The approximate probability that the total aggregate cost of fighting
The approximate probability that less than 1801800 citizens will get vaccinated can be calculated using the de Moivre-Laplace theorem. This theorem states that the probability distribution of the sum of a large number of independent random variables approaches the normal distribution as the number of variables increases. In this case, the random variable is whether or not a citizen gets vaccinated, and the sum is the total number of citizens who get vaccinated.
To calculate the approximate probability, we need to find the mean and standard deviation of the distribution. The mean is equal to the number of citizens times the probability of getting vaccinated, which is 9.10^6 * (1/5) = 1820000. The standard deviation is equal to the square root of the number of citizens times the probability of getting vaccinated times the probability of not getting vaccinated, which is sqrt(9.10^6 * (1/5) * (4/5)) = 1200.
Using the de Moivre-Laplace theorem, we can approximate the probability that less than 1801800 citizens will get vaccinated as the probability that a normal random variable with mean 1820000 and standard deviation 1200 is less than 1801800. This can be calculated using the standard normal distribution:
P(Z < (1801800 - 1820000)/1200) = P(Z < -1.52) = 0.064
Therefore, the approximate probability that less than 1801800 citizens will get vaccinated is 0.064.
The approximate probability that the total aggregate cost of fighting the virus-inflicted illness for all citizens of the country will surpass 7207200000 dollars can be calculated using the Central Limit Theorem (CLT). The CLT states that the sum of a large number of independent random variables approaches the normal distribution as the number of variables increases. In this case, the random variable is the cost of treating a single non-vaccinated individual, and the sum is the total cost of treating all non-vaccinated individuals.
To calculate the approximate probability, we need to find the mean and standard deviation of the distribution. The mean is equal to the number of citizens times the probability of not getting vaccinated times the expected value of the cost of treating a single non-vaccinated individual, which is 9.10^6 * (4/5) * (2000/2) = 7207200000. The standard deviation is equal to the square root of the number of citizens times the probability of not getting vaccinated times the variance of the cost of treating a single non-vaccinated individual, which is sqrt(9.10^6 * (4/5) * (2000^2/12)) = 1633333.33.
Using the CLT, we can approximate the probability that the total aggregate cost of fighting the virus-inflicted illness for all citizens of the country will surpass 7207200000 dollars as the probability that a normal random variable with mean 7207200000 and standard deviation 1633333.33 is greater than 7207200000. This can be calculated using the standard normal distribution:
P(Z > (7207200000 - 7207200000)/1633333.33) = P(Z > 0) = 0.5
Therefore, the approximate probability that the total aggregate cost of fighting the virus-inflicted illness for all citizens of the country will surpass 7207200000 dollars is 0.5.
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What are the solutions of the equation 0=x^2-9x+8
The solutions of the equation 0=x^2-9x+8 are x = 8 and x = 1
How to determine the solutions of the equationFrom the question, we have the following parameters that can be used in our computation:
0=x^2-9x+8
Rewrite as
x^2 - 9x + 8 = 0
Expand the equation
So, we have the following representation
x^2 - 8x - x + 8 = 0
When the equation is factorized, we have
(x - 8)(x - 1) = 0
This gives
x - 8 = 0 and x - 1 = 0
Evaluate
x = 8 and x = 1
Hence, the solutions are x = 8 and x = 1
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What is the largest possible value x could take given that it must be an integer? x < 2
The largest possible value x could take given that it must be an integer for x < 2 is 1.
Difference between an inequality and an equation?The key distinction between an inequality and an equation is that an inequality describes a connection of inequality between two expressions, whereas an equation expresses equality between two expressions. In other words, an inequality shows that one expression is more or less than the other expression, but an equation shows that two expressions have the same value.
The highest number x might have is 1 if x must be an integer and x 2. This is due to the fact that any number higher than one would break the inequality x 2, and any number between one and two that is not an integer would also violate the stipulation that x must be an integer.
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Use the Intermediate Value Theorem to show thatf has a zero
between a and b .
f(x)=2x 3 +6x 2
-3 a -2
There is a zero for f(x) between a and b.
How to calculateUsing the Intermediate Value Theorem, we can show that the function f(x)=2x3+6x2-3a-2 has a zero between a and b.
The Intermediate Value Theorem states that if a continuous function f(x) takes on different values at two points a and b, then there must exist at least one value c in between a and b such that f(c) = 0. Since f(x) is a continuous function, it takes on different values at a and b.
Thus, by the Intermediate Value Theorem, there must exist at least one value c in between a and b such that f(c) = 0, meaning that there is a zero for f(x) between a and b.
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Identify the following models as ARMA(p, q) models (watch out for parameter redundancy), and determine whether they are causal and/or invertible:
(a) xt =. 80xt-1 −. 15xt−2 + wt −. 30wt−1.
(b) xt = xt−1 −. 50xt−2 + wt − wt−1.
The first model (a) is an ARMA(1,2) model and is both causal and invertible, while the second model (b) is an ARMA(2,1) model and is also both causal and invertible.
What are Autoregressive (AR) models?Autoregressive (AR) models are a type of statistical model that uses the past values of a variable to predict its future values. The main assumption of AR models is that the future values of the variable are correlated with its past values. They are used to analyze time series data and are commonly used in forecasting, price and demand prediction, and other time-dependent processes.
The first model (a) is an ARMA(1,2) model, which is a combination of an autoregressive (AR) and a moving average (MA) model. This model is both causal and invertible. Causal models are models that have a lag of only one period, while invertible models are those that have a lag of two or more periods. The second model (b) is an ARMA(2,1) model, which is a combination of an autoregressive (AR) and a moving average (MA) model. This model is both causal and invertible. Since the lags for both models are greater than one, both models are invertible.
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-15y-4
45
27
38%
十
15
24
Find X and
Find Y
Answer:
42
Step-by-step explanation:
you asding it all up
Find the total cost of tiling a triangular area having a base
length of 3 meters and a height of 9 meters if it costs $9.71 to
tile one square meter. Round to the nearest cent
The total cost of tiling a triangular area having a baselength of 3 meters and a height of 9 meters is $131.29.
Given base length of triangular area is 3 metersHeight of triangular area is 9 metersCost of tiling one square meter = $9.71 We need to find the total cost of tiling the triangular area. The area of a triangle is given by the formula as shown below,
Area of a triangle = 1/2 × base length × height, Therefore, Area of the given triangle = 1/2 × 3 meters × 9 meters= 13.5 square meters. Now, the total cost of tiling the triangular area can be found by multiplying the area by the cost per square meter. Total cost of tiling triangular area = 13.5 square meters × $9.71/square meter = $131.29 (approx)
Hence, the total cost of tiling a triangular area having a baselength of 3 meters and a height of 9 meters is $131.29.
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theres a picture of what I need help with thank you so much! Have an amazing day and will also mark brainliest <3
Answer:
5x4
Step-by-step explanation:
The dimensions of the rectangle are 20x16
The reducing factor is 0.25.
Multiple 20 * 0.25= 5
Multiple 16 * 0.25= 4
Therefore the new dimensions are 5x4.
1 Select the correct answer. What is the simplified form of this expression? (-3x² + 4x) + (2x²-x-11)
a. -x2 + 5x − 11
b. -x² + 3x - 11
c. -x² + 3x + 1
d. -x2 + 5x + 11
Blynomials: Mastery Test
The value of the given expression is - x² + 3x - 11 and option b is the correct answer.
What is binomial expression?Binomial is the name for an algebraic expression with only two terms. It is a polynomial with two terms. It is sometimes referred to as the sum or difference of two or more monomials. It is a polynomial's most basic form. Therefore, A binomial is a two-term algebraic statement that includes a constant, exponents, a variable, and a coefficient.
The given expression is:
(-3x² + 4x) + (2x²-x-11)
-3x² + 4x + 2x² - x - 11
Subtract the like terms:
- x² + 3x - 11
Hence, the value of the given expression is - x² + 3x - 11 and option b is the correct answer.
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O is the center of the regular octagon below. Find its perimeter. Round to the nearest tenth if necessary.
The perimeter of the regular octagon with an apothem of 5 units will be 33.14 units.
What is the perimeter of the regular polygon?All the sides of the regular polygon are congruent to each other. The perimeter of the regular polygon of n sides will be the product of the number of the side and the side length of the regular polygon.
P = (Side length) x n
The Apothem of a regular octagon is 5 units. Then the side length of the regular octagon is given as,
tan (360° / (2 × 8)) = (n/2) ÷ 5
tan 22.5° = n / 10
n = 4.142
Then the perimeter is given as,
P = 8 x 4.142
P = 33.14 units
The perimeter of the regular octagon with an apothem of 5 units will be 33.14 units.
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Which system of inequalities is represented by the graph?
The following system of inequalities is represented by the graph
x+y>3
-x+y< -4
What is inequality?
An inequality in mathematics depicts the connection between two values in an algebraic statement that are not equal. One of the two variables on the two sides of the inequality may be greater than, greater than or equal to, less than, or less than or equal to another value, according to inequality signals.
Consider the inequalities:
x+y>3-------(1)
-x+y< -4------(2)
Find x and y intercepts of both by considering them as equations by using equal sign in the place of inequality sign
x+y=3-------(3)
-x+y= -4------(4)
Find x and intercepts of these 2 equations:
we get x intercept when y=0 ( substitute y=0 into the respective equations and find x)
we get y intercept when x=0 ( substitute x=0 into the respective equations and find y)
x intercept of (3) is (3,0)
y intercept of (3) is (0,3)
x intercept of (3) is (4,0)
y intercept of (3) is (0,-4)
plot these points on a the plane and join them with lines
use dotted line and shade under the lines because of less than symbol
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Choose the correct answer from the drop-down menu. Use properties of operations to determine whether or not 3(x+2)+8 and 3x+14 are equivalent. Select... We can not determine whether the expressions are equivalent or not. The expressions are equivalent. The expressions are not equivalent.
"The expressions are equivalent." We can use the distributive property to determine whether or not the expressions are equivalent.
First, let's apply the distributive property to the first expression:
3(x+2) + 8 = 3x + 6 + 8
Next, let's simplify the expression by combining like terms:
3x + 6 + 8 = 3x + 14
Now, we can see that the two expressions are equivalent because they both simplify to the same expression, 3x + 14. Therefore, we can conclude that the expressions are equivalent.
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We measure three dimensional space with volume. Volume is how much three dimensional space something takes up. We usually measure it in cubic meters or cubic feet. 90 ft
We usually measure it in cubic meters or cubic feet. 90 ft³ is equal to 2,544.48 cm³.
What is length?Length is a term used to describe the magnitude of a line, distance, or size. It usually refers to the measurement of something from end to end, such as the length of a river, the height of a building, or the size of a piece of fabric. Length is typically measured in units such as feet, meters, or even inches. It is an important concept in science, engineering, and mathematics. Length helps us to understand and quantify the size of objects and the space they occupy.
We can find the volume of any three dimensional object by using the formula V = l x w x h, where V is the volume, l is the length of the object, w is the width, and h is the height. This formula is applicable to all three dimensional shapes, including cubes, rectangles, prisms, cylinders, and so on.
To find the volume of a cylinder, we use the formula V = π x r² x h. Here, V is the volume, π is the constant pi, r is the radius of the cylinder, and h is the height. To find the volume of a sphere, we use the formula V = 4/3 x π x r³. Here, V is the volume, π is the constant pi, and r is the radius of the sphere.
We can also use volume to measure liquids or gases. We measure liquids in liters or milliliters, and gases in cubic meters or cubic feet. For example, 1 liter of water is the same as 1,000 milliliters of water.
Volume is an important concept in mathematics and is used to measure many different things. It is used to measure the size of objects, the volume of liquids and gases, and the amount of three dimensional space something occupies. Understanding volume and how to calculate it is an essential skill for anyone studying mathematics.
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The height of a plant over time is shown in the table below. Using a logarithmic model, what is the best estimate for the age of the plant when it is 19 inches tall?
Moreover, we should evaluate the model's goodness of fit and take into expressions account additional elements that can influence plant development.
what is expression ?Mathematical operations include doubling, dividing, adding, and subtracting. A phrase is constructed as follows: Expression, monetary value, and mathematical operation Numbers, parameters, and functions make up a mathematical expression. It is possible to use words and terms in contrast. Every mathematical statement including variables, numbers, and a mathematical operation between them is called an expression, sometimes referred to as an algebraic expression. For example, the expression 4m + 5 is composed of the expressions 4m and 5, as well as the variable m from the above equation, which are all separated by the mathematical symbol +.
In the formula, h is the height, t is the time, and a and b are the parameters that need to be approximated.
The information in the table may be used to estimate the values of a and b. The equation is first transformed to yield:
[tex]log(b*t) = log(h/a)[/tex]
[tex]19 = 19.24 * log(53.89*t)[/tex]
t = 0.186 months, or approximately 5.58 days, or log(53.89*t) = 1 53.89*t = 10
Hence, 5.58 days is the best guess for the age of the plant at 19 inches tall. Seeing that this is a very little period of time, it is probable that the model will not be correct for values of t this low. Moreover, we should evaluate the model's goodness of fit and take into account additional elements that can influence plant development.
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Please I news help please send me the full explanation please
Please help me answer this
Answer: I think B & C not super sure though
The volume of a cylinder is 12,566.4 cm cubed. The height of the cylinder is 8 cm.
a) Find the radius of the cylinder to the nearest tenth of a centimeter.
b) Find the area of the base of the cylinder to the nearest tenth of a centimeter.
c) Find the lateral area to the nearest tenth of a centimeter.
d) Find the surface area of the cylinder.
As a result of the cylinder's volume being 12,566.4 centimetres³ and its height being 8 cm, the surface area of the cylinder is approximately 942.5 cm².
what is volume ?
Volume in mathematics refers to how much room a three-dimensional object takes up. It is a way to quantify how much enclosed room there is overall in a solid figure. Depending on the shape of the item, a number of formulas can be used to calculate its volume. A rectangular prism's volume, for instance, can be calculated by multiplying its length, breadth, and height, whereas a cylinder's volume can be calculated by dividing its base area by its height. The system being used will determine the unit of measurement for volume, but typical units include cubic metres (m³) and cubic centimetres (cm³).
given
a) V = πr²h, where V is the volume, r is the radius, and h is the height, is the expression for a cylinder's volume. By rearranging the calculation, we can find r:
V/(h) = √12,566.4/(*8)) Equals r ≈ 10 centimetres (rounded to the closest tenth of a cm) (rounded to the nearest tenth of a cm)
Consequently, the cylinder's radius is roughly 10 centimetres.
b) The equation A = r² determines the area of a cylinder's base. Using the r number we just discovered, we have:
A = π(10)² ≈ 314.2 cm² (rounded to the closest tenth of a cm) (rounded to the nearest tenth of a cm)
Consequently, the cylinder's base has a surface area of about 314.2 cm².
c) The equation L = 2πrh, where r is the radius and h is the height, determines the lateral area of a cylinder. With the numbers from the problem substituted, we obtain:
L = 2π(10)(8) ≈ 502.7 cm² (rounded to the closest tenth of a cm) (rounded to the nearest tenth of a cm)
Consequently, the cylinder's side area is roughly 502.7 cm².
d) The equation S = 2πr² + 2πrh gives the surface area of a cylindrical. Using the r and h numbers we discovered earlier, we have:
S = 2π(10)² + 2π(10)(8) ≈ 942.5 cm² (rounded to the nearest tenth of a centimetre) (rounded to the nearest tenth of a cm)
As a result of the cylinder's volume being 12,566.4 centimetres³ and its height being 8 cm, the surface area of the cylinder is approximately 942.5 cm².
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Find the volume of the figure below in terms of pi.
A. 36pi
B: 288pi
C: 144pi
D: 864pi
Work Shown:
[tex]V = \text{Volume of a sphere}\\\\V = \frac{4}{3}\pi*r^3\\\\V = \frac{4}{3}\pi*6^3\\\\V = \frac{4}{3}\pi*216\\\\V = \frac{4}{3}*216\pi\\\\V = 288\pi\\\\[/tex]
Question 4 Solve the inequality and write your answer in interval notation 16+12x<19x+12
The solution to the inequality 16 + 12x < 19x + 12 is all the values of x between the interval notation (4/7, ∞).
To solve the inequality 16 + 12x < 19x + 12, we need to isolate the variable x on one side of the inequality. We can do this by subtracting 12x from both sides and subtracting 12 from both sides:
16 + 12x - 12x - 12 < 19x + 12 - 12x - 12
4 < 7x
Solving for x, we can divide both sides by 7:
4/7 < x or x > 4/7
In interval notation, this would be (4/7, ∞). Therefore, the solution to the inequality is (4/7, ∞) in interval notation.
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Talia deposits $350 in her savings account. The account earns 2.5% simple interest per year. What is the balance in the account after 4 years?
Answer:385
Formulate and substitute:F=350+350rt
Calculate the product or quotient:350x1+0.1
Calculate the sum or difference:350x1.1
Calculate the product or quotient:385
what is the quadratic formula multiplied by pie divided by X?
The quadratic formula multiplied by π divided by x is: π(-b ± √(b² - 4ac)) / (2ax).
What is the Quadratic formula?
The quadratic formula is used to solve quadratic equations, and is given by: x = (-b ± √(b² - 4ac)) / 2a.
Pi otherwise denoted by the symbol π in real terms is a mathematical constant that represents the ratio of the circumference of a circle to its diameter. It is approximately equal to 3.14159, although its decimal representation goes on infinitely without repeating.
Since the rational objective of every mathematical expression or problem is to simplify, we will leave Pi in it's symbolic form - π.
Thus, multiplying quadratic formula by π and dividing by x, we get:
π(-b ± √(b² - 4ac)) / (2ax)
Therefore, the quadratic formula multiplied by π divided by x is:
π(-b ± √(b² - 4ac)) / (2ax).
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Answer: π(-b ± √(b² - 4ac)) / (2ax)
Step-by-step explanation:
take the standard quadratic formula and plug in pi and x and you get you answer hope this helps
Determine the x-intercepts of each of the following functions. 2. y=x^2+5x−24 3. y=x^2−11x+10
The x-intercepts of y=x2+5x−24 can be determined by solving the equation 0=x2+5x−24. Using the quadratic formula, we can find that x = 6 and x = -4 are the two x-intercepts.
The x-intercepts of y=x2−11x+10 can be determined by solving the equation 0=x2−11x+10. Using the quadratic formula, we can find that x = 5 and x = -2 are the two x-intercepts.
To determine the x-intercepts of the given functions, we need to find the values of x that make y equal to 0. We can do this by factoring the equations and setting each factor equal to 0.
2. y = x^2 + 5x - 24
0 = x^2 + 5x - 24
0 = (x + 8)(x - 3)
x + 8 = 0 or x - 3 = 0
x = -8 or x = 3
The x-intercepts are (-8, 0) and (3, 0).
3. y = x^2 - 11x + 10
0 = x^2 - 11x + 10
0 = (x - 1)(x - 10)
x - 1 = 0 or x - 10 = 0
x = 1 or x = 10
The x-intercepts are (1, 0) and (10, 0).
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sharah has 35 coins in her pocket, all of which are dimes and quarters. if they are worth a total of $5.30, how many of each kind dose she have?
The number of each kind of coins Sharah have is 23 dimes and 12 quarters.
Let's use a system of equations to solve this problem. Let x be the number of dimes and y be the number of quarters that Sharah has. Then, we can write the following equations:
x + y = 35 (the total number of coins)
0.10x + 0.25y = 5.30 (the total value of the coins)
We can use the first equation to solve for one of the variables in terms of the other. Let's solve for x:
x = 35 - y
Now we can substitute this into the second equation:
0.10(35 - y) + 0.25y = 5.30
3.50 - 0.10y + 0.25y = 5.30
0.15y = 1.80
y = 12
Now we can use this value of y to solve for x:
x = 35 - 12 = 23
So Sharah has 23 dimes and 12 quarters.
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Which are correct representations of the inequality –3(2x – 5) < 5(2 – x)? Select two options. x < 5 –6x – 5 < 10 – x –6x + 15 < 10 – 5x A number line from negative 3 to 3 in increments of 1. An open circle is at 5 and a bold line starts at 5 and is pointing to the right. A number line from negative 3 to 3 in increments of 1. An open circle is at negative 5 and a bold line starts at negative 5 and is pointing to the left.
The correct representations of the inequality –3(2x – 5) < 5(2 – x) are given as follows:
x > 5.An open circle is at 5 and a bold line starts at 5 and is pointing to the right.What are the inequality symbols?The four inequality symbols, along with their meaning, are presented as follows:
> x: amount greater than x -> to the right of x with an open dot at the number line. -> above the dashed horizontal line y = x on the coordinate plane.< x: amount less than x. -> to the left of x with an open dot at the number line. -> below the dashed horizontal line y = x on the coordinate plane.≥ x: amount at least x. -> to the right of x with a closed dot at the number line. -> above the solid horizontal line y = x on the coordinate plane.≤ amount at most x. -> to the left of x with a closed dot at the number line. -> above the dashed horizontal line y = x on the coordinate plane.The inequality for this problem is defined as follows:
–3(2x – 5) < 5(2 – x)
Expanding the operations, the solution is obtained as follows:
-6x + 15 < 10 - 5x
-6x + 5x < 10 - 15
-x < -5
x > 5.
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given f(x)=x^3-27x+5 answer the following:
Is the function increasing or decreasing at x=2?
List the interval (a,b) where the f(x) is increasing.
At what x-value does f(x) have a relative maximum?
(a) The function is decreasing at x=2.
(b) The interval where f(x) is increasing is (-3, 3).
(c) The function, f(x) has a relative maximum at x=-3.
Is the function increasing or decreasing at x=2?
To determine whether the function is increasing or decreasing at x=2, we need to find the derivative of f(x) and evaluate it at x=2.
f(x) = x³ - 27x + 5
f'(x) = 3x² - 27
At x=2, f'(2) = 3(2)² - 27 = -15, which is negative.
Therefore, the function is decreasing at x=2.
To find the interval where f(x) is increasing, we need to find the values of x where f'(x) > 0.
f'(x) = 3x² - 27
3x² - 27 > 0
3(x² - 9) > 0
(x - 3)(x + 3) > 0
The critical points are x=-3 and x=3.
We can test each of the intervals created by these critical points to see where f(x) is increasing or decreasing.
When x < -3, f'(x) < 0, so f(x) is decreasing.
When -3 < x < 3, f'(x) > 0, so f(x) is increasing.
When x > 3, f'(x) > 0, so f(x) is increasing.
Therefore, the interval where f(x) is increasing is (-3, 3).
To find the relative maximum of f(x), we need to find the critical points where f'(x) = 0.
3x² - 27 = 0
x² - 9 = 0
(x - 3)(x + 3) = 0
The critical points are x=-3 and x=3.
To determine which of these critical points corresponds to a relative maximum, we need to use the second derivative test.
f''(x) = 6x
At x=-3, f''(-3) = -18, which is negative.
Therefore, f(x) has a relative maximum at x=-3.
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A company makes a single serving cereal box that contains a volume of 1. 2 ounces of cereal. They plan to make an extra large box for school cafeterias. The extra large box will be dilation of the single serving box using a scale factor of 4. How many ounces of cereal will the extra large box contain?
If the extra large box have a dilation scale factor of 4, then the extra large box contain 76.8ounces.
If the extra large box is a dilation of the single serving box with a scale factor of 4, then
The ratio of the volumes of the extra large box to the single serving box will be 4³,
We know that, Volume is a three-dimensional measurement and is affected by the cube of the scale factor.
So, the volume of the extra large box will be;
⇒ 4³ × 1.2 ounces = 4×4×4×1.2 ounces = 76.8 ounces,
Therefore, the extra large box will contain 76.8 ounces of cereal.
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Abbie bought 82 cases of water for her restaurant Each case had 24 bottles of water How many bottle of water did Abbie buy in all?
Answer:
1968 bottles of water
Step-by-step explanation:
24×82=1968
1968 bottles of water
For g(x)=2x/3, find g(3) and g(12)
In response to the supplied query, we may state that Therefore, equation g(12) = 8.
What is equation?Using the equals symbol (=) to indicate equivalence, a math equation links two statements. Algebraic equations prove the equality of two mathematical expressions by a mathematical assertion. The equal sign, for example, provides a gap between the numbers 3x + 5 and 14 in the equation 3x + 5 = 14. You can use a mathematical formula to understand the connection between the two phrases that are written on opposite sides of a letter. Most of the time, the logo and the particular software match. e.g., 2x - 4 = 2 is an example.
To find g(3), we substitute x=3 into the function g(x):
g(3) = 2(3)/3
g(3) = 6/3
g(3) = 2
Therefore, g(3) = 2.
To find g(12), we substitute x=12 into the function g(x):
g(12) = 2(12)/3
g(12) = 24/3
g(12) = 8
Therefore, g(12) = 8.
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DUE TODAY PLEASE HELP NOW!!!!!!!!!!!!!
Here is another triangle similar to DEF found in the lesson section labeled “Shrinking Triangles”.
• Label the triangle D”E”F”.
• What is the scale factor from triangle DEF to triangle D”E”F”?
• What are the coordinates of F”? Explain how you know.
• What are cos(D”), sin(D”), and tan(D”)?
The scale factοr οf dilatiοn is 1/40 and the cοοrdinates οf F" are (1440, 600)
Labelling the image οf the triangle
The image οf the label is attached
The scale factοr οf the dilatiοn
Given that
D'E' = 36 units
Then, we have
D"E" = 0.9 units
The scale factοr is calculated as
Scale factοr = D"E"/D'E'
Sο, we have
Scale factοr = 0.9/36
Evaluate
Scale factοr = 1/40
Sο, the scale factοr οf dilatiοn is 1/40
The cοοrdinates οf F"
This is calculated as
F = F'/Scale factοr
Sο, we have
F = (36, 15)/(1/40)
F = (1440, 600)
The trigοnοmetry ratiοs
The trigοnοmetry ratiοs are calculated as
sin(D") = EF/DF
cοs(D") = DE/DF
tan(D") = EF/DE
Sο, we have the fοllοwing apprοximated values
sin(D") = 15/39 = 0.36
cοs(D") = 36/39 = 0.92
tan(D") = 0.36/0.92 = 0.39
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the population in a particular country is growing at the rate of 1.6% per year. If 5,092,000 people lived there in 1999, how many will there be in the year 2003? Use f(x)=y 0^e^0.016t and round to the nearest ten-thousand.
The population in 2003 is 5,830,000.
The population in a particular country is growing at the rate of 1.6% per year. To calculate the population for 2003, we can use the formula f(x)=y[tex]0^e^0.016t[/tex] .
Where y0 is the population in 1999 and t is the time in years.
Plugging in the numbers we have y0 = 5092000 and t = 4 for the year 2003, the formula looks like this: f(x)=5092000e0[tex]^{016(4)[/tex].
Solving this equation, we get f(x)=5837280, which is the population in 2003. Rounding this number to the nearest ten-thousand, the population in 2003 is 5,830,000.
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Find the LCM of:
x² - 3x + 2, x² + x + 2
Answer:
The two polynomials cannot be factored using integer coefficients. Therefore, we need to use the quadratic formula to find their roots:
For x² - 3x + 2 = 0:
a = 1, b = -3, c = 2
x = (-(-3) ± √((-3)² - 4(1)(2))) / (2(1)) = (3 ± √1) / 2
x = 1 or x = 2
For x² + x + 2 = 0:
a = 1, b = 1, c = 2
x = (-1 ± √(1² - 4(1)(2))) / (2(1)) = (-1 ± √(-7)) / 2
x = (-1 ± i√7) / 2
Therefore, the LCM of x² - 3x + 2 and x² + x + 2 is:
(x - 1)(x - 2)(x - (-1/2 + i√7/2))(x - (-1/2 - i√7/2))