The height of the new building in the zoo is calculated to be 6.375 m
How to find the height of the new buildingThe problem is solved by using the scale factor to increase or decrease the model.
When the scale factor is less than it leads to decrease but when above it leads to increasing.
The case in the problem is increasing.
First, they made a model that was 1.7 meters tall
the height of the model = 1.7 m
a more detailed model that was 1.5 times as tall as the first model
the height of the detailed model = 1.7 * 1.5 = 2.55 m
The building will be 2.5 times as tall as the height of the detailed model
= 2.5 * height of the detailed model
= 2.5 * 2.55
= 6.375 m
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helppppp right answers only with explanition.
Answer:
1
Step-by-step explanation:
anything to the power of 0 is 1
hopes this helps
Help wanted proportinal relationship
The proportional relationship of the table are as follows:
h = 1 / 5 kk = 5 / 4 hh = 5kHow to find proportional relationship?Proportional relationships are relationships between two variables where their ratios are equivalent.
A proportional relationship is one in which two quantities vary directly with each other. We say the variable y varies directly as x if:
y = k x
for some constant k , called the constant of proportionality.
First table
k =hx
10 = 2x
x = 5
Hence,
k = 5h
h = 1 / 5 k
Second table
k = hx
5 = 4x
x = 5 / 4
Hence,
k = 5 / 4 h
Third table
k = hx
5 = 25x
x = 5 / 25
Hence,
k = 1 / 5 h
h = 5k
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A parachutist's rate during a free fall reaches 55 meters per second. What is this rate in feet per second? At this rate, how many feet will the parachutist fall during 15 seconds of free fall? In your computations, assume that meter is equal to 3.3 feet. Do not round your answers.
The speed is 181.5 feet per second. Then the parachutist fall during 15 seconds of free fall will be 2,722.5 feet.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
A parachutist's rate during a fast drop arrives at 55 meters each second. In your calculations, accept that the meter is equivalent to 3.3 feet.
Convert the speed into feet per second. Then we have
S = 55 x 3.3
S = 181.5 feet per second
The parachutist fall during 15 seconds of free fall will be given as,
D = 181.5 x 15
D = 2,722.5 feet
The speed is 181.5 feet per second. Then the parachutist fall during 15 seconds of free fall will be 2,722.5 feet.
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31. Across a horizontal distance of 20 feet, a roller coaster has a steep drop. The height of the roller coaster at the bottom of the drop is-100 feet, compared to its height at the top of the drop. What is the average amount that the roller coasters height drops over each horizontal foot?
The average amount that the roller coaster's height drops over each horizontal foot will be -5 feet.
What is an arithmetic operation?The four basic mathematical operations are the addition, subtraction, multiplication, and division of two or even more integers. Among them is the examination of integers, particularly the order of actions, which is crucial for all other mathematical topics, including algebra, data organization, and geometry.
As per the given data in the question,
Slope = change in y/change in x
Slope = Δy/Δx
A 20-foot horizontal drop is present on a roller coaster.
So, Δx = 20-foot
The roller coaster is 100 feet tall when it is at the bottom of the drop.
So, Δy = -100 feet.
Now, the average rate of change will be,
= -100/20
= -5/1 = -5
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which of the following graphs represents the solution set for the inequality - x < 2
The solution set for the inequality - x < 2 is - x < 2.
What is inequality?
In mathematics, inequalities specify the connection between two non-equal numbers. Equal does not imply inequality. Typically, we use the "not equal sign ()" to indicate that two values are not equal. But several inequalities are utilized to compare the numbers, whether it is less than or higher than.
An inequality in mathematics depicts the connection between two values in an unbalanced algebraic statement. A sign of inequality can be used to show that one of the two variables is larger than, more than or equal to, less than, or equal to another value.
-x<2
Multiply both sides by -1 (reverse the inequality)
(-x)(-1)>2(-1)
Simplify
x>-2
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help please and thanksss
8,9,10 is the value from the given replacement set make-up the solution set for inequality.
What is inequality?In mathematics if a statement of an order relation greater or greatest then or equal to is called inequality. To compute the inequality:
Just formulate an equationSolve itTo get the interval, mark the zero on the number lineTake any number from them for the inequality and test the interval.if we replace m with 8 it will be 8+7 which is 15 and less then 18
for 9 its 9+7 which is 16 which is less then 18
and for 10 its 10+7 which is 17 which is less then 18
and for 11 its 11+7 is 18 which is equal to 18 so it would not apply to this equation.
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3. Check for Reasonableness The proportion 75/w=150/100 can be used to find the whole, w. Use the language of percent to explain whether w is less than or greater than 75.
w is less than 75.
What do you mean by algebraic expression?
An expression constructed using integer constants, variables, and algebraic operations is known as an algebraic expression (addition, subtraction, multiplication, division and exponentiation by an exponent that is a rational number)
An equation that only uses algebraic expressions is known as an algebraic equation.
Any mathematical operation that involves variables, such as addition, subtraction, multiplication, or division, can have its solutions calculated using algebraic expressions.
Given expression:
[tex]\frac{75}{w}=\frac{150}{100}[/tex]
⇒ w = [tex]\frac{75 \times 100}{150 }[/tex]
⇒ w = 50
Convert the value of w into percentage.
w = 50 × 100 % = 500%
Therefore, w is less than 75.
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Please help me with this! Thank you so much ahead!
The area of the shaded region will be equal to 120 square cm.
What is an area?The space occupied by any two-dimensional figure in a plane is called the area. The space occupied by the rectangle in a two-dimensional plane is called the area of the rectangle.
Given that the sides of the rectangle are 24 cm and 10 cm. The area of the shaded region will be calculated by subtracting the area of the whole rectangle and the area of the triangle which is not shaded.
Area of the shaded region = ( 24 x 10 ) - ( 1/2 x 24 x 10)
Area of the shaded region = 240 - 120
Area of the shaded region = 120 square cm
Therefore, the area of the shaded region will be equal to 120 square cm.
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Consider the function c(x) = (x + 5)(x - 2)².
1. What are the zeroes of c(x)?
2. What is the degree of c(x)?
Step-by-step explanation:
Set each binomial equal to 0, solve for x.
[tex](x + 5) = 0[/tex]
[tex]x = - 5[/tex]
[tex](x - 2) {}^{2} = 0[/tex]
[tex]x - 2 = 0[/tex]
[tex]x = 2[/tex]
The zeroes are -5, and 2(with a multiplicity of 2)
We have a degree of 3.
[tex](x + 5)(x {}^{2} - 4x + 4)[/tex]
the first term in each binomail when using FOIL, become x^3 since that is the highest degree, 3 is the degree of c.
answer the 5 questions below ⬇️
Using some mathematical operations, we know that the total cost of the fencing will be $737 approximately.
What are mathematical operations?An operation is a function in mathematics that transforms zero or more input values into a clearly defined output value.
The operation's arity is determined by the number of operands.
Mathematical operations include addition, subtraction, multiplication, division, and finding the root.
So, the total cost of fencing is:
According to the given figure, the total length of fencing will be:
8m + 8m + 6m + 2m + 2m + 6m
32 m
Now, 4% more of the total fence:
4/32 * 100
1.28 m
Now the total fencing length:
32 + 1.28
33.28 m
We know that:
1m = 3.2 ft
33.28m = 109.18 ft
We are given that fencing of 4 feet costs: $27. Then,
109.18/4
27.295 * $27
$736.965
Rounding off: $737 approximately
Therefore, using some mathematical operations, we know that the total cost of the fencing will be $737 approximately.
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Graph f(x)=3x-1 and h(x)=-4x-5
The coordinates to plot the graph after solving the equation will be 0.33 and 1.2.
What is a graph?
In math, graph science is the theory of geometric structures called graphs that are used to represent pairwise different objects. Vertices—also known as nodes or points—that are joined by edges make form a network in this sense.
Undirected graphs, where edges connect two vertices equally, and focused therapy, where edges connect two vertices unevenly, are distinguished.
As per the given expressions to plot, the graph is,
f(x) = 3x - 1 and, (i)
h(x) = -4x - 5 (ii)
From equation (i),
f(x) = 3x - 1
3x = 1
x = 1/3
x = 0.33
From equation (ii)
h(x) = -4x - 5
-4x = 5
x = -5/4
x = 1.2
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You intend to estimate a population proportion with a confidence interval. The data suggests that the normal distribution is a reasonable approximation for the binomial distribution in this case.
Find the critical value that corresponds to a confidence level of 99.9%.
(Report answer accurate to three decimal places with appropriate rounding.)
The critical value that corresponds to a confidence level of 99% is, 2.58.
What is a 3 decimal place number?1 decimal place (tenths) 2 decimal places (hundredths) 3 decimal places (thousandths) 4 decimal places (ten-thousandths)
Consider a random variable X that follows a Binomial distribution with parameters, sample size n and probability of success p.It is provided that the distribution of proportion of random variable X, , can be approximated by the Normal distribution.The mean of the distribution of proportion is, The standard deviation of the distribution of proportion is, .Then the confidence interval for the population proportion p is:The confidence level is 99%.
The significance level is:
Compute the critical value as follows:
That is:
Use the z-table for the z-value.
For z = 2.58 the P (Z < z) = 0.995.
And for z = -2.58 the P (Z > z) = 0.005.
Thus, the critical value is, 2.58.
active attachment
In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 87.3% of confidence, our significance level would be given by and . And the critical value would be given by:And we can use the following excel codes to find the solution:"=NORM.INV(0.0635,0,1)"
"=NORM.INV(1-0.0635,0,1)"
Previous concepts
A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval". The margin of error is the range of values below and above the sample statistic in a confidence interval. Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean". The population proportion have the following distribution (assuming the normal approximation)Solution to the problemThe confidence interval for the mean is given by the following formula: In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 87.3% of confidence, our significance level would be given by and . And the critical value would be given by:And we can use the following excel codes to find the solution:
"=NORM.INV(0.0635,0,1)"
"=NORM.INV(1-0.0635,0,1)"
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1 1/3 inches = how many feet
if an ionic oxide has both x amount of fe2 and y amount fe3 , where x and y do not have to be integers, the formula would be (fe2 )x(fe3 )yoz. calculate the amount of oxide ions, z, in terms of x and y (an algebra problem).
Fe^2 + → Fe^3 + + e^- is an example of oxidation
How many oxidations do Fe3+ and Fe2+ ions have?
For instance, the oxygen ion O2+ has an oxidation number of 2 because it can contribute two electrons, whereas the iron ion Fe3+ has an oxidation number of +3 because it can take on three electrons to establish a chemical bond.
[tex]$\mathrm{Fe}_3 \mathrm{O}_4$[/tex] contains [tex]$\mathrm{F}$ e[/tex] atoms of both[tex]$+2$ and $+3$[/tex]oxidation number.
It is a stoichiometric mixture of[tex]Ferrous $(\mathrm{FeO})$[/tex]
and Ferric [tex]$\left(\mathrm{Fe}_2 \mathrm{O}_3\right)$ oxides combined as $\mathrm{FeO} \cdot \mathrm{Fe}_2 \mathrm{O}_3$.[/tex]
[tex]Oxidation state of oxygen in $\mathrm{FeO}$ and $\mathrm{Fe}_2 \mathrm{O}_3$ is $-2$.[/tex]Let the oxidation state of [tex]$\mathrm{Fe}$ in $\mathrm{FeO}$ and $\mathrm{Fe}_2 \mathrm{O}_3$ be $\mathrm{x}$ and $y$[/tex]
As we know that the sum of the oxidation states of all the atoms or ions in a neutral compound is zero.
ThereforeOxidation state of [tex]$\mathrm{F}$ e in $\mathrm{F}$ eO-[/tex]
&[tex]x+(-2)=0 \\& \Rightarrow x=2[/tex]
Oxidation state of[tex]$\mathrm{F}$ e in $\mathrm{Fe}_2 \mathrm{O}_3-$[/tex]
&[tex]2(\mathrm{y})+3(-2)=0 \\& \Rightarrow 2 \mathrm{y}=6 \\& \Rightarrow \mathrm{y}=3\end{aligned}[/tex]
Hence the oxidation number of [tex]$\mathrm{Fe}$ in $\mathrm{Fe}_3 \mathrm{O}_4$ are $+2$ and $+3$[/tex]respectively.
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Which of the following forms of organization is a separate legal entity?
A corporation—also known as a C corp—is a legal entity distinct from its owners.
What is a corporation?A corporation also referred to as a C corp, is a separate legal entity from its owners.
Corporations are able to generate revenue, pay taxes, and face legal consequences.
The strongest protection against personal liability is provided to owners by corporations, although forming a corporation is more expensive than creating other types of entities.
A corporation is a collection of people or a business that has been given legal status as a single entity by the state and is used for specific legal purposes.
Early corporations were created with a charter.
The majority of governments currently permit the registration of new corporations.
Therefore, a corporation—also known as a C corp—is a legal entity distinct from its owners.
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Correct question:
Which form of organization is a separate legal entity?
One label on a package of bolts says that each bolt has a diameter of 0.45 inch. To be in the package, the percent error of the diameter must be less than 3%. A test on the production line shows a bolt with a diameter of 0.46 inch. Should this bolt go into the package?
This bolt should go into the package. The percentage of error is 2.22% which is less than 3%.
What is the meaning of error?
The discrepancy between a variable's observed value and its actual but unseen value
Given that the diameter of each bolt is 0.45 inch.
The percentage of error the diameter of each bolt must be less than 3%.
A bolt picks for a test. The diameter of the bolt is 0.46 inch.
The formula of percent error is
The difference of the diameters/ the original diameter of bolt )× 100%
= [(0.46 - 0.45)/0.45] × 100%
= (0.1/0.45) × 100%
= 0.0222 × 100%
= 2.22%
The percentage of error is less than 3%. So the lot is good to go.
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WRITE THE EQUATION OF THE CONIC SHOWN BELOW
The required equation of conic section that shows eclipse is [tex]\frac{(x-2)^2}{4^2} + \frac{(y-4)^2}{6^2}=1[/tex].
What is an equation?An equation is a combination of different variables, in which two mathematical expressions are equal to each other.
Let the standard equation of conic section,
[tex]\frac{(x-h)^2}{a^2} + \frac{(y-k)^2}{b^2}=1[/tex] (1)
From the given diagram,
The center of the eclipse is (2, 4),
Here h = 2, and k = 4
The length of minor axis 2a = 8 ⇒ a = 4
The length of major axis 2b = 12 ⇒ b = 6
Substitute the values of a, b and h, k in equation (1)
[tex]\frac{(x-2)^2}{4^2} + \frac{(y-4)^2}{6^2}=1[/tex]
The required equation of the given conic section is [tex]\frac{(x-2)^2}{4^2} + \frac{(y-4)^2}{6^2}=1[/tex].
The conic section represents the eclipse.
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If I earn one dollar every second how many hours would it take for me to get to 230,000 dollars?
Answer:
It will take 64 hours
Step-by-step explanation:
It will be more specifically 63.889 hours, but rounding up it's 64
Jenny has decided that she can afford a monthly mortgage payment of $390. She has been offered a 3.5% 20 year mortgage from her bank. What formula could you type into Excel to determine what the largest mortgage loan she can afford?
The biggest mortgage loan Jenny can afford will be determined using the Excel formula PV(.035/12, 15*12, -485) in the situation that has been provided.
What are excel formulas?A formula in Microsoft Excel is an expression that modifies values in a set of cells.
Even if the result is incorrect, these formulas nonetheless return a result.
We may execute calculations like addition, subtraction, multiplication, and division using Excel formulae.
To make complex computations simpler, Excel features prewritten formulas known as functions.
A function takes one or more values, runs an operation, and then outputs the outcome to a cell.
Arguments are the values that you pass to a function.
So, in the given situation of Jenny, the excel formula PV(.035/12, 15*12, -485)will be used to determine the largest mortgage loan she can afford.
Therefore, the biggest mortgage loan Jenny can afford will be determined using the Excel formula PV(.035/12, 15*12, -485) in the situation that has been provided.
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Complete question":
Jenny has decided that she can afford a monthly mortgage payment of $390. She has been offered a 3.5% 20-year mortgage from her bank. What formula could you type into Excel to determine the largest mortgage loan she can afford is?
(A) PV(.035/12, 15*12, -485)
(B) PMT(.035/12, 15*12, -485)
(C) PV(.035, 15*12, -485)
(D) 390*.035/20
Help
The Christmas cheer from the crowd singing in the park brings up the Clausometer to 80%!
What is this number written as a fraction in simplest form?
The number written as a fraction in simplest form is 4/5
What is this number written as a fraction in simplest form?From the question, we have the following parameters that can be used in our computation:
Clausometer = 80%
Turn the percentage to fraction
So, we have the following representation
Clausometer = 80/100
Divide 80 and 100 by 10
So, we have the following representation
Clausometer = 8/10
Divide 8 and 10 by 2
So, we have the following representation
Clausometer = 4/5
Hence, the fraction is 4/5
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Mary saw two poison dart frogs. One was 7/8 inch long and the other was 5/8 inch long. How much longer was one than the other?
The one poison dart frog is 1/4 inch longer than the other.
What is Poison dart frog?
A family of frogs known as the Dendrobatidea that are indigenous to tropical Central and South America go by the common name "poison dart frog." These species are nocturnal and frequently have colorful bodies. These aposematic species have a bright coloration that is linked to the species' toxicity.
Given: Mary saw two poison dart frogs.
One was 7/8 inch long and the other was 5/8 inch long.
So, 7/8 - 5/8 = 2/8 = 1/4
Hence, the one poison dart frog is 1/4 inch longer than the other.
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What is the distance between the bank and Hiroto's house on the map? Enter the distance to the nearest quarter mile.(Each unit represents 1 mile.)
The distance between the bank and Hiroto's house on the map is 11.5 units.
What is coordinate geometry?A coordinate plane is a 2D plane that is formed by the intersection of two perpendicular lines known as the x-axis and y-axis. A coordinate system in geometry is a method for determining the positions of the points by using one or more numbers or coordinates.
The distance between the bank and Hiroto's house will be calculated as,
The coordinates are, B(-8,6) and H(3.5,6).
D=√(3.5-(-8))²+(6-6)²
D = √11.5²
D = 11.5
Therefore, the distance between the bank and Hiroto's house on the map is 11.5 units.
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When performing a ? test for independence in a contingency table with rrows and c columns, determine the upper-tail critical value of the test statistic in each of the following
circumstances.
a. a=0.05, r=3, c=4
b. a=0.01, r=5, c=6
c. a=0.01, r=5, c=4
d. a=0.01, r=3, c=4
e. α=0.01, r=6, c=5
Click the icon to view a table of critical values of
a. The critical value is (Round to three decimal places as needed)
an example
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Answer:
look below
Step-by-step explanation:
To determine the upper-tail critical value of the test statistic for a chi-square test for independence in a contingency table, you can use a table of critical values for the chi-square distribution or you can use a statistical software package or calculator to compute the critical value.
In each of the following circumstances:
a. a=0.05, r=3, c=4: The critical value would be the upper-tail critical value of the chi-square distribution with 3 degrees of freedom and an alpha level of 0.05.
b. a=0.01, r=5, c=6: The critical value would be the upper-tail critical value of the chi-square distribution with 5 degrees of freedom and an alpha level of 0.01.
c. a=0.01, r=5, c=4: The critical value would be the upper-tail critical value of the chi-square distribution with 5 degrees of freedom and an alpha level of 0.01.
d. a=0.01, r=3, c=4: The critical value would be the upper-tail critical value of the chi-square distribution with 3 degrees of freedom and an alpha level of 0.01.
e. α=0.01, r=6, c=5: The critical value would be the upper-tail critical value of the chi-square distribution with 6 degrees of freedom and an alpha level of 0.01.
It's important to note that the critical value is dependent on the degrees of freedom and the alpha level, so you will need to use the appropriate values for these parameters in order to determine the correct critical value.
pls help me with math i’ll give you brainlist
Answer: y = 11x + 31, the y - intercept is 31!
Step-by-step explanation:
The equation that models this situation is y = mx + b
We already have the slope, m, of 11.
since we have 2 coordinates, we can substitute all the known values into the equation.
==> 108 = 11 (7) + b
Multiply.
==> 108 = 77 + b
Take 77 from both sides
==> 108 - 77 = 77 - 77 + b
==> 31 = b
==> This means that the y intercept of this linear function is;
f(x) = 11x + 31
or
y = 11x + 31
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Brainliest to best answer
7) ∠EFG = 88 degree
8) DC and AB are parallel to each other.
AE and AB are perpendicular to each other
CG and AB are perpendicular to each other.
9) ∠ACD = 102 degree
What do you mean by co interior angle?
Co-interior angles, or consecutive interior angles, are two angles on the same side of a transverse line. Co interior angles are interior angles that add up to 180 degrees. This means that the sum of the two interior angles on the same side of the horizontal side are complementary.
7) Given :
∠EFG = 32 degree
∠GFH = 56 degree
∠EFG = ∠EFG + ∠GFH = 32 + 56 = 88 degree
Therefore, ∠EFG = 88 degree
8) DC and AB are parallel to each other.
AE and AB are perpendicular to each other
CG and AB are perpendicular to each other.
9) As AB and CD are parallel to each other therefore , ∠BAC and ∠ACD are cointerior angle and sum of co interior angles is 180 degree.
6x + 6 + 9x - 6 = 180
15x = 180
x = 180/15 = 12
∠ACD = (9x - 6) degree = 9(12) - 6 = 108 - 6 = 102
Therefore, ∠ACD = 102 degree
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If a sample is selected using random sampling methods, the primary reason that the sample mean might be different from the corresponding population mean is that the sample might be biased.
True
False
The given statement is false. If a sample is selected using random sampling methods, the primary reason that the sample mean might be different from the corresponding population mean is not that the sample might be biased.
Because random sampling ensures that results obtained from the sample should approximate what would have been obtained if the entire population had been measured. And the simplest random sample allows all the units in the population to have an equal chance of being selected. In this case, the sample might not be biased.
What is random sampling method?Random sampling is a part of the sampling technique where each sample has an equal probability of being chosen. A sample chosen randomly is meant to be an unbiased representation of the total population.
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A Question 9 (2 points) Retake question
Evaluate the function f(x), if f(x) = 4x - 2, what is the value of f(3)?
Enter your answer in the box below.
f(3) =
A
A Question 10 ( 2 points) Retake question
A function f(x) is graphed on the coordinate plane. What is the function rule in slope-intercept form?
- Rule written in function notation (1 point)
- Correct slope and intercept (1 point)
Suppose that the functions g and f are defined as follows.
g(x)=(x+6)(x+6)
f(x)=-6 x+7
(a) Find g/f
(b) Find all values that are NOT in the domain of g/f}. If there is more than one value, separate them with commas.
By using the concept of function, it can be calculated that-
a) [tex]\frac{g}{f}(-4) = \frac{4}{31}[/tex]
b) The point [tex]\frac{7}{6}[/tex] is not in the domain of [tex]\frac{g}{f}[/tex]
What is a function?
A function from A to B is a rule that assigns to each element of A a unique element of B. A is called the domain of the function and B is called the codomain of the function.
There are different operations on functions like addition, subtraction, multiplication, division and composition of functions.
Here,
a) The given functions are -
g(x) = (x + 6)(x + 6)
f(x)= -6x+7
[tex]\frac{g}{f}(x) = \frac{g(x)}{f(x)} = \frac{(x+6)(x+6)}{-6x+ 7} = \frac{(x+6)^2}{-6x + 7}[/tex]
[tex]\frac{g}{f}(-4) = \frac{g(-4)}{f(-4)} = \frac{(-4+6)^2}{-6(-4) + 7} = \frac{4}{31}[/tex]
b) [tex]\frac{g}{f}(x)[/tex] is not defined if -6x + 7 = 0
[tex]\frac{g}{f}(x)[/tex] is not defined if [tex]x = \frac{7}{6}[/tex]
So the point [tex]\frac{7}{6}[/tex] is not in the domain of [tex]\frac{g}{f}[/tex].
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Consider goods and that are perfect substitutes. The original prices were $10 and $9 respectively.
His income is $720. If one day the price of is 8$, what will happen
a. The quantity of becomes 90 due to income
effect.
b. The quantity of is 80 due to substitution effects
will grow to
c. The quantity of is 90 due to substitution effects
will grow to
d. The quantity of is 80 due to substitution effects
will grow to
e. The above answers are incorrect
Answer:
The above answers are incorrect.
Step-by-step explanation:
If the price of one of the goods decreases, the quantity demanded of that good will increase due to the substitution effect. This means that the consumer will choose to buy more of the cheaper good and less of the more expensive good. The income effect may also come into play, as the consumer now has more disposable income due to the lower price of one of the goods. However, it is not possible to determine the exact quantity of each good that the consumer will purchase without further information.
In this case, if the price of one of the goods decreases from $10 to $8, the consumer will likely purchase more of that good and less of the other good, which is a substitution effect. The income effect may also come into play, as the consumer now has more disposable income due to the lower price of one of the goods. However, it is not possible to determine the exact quantity of each good that the consumer will purchase without further information.
Therefore, the correct answer is e. The above answers are incorrect.
on average, the number of days it takes for a caterpillar to become a butterfly is 15 days with a standard deviation of 3.5 days.
If there are 10000 caterpillars at a sanctuary, how many out of the 10000 would you expect to become a butterfly in 17.8 days or more?
2,200 caterpillars are expected to become a butterfly in 17.8 days or more.
Step-by-step explanation:1. Find the Z value of 17.8.Formula: Z= (x-bar-mean)/σ: where x-bar is the score to which we are calculating a Z value; mean is just the arithmetic mean of the sample or population, and σ is the standard deviation of the sample or the population. Check attached image 1 below.
Substitute and calculate:
[tex]Z=(17.8-15)/3.5\\\\ Z=0.8[/tex]
2. Find the probability.For this solution, we are going to b e using Microsoft Excel's tools to calculate the probabilities. Check attached image 2.
[tex]IP(Z\leq 17.8)=0.7881[/tex]
This is the probability that any caterpillar becomes a butterfly in 17.8 days or less. This is how Microsoft Excel calculates probabilities for default. Now, in order to get the probability that the problem asks for (17.8 days or more) we just need to do the following operation:
[tex]1-0.778=0.222[/tex]
3. Calculate the amount of caterpillalrs.[tex](0.222)(10,000)=2,220[/tex]
4. Conclude.2,200 caterpillars are expected to become a butterfly in 17.8 days or more.