Answer:
52kg
Step-by-step explanation:
Can somebody help me? I am learning about Basic Exponent Properties in Algebra and I do not understand how to solve equations with exponents. Please tell me how to do it?
Here are some examples:
1. (4xy²)(-2x²y³)
2. 6y³/18x · 2xy
3. Which expression has the greater value? 2³ · 2(exponent 5) or 4(exponent 7)/4³
4. (3x)exponent1/3 · (3x)exponent7/3 / (3x)exponent2/3
Please Answer ASAP!! I will give 40 points!!
Answer:
Provided an explanation below.
The examples are not asking you to solve, only to simplify the expression
For the examples you posted, not sure if you want the solutions are not; I have gone ahead and simplified
[tex]1.\; -8x^3y^5\\\\2\; \dfrac{2y^3}{3}\\\\3.\; They are both equal\\\\4.\; 3x^2\\\\[/tex]
Step-by-step explanation:
First let's understand what an exponent is.
When a number or a term or an expression is multiplied repeatedly by itself, an exponent can be used to represent this situation
for example,
5 x 5 x 5 x 5 x 5 x 5 = 5⁶ since 5 is multiplied by itself 6 times
Here the number being multiplied(5) is called the base and the number of times it is multiplied(6) is called the exponent.
There are some rules regarding exponentiation
1 Zero Exponent
Any number raised to the power zero is 1
[tex]4^0 = 1\\\\123.456^0 = 1\\\\x^0 = 1[/tex]
2. Negative Exponent
If the exponent if negative, the expression is equivalent to the reciprocal of the term raised to the positive exponent
In general
[tex]a^{-m} = \dfrac{1}{a^m}\\\\and\\\\\dfrac{1}{a^{-m}} = a^m\\\\[/tex]
Examples:
[tex]x^-1 = \dfrac{1}{x}\\\\\left({x + y}\right)^{-a} = \dfrac{1}{(x+y)^a}[/tex]
[tex]\dfrac{1}{x^{-3}} = x^3[/tex]
3. Product Rule
When you multiply exponents with the same base the exponents get added
In general
[tex]\displaystyle {a^m a^n = a^{m + n}}[/tex]
Examples
[tex]x^3x^6 = x^{(3+6)} = x^9\\\\[/tex]
4. Quotient Rule
When you divide an exponentiated term by another exponentiated term with the same base the resulting exponent is the difference between the two exponents:
In general
[tex]\dfrac{a^m}{a^n} = a^{m-n[/tex]
Examples
[tex]\dfrac{y^3}{y^2} = y^{3-2} = y^1 = y[/tex]
5. Power Rule 1
An exponent term raised to another power will be the base raised to the product of the two exponents
In general
[tex](a^m)^n = a^{mn}[/tex]
[tex](x^3)^4 = x^{3 \cdot 4} = x^{12}[/tex]
6. Power Rule 2
If the base is the product of two or more terms and the whole expression is raised to a power then each individual term gets raised to that power.
[tex](ab)^m = a^mb^m\\\\(2x^3y^2z^4)^4 = 2^4x^{3.4}y^{2.4}z^{4.4} = 16x^{12}y^8z^{16}[/tex]
7. One exponent
Any term raised to the power 1 is itself
[tex]a^1 = a[/tex]
example: 5¹ = 5
x¹ = x
You may have to use some or all of the rules when confronted with a specific problem
There are plenty of excellent resources on the web which can explain far more lucidly than I can.
Here are a few. Just search for them and you will get the site links
LibreTexts, OpenStax, cK-12.org etc
As for the specific examples you posted:
[tex]1. (4xy^2)(-2x^2y3)\\[/tex]
Multiply the constant coefficients: 4 x -2 = -8Multiply each term with the same base by the other term with the same base[tex]\textrm{2. }\dfrac{6y^2}{18x}\cdot 2xy[/tex]
[tex]\mathrm{Cancel\:}\dfrac{6y^2}{18x}:\quad \dfrac{y^2}{3x}\\\\[/tex]3. Which expression has the greater value?
[tex]2^3.2^5 \; or\; \dfrac{4^7}{4^3}[/tex]
[tex]2^3\cdot2^5 = 2^8\\\\\dfrac{4^7}{4^3}= 4^{7-3}=4^4\\\\\mathrm{Since \;4 = 2^2, 4^4 = (2^2)^4=2^8}[/tex]
[tex]4. \dfrac{\left(3x^{\frac{1}{3}}\cdot 3x^{\frac{7}{3}}\right)}{3x^{\frac{2}{3}}}[/tex]
[tex]\\\\\\\mathrm{Cancel\:the\:common\:factor:}\:3[/tex]Which correlation can you draw from the following scatterplot?
a. The warmer the air temperature, the more people there are in the pool.
b. The warmer the air temperature, the fewer people there are in the pool.
c. As the air temperature increased, most people left the pool.
d. There is no visible correlation between air temperature and the number of people in the pool.
The correlation is that; The warmer the air temperature, the more people there are in the pool. Option A
What is the correlation?We know that the correlation would help us to obtain the relationship that we have between the two variables that have been shown in the scatter plot.
The correlation coefficient is the determinat of the relationship between the variables. As we look at the scatter plot that have been shown here, we would need to use it to know the way that the air temperature and the people in the pool are related.
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is the solution of b x 5/6 = 25 greater than or less than 25
The value of the equation is b = 30 , which is greater than 25
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is
Substituting the values in the equation , we get
b x ( 5/6 ) = 25 be equation (1)
On simplifying the equation , we get
Multiply by 6 on both sides of the equation , we get
5b = 25 x 6
5b = 150
Divide by 5 on both sides of the equation , we get
b = 150 / 5
b = 30
So , the value of b is 30 and is greater than 25
b > 25
Hence , the equation is b = 30
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Factor the trinomial by grouping. -
5x² - 28x+15
a. Find two numbers whose product is 5.15= 75 and whose sum is - 28.
b. Write - 28x using the factors from part (a).
c. Factor by grouping.
a. The two numbers whose product is 75 and whose sum is -28 are -25 and 3.
b. -28x = -25x + 3x
c. -5x² - 25x + 3x + 15
= -5x(x-5) + 3(x-5)
= (3x-15) + (-5x+25)
= (-5x+3x) + (25-15)
= -2x +10
The trinomial -5x² - 28x + 15 can be factored by grouping as (-2x+10)
In a particular class of 32 students, 11 are men. What fraction of the students in the class are men?
Please help.
Answer:
11/32 of the students are men.
Step-by-step explanation:
Since there are 11 male students and 32 total, we can use the number 11 as the numerator, and 32 as the denominator.
[tex]\frac{11}{32}[/tex]
The fraction of male students in the class is 11/32.
What is meant by fraction?A fraction is a piece of the entire. In mathematics, the number is represented as a quotient, where the numerator and denominator are divided. Both are integers in a straightforward fraction. In the numerator or denominator of a complex fraction is a fraction. A correct fraction has a numerator that is lower than its denominator.
Fractions are used to depict the components of a whole or group of items. Two components make up a fraction. The numerator is the number that appears at the top of the line. It indicates how many equally sized pieces of the entire thing or collection were removed. The denominator is the quantity listed below the line.
11/32 is the fraction of the students in the class that are men.
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Calculate the acceleration produced by a bus moving with velocity of 72 km / hr to stop a distance of 50
As a result, the bus accelerates at a rate of -4 m/s2, and it travels 50 m after applying the brakes.
Find the acceleration ?Bus's initial speed was 72 km/h.
Bus's last speed is 0 km/h.
(Therefore, the bus driver stops)
Bus travel time, t=5 s
To Locate
Bus acceleration and the distance it travels before stopping once the brakes are applied
Solution:
Final velocity is v.
Initial velocity is u.
Acceleration is a.
It takes time.
displacement is s.
Considering that
u = 20m/s
v = 0 m/s
Bus acceleration should be "a"
When using the first law of motion on a bus, we obtain
Let d represent the bus's distance traveled after braking.
a = -4 m/s²
Thus, when we use the third equation of motion on a bus, we obtain
As a result, the bus accelerates at a rate of -4 m/s2, and it travels 50 m after applying the brakes.
d = 50 m
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Given: GH is parallel to KL; GJ is congruent to KJProve: J is the midpoint of HLThe shape is an hour glass figure. GH on the left side J in the middle and LK on the right side.
The distance between J and L is (Gx/2)2 + (Gy/2)2. This proves that J is the midpoint of HL.
Given: GH is parallel to KL and GJ is congruent to K
To prove: J is the midpoint of HL
We can use the Midpoint Formula to prove that J is the midpoint of HL. The midpoint formula states that the midpoint of a line segment is the average of the x-coordinates and the average of the y-coordinates. In this case, the x-coordinate of J is (Gx + Kx) ÷ 2 and the y-coordinate of J is (Gy + Ky) ÷ 2. Since GH and KL are parallel, Gx = Kx and Gy = Ky. Therefore, the x-coordinate of J is (Gx + Kx) ÷ 2 = Gx ÷ 2 and the y-coordinate of J is (Gy + Ky) ÷ 2 = Gy ÷ 2. Since GJ is congruent to KJ, Gx = Kx and Gy = Ky. Therefore, J is the midpoint of HL.
We can also use Distance Formula to prove that J is the midpoint of HL. The distance formula states that the distance between two points is the square root of the difference of the x-coordinates squared plus the difference of the y-coordinates squared. In this case, the distance between G and J is the square root of (Gx - Jx)2 + (Gy - Jy)2. Since GJ is congruent to KJ, Gx = Kx and Gy = Ky. Therefore, the distance between G and J is the square root of (Gx - Jx)2 + (Gy - Jy)2 = (Gx - Gx/2)2 + (Gy - Gy/2)2 which simplifies to (Gx/2)2 + (Gy/2)2. This is the same distance as the distance between J and L, since GJ is congruent to KJ, Gx = Kx and Gy = Ky. Therefore, the distance between J and L is (Gx/2)2 + (Gy/2)2. This proves that J is the midpoint of HL.
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Suppose you want to choose two colors, without replacement, from the three colors, red, blue, and green.
A) how many ways can this be done, if the order of the choices matters?
B) how many ways can this be done, if the order of the choices does not matter?
Statistics describes the examination of events subject to probability. Choices are therefore 6 and 3.
What is a probability simple definition?How likely something is to occur is known as its probability. We can discuss the probabilities of various outcomes—how likely they are—when we aren't sure how a particular event will turn out.
Statistics describes the examination of events subject to probability.
a) Six options
(b) 3 Options
Given:
(3) Colors
Red, Blue, and Green are the options.
(a) The choices that were considered in the following order:
There are three color options when choosing the first hue.
There are two options when choosing the second color, and so on.
As a result, there are a total of = 3*2 = 6 options.
(b) The order of the options not taken into account:
When selecting this option, we decide on 3*2 and then eliminate duplicates.
Choices are therefore 6/2=3 Choices.
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At what height above the surface of the earth, the value of g becomes 64% of its value on the surface is the earth? (Radius of the earth is 6400km )
O 1600kmO 2650kmO 3200kmO 9038km
The value of g becomes 64% of its value on the surface of the earth when it is at a height of 3200km above the surface, with the radius of the earth being 6400km.
Radius of Earth = 6400 km
Height above the surface of Earth = 3200 km
Gravitational Acceleration on surface of Earth = 9.8 m/s2
Gravitational Acceleration at 3200 km above the surface of Earth = 9.8 x 0.64 = 6.272 m/s2
The gravitational acceleration (g) on the surface of the earth is 9.8 m/s2. This value is constant, regardless of the height of an object above the surface. However, as the height of an object increases, the gravitational force experienced by the object decreases. The radius of the earth is 6400 km, so at a height of 3200 km above the surface, the gravitational acceleration experienced by an object is 64% of its value on the surface of the earth, which is 6.272 m/s2. This is because the gravitational force decreases as the object moves further away from the surface, and at 3200 km the force is only 64% of the force at the surface.
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Mike is loading a moving van by walking up a ramp. The ramp is 10 feet long and the bed of the van is 2.5 feet above the ground. How far does the ramp extend past the back of the van?
Using the Pythagorean theorem, the ramp extends 9.68 feet past the back of the van.
What is the Pythagorean theorem?
Pythagoras Theorem (also called Pythagorean Theorem) is an important topic in Mathematics, which explains the relation between the sides of a right-angled triangle. The sides of the right triangle are also called Pythagorean triples. Pythagoras theorem is basically used to find the length of an unknown side and the angle of a triangle. By this theorem, we can derive the base, perpendicular and hypotenuse formulas.
Pythagoras formula:-
Hypotenuse² = Perpendicular² + Base²
c² = a² + b²
Where “a” is the perpendicular,
“b” is the base,
“c” is the hypotenuse
Now,
For given situation,
Hypotenuse=10feet, perpendicular=2.5feet and we have to find base
Therefore
10^2=b^2+2.5^2
b^2=100-6.25
b=√93.75
b=9.68 feet
Hence,
The ramp extends 9.68 feet past the back of the van.
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A 6-sided die is rolled 2 times. What is the probability of getting 1 both times? (Give your answer as a fraction in simplest form.
Answer:1/36
Step-by-step explanation:
you have a 1 in 6 chance to get one out of a 6 sided die. U double that to get 1/36.
Relationships between short- and long-term exposure to violent video games and desensitization, as measured through components of moral evaluation, were examined. Sixty-six children aged 5-12 years old completed questionnaires assessing video game experience and preferences and empathy and attitudes toward violence. The children played a violent or nonviolent video game and then responded to vignettes about everyday occurrences. Vignette responses were coded for aggression and empathy. Preexisting empathy and attitudes towards violence were positively related to the corresponding vignette scores. Long-term exposure to violent video games contributed to lower empathy vignette scores. Playing a violent versus a nonviolent game did not affect vignette responses. Results suggest that long-term exposure to violent video games may be associated with desensitization as reflected in lower empathy, although the direction of causality remains unclear.What is the main IV?What is the main DV?
This study examines the relationship between long-term exposure to violent video games and desensitization as measured by empathy and attitudes to violence in children aged 5 to 12 years.
They completed a questionnaire assessing their experience and preference for video games and their empathy and attitudes toward violence. Children then played violent or non-violent video games and responded to snippets of everyday events.
vignette reactions were coded for aggression and empathy. Results showed that pre-existing empathy and attitudes toward violence were positively associated with the corresponding vignette scores.
Prolonged exposure to violent video games has been found to reduce empathy vignette scores. However, the study found no significant difference in vignette responses depending on whether children played violent or non-violent games.
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Which of the following are options you can select in the Top Values list for a query? Select all the options that apply.a. all b. 25% c. 5 d. none
All, 25%, and 5 are all valid options that can be selected in the Top Values list for a query.
All will display all the values in the query, 25% will display the top 25% of the values, and 5 will display the top 5 values.
To calculate 25%, we can use the formula (value/total)*100. For example, if the total number of values is 20, then 25% would be (20/20)*100 = 100. This would display all 20 values in the query. Similarly, if the total number of values is 50, then 25% would be (50/50)*100 = 100, which would also display all 50 values.
To calculate 5, we can use the same formula (value/total)*100. For example, if the total number of values is 20, then 5 would be (5/20)*100 = 25. This would display the top 5 values in the query. Similarly, if the total number of values is 50, then 5 would be (5/50)*100 = 10, which would also display the top 5 values.
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A small bead with a mass of m slides along a semicircular wire with a radius r that rotates about a vertical axis with an angular velocity o-Vgir as shown. When the angle 0 30 the bead remains stationary relative to the rotating wire. The coefficient of static and kinetic friction between the bead and the wire are s and , respectively. Find the force the wire exerts on the bead. and the wire are, and 1ry
A bead's resistance to the wire's force. the wire are, and ry is equal to sqrt(5)mg/2.
What is meant by static friction?The friction between two or more items that is present but not moving in relation to the other objects is known as static friction. Kinetic friction is the resistance that exists between two or more things when they are moving relative to one another. An item is kept at rest by the force of static friction. The phrase "static friction" can be defined as "the friction people perceive when they attempt to move a stationary object on a surface, but without actually causing any relative motion between the body and the surface it is on." Measuring the angle at which an object begins to slide down an incline or ramp is one way to figure out the static coefficient of friction.To learn more about static friction, refer to:
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Find the least common denominator of 1/2x-6 and 2x/7x-21.
The least common denominator of 1/2x-6 and 2x/7x-21 is (2x -6)(7x - 21)
What is a fraction?A fraction can be described as the part of a whole variable, element or number.
There are some number of fractions in mathematics which includes;
Complex fractionsImproper fractionsProper fractionsSimple fractionsMixed fractionsExamples of simple fractions 1/2, 1/3
Examples of proper fractions; 3/4, 5/6
Examples of improper fractions; 4/3, 6/3
Examples of mixed fractions; 1 2/3, 5 4/6
From the information given,
1/2x-6 and 2x/7x-21
The least common denominator is (2x -6)(7x - 21)
Hence, the value is (2x -6)(7x - 21)
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A ball dropped vertically fall d meters in t seconds. D is directly proportional to the square of t the ball drops 80 meters in the first 4 seconds . how far does the ball drop in the next 8 seconds
The distance the ball drops in the next 8 seconds is 320 meters.
What is direct proportion?Direct proportion is when two variables move in the same direction. If one variable increases, the other variable increases.
The equation that is used to represent direct proportion is: D = kt²
Where: k is the constant of variation
80 = k4²
80 = 16k
k = 80 / 16
k = 5
Distance the ball drops in the next 8 seconds : 5 x 8²
= 64 x 5 = 320 meters
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in the expansion of (2a 4b)8, which of the following are possible variable terms? explain your reasoning. a2b3; a8; a5b3; ab8; a3b5; a7b; a6b5; b8
The possible variable terms are a2b3, a5b3, ab8, a3b5, a7b, and a6b5. These terms all contain the same number of a's and b's as the original expression, (2a4b)8.
The expansion of (2a 4b)8 can be found by multiplying the a coefficients and b coefficients by 8. The a coefficients would increase by a factor of 8 and the b coefficients would increase by a factor of 8. This means that the possible variable terms for (2a 4b)8 are all those that have 8 a's and 8 b's. This includes a2b3, a5b3, ab8, a3b5, a7b, and a6b5. These terms all contain the same number of a's and b's as the original expression, (2a4b)8, but with the coefficients multiplied by 8. For example, the term a2b3 would be the result of multiplying 2a4b by 8, which results in 16a32b. This can be simplified to a2b3. Similarly, a5b3 would be the result of multiplying 2a4b by 8, which results in 16a32b. This can be simplified to a5b3.
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If so, what are the two expressions being cubed? In other words, if the expression is rewritten In the form (p^3 - q^3), what are p and q?
The two expressions being cubed are p and q. The expression (p^3 - q^3) is equivalent to cubing both p and q. This means that the expression can be written as (p * p * p - q * q * q). Rewriting it in the form (p^3 - q^3) shows that the two expressions being cubed are p and q.
The expression (p^3 - q^3) is equivalent to cubing both p and q. This means that the expression can be written as (p * p * p - q * q * q). Rewriting it in the form (p^3 - q^3) shows that the two expressions being cubed are p and q.
The expression (p^3 - q^3) is the result of cubing two different expressions, p and q. This is equivalent to multiplying each expression by itself three times. Rewriting the expression in the form (p^3 - q^3) indicates that the two expressions being cubed are p and q. In other words, the expression is the result of taking p and raising it to the third power and then taking q and raising it to the third power. The result is then subtracting q^3 from p^3. This is commonly referred to as cubing both p and q, and the two expressions being cubed are p and q.
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Marge simplified the expression as show. -8b+15b+14=21b. What mistake did marge make, what is the correct simplified version of the expression
The value of expression is 1 of the equation -8b+15b+14=21b
What is Equation?Two or more expressions with an Equal sign is called as Equation.
The given expression is -8b+15b+14=21b
Minus eight times of b plus fifteen b plus forteen equal to twenty one.
In the given expression b is the variable and minus and plus are the operators.
-8b+15b+14=21b
Take the variable terms on one side and constant on other side.
-8b+15b-21b=-14
-14b=-14
Divide both sides by -14
b=1
Hence, the value of expression is 1 of the equation -8b+15b+14=21b
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HOW can you use a bar diagram to show a percent of change?
There are two ways in which one can show percent of change in bar diagram: Input helper column using error bars, and arrows of error bar.
What are bar diagrams?Diagrams known as bar diagrams are ones in which data is shown using bars and rectangles.
First, an input helper column as indicated in the data below in order to produce a column chart with percentage change using error bars, and then base the chart on the helper data.
Second, use some arrows in place of the error bars; if the data rises in the following year, an up arrow is shown; if it falls in the following year, a down arrow is shown. The arrows and data labels will both be dynamically altered when the data changes at the same time.
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Given that 2log (x^2 y)=3 + logx- log y where x and y are both positive, express y in terms of x. If x-y=3, find the value of x and of y.
The values of x and y for the given logarithmic function, 2 log (x²y) = 3 + logx - logy are respectively, 13/2 and 7/2
What is a logarithmic function ?The logarithmic function is an expression which we can write as, y = logₐx, where a>0 & x>0, It is the inverse of exponential function.
Formulae for logarithmic function are,
LogAB = LogA + LogB
Logₐaᵇ = b
Given that,
the logarithmic function,
2 log (x²y) = 3 + logx - logy
x - y = 3 .....................(i)
2 log (x²y) = 3 + logx - logy
2[ logx² + logy] = 3 + logx - logy
2[ 2logx + logy] = 3 + logx - logy
4logx + 2logy = 3 + logx - logy
3logx + 3logy = 3
logx + logy = 1
logx + logy = log10
x + y = 10 .............(ii)
By solving the equation (i) & (ii)
x - y = 3
x + y = 10
2x = 13
x = 13/2
13/2 - y = 3
y = 7/2
Hence, the values of x and y is, 13/2 and 7/2
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an even number. each card is worth a different number of points (this point value is written on the card). alice and bob then take turns removing either the leftmost or rightmost card from the row, until all the cards are gone. at that point, the player who has collected the most points is declared the winner.
The best strategy for Alice is to take the card with the highest point value. This will maximize her chances of winning, since she can then choose the last card from the remaining cards. Bob should take the card with the lowest point value, as this will minimize Alice's chances of winning.
Alice always takes the first turn. Bob can either take the leftmost card or the rightmost card. If Alice takes the leftmost card and Bob takes the rightmost card, then Alice will have the advantage of being able to make the last move. If Bob takes the leftmost card and Alice takes the rightmost card, then Bob will have the advantage of being able to make the last move.
The best strategy for Alice is to take the card with the highest point value. This will maximize her chances of winning, since she can then choose the last card from the remaining cards. Bob should take the card with the lowest point value, as this will minimize Alice's chances of winning.
Alice should also be aware of Bob's strategy and try to anticipate what card he will take. If Alice can guess correctly, she can adjust her strategy to ensure she takes the card with the highest point value. If she guesses incorrectly, she should still attempt to take the card with the highest point value.
Alice should take the card with the highest point value and Bob should take the card with the lowest point value. Alice should also anticipate Bob's strategy and adjust accordingly to ensure she takes the card with the highest point value.
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Question 3 (5 points)
(05.02)
Solve log x = 2.
O a
Ob
Oc
Od
2
20
100
1,000
Therefore , the solution of the given problem of logarithm comes out to be x =100.
What exactly is a logarithm?Mathematically speaking, the reciprocal of a power is the logarithm. Therefore, the base-b logarithm of a given number, x, is equal to the exponential by which bc must be extended to acquire it. For instance, because 1000 = 103, whose base-10 logarithm, or log10 = 3, is 3. As an example, the square of ten is one hundred, but the base-10 logarithm of ten is two. Log 100 = 2. The mathematical concept of a logarithmic (or log) is used to respond to questions like.
Here,
Given : log x =2
=> log x =2
=> x = antilog (2)
=> x = 100
Therefore , the solution of the given problem of logarithm comes out to be x =100.
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find all solutions $x$ of the inequality$$\frac{5}{24} \left|x-\frac{11}{48}\right| < \frac{5}{16}.$$
The solutions are all real numbers x such that [tex]$$\frac{5}{24}\left(\frac{11}{48}-x\right) < \frac{5}{16} \qquad \text{and} \qquad \frac{5}{24}\left(x-\frac{11}{48}\right) < \frac{5}{16}.$$[/tex]
This is equivalent to
[tex]$$-\frac{5}{8} < x-\frac{11}{48} < \frac{5}{8}.$$[/tex]
Solving for $x$, we get
[tex]$$-\frac{5}{8} < x-\frac{11}{48} < \frac{5}{8}.$$[/tex]
1. We are given the inequality[tex]$\frac{5}{24} \left|x-\frac{11}{48}\right| < \frac{5}{16}$.[/tex]
2. To solve for $x$, we must first rewrite the expression in terms of two inequalities. We do this by separating the absolute value into two parts: [tex]\frac{5}{24}\left(\frac{11}{48}-x\right) < \frac{5}{16}$ and $\frac{5}{24}\left(x-\frac{11}{48}\right) < \frac{5}{16}$.[/tex]
3. Next, we solve each inequality for $x$. We get [tex]-\frac{5}{8} < x-\frac{11}{48} < \frac{5}{8}$.[/tex]
4. Finally, we solve for $x$ and get the solution set [tex]\frac{13}{48} < x < \frac{25}{48}$.[/tex]
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{0,1,2,3} set builder notation
The set {0,1,2,3} as a set builder notation is {x ∈ N | 0 <= x <= 3}
How to determine the set using set builderFrom the question, we have the following parameters that can be used in our computation:
Set = {0, 1, 2, 3}
As a general rule:
The set-builder notation is a notation that describes a set by representing its elements or explaining the properties that its members must satisfy
Using a set builder notation, we have the following representation
{x | x ∈ {0, 1, 2, 3}}
It can also be represented as
{x ∈ N | 0 <= x <= 3}
where N is the set of all natural numbers.
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Please help me I will mark you as a brainliest
The different values of modulus function are 9, 6, 6, 12.
A modulus function is a function that determines a number or variable's absolute value. It generates the size of the variable count. A function with absolute values is another name for it. No matter what input was provided to this function, the outcome is always favorable.
The non-negative value of a real number x, regardless of its sign, is its absolute value (or modulus), | x |. For instance, 5 has an absolute value of 5, and 5 has a value of 5.
Given the modulus function is, |3x|
the values of modulus function is always positive.
The different values for given function are -
x |3x|
-3 9
-2 6
2 6
4 12
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Find the smallest positive integer b for which x^2+bx+2008 factors into a product of two binomials, each having integer coefficients.
Answer:
b = 259
Step-by-step explanation:
You want the smallest positive 'b' that makes x² +bx +2008 have integer solutions.
FactorsWhen the polynomial is factored, you have ...
(x +p)(x +q) = x² +(p+q)x +pq
Comparing this to the given expression, we see that ...
p + q = b
pq = 2008
This means the values of p and q will be divisors of 2008.
Factor pairsThe positive integer factor pairs of 2008 are ...
2008 = 1·2008 = 2·1004 = 4·502 = 8·251
The pair with the smallest sum is 8·251. The corresponding sum is ...
8 +251 = 259
The smallest positive value of 'b' that makes x² +bx +2008 have integer solutions is 259.
__
Additional comment
The factorization is x² +259x +2008 = (x +8)(x +251).
A total of $6000 is invested: part at 7% and the remainder at 11 %. How much is invested at each rate if the annual interest is $460?
Based on a system of equations, the investment at each rate is as follows:
At 7% = $5,000At 11% = $1,000.What is a system of equations?A system of equations, also known as simultaneous equations, yields the solutions to two or more equations solved concurrently or simultaneously.
We use the let statements to state the variables of simultaneous equations.
The total investment = $6,000
The total interest earned = $460
Interest rates:
A = 7%
B = 11%
Let investment A = a and investment B = b
Equations:0.07a + 0.11b = 460 ... Equation 1
a + b = 6,000 ... Equation 2
Multiply Equation 2 by 0.07:
Equation 3: 0.07a + 0.07b = 420
Subtract Equation 3 from Equation 1:
0.07a + 0.11b = 460
-
0.07a + 0.07b = 420
0.04b = 40
b = 1,000
= $1,000
From Equation 2:
a + b = 6,000
a + 1,000 = 6,000
a = 5,000
= $5,000
Thus, whereas $5,000 is invested at 7%, $1,000 is invested at 11%.
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Simplify (√3+√2)-(√3-√2)
Answer:
[tex]2\sqrt{2}[/tex]
Step-by-step explanation:
Think of it in terms of a and b if its too difficult to understand what it is in its current state.
[tex]\sqrt{3} = a & \sqrt{2} = b\\(\sqrt{3} + \sqrt{2}) - (\sqrt{3} - \sqrt{2})\\(a + b) - (a - b)\\a + b - a + b\\2b \\2\sqrt{2}[/tex]
Mariam wants to rent out her house. She researches similar listings in an online rental marketplace and sees that she can rent her home for $210$ per night or $1300 per month. Mariam's house is near a beach in a moderate-sized city with good weather year-round, a famous aquarium, a water park, and lots of restaurants.
To figure out if she should list her home as a short-term rental or a long-term rental, first Mariam divides 1300 by 210.
1300/210=6.2
She needs to rent her home 6-7 nights per month to match the revenue from a long-term rental. Since Mariam lives in a location likely to have tourists, she should find plenty of renters. She lists her home as a short-term rental.
In her reasoning, Mariam divided 1300 by 210. If this is correct, explain why. If this is not correct, explain what she should have done.
This is absolutely correct as dividing the rate per month by the rate per night gives the number of nights per month needed for the revenues to match: [tex]$$month$\div $night=r/month \cdot \ $night/r$=# $nights/month$$[/tex]
What is revenue?A company's income is the cash that is generated by its operations. Depending on the accounting technique used, there are various methods for calculating revenue.
Sales made with credit will be counted as revenue when it comes to the delivery of goods or services to the customer in accrual accounting. Even if payment hasn't yet been received, revenue may still be recognised in accordance with certain rules.
To evaluate how successfully a business collects debt, it is important to review the cash flow statement. Contrarily, sales are only recorded as revenue in cash accounting after money has been exchanged. A "receipt" is the term for a sum of money given to a business. Receivables without income are possible.
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