Answer with explanation:
The equation of a line passing through (a,b) and (c,d) is given by :-
[tex](y-b)=\dfrac{d-b}{c-a}(x-a)[/tex]
Equation of line passing through (2,-1) and (6,5) is given by :-
[tex](y-(-1))=\dfrac{5-(-1)}{6-2}(x-2)\\\\\Rightarrow\ (y+1)=\dfrac{6}{4}(x-2)[/tex]
[tex]\\\\\Rightarrow\ (y+1)=\dfrac{3}{2}(x-2)\ \ \ \ \ \text{[point slope form} : (y-y_1)=m(x-x_1)] \\\\\Rightarrow\ y+1=\dfrac{3}{2}x-3\\\\\Rightarrow\ y=\dfrac32x-4\ \ \ \ \ [\text{ slope intercept form} : y= mx+c]\\\\\Rightarrow\ 2y= 3x-2\times4\\\\\Rightarrow\ 2y=3x-8\\\\\Rightarrow\ 3x-2y=8 \ \ \ \ [\text{Standard form : Ax + By = C}][/tex]
A student decided to make random guesses for all the above 5 true/false questions. What is the probability of this student getting one or more correct answer
Answer: 25%
Step-by-step explanation:
The probability of getting at least one correct answer is 255/256 ≈ 0.996
The probability of getting exactly one correct answer is 5/256 ≈ 0.0195
What is probability?The probability is defined as the possibility of an event being equal to the ratio of the number of outcomes and the total number of outcomes.
As there are two possible results for each of the 5 questions, there are
2⁵ = 256 possibilities total.
To calculate the probability, then, we only need to know how many ways the student can get one correct answer.
The question's wording contains a small amount of uncertainty, therefore we will discuss both possibilities.
Probability of at least one correct answer:
There is only one way the student can have no correct answers, meaning there are 256 -1 = 255 ways the student can have at least one correct answer.
Thus, the probability of getting at least one correct answer is
255/256 ≈ 0.996
Probability of exactly one correct answer:
There are 5 ways the student can get exactly one correct answer
Thus, the probability of getting exactly one correct answer is 5/256 ≈ 0.0195
Learn more about probability here:
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Please!!!!! help me fill the blanks. I really need it!!! It due tomorrow!!!!
Answer:
The first blank which is in the first row would be 9
The second blank under the 5 is 100
The third blank below the 8 is 160
And the last blank is 240
Step-by-step explanation:
It you do 60 divided by 3, it would be 20, meaning each sweater costs $20.
Answer:
5 shirts=100. 8 shirts=160. 12 shirts.=240. 180$=9
Step-by-step explanation:
1 sweatshirt is 20. 60 divided by 3.
multiply 20 by the sweatshirt numbers for answers
Need help with geometry.
Answer:
x = 23
Step-by-step explanation:
m<1 and m<3 will be the same because they are vertical
m<3 and m<5 will be the same (I forgot their relationship)
which means m<5 and m<7 will be the same
which ALSO means that m<1 =7
So you know that m<1 = m<7 (4x -6 = 2x +40)
x = 23
Shahwhehehehdjdjendbxbsnenenen
Answer:
Shahwhehehehdjdjendbxbsnenenen
The Height H(t) (in feet) of a projectile fired vertically into the air from the ground is given by the equation H(T) = -16t^2 + 96t, where t is time (in sec) after the launch.
A) How long will it take the projectile to reach its maximum height?
B) What is the maximum height?
C) How long does it take the projectile to reach the ground again.
Answer:
a) 3s
B) 144m
C) 6s
Step-by-step explanation:
Given the height modeled by the function;
H(T) = -16t^2 + 96t,
The body will reach its maximum height when dh/dt = 0 (when velocity is zero)
dh/dt = -32t + 96
0 = -32t + 96
32t = 96
t = 96/32
t = 3s
Hence it will take the projectile 3s to reach its maximum height'
B) To get the maximum height we will substitute t = 3 into the equation
H(T) = -16t^2 + 96t,
H(3) = -16(3)^2 + 96(3)
H(3) = -144+ 288
H(3) = 144m]
Hence the maximum height is 144m
C) The projectile reaches the ground at h = 0
H(T) = -16t^2 + 96t,
0= -16t^2 + 96t,
16t² = 96t
16t = 96
t = 96/16
t = 6
Hence it will take the projectile 6s to reach the ground again
what is 494 divided by 6.5
Answer:
76
Step-by-step explanation:
Answer:
494 divided by 6.5 =76
Step-by-step explanation:
The circumference of a circular piece of plot is 440m. find the area
pie is 22/7
Answer:
Step-by-step explanation:
Circumference = 2pi r
440 = 2 *22\7 *r
70 = r
Area= pi r^2
Area= 22\7 *70*70
Area =15400
Evaluate the given expression for x=-14. -3x-5
Answer:
The answer is: 37
Step-by-step explanation:
The reason its this answer because first thing you have to do is the order operations Please Excuse My Dear Aunt Sally, since there is no parenthesis, or exponents we cross those out. Since, there is multiply we put in -14 where is x.
-3x-5=-3(-14)=5
Next, we multiply -3 and -14 and we get:
42, there reason its not a negative because two negatives equal to a positive.
There is Division or Addition, those are out. The only thing that is left Subtraction... So we are going to subtract 42-5 which equals;
37
I hope my answer helps!!
can u pls help me with this question
Answer:
[tex]\frac{1}{8}[/tex]
Step-by-step explanation:
We know that the artist can complete [tex]\frac{1}{4}[/tex] of a painting in 2 weeks. So, we just have to find half of [tex]\frac{1}{4}[/tex] to find how much of a painting the artist can do in a week, which is [tex]\frac{1}{8}[/tex] because half of [tex]\frac{1}{4}[/tex] is [tex]\frac{1}{8}[/tex].
Hope this helps! :)
6.203x4.5
Help pls asap
Answer:
27.9135
Step-by-step explanation:
QUADRATIC FORMULA SIMPLIFIED PLZ HELP
Answer:
3x² + 5x + 1 = 0 simplifiedx = (-5 ± [tex]\sqrt{13}[/tex])/6 rootsStep-by-step explanation:
Given quadratic formula
3x² + 5x - 5 = - 6Standard form
ax² + bx + c = 0Simplifying
3x² + 5x - 5 + 6 = 03x² + 5x + 1 = 0Solving
x = (-5 ± [tex]\sqrt{5^2 -4*3*1}[/tex])/(2*3)x = (-5 ± [tex]\sqrt{13}[/tex])/6what is the length of rs?
Answer:
SR=15units
‹RTQ=90° since ‹RTQ and ‹RTS are supplementary
Given that ‹RTQ is a right angle then RTQ is a right-angled triangle making RQ the hypotenuse
With that knowledge we calculate RT using Pythagorean theorem
RT=√(20)²-(16)²
RT=√400-256
RT=√144=12units
Now for triangle RST, SR is the hypotenuse and should have the longest length whose adjacent,ST should also sum up with 16 to give a number which when combined will give the square root of the sum of the squares of RQ and SR
Plug in 9 for ST and SR becomes
√(12)²+(9)²=√144+81=√225=15 units
This is true because SQ=16+9=25 units
and using Triangle RSQ,
SQ=√(20)²+(15)²=√400+225=√625=25 units
At the beginning of the semester, a professor tells students that if they study for the tests, then there is a 55% chance they will get a B or higher on the tests. If they do not study, there is a 20% chance that they will get a B or higher on the tests. The professor knows from prior surveys that 60% of students study for the tests. What is the probability that a randomly selected student studies for a test and gets a B or higher?
0.08
0.11
0.33
0.55
Answer:
.33
Step-by-step explanation:
Which ordered pair could be removed to
make the set a function?
{(1,3), (2,4), (3,4), (3,6), (5, 10), (6,3)}
A. (1,3)
B. (6,3)
C. (5, 10)
D. (3,4)
Answer:
The answer is choices D.
Step-by-step explanation:
hope this helps
expand the number 0.398
Answer:
00.398
Step-by-step explanation:
Answer:
Do you mean in expanded form? If so it's 0.3+0.09+0.008 I believe.
help plz need it so so much
Answer:
C
Step-by-step explanation:
The number line does not end at -2 and the solution should exclude 3 as it is a hollow circle instead of a filled one.
I need help with this I’ll mark you
Answer:
The answer is C
for all values of x , a function f is defined by f(x)=x^2+7x+12 if f(a)=2, what could be the value of a?
Answer:
a = -2 or a = -5
Step-by-step explanation:
We want [tex]f(a) = a^2 + 7a + 12 = 2[/tex]. We can subtract 2 from both sides of this equation to get [tex]a^2+7a+10=0[/tex]. We can factor this to get that [tex](a+2)(a+5)=0[/tex]. When the product of two numbers is equal to zero, one of the numbers must be equal to zero. This means that either a + 2 = 0, in which case a = -2, or a + 5 = 0, in which case a = -5.
What is the equation of the line shown below? Give your answer in slope-
intercept form.
Serial numbers for a product are to be made using 2 letters followed by 3 digits. The letters are to be taken from the first 6 letters of the alphabet, with no repeats. The digits are taken from the 10 digits 0, 1, 2, ..., 9, with no repeats. How many serial numbers can be generated?
==========================================================
Explanation:
There are 6 letters to pick from {A,B,C,D,E,F} and we have two slots to fill, where no repeats are allowed. This means we have 6*5 = 30 different ways to pick two letters.
There are 10 digits to pick from {0,1,2,...,9} and there are 3 slots to fill. This gives 10*9*8 = 720 different permutations for this portion.
Overall, we have 30*720 = 21600 different serial numbers possible.
Which expression is equivalent to 2x^2-
2x + 72
Answer:
36
Step-by-step explanation:
2x•2x=4x
4x-2x=2x
72÷2=36
Solve for l P = 2 ( l + b )
A. l = P - 2b/2
B. l = P - b/2
C. l = 4 ( P + b )
D. l = P - b/4
Please help geometry
Answer:
Step-by-step explanation:
if the triangles are similar their sides should be in proportion so
(56/70)=(48/60) and they are in proportion because .8 = .8
ΔNQR ~ ΔNLM
The difference of the product of 3 and a number -1/2
Answer:
(3 ⋅ x) - (-1/2)
Step-by-step explanation:
Since it says the product of 3 and a number, it can be written as 3 ⋅ x, where you need to multiply 3 by x, and it only says “a number” so you can just put x. Then, it says the difference of that product and -1/2. Now, you can put the product part in, which is 3 ⋅ x, and subtract that with -1/2 to get (3 ⋅ x) - (-1/2)
Hope this helps! :)
A circular pool is 3.5 meters deep and has a radius of 9 meters. What is the volume
Answer:
[tex]890.75m^3[/tex]
Step-by-step explanation:
Step one:
given data
heigth/depth = 3.5m
radius= 9m
Step two:
The shape is that of a cylinder
Hence the volume of the pool is
[tex]V= \pi r^2h[/tex]
substitute
[tex]V= 3.142*9^2*3.5\\\\V=890.75 m^3[/tex]
A major-league baseball diamond is shaped like a square with side lengths of 30 yards, as shown in the diagram.
Answer:
42
Step-by-step explanation:
What is the slope of line M.
What is a?
What is B?
Answer: A 2,2
Step-by-step explanation: 1 - 1 something
4 × 22 + 16 ÷ 4 - (4.9 + 5.5)
Answer:
81.6
Step-by-step explanation:
4 × 22 + 16 ÷ 4 - (4.9 + 5.5)
88 + 4 - (10.4)
81.6
Find the midpoint of (6, 1) and (2, 3).
Answer:
(4,2)
Step-by-step explanation:
need help with this problem it’s math so if you know math come on in
Answer:
The line is super close to 15 or 20. So one of those for sure
Step-by-step explanation:
Answer: its got to be 15 because the line isn't on 20
Step-by-step explanation: