2}{x^{2} } + \frac{4}{x^{2} } \\\\[/tex]
= (2+4) / x²
= 6/x²
30 POINTS!!!!!!!!PLS COME AND LOOK!!! I NEED YOU GENIUSES!!! I WILL GIVE BRAINLIEST!!!!! AT LEAST COME AND LOOK!!!! WILL FOREVER BE GREAT FULL!!! EASY IM JUST DUMB!! The graph represents the equation 2 + 2 = 8. Use this graph to answer questions 6, 7, and 8. PART A) Look at the graph of the equation 2 + 2 = 8. Give its domain and range. PART B) Use algebraic means to show that 2 + 2 = 8 is not a function. Explain your process.
Answer:
See below.
Step-by-step explanation:
So we have the graph of:
[tex]x^2+y^2=8[/tex]
As given, the graph is a circle with a radius of 2√2 and a center of (0,0)
Part 1)
The domain of a function is the span of x-values it covers and the range of a function is the span of y-values it covers.
From the graph, we can see that the x-values the graph covers goes from -2√2 to +2√2. The graph includes these values.
Thus, the domain is, in interval notation:
[tex][-2\sqrt2,2\sqrt2][/tex]
From the graph, we can see that the y-values the graph covers also goes from -2√2 to 2√2.
Therefore, like the domain, the range in interval notation is:
[tex][-2\sqrt2,2\sqrt2][/tex]
Part 2:
First of all, we can use the vertical line test to prove that the graph is indeed not a function.
Algebraically, we have to do some more.
First, recall what it means when an equation is not a function. It means that one x maps onto two or more ys.
In other words, to prove that the equation is not a function, we can substitute an x for a value and solve for y.
For instance, let's use 0 for x (and 0 is within the domain). Thus:
[tex]x^2+y^2=8\\(0)^2+y^2=8[/tex]
Simplify:
[tex]y^2=8[/tex]
Take the square root of both sides:
[tex]y=\pm\sqrt8\\y=\pm2\sqrt2[/tex]
In other words, when x is 0, y can be either -2√2 or 2√2. So we have two different y-values with the same x-coordinate.
[tex](0,-2\sqrt2)(0,2\sqrt2)[/tex]
Therefore, the equation is not a function.
The shaded area below represents the pieces of tile installed in the hallway what percent of the hallway has not been installed tile
Answer:
35%
Step-by-step explanation:
There are 20 sqaures, 7 of them are not shaded, 7/20=35%
Which of the following provides an object with rotational symmetry?
Answer: Choice C) Star shaped symbol
We can rotate the star symbol 90 degrees to have it line up with its original image. The before and after images would be identical after doing such a rotation. So this figure has rotational symmetry.
The other figures would change if we rotated them some angle x such that [tex]0 < x < 360[/tex], so they do not have rotational symmetry.
Represent 3kg 9gm using decimals
Answer:
3.009
Step-by-step explanation:
1 Kg is 1000 grams therefore
3 kg 9 g is
3.009
hope this helps you
-5x + 32 = 47
What is the answer to the equation
Answer:
x = -3
Step-by-step explanation:
-5x + 32 = 47
-5x + 32 - 32 = 47 - 32
-5x = 15
-5x / -5 = 15 / -5
x = -3
Answer:
[tex]\Huge \boxed{x=-3}[/tex]
Step-by-step explanation:
[tex]\sf -5x + 32 = 47[/tex]
Subtract 32 from both sides.
[tex]\sf -5x + 32-32 = 47-32[/tex]
[tex]\sf -5x=15[/tex]
Divide both sides by -5.
[tex]\sf \displaystyle \frac{-5x}{-5} =\frac{15}{-5}[/tex]
[tex]\sf x=-3[/tex]
1) An elevator is on the 15th floor, it goes down 18 floors
and then up 5 floors. What floor is it on now?
Answer:
The elevator is now on the 2nd floor.
Step-by-step explanation:
15 - 18 = -3
-3 + 5 = 2
Answer:2nd floor
Step-by-step explanation:
since the elevator is on the 15th floor and you go down 18 that’s equals negative 3 then you go back up 5 floors and you add 5 to negative 3 which leaves you with the 2nd floor
Solve the following equation for the value of d.
4(-2d – 3) = 12
Type your answer...
1 point
Solve the following equations for the value of n.
60 = 6 (6 – 2n)
Type your answer...
1 point
Solve the following equations for the value of 2.
-2 (x + 10) + x = 12
Answer:
the full solution is in the picture
d= -3
n= -2
x= -32
Select the correct answer from each drop-down menu. The product of sin 30° and sin 60° is same as the product of and .
The product of sin 30 and sin 60 is same as the product of cos 60 degrees tan 30 degrees and cos 30 degrees tan 60 degrees .
The product of sin 30° and sin 60° is same as the product of cos 60° and cos 30°.
Sine and cosine of complementary anglesFrom the complementary angle theorem, we have that
sinθ = cos (90° - θ)
and
cosθ = sin (90° - θ)
By applying the theorem,
sin 30° = cos (90° - 30°)
∴ sin 30° = cos 60°
Also,
sin 60° = cos (90° - 60°)
∴ sin 60° = cos 30°
Thus, sin 30° = cos 60° and sin 60° = cos 30°
Hence, the product of sin 30° and sin 60° is same as the product of cos 60° and cos 30°.
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