Answer: x - 4y = -16
Step-by-step explanation: Since we're given a point and a slope, we can write the equation of this line using the point-slope formula.
y - y₁ = m(x - x₁)The given point, (4, 5), represents (x₁, y₁).
So if we plug all our given information into the formula,
including our slope of 1/4, we get y - 5 = 1/4(x - 4).
To put our equation in standard form, first, distribute
the 1/4 through the parentheses.
So we get y - 5 = 1/4x - 1.
Remember that standard form cannot have any fractions in it so our next step is to multiply both sides of the equation by 4 to get rid of the fraction.
That gives us 4y - 20 = x - 4.
Now moves the -20 to the right side by adding 20 to both sides.
So we get 4y = x + 16.
Now subtract x from both sides to get -x + 4y = 16.
Finally, our coefficient on our x term must be positive so we
divide both sides by -1 to get x - 4y = -16.
Example 3:
In how many ways can a supermarket manager display 5 brands of cereals
in 3 spaces on a shelf?
Solution:
Answer:
10
Step-by-step explanation:
5
C
3
5!/(3!(5-3)!)
5!/(3!x2!)
120/12
10
In 10 ways can a supermarket manager display 5 brands of cereals
in 3 spaces on a shelf.
What is Combination?Combinations are mathematical operations that count the number of potential configurations for a set of elements when the order of the selection is irrelevant. You can choose the components of combos in any order. Permutations and combinations can be mixed up.
Given:
Total brands of cereals= 5
Using Combination, C(n, r)
= n!/ r! (n- r)!
So, the number of ways
= C(5, 3)
= 5!/(3!(5-3)!) 5
= 5 x 4 x 3! / 3! x 2!
= 5 x 4 /2
= 10
Thus, the total number of ways is 10.
Learn more about Combination here:
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Solve for y
4
_ =6
y
Answer:
y=2/3
Step-by-step explanation:
Since y is in the denominator, we take it to the other side to make it the numerator. And 6 also changed sides which results in y=4/6. Reducing to lowest terms we get, y=2/3.
The augmented matrix is given for a system of equations. If the system is consistent, find the general solution. Otherwise state that there is no solution.
[1 -5 -4
0 0 7]
A. X1 = - 4 + 5x2 X2 is free
B. (-4,7)
C. X1 = - 4 +5x2
X2=7
X3 is free
D. There is no solution.
Answer:
Option D (There is no solution) is the correct answer.
Step-by-step explanation:
According to the question, the matrix is:
⇒ [tex]\left[\begin{array}{ccc}1&-5&-4\\0&0&7\end{array}\right][/tex]
The linear equation will be:
⇒ [tex]x-5y=-4[/tex]
and
⇒ [tex]0.x+0.y=7[/tex]
i.e,
[tex]0=7[/tex] (Not possible)
Thus the above given matrix has no solution. So the above is the correct option.
Morning donuts recently sold 14 donuts, of which 7 we're cake donuts. Considering this data,how many of the next 6 donuts sold would you expect to be cake donuts
Answer:
Three of your next six donuts sold will be cake donuts.
Step-by-step explanation:
14:7 simplified to a unit ratio is 2:1. Using this information, we know that 6:3 is the ratio for the next 6 donuts.
GIVING OUT BRAINLIEST HELP MEEE PLSS!!
Answer:
I'm like positive it's C...
Step-by-step explanation:
Answer:
45/28
Step-by-step explanation:
take angle R as reference angle
tan R=opposite/adjacent
=45/28
Find the equation of the least squares regression line. Show all calculations, and be sure to define any variables used.
a cyclist and a motorist start from the same point at 8.30 am and travels in opposite directions. the cyclist at 12km and the motorist at 50km/hr,how far apart will they be at 10am
Answer:
Step-by-step explanation:
A multiple-choice test contains 25 questions, each with 4 answers. Assume a student just guesses on each question. (a) What is the probability that the student answers more than 20 questions correctly
Answer:
9.68*10^-10
Step-by-step explanation:
The problem above can be solved using the binomial probability relation :
Where ;
P(x = x) = nCx * p^x * q^(n-x)
n = number of trials = 25
p = 1/4 = 0.25
q = 1 - p = 0.75
x = 20
P(x > 20) = p(x = 21) + p(x = 22) +.. + p(x = 25)
Using the binomial probability calculator to save computation time :
P(x > 20) = 9.68*10^-10
PLS HELP ASAP !!! WILL MARK BRAINLIEST !!
Answer:
c is equal to e
Step-by-step explanation: a
Five minivans and three trucks are traveling on a 3.0 mile circular track and complete a full lap in 98.0, 108.0, 113.0, 108.0, 102.0, 101.0, 85.0, and 95.0 seconds, respectively. Assuming all vehicles are traveling at constant speeds, what is the time-mean speed of the minivans
Answer:
The time-mean speed of the minivans is of 105.8 seconds.
Step-by-step explanation:
Mean of a data-set:
The mean of a data-set is the sum of all values in the data-set divided by the number of values.
Five minivans, times of: 98.0, 108.0, 113.0, 108.0, 102.0, in seconds.
Thus, the mean is:
[tex]M = \frac{98 + 108 + 113 + 108 + 102}{5} = 105.8[/tex]
The time-mean speed of the minivans is of 105.8 seconds.
Bill Dollar is playing a video game. After level one he has - 17 points. You decide to challenge Bill online and after level one you have a score that is 29 points less than Bill's score. What is your score?
Answer:
-46
Step-by-step explanation:
To find your score, take Bill's score which is -17 and if it is 29 less than, you subtract 29
So, - 17 - 29 is -46
Will mark Brainlest (from a deck of cards,pemba withdraw a card at random what is the probability that the card is queen) step by using formula
Answer:
1/13
Step-by-step explanation:
there are total no of 52 cards
out of that there are 4 queen
propability = tatal no of favorable outcomes / total no of possible outcomes
=4 / 52
=1/13
Answer:
1/13
Step-by-step explanation:
Total cards = 52
Number of Queen = 4
Probability of the chosen card to be queen
[tex]=\frac{Number \ of \ queen}{total \ number \ of \ cards}\\\\=\frac{4}{52} \\\\= \frac{1}{13}[/tex]
Determine whether the stochastic matrix P is regular. Then find the steady state matrix X of the Markov chain with matrix of transition probabilities P. P=
0.22 0.20 0.65
0.62 0.60 0.15
0.16 0.20 0.20
Answer:
Step-by-step explanation:
Given that:
[tex]P = \left[\begin{array}{ccc}0.22&0.20&0.65\\0.62&0.60&0.15\\0.16&0.20&0.20\end{array}\right][/tex]
For a steady-state of a given matrix [tex]\bar X[/tex]
[tex]\bar X = \left[\begin{array}{c}a\\b\\c\end{array}\right][/tex]
As a result P[tex]\bar X[/tex] = [tex]\bar X[/tex] and a+b+c must be equal to 1
So, if P[tex]\bar X[/tex] = [tex]\bar X[/tex]
Then;
[tex]P = \left[\begin{array}{ccc}0.22&0.20&0.65\\0.62&0.60&0.15\\0.16&0.20&0.20\end{array}\right]\left[\begin{array}{c}a\\b\\c\end{array}\right] =\left[\begin{array}{c}a\\b\\c\end{array}\right][/tex]
[tex]\implies \left\begin{array}{ccc}0.22a+&0.20b+&0.65c\\0.62a+&0.60b+&0.15c\\0.16a+&0.20b+&0.20c\end{array} \right = \left \begin{array}{c}a ---(1)\\b---(2)\\c---(3)\end{array}\right[/tex]
Equating both equation (1) and (3)
(0.22a+ 0.2b + 0.65c) - (0.16a + 0.2b + 0.2c) = a - c
0.06a + 0.45c = a - c
collect like terms
0.06a - a = -c - 0.45c
-0.94 a = -1.45 c
0.94 a = 1.45 c
[tex]c =\dfrac{ 0.94}{1.45}a[/tex]
[tex]c =\dfrac{ 94}{145}a --- (4)[/tex]
Using equation (2)
0.62a + 0.60b + 0.15c = b
where;
c = 94/145 a
[tex]0.62a + 0.60b + 0.15(\dfrac{94}{145}) a= b[/tex]
[tex]0.62a + 0.15(\dfrac{94}{145}) a= -0.60b+b[/tex]
[tex]0.62a + (\dfrac{141}{1450}) a= 0.40b[/tex]
[tex](0.62+\dfrac{141}{1450}) a= 0.40b[/tex]
[tex](\dfrac{62}{100}+\dfrac{141}{1450}) a= 0.40b[/tex]
[tex](\dfrac{1043}{1450})a= 0.40b[/tex]
[tex](\dfrac{1043}{1450})a= \dfrac{4}{10} b[/tex]
[tex](\dfrac{1043 \times 10}{1450 \times 4})a = \dfrac{4}{10} \times \dfrac{10}{4}[/tex]
[tex]b = (\dfrac{1043}{580}) a --- (5)[/tex]
From a + b + c = 1
[tex]a + \dfrac{1043}{580}a + \dfrac{94}{145} a = 1[/tex]
[tex]a + \dfrac{1043}{580}a + \dfrac{94*4}{145*4} a = 1[/tex]
[tex]a + \dfrac{1043}{580}a + \dfrac{376}{580} a = 1[/tex]
[tex]\dfrac{580+ 1043+376 }{580} a= 1[/tex]
[tex]\dfrac{1999}{580} a= 1[/tex]
[tex]a = \dfrac{580}{1999}[/tex]
∴
[tex]b = \dfrac{1043}{580} \times \dfrac{580}{1999}[/tex]
[tex]b = \dfrac{1043}{1999}[/tex]
[tex]c = \dfrac{94}{145} \times \dfrac{580}{1999}[/tex]
[tex]c= \dfrac{376}{1999}[/tex]
∴
The steady matrix of [tex]\bar X[/tex] is:
[tex]\bar X = \left[\begin{array}{c}\dfrac{580}{1999} \\ \\ \dfrac{1043}{1999}\\ \\ \dfrac{376}{1999}\end{array}\right][/tex]
Question 6 of 10
Which expression gives the volume of a sphere with radius 7?
A 4/3pi(7^2)
B. 4/3pi (7^3)
C. 4pi(7^3)
D. 4pi(7^2)
Answer:
B. 4/3pi (7^3)
Step-by-step explanation:
The volume of a sphere is given by
V = 4/3 pi r^3
We know the radius is 7
V = 4/3 pi 7^3
Given a circle with a diameter of which equation expresses it as the ratio of the circumference of a circle to its diameter?
Answer:
B. π = 8C/5
Step-by-step explanation:
Given the following data;
Diameter = ⅝
To find the ratio;
Mathematically, the circumference of a circle is given by the formula;
C = πD
Where;
C is the circumference of a circle.
D is the diameter of a circle.
Substituting the value of D, we have;
C = π * ⅝
Cross-multiplying, we have;
8C = 5π
π = 8C/5
A colony contains 1500 bacteria. The population increases at a rate of 115% each hour. If x represents the number of hours elapsed, which function represents the scenario?
f(x) = 1500(1.15)x
f(x) = 1500(115)x
f(x) = 1500(2.15)x
f(x) = 1500(215)x
Answer:
C) f(x) = 1500(2.15)x
Step-by-step explanation:
Got it right on Edge :)
The base of a solid is a circular disk with radius 4. Parallel cross sections perpendicular to the base are squares. Find the volume of the solid.
Answer:
the volume of the solid is 1024/3 cubic unit
Step-by-step explanation:
Given the data in the question,
radius of the circular disk = 4
Now if the center is at ( 0,0 ), the equation of the circle will be;
x² + y² = 4²
x² + y² = 16
we solve for y
y² = 16 - x²
y = ±√( 16 - x² )
{ positive is for the top while the negative is for the bottom position }
A = b²
b = 2√( 16 - x² ) { parallel cross section }
A = [2√( 16 - x² )]²
A = 4( 16 - x² )
Now,
VOLUME = [tex]\int\limits^r -rA dx[/tex]
= [tex]\int\limits^4_4 {-4(16-x^2)} \, dx[/tex]
= 4[ 16x - (x³)/3 ] { from -4 to 4 }
= 4[ ( 64 - 64/3 ) - (-64 = 64/3 0 ]
= 4[ 64 - 64/3 + 64 - 64/3 ]
= 4[ (192 - 64 + 192 - 64 ) / 3 ]
= 4[ 256 / 3 ]
= 1024/3 cubic unit
Therefore, the volume of the solid is 1024/3 cubic unit
What is the integer x
so that x/9
lies between 71/7
and 113/11 ?
Answer:
(A) 89 (B) 91 (C) 92 (D) 95 4.If |x−2| = p, where x < 2, then x+1 equals (A) −2 (B) 3− p (C) |2p−2| (D) 2p−2 5.A
Step-by-step explanation:
Following are the calculation to the find the value of x:
Given:
Please find the question.
To find:
x=?
Solution:
[tex]\frac{71}{7} <\frac{x}{9} < \frac{113}{11}\\\\10 <\frac{71}{7} < 11 \\\\10< \frac{113}{11}<11\\\\\frac{x}{9} >10\\\\x>90\\\\\text{When}\ x=91 \\\\\frac{71}{7} > \frac{91}{9}\\\\x=92\\\\ \frac{71}{7}< \frac{92}{9} <\frac{113}{11}\\\\[/tex]
so, x= 92 \\\\
by compare score value x= 92
Learn more:
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Hhhelllllppp qqquuuiiiccckkk
Answer:
F
E or C (depending on the actual angles - see below in the details)
Step-by-step explanation:
two triangles are congruent, when after some rotation or mirroring they can cover each other exactly.
that means they must both have the same angles and side lengths.
these are the possible conditions to determine that 2 triangles are congruent (without knowing ALL of the sides and angles) :
SSS (Side-Side-Side) - all 3 sides of triangle 1 are exactly of the same length as the 3 sides of triangle 2.
SAS (Side-Angle-Side) - 2 sides and one angle are the same
ASA (Angle-Side-Angle) - 2 angles and the side between these 2 angles are the same
AAS (Angle-Angle-Side) - 2 angles and any not-included side are the same
RHS (Right angle-Hypotenuse-Side) - both triangles are right-angled (one angle is 90 degrees), and the Hypotenuse (the side opposite to the 90 degree angle) and another side are the same.
so, now look at a).
we only know the angles. but we could use a zoom lens of a camera and make them bigger and smaller, while their angles remain actually the same.
therefore, we cannot say, if they are actually congruent (only if their side lengths are the same too).
but we can say that they could be congruent.
and therefore also none of the congruent conditions apply, because for all of them we always need at least one side length. and we don't have that.
now looking at b)
I am not sure I can read one of the given angles correctly.
case one: I read the angles in triangle 2 as 66 and 58 degrees. that would make the third angle
180 - 66 - 58 = 56
but triangle 1 has the angles of 68, 54 and
180 - 68 - 54 = 58
=> the three angles are not the same, so the triangles are definitely not congruent
case two: I could read the angles in triangle 2 also as 68 and 58. that would make the third angle
180 - 68 - 58 = 54
and the side connecting the 68 and 58 angles has the same length, so the ASA criteria are fulfilled, and the triangles are congruent. C
Alex is planning to surround his pool ABCD with a single line of tiles. How many units of tile will he need to surround his pool? Round your answer to the nearest hundredth.
Answers:
8.96
10.48
13.42
20.42
Answer:19.82
Step-by-step explanation:
Got it right i did it on a test
Match the terms to their definition.
1. expression
a branch of mathematics that uses variables
2. opposite numbers
a mathematical statement that shows two expressions are equal using an equal sign
3. equation
a line that graphically represents all numbers
4. arithmetic sequence
a value that is substituted in for the variable in a function in order to generate an output value
5. function
two numbers that are the same distance from zero on the number line, but in opposite directions
6. family of facts
a single term; multiple terms connected by an addition or subtraction sign
7. input
a number belonging to the set made up of the counting numbers: 1, 2, 3, and so on
8. coordinate plane
a set of numbers where the difference is the same between any two consecutive terms
9. integer
all possible combinations for a set of numbers (2 + 3 = 5, 3 + 2 = 5, 5 - 3 = 2, 5 - 2 = 3)
10. negative number
a relation in which for any given input value, there is only one output value
11. natural number
a number that is less than zero
12. number line
a two-dimensional system in which a location is described by its distance from two intersecting, perpendicular axes
13. algebra
a number belonging to the set made up of the whole numbers and their opposites
Answer:
sim eu também preciso desta respota
Dr. smith determined that that the average human pregnancy is 266 days from conception to birth. Assume the length of human pregnancies can be approximated by a normal distribution with a mean of 266 days and standard deviation = 16 days. Find the prob. that a pregnancy will last:__________
Answer:
[tex]P(x< 240) = 0.0521[/tex]
Step-by-step explanation:
Given
[tex]\bar x = 266[/tex]
[tex]\sigma = 16[/tex]
Required
[tex]P(x < 240)[/tex] --- pregnancy will last less than 240 days
First, calculate the z score
[tex]z = \frac{x - \bar x}{\sigma}[/tex]
Where:
[tex]x = 240[/tex]
So, we have:
[tex]z = \frac{240 - 266}{16}[/tex]
[tex]z = \frac{-26}{16}[/tex]
[tex]z = -1.625[/tex]
So:
[tex]P(x< 240) = P(z < -1.625)[/tex]
From z probability:
[tex]P(z < -1.625) = 0.052081[/tex]
[tex]P(z < -1.625) = 0.0521[/tex] --- approximated
So:
[tex]P(x< 240) = 0.0521[/tex]
Rewrite each equation in slope-intercept form 3x + 5y = 12
Answer:
y= -3/5x + 12/5
Step-by-step explanation:
Answer:
y= - 3/5 x 12/5
Step-by-step explanation:
See imagr below:)
Find the value of x I need help
Answer:
x =35
Step-by-step explanation:
The sum of the angles of a triangle add to 180
x+10 +x + 3x-5 = 180
Combine like terms
5x+5 = 180
Subtract 5 from each side
5x+5-5 =180-5
5x = 175
Divide by 5
5x/5 =175/5
x =35
A rectangular field is covered by circular sprinklers as
shown in the diagram. What percentage of the field is not
being watered by the sprinklers?
Answer:
21%
Step-by-step explanation:
Area of one sprinkler
a = πr²
a = π10²
a = 314.159 ft²
8 sprinklers
a = 8 * 314.159
a = 2,513.272
---------------------
area of field
a = lw
a = 80 * 40
a = 3200
------------------------
area not watered
a = 3200 - 2,513.272
a = 686.728
------------------
percentage not watered
p = 686.728 / 3200 * 100%
p = 21.46025%
Rounded
21%
Which expression gives the measure of XYZ?
V
110°
w
D
42
O A. 110° - 42°
O B. 2(110° + 42°)
O c. 2(110° - 42°)
OD. 110° +420
Answer:
1/2( 110+42)
Step-by-step explanation:
Angle Formed by Two Chords= 1/2(sum of Intercepted Arcs)
<<XYZ = 1/2( 42+110)
What is 30 rounded to the nearest whole number percent?
Answer:
Thirty rounded to the nearest whole number percent is 30% (%=percent)
Step-by-step explanation:
Well, you see that if you have 30 out of one hundred then that's when all you have to do is go with the same number and just add percent or % to the end.
Please Mark as Brainliest
Hope this Helps
This is just evidence
I’m not sure how to do this one, can anyone help me? Please?
Here's an answer! :)
a tv cost £800 plus VAT at 20% what is the total cost of the tv?
Answer:
Given:
Cost = £ 800
Tax = 20%
To find:
The total cost
Solution:
Total cost = Cost + Tax
Tax = 20 % of cost
20 / 100 * 800
Tax = £ 160
Hence,
Total cost = £ 800 + £ 160
Total cost = £ 960
Please help me!!!!!!!!!!!!!!!!
Answer:
I think it might be SAS. (side angle side)
