Answer:
Vertical Compression by factor of 1/4
Step-by-step explanation:
Two methods:
Method 1. Transformations
Method 2. Algebraic input-output tables
Method 1. Transformations
The Main concept of this question is about Transformations of functions -- specifically, multiplying on the outside by a positive number less than 1.
The transformation that occurs when multiplying a function by a positive number on the outside of the function is a vertical stretch or compression.
Positive numbers larger than 1 will stretch it vertically, whereas positive numbers smaller than 1 will compress it vertically.
Therefore, multiplying by 1/4 on the outside, a positive number less than 1, will vertically compress the function down to one-fourth the size.
This means that for g(x), all points on the original function f will have their heights reduced to 1/4 their original height (or depth) -- making all points on g(x) 1/4 their previous distance from the x-axis on the "f" function.
Method 2. Algebraic input-output tables
Observe on the graph three points on the function f:
(0,0), (1,4) and (3,0) --- points on the function "f"In function notation, this means [tex]f(0)=0[/tex], [tex]f(1)=4[/tex], and [tex]f(3)=0[/tex]Using the equation relating f and g, [tex]g(x)=\frac{1}{4}f(x)[/tex], we can find how those points would look like on the new function g(x).
For [tex]f(0)=0[/tex]
[tex]g(0)=\frac{1}{4}[f(0)]\\g(0)=\frac{1}{4}[0]\\g(0)=0[/tex]
For [tex]f(1)=4[/tex]
[tex]g(1)=\frac{1}{4}[f(1)]\\g(1)=\frac{1}{4}[4]\\g(1)=1[/tex]
For [tex]f(3)=0[/tex]
[tex]g(3)=\frac{1}{4}[f(3)]\\g(3)=\frac{1}{4}[0]\\g(3)=0[/tex]
These known points should correctly identify the graph from the possible choices.
If jones use online banking and averages 40 transactions monthly how much would he save in 2 months if he choose texas bank rather than lone star bank
Jones would save $20 over 2 months by choosing Texas Bank over Lone Star Bank for his online banking needs.
What are the fees and charges associated with online banking?To answer this question, we need to know the fees and charges associated with online banking at Texas Bank and Lone Star Bank. Without this information, it's impossible to accurately calculate how much Jones would save by choosing one bank over the other.
Assuming we have this information, we can use the following steps to calculate Jones' potential savings:
Calculate the fees and charges associated with 40 transactions per month at each bank.
Subtract the total fees and charges at Texas Bank from the total fees and charges at Lone Star Bank to determine the difference.
Multiply the difference by 2 to determine how much Jones would save in 2 months by choosing Texas Bank over Lone Star Bank.
For example, let's say that the fees and charges at Lone Star Bank for 40 transactions per month total $20, while the fees and charges at Texas Bank for the same number of transactions total $10. In this case, the difference would be $10 per month.
To calculate Jones' potential savings over 2 months, we would multiply $10 by 2, giving us a total potential savings of $20.
So, in this hypothetical scenario, Jones would save $20 over 2 months by choosing Texas Bank over Lone Star Bank for his online banking needs.
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Consider the expression 16 - y^2/square root of 49 + 12. What is the value of the expression when y=-5?
Answer:
Step-by-step explanation:
16 - (y^2/sqrt(49)) +12
at y = -5
16 - ( (-5)^2 / sqrt(49)) +12
16 - ( 25 / 7) + 12
28 - (25/7)
(28*7 - 5) / 7 (LCM)
(196 - 5) / 7
(191/7)
27.2857 = Ans
Are the events mutually exclusive?
event a: rational numbers
event b: irrational numbers
no - overlapping
yes - mutually exclusive
Answer:
Yes they are mutually exclusive
Step-by-step explanation:
You cannot both be a rational number and an irrational number
The greenery landscaping company puts in an order for 2 pine trees and 5 hydrangea bushes for a neighborhood project. the order costs $150. they put in a second order for 3 pine trees and 4 hydrangea bushes that cost $144.50.
2(2.5) + 5(23) = 150
3(2.5) + 4(23) = 144.5
Both equations are satisfied, so our solution is correct.
The greenery landscaping company orders how many trees and bushes for the neighborhood?To solve the problem, let's first assign some variables. Let x be the cost of one pine tree and y be the cost of one hydrangea bush. We can then use these variables to set up a system of equations:
2x + 5y = 150 (equation 1)
3x + 4y = 144.5 (equation 2)
We can solve this system of equations using various methods. Here, we will use the substitution method.
From equation 1, we can solve for x in terms of y:
2x = 150 - 5y
x = (150 - 5y)/2
We can then substitute this expression for x into equation 2:
3((150 - 5y)/2) + 4y = 144.5
Multiplying both sides by 2 to eliminate the fraction:
3(150 - 5y) + 8y = 289
Expanding and simplifying:
450 - 15y + 8y = 289
-7y = -161
y = 23
We can now substitute this value for y into either equation 1 or 2 to solve for x:
2x + 5(23) = 150
2x = 5
x = 2.5
Therefore, one pine tree costs $2.50 and one hydrangea bush costs $23.
To check our work, we can substitute these values into both equations:
2(2.5) + 5(23) = 150
3(2.5) + 4(23) = 144.5
Both equations are satisfied, so our solution is correct.
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The relative frequency table describes the relationship between students who completed an exam review and their performance on the exam. Passed exam Did not pass exam Row Totals Completed exam review 55% 10% 65% Did not complete exam review 20% 15% 35% Column Totals 75% 25% 100% Part A: What is the percentage of students who passed the exam, given that they completed the exam review? Round to the nearest percentage. (2 points) Part B: What is the percentage of students who passed the exam, given that they did not complete the exam review? Round to the nearest percentage. (2 points) Part C: Is there an association between passing the exam and completing the exam review? Justify your answer. (2 points
The values on the relative frequency table indicates;
Part A; 55%
Part B; 20%
Part C; There is an association between passing the exam and completing the exam review
What is a relative frequency table?The relative frequency table shows the mode of a dataset, from the sample obtained from a population.
The data in the table can be expressed as follows;
[tex]{}[/tex] Passed exam Did not pass exam Row totals
Completed exam review [tex]{}[/tex] 55% 10% 65%
Did not completed exam review[tex]{}[/tex] 20% 15% 35%
Column Total [tex]{}[/tex] 75% 25% 100%
Part A; The above table indicates that the percentage who passed the exam given that they completed the exam review is 55%
Part B; The percentage that passed the exam given that they did not complete exam review is 20%
Part C; The conditional percentages of passing the exam and completing the exam review are very different indicating that there is an association between passing the exam and completing exam review
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What kind of triangle is this?
The triangle is a right triangle.
What is a right triangle?Any given triangle in which one of its internal angles measures 90^o is said to be a right angle. Thus there is a common relations among the three sides of the triangle which is shown by the Pythagorean theorem.
The Pythagorean theorem states that;
For a right triangle, this relation holds among its three sides;
/Hyp/^2 = /Adj/^2 + /Opp/^2
Considering the given diagram, we have;
/Hyp/^2 = /Adj/^2 + /Opp/^2
= 4^2 + 3^2
= 16 + 9
= 25
so that;
Hyp = 25^1/2
= 5
Therefore the given triangle is a right triangle.
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Find the derivative.
f(X) = (2e^3x + 2e^-2x)^4
To find the derivative of f(x) = (2e^(3x) + 2e^(-2x))^4, we can use the chain rule and the power rule.
First, we need to find the derivative of the function inside the parentheses, which is:
g(x) = 2e^(3x) + 2e^(-2x)
The derivative of g(x) is:
g'(x) = 6e^(3x) - 4e^(-2x)
Now, using the chain rule and power rule, we can find the derivative of f(x):
f'(x) = 4(2e^(3x) + 2e^(-2x))^3 * (6e^(3x) - 4e^(-2x))
Simplifying this expression, we get:
f'(x) = 24(2e^(3x) + 2e^(-2x))^3 * (e^(3x) - e^(-2x))
To find the derivative of f(x) = (2e^(3x) + 2e^(-2x))^4, we can use the chain rule. The chain rule states that the derivative of a composite function is the derivative of the outer function times the derivative of the inner function.
Let u = 2e^(3x) + 2e^(-2x). Then f(x) = u^4.
First, find the derivative of the outer function with respect to u:
df/du = 4u^3
Next, find the derivative of the inner function with respect to x:
du/dx = d(2e^(3x) + 2e^(-2x))/dx = 6e^(3x) - 4e^(-2x)
Now, use the chain rule to find the derivative of f with respect to x:
df/dx = df/du * du/dx = 4u^3 * (6e^(3x) - 4e^(-2x))
Substitute the expression for u back into the equation:
df/dx = 4(2e^(3x) + 2e^(-2x))^3 * (6e^(3x) - 4e^(-2x))
This is the derivative of f(x) with respect to x.
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Consider the function f(x) = sinº (4x). a) Determine f '(x). [/2]
The derivative of f(x) = sinº (4x) is f '(x) = 4cos (4x).
How did derivative of f(x) evaluate?To find the derivative of f(x) = sinº (4x), we can use the chain rule.
First, we need to find the derivative of the outer function, which is sinº (4x). This can be done using the derivative of the sine function:
f '(x) = cos (4x)
Next, we need to multiply this by the derivative of the inner function, which is 4.
f '(x) = cos (4x) * 4
Simplifying this expression, we get:
f '(x) = 4cos (4x)
Therefore, the derivative of f(x) = sinº (4x) is f '(x) = 4cos (4x).
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PLEASE ONLY PROVIDE A CORRECT ANSWER IF YOU KNOW HOW TO SOLVE!! CLICK PICTURE TO SEE.
Any function of the form [tex]y = \sqrt[3]{x + a}[/tex] is a translation left a units of the graph of [tex]g(x) = \sqrt[3]{x}[/tex], which has one x-intercept.
What is a translation?A translation happens when either a figure or a function is moved horizontally or vertically on the coordinate plane.
The four translation rules for functions are defined as follows:
Translation left a units: f(x + a).Translation right a units: f(x - a).Translation up a units: f(x) + a.Translation down a units: f(x) - a.The function in this problem has a single x-intercept, hence a translation left only moves the function laterally, meaning that it would also have only one x-intercept.
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the average weight of 40 randomly selected minivans was 4,150 pounds. the minivan population standard deviation was 490 pounds. find the 99% confidence interval of the true mean weight of minivans.
The 99% confidence interval of the true mean weight of minivans with 4150 pounds is CI = (3950, 4350).
The percentage (frequency) of acceptable confidence intervals that include the actual value of the unknown parameter is represented by the confidence level. In other words, a limitless number of independent samples are used to calculate the confidence intervals at the specified degree of assurance. in order for the percentage of the range that includes the parameter's real value to be equal to the confidence level.
Most of the time, the confidence level is chosen before looking at the data. 95% confidence level is the standard degree of assurance. Nevertheless, additional confidence levels, such as the 90% and 99% confidence levels, are also applied.
Point estimate is the sample mean, which is 4150 pounds. It is the best "guess" one has.
selected minivans was 4,150 pounds,
(z < 0.99) = 2.58
99% CI = ±2.58
Standard Error of the mean.
It is the = [tex]\frac{standard \ deviation}{\sqrt{sample \ size} }[/tex]
SE = [tex]\frac{490}{\sqrt{40} }[/tex]
SE = 77.475
To the nearest decimal ,
z x SE = ±200
CI = (3950, 4350) units are pounds.
Therefore, the confidence interval of the true mean weight of minivans is (3950, 4350).
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Can someone help me with this question and show the steps please
PLEASE HELP!!! worth a lot of Points !
The table shows the average cost of gasoline in the United States in dollars per gallon for the given years.
Year
1995 1996 2000 2001 2005 2006 2010 2011 2013 2014
Price per gallon ($) ( 1. 13) (1. 14) (1. 33) (1. 49) (1. 88) (2. 36) (2. 77) (3. 15) (3. 39) (3. 40)
(a) Write the least squares regression equation that models the data. Let x = time in years since
1995 and let y = price per gallon.
(b) Use the equation to estimate the price per gallon in 2030. Show your Work
(a) The least squares regression equation that models the data is: y = 0.091x + 1.125, where x is the time in years since 1995 and y is the price per gallon.
(b) To estimate the price per gallon in 2030, we need to find the value of y when x = 35 (2030 - 1995). Substituting x = 35 in the equation, we get: y = 0.091(35) + 1.125 = 4.22 dollars per gallon. Therefore, the estimated price per gallon in 2030 is 4.22 dollars.
(a) The least squares regression equation is used to model the relationship between two variables, in this case, time and gasoline price. It calculates the line that best fits the data points and can be used to estimate the value of the dependent variable (gasoline price) for any given value of the independent variable (time).
(b) To estimate the price per gallon in 2030, we simply need to substitute the value of x = 35 in the equation and solve for y. The equation shows that the price per gallon increases by 9.1 cents every year since 1995.
However, this is just an estimate based on the data available, and other factors such as changes in supply and demand, government policies, and global events can also influence gasoline prices in the future.
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A planet's radius is approximately 2,812 mi. About two-thirds of the planet's surface is covered by water.
Enter an estimate for the land area on the planet. Round the answer to the nearest million.
An estimate for the land area on the planet is
mi?
A planet's radius is approximately 2,812 mi. About two-thirds of the planet's surface is covered by water. An estimate for the land area on the planet is 33 million mi²
The surface area of a sphere is given by the formula:
S = 4πr²
where S is the surface area and r is the radius.
Substituting the given radius, we get:
S = 4π(2,812)²
S ≈ 99,392,252.4 mi²
Since two-thirds of the planet's surface is covered by water, we can estimate the land area as one-third of the total surface area:
Land area ≈ (1/3) x 99,392,252.4
Land area ≈ 33,130,750.8 mi²
Rounding this to the nearest million, we get an estimate of 33 million mi² for the land area on the planet.
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Jun’s fruit stand sold 12 fewer watermelons than bananas last week. The stand sold 48 bananas last week.
Complete the sentences using the correct numbers or ratios from the drop down menu.
Last week, the ratio of bananas sold to watermelons sold was (Select).
This ratio means that for every (Select) bananas sold, the number of watermelons sold was (Select) HELP SOON ASAP PLEASE
Last week, the ratio of bananas sold to watermelons sold was 4 : 3.
This ratio means that for every 4 bananas sold, the number of watermelons sold was 3.
Since there were 48 bananas sold, we can find the number of watermelons sold by subtracting 12 from 48:
48 bananas - 12 = 36 watermelons
Now, we can determine the ratio of bananas sold to watermelons sold. The ratio would be:
Bananas : Watermelons = 48 : 36
To simplify this ratio, we can divide both numbers by their greatest common divisor (GCD), which in this case is 12:
48 ÷ 12 = 4
36 ÷ 12 = 3
So, the simplified ratio is:
4 : 3
This ratio means that for every 4 bananas sold, the number of watermelons sold was 3. In other words, out of every 7 fruits sold (4 bananas + 3 watermelons), 4 were bananas and 3 were watermelons. This provides an easy way to understand the proportion of each type of fruit sold at Jun's fruit stand last week.
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Simplify rational ( trinomial only)
Simplify the following expression completely.
Answer: [tex]\frac{x-4}{x-7}[/tex]
Step-by-step explanation:
[tex]\frac{x^{2}-5x+4 }{x^{2} -8x+7}[/tex]
factor the top and bottom by finding numbers that multiply to the last term but add to middle
for top part:
-4 and -1 multiply to +4 and add to -5
for bottom part:
-7 and -1 multiply to to +7 and add to -8
Those are your factored numbers, put into factored form
[tex]\frac{(x-4)(x-1)}{(x-7)(x-1)}[/tex] now cross off same factors from top and bottom only
[tex]\frac{x-4}{x-7}[/tex]
Find the solution of the following initial value problem. 3x N이 =3 f'(u) = 5( cosu - sin u) and f(u)= Use Newton's method to approximate all the intersection points of the following pair of curves. Some preliminary graphing or analysis may help in choosing good intro y=16/* and y=x+1 The graphs intersect when x (Do not round until the final answer. Then found to six decimal places as needed. Use a comma to separate med
the intersection point is approximately (2.215421, 3.256684). For the first question, the initial value problem is given by the differential equation f'(u) = 5(cost - sinus) with the initial condition f(3xN) = 3.
To solve this problem, we can separate the variables and integrate both sides as follows:
f'(u) = 5(cosu - sinu)
∫ f'(u) du = ∫ 5(cosu - sinu) du
f(u) = 5sinu + 5cosu + C
Using the initial condition f(3xN) = 3, we can solve for the constant C:
f(3xN) = 5sin(3xN) + 5cos(3xN) + C = 3
C = 3 - 5sin(3xN) - 5cos(3xN)
Thus, the solution to the initial value problem is given by:
f(u) = 5sinu + 5cosu + 3 - 5sin(3xN) - 5cos(3xN)
For the second question, we are asked to find the intersection points of the two curves y = 16/* and y = x + 1 using Newton's method. To applyhttps://brainly.com/question/2228446 we need to find the function f(x) that represents the difference between the two curves:
f(x) = 16/x - (x + 1)
The intersection points correspond to the roots of f(x), which can be found using Newton's method:
x_{n+1} = x_n - f(x_n)/f'(x_n)
where x_n is the nth approximation of the root. We start with an initial guess of x_0 and iterate until we reach a desired level of accuracy. For example, if we start with x_0 = 1, the iterations are as follows:
x_1 = 1 - (16/1 - (1 + 1))/(16/1^2 + 1) = 2.5
x_2 = 2.5 - (16/2.5 - (2.5 + 1))/(16/2.5^2 + 1) = 2.267857
x_3 = 2.267857 - (16/2.267857 - (2.267857 + 1))/(16/2.267857^2 + 1) = 2.219208
x_4 = 2.219208 - (16/2.219208 - (2.219208 + 1))/(16/2.219208^2 + 1) = 2.215430
x_5 = 2.215430 - (16/2.215430 - (2.215430 + 1))/(16/2.215430^2 + 1) = 2.215421
Thus, the intersection point is approximately (2.215421, 3.256684).
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The first floor of a tiny house has has a length of 11 feet. The width of the kitchen if is 7 feet and the width of the bathroom is 4 feet. The expression 11(7+4) represents the total area in square feet. Write an expression to represent the total area as the sum of the areas of each room
The total area of the first floor of the tiny house is 121 square feet
The total area of the first floor of the tiny house can be expressed as the sum of the areas of each room. The area of a rectangle is calculated by multiplying the length by the width. Therefore, we can write:
Total area = Area of kitchen + Area of bathroom
The area of the kitchen is given by the product of the length and the width of the kitchen, which is 11 feet and 7 feet, respectively. Therefore, the area of the kitchen can be written as:
Area of kitchen = 11 x 7 = 77 square feet
Similarly, the area of the bathroom is given by the product of the length and the width of the bathroom, which is 11 feet and 4 feet, respectively. Therefore, the area of the bathroom can be written as:
Area of bathroom = 11 x 4 = 44 square feet
Substituting these expressions into the equation for the total area, we get:
Total area = Area of kitchen + Area of bathroom
= 77 + 44
= 121 square feet
Therefore, the total area of the first floor of the tiny house is 121 square feet, which can also be expressed as the sum of the areas of the kitchen and bathroom.
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The population of pine trees in a 200-acre area has decreased by roughly the same percentage over the past 4 years. The table below shows data values for the population of these trees, p (t) , after t years.
The function that would best represent this is given as p(t) = 1150 (0.8769)^t
What is an exponential function?An exponential function is a mathematical function of the form f(x) = a^x, where "a" is a constant called the base and "x" is the variable. The base is usually a positive number greater than 1, but it can also be a fraction between 0 and 1, or even a negative number.
Exponential functions are characterized by the fact that the variable "x" appears as an exponent. As a result, these functions grow or decay very rapidly as "x" increases or decreases, depending on the value of the base "a".
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I just need the FOIL for this, no solving the equation.
(x-3)(x+1)
Answer: x² - 2x - 3
Step-by-step explanation:
What is FOIL? The FOIL method is used to multiply two binomials.
F ➜ First
O ➜ Outer
I ➜ Inner
L ➜ Last
Let us break it down into each piece by multiplying, following the pattern.
F ➜ x * x ➜ x²
O ➜ x * 1 ➜ x
I ➜ x * -3 ➜ -3x
L ➜ -3 * 1 ➜ -3
Lastly, we add these pieces together.
x² + x - 3x - 3 = x² - 2x - 3
A pet border keeps a dog-to-cat ratio 5;2. If the boarder has room for 98 animals then how many of them can be dogs?
Answer:
70 dogs
Step-by-step explanation:
sum the parts of the ratio , 5 + 2 = 7 parts
divide total by 7 to find the value of one part of the ratio
98 ÷ 7 = 14 ← value of 1 part of the ratio , then
5 × 14 = 70 ← number of dogs
A convention center is hosting a home show where different businesses provide information and examples for improvements that can be made to homes. The sponsors are also holding a lottery to give away $10,000 in home improvements. In a giant bin, 20 balls numbered 1 - 20 are mixed together. Then , 3 balls are selected from the bin, without replacement For $5. 00a customer can try to predict the 3 numbers that will be selected. If the order in which the numbers are selected does not matter , how many different predictions are possible for this game of chance ?
There are 1140 different predictions possible for this game of chance.
In this scenario, customers have an opportunity to predict three numbers out of 20, which will be drawn from a bin. The order in which the numbers are selected does not matter, which means the same set of numbers in different orders will be considered as the same prediction.
To solve this problem, we can use the formula for combinations, which is
=> [tex]^nC_x = \frac{n!}{ x! \times (n-x)!}[/tex]
where n is the total number of items, and x is the number of items to be selected.
In this case, we have 20 balls, and we want to select three balls without replacement. So, the formula becomes
=> [tex]^{20}C_3 = \frac{20!} { 3! \times (20-3)!}[/tex]
Using a calculator or simplifying the equation, we get:
[tex]= > ^{20}C_3 = \frac{201918} { 321} = 1140[/tex]
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Write five expressions: a sum, a difference, a product, a quotient, and one that involves at least two operations that have the value of -3/4.
By using sum , difference , product , quotient and one that involves at least two operations that have the value of -3/4.
Now, We have to find the five expressions :
A sum, A difference, A product, A quotient, and One that involves at least two operations.Expression for sum is -
1/4 + (-1) = -3/4
Expression for difference is -
(1/4 - 1) = -3/4
Expression for product is -
(-3/2)(1/2) = -3/4
Expression for quotient is -
(1 - 4)/4 = -3/4
Expression that involves at least two operations is -
-(1/4 + 2/4) = -3/4
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An object has a mass of 4. 70g. Calculate the Density of the object volume is 2. 55L
The density of the object is 0.0018 g/mL.
To calculate the density of the object, we need to use the formula:
Density = Mass / Volume
Given that the mass of the object is 4.70g and the volume is 2.55L, we can substitute these values into the formula:
Density = 4.70g / 2.55L
We need to convert the units of mass and volume to a consistent unit. Let's convert the volume from liters to milliliters (1L = 1000mL):
Density = 4.70g / 2550mL
Now we can simplify by dividing both the numerator and denominator by 10:
Density = 0.47g / 255mL
Finally, we can express the answer in units of g/mL:
Density = 0.0018 g/mL
Therefore, the density of the object is 0.0018 g/mL.
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Does anyone have answers 3 and 4 for 4. 4. 3 Practice: Modeling: Solids?
Extremely lost and help with be appreciated :)
Answer:
search them up it should give you the answers
Step-by-step explanation:
the average time it takes a salesperson to finish a sale on the phone is exponentially distributed with a mean of 18 minutes. find the probability that more than 2 minutes pass before a sale is completed.
The probability that more than 2 minutes pass before a sale is completed is approximately 0.895 or 89.5%.
The CDF of the exponential distribution is given by:
F(x) = 1 - e^(-λx)
where λ is the rate parameter, which is the reciprocal of the mean, λ = 1/18 in this case. The variable x is the time it takes for a sale to be completed.
To find the probability that more than 2 minutes pass before a sale is completed, we need to find the complement of the probability that a sale is completed within the first 2 minutes. That is:
P(X > 2) = 1 - P(X ≤ 2)
Substituting into the CDF formula:
P(X > 2) = 1 - F(2) = 1 - [tex](1 - e^{(-\lambda_2)} = e^{(-\lambda_2)}[/tex]
Plugging in the value of λ:
P(X > 2) = [tex]e^{(-(1/18)\times2)}[/tex] ≈ 0.895
This means that there is a high chance that it will take more than 2 minutes for a sale to be completed on the phone.
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(-10x-4y) and (7x-5y) in simplest form
The simplification of the given algebraic expression is: -3x - 9y
How to simplify Algebraic Expressions?Algebraic expressions are defined as the idea of expressing numbers with the aid of letters or alphabets without really specifying their actual values.
Now, the algebraic operations are known by the acronym PEMDAS which denotes:
P- Parentheses, E- Exponents, M- Multiplication, D- Division, A- Addition, and S- Subtraction.
We want to find the sum of the algebraic expressions given as (-10x - 4y) and (7x - 5y) in simplest form.
Thus, we have:
(-10x - 4y) + (7x - 5y)
= -10x - 4y + 7x - 5y
= -3x - 9y
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Complete question:
Find an expression which represents the sum of (-10x - 4y) and (7x - 5y) in simplest terms.
Find x.
Please help thank you
consider the first month's sales data for the south region.
select the correct answer from each drop-down menu.
for the south region, the proportion of sales from current stores is approximately______ %.
a.63
b.37
c.58
d.24
because this proportion is_________
a. relatively close to
b. significantly different from
the sales director's statistical model, the data is______
a. inconsistent
b. consistent
with the model.
Answer is:
For the south region, the proportion of sales from current stores is approximately 58 %.
because this proportion is relatively close to the sales director's statistical model, the data is consistent with the model.
The given information states that the proportion of sales from current stores in the South region is approximately 58%. This value falls within the range of the sales director's statistical model, which could be an estimated value or a range of values based on past data or other sources. Since the proportion of sales falls within the expected range, the data is consistent with the model. This means that the actual value observed is not significantly different from the expected value, and there is no evidence to suggest that the model needs to be revised or updated.
Therefore, the answer to the second drop-down menu is "consistent". If the actual proportion of sales from current stores in the South region was significantly different from the expected value in the sales director's statistical model, then the answer would be "inconsistent". However, since the observed proportion is relatively close to the expected value, the data is consistent with the model.
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An object is shot upwards from ground level with an initial velocity of 3 meters per second; it
is subject only to the force of gravity (no air resistance). Find its maximum altitude and the
time at which it hits the ground.
The maximum altitude the object reaches is approximately 0.459 meters, and it takes approximately 0.612 seconds for the object to hit the ground after being shot upwards from ground level.
To find the maximum altitude and the time at which the object hits the ground after being shot upwards from ground level with an initial velocity of 3 meters per second and subject only to the force of gravity,
we can use the following steps:
1. Calculate the time it takes to reach its maximum altitude:
To do this, we can use the formula vf = vi - gt, where vf is the final velocity (0 m/s at the peak), vi is the initial velocity (3 m/s), g is the acceleration due to gravity (9.81 m/s²), and t is the time. Rearranging and solving for t:
0 = 3 - 9.81t
t = 3 / 9.81 ≈ 0.306 seconds
2. Calculate the maximum altitude:
We can use the formula h = vit - 0.5gt², where h is the maximum altitude. Plugging in the values:
h = (3 m/s)(0.306 s) - 0.5(9.81 m/s²)(0.306 s)²
h = 0.459m
3. Calculate the time it takes to hit the ground:
Since the object will take the same amount of time to fall from its maximum altitude to the ground as it took to reach the maximum altitude, the total time to hit the ground is double the time it took to reach the maximum altitude:
total time = 2 × 0.306 s ≈ 0.612 seconds
So, the maximum altitude the object reaches is approximately 0.459 meters, and it takes approximately 0.612 seconds for the object to hit the ground after being shot upwards from ground level.
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A pizza recipe calls for 2/3 cup of tomato sauce. If you have 1/4 cup of tomato sauce ,how much more tomato sauce do you need to make the recipe
The amount of more sauce needed is 5/12.
Thus we are given that the total amount of sauce required for making the pizza is 2/3 cup.
Thus we already have 1/4 cup of tomato sauce present.
Hence, for making the recipe the leftover amount of sauce will be the difference in the sauce we have got to the sauce required.
Tomato sauce required= Total tomato sauce needed - Sauce already present
Therefore,
Tomato sauce required= 2/3-1/4
Thus we have to make the denominators qual by taking their LCM as the denominator.
The LCM of the denominators comes out to be 12.
Therefore,
[tex]=\frac{8-3}{12}[/tex]
[tex]=\frac{5}{12}[/tex]
Therefore, the amount of sauce required is 5/12.
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