Answer:
Events that mutually exclusive are 1. Landing on a shaded portion and landing on a 3.2. Landing on an unshaded portion and landing on a number less than 2.
what is the formula to calculate area of square
Answer:
Step-by-step explanation:
A square is made up of 4 sides that are equal in length. They can all be called "x" or "s" or whatever variable you want. The formula for the area of a square (and also the area of a rectangle) is Area = side × side.
If you called your sides "x", then the formula is A = x × x or A = x². Another way to note the area of either a square or a rectangle is to call the "bottom" the base and one of the sides the height and then the area formula looks like this:
A = b × h
or
A = length × width
They are all the same thing.
Joseph paid $105,000 for his home twenty years ago. since then, his house has increased its property value by 2.0% every year. in addition, joseph has made renovations and improvements to the house which will increase its sale value by $28,700. if joseph sells his home, how much profit will he make, to the nearest hundred dollars? a. $79,700 b. $84,700 c. $93,700 d. $122,400
If joseph sells his home, profit will he make = (a) $79720
What is profit and its example?
Profit is a term that often describes the financial gain a business receives when revenue surpasses costs and expenses. For example, a child at a lemonade stand spends one quarter to create one cup of lemonade. She then sells the drink for $2. Her profit on the cup of lemonade amounts to $1.75.Profit earned on the house if he sells = $79720
Amount paid by Joseph for his home = $105000
His house has increased its property value by 2.0% every year
So, Property cost after 20 years :
[tex]Cost = 105000 * (1.02)^{20}[/tex]
Cost = 105000 × 1.4859
Cost = 156020
Also, Due to renovations and improvements to the house, the property cost is increased by $28700
So, Total cost of the house after 20 years = 156020 + 28700
= $184720
So, Profit earned on the house if he sells = 184720 - 105000
= $79720
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Answer:a) $79720
Step-by-step explanation:edge
What is the area of the parallelogram shown above
The area of the parallelogram is 55 square feet
How to determine the area of the parallelogram?From the figure, we have the following dimensions:
Height = 5 ft
Base = 11 ft
The area of the parallelogram is calculated as:
Area = Base * Height
This gives
Area = 5ft * 11ft
Evaluate the product
Area = 55 square feet
Hence, the area of the parallelogram is 55 square feet
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130 The perimeter of the sector is 1m. Find the length of y, the radius of the circle.
Answer: 16.63 cm
Step-by-step explanation:
The length of the arc = [tex]\frac{360-130}{360}[/tex] * 2[tex]\pi[/tex]y = [tex]\frac{23}{18}[/tex][tex]\pi[/tex]y
The perimeter = [tex]\frac{23}{18}[/tex][tex]\pi[/tex]y + y + y = y([tex]\frac{23}{18}[/tex][tex]\pi[/tex] + 1 + 1) = 6.01y = 1 m
y = 16.63 cm
Write 7.21 as a mixed number in simplest form. 7.21 =
Answer:7 21/100
Step-by-step explanation: We will covert 7.21 into a fraction. .21 = 21/100. Since 21 can only be divided by 3 and 7, the simplest form of 21/100 is 21/100. So, the mixed number is 7 and 21/100
Answer:
7 and 21/100
Step-by-step explanation:
Since .01 is 1/100, 7.21 will be 7 and 21/100. There is no way to further simplify this, therefore, it is our final answer. Hope this helps! :)
Find the surface area of the prism.
PLEASE HELP IM STUCK
Answer:
6x + 4y = 16
Step-by-step explanation:
2(3x + 2y = 8)
2(3x + 2y) = 2(8)
6x + 4y = 16
Answer:
6x+4y=16
Step-by-step explanation:
2 (3x+2y=8)
2×3x+2×2y=2×8
=6x+4y=16 ans.
Jamie has 2 dimes, 4 nickels and 8 pennies. in how many different ways can she make 26 cents?
Answer:
(2 dimes + 6 pennies)
(4 nickels + 6 pennies)
(1 dime + 2 nickels + 6 pennies)
( 2 dimes + 1 nickels + 1 penny)
(1 dime + 3 nickels + 1 penny)
5 different ways that Jamie can make 26 cents.
OA=
Please help asap!! Thanks so much :))
In the given diagram, the value of the dashed side of rhombus OABC is 5
Distance between two pointsFrom the question, we are to determine the length of the dashed line (OA), in rhombus OABC
In the diagram, we can observe that the length of OA is the distance between point A and the origin (O).
Using the formula for calculating distance between two points,
d =√[(x₂-x₁)² + (y₂-y₁)²]
In the diagram,
The coordinate of the origin is (0, 0)
The coordinate of point A is (3, 4)
Thus,
x₁ = 0
x₂ = 3
y₁ = 0
y₂ = 4
Putting the parameters into the formula, we get
OA =√[(3-0)² + (4-0)²]
OA =√(3² + 4²)
OA =√(9+16)
∴ OA =√25
OA = 5
Hence, in the given diagram, the value of the dashed side of rhombus OABC is 5
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The growth of algae can be modelled by the function f(t) = 2¹.
Find the value of t such that f(t) = 128.
Answer:
t = 7
Step-by-step explanation:
You can use your knowledge of powers of 2, or you can use logarithms to find the value of t.
Powers of 22^1 = 2
2^2 = 4
2^4 = 16
128 = 16×4×2 = (2^4)(2^2)(2^1) = 2^(4+2+1) = 2^7
Now, the equation is ...
f(t) = 2^t = 2^7
Equating exponents, we have ...
t = 7
LogarithmsTaking the log of both sides of the equation ...
2^t = 128
we have ...
t×log(2) = log(128)
t = log(128)/log(2) = 7 . . . . . divide by the coefficient of t
The value of t is 7.
__
Additional comment
The relevant rule of exponents is ...
(a^b)(a^c) = a^(b+c)
The relevant rule of logarithms is ...
log(a^b) = b×log(a)
pls solve this. this is of set class 9.
Here is the answer :
people who like both the songs is 35 and
people who like only folk songs is 100.
A steel hex nut has two regular hexagonal bases and a cylindrical hole with a diameter of 1.6 centimeters through the middle. the apothem of the hexagon is 2 centimeters. a cylinder is cut out of the middle of a hexagonal prism. the hexagon has an apothem with a length of 2 centimeters and base side lengths of 2.3 centimeters. the prism has a height of 2 centimeters. the cylinder has a diameter of 1.6 centimeters. the equation for the area of a regular hexagon = one-half (apothem) (perimeter). what is the volume of metal in the hex nut, to the nearest tenth? use 3.14 for π.
Subtracting the volume of the cylinder from the volume of the prism, the volume of metal in the hex nut to the nearest tenth exists [tex]$$23.6 cm^3[/tex]
How to estimate the volume of metal in the hex nut?Diameter of the cylinder be d = 1.6 cm
Apothem of the hexagon be a = 2 cm
Thickness of the steel hex nut be t = 2 cm
Volume of the prism be [tex]V_p[/tex]
Volume of the cylinder be [tex]V_c[/tex]
Volume of metal in the hex nut,
[tex]$$V = V_p - V_c[/tex]
To estimate the volume of a prism,
[tex]$$V_p = A_b h[/tex]
Ab = n L a / 2
Number of the sides, n = 6
The side of the hexagon be L
Height of the prism, h = t = 2 cm
Central angle in the hexagon, A = 360°/n
A = 360°/6 = 60°
[tex]$tan (\frac{A}{2} )=(\frac{L/2}{a})[/tex]
simplifying the value of L, we get
[tex]$tan (\frac{60}{2} )=(\frac{L/2}{2})[/tex]
[tex]$tan 30}=(\frac{L/2}{2})[/tex]
[tex]$tan (\frac{\sqrt{3}}{3} )=(\frac{L/2}{2})[/tex]
Solving for L/2:
[tex]$\frac{2 \sqrt{3}}{3} =\frac{L}{2}[/tex]
Solving the value of L, we get
[tex]$2\frac{2 \sqrt{3}}{3} =L[/tex]
[tex]$\frac{4 \sqrt{3}}{3} =L[/tex]
[tex]$L=4 \sqrt{3}/3 cm[/tex]
Ab = n L a / 2
Substitute the values in the above equation, we get
[tex]$A_b=\frac{6 (4 \sqrt{3}/3)(2)}{2}[/tex]
[tex]$$A_b=24 \sqrt{3}/3 $$cm^2[/tex]
[tex]$A_b=8 \sqrt{3} cm^2[/tex]
[tex]V_p = A_b h[/tex]
substitute the values in the above equation, we get
[tex]$V_p=(8 \sqrt{3})(2)[/tex]
[tex]$V_p=16 \sqrt{3} cm^3[/tex]
[tex]$$V_p=16 (1.732) cm^3[/tex]
[tex]$$V_p=27.712 cm^3[/tex]
To estimate the volume of cylinder,
[tex]$V_c[/tex] = (π[tex]d^2[/tex]/4) h
Here, π = 3.14 and d = 1.6 cm
Height of the cylinder, h = t = 2 cm
substitute the values in the above equation, we get
[tex]$V_c=[3.14 (1.6) / 4] (2)[/tex]
[tex]$V_c=[3.14 (2.56) / 4] (2)[/tex]
[tex]$V_c=(2.0096) (2)[/tex]
[tex]$$V_c=4.019 cm^3[/tex]
Substitute the values in the equation, we get
[tex]$$V=V_p-V_c[/tex]
[tex]$$V=27.712 - 4.019[/tex]
[tex]$$V=23.693 cm^3[/tex]
[tex]$$V=23.6 cm^3[/tex]
Therefore, the volume of metal in the hex nut, to the nearest tenth exists [tex]$$23.6 cm^3[/tex].
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The mean if four numbers is 25 if three numbers are 36, 12 and 24 what is the fiurth number
correct answer is 28.
If the mean of four numbers is 25 and three numbers are 36, 12 and 24 then fourth number is 28.
Find fourth number?given terms are:
first number =36
second number=12
third number=24
fourth number=?
let us assume the fourth number be x.
what is mean?we know the formula to find mean is:
Mean=addition of given terms / total number of terms
According to given statement, we put the values in above equation and we get,
25=(36+12+24+x) / 4
By rearranging, we get
36+12+24+x=100
72+x=100
x=100-72
x=28
so, the fourth number is 28.
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[tex]\frac{12}{20}[/tex] = ______% = ______ hundredths
The percentage form of given fraction is 60% and the hundredths form is 0.60
According to the statement
we have given that the a fraction and we have to find the percentage of that fraction and write in the form hundredths.
So, For this purpose,
The given fraction is 12/20.
Then the definition of the percentage is that
The Percentage, a relative value indicating hundredth parts of any quantity.
so, the percentage of given fraction is :
Percentage fraction = 12/20 * 100
After solving it, The percentage fraction will become:
Percentage fraction = 60%
and Now convert into the hundredths form then
In the hundredths form it will become
from 60% to 0.60.
So, The percentage form of given fraction is 60% and the hundredths form is 0.60
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Assume the four intersecting lines are parallel. In this figure, A = 36, B = 24, and C = 60 . If D = 33,
what are the measurements of E and F?
Using the proportionality theorem, the measurements are: c. E = 22 and F = 55.
What is the Proportionality Theorem?If two transversals intersect three or more parallel lines, they divide the lines in such a way that the smaller segments are proportional to each other or have ratios that are equal to each other.
Given the following:
A = 36,
B = 24,
C = 60
D = 33.
Since all lines are parallel, then:
A/D = B/E = C/F
Find the measure of E using the ratio, A/D = B/E:
36/33 = 24/E
Cross multiply
E = (24 × 33)/36
E = 22
Find the measure of F using the ratio, A/D = C/F:
36/33 = 60/F
Cross multiply
F = (60 × 33)/36
F = 55
The answer is: c. E = 22 and F = 55.
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Which statement is true about the value of Dante’s assets and liabilities?
He has $50,000 more in assets than in liabilities.
He has $50,000 more in liabilities than in assets.
He has $110,000 more in liabilities than in assets.
He has $160,000 more in assets than in liabilities.
Answer: te correct answer is A
Step-by-step explanation:
He has $50,000 more in assets than in liabilities.
Answer:
1. He has $50,000 more in assets than in liabilities.
Step-by-step explanation:
If A c B and A N B= • then which of the following can be concluded about the sets A and B!
Step-by-step explanation:
Set A is a subset of set B if all the elements of A are also the elements of Set B.. (common element)
The above set have 0 common elements so.. if there is no common element and are subsets then it means that there arent any elements in both the sets
so, the answer for the question would be "both the Sets A and B are the empty sets"
What is the solution of square root 1-3x = x+3?
O x = -8 or x = -1
O x=-8
O x=-1
O no solution
Answer: x = -1
Step-by-step explanation:
To remove the radical on the left side of the equation, square both sides of the equation.
√1−3x2=(x+3)2
Simplify each side of the equation.
1−3x=x2+6x+9
Solve for x
x=−1−8
Exclude the solutions that do not make true
√1−3x=x+3
x=−1
Use the recursive formula to find the first five terms in the arithmetic sequence.
Answer:
3, 1, - 1, - 3, - 5
Step-by-step explanation:
using the recursive formula and f(1) = 3 , then
f(2) = f(1) - 2 = 3 - 2 = 1
f(3) = f(2) - 2 = 1 - 2 = - 1
f(4) = f(3) - 2 = - 1 - 2 = - 3
f(5) = f(4) - 2 = - 3 - 2 = - 5
first 5 terms are 3, 1, - 1, - 3, - 5
Guess my number when i tripple my number snd add five,i get 26 what is my number
7. [Decimal +,-]
16
9.74
+2 6.80
Answer:
169.74+26.80
= 196.54
the correct decimal answer is 196.54
factor the gratest common factor: -5k^2+20k-30
Answer:
±5
Step-by-step explanation:
-5k²+20k-30
if u look at the equation ±5 are the greatest common factors so we ±5(±k²±4k±6)
The given decimal is 0.571
Convert the decimal into fraction :
Write down the decimal divided by1
:
0.571
1
Multiply both top and bottom by1000
:
0.571
1
×1000
1000
=571
1000
At which points on the curve y = 1 60x3 − 2x5 does the tangent line have the largest slope?
The tangent line has the largest slope at x = 3√2 and x = -3√2 on the curve y = 1 + 60x³ − 2x⁵.
First, let's find the derivative of the given function y = 1 + 60x³ − 2x⁵ using the power rule for differentiation:
dy/dx = 0 + 3(60)x² - 5(2)x⁴
= 180x² - 10x⁴
To find the critical points, we set the derivative equal to zero and solve for x:
180x² - 10x⁴ = 0
Factoring out common terms, we get:
10x²(18 - x²) = 0
Setting each factor equal to zero, we have:
10x² = 0 or 18 - x² = 0
From the first equation, we find x = 0.
From the second equation, we have:
18 - x² = 0
x² = 18
Taking the square root, we get:
x = ±√18
= ±3√2
So the critical points are x = 0, x = 3√2, and x = -3√2.
Now we need to evaluate the slope at these critical points. We can do this by plugging each x-value into the derivative:
When x = 0:
dy/dx = 180(0)² - 10(0)⁴ = 0
When x = 3√2:
dy/dx = 180(3√2)² - 10(3√2)⁴ = 180(18) - 10(216) = 3240 - 2160 = 1080
When x = -3√2:
dy/dx = 180(-3√2)² - 10(-3√2)⁴ = 180(18) - 10(216) = 3240 - 2160 = 1080
The slope is 0 when x = 0 and 1080 when x = 3√2 or x = -3√2.
Therefore, the tangent line has the largest slope at x = 3√2 and x = -3√2 on the curve y = 1 + 60x³ − 2x⁵.
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The complete question is as follows:
At which points on the curve y = 1 + 60x³ − 2x5⁵ does the tangent line have the largest slope?
Find the surface area of the prism
Area of the base = 60 inches²
Height of the prism = 4 inches
perimeter of the base = 34 inches
Surface area of the rectangular prism = 256 inches²
How to find the surface area of a rectangular prism?The surface area of a rectangular prism can be calculated as follows;
area of the base = B = 12 × 5 = 60 inches²
Height of the prism = 4 inches
Perimeter of the base is the sum of the whole side of the base of the rectangular prism.
Therefore,
perimeter of the base = 12 + 12 + 5 + 5 = 34 inches
Surface area of the rectangular prism = 2B + ph
where
B = base areap = perimeter of the baseh =height of the rectangular prismTherefore,
Surface area of the rectangular prism = 2(60) + 34(4)
Surface area of the rectangular prism = 120 + 136
Surface area of the rectangular prism = 256 inches²
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solve the equation (39+5=5a=9)
Answer:
EVALUATE
false
Step-by-step explanation:
Complex number
(39+5=5a=9)
What is the Value of x
Answer:
x = 11
Step-by-step explanation:
A segment parallel to a side of a triangle cuts off proportional segments on the sides.
48/6 = (3x + 7)/5
8 = (3x + 7)/5
3x + 7 = 40
3x = 33
x = 11
Q2. A train travels at a constant speed of 45 m/s. a) Calculate the distance travelled by the train in:
i) 30 s
ii) 2 minutes.
the train travels at 45 meters per each second
this question can be rewritten into the equation d = 45t, where d represents the distance traveled and t represents the time elapsed.
we are given two seperate times, so we can replace the variable t with each respective time. this leaves us with only one missing variable, so we can successfully isolate to find the other.
for i), we substitute t for 30 seconds, shown as follows
d = 45t
d = 45(30)
d = 1350m
for ii), we know that there are 60 seconds in every minute, so in multiplying 60 seconds by two we get the total amount of seconds in two minutes, which is 120.
we can now use 120 to substitute t in our equation
d = 45t
d = 45(120)
d = 5400m
hope this helps!!
Answer:
i) 1350 m
ii) 5400 m
Step-by-step explanation:
To calculate the distance traveled by the train, we can use the formula:
[tex]\large\boxed{\sf Distance=Speed \times Time}[/tex]
[tex]\hrulefill[/tex]
Question (i)Given values:
Speed = 45 m/s (meters per second)Time = 30 secondsSubstitute the given values into the formula for distance:
[tex]\begin{aligned}\sf Distance&= \sf 45\; m/s \times 30\;s\\& = \sf 1350\:m\end{aligned}[/tex]
Therefore, the train travelled a distance of 1350 meters in 30 seconds.
[tex]\hrulefill[/tex]
Question (ii)Given values:
Speed = 45 m/s (meters per second)Time = 2 minutesAs the time is given in a different unit of time than the speed, we must first convert the time into seconds. As 1 minute = 60 seconds, then:
[tex]\sf 2\; minutes = 60 \;s \times 2 = 120 \;s[/tex]
Substitute the given values into the formula for distance:
[tex]\begin{aligned}\sf Distance&= \sf 45\; m/s \times 120\;s\\& = \sf 5400\:m\end{aligned}[/tex]
Therefore, the train travelled a distance of 5400 meters in 2 minutes.
Solve question in image (yr 8 math, 40 pt)
Answer:
y = 3
Step-by-step explanation:
(5y - 3)/4 + 6 = 3y
5y - 3 + 24 = 12y
7y = 21
y = 3
Check.
(5*3 - 3)/4 + 6 = 3*3
(15 - 3)/4 + 6 = 9
12/4 + 6 = 9
3 + 6 = 9
9 = 9
Answer: y = 3
Step-by-step explanation:
Given equation
[tex]\frac{5y~-~3}{4} ~+~6~=~3y[/tex]
Multiply 4 on both sides (to eliminate fraction)
[tex]\frac{5y~-~3}{4} *4~+~6*4~=~3y*4[/tex]
[tex](5y~-~3)~+~24~=~12y[/tex]
Expand parenthesis and combine like terms
[tex]5y~-~3~+~24~=~12y[/tex]
[tex]5y~+~21~=~12y[/tex]
Subtract 5y on both sides
[tex]5y~+~21~-~5y~=~12y~-~5y[/tex]
[tex]21~=~7y[/tex]
Divide 7 on both sides
[tex]21~/~7~=~7y~/~7[/tex]
[tex]\Large\boxed{y=3}[/tex]
Hope this helps!! :)
Please let me know if you have any questions
what is the volume of a triangular pyramid that is 5 feet tall and has a base area of 9 square feet
The volume of the triangular prism as described is; 15 cubic foot.
What is the volume of the triangular pyramid?A triangular pyramid simply refers to any geometric solid with a triangular base, and all three lateral faces are also triangles with a common vertex
It follows from the formula for calculating the volume of a triangular prism that;
Volume = (1/3) × base area × height.
Consequently,
volume of the prism is; = (1/3) ×9 × 5
Volume = 15 cubic foot
Therefore, volume of the triangular prism as described is; 15 cubic foot.
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