Is the simplified form of 2 square foot 3. Square Foot 12 rational
The simplified form of the given radical expression is rational.
What is exponent ?Exponent can be defined as the method of expressing large numbers in terms of powers. Exponent refers to how many times a number multiplied by itself. For example, 6 is multiplied by itself 4 times, i.e. 6 × 6 × 6 × 6.
We are asked to determine whether the simplified form of 2√3.√12
To solve our given problem we will use exponent property for radicals
√m.√n = a√m.n
2√3.√12=2√3.12
2√3.√12=2√36
2√3.√12=2×6
2√√3.√12=12
The simplified form of the given radical expression is rational.
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Since our given radical expression simplifies to a rational, therefore, our answer is yes
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is 120,110,105… a geometric sequence
Answer: No
Step-by-step explanation:
Look at the 3 numbers in the sequence,
Geometric sequence means the ratio between two consecutive numbers in the sequence is a constant (eg. 10, 5, 2.5 is a geometric sequence as the ratio is a constant at 1/2)
However, for the sequence listed above
Looking at 1st and 2nd term,
Ratio = 110/120 = 11/12
Looking at 2nd and 3rd term,
Ratio = 105/110 = 21/22 which is not the same as 11/12.
Hence, since the ratio is not the same, this sequence is not a geometric sequence.
What is the modulus of 2 - 3i?
Oi
O √√√5
O
1-√√5
O√13
The modulus of 2 - 3i is √13. So, the correct option is d.
What is modulus?Modulus is a mathematical operation used to find the remainder when dividing two numbers. This is called a percent sign (%) and is represented by a single number such as 12. Used to determine if two numbers are divisible (no remainder). You can also use the modulus to compare two numbers to see which is greater or lesser. Additionally, this module can be used to calculate the distance between two points on the coordinate plane.
It is computed by taking the square root of the sum of the squares of the real and imaginary components, so √(2^2 + (-3)^2) = √13. The modulus of a complex number, also called absolute value, is a measure of distance from the origin.
Let z = -2 - 3i
z = (-2) + (-3)i
Modulus of z = √((-2)² + (-3)²)
√(4 + 9) = √13
Modulus of z = √13
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The question is in the picture
Answer:
For the first line its distributive property
The 2nd is combining like terms
4th is simplifying it
Im not sure about the last one since its just the answer of the problem
Step-by-step explanation:
. A polling organization announces that the proportion of American voters who favor congressional term limits is 64%, with a 95% confidence margin of error of 3%. If the opinion poll had announced the margin of error for 80% confidence rather than 95% confidence, this margin of error would be (a) 3%, because the same sample is used. (b) less than 3%, because we require less confidence. (c) less than 3%, because the sample size is smaller. (d) greater than 3%, because we require less confidence. (e) greater than 3%, because the sample size is smaller.
When C.I. is given as 80% then the margin of error will be 1.9591% as calculated from the given data.
We are given that the first margin of error (MOE) is 3%.
Also, confidence interval
first C.I.=95%
second C.I.=80%
Therefore , MOE at 80% will be ,
The formula for proportion is given as (P),
P=x/n , here 64%.
The values are same or constant as in general, this means standard deviation is also constant
Now formula for MOE is given by
MOE = Z x ( SD ) / √n
where , Z is value for confidence interval
MOE ∞ Z-value
So we can say that ,
MOE = k x Z ( where k = proportionality constant).
So , for 95 % Z=1.96 and for 80% Z=1.28
MOE then calculated will be , 1.95% .
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The coordinates of 3 of the vertices of a parallelogram are (-3, 4), (-2, 1), and (2, 6). What is the equation for the
line containing the side opposite the side containing the first two vertices? (Remember, opposite sides of a
parallelogram are parallel.)
A.
B.
-2
y=-x
5
2
y=-x+5
52.38
C. y=-3x
D. y=-3x+12.
y = -3x + 12 is the equation for the line containing the side opposite the side containing the first two vertices.
Given coordinates:
(-3,4) ; (-2,1) ; and (2,6)
let us solve for the slope.
Since , parallel sides have the same slope.
m = y2-y1 / x2-x1
m = 1 - 4 / -2-(-3)
m = -3 / 1
m = -3
y = mx + b
Since , (2,6) is a point which passes through the line . Hence , it must satisfy the equation.
Therefore,
6 = -3(2) + b
6 = -6 + b
6 + 6 = b
12 = b
On Substituting , values of m and b in y = mx +b , we get y = -3x +12 which is the required equation of the line.
Hence, y = -3x + 12 is the equation for the line containing the side opposite the side containing the first two vertices.
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sqrt{2x-1}-x=-8
solve for x
The values of x are 5 or 13.
What are equations?An equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
Given is an equation, [tex]\sqrt{2x-1}[/tex] - x = -8
[tex]\sqrt{2x-1}[/tex] - x = -8
[tex]\sqrt{2x-1}[/tex] = -8+x
Squaring both sides,
2x-1 = x²+64-16x
x²-16x-2x+1+64 = 0
x²-18x+65 = 0
Factorizing the equation,
x²-18x+65 = 0
x²-13x-5x+65 = 0
x(x-13)-5(x-13) = 0
(x-5)(x-13) = 0
x = 5 or 13
Hence, the values of x are 5 or 13.
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Let f(x)=5x and g(x)=sinx and h(x)=g(f(x))=sin(5x) What is h’(x)?
Answer:
Step-by-step explanation:
Derivation of composite functions concept.
h'(x)=g'(f(x))·f'(x)=(sin(5x))'×(5x)'=cos(5x)×5=5cos(5x)
Your teacher has disabled instant marking. Your marks will appear after the due date.
35%
Patryk has 7 cards.
There is a number on each card.
|2||3||4||5|| 6 ||7|| 8
Patryk takes two of the cards at random.
He works out the product of the numbers on the two cards.
Work out the probability that the product is an odd number.
EH
Type here to search
O
1/7 is the probability that the product is an odd number.
What is the simple definition of probability?
A probability is a number that expresses the possibility or likelihood that a specific event will take place.
Probabilities can be stated as proportions with a range of 0 to 1, or as percentages with a range of 0% to 100%.
Total Cards are 7
2 cards out of 7 cards can be selected in ⁷C₂ = 21 ways
Product would be odd if both cards are odd
3 , 5 , 7 are odd cards
2 cards out of 3 Can be selected in ³C₂ = 3 ways
( 3 , 5) , ( 3 , 7) , ( 5 , 7)
Hence probability the product of the numbers on the 2 cards is odd number
= 3/21
= 1/7
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What is '__ main __'?
In Python, __main__ is the name of the environment where top-level code is run.
We know that in Python, the main function acts as the starting point of execution for any software program.
As we know the program executes only when it runs directly, and if it is imported as a module, then it will not run, the execution of the program starts only when the main function is defined in Python.
__main__ is the name of the top-level scope in which top-level code executes.
Also, all the functions and modules will be executed in the top-level scope __main___ in the interpreter shell.
Using the top-level scope __main__ increases the reusability.
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4 Select the correct answer. Annabelle wanted to find out how many people in her neighborhood were going to the rock concert over the weekend. She asked a couple of her immediate neighbors. On the basis of the answers she got, she drew her conclusion. What kind of statistical investigation did Annabelle perform
Annabelle collected data from a sample of people that were convenient for her to access, such as her immediate neighbors, and used this to draw her conclusion.
Annabelle performed a convenience sample investigation, which is a type of statistical investigation. This involves collecting data from a sample of people that are convenient for the researcher to access. In this case, Annabelle asked a couple of her immediate neighbors to find out how many people in her neighborhood were going to the rock concert..
Convenience sampling is useful when time or resources are limited, however the results may not be representative of the larger population. Therefore, it is important to consider the limitations of the sample when drawing conclusions. For example, Annabelle may not have considered that the neighbors she asked may not be representative of the whole neighborhood.
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`y=7/(1,000)-(9x)/8` is this proportional or nonproportional
The following is a stem-and-leaf display representing the amount of gasoline purchased, in gallons (with leaves in tenths of gallons), for a sample of 25 cars that use a particular service station on the New Jersey Turnpike: 9 147 10 02238 11 125566777 12 223489 13 02 (a) Construct an ordered array. (b) Which of these two displays seems to provide more information? Discuss
The ordered array will be 9.1 9.4 9.7 10.0 10.2 10.2 10.3 10.8 11.1 11.2 11.5 11.5 11.6 11.6 11.7 11.7 12.2 12.2 12.3 12.4 12.8 12.9 13.0 13.2
What is leaf plot?
A stem and leaf plot, also known as a stem and leaf diagram, is a way to arrange data so that it is simple to see how frequently various sorts of values occur. It is a graph that displays ordered numerical data. A stem and a leaf are divided into each piece of data.
In this instance, the number on the left of the division stands in for the number in the tens place. The value or values on the right side are the ones that fall between the tens and ones places. The number "9.1" is the equivalent of the word "911," for instance. When a number appears more than once on the right side of a division, that number appears more than once in the tens place. In this case, the three numbers 9.1, 9.4, and 9.7 are represented by the string "9 | 147".
Hence, There is an ordered array when reading the stem and leaf plot from top to bottom:
9.1 9.4 9.7 10.0 10.2 10.2 10.3 10.8 11.1 11.2 11.5 11.5 11.6 11.6 11.7 11.7 12.2 12.2 12.3 12.4 12.8 12.9 13.0 13.2
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Becky is able to run up a 3. 00 m high flight of stairs in 2. 5 s if she has a mass of 50 kg how much power did she develop during her run up the stairs how long will it take becky in question 6 to run up a flight of stairs 4. 5 m high?
With a mass of 50 kg, Becky used 588 watts power to sprint up a 3.0 m high set of stairs in 2. 5 seconds. She is able to run up a 4.5 m high flight of stairs in 3.75 s.
How do you calculate power going up stairs?Work (in joules) equals your weight (in newtons) x the height of the stairs (in meters.) The power you now possess is equal to the sum of your labor times the duration of that labor, or: Work (measured in joules) divided by time equals power, measured in watts (in seconds.)
Given that mass of Becky is 50 Kg
gravity of earth is 9.8 m/s²
height of stairs is 3.0 m
time taken to run up in stairs is 2.5 s
Power = work done/ time taken
P = (50*9.8*3.0)/2.5
P = 1470/2.5
P = 588 watt
Becky is able to run up a 3.0 m high flight of stairs in 2.5 s
She is able to run up a 4.5 m high flight of stairs in t = (2.5 * 4.5)/3
t = 11.25/3
t = 3.75 s
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How do you find the coordinates of a point example?
To find the coordinates of a point in a coordinate system, do the inverse. Start at the point and trace a vertical line up or down to the x-axis. There you have your x-coordinate. Then repeat the process, but this time follow a horizontal line to determine the y-coordinate.
A point is identified by its ordered pair of (x, y). The first number represents the x-coordinate, while the second represents the y-coordinate.
To graph a point, you draw a dot at the coordinates of the ordered pair. It's usually a good idea to begin at the beginning.
An ordered pair of integers, such as an x-coordinate, which is a number on the x-axis, and a y-coordinate, which is a number on the y-axis, can be used to identify each point. Parentheses are used to indicate ordered pairings (x-coordinate, y-coordinate). The starting point is at (0,0).
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Katie says that if a number is a multiple of 8, it is also a multiple of 4. Is Katie correct? Explain.
Katie is correct. Any number that has 4 as a factor will also have 8 as a factor; therefore, any number that has 8 as a factor will have 4 as a factor.
Katie is correct. Since 4 is a factor of 8, any multiple of 8 will also be a multiple of 4.
Katie is incorrect. 80 is a number that has 8 as a factor but not 4.
Katie is incorrect; just because 4 is half of 8 does not mean that a number that has 8 as a factor will also have 4 as a factor. HELP PLS ASAP PLS AND THANK U
Katie is correct. Any number with 4 as a factor will also have 8 as a factor; therefore, any number with 8 as a factor will have 4 as a factor.
Katie is correct. Any number that is a multiple of 8 will also be a multiple of 4 because 8 is divisible by 4. For example, 8 is a multiple of 4 (8 = 2 x 4) and 16 is a multiple of 8 (16 = 2 x 8) and also a multiple of 4 (16 = 4 x 4). So, any number that is a multiple of 8 will also be a multiple of 4. So any number that is a multiple of 8 will also be a multiple of 4. Note that 80 is a multiple of 8, but not 4.
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How do i convert £10 to dollar? and what calculation do i ue
(it' on exchange rate)
We convert 10 pounds to Dollars and get 12.2 United states Dollars.
What does currency convert and exchange rate?Exchange rate is the rate at which one currency can be exchanged to another currency. The rate represents the relative value of one currency against the currency from another country. Currency conversion means convert one currency to another at an exchange rate.
How do we convert 10-pound sterling to dollar?We can convert pound to dollar by using currency exchange rate determined by the world market. The exchange rate is vary depending on the current situation of two country in which currency is converted between. The rate may be differed from one day to another.
1 pound sterling = 1.22 United States Dollar
10-pound sterling = 12.2 US Dollars
1 pound sterling = 1.76 Australian Dollar
10-pound sterling = 17.6 Australian Dollars
1 pound sterling = 1.64 Canadian Dollar
10-pound sterling = 16.4 Canadian Dollars
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Write the equation in standard form with integer coefficients. 0.5x - 2y - 0.75 = 0, y = - 3 x - 5
Answer:
50x - 200y = 75
3x + y = -5
Step-by-step explanation:
Standard form of a line
Ax + By = C
0.5x +-2y -0.75 Multiply through by 100
50x - 200 - 75 = 0 Add 75 to both sides
50x - 200y = 75
y = -3x - 5 Add 3x to both sides
3x + y = -5
Maisy and Oliver converted some pounds (£) into euros (€) at two different shops. Maisy converted £40 into €47.20 at shop A. Oliver converted £83 into €96.28 at shop B. Byron converted some pounds at one of these shops and received €68.44. What is the smallest amount that he could have converted?
The smallest amount that Byron could have converted is £73.44.
What is exchange rate?An exchange rate is the rate at which one currency can be exchanged for another currency. It is the value of one country's currency against another country's currency. Exchange rates fluctuate based on supply and demand for a particular currency, as well as economic and political factors.
Exchange rates are typically quoted as the value of one currency in terms of another currency. For example, an exchange rate of 1.2 US dollars (USD) to 1 Euro (EUR) means that 1 EUR can be exchanged for 1.2 USD.
There are two types of exchange rates, Floating and Fixed exchange rate.
According to question :-
To determine the smallest amount that Byron could have converted, we can use the exchange rate from shop A, which is €47.20 for £40.
If we divide the amount of euros he received (€68.44) by the exchange rate (€47.20 for £40), we get:
€68.44 ÷ €47.20/£40 = £73.44
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According to your graphing calculator what is the approximate solution to the trigonometric inequality tan(x/4)<1/5 over the interval 0<= x<=2pi radians 
0<=x<0.7896
0<=x<0.9799
0<=x<0.9870
0<=x<1.2249
The graph of tan(x/4) < 1/5 over the interval 0<= x<=2pi radians is attached. An approximate solution to the trigonometric inequality tan(x/4)<1/5 over the interval 0<= x<=2pi radians is 0 <= x < 0.7896.
y = 1/5 is a horizontal straight line parallel to x-axis.
Plot of tan(x/4)<1/5 over the interval 0<= x<=2pi radians is attached. The shaded region is the solution.
tan(x/4) < 1/5
Taking tan inverse on both sides
tan⁻¹(tan(x/4)) < tan⁻¹(1/5)
x/ 4 < tan⁻¹(1/5)
Multiplying by 4 on both sides
x < 4tan⁻¹(1/5)
x < 0.7896
Applying the limits of intervals
0 <= x <= 2pi ≈ 6.28
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What is the measure of angle OAC if major arc AB measures 220 degrees?
55°
70°
110°
140°
I already know the answer is 55 but I need to know why and how to get 55?
Therefore , the solution of the given problem of triangle comes out to be
OAC angle arc is = 55 degrees.
What is triangle?Triangular polygons in geometry are those with right side and three vertices. There are three straight sides to this two-dimensional shape. Three-sided polygons include triangles. A triangle's three angles add up to a whole 180 degrees. A single plane contains the triangle.
Here,
Half of the arc AB is the measure of angle OAC, hence the measure of angle OAC is:
OAC = 0.5 times 220 degrees.
110 degrees is OAC.
If the angle OAC is measured as a quarter of an arc AB, then the angle OAC is measured as follows:
OAC equals 0.25 x 220 degrees
OAC = 55 degrees
Therefore , the solution of the given problem of triangle comes out to be
OAC angle arc is = 55 degrees.
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x + y = 3
Which of the following equations is equivalent to the given equation?
3x + 2y = 18
2x + 3y = 18
3x + 2y = 3
The equation equivalent to the equation x + y = 3 is 6x + 6y = 18.
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
Example:
2x + 4 = 9 is an equation.
We have,
x + y = 3
Multiply 6 on both sides.
6x + 6y = 18
Thus,
The equation that is equivalent is 6x + 6y = 18.
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A geologist visits 60 volcanoes in Alaska and California. What if 40% of the volcanoes were in California? How many volcanoes would the geologist have visited in California and how many in Alaska?
Answer : in California there are 24 volcanoes while in Alaska there are 36 volcanoes.
Step-by-step explanation:
Total number of volcanoes = 60.
40% of the volcanoes where in California.
i.e 100% - 40% = 60%.
60% of the volcanoes were in Alaska.
In California = 40/100 × 60 = 24 volcanoes.
In Alaska = 60/100 × 60 = 36 volcanoes.
There are 12 girls and 16 boys in Mr jonsons 3rd period class of these students 3 girls and 4 boys wear glasses what percentage of the Stu in Mr jonsons class wear glasses
Answer:
25%
Step-by-step explanation:
Of the 12 girls and 16 boys in Mr. Johnson's class, 3 girls and 4 boys wear glasses. You want to know the percentage of students in the class who wear glasses.
PercentageThe percentage is the fraction multiplied by 100%. The fraction is the ratio of glasses-wearers to total students.
percentage = (girls w/ glasses + boys w/ glasses)/(girls + boys)×100%
percentage = (3 +4)/(12+16) × 100% = 7/28 × 100% = 25%
25% of the students in Mr. Johnson's class wear glasses.
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13. The number of pictures your printer
can print are shown in the table. Find
the rate in pictures per minute.
Minutes 2 4 6
8
Pictures 16 32 48 64
15.
16
Answer: The table shows the number of pictures that a printer can print at different intervals of time (measured in minutes). To find the rate in pictures per minute, we need to divide the number of pictures printed by the number of minutes it took to print them.
For example, at 2 minutes the printer printed 16 pictures. The rate of pictures printed per minute is 16 pictures / 2 minutes = 8 pictures/minute.
Similarly, at 4 minutes the printer printed 32 pictures. The rate of pictures printed per minute is 32 pictures / 4 minutes = 8 pictures/minute
And, at 6 minutes the printer printed 48 pictures. The rate of pictures printed per minute is 48 pictures / 6 minutes = 8 pictures/minute.
And, at 8 minutes the printer printed 64 pictures. The rate of pictures printed per minute is 64 pictures / 8 minutes = 8 pictures/minute.
From this it can be seen that the printer has a constant rate of 8 pictures per minute, independent of the number of minutes, it is producing 8 pictures/min.
The value 15 is not related to the table, so it's not the rate, and 16 is not the rate either, it is the number of pictures printed at 8 minutes.
Step-by-step explanation:
Approximately 297 million guests visit the 400 American amusement parks annually, and take 1.7 billion safe rides. The National Safety Council publishes a report titled "Fixed-Site Amusement Ride Injury Survey" for the International Association of Amusement Parks and Attractions. The number of injuries per million patron-rides, X, has a Poisson distribution with parameter 0.8. In one million patron-rides, what is the probability that there are
a) No injuries?
b). More than TWO injuries?
The probabilities are given as follows:
a) No injuries: 0.4493 = 44.93%.
b) More than two injuries: 0.0474 = 4.74%.
What is the Poisson distribution?In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following equation:
[tex]P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}[/tex]
The parameters are:
x is the number of successes that we want to find the probability of.e = 2.71828 is the Euler number[tex]\mu[/tex] is the mean in the given interval or range of values of the input parameter.The mean for this problem is of:
[tex]\mu = 0.8[/tex]
The probability of no injuries is of P(X = 0), hence:
[tex]P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}[/tex]
[tex]P(X = 0) = \frac{e^{-0.8}(0.8)^{0}}{(0)!} = 0.4493[/tex]
The probability of more than two injuries is of:
P(X > 2) = 1 - P(X <= 2)
In which:
P(X <= 2) = P(X = 0) + P(X = 1) + P(X = 2)
Hence:
[tex]P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}[/tex]
[tex]P(X = 0) = \frac{e^{-0.8}(0.8)^{0}}{(0)!} = 0.4493[/tex]
[tex]P(X = 1) = \frac{e^{-0.8}(0.8)^{1}}{(1)!} = 0.3595[/tex]
[tex]P(X = 2) = \frac{e^{-0.8}(0.8)^{2}}{(2)!} = 0.1438[/tex]
Then:
P(X <= 2) = P(X = 0) + P(X = 1) + P(X = 2) = 0.4493 + 0.3595 + 0.1438 = 0.9526.P(X > 2) = 1 - P(X <= 2) = 1 - 0.9526 = 0.0474.More can be learned about the Poisson distribution at https://brainly.com/question/7879375
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Helen delivers parcels on tuesday helen delivered 20% more parcels than on monday.
On Wednesday, helen delivered 50% fewer parcels than on Tuesday.
On Wednesday, helen delivered 72 parcels
calculate the number of parcels that helen delivered on monday
So the number of parcels that Helen delivered on Monday is 120 parcels.
Define Percentage.A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to compute a percentage of a number, we should divide it by its whole and then multiply it by 100. The proportion therefore refers to a component per hundred. Per 100 is what the term percent signifies. The letter "%" stands for it.
Define Proportion.An equality of two ratios is a percentage. We use proportions to construct comparable ratios and find solutions to problems involving unknown numbers.
If on Wednesday Helen delivered 50% fewer parcels than on Tuesday, then on Tuesday Helen delivered 72 / (1 - 0.5) = 72 * 2 = 144 parcels.
On Tuesday Helen delivered 20% more parcels than on Monday, so the number of parcels Helen delivered on Monday is (144 / 1.2) = 120
So Helen delivered 120 parcels on Monday.
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y=mx+b give the equation of the line in slope intercept form that runs through (-3,6) and (5,-2)
Answer:
y = -x +3
Step-by-step explanation:
You want the equation of the line through the points (-3, 6) and (5, -2) in slope-intercept form.
SlopeThe slope can be found using the formula ...
m = (y2 -y1)/(x2 -x1)
m = (-2 -6)/(5 -(-3)) = -8/8 = -1
InterceptThe y-intercept can be be found using the formula ...
b = y -mx
b = 6 -(-1)(-3) = 3
EquationThe equation in slope-intercept form is ...
y = mx +b
Using the found values, the equation is...
y = -x +3
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TOLL ROAD Mr. Espinoza randomly chooses one of five toll booths when
entering a toll road when driving to work. What is the probability he will
select the middle toll booth on Monday and Tuesday?
Answer: Assuming that the selection of the toll booth is a random and independent event, the probability that Mr. Espinoza chooses the middle toll booth on Monday is 1/5 (or 20%), since there are five total toll booths and the middle booth is one of those options. Similarly, the probability that he chooses the middle booth on Tuesday is also 1/5 (or 20%).
To find the probability that he chooses the middle booth on Monday and Tuesday, we can multiply the probabilities of each event.
Probability of selecting middle booth on Monday AND selecting middle booth on Tuesday = (1/5) * (1/5) = 1/25 = 0.04 or 4%
So, Mr. Espinoza will select the middle toll booth on Monday and Tuesday with a probability of 4%. This means that the chance that both events will happen is low and quite rare, but not impossible.
Step-by-step explanation:
Members of the science club voted for their favorite planet. The picture graph shows the total votes. How many more members voted for Mars than for Earth?
The members voted 2 more for mars than earth.
What are the number of planets in the solar system?The Solar System has at least eight planets: the terrestrial planets Mercury, Venus, Earth and Mars, and the giant planets Jupiter, Saturn, Uranus and Neptune.
Given here, Mars has 8 votes while earth has 6 votes
Thus difference in votes is =8-6
= 2
Hence, Mars got two more members than earth
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