In response to the stated question, we can state that here Hence, the linear equation (6 2 • 35) 2 equals 1/4096
What is a linear equation?A linear equation is one that satisfies the algebraic formula y=mx+b. m is the y-intercept, while B is the slope. The foregoing sentence is sometimes referred to as a "linear equation with two variables" because y and x are variables. Bivariate linear equations are two-variable linear equations. Examples of linear equations include 2x - 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, x + y = 2, and 3x - y + z = 3. An equation is said to be linear if its formula is y=mx+b, where m denotes the slope and b the y-intercept. It is referred to as being linear when an equation has the form y=mx+b, where m stands for the slope and b for the y-intercept.
We must do the following operations in the correct order to simplify the formula (62 • 35)2:
To start, we must multiply 2 by 35, which results in the number 70.
The result is -64 when we remove 70 from 6.
The final step is to raise the unfavorable integer -64 to the power of -2.
Hence, we can write:
[tex](6-2 * 35)-2 = (-64)^{-2}[/tex]
To make this statement easier to understand, keep in mind that taking the reciprocal of a number raised to a positive power is the same as raising it to a negative power. With those words:
[tex]a^-n = 1/a^n\\(-64)^-2 = 1/(-64)^2\\1/(-64)^2 = 1/4096[/tex]
Hence, the expression (6 2 • 35) 2 equals 1/4096.
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los ladrillos de una balanza está en equilibrio pesan todos lo mismo en un en un lado de la balanza hay 5 kg y 9 ladrillos en el otro hay 22 kilogramos y 4 ladrillos Cuánto pesa un ladrillo
The brick weighs 3.4 kilograms.
Define the term Quantities?Quantities are values that can be measured or counted. They are typically represented by numerical values and units of measurement.
Let's assume that the weight of each brick is the same. Let's also denote the weight of each brick by "w" (in kilograms).
On one side of the scale, we have 9 bricks and 5 kilograms. So the total weight on this side is:
Total weight = (9 x w) + 5
On the other side of the scale, we have 4 bricks and 22 kilograms. So the total weight on this side is:
Total weight = (4 x w) + 22
Since the bricks on the scale are in balance, the total weight on both sides must be equal. Therefore, we can set the two expressions for total weight equal to each other and solve for w:
(9 x w) + 5 = (4 x w) + 22
Expanding and simplifying the equation, we get:
5 x w = 17
Therefore, the weight of each brick is:
w = 17 / 5
w = 3.4 kilograms
So each brick weighs 3.4 kilograms.
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*PLS HELP ASAP*
what is the median of the graph?
(btw the graph is in height (feet and inches)
Answer:
5'6 and 5'0
Step-by-step explanation:
Put the graph in order of dots
4'11- 1
5'1- 1
5'3- 1
5'6- 1
5'0- 2
5'2- 2
5'5- 2
5'4- 5
The middle values are 5'6 and 5'0, so that should be the answer.
HELP ASAP
i will mark you brainleast (30 points)
graphing quadratic functions in vertex form
*please answer correctly*
5. Vertex: (2, 2)
Dοmain: All real numbers
Axis οf symmetry: x = 2
Increasing οn: (-∞, 2)
Decreasing οn: (2, ∞)
What is quadratic functiοns?A quadratic functiοn is a pοlynοmial functiοn οf degree 2, where the highest pοwer οf the variable is 2. It has a parabοlic graph and is cοmmοnly used tο mοdel real-wοrld phenοmena.
5. Vertex: (2, 2)
Dοmain: All real numbers
Axis οf symmetry: x = 2
Increasing οn: (-∞, 2)
Decreasing οn: (2, ∞)
7. Vertex: (2, 3)
Dοmain: All real numbers
Axis οf symmetry: x = 2
Increasing οn: (-∞, 2)
Decreasing οn: (2, ∞)
Range: y ≥ 3
6.Vertex: (-2, -4)
Vertical shift: -4 units
Hοrizοntal shift: -2 units
Width: Cοmpressed hοrizοntally by a factοr οf 1/3
Reflected: Nο
8. Vertex: (-2, -2)
Vertical shift: -2 units
Hοrizοntal shift: -2 units
Width: Stretched by a factοr οf 3 in the vertical
Reflected: Nο
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The function h is defined by the following rule.
h(x) = 5x - 1
complete the function table
x h(x)
-5
-4
1
2
3
sorry for the bad formatting i couldn't copy and paste the table
We can use the rule for h(x) to calculate the output values of the function for each given input value of x, which allows us to complete the function table mathematically.
What is a function?In mathematics, a function is a rule or mapping that assigns a unique output value for every input value in a specified set
According to question:To complete the function table mathematically, we need to use the given rule for the function h(x) = 5x - 1 and substitute the given values of x to find the corresponding values of h(x).
For example, when x = -5, we can find the corresponding value of h(x) as follows:
h(-5) = 5(-5) - 1
= -26
Similarly, we can substitute x = -4, 1, 2, and 3 into the rule for h(x) to find the corresponding values of h(x) for each input value of x. This gives us the completed function table:
x h(x)
-5 -26
-4 -21
1 4
2 9
3 14
Therefore, we can use the rule for h(x) to calculate the output values of the function for each given input value of x, which allows us to complete the function table mathematically.
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classfify each number below as a rational or irrational number
Answer:
Step-by-step explanation:
-14.76: Rational
-sqrt(64): 64 is a perfect square so it is rational
1.4444444… rational numbers repeat their decimal digits at one point or another, so this is rational
pi is irrational, so 19pi is irrational.
sqrt(2)*sqrt(2) is rational, but not 2sqrt(2). Irrational.
A city is building a new pool. A scale drawing of the pool is shown below.
Scale,
1 in: 3 ft
What is the area, in square feet, of the pool?
4 in.
A.16n
B.24n
C.48n
D.144n
After answering the provided question, we can conclude that As a result, expression the answer is D. 144n.
what is expression ?In mathematics, an expression is a collection of symbols, digits, and companies that portray a statistical correlation or formula. An expression can be a single number, a mutable, or a combination of both of them. Addition, subtraction, proliferation, division, and exponentiation are examples of mathematical operators. Expressions are used extensively in mathematics, including arithmetic, calculus, and geometry. They are used in mathematical formula representation, equation solution, and mathematical relationship simplification.
According to the scale, 1 inch on the drawing equals 3 feet in real life. As a result, the pool's length is 4 inches x 3 feet/inch = 12 feet. Similarly, the pool's width is 4 inches x 3 feet/inch = 12 feet.
As a result, the pool's area equals the length multiplied by the width, which is:
144 square feet = 12 feet x 12 feet.
As a result, the answer is D. 144n.
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y=x^2-8x-8 quadratic function in vertex form
Answer:
[tex]y=(x+4)^2-8[/tex]
Step-by-step explanation:
[tex]y=x^2-8x-8[/tex]
complete the square.
[tex](x+4)^2-8[/tex]
set y equal to the new right side.
[tex]y=(x+4)^2-8[/tex]
Hope this helps!
Brainliest is much appreciated!
Answer:
Answer is Below!Step-by-step explanation:
a = 1
c = -8
b= -8
the formula of vertex form is a(x-h)^2 +k = y
First find H and k using the formula -b/2a = h
h = 4
so, k = -24
y =1(x-4)^2 -24
Let S = {-4, 0, 2, 3}. A new sequence of numbers is formed by repeating the numbers in S, IN ORDER from lowest to highest, until 80 numbers have been listed in the new sequence, i. E. , NEW_SEQUENCE = {-4, 0, 2, 3, -4, 0, 2, 3,. }. What is the sum of the first 31 terms in the new sequence?
The sum of the first 31 terms in the new sequence is 5.
Let S = {-4, 0, 2, 3}
New Sequence = {-4, 0, 2, 3, -4, 0, 2, 3, -4, 0, 2, 3, ...............}
The four terms are repeatedly separated, as we can see above. Below are some of the first four terms = -4 + 0 + 2 + 3 = 1
Now, first four terms sum = 1
Next four terms sum = 1.
So sum of first 28 terms is given as
1 + 1 + 1 + 1 + 1 + 1 + 1 = 7
Now we find sum of first 31 terms = 7 - 4 + 0 + 2 = 5
So, sum of first 31 terms of new sequence {-4, 0, 2, 3, -4, 0, 2, 3, -4, 0, 2, 3, ...............} is 5.
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(NEED HELP ASAP)
What side is opposite from angle B?
What side is adjacent to angle B but is not the hypotenuse?
What side is hypotenuse?
Answer:
Step-by-step explanation:
What side is opposite from angle B? AC
What side is adjacent to angle B but is not the hypotenuse? BC
What side is hypotenuse? AB
The marked price of the mobile set is Rs 2,800 more than the selling price. If the price of the mobile with 13% VAT is Rs 28,476 then find the discount percent given in the mobile.
If the price of the mobile with 13% VAT is Rs 28,476, the discount percent is 10%.
What is the discount?The discount is the difference between the marked price and the selling price.
Discounts are depicted in percentages to show the rates at which the discounts are given.
The selling price of the mobile set with 13% VAT = Rs. 28,476
The selling price of the mobile set without VAT = Rs. 25,200 (Rs. 28,476/1.13)
The difference (discount) between the marked price and the selling price = Rs. 2,800
The marked price = Rs. 28,000 (Rs. 25,200 + Rs. 2,800)
The discount percent given = 10% (Rs. 2,800/Rs. 28,000 x 100)
Thus, we can conclude that the discount percent is 10%.
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Find the area of the trapezoid to the nearest tenth.
PLS HELP ITS URGENT
AND THIS IS GEOMETRY
Area of the given trapezoid is 1.8m²
What is trapezoid?A trapezoid is a polygon having four sides, two of which are parallel and two of which are not. The bases and legs of the trapezoid are known as the parallel and non-parallel sides, respectively. The height or altitude of the trapezoid is defined as the distance between the bases.
The formula, which may be used to determine a trapezoid's area,
[tex]A= \frac{a+b}{2}h[/tex]
where, a and b are the lengths of the two bases and h is the height between two bases.
Given in the trapezoid figure, a= 2, b= 0.9, h is the base upper triangle.
We use the following trigonometric relationship to find the base of the upper triangle,
Apply sine rule in upper triangle with connecting line h.
Sin 45° = [tex]\frac{h}{1.8}[/tex]
h = 1.8 × Sin 45°
h = 1.8 × 0.707
h = 1.273m
Then, the area of trapezoid:
[tex]A= \frac{a+b}{2}h= \frac{2+0.9}{2}*h[/tex]
[tex]A= \frac{2.9}{2}*1.273[/tex]
A = 1.845m²
Therefore, the area of the trapezoid to the nearest tenth is 1.8m²
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A random sample of 10 venture-capital investments in the fiber optics business sector yielded the following data, in millions of dollars. Determine a 95% confidence interval for the mean amount, mu, of all venture-capital investments in the fiber optics business sector. Assume that the population standard deviation is $2. 84 million. (Note: The sum of the data is $62. 32 million. )
The 95% confidence interval for tthe population mean, μ of all venture-capital investments in the fiber optics business sector is equals to the 4.472 ≤ μ ≤ 7.990 that is ( 4.472, 7.990).
We have a random sample of venture capital investments in the fiber optics business sector.
Sample size, n = 10
Standard deviations, σ = $2.84 million
Sum of data, ∑xᵢ = $62.32 million
Confidence interval, CI = 95% = 0.95
We have to determine the 95% confidence interval for the mean amount.
Sample mean is defined as the sum of observations divided by number of observations. Mathematically, X-bar
= ∑xᵢ /n
= 62.32/10 = 6.232
Now, using the Z distribution table, the critical value at 0.05 significance level for two tailed test is = Z₀.₀₅/₂ = Z₀.₀₂₅
= 1.96
So, 95% confidence interval for the population mean is written as
CI₀.₉₅ = X-bar - Z(σ/√n ) ≤ μ ≤ X-bar + Z(σ/√n)
= 6.232 - 1.96(2.84/√10) ≤ μ ≤ 6.232 +
1.96(2.84/√10)
= 6.232 - 1.760 ≤ μ ≤ 6.232 + 1.760
= 4.472 ≤ μ ≤ 7.990
Hence, required interval is ( 4.472, 7.990).
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7.1 Calculate: -24÷-8-13 (1)
Answer:
-10
Step-by-step explanation:
BODMAS
Brackets
Of
Division
Multiplication
Addition
Subtraction
●When simplifying an equation follow the above order.
•Since division comes before subtraction, first divide -24 by -8 to get 3
•Then subtract 13 from 3 to give you -10.
Rosa is using a balance scale. She has a set of weights which consists of two one-gram, six two-gram, four eight-gram, and two thirty-two gram pieces. What could she use to balance a mass of 45 grams?
The combination of weights listed above would balance a mass of 45 grams on the balance scale.
How exactly does a balancing scale operate?A instrument used to determine an object's mass is a balancing scale. It is made out of a beam suspended from a fixed point, with two pans or trays hanging from either end. The beam is balanced when the mass of the objects on one tray equals the mass of the objects on the other tray. The principle of moments, according to which, when the beam is in equilibrium, the moment of force on one side of the balance is equal to the moment of force on the other, governs how a balancing scale functions.
Given that, Rosa can balance a mass of 45 grams using the given combinations.
Thus, total weight on the two sides are:
Left side: 32g + 6g + 6g + 1g = 45g
Right side: 8g + 8g + 2g + 2g = 20g
Hence, the combination of weights listed above would balance a mass of 45 grams on the balance scale.
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Glenn has 2/5 of a granola bar. If he eats 7/8 of it, how much of the granola bar is left.
Glenn has 1/20 of the granola bar left.
How to find?
If Glenn has 2/5 of a granola bar and eats 7/8 of it, we need to find out how much is left.
First, we need to find out how much Glenn ate. To do this, we can multiply the fraction of the granola bar that Glenn had (2/5) by the fraction that he ate (7/8):
2/5 × 7/8 = (27)/(58) = 14/40
Simplifying this fraction, we get:
14/40 = 7/20
So, Glenn ate 7/20 of the granola bar.
To find out how much is left, we can subtract the fraction that he ate from the fraction that he had:
2/5 - 7/20
To subtract these fractions, we need to find a common denominator. The least common multiple of 5 and 20 is 20, so we can convert both fractions to have a denominator of 20:
2/5 = 8/20
7/20 = 7/20
Now we can subtract the fractions:
8/20 - 7/20 = 1/20
So, Glenn has 1/20 of the granola bar left.
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After Angela drank 390 millilitres of soup from a can of the soup was left in the can. How much soup was in the can at first?
The volume of soup in the can at first is 546 millilitres.
How to find the amount of soup in the can?Angela drank 390 millilitres of soup from a can of the soup. 2 / 7 of the soup was left in the can after drinking the soup.
Therefore, the amount of soup in the can at first can be calculated as follows:
let
x = amount of soup initially in the can
Therefore, using equation let's find the volume of soup initially in the can.
2 / 7 x + 390 = x
390 = x - 2 / 7 x
390 = 7x - 2x / 7
390 = 5x / 7
cross multiply
5x = 390 × 7
5x = 2730
divide both sides by 5
x = 2730 / 5
x = 546
Therefore,
volume of soup in the can = 546 millilitres
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Rewrite the following fraction as a decimal.
1/12
Answer pls
Answer:0.833333
Step-by-step explanation:
Answer:
0.08333
Step-by-step explanation:
pls mrk me brainliest
Team batting averages for Major League Baseball in a certain year are represented below. Find the variance and standard deviation for each league. Compare the results. Use a graphing calculator. Round the answers to five decimal places for variance and four decimal places for standard deviation. The National League variance is and the standard deviation is
The National League variance is 0.00020 and the standard deviation is 0.0141 while the American League variance is 0.000191 and the standard deviation is 0.0138.
According to question, the team batting averages for Major League Baseball in a certain year are represented below. We have to find the variance and standard deviation for each league. Given below is the table of team batting averages in National League and American League.
National League American League
.240 .237
.242 .244
.240 .251
.247 .233
.256 .243
.249 .248
.256 .238
.240 .241
.243 .250
.237 .238
We know that,
variance = (1/N)* Σ(xi - µ)²
Standard deviation = √variance
National League:
The mean of National League, µ = (0.240 + 0.242 + 0.240 + 0.247 + 0.256 + 0.249 + 0.256 + 0.240 + 0.243 + 0.237)/10 = 2.443/10 = 0.2443.
Substitute the values in the formula, variance = (1/10)* Σ(xi - µ)² = (1/10)* [ (0.240 - 0.2443)² + (0.242 - 0.2443)² + (0.240 - 0.2443)² + (0.247 - 0.2443)² + (0.256 - 0.2443)² + (0.249 - 0.2443)² + (0.256 - 0.2443)² + (0.240 - 0.2443)² + (0.243 - 0.2443)² + (0.237 - 0.2443)² ]= 0.00019749
Standard deviation = √variance = √0.00019749 = 0.01405
The National League variance is 0.00020 and the standard deviation is 0.0141
American League:
The mean of American League, µ = (0.237 + 0.244 + 0.251 + 0.233 + 0.243 + 0.248 + 0.238 + 0.241 + 0.250 + 0.238)/10 = 2.423/10 = 0.2423
Substitute the values in the formula, variance = (1/10)* Σ(xi - µ)² = (1/10)* [ (0.237 - 0.2423)² + (0.244 - 0.2423)² + (0.251 - 0.2423)² + (0.233 - 0.2423)² + (0.243 - 0.2423)² + (0.248 - 0.2423)² + (0.238 - 0.2423)² + (0.241 - 0.2423)² + (0.250 - 0.2423)² + (0.238 - 0.2423)² ]= 0.00019119
Standard deviation = √variance = √0.00019119 = 0.01383
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You pay $3.00 to play. The dealer deals you one card. If it is a spade, you get $10. If it is anything else,
you lose your money. Is this game fair?
The game is fair in the sense that the expected value is not negative.
What is expected value?The expected value serves as a gauge for a random variable's typical value. It is determined by multiplying each of the variables' potential outcomes by its corresponding probability, then adding the resulting products. In order to comprehend the typical outcome of a random process and determine if a given course of action is likely to be lucrative or not, the expected value is a valuable tool in decision-making.
The probability of getting a spade is 13/52 or 1/4.
The probability of getting anything else is 3/4.
he expected value of playing the game can be calculated as:
Expected value = (probability of winning x amount won) - (probability of losing x amount lost)
Expected value = (1/4 x $10) - (3/4 x $3)
Expected value = $2.50 - $2.25
Expected value = $0.25
Since the expected value is positive, this means that on average, you can expect to win $0.25 for every time you play the game.
Hence, game is fair in the sense that the expected value is not negative.
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Answer this ASAP will give the brainliest answer
Given that y = 11 cm and θ = 38°, work out x rounded to 1 DP.
Answer:
6.8 I think
Step-by-step explanation:
Find the value of x, y, and z. (Round to the 3rd decimal place if possible)
Addressing issue hand, we state that Therefore, the linear equation solution to the system of equations is: x = 0.5, y = 0.1667, z = -0.5 and x = 0.500, y = 0.167, z = -0.500
What is a linear equation?In algebra, a linear equation refers to one with its form y=mx+b. B is the gradient, and m is the esta. The preceding clause is commonly referred to as a "linear function with two variables" so even though y and x are variables. Bivariate linear equations are linear equations with two variables. There are several linear equations: 2x - 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, x + y = 2, and 3x - y + z = 3. When an equation seems to have the structure y=mx+b, where m is the slope and b is the y-intercept, it is said to be linear. When a measurement seems to have the formula y=mx+b, both with m identifying its slope and b denoting the y-intercept, it is said to be linear.
values of x, y, and z, we can use the system of equations
3x - 2y + z = 1
2x + y - z = 0
x + 2y + 3z = -1
We can use Gaussian elimination or any other suitable method to solve the system. Here's one way to do it:
3x - 2y + z = 1 (eq. 1)
2x + y - z = 0 (eq. 2)
x + 2y + 3z = -1 (eq. 3)
3x - 2y + z = 1 (eq. 1)
0.6667x + 1.3333y - 1.3333z = -0.6667 (eq. 2')
-0.3333y + 2.3333z = -1.3333 (eq. 3')
3.3333x - 0.3333z = 0.1667 (eq. 1')
0.6667x + 1.3333y - 1.3333z = -0.6667 (eq. 2')
2.1667z = -1.0833 (eq. 3')
z = -0.5
y = 0.1667
x = 0.5
Therefore, the solution to the system of equations is:
x = 0.5, y = 0.1667, z = -0.5
x = 0.500, y = 0.167, z = -0.500
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Please answer this its for a test
1) The surface area of the figure is of 72 square units.
2) Removing the top two cubes, the surface area of the figure would be of 60 square units.
How to obtain the surface area of a cube?The surface area of a cube of side length a is given by the equation presented as follows:
S = 6a².
For this problem, we have that the parameters are given as follows:
12 cubes.Each cube has a side length of one unit.Hence the surface area of the figure is given as follows:
S = 12 x 6 x 1
S = 72 square units.
Removing the top two cubes, the surface area of the figure would be given as follows:
S = (12 - 2) x 6 x 1
S = 60 square units.
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Without graphing, tell whether the slope of a line that models the linear relationship is positive, negative, zero, or undefined. Then find the slope.
A laptop battery has 85% power after 1 hour of use and 40% after after 4 hours of use
Answer:
its a negative slope because the battery is going down, not staying the same, or going up
Step-by-step explanation:
Greatest common factor of 14b with a exponent of 3 and 5b with a exponent of 2
The only common factor is [tex]b^{2}[/tex] so the GCF is [tex]14b^{3}[/tex] and [tex]5b^{2}[/tex] is [tex]b^{2}[/tex]
Define common factor.The term "common" means "same for both." The two numbers' common factor is one that applies to both numbers.
The common factor between [tex]6[/tex] and [tex]10[/tex] is [tex]2[/tex], for instance. Although it is not the sole quality shared by each number, it is a trait that they both have in common.
To find the GCF of [tex]14b^{3}[/tex] and [tex]5b^{2}[/tex] we need to find the largest factor for both
[tex]14b^{3}[/tex] = 2*7*[tex]b^{2}[/tex]*[tex]b[/tex]
[tex]5b^{2}[/tex] = [tex]5*b^{2}[/tex]
Therefore the only common factor is [tex]b^{2}[/tex] so the GCF is [tex]14b^{3}[/tex] and [tex]5b^{2}[/tex] is [tex]b^{2}[/tex]
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The lenght of a rectangle is twice its breath. if the perimeter of a rectangle is 60cm, find the dimension of the rectangle.
Answer:
L = 20 , B = 10
Step-by-step explanation:
L = 2B
we know perimeter of rectangle = 2( L + B )
By substitution , 2( 2B+ B) =60
4B + 2B = 60
6B = 60
B= 10
L = 2 * B = 2 * 10 = 20
22. At a wedding, guests are given cone-
shaped cups filled with flower petals. The cups
have a radius of 5 centimeters and a height of
10 centimeters. If there are 150 cups, what is
the total volume of petals that all the cones will
hold? Round to the nearest whole number.
Answer:
The volume of one cone-shaped cup can be calculated using the formula V = (1/3)πr^2h, where r is the radius of the cone and h is the height. Substituting the given values, we get:
V = (1/3)π(5 cm)^2(10 cm)
V ≈ 261.8 cm^3
Therefore, one cup can hold approximately 261.8 cubic centimeters of flower petals.
To find the total volume of petals that all 150 cups will hold, we can multiply the volume of one cup by the total number of cups:
Total volume = 150 cups × 261.8 cm^3/cup
Total volume ≈ 39,270 cm^3
Rounding to the nearest whole number, we get that the total volume of petals that all the cones will hold is approximately 39,270 cubic centimeters.
Answer:
I forgot how to do this sorry
Dave makes $2,300 each month and pays $840 for rent. To the nearest tenth of a percent, what percent of Dave’s earnings are spent on rent?
To calculate the proportion of Dave's wages spent on rent, divide the amount of rent by his monthly earnings and multiply by 100 to obtain the percentage Rent as a percentage of earnings = (Rent / Earnings) x 100%.
When we substitute the provided values, we get: Rent as a percentage of wages = (840 / 2300) x 100% = 36.5% As a result, to the closest hundredth of a percent, Dave spends about 36.5% of his salary on rent. This indicates that rent accounts for around 36.5% of Dave's monthly income. This proportion might provide us with information about Dave's financial status. Financial experts often advise consumers to spend no more than 30% of their income on housing expenditures, including rent and utilities. In Dave's situation, his rent is somewhat higher than the recommended amount. This might signal that he is struggling to make ends meet or that he should look into more cheap housing possibilities. If David can easily pay his existing rent, this percentage may not be a reason for concern.
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Time length (in months) of uninterrupted functioning of soil moisture measuring
sensors until failure follows a distribution, 1/7e−x/7. The sensors are inspected at
every 2 months.
(a) What is the probability that the sensors need to be replaced at the first inspection?
(b) What is the probability of proper functioning of the sensors till the second scheduled
inspection? (Ans 0.564)
The probability of proper functioning of the sensors till the second scheduled inspection is `0.564`.
Given that the time length (in months) of uninterrupted functioning of soil moisture measuring sensors until failure follows a distribution, `1/7e−x/7`.The sensors are inspected at every 2 months.(a) Probability that the sensors need to be replaced at the first inspection= Probability that the sensors fail at the first inspection= Probability that the sensors fail before first inspection= Probability that the sensor functioned well up to the first inspection= `F(2) = 1-e^(-2/7)` (Using the given exponential distribution)Therefore, the probability that the sensors need to be replaced at the first inspection is `0.226`. (Approximately, 0.23)(b) The probability of proper functioning of the sensors till the second scheduled inspection is the probability that the sensors do not fail in the first two months. That is, `P(t≥2)` = `1-P(t<2)`= `1-F(2)` = `1-(1-e^(-2/7))` = `0.564`.Therefore, the probability of proper functioning of the sensors till the second scheduled inspection is `0.564`.
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Aysha and ahmed are going to dubai shopping festival next week. The table
shows the amount that each person spent on snacks ,games and sovenirs the last
time they went to shopping festival. Aysha wants to spend money using the same ratios as on her last trip to shopping
snacks games Souvenirs
Aysha Dh. 20 Dh25 Dh10
Ahmed Dh40 Dh20 Dh15
festival. If she spends Dh 100 this time on games how much she will spend on
souvenirs
As per the unitary method, Aysha will spend Dh45.45 on souvenirs if she spends Dh100 on games, using the same ratios as on her last trip to the shopping festival.
Now, let's use the unitary method to solve the problem at hand. We know that Aysha wants to spend money using the same ratios as on her last trip to the shopping festival. So, let's find out the ratio of the amount she spent on games to the total amount she spent on all three items (snacks, games, and souvenirs) on her last trip:
Amount spent on games = Dh25
Total amount spent on all three items = Dh20 + Dh25 + Dh10 = Dh55
So, the ratio of the amount spent on games to the total amount spent on all three items is:
Dh25/Dh55
Now, we know that Aysha wants to spend Dh100 on games this time. Let's use the unitary method to find out how much she will spend on souvenirs, given the ratio we just found.
If Dh25 is spent on games, then the total amount spent on all three items will be:
(Dh25/Dh55) * Total amount spent
And we know that the total amount spent is Dh100 (the amount Aysha wants to spend on games). So, substituting this value, we get:
(Dh25/Dh55) x Dh100
Simplifying this expression, we get:
Dh45.45
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What should your units on your base area calculations be, and why? How is this different from the units on your volume calculations
The units for base area calculations are squared units and the units for volume calculations are cubed units. This is because the area and volume calculations require different equations and different units of measurement.
The units on your base area calculations should be squared units, such as square meters, square centimeters, square inches, or square feet. This is because the area of a two dimensional shape is the amount of space occupied by the shape and is calculated by taking the length of the base and multiplying it by the width of the base. For example, if a rectangle has a length of 5 meters and a width of 3 meters, the area of the rectangle would be 5 x 3 = 15 square meters.
The units on your volume calculations should be cubed units, such as cubic meters, cubic centimeters, cubic inches, or cubic feet. This is because the volume of a three dimensional shape is the amount of space occupied by the shape and is calculated by taking the area of the base and multiplying it by the height of the shape. For example, if a cube has an area of 15 square meters and a height of 4 meters, the volume of the cube would be 15 x 4 = 60 cubic meters.
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