a. A function to model taking the 10% discount will be 0.9x.
b. A function to model taking the 25% discount first will be 0.75x.
c. If I was an employee, I'll prefer the 25% discount.
How to illustrate the functionFrom the information given, the store is offering a 10% discount on all items and in addition, employees get a 25% discount.
Let the price of the goods be given as x.
A function to model taking the 10% discount will be:
= x - (10% × x)
= x - 0.1x
= 0.9x
A function to model taking the 25% discount first will be:
x - (25% × x)
= x - 0.25x
= 0.75x
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Determine whether the statement below is true or false. Justify the answer The points in the plane corresponding to [-2 5] and [-5 2] lie on a line through the origin. Choose the correct answer below. A. The statement is false [-2 5] and [-5 2] correspond to arrows that meet at right angles. B. The statement is false. If [-2 5] and [-5 2] were on the line through the origin, then [-5 2] would be a multiple of [-2 5] which is not the case. C. The statement is true [-2 5] and [-5 2] correspond to arrows pointing in precisely opposite directions and so are on the same line through the origin. D. The statement is true [-2 5] and [-5 2] are on a line through the origin since [-5 2] is a positive multiple of [-2 5].
A. The statement is false. [-2 5] and [-5 2] do not lie on a line through the origin, as they do not have the same slope. The arrows they correspond to meet at right angles, which means they form a line perpendicular to the origin.
B. Correct! The statement is false. [-2 5] and [-5 2] do not lie on a line through the origin, as they do not have the same slope. The arrows they correspond to meet at right angles, which means they form a line perpendicular to the origin.
C. Correct! The statement is true. [-2 5] and [-5 2] correspond to arrows pointing in precisely opposite directions and so are on the same line through the origin.
D. Incorrect. The statement is false. [-2 5] and [-5 2] do not lie on a line through the origin, as they do not have the same slope. The arrows they correspond to meet at right angles, which means they form a line perpendicular to the origin.
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At the fair, Lisa stumbled upon a game called Cool Down. In this game, there is a container with
8 cups of hot water (at a temperature of 50ºC). The object is to determine how many cups of
cold water (at a temperature of 20ºC) to add to the container to reduce the temperature to 40ºC.
a. Find an equation expressing the temperature (in ºC) of the water in the container as a
function of the volume (cups) of cold water added.
Equation: ________________________
b. Explain how you obtained the equation in part (a) above.
c. Use your equation to determine the amount of cold water that must be added to reduce the
temperature to 40ºC.
Answer:
t = (400 + 20c)/(8+c)weighted sum of temperatures4 cupsStep-by-step explanation:
You want an equation for the temperature of 8 cups of hot (50 °C) water combined with c cups of cold (20 °C) water, along with an explanation of it. Then you want the number of cups required to reduce the temperature to 40 °C.
(a) EquationAssuming constant heat capacity and volume as a function of temperature, the temperature of the mix will be the weighted average of the temperatures of the contributors. That is c cups of water at 20 °C combined with 8 cups of water at 50 °C will have a temperature (t) of ...
t = (20c +8(50))/(c+8)
t = (20c +400)/(c +8)
(b) ExplanationThe thermal energy contained in the water is assumed to be jointly proportional to its volume and its temperature. The combined thermal energy of the mixture will be the total of that of its contributors.
That is, the temperature of the mix is the weighted sum of the temperatures of the contributors, the weights being their respective volumes.
(c) 40°The value of c for a temperature of 40 °C is ...
40 = (20c +400)/(c+8)
2(c +8) = c +20) . . . . divide by 20, multiply by (c+8)
2c +16 = c +20 . . . . eliminate parentheses
c = 4 . . . . . . . . . . . . subtract (c+16)
4 cups of cold water must be added to reduce the temperature ot 40 °C.
(a) t = (400 + 20c)/(8+c)
(b)weighted sum of temperatures
(c) 4 cups
What is an equation?An equation is a statement that asserts the equality of two expressions, the expressions are written one on each side of an '=' equal to sign.
Let t be the temperature of water.
Let c be the number of cold cup of water at 20°C
(a)c cups of water at 20 °C combined with 8 cups of water at 50 °C will have a temperature (t) of
[tex]t= \frac{20c+8*50}{c+8}[/tex] --------(1)
(b)The temperature of the mix is the weighted sum of the temperatures of the contributors, the weights being their respective volumes.
(c)The value of c for a temperature of 40 °C is
40 = (20c +400)/(c+8)
2(c +8) = c +20) . . . . divided by 20, multiply by (c+8)
2c +16 = c +20 . . . . eliminate parentheses
⇒ c = 4
Hence, the required equation is [tex]t= \frac{20c+8*50}{c+8}[/tex] and for part (c) 4 cups.
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Which equation is an equation of a circle with a radius of 4 and its center is at (3, -2)?
(x - 3)2 + (y + 2)2 = 4
(X + 3)2 + (y - 2)2 = 16
(x 3)2 + (y - 2)2 = 4
(x - 3)2 + (y + 2)2 = 16
The answer to the query is that option D) is correct. A circle with the radius if 4 and a point at (3, -2) has the following equation [tex](x - 3)^2 + (y + 2)^2 = 16[/tex]
What does a radius look like?Your youngster will get familiar with the term "radius" as they study circles. It speaks about the separation between any point on a circle's perimeter and its center (circumference). It crosses the center, by one of the circle's sides to the other, and is half the size of diameter.
The radius of a circle is the distance between the center to any location on the edge. The diameter and radius are inversely proportional, or 2r=d2 r=d. the section of a line that connects two locations on a circle chord.
The equation of a circle is
[tex](x-h)^2 + (y-k)^2 = r^2[/tex]
Where (h, k) is the circle's center and r is its radius.
The center is at (3, -2)
[tex](x-3)^2 + (y-(-2))^2 = 4^2[/tex]
[tex](x - 3)^2 + (y + 2)^2 = 16[/tex]
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The Complete Question :
Which equation is an equation of a circle with a radius of 4 and its center is at (3, -2)?
A. [tex](x - 3)^2 + (y + 2)^2 = 4[/tex]
B. [tex](x+ 3)^2 + (y - 2)^2 = 16[/tex]
C. [tex](x-3)^2 + (y - 2)^2 = 4[/tex]
D. [tex](x - 3)^2 + (y + 2)^2 = 16[/tex]
PLS HELP DUE RIGHT NOW ASAP!!!!!!
Answer:-4,-3
Step-by-step explanation:
-4 is lower then -3 and the arrow faces the x meaning it is lower than -3.
Need help for the question attached in the picture
The probabilities are given as follows:
a) At most 3.8 percent: 0.0455 = 4.55%.
b) At most 8 percent: 0.9382 = 93.82%.
c) Between 3.8 and 8 percent: 0.8927 = 89.27%.
How to obtain probabilities using the normal distribution?The z-score of a measure X of a variable that has mean symbolized by [tex]\mu[/tex] and standard deviation symbolized by [tex]\sigma[/tex] is obtained by the rule presented as follows:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score represents how many standard deviations the measure X is above or below the mean of the distribution, depending if the obtained z-score is positive or negative.Using the z-score table, the p-value associated with the calculated z-score is found, and it represents the percentile of the measure X in the distribution.The mean and the standard deviation for this problem are given as follows:
[tex]\mu = 6, \sigma = 1.3[/tex]
The probability of at most 3.8% is the p-value of Z when X = 3.8, hence:
Z = (3.8 - 6)/1.3
Z = -1.69
Z = -1.69 has a p-value of 0.0455.
The probability of at most 8% is the p-value of Z when X = 8, hence:
Z = (8 - 6)/1.3
Z = 1.54
Z = 1.54 has a p-value of 0.9382.
Hence the probability of a value between these two values is given as follows:
0.9382 - 0.0455 = 0.8927.
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If the line segment joining the points A (x1, y1) and B(x2, y2) is divided by a point P in the ratio 1 : k internally,then the coordinates of the point P are
If the line segment joining the points A (x1, y1) and B(x2, y2) is divided by a point P in the ratio 1 : k internally, then the coordinates of the point P are P[(1x₂ + kx₁)/(1 + k)], [(1y₂ + ky₁)/(1 + k)].
How to determine the coordinates of point P?In this scenario, we would use line ratio to determine the coordinates of the point P on the directed line segment that partitions the segment into a ratio of 1 to k.
In Mathematics, line ratio can be used to determine the coordinates of the point P and this is modeled by this mathematical expression:
P(x, y) = [(mx₂ + nx₁)/(m + n)], [(my₂ + ny₁)/(m + n)]
Substituting the given parameters into the line ratio formula, we have the following;
P(x, y) = [(1x₂ + kx₁)/(1 + k)], [(1y₂ + ky₁)/(1 + k)]
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The cam's mandible history is 100 page loose leaf history randomly mixed and its objective is to rearrange the pages on the right order. How many possibilities of combinations are there? And what's the probability of getting the story in the right order?
The possibilities of the combinations that are there for rearranging the pages in the right order are 100 !.
The probability of getting the story in the right order is 1 / 100 !.
How to find the combination ?There are 100 pages in the history text which means that when they are randomly mixed, each page could take a different position out of the 100 and so lead to a new combination.
The possibilities of combinations is therefore:
= n !
= 100 !
The probability that the story is in the right order will happen with only a single combination which means the probability is:
= Number of correct orders / Number of combinations
= 1 / 100 !
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Mr Saver invests $X at t = 0 in an account that pays a nominal rate of R convertible quarterly. The interest he earns during t = 0.5 to t = 1.5 is 1.0816 times the interest he earns during t = 0 to t = 1. Find the exact value of R.
Mr. Saver's nominal interest rate is 8%.
What is Percentage?percentage, a relative value indicating hundredth parts of any quantity.
Given that the interest he earns during t = 0.5 to t = 1.5 is 1.0816 times the interest he earns during t = 0 to t = 1. We can use this information to set up an equation as follows:
P(1+R/4)²=1.0816×P(1+R/4)
We can simplify this equation by canceling out the P and the (1+R/4) on the right side:
(1+R/4)=1.0816
We can then solve for R:
R/4=√1.0816-1
R=0.08 is the exact value of R.
Now multiply with 100
0.08×100=8%
Hence, Mr. Saver's nominal interest rate is 8%.
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6x+2y= −4 simplified all fractions
According to the problem the simplified form of the equation is x = -1/2 and y = -3.
What is equation?An equation is a mathematical statement that expresses the equality of two expressions by showing that they have the same value. Equations can be used to describe a variety of physical, chemical and biological processes. They are often used to solve problems in a variety of fields, including engineering, finance and physics.
6x + 2y = -4
This equation can be simplified by combining all like terms on one side of the equation and all constants on the other. In this case, we can combine the 6x and 2y terms to get 8x = -4. We can then divide both sides of the equation by 8 to get x = -1/2. Substituting this value into the original equation, we get 2y = -6. We can then divide both sides by 2 to get y = -3. Therefore, the simplified form of the equation is x = -1/2 and y = -3.
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An investor manages to earn the equivalent of 50/10 of his initial investment in the first year. During the second year it loses 30/10 part of it. However, for the third year the market fluctuations favor him and he returns to earn 200/10 parts of his initial investment. At the end of the year, how many parts of the initial investment have you managed to capture?
Answer: This investor has managed to earn 220/10 shares of his initial invention.
Step by step explanation:
Data for the fraction:
An investor manages to win = 50/10During the second year you lose = 30/10In the third year he wins again = 200/10In this problem we must apply the addition and subtraction of Fractions in order to obtain an answer about the parts of the initial investment that have been achieved. For this we pose the problem:
[tex]\bf \: \cfrac{50}{10} - \cfrac{30}{10} + \cfrac{200}{10} = \boxed{ \bf\frac{220}{10} }[/tex]
Rpt: This investor has managed to earn 220/10 shares of his initial invention.
Write this number in scientific notation.
.00000092
[?] ×
]
The number in scientific notation is 9.2 × 10^-7.
How to convert the numberFrom the question, we have the following parameters that can be used in our computation:
Number = .00000092
The number of points from the initial position to a point between 9 and 2 is -7
This means that the coefficient is 9.2 and the power of ten is -7
So, we have
9.2 × 10^-7.
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Answer:
10^(-7)
Step-by-step explanation:
put first non-zero number, then decimal, then rest of numbers as so
9.2
multiply by +/- depending on where decimal is
9.2*10^(-7)
so 10^(-7)
23. The escape velocity from the surface of the Moon is 2.4 × 10³ ms ¹.
(a)
An object is projected from the surface of the Moon with a speed
of 2.0 10³ ms ¹.
Calculate the maximum height reached above the Moon's surface.
The object will reach a maximum height of approximately -89,898.36 meters, or 89.9 kilometers, above the Moon's surface before it falls back down.
What do you mean by escape velocity?Escape velocity is the minimum speed an object must have in order to escape the gravitational pull of a celestial body, such as a planet or moon, and travel into space. It is calculated based on the mass and radius of the celestial body and the distance of the object from its surface. The greater the mass and radius of the celestial body, the greater the escape velocity.
The formula for escape velocity is given by v_escape = √(2GM/R), where G is the gravitational constant, M is the mass of the object, and R is the radius of the object.
In this case, v_escape = 2.4 × 10³ m/s and v_projected = 2.0 × 10³ m/s.
The maximum height can be calculated using the following formula:
h = (v_projected^2 - v_escape^2) / (2g), where g is the acceleration due to gravity.
Since the escape velocity is greater than the projected velocity, the object will not escape the Moon's surface and will eventually fall back down. The maximum height it reaches is given by:
h = (2.0 × 10³ m/s)^2 - (2.4 × 10³ m/s)^2 / (2 * 9.8 m/s^2) = (4.0 × 10^6 - 5.76 × 10^6) m / 19.6 = -1.76 × 10^6 m / 19.6 = -89,898.36 m.
The object will reach a maximum height of approximately -89,898.36 meters, or 89.9 kilometers, above the Moon's surface before it falls back down.
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Make x the subject of the formula:
4y = 4x - 6z/6
Making x the subject of the formula in this equation 4y = 4x - 6z/6 gives x = (24y + 6z)/4.
How to make x the subject of the formula?In this exercise, you are required to make "x" the subject of the formula in the given mathematical expression by using the following steps.
By multiplying both sides of the mathematical expression by 6, we have the following:
4y = (4x - 6z)/6
6 × 4y = (4x - 6z)/6 × 6
24y = 4x - 6z
By adding "6z" to both sides of the mathematical expression, we have the following:
24y + 6z = 4x - 6z + 6z
24y + 6z = 4x
By dividing both sides of the mathematical expression by 4, we have the following:
x = (24y + 6z)/4
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 Look at the steps for solving the equation and choose a true statement.
3x - 9x + 1 = 2(-3x + 1) - 1
-6x + 1 = -6x + 2 - 1
-6x + 1 = -6x + 1
O a
Ob
0 c
0 d
0 e
There is no way to know if there is a solution to this equation.
There are no solutions to the equation.
There are infinitely many solutions to the equation.
The only solution to the equation is -6.
The only solution to the equation is 1.
A finite arrangement of symbols that adheres to context-specific standards and is well-formed is referred to as a mathematical expression.
What is meant by equation?A mathematical expression is a finite combination of symbols that is well-formed in accordance with context-specific norms. In mathematics, an equation is an equality statement that includes one or more variables or unknowable quantities.
When two expressions in a variable (or variables) have the same value, the condition is said to be an equation. The equation's solution, or root, is the value of the variable for which the equation holds true. Even if the RHS and LHS are switched, an equation still holds true.
An equation is a mathematical statement that proves two mathematical expressions are equal in algebra, and this is how it is most commonly used. A sentence in math is called an equation.
Let the equations be
3x - 9x + 1 = 2(-3x + 1) - 1
-6x + 1 = -6x + 2 - 1
-6x + 1 = -6x + 1
Therefore, the correct answer is option There are infinitely many solutions to the equation.
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Find the linear function, f (x), passing through the points (-1,-5) and (-8,-5)
we could go ahead and check its slope and so forth, OR we can just take a peek that the y-coordinates are the same -5, hmmmm well, hell that's just a horizontal line, Check the picture below.
Which graph represents y= ^3 square root x + 2?
Answer:
cubic
Step-by-step explanation:
You are given the equation 13 = 2x + 5 with no solution set.
Part A: Determine two values that make the equation false.
Part B: Explain why your integer solutions are false. Show all work.
Answer:
Part A: x = 1, 2
Part B: 13 != 7, 13 != 9
Step-by-step explanation:
We pick x values that when plugged into the equation, creates a false statement.
x = 1
13 = 2(1) + 5
13 = 2 + 5
13 = 7
As you can see 13 does not equal 7
x = 2
13 = 2(2) + 5
13 = 4 + 5
13 = 9
As you can see 13 does not equal 9
HELP please i have 6 m more to do in 35ish minutes
Triangle AHIJ is theree-sided polygon where the measure of angle JHI is (3x + 28) degrees.
prove if 1-norm less than 2 norm less then infinty norm the there is no c such that inginity norm is less than c 1 norm
There does not exist a constant C > 0 such that p∞(v) ≤ Cp1(v) for all vectors v in V. Therefore, p1-norm < p2-norm < p∞-norm implies there is no c such that p∞-norm < c p1-norm.
Given two norms, p and q, on a vector space V, we say that p is less than q, written p ≤ q, if there exists a constant C > 0 such that for all vectors v in V,
p(v) ≤ Cq(v)
Now, let's consider the three norms:
The 1-norm: p1(v) = ∑|v_i|
The 2-norm: p2(v) = √(∑v_i^2)
The infinity-norm: p∞(v) = max{|v_i|}
We are given that p1(v) ≤ p2(v) for all vectors v in V and that p2(v) ≤ p∞(v) for all vectors v in V. We want to show that there does not exist a constant C > 0 such that p∞(v) ≤ Cp1(v) for all vectors v in V.
Suppose for the sake of contradiction that such a constant C does exist. Then, for any non-zero vector v in V,
p∞(v) ≤ Cp1(v)
max{|v_i|} ≤ C ∑|v_i|
Since v is non-zero, there exists an index i such that |v_i| > 0. We can divide both sides of the inequality by |v_i| to get:
1 ≤ C ∑|v_j| / |v_i|
Now, since p1(v) ≤ p2(v) for all vectors v in V, we have:
p1(v) = ∑|v_j| ≤ √(∑v_j^2) = p2(v)
So, we can substitute this into the inequality above to get:
1 ≤ C √(∑v_j^2) / |v_i| = Cp2(v) / |v_i|
Finally, since p2(v) ≤ p∞(v) for all vectors v in V, we have:
p2(v) / |v_i| ≤ p∞(v) / |v_i| = 1
So, we have reached a contradiction:
1 ≤ Cp2(v) / |v_i| ≤ C
This contradicts the assumption that C > 0, so there does not exist a constant C > 0 such that p∞(v) ≤ Cp1(v) for all vectors v in V. Therefore, p1-norm < p2-norm < p∞-norm implies there is no c such that p∞-norm < c p1-norm.
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An entry-level salary for teachers in Boston was $13,579 in 1981. According to the NEA, the average entry-level salary for Massachusetts had risen to $45,498 in 2017. What should the entry-level salary have been in 2017 if the 1981 figure was adjusted for inflation?
The entry-level salary for teachers in Boston in 2017 should have been $42,086 if adjusted for inflation using the Consumer Price Index.
What should the entry-level salary have been in 2017 if the 1981 figure was adjusted for inflation?This question is asking for a calculation of the real value of the 1981 entry-level salary for Boston teachers in 2017 dollars. This calculation requires the use of a “price index” to account for inflation and is known as “inflation adjustment” or “inflationary adjustment”.Inflation adjustment involves determining the purchasing power of a given amount of money in one year compared to another year. To calculate the amount of money needed to purchase the same amount of goods and services in 2017 as was purchased with $13,579 in 1981, the 1981 amount is multiplied by the ratio of the price index of 2017 to the price index of 1981.Using the Consumer Price Index (CPI), the price index of 2017 was 259.5 and the price index of 1981 was 82.4. Therefore, the inflation-adjusted entry-level salary for Boston teachers in 2017 would be $13,579 x (259.5/82.4) = $42,633. This is slightly lower than the actual average salary of $45,498 reported by the NEA.To learn more about inflationary adjustment refer to:
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It is estimated that each guest at a party will eat 2/3 pounds of chocolates. How many guests can be served with 6 pounds of chocolate?
Answer: 9 guest can be served.
Step-by-step explanation:
2/3 pounds of chocolate for each guest
6 pounds of chocolate can be served to
So let's do 6/ (2/3)
=6* 3/2
that will equal 9 guests
Please help me with this question.
7. The statement regarding the set is false.
8. The statement regarding the set is correct.
How to analyze the statements?In problem 7, we are given the subsets of a set, and then the statement is that the subset {a,e} is contained into the set S.
The subset {a,e} is not one element of the set S, which are a, ... {e, empty}, hence the statement is false.
In problem 8, we are given the union operation, which has the result given by the elements that belong to at least one of the sets.
The empty set belongs to set T, hence it belongs to the union of sets S and T, and thus the statement is correct.
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After a big snowfall, you take your favorite rocket‑powered sled out to a wide field. The field is 205 m across, and you know that your sled accelerates at a rate of 3.95 m/s2 when the rocket is on. How fast will the sled be moving when it is halfway across the field?
Answer:
Below
Step-by-step explanation:
Find time to get to 102.5 m (Half of the field)
d = 1/2 a t^2
102.5 = 1/2 * 3.95 t^2 shows t = 7.2 s
then v = at
= 3.95 * 7.2 = 28.5 m/s
Steve wants to take all of his 145 employees on a fishing trip. If each fishing boat holds 13 people, how many boats does Steve need to rent?
Answer:
Approximately 11 boats.
Step-by-step explanation:
To get this answer, we simply need to divide 145, which is the number of his employees, but 13, the amount of people each boat holds. You get the answer 11.1538462.
Answer:
12 Boats
Step-by-step explanation:
Since it given that;
Steve wants to take all of his 145 employees on a fishing trip.Each fishing boat holds 13 peopleAll we have to do is divide the total number of people by how much a fishing boats can hold.
Which is;
145/13
= 11.1538461538
So, we need 12 boats due to 145/13 = 11.15... because you can't cut a person in half. Thus, we need an extra boat to hold the extras.
RevyBreeze
How can consumers use their spending power to prevent cruelty to animals?
OA. Buy fair-trade coffee
OB. Eat less meat
OC. Purchase local vegetables
OD. Reduce plastic use
SUBMIT
Answer:
OC. Eat less meat
Step-by-step explanation:
Not really sure how this is math, but meat comes from butchered animals. Buying less meat means fewer animals are killed.
Which of the following statements are true? I. The sampling distribution of ¯x¯ has standard deviation σ /√n even if the population is not normally distributed. II. The sampling distribution of ¯x¯ is normal if the population has a normal distribution. III. When n is large, the sampling distribution of ¯x¯ is approximately normal even if the the population is not normally distributed. I, II, and III
All three statements are true. The sampling distribution of the sample mean has standard deviation σ/√n even if the population is not normally distributed.
The sampling distribution of the sample mean is normal if the population is normally distributed. Lastly, when the sample size is large, the sampling distribution of the sample mean is approximately normal even if the population is not normally distributed .
The sampling distribution of the sample mean is a probability distribution of the means of all possible samples of a given size from a given population. It is used to describe the behavior of the sample mean in relation to the population mean. The sampling distribution of the sample mean has a mean of μ (the population mean) and a standard deviation of σ/√n, where σ is the population standard deviation and n is the sample size
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slope =-2/5; y-intercept =0
Write the equation of the line in slope-intercept form.
Answer:
Step-by-step explanation:
Standard slope intercept equation is
[tex]y=mx+b[/tex]
where m is the slope and b is the intercept.
substitute the values given
[tex]y=-\frac{2}{5} x+0[/tex]
simplify
[tex]y=-\frac{2}{5} x[/tex]
Many students choose to take courses in statistics and computer science as elective. Suppose that in a certain university 41% take computer science, 48% take statistics, and 63% take at least one of these two courses. What is the probability a randomly selected student takes both a computer science and a statistics courses as elective? Round your answer to two decimal places.
The probability that a randomly selected student takes both computer science and statistics courses is 26%.
Let's call the event that a student takes a computer science course "C" and the event that a student takes a statistics course "S". We want to find the probability that a student takes both C and S, which can be written as P(C ∩ S).
The probability that a student takes at least one of these two courses can be written as P(C ∪ S), which is equal to 63%. This means that 63% of the students take either computer science or statistics, or both.
To find the probability that a student takes both courses, we can use the formula for the intersection of two events:
P(C ∩ S) = P(C | S) × P(S)
where P(C | S) is the probability that a student takes a computer science course given that they also take a statistics course. To find this value, we can use the formula:
P(C | S) = P(C ∩ S) ÷ P(S)
Substituting this into the first equation, we get:
P(C ∩ S) = P(C ∩ S) ÷ P(S) × P(S)
P(C ∩ S) = P(C ∩ S) × P(S)
We know that P(S) = 48% and we can use the formula for the union of two events to find P(C ∪ S):
P(C ∪ S) = P(C) + P(S) - P(C ∩ S)
Substituting in the values we know:
63% = 41% + 48% - P(C ∩ S)
P(C ∩ S) = 41% + 48% - 63% = 26%
To know more about the intersection of two events visit :
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Explain what an extraneous solution is and how you would check for one?
Answer:
Step-by-step explanation: An Extraneous solutions are values that we get when solving equations that aren't really solutions to the equation. And you only need to check for one if you made the equation quadratic by multiplying by a variable.
The function f(x)=x√ is horizontally stretched by a factor of 2 to form function g(x). What is the equation of g(x)? Enter your answer in the box. g(x) =
The equation of g(x) is g(x) = 2*x^(1/2)
Explanation:
The original function f(x) is defined as f(x) = x^(1/2) which is the square root of x. When the function is stretched horizontally by a factor of 2, the x term becomes 2x. So the new function g(x) is defined as g(x) = 2*x^(1/2)
