The conversion factor to use depends on the type of angle tat is to be converted
How do you know which conversion factor to use?From the question, we have the following parameters that can be used in our computation:
Conversion factors = xrad/180 or 180/x rad
The conversion factor to use depends on the type of angle tat is to be converted
Take for instance, we use 180/x rad from radians to degree and the other from degree to radians
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Can some help me with the answer
The domain of the composite function (f o g)(-5) for f(x) = 4x + 8 and g(x) = x² + x is equal to 88.
What is composite functionA function is composite when the co- domain of the first mapping is the domain of the second mapping
We shall evaluate the domain of the function (f o g)(-5) as follows:
(f o g) = 4(x² + x) + 8
(f o g) = 4x² + 4x + 8
(f o g)(-5) = 4(-5)² + 4(-5) + 8
(f o g)(-5) = 100 - 20 + 8
(f o g)(-5) = 88
Therefore, the domain of the composite function (f o g)(-5) for f(x) = 4x + 8 and g(x) = x² + x is equal to 88.
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the vector a2 is in w if and only if a2 can be written in the form c1a1 c2a2 c3a3 with
Vector a2 is in the subspace spanned by vectors a1, a2, and a3 if it can be written as a linear combination of these vectors.
What is vector ?
A vector is a quantity or phenomenon that has two independent properties: magnitude and direction. The term also denotes the mathematical or geometrical representation of such a quantity. Examples of vectors in nature are velocity, momentum, force, electromagnetic fields and weight.
Let W be a subspace of a vector space V and let a1, a2, and a3 be vectors in V. The vector a2 is in the subspace W if and only if it can be written as a linear combination of the vectors a1, a2, and a3. That is, there exist scalars c1, c2, and c3 such that:
a2 = c1 * a1 + c2 * a2 + c3 * a3
This equation can be written in matrix form as:
[a2] = [a1 a2 a3] * [c1; c2; c3]
where [a2] is the column vector representation of a2, [a1 a2 a3] is the matrix with a1, a2, and a3 as columns, and [c1; c2; c3] is the column vector of scalars c1, c2, and c3.
Vector a2 is in the subspace spanned by vectors a1, a2, and a3 if it can be written as a linear combination of these vectors.
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Solve using elimination.
–3x + 10y = –7
–3x + 4y = –19
Answer:
Approximately 6.78
Step-by-step explanation:
–3x + 10y = –7 - - - - - - > (1)
–3x + 4y = –19 - - - - - - > (2)
(1) - (2) Because if same sign then you have subtract to cancel out the equal numbers therefore - 3x and - 3x is cancelled out
6y = +2
y = 2 ÷ 6
y = 1/3
Then to find the value of x substitute value of y
-3x + (4 × 1/3) = - 19
-3x + 4/3 = - 19
- 3x = - 19 - 4/3
- 3x = - 61/3
x = ( - 61/3 ÷ -3)
x = 6.78
right ascension 15 06 53.62 declination 62 20 10.0 1
The celestial coordinates of the given point are (0.92868, 0.36983, 0.04921).
The right ascension and declination of a particular point in the sky can be used to calculate its corresponding celestial coordinates. Right ascension (RA) is measured in hours, minutes and seconds, while declination (Dec) is measured in degrees, minutes and seconds.
The RA of the given point is 15 h 06 m 53.62 s. This can be converted to degrees by multiplying by 15. The result is 225.1045 degrees. The Dec of the given point is 62° 20' 10.0" which can be converted to radians by multiplying by pi/180. The result is 1.08269 radians.
The celestial coordinates can then be calculated using the formula:
sin(RA)cos(Dec) = sin(225.1045)*cos(1.08269) = 0.92868
cos(RA)cos(Dec) = cos(225.1045)*cos(1.08269) = 0.36983
sin(Dec) = sin(1.08269) = 0.04921
Therefore the celestial coordinates of the given point are (0.92868, 0.36983, 0.04921).
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For the function shown below, the definite integral integral_0^10 f(x) dx is closest to which of the following? a.-8 b.4 c.-4 d.0 e.8
The provided function's definite integral from 0 to 10 is closest to 4.
The area of each zone that the function, the x-axis, and the two vertical lines at x = 0 and x = 10 bounds is added to form the definite integral of the function. The definite integral that results from adding up each of these areas is the one that is closest to 4. The area of the region above the x-axis is larger than the area of the region below the x-axis, which explains this. The area of the region above the x-axis is higher than the area below the x-axis because the function is rising across the interval. The overall area is closer to 4 since the area of the region below the x-axis is negative. As a result, 4 is the closest value for the definite integral of the 0–10 function.
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a continuous probability distribution that is useful in describing the time, or space, between occurrences of an event is a(n) probability distribution. a. normal b. uniform c. exponential d. poisson
A continuous probability distribution that is useful in describing the time, or space, between occurrences of an event, is an exponential probability distribution.
The probability density function or pdf of the exponential distribution is given by the formula
[tex]$$f(x) = \begin{cases} \lambda e^{-\lambda x} & \text{for } x \ge 0 \ 0 & \text{otherwise} \end{cases}$$[/tex]
where λ is the rate parameter and e is the natural logarithm base.
The pdf gives the probability distribution of a random variable x, which represents an exponential distribution.
The exponential distribution is a continuous probability distribution that simulates the interval between events with an average occurrence rate that is constant.
In this distribution, the likelihood that an event will occur in the future is independent of when that event occurred in the past
The time interval between customers joining a line, the interval between device failures, or the separation between two places in space are all frequently modeled using the exponential distribution.
The rate parameter, which denotes the average number of events per unit of time or space, is what defines the exponential distribution.
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ZA and ZB are vertical angles. If mA = (8x 23)° and m/B = (6x - 5)°, then find the measure of ZA.
The numerical measure of angle A is 49 degrees.
What is the measure of angle A?Vertical angles are simply angles that are opposite one another when two starlight lines cross. They are congruent.
Given the data in the question;
∠A and ∠B are vertical angles
mA = ( 8x - 23)° mB = ( 6x - 5)°Numerical value of angle A = ?Since ∠A and ∠B are vertical angles and vertical angles are congruent,
∠A = ∠B
(8x - 23)° = (6x - 5)°
Solve for x
8x - 23 = 6x - 5
8x - 6x = -5 + 23
2x = 18
x = 18/2
x = 9
Now, the numerical value of angle A will be;
mA = ( 8x - 23)°
Plug in x = 9
mA = ( 8(9) - 23)°
mA = ( 72 - 23)°
mA = 49°
Therefore, the measure of mA is 49°.
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Two teams need to raise $100 each for their end-of-the-year field trips. Team A wants to sell popcorn at the Spring Fling Carnival, and Team B wants to sell cotton candy. It costs $15 to rent a popcorn machine and it costs $25 to rent a cotton candy maker. The cost of additional supplies for the popcorn is $0.05 per bag. The additional cost for the cotton candy is $0.10 per stick. Team A will sell the bags of popcorn for $0.50 each. Team B will sell the cotton candy for $0.75 per stick.
What is the least number of items Team B will need to sell to avoid losing money?
Team B will need to sell at least 192 candies to avoid losing money.
What is a linear equation?When an algebraic equation is graphed, it always results in a straight line since each term in a linear equation has an exponent of 1. For this reason, it is referred to as a "linear equation."
There are both one-variable and two-variable linear equations.
Given total amount to be raised by each team is $100,
Team B wants to sell cotton candy,
rent of candy machine = $25
total cost to be earned for team B = $100 + $25 = $125
let the number of candies sold be x
cost used in candy sticks = $0.10 per stick
cost used in x candy sticks = $0.10x
the selling price of each candy = $0.75
the selling price of x each candy = $0.75x
total gain = $0.75x - $0.10x
total gain = $0.65x
minimum candies to be sold for no loss
$0.65x = $125
x = 125/0.65
x = 192.30
x = 192
Hence for no loss, at least 192 candies are to be sold.
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he amygdala is a brain structure involved in the processing and memory of emotional reactions.
In a research project, subjects were shown emotional video clips. Then they had their brains scanned with position emission tomography (PET), and their memory of the clips was assessed quantitatively.
The data will be used to investigate whether there is an association between relatively amygdala activity and memory score.
What would the test statistic be, the null hypothesis, and the type of test.
The test statistic be Pearson's correlation test.
What is Null hypothesis ?
The null hypothesis assumes that any difference between the selected attributes in a set of data is attributable to chance.
The test statistic could be Pearson's correlation coefficient, which measures the linear association between two continuous variables (here, amygdala activity and memory score).
The null hypothesis would be that there is no association between amygdala activity and memory score, which can be represented as:
H0: r = 0
The type of test would be a Pearson's correlation test, which is a parametric test that assesses the strength and direction of the linear relationship between two continuous variables.
Hence, The test statistic be Pearson's correlation test.
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Now examine the lower panel (butterflies), where the curve continues to rise linearly. What does this indicate about the brocesses structuring the butterfly community? It suggests that the communities are unsaturated and that the size of the regional pool determines local species richness. It suggests that the communities are becoming saturated and that local processes are likely becoming increasingly important. It does not tell us anything about the relative importance of the regional species pool and local interactions.
It suggests that the communities are unsaturated and that the size of the regional pool determines local species richness.
The correct option is (A)
Now, According to the question:
This suggests that the processes structuring the butterfly community are likely related to the presence and abundance of resources such as food plants and suitable habitat for the butterflies. As the number of individuals in the community increases, the number of different species that can be supported also increases, resulting in a linear relationship between the two. Additionally, this indicates that the butterfly community is likely experiencing a relatively stable and predictable environment, where resources are available to support a diverse population of butterflies.
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The complete question in the form is:
Now examine the lower panel (butterflies), where the curve continues to rise linearly. What does this indicate about the processes structuring the butterfly community?
(A) It suggests that the communities are unsaturated and that the size of the regional pool determines local species richness.
(B) It suggests that the communities are becoming saturated and that local processes are likely becoming increasingly important.
(C) It does not tell us anything about the relative importance of the regional species pool and local interactions.
A construction project calls for attaching plywood to floor joists using either nails or screws . When screws are used, there must be at least 2 screws for every square foot of flooring . When nails are used, there must be at least 4 nails per square foot. A floor that was 144 square feet was constructed using a mixture of screws and nails. The worker has planned to use no more than 500 screws and nails combined . Can he complete 90 square feet of flooring with nails?
Yes, we may install 90 square feet of flooring with 360 nails, as the total number of nails and screws used shouldn't exceed 500.
what is unitary method ?The facility is a method to problem-solving and involves essentially figuring out the price of a single unit, following multiplication that value to figure out the desired value. Clearly explained, the unit method is employed to derive a single property value out of a specified multiple. For contrast, 40 pens should cost (400 rupees, which is equal to the cost among one pen. This procedure might be standardized. undivided nation. anything does indeed have a distinctive element. Its adjoint and reciprocal are equal in terms of mathematics (algebra), abstract algebra, mathematical analysis, or mathematics of matrices or operators.
given
Let x be the number of screws and y be the number of nails,
then the answer to the question is 500.
For 90 square feet, it takes
144 = (2x + 4y) nails, or
4 nails per square foot, for a total of 360 nails.
Yes, we may install 90 square feet of flooring with 360 nails, as the total number of nails and screws used shouldn't exceed 500.
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cual es el mayor numero de cuatro cifras que se puede formar de esta manera
1720
The largest digit number that can be formed from 1720 is 7210
What are integers?An integer is the number zero, a positive natural number or a negative integer with a minus sign. The negative numbers are the additive inverses of the corresponding positive numbers.
Examples of integers include -2, 567, -1000, 0, e.t.c
Numbers that can be formed from 1720 are:
1270,
1072,
1027
1207
7201
7102
7210
Among all the numbers , 7210 is the highest number that can be formed from 1720
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There are 50 cds if 30% of them are country music and 40% are pop music how many cds are other types of music
Answer:
15 CDs
Step-by-step explanation:
The total percentage of the CDs is 100% because it basically means all the CDs. Therefore, the percentages of types need to add up to 100%. If 30% are country and 40% are pop, 100 - 30 - 40 = 30% are other.
30% is equivalent to 30/100 or 0.3 when written as a decimal. You would then multiply this by the number of CDs to get the number of other CDs:
[tex]50 * 0.3 = 15[/tex]
Therefore, 15 CDs are other types of music
What is a congruent tile?
If a rigid motion of the plane—that is, a combination of rotations, translations, and reflections—can turn one tile into the other while without stretching or contracting, then two tiles are said to be congruent.
What is congruent ?
Congruent refers to having a precise match in size and shape. Even after the forms have been flipped, turned, or rotated, the shape and size ought to remain constant.
We are surrounded by tiling. Human nature makes us curious about how various small bits fit together when presented.
In the broadest sense, tiling simply refers to the process of breaking up a large area into several little parts (tiles) that seamlessly interlock one another.
Even human bodies, for instance, can be thought of as tilings with cells serving as the "tiles." The earth's surface is tiled by land ownership! There are tiles almost everywhere.
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use the definition of a limit to fill in the blanks and prove the statement below. lim x → 2 1 2 x + 2 = 3
The limit of 1/2x + 2 as x approaches 2 is equal to 3.
The definition of a limit states that as the x-value approaches a specific number, in this case 2, the y-value of the expression 1/2x + 2 approaches 3. The definition states that for any ε > 0, there exists a δ > 0, such that for all 0 < |x - 2| < δ, we have |1/2x + 2 - 3| < ε. We can rearrange this to find that for all 0 < |x - a| < δ, we have |f(x) - L| < ε. This means that when x is close to 2, the difference between 1/2x + 2 and 3 is less than ε. Therefore, if we take ε to be very small, we see that 1/2x + 2 gets very close to 3, so the limit is 3. To prove this statement, we can calculate the y-value of the expression when x is equal to 1.5, 1.99, and 1.999. As we can see, the y-values get closer and closer to 3 as the x-values get closer and closer to 2. As x gets closer and closer to 2, the y-values of 1/2x + 2 get closer and closer to 3, so the limit of 1/2x + 2 as x approaches 2 is equal to 3.
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If AE=6x-55 and EC=3x-16, find DB quetion 8 6. 3 polygon and quadrilateral geometry
The length of side DB can be expressed as [tex]\sqrt{ (15x - 55)(3x - 28).}[/tex]
To solve this, we can use the Pythagorean theorem:
[tex]DB^2 = AE^2 + EC^2[/tex]
Substituting the values of AE and EC:
[tex]DB^2 = (6x - 55)^2 + (3x - 16)^2[/tex]
[tex]DB^2 = 36x^2 - 720x + 3025 + 9x^2 - 96x + 256[/tex]
[tex]DB^2 = 45x^2 - 816x + 3281[/tex]
[tex]DB =[/tex] [tex]\sqrt{ (15x - 55)(3x - 28).}[/tex]
Key points:
The Pythagorean theorem states:
In a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.Symbolically, this can be expressed as [tex]a^2 + b^2 = c^2[/tex], where c is the length of the hypotenuse, and a and b are the lengths of the other two sides.The theorem can be used to find the length of one side of a right triangle if the lengths of the other two sides are known.It is named after the ancient Greek mathematician Pythagoras, who is credited with its discovery and proof.The theorem has many applications in mathematics, physics, engineering, and construction, among others.Learn more about the Pythagorean theorem here:
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The complete question is:
In a quadrilateral ABCD, the length of sides AB and CD are equal and measure x units. If AE = 6x - 55 and EC = 3x - 16, find the length of side DB.
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Mr. Autin who work in an office in the city, pend 2/5of hi alary on food and
end 2/3 of the remaining amount to hi wife. (i) What fraction of hi alary remain after he ha pent for hi food?
(ii) What fraction of hi alary doe he end hi wife?
(iii) What fraction of hi alary i left over after thee expene are met?
Fraction amount left 21/50
What is fraction?A fraction is a part of a whole. In arithmetic, the number is expressed as a quotient, in which the numerator is divided by the denominator. In a simple fraction, both are integers. A complex fraction has a fraction in the numerator or denominator. In a proper fraction, the numerator is less than the denominatorIn Maths, there are three major types of fractions. They are proper fractions, improper fractions and mixed fractions. Fractions are those terms which have numerator and denominator. Based on these two terms we define its types.In Maths, a fraction is used to represent the portion/part of the whole thing. It represents the equal parts of the whole. A fraction has two parts, namely numerator and denominator. The number on the top is called the numerator, and the number on the bottom is called the denominator.
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2( T + 1) = 10
thank u
T=
Answer: T=4
Step-by-step explanation:
Good evening.
The first thing you want to do is distribute the 2.
[tex]2t+2=10[/tex]
Then, we need to subtract the 2 on both sides.
[tex]2t=8[/tex]
Then we divide both sides by 2, giving us the ultimate answer of T=4.
[tex]t=4[/tex]
A mass of 6.005 g of carbon contains
The 6.005 g of carbon contains 0.5000 moles of C. option C
What is the mole?The mole is a unit of measurement in chemistry used to quantify the amount of a substance. One mole of a substance contains Avogadro's number of entities of that substance. Avogadro's number is defined as 6.022 x 10^23 entities per mole and is a fundamental constant in chemistry.
The mole is used to convert the amount of a substance in mass or volume to the number of entities (such as atoms, molecules, or ions) of that substance. The mole is useful in chemical reactions, where it provides a convenient way to express the amounts of reactants and products involved in a reaction.
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How do I solve this to find the points?
Answer:
Step-by-step explanation:
4x+5y=15
-4x. -4x
5y=-4x+15
divide by 5 on both sides
y = 4/5x+3
Two points would be : (0,3) & (7,5)
extra : 4/5 means on the graph you go up 4 spaces, and to the right 5 spaces, in reverse you would go down 4 spaces and 5 spaces to the left
hope this helped =)
-YinAhara
A group of students was surveyed in a middle school class. They were asked how many hours they work on math homework each week. The results from the survey were recorded.
Number of Hours Total Number of Students
0 1
1 8
2 2
3 5
4 9
5 7
6 3
Determine the probability that a student studied for exactly 1 hour. Round to the nearest hundredth.
0.03
0.23
0.30
0.77
The probability that a student studied for 5 hours is 0.23.
What is the probability?Probability refers to the likelihood or chance that an expected success is observed over many possible observations, outcomes, or events.
Probability can be expressed as a percentage, decimal, or fraction.
here, we have,
In this situation, the probability that a student studied for 5 hours is the quotient of the division of the number of students who studied for 5 hours and the total number of students who studied.
Number of hours Total number
of students
0 1
1 3
2 2
3 5
4 9
5 7
6 3
Total 30
Probability a student studied 5 hours = 0.23 (7/30)
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Please help need this done asap
A. KP = ST is given
B. Given as PR = TV is known
C. KP + PR = ST + TV using the addition property.
D. Segment addition in KP + PR = KR
E. ST + TV = SV
F. Segment addition has obtained this answer
G. KR = SV by substitution property
The solution has been obtained by using the concept of mathematical reasoning.
What is mathematical reasoning?
In mathematics, reasoning entails making logical deductions from data or presumptions.
A. For this, we are stated a reason that it is given.
So, the statement is KP = ST.
B. We are given the statement as PR = TV
The reason is that it is given.
C. For this, we are stated a reason that it is obtained by addition property.
So, the statement is KP + PR = ST + TV.
D. We are given the statement as KP + PR = KR
The reason is that it is obtained by segment addition.
E. ST + TV = SV is the statement
F. The reason for the statement is that it is obtained by segment addition.
G. For this, we are stated a reason that it is obtained by substitution property.
So, the statement is KR = SV.
Hence, the statements and their respective reasons have been arranged.
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How much is 37.7 C in F?
37.7 °Celsius = 99.8 °Fahrenheit. Your normal body temperature is approximately 37°C. A fever is usually when your body temperature is 37.8°C or higher.
Define Fahrenheit?Fahrenheit is a temperature scale on which water freezes at 32 degrees and boils at 212 degrees. It is represented by the symbol ° F. By mid-morning, the temperature had risen above 100 degrees Fahrenheit. Fahrenheit is also a noun.The conversion formulas we use are the same ones found in most textbooks. To convert temperatures from Fahrenheit to Celsius, subtract 32 and multiply by.5556 (or 5/9). To convert degrees Celsius to Fahrenheit, multiply by 1.8 (or 9/5) and add 32.Different systems were developed as a result of different scientists' tools, backgrounds, and goals. The Celsius scale is named after Swedish astronomer Anders Celsius, who invented it in 1742.To learn more about Fahrenheit refer to:
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When the p-value is used for hypothesis testing, the null hypothesis is rejected ifa)p-value ≤ αb)α < p-valuec)p-value ≥ αd)p-value = 1 - α
If he p-value is used for hypothesis testing , then the Null Hypothesis is rejected if (a) p-value ≤ α .
In a hypothesis testing, the p-value represents the probability of observing a test statistic as extreme or more extreme than the one observed, provided that the null hypothesis is True.
The significance level, represented by "α" , is a pre-determined threshold which determines the level of evidence required to reject the null hypothesis.
If the p-value is less than or equal to α, this indicates that the observed test statistic is sufficiently unlikely to occur under the null hypothesis, and therefore the null hypothesis is rejected.
Therefore , the Null hypothesis is rejected if (a) p-value ≤ α .
The given question is incomplete , the complete question is
When the p-value is used for hypothesis testing, the null hypothesis is rejected if
(a) p-value ≤ α
(b) α < p-value
(c) p-value ≥ α
(d) p-value = 1 - α
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The correct answer is a) p-value ≤ α. In hypothesis testing, the null hypothesis is typically assumed to be true initially. The p-value is used to determine the probability of observing a test statistic as extreme or more extreme than the one obtained from the data, assuming that the null hypothesis is true.
The significance level (α) is chosen beforehand and represents the maximum acceptable probability of rejecting the null hypothesis when it is actually true.
If the p-value is less than or equal to the significance level (p-value ≤ α), then the result is considered statistically significant and the null hypothesis is rejected. This implies that the observed effect is unlikely to have occurred by chance alone and that the alternative hypothesis is more likely to be true.
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the marginal benefit is the ___________________benefit associated with an increase in the activity.
The marginal benefit is the additional number of benefit associated with an increase in the activity.
The marginal benefit is the amount of benefit that is gained from a one-unit increase in the activity, and is measured by the additional satisfaction or utility that the individual or organization receives from the increase in the activity.
The marginal benefit is the additional number of benefit associated with an increase in the activity.
The marginal benefit is the additional benefit or satisfaction that is derived from an increase in the activity or product. It is the amount of pleasure or utility that a person or organization receives from the marginal increase in the activity or product. This is measured by the additional revenue, utility, or satisfaction that is experienced from the increase in activity. Marginal benefit can also refer to the additional money, time, or other resources that are invested in an activity or product, as well as the amount of value that is gained from the increase in the activity or product.
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Someone help I need this because I’m kinda failing math
The value function for g(7), g(0) and g(-5) are 14, 7 and 2 respectively.
What is the function?Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.
From the graph, we have y-intercept (0, 7) and slope (m)=3/3 =1
Here, y=x+7
g(x)=x+7
g(7)=7+7
g(7)=14
g(0)=0+7
g(0)=7
g(-5)=-5+7
g(-5)=2
g(x)=3
So, x+7=3
x=-4
Therefore, the value function for g(7), g(0) and g(-5) are 14, 7 and 2 respectively.
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Hanz and Franz are in a shooting competition. The object of the match is to be the first to hit the bull's eye of a target 100 feet away. The two opponents alternate turns shooting, and each opponent has a 40% chance of hitting the bull's-eye on a given shot. If Hans graciously allows Franz to shoot first, what is the probability that Hans will win the competition and take no more than three shots? HELP FAST
The probability of Hans winning the competition and taking no more than three shots is 0.784.
How to find the possibility?To calculate the probability that Hans wins after taking no more than 3 shots, we can use the cumulative distribution function (CDF) of the binomial distribution.
The CDF gives the probability of getting k or fewer successful shots in n trials, with a success probability of p.
In this case, n = 3, p = 0.4, and k = 2 (since Hans wins if he hits the bull's-eye with 2 shots or fewer).
Using the cumulative binomial distribution formula, the probability of Hans winning the competition and taking no more than three shots is 0.784.
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Allison has a loyalty card good for a discount at her local hardware store. The item she wants to buy is priced at $36, before discount and tax. After the discount, and before tax, the price is $30. 96. Find the percent discount
the percent discount is 14% when the original price and new price are given $36 and $30.96.
Given that,
Original price of item = $36 (that is before discount and the tax)
Price after discount = $30.96
Let the percentage discount be = x
A discount is the reduction of either the monetary amount or a percentage of the normal selling price of a product or service.
To get the percent discount :
x = (original cost - new price)/original price
x = (36 - 30.96)/36
x = 5.06/36
x = 0.14
Percentage discount x , in percentage = 0.14 x 100
Percentage discount = 14%
therefore, the percent discount is 14%
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Find the area of △ABC. Where: A=(2,−1,−1), B=(1,−3,2), C=(2,−3,0)
The area of △ABC is equal to 6√6 / 2.
What is the area of triangle 3-dimensional space?
The area of a triangle in 3-dimensional space can be found using the cross product of two vectors formed by the three vertices of the triangle.
The formula for the area of a triangle with sides u and v is given by:
Area = |u × v| / 2
Where × represents the cross product of the two vectors u and v, and |•| represents the magnitude of the resulting vector.
To find the area of △ABC, we can form the vectors AB and AC and find their cross-product:
AB = B - A = (1 - 2, -3 - (-1), 2 - (-1)) = (-1, -2, 3)
AC = C - A = (2 - 2, -3 - (-1), 0 - (-1)) = (0, -2, 1)
Cross product of AB and AC: AB × AC =
| i j k |
|-1 -2 3 |
| 0 -2 1 |
= (6, 6, -6)
Area of △ABC = |AB × AC| / 2 = |(6, 6, -6)| / 2 = √(6^2 + 6^2 + (-6)^2) / 2 = 6√6 / 2
Hence, the area of △ABC is equal to 6√6 / 2.
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Consider the initial value problem y' = 3y^2, y(0) = y0. What value(s) of y0| will the solution have a vertical asymptote at t = 2 and a thinterval of existence - [infinity]
Consider the initial value problem y' = 3y^2, at the value of y(0) = 1/6 will the solution have a vertical asymptote at t = 2.
The differential equation is y'=3y^2.
We can write this equation as:
dy/dt = 3y^2
dy/y^2 = 3dt
Now integrating on both side
[tex]\int \frac{dy}{y^2} = \int 3dt[/tex]
After integrating we get,
- 1/y = 3t + c
Multiply by y on both side, we get
(3t + c)y = -1
Divide by (3t + c) on both side, we get
y = -1/(3t + c).................(1)
Since there is vertical asymptote at t = 2
So 3t + c = 0 at t = 2
3(2) + c = 0
6 + c = 0
Subtract 6 on both side, we get
c = -6
Put the value of c in equation 1
y = -1/(3t - 6)
At t = 0
y(0) = -1/(3(0) - 6)
y(0) = 1/6
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