Which expression gives the distance between the points
(-3, 4) and (6,-2)?
O A. (-3 - 4) * +(6+2)
O B. (-3-6)* + (4 +2)
O c. +(-3-6)* +(4+2) ?
O D. (-3 - 4) * +(6+2)
Answers
Answer:
C. sqrt((-3-6)² + (4+2)²)
Step-by-step explanation:
as we are using Pythagoras and asking for the distance as a side length (actually the Hypotenuse, the side opposite of the 90 degree angle) in a right-angled triangle, only an expression of a square root of a sum of squares can be right.
so, A and B are automatically out without even further analysis.
for the distance between 2 points on a coordination grid we build the mentioned right-angled triangle with the difference in x-direction as one side (e.g. "a"), the difference in y-direction as a second side (e.g. "b").
and the direct distance is then the Hypotenuse "c".
you remember Pythagoras :
c² = a² + b²
and therefore
c = sqrt(a² + b²)
in our example "a" is the difference between the 2 x-values.
a = (-3 - 6)
and "b" is the difference between the 2 y-values.
b = (4 - -2) = (4 + 2)
since we have to square them for the formula, the direction of what is subtracted from what is irrelevant, as the square of a negative value is also positive.
c = sqrt((-3 - 6)² + (4 + 2)²)
and that is answer option C
Related Questions
Example 3:
In how many ways can a supermarket manager display 5 brands of cereals
in 3 spaces on a shelf?
Solution:
Answers
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:
https://brainly.com/question/13387529
#SPJ6
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.
Answers
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.
A box of 10 flashbulbs contains defective . A random sample of 2 is selected and tested. Let X be the random variable associated with the number of defective bulbs in the sample. a. Find the probability distribution of X. b. Find the expected number of defective bulbs in a sample.
Answers
Answer:
(a)
[tex]Pr(x = 0) = \frac{^7C_2}{45}[/tex] [tex]Pr(x = 1) = \frac{^7C_1 * ^3C_1}{45}[/tex] [tex]Pr(x = 2) = \frac{^3C_2}{45}[/tex]
(b)
[tex]E(x) = \frac{3}{5}[/tex]
Step-by-step explanation:
Given
[tex]n = 10[/tex] --- flashbulbs
[tex]k = 3[/tex] --- defective bulbs
[tex]r = 2[/tex] --- selected
Solving (a): The distribution of x
The total outcome is: [tex]^nC_r[/tex]
This gives:
[tex]^{10}C_2 = 45[/tex]
Having 3 defective bulbs means 7 are not.
When there is no defective bulb among the selected, the probability is:
[tex]Pr(x = 0) = \frac{^7C_2}{45}[/tex]
When 1 is defective:
[tex]Pr(x = 1) = \frac{^7C_1 * ^3C_2}{45}[/tex]
When both are defective
[tex]Pr(x = 2) = \frac{^3C_2}{45}[/tex]
So, the distribution is:
[tex]Pr(x = 0) = \frac{^7C_2}{45}[/tex]
[tex]Pr(x = 1) = \frac{^7C_1 * ^3C_1}{45}[/tex]
[tex]Pr(x = 2) = \frac{^3C_2}{45}[/tex]
Solving (b): The expected value
This is calculated as:
[tex]E(x) = \sum x * Pr(x)[/tex]
So, we have:
[tex]E(x) = x_1 * Pr(x_1) +x_2 * Pr(x_2) + ............... + x_n * Pr(x_n)[/tex]
The equation becomes:
[tex]E(x) = 0* Pr(x=0) +1* Pr(x=1) + 2 * Pr(x=2)[/tex]
[tex]E(x) = 1* Pr(x=1) + 2 * Pr(x=2)[/tex]
[tex]E(x) = Pr(x=1) + 2 * Pr(x=2)[/tex]
From the distribution in (a), we have:
[tex]E(x) = \frac{^7C_1 * ^3C_1}{45} + 2 * \frac{^3C_2}{45}[/tex]
[tex]E(x) = \frac{7 * 3}{45} + 2 * \frac{3}{45}[/tex]
[tex]E(x) = \frac{21}{45} + \frac{6}{45}[/tex]
[tex]E(x) = \frac{21+6}{45}[/tex]
[tex]E(x) = \frac{27}{45}[/tex]
Simplify
[tex]E(x) = \frac{3}{5}[/tex]
What is the integer x
so that x/9
lies between 71/7
and 113/11 ?
Answers
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:
brainly.com/question/3922668
Solve for y
4
_ =6
y
Answers
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.
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
Answers
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)
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)
Answers
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
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
Answers
Answer:19.82
Step-by-step explanation:
Got it right i did it on a test
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
Answers
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.
What is 30 rounded to the nearest whole number percent?
Answers
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
Find the equation of the least squares regression line. Show all calculations, and be sure to define any variables used.
Answers
Step 1: For each (x,y) point calculate x2 and xy.
Step 2: Sum all x, y, x2 and xy, which gives us Σx, Σy, Σx2 and Σxy (Σ means "sum up")
Step 3: Calculate Slope m:
m = N Σ(xy) − Σx Σy N Σ(x2) − (Σx)2
Step 4: Calculate Intercept b:
b = Σy − m Σx N.
Step 5: Assemble the equation of a line.
Find the value of x I need help
Answers
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
Please help me!!!!!!!!!!!!!!!!
Answers
Answer:
I think it might be SAS. (side angle side)
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
Answers
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]
PLS HELP ASAP !!! WILL MARK BRAINLIEST !!
Answers
Answer:
c is equal to e
Step-by-step explanation: a
Given a circle with a diameter of which equation expresses it as the ratio of the circumference of a circle to its diameter?
Answers
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
GIVING OUT BRAINLIEST HELP MEEE PLSS!!
Answers
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
Gina sells 216 cakes in the ratio small:medium:large=5:7:12,the profit for one medium cake is twice the profit for one small one.the profit for one large cake is three times the profit for one small cake.her total profit is £648.45,Work out the profit for one small cake.
Answers
Answer:
Profit of one small cake =£108.08
Step-by-step explanation:
small : medium : large = 5 : 7 : 12
Sum of the ratio = 5 + 7 + 12 = 24
Total number of cakes = 216
Number of small cakes
[tex]= \frac{5}{24} \times 216 = 5 \times 9 = 45[/tex]
Number of medium cakes
[tex]= \frac{7}{24} \times 216 = 7 \times 9 = 63[/tex]
Number of large cakes
[tex]=\frac{12}{24} \times 216 = 12 \times 9 = 108[/tex]
Let profit of one small cake be = x
Profit of medium cake is twice profit of small cake = 2x
Profit of large cake is thrice profit of small cake = 3x
Total profit = £648.45
x + 2x + 3x = £648.45
6x = 648.45
x = 108.075
Therefore , profit of one small cake =£108.08
Step-by-step explanation:
216 cakes =5+7+12
=24
5 = 216 cakes ÷ 24 × 5
= 45 cakes
7 = 216 cakes ÷ 24 × 7
= 63 cakes
12 = 216 cakes ÷ 24 × 12
=108 cakes
£648.45 ÷ (45+63+63+108+108+108)cakes = £648.45 ÷ 495
= £1.31
45 cakes × £1.31 = £58.95
i not sure,hope it help.
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
Answers
Answer:
Step-by-step explanation:
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?
Answers
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%
a tv cost £800 plus VAT at 20% what is the total cost of the tv?
Answers
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
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?
Answers
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
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
Answers
Answer:
C) f(x) = 1500(2.15)x
Step-by-step explanation:
Got it right on Edge :)
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
Answers
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.
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:__________
Answers
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]
I’m not sure how to do this one, can anyone help me? Please?
Answers
Here's an answer! :)
Rewrite each equation in slope-intercept form 3x + 5y = 12
Answers
Answer:
y= -3/5x + 12/5
Step-by-step explanation:
Answer:
y= - 3/5 x 12/5
Step-by-step explanation:
See imagr below:)
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.
Answers
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
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
Answers
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
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
Answers
Answer:
sim eu também preciso desta respota
