It is possible for Angela to have spent 80 minutes playing soccer if she plays for a total of exactly 125 minutes and plays soccer for 45 minutes longer than she plays golf because 80+45 adds up to 125.
What is a linear equation?A linear equation is an equation that has the variable of the highest power of 1. The standard form of a linear equation is of the form Ax + B = 0.
Angela plays soccer and golf for a total of 125 minutes every day. She plays soccer for 45 minutes longer than she plays golf.
Part A: A pair of linear equations to show the relationship between the number of minutes Angela plays soccer (x) and the number of minutes she plays golf (y) every day.
x = y + 45
Part B: A pair of linear equations to show how much Angela spends playing golf every day.
125 - 45 = 80,
80/2 = 40
Part C: Yes, it is possible for Angela to have spent 80 minutes playing soccer if she plays for a total of exactly 125 minutes and plays soccer for 45 minutes longer than she plays golf because 80+45 adds up to 125.
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NO LINKS!!!
55, Write an equation satisfying the given conditions.
Part (a)
The two limit statements tell us that this an exponential decay function.
The curve goes up forever when heading to the left (negative infinity) as indicated by the notation [tex]\displaystyle \lim_{\text{x}\to-\infty}f(x) = \infty[/tex]
At the same time, the curve slowly approaches the horizontal asymptote y = -2, when moving to the right, because of this notation [tex]\displaystyle \lim_{\text{x}\to\infty}f(x) = -2[/tex]
An exponential decay function like [tex]\text{y} = (0.5)^{\text{x}}[/tex] has a horizontal asymptote of y = 0, aka the x axis. The y value approaches 0 but never gets there. Each output is positive.
Shift everything down 2 units to arrive at [tex]\text{y} = (0.5)^{\text{x}}-2[/tex] and this will move the horizontal asymptote down the same amount.
There's nothing really special about the 0.5; you can replace it with any value in the interval 0 < b < 1.
---------
Answer: [tex]\text{f(x)} = (0.5)^{\text{x}}-2[/tex]====================================================
Part (b)
I'll use this template
[tex]\text{y} = ab^{\text{x}}+c[/tex]
Plugging in x = 0 leads to y = a+c which is the y intercept. Set this equal to the stated y intercept 7 and we get a+c = 7.
We want the [tex]ab^{\text{x}}[/tex] portion to approach zero, which leads to c = 4 so we approach the stated horizontal asymptote.
So,
a+c = 7
a+4 = 7
a = 7-4
a = 3
We go from this
[tex]\text{y} = ab^{\text{x}}+c[/tex]
to this
[tex]\text{y} = 3b^{\text{x}}+4[/tex]
The value of b doesn't matter.
I'll go for b = 0.7 so we get to [tex]\text{f(x)} = 3(0.7)^{\text{x}}+4[/tex]
---------
Answer: [tex]\text{g(x)} = 3(0.7)^{\text{x}}+4[/tex]====================================================
Part (c)
The parent function [tex]\text{y} = \log(\text{x}})[/tex] has a domain of [tex](0, \infty)[/tex]. In other words it is the interval [tex]0 < \text{x} < \infty[/tex]
If we replaced each input x with x-5, then we shift the xy axis 5 units to the left. It gives the illusion the log curve moves 5 units to the right.
The vertical asymptote also moves 5 units to the right. We go from a domain of [tex](0, \infty)[/tex] to a domain of [tex](5, \infty)[/tex]
The base of the log doesn't matter.
---------
Answer: [tex]\text{h(x)} = \log(\text{x}-5)[/tex]Check out the graphs below. I used GeoGebra, but Desmos is another good option.
Answer and Explain Please
a) The final coordinates are given as follows:
X(-5,-4) -> X'(-4,5).Y(2,-2) -> Y'(-2,-2).Z(-3,-6) -> Z'(-6,3).b) The rotation rule is given as follows: (x,y) -> (y,-x).
What are the rotation rules?The five more known rotation rules are given as follows:
90° clockwise rotation: (x,y) -> (y,-x)90° counterclockwise rotation: (x,y) -> (-y,x)180° clockwise and counterclockwise rotation: (x, y) -> (-x,-y)270° clockwise rotation: (x,y) -> (-y,x)270° counterclockwise rotation: (x,y) -> (y,-x)The rotation in this problem is the last rotation, 270º counterclockwise about the origin, hence the rule is given as follows:
(x,y) -> (y,-x).
The rule is applied to each of the vertices X, Y and Z to obtain the vertices of the reflected triangle X', Y' and Z'.
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Standardized tests for certain subjects, given to high school students, are scored on a scale of 1 to 5. Let A represent the score on a randomly selected exam for subject A and let B represent the score on a randomly selected exam for subject B. The distributions of scores for each subject’s standardized tests are displayed in the table and the histograms.
The probability of a score lower than three is given as follows:
0.38.
How to obtain the probabilities?A probability is obtained as the division of the number of desired outcomes by the number of total outcomes.
As the table gives the probability distribution, we must just take the probabilities of the desired events from the table.
The probability of a score lower than three is given as follows:
P(X < 3) = P(X = 1) + P(X = 2).
Taking the values from the table, the probability is of:
P(X < 3) = 0.18 + 0.20
P(X < 3) = 0.38.
Missing InformationThe problem is given by the image presented at the end of the answer.
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Sales of portable MP3 players grew approximately exponentially from $0.08 billion in 1999 to $0.88 billion in 2004. Predict the sales of MP3 players in 2008.
The sales of MP3 players in 2008 is $ billion.
(Type an integer or a decimal. Round the final answer to one decimal place as needed. Round all intermediate values to three decimal places as needed.)
Based on the exponential function, the sales of MP3 players in 2008 is $1.82 billion.
What is an exponential function?An exponential function is a function that has the general form y = abˣ
where
a ≠ 0,
b is the base b is a constant (b is a positive real number and b ≠ 1)
x is the independent variable whose domain is the set of real numbers.
Using the equation for exponential growth
y = ab^x
y = 0.88
a = 0.08
0.88 = 0.08bˣ
bˣ = 0.88/0.08
bˣ = 11
x = 4
Hence;
b⁴ = 11
b = 1.82
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A grocery chain determines the cost and revenue models using the following functions: C(x)=1.2x−0.012x2, 0≤x≤150 R(x)=3.6x−0.06x20≤x≤150, where x is the number of unit items sold. Determine the interval on which the profit function P(x) = R(x) − C(x) is increasing.
Answer:
Yesterday I have received amount of be with you i need to pay
The interval on which the profit function is increasing is [0, 25).
Given that:
The cost function is, C(x) = 1.2x - 0.012x²
The revenue function is, R(x) = 3.6x - 0.06x²
Here, x i is the number of units sold, and 0 ≤ x ≤ 150.
The profit function is:
P(x) = R(x) - C(x)
= (3.6x - 0.06x²) - (1.2x - 0.012x²)
= 2.4x - 0.048x²
Find P'(x).
P'(x) = 2.4 - 0.096x
The profit function is increasing when P'(x) > 0.
2.4 - 0.096x > 0
2.4 > 0.096x
25 > x
That is x < 25.
Hence the function is increasing in the interval [0, 25).
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Pythagoras is very tall for ancient Greck standards: 1.78 m. He notices that when he stands with his back to the sun, his shadow is 3.08 m in length, while the shadow cast by the lighthouse is 26 m long How tall is the lighthouse?
The lighthouse is 8.88 m tall.
What is the ratio?
A ratio is a mathematical comparison of two or more quantities. It expresses the relationship between the values of the quantities in terms of a numerical fraction.
This problem can be solved using similar triangles. Since the ratio of the heights of Pythagoras and the lighthouse is the same as the ratio of their corresponding shadow lengths, we can set up the following proportion:
(Height of lighthouse) / (Height of Pythagoras) = (Shadow length of lighthouse) / (Shadow length of Pythagoras)
Plugging in the given values:
(Height of lighthouse) / 1.78 = 26 / 3.08
To solve for the height of the lighthouse, we can cross-multiply and divide:
(Height of lighthouse) = (26 / 3.08) * 1.78
The lighthouse is approximately:
(26/3.08)*1.78 = 8.88 m
Hence, The lighthouse is 8.88 m tall.
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part a: the number of transistors per ic in 1972 seems to be about 4,000 (a rough estimate by eye). using this estimate and moore's law, what would you predict the number of transistors per ic to be 20 years later, in 1992? prediction
Using Moore's Law, which states that the number of transistors on a chip doubles approximately every two years, the estimated number of transistors per IC in 1992 would be 64,000.
The law claims that we can expect the speed and capability of our computers to increase every two years because of this, yet we will pay less for them. In more simple terms, the observation by Gordon Moore in 1965 that the number of transistors in a dense integrated circuit (IC) doubles roughly every two years is known as Moore's law.
This is calculated by doubling the estimate of 4,000 transistors every two years for a total of 8 doublings (16 years).
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Your kite is stuck in a tree that is 45 feet tall. The angle your string makes with the ground is 68°. Rather than worrying about the kite, you decide to calculate how much string you have let out. Assuming the string is held tight and makes a straight line to the ground, how much string have you let out?
Answer:
48.53 = 49 feet
Step-by-step explanation:
sin 0 = opposite/hypotenuse
sin 68 = AB/AC = 45/x
x = 45/sin 68 = 45/0.9272 = 48.53
48.53 rounded = 49 feet
Answer:
You have let out 48.5 feet of string
Step-by-step explanation:
Attached is a sketch of the problem.
We can use SOH CAH TOA to find our answer.
In this acronym, O is the opposite side, A is the adjacent side, and H is the hypotenuse. S is for the SIN function. C is for the COS function. T is for the TAN function.
We can calculate the length of the string by using the SIN function.
So we can say the sine of angle x is the opposite side divided by the hypotenuse.
[tex]sin(x)=\frac{O}{H}[/tex]
Lets solve for [tex]H[/tex].
Multiply each term by [tex]H[/tex].
[tex]H*sin(x)=\frac{O}{H} *H[/tex]
Simplify the right side by cancelling the common factor of [tex]H[/tex].
[tex]H*sin(x)=O[/tex]
Divide both sides of the equation by [tex]sin(x)[/tex].
[tex]\frac{H*sin(x)}{sin(x)} =\frac{O}{sin(x)}[/tex]
Simplify the right side by cancelling the common factor of [tex]sin(x)[/tex].
[tex]H=\frac{O}{sin(x)}[/tex]
Now lets evaluate the length of the string.
In this example we are given
[tex]x=68\\O=45[/tex]
[tex]H=\frac{45}{sin(68)}[/tex]
[tex]H=48.5341[/tex]
60⁰
m
Find the area of each triangle round to the nearest tenth
For math thanks !!!!!
Answer:
5.2 square units
Step-by-step explanation:
You want the area of a triangle with sides 4 and 3, and the angle between them measuring 60°.
AreaThe formula for the area of a triangle is ...
A = 1/2ab·sin(C)
ApplicationHere, we have a=4, b=3, C=60°, so the area is ...
A = 1/2·4·3·sin(60°) = 3√3 ≈ 5.2 . . . . square units
The area of the triangle is about 5.2 square units.
what is the hypothesis of the following conditional statement?
If we walk home from school, it takes 30 minutes.
a. we walk home from school
b. it takes 30 minutes
c. we do not walk home from school
d. we walk
The hypothesis of the conditional statement is;
Option A: we walk home from school
How to identify the hypothesis?A hypothesis is defined as an educated guess while using reasonable thought patterns, about the answer to a scientific question. Now, the hypothesis can either be supported or not supported at all, but then it depends on the data gathered.
A conditional statement is defined as a set of rules performed provided a certain condition is met. Thus, it is sometimes referred to as If-Then statement because if a condition is said to be met, then an action is said to have been performed " .
Thus, the conditional statement here is: " we walk home from school ".
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PLEASE HELP
A recipe for soup calls for 4 tablespoons of lemon juice and 1/2 cup of olive oil. The given recipe serves 4 people, but a cook wants to make a larger batch that serves 120 .
a) How many cups of lemon juice will the chef need for the larger batch?
b) How many pints of olive oil will the chef need for the larger batch?
120 table spoons of lemon juice.
15 cups of olive oil.
if the relation represents a function, find the domain and range. (enter your answers using interval notation. if the relation is not a function, enter none in the domain and range answer blanks.)
If the relation is represented by the equation y = 2x + 1, the domain would be all real numbers (-infinity, +infinity) and the range would be all real numbers greater than or equal to 1 (1, +infinity).
A relation is a function if for every input (x) there is exactly one output (y). To determine if a relation is a function, we can use the vertical line test, which states that if a vertical line can be drawn through the graph and intersects the relation more than once, then the relation is not a function.
If the relation is a function, we can find the domain and range by analyzing the relation. The domain is the set of all x-values and the range is the set of all y-values. In interval notation, the domain is written as (a, b) and the range is written as (c, d).
So, the domain and range answers depend on the relation which is given and it should be specified.
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A new apartment building has 33 floors, with 24 apartments on each floor. How many apartments are in the building?
(Partial product)
Red :
Blue :
Green :
Yellow :
Total Product:
Simple equation when u break it down: 33 x 24=792 apartments
How many apartments are in the building?A building, or edifice, is an enclosed structure with a roof and walls that is standing in one location more or less permanently, such as a house or factory (although there are also portable buildings). Buildings come in a variety of sizes, shapes, and uses, and they have been modified throughout history for a wide range of reasons, including the availability of building materials, weather, land prices, ground conditions, particular uses, prestige, and aesthetic considerations.
given:
new apartments' building =33 floor
apartments on each =24 floor
33*24=792
792 apartments are in the building
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How many full 2 3/4-in. sheets can be cut from 26 1/8-in. stock?
The required number of sheets cut from the stock are 9.
What is mixed fraction?A mixed fraction is one that is represented by both its quotient and remainder. For example, 2 1/3 is a mixed fraction, where 2 is the quotient, 1 is the remainder. An amalgam of a whole number and a legal fraction is a mixed fraction.
According to question:
We have,
We need sheets of length = 2 (3/4) in from 26 (1/8) in stock.
So, 2 (3/4) = 11/4 in
26 (1/8) = 209/8
Then,
Number of sheets = 209/8 / 11/4
Number of sheets = 836/88
Number of sheets = 9.5
So, 9 sheets can be cut.
Thus, required number of sheets are 9.
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Find the component form of u + v given the lengths of u and v and the angles that u and v make with the positive x-axis. ||u||= 4, θu =6 , ||v|| = 1, θv = 4
The component of u+v along the length of u and v is (6.3, 0.66).
A vector is quantity which has both magnitude and direction. A magnitude is the length of the vector.
Here in the question u and v makes angle with the positive x axis.
||u||= 4 and θu =6 and ||v|| = 1, θv = 4
To determine the component of u = |u||(cosu, sinu)
Component of u = 6(0.9, 0.1) = (5.4, 0.6)
Component of v = ||v||(cosv sinv)
Component of v along the x axis = 1(0.9, 0.06 ) = (0.9, 0.06)
In the question value of u+v needs to be find.
Value of u + v = (5.4 + 0.9 , 0.6+ 0.06)
Value of the component form of u + v = (6.3, 0.66).
Hence, the component of u+v along the length of u and v is (6.3, 0.66).
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Si el costo de 1 Kg de azucar es $8?cual es el precio de 3 3/4 kg?
On evaluating the fraction 3 3/4 the cost of 3 3/4 kg of sugar is $30.
What is fraction?
In mathematics, a fraction is used to denote a portion or component of the whole. It stands for the proportionate pieces of the whole. Numerator and denominator are the two components that make up a fraction. The numerator is the number at the top, and the denominator is the number at the bottom.
The cost of 1 kg of sugar is = $ 80
The amount of sugar is given in fractional form - 3 3/4 kg
The equation for cost of 3 3/4 kg sugar is -
Cost = 3 3/4 × 8
Solve the fractional part first -
Cost = 15/4 × 8
Simplify the equation -
Cost = 15/4 × 8
Cost = 120/4
Cost = 30
Therefore, the cost value is obtained as $ 30.
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If the cost of 1 kg of sugar is $8, what is the price of 3 3/4 kg?
Sam has 3 1/4 pounds of blueberries. Ben also has some blueberries. Together, they have 9 2/3 pounds of blueberries. Create an equation to represent the number of pounds of blueberries, b, Ben has.
The required blueberries Ben has 6 5/12 pounds.
What are equation models?The equation model is defined as the model of the given situation in the form of an equation using variables and constants.
Here,
Let the amount of blueberries Ben has to be x,
According to the question,
Together, they have 9 2/3 pounds of blueberries.
x + 3 1/4 = 9 2/3
x = 9 2/3 - 3 1/4
x = 9 + 2/3 - 3 -1/4
x = 6 + 5/12
x = 6 5/12 pounds
Thus, the required blueberries Ben has 6 5/12 pounds.
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need the answer please
The number of feet that canyon wall away from the person will be 3,300 feet.
What is speed?Speed is defined as the length traveled by a particle or entity in an hour. It is a scale parameter. It is the ratio of length to duration.
We know that the speed formula
Speed = Distance/Time
Sound travels about 750 miles per hour. If you stand in a canyon and sound a horn, you will hear an echo.
Convert the speed in feet per second. Then we have
Speed = 750 x 5280 / 3600
Speed = 1,100 feet per second
Let 'n' be the number of seconds. Then the distance is given as,
1,100 = (d / 2) / n
d = 2,200 n
If n = 1.5, then we have
d = 2,200 x 1.5
d = 3,300 feet
The number of feet that canyon wall away from the person will be 3,300 feet.
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What is the effect on the graph of f(x) = x² when it is transformed to
• h(x) = 5x2 + 10?
The transformation applied is the one in option D, a vertical dilation of scale factor of 5, and a shift of 10 units up.
What is the effect of the transformation?Here we start with the parent quadratic function:
f(x) = x²
And we have the transformed function:
h(x) = 5x² + 10
We can write this as:
A vertical dilation of a scale factor 5, which will give:
h(x) = 5*f(x)
And then a translation of 10 units upwards, which gives:
h(x) = 5*f(x) + 10
Replacing the function f(x) we will get:
h(x) = 5*x² + 10
Then the correct option is D.
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Jose is building a rectangular shaped garden and needs to know how many square feet it will cover. The dimensions of the garden will be 8 feet in length and (3n+2) in width. What is the area of the garden space?
A) 24n+16
B) 11n+10
C) 40n
Thank you!!!
Answer:
The equation for the area of a rectangle is length*width. For this problem, it says the length is 8 and the width is (3n+2). All you have to do is multiply 8 by (3n+2).
8(3n+2)=A
24n+16=A
Option A is correct
determine the relative order of the metric prefixes of kilo-, micro-, centi-, and milli-. for the same base unit, choose... is less than choose... , which is less than choose... , which is less than choose... .
The relative order of the metric prefixes Milli- < Centi- < Micro- < Kilo-
The relative order of the metric prefixes of kilo-, micro-, centi-, and milli- is milli-, centi-, micro-, and kilo-. This order is determined by the exponential values of each prefix.
Milli- is equal to 10-3, centi- is equal to 10-2, micro- is equal to 10-6 and kilo- is equal to 103. The exponential values are used to determine the relative order of the prefixes. The lowest exponential value is milli-, making it the smallest metric prefix and the highest exponential value is kilo-, making it the largest metric prefix.
When the exponential values are compared, it is clear that the order of the prefixes is milli- < centi- < micro- < kilo-. This order is used to determine the relative size of the metric prefixes when measuring the same base unit.
For example, if the base unit is meter, then millimeter is the smallest measure and kilometer is the largest measure. The exponential values of the metric prefixes determine the relative order of the base unit.
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A cylinder has a height of 7 yards and a diameter of 26 yards. What is its volume? Use ≈ 3.14 and round your answer to the nearest hundredth.
The volume of the cylinder is 3,714.62 cubic yards.
How to get the volume of the cylinder?We know that the volume of a cylinder of radius R and height H is given by:
V = pi*R²*H
where pi = 3.14
In this case, we also know that:
H = 7yd
And the diameter is 26 yards, the radius is half of that, then:
R = 26yd/2 = 13yd
Then the volume is:
V = 3.14*(13 yd)²*7yd = 3,714.62 yd³
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There are three quarters, five dimes, and twelve pennies in a bag.
Once a coin is drawn from the bag, it is not replaced. If two coins
are drawn at random, determine each probability.
1. P(a quarter and then a penny)
2. P(a nickel and then a dime)
3. P(two pennies)
4. P(a dime and then a quarter)
The probability for these are
Probability(a dime and then a quarter)=3/76
Probability(two pennies)=33/95
Probability(a quarter and then a penny)=9/95
What is probability?
Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one. Probability has been introduced in Maths to predict how likely events are to happen. The meaning of probability is basically the extent to which something is likely to happen. This is the basic probability theory, which is also used in the probability distribution, where you will learn the possibility of outcomes for a random experiment. To find the probability of a single event to occur, first, we should know the total number of possible outcomes.
Probability of event to happen P(E) = Number of favourable outcomes/Total Number of outcomes
Now,
Quarters=3, Dimes=5 and Pennies=12
Total=20
Probability(a dime and then a quarter)=5/20*3/19=15/380=3/76
Probability(two pennies)=12/20*11/19=132/380=33/95
Probability(a quarter and then a penny)=3/20*12/19=36/380=9/95
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Check image for questions!
(Answers are already there, just gotta figure out where they go)
50 points!
The equation y is 2x - 3 describes the line with a slope of 2 and a Y-intercept of -3.
Linear equation?Use m is used to show the slope of a line.
m = 2
c is used to signify the line's y-intercept. c = -3
For the line's equation, the slope-intercept is: y = mx + c
In the equation above, replace c = -3 with m = 2 ,y = 2x - 3
Consequently, the equation of the line with a Y-intercept of -3 and a slope of 2 is as follows: y = 2x - 3.
For the line's equation, the slope-intercept is: y = mx + c
In the equation above, replace c = -3 with m = 2 ,y = 2x - 3
Consequently, the equation of the line with a Y-intercept of -3 and a slope of 2 is as follows: y = 2x - 3.
The complete question is,
The line with a -3 Y-intercept and a 2 slope has what equation?
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4 groups of 3 give me answer
The question 4 groups of 3 can be calculated to be a total of 12 objects across all groups.
How to solve for the total number in the groupThe total number of groups are 4 in number
Each of the 4 groups have 3 objects in it.
That is 3 in 4 places
This can be solved by 4 * 3 = 12
Hence we can say that the solution for the questions that says 4 groups of 3 is 12
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determine its average speed when it goes around the closed path. express your answer to three significant figures and include the appropriate units.
The average speed is 0 m/s since the object does not move.
Since the object does not change its position, it does not move. Therefore, its average speed is 0 m/s.
The object in question does not move in a closed path, meaning that its position remains the same throughout the entire path. As a result, its average speed is 0 m/s. This is because average speed is the total distance traveled divided by the total time taken, and since the object does not move its distance traveled is 0 and its time taken is also 0. Therefore, when the object goes around the closed path, its average speed is 0 m/s.
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Write two different expressions you could use to represent the
combined area of the Activities and Quotations sections. What
information about the sections does each expression show?
The area expressions are (2x + 1) * (x^2 + 4x - 5) and 2x^3 + 9x^2 - 6x - 5
How to determine the area expressionsThe missing figure is added as an attachment
From the question, we have the following parameters that can be used in our computation:
Length = 2x + 1
Width = x^2 + 4x - 5
The area is calculated as
Area = (2x + 1) * (x^2 + 4x - 5)
When expanded, we have
Area = 2x^3 + 8x^2 -10x + x^2 + 4x - 5
Evaluate the like terms
Area = 2x^3 + 9x^2 - 6x - 5
Hence, the area expression is 2x^3 + 9x^2 - 6x - 5
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Factor the following examples of difference perfect squares for X to power of 2-9
Answer: X^2 - 9 can be factored into (X - 3)(X + 3) which is the difference of squares.
The difference of squares factorization of X^2 - 9 is (X - 3)(X + 3)
Step-by-step explanation:
Santiago has planned a basketball game for the weekend.
The chance of snow on Saturday is 35%, with a 70% chance on
Sunday. If these probabilities are independent, what is the
chance that it will snow on both days?
The probability that it will snow on both days, given the chances of snow on Saturday and Sunday, is 24.5%.
How to find the probability ?The chance of it snowing on both days is calculated by multiplying the probability of it snowing on Saturday by the probability of it snowing on Sunday. If the probabilities are independent, we can assume that one event occurring doesn't affect the other event, therefore the probability of both events happening is just the product of the individual event probabilities.
So, the chance of it snowing on both days is:
P(Saturday and Sunday) = P(Saturday) x P(Sunday)
P(Saturday and Sunday) = 0.35 x 0.70
P(Saturday and Sunday) = 24.5 %
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