Answer:
(i) The slope of line 'T' is 2.
(ii) The slope of line 'R' is -[tex]\frac{1}{2}[/tex]
Step-by-step explanation:
(i) A line 'T' is parallel to line whose equation is; 3y = 6x + 9
We are to find the slope of this line;
The slopes of two parallel lines is the same.
To put the equation of our second line in cartesian plane format;
3y = 6x + 9
Dividing throughout by 3 we get;
y = 2x + 3
So the slope of our line is 2 and so the slope of the line 'T' is 2.
(ii) Another line 'R' is perpendicular to the line whose equation is 3y = 6x + 9
We are to find the gradient/slope of this line;
The product of any two perpendicular lines is -1.
To put the equation of our second line in cartesian plane format;
3y = 6x + 9
Dividing throughout by 3 we get;
y = 2x + 3
The slope of our second line is 2
Let the slope of line 'R' equal to a
So a × 2 = -1
Hence the slope of our line 'R' = a = [tex]\frac{-1}{2}[/tex] = -[tex]\frac{1}{2}[/tex]
the hawaiian alphabet has 12 letters. How many permutations are possible for five of these letters
Answer: The answer is 50980
Step by Step Explanation:
First, temporarily assume that two letters with I are different, call them i 1 and i 2. Three "a" are also called as a 1, a 2 and a 3, and two h as h 1 and h 2. Then there are 11 * 10 * 9 * 8 * 7 = 55440 possible "words" (one of 11 is the first letter, 10 is the second, and so on). But because equal letters do the same "words," some "words" were counted twice or more. We have to deduct the number of "parasitic" counts although it is fairly small. The words that counted more than once are divided into many disjoint sets: 1) with two I but without repetitions of a and h; 2) with two h but without repetitions of a and I 3) with two a but without repetitions of I and h; 4) with three a but without repetitions of I and h; 5) with two I and two a's; 6) two i's and tree a's; 7) two i's and two h's 8) two h's and two a's; 9) two h's and one tree. The first category includes terms counted twice and its scale is (5 * 4) * (6 * 5 * 4) = 2400 (the first I stays at one of the 5 positions, the second at one of the 4, then 11-2i-1h-2a=6). So we have 2400/2 = 1200 to subtract. Group 2 gives -600 as well, and group 3 also. Group 4 gives * (6 * 5) = 1800 (5 * 4 * 3), and the terms are counted 6 times, -300. Groups 5, 7 , 8: 5 * 4 * 3 * 2 * 6 = 720 and counted four times, therefore -180. Group 6 and 9: 5 * 4 * 3 * 2 * 1 = 120, with 12 counts, -10. Altogether -(1200 * 3 + 300 + 180 * 3 + 10 * 2) = -4460.The answer will be 55440-4460 = 50980.
The number of permutations which are possible with the five letters of HAWAIIAN is 1488.
What is permutations?It is the number of times a word can be arranged in a defined order. to calculate the number of permutations we often use nPr formula which states n!/(n-r)!
How to calculate the permutations?We are total 12 letters in the word hawaiian and letters in the alphabet for which permutations need to be calculated are 5. So the number of permutations are:
12P1+12P3+12P2+12P1+12P1
=12!/11!+12!/9!+12!/10!+12!/11!+12!/11!
=3*12*11!/11!+12*11*10*9!/9!+12*11*10!/10!
=36+1320+132
=1488
Hence the number of permutations in the word hawaiian for the 5 letters is 1488.
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Suppose that Bob is paid two times his normal hourly rate for each hour worked in excess of 40 hours in a week. Last week
he earned $420 for 50 hours of work. What is his hourly wage?
Answer:
The answer is 7
because 40 times 7 is 280 then we double 7 to 14 because remember it says he paid 2 times his hourly rate after 40 hours so then we multipy 14 times 10 and it will give you 140 so then u add them to get his total of $420
5.
Find the sum of all two - digit natural numbers which are divisible by 3.
Answer:
1665
Step-by-step explanation:
This is AP, where:
First term is: 12= 3*4Last term is: 99= 3*33Common difference is: 3Number of terms is: 33- 3= 30 (because the 4th term is included)S=1/2*30(12+99)= 1665The sum of all two - digit natural numbers which are divisible by 3 is 1665
Find the sum of natural number from 1 to 30
nth term of an arithemetic sequence 20,50,80,.......
write the algebric form
write the sequence of natural numbers term in the above sequence
Answer:
1. sum of term = 465
2. nth term of the AP = 30n - 10
Step-by-step explanation:
1. The sum of all natural number from 1 to 30 can be computed as follows. The first term a = 1 and the common difference d = 1 . Therefore
sum of term = n/2(a + l)
where
a = 1
l = last term = 30
n = number of term
sum of term = 30/2(1 + 30)
sum of term = 15(31)
sum of term = 465
2.The nth term of the sequence can be gotten below. The sequence is 20, 50, 80 ......
The first term which is a is equals to 20. The common difference is 50 - 20 or 80 - 50 = 30. Therefore;
a = 20
d = 30
nth term of an AP = a + (n - 1)d
nth term of an AP = 20 + (n - 1)30
nth term of an AP = 20 + 30n - 30
nth term of the AP = 30n - 10
The nth term formula can be used to find the next term progressively. where n = number of term
The sequence will be 20, 50, 80, 110, 140, 170, 200..............
On January 1, 2009, Caitlyn owed $16,512 to her friend Miguel, who was kind enough not to charge Caitlyn any interest. Each month during 2009, Caitlyn paid Miguel some of the money she owed. If Caitlyn still owed Miguel $6,144 on January 1, 2010, what was the average amount of Caitlyn's monthly payments?
Answer:
864
Step-by-step explanation:
Im not for sure i am correct but i did 16,512- 6,144 which gave me 10,368, i then took that number and divided it by 12, for the months between 01/01/09 and 01/01/10, and gave me 864
of a class of 32 students ,17 study music and 20 studyart what is the least number of students who could study both music and art
Answer:
5
Step-by-step explanation:
The sets of numbers 7,24,25 and 9,40,41 are Pythagorean triples. Use what you know about the Pythagorean Theorem and explain or show why they are Pythagorean triples. Be sure to show your work for each set of triples
Answer:
Pythagorean Theorem: a² + b² = c²
Step-by-step explanation:
7-24-25
7² + 24² = 25²
49 + 576 = 625
625 = 625
9-40-41
9² + 40² = 41²
81 + 1600 = 1681
1681 = 1681
Answer: See Explanation
Step-by-step explanation:
Pythagoras' theorem is [tex]a^{2}[/tex] + [tex]b^{2}[/tex] = [tex]c^{2}[/tex].
So [tex]7^{2}[/tex] (49) + [tex]24^{2}[/tex] (576) = [tex]25^{2}[/tex] (625)
Same goes for the other one. It is always the smallest number squared (smallest side of triangle) + the middle number squared (middle length side of triangle, = the biggest side/number squared.
Suppose that x is a binomial random variable with n=5, p=. 3,and q=. 7.1. Write the binomial formula for this situation and listthe possible value of x. For each value of x calculate p(☓ =x)
Answer:
[tex]P(X = x) = C_{5,x}.(0.3)^{x}.(0.7)^{5-x}[/tex]
Possible values of x: Any from 0 to 5.
[tex]P(X = 0) = C_{5,0}.(0.3)^{0}.(0.7)^{5-0} = 0.16807[/tex]
[tex]P(X = 1) = C_{5,1}.(0.3)^{1}.(0.7)^{5-1} = 0.36015[/tex]
[tex]P(X = 2) = C_{5,2}.(0.3)^{2}.(0.7)^{5-2} = 0.3087[/tex]
[tex]P(X = 3) = C_{5,3}.(0.3)^{3}.(0.7)^{5-3} = 0.1323[/tex]
[tex]P(X = 4) = C_{5,4}.(0.3)^{4}.(0.7)^{5-4} = 0.02835[/tex]
[tex]P(X = 5) = C_{5,5}.(0.3)^{5}.(0.7)^{5-5} = 0.00243[/tex]
Step-by-step explanation:
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
In this question:
[tex]n = 5, p = 0.3, q = 1 - p = 0.7[/tex]
So
[tex]P(X = x) = C_{5,x}.(0.3)^{x}.(0.7)^{5-x}[/tex]
Possible values of x: 5 trials, so any value from 0 to 5.
For each value of x calculate p(☓ =x)
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{5,0}.(0.3)^{0}.(0.7)^{5-0} = 0.16807[/tex]
[tex]P(X = 1) = C_{5,1}.(0.3)^{1}.(0.7)^{5-1} = 0.36015[/tex]
[tex]P(X = 2) = C_{5,2}.(0.3)^{2}.(0.7)^{5-2} = 0.3087[/tex]
[tex]P(X = 3) = C_{5,3}.(0.3)^{3}.(0.7)^{5-3} = 0.1323[/tex]
[tex]P(X = 4) = C_{5,4}.(0.3)^{4}.(0.7)^{5-4} = 0.02835[/tex]
[tex]P(X = 5) = C_{5,5}.(0.3)^{5}.(0.7)^{5-5} = 0.00243[/tex]
Quadrilateral
Wy has vertices W. 19), X10, 10x10,2), and 32,2). Determine if quadrilateral WXYZ is a rhombus,
Answer: no it’s not
Step-by-step explanation:
it’s a square
The times of the runners in a marathon are normally distributed, with a mean of 3 hours and 50 minutes and a standard deviation of 30 minutes. What is the probability that a randomly selected runner has a time less than or equal to 3 hours and 20 minutes? Use the portion of the standard normal table below to help answer the question. z Probability 0.00 0.5000 0.50 0.6915 1.00 0.8413 2.00 0.9772 3.00 0.9987
Answer: 0.16
Step-by-step explanation:
Given that the run times provided are normally distributed ;
Mean(x) of distribution = 3 hours 50 minutes
Standard deviation(s) = 30 minutes
The probability that a randomly selected runner has a time less than or equal to 3 hours 20 minutes
3 hours 20 minutes = (3 hrs 50 mins - 30 mins):
This is equivalent to :
[mean(x) - 1 standard deviation]
z 1 standard deviation within the mean = 0.84
z, 1 standard deviation outside the mean equals:
P(1 - z value , 1standard deviation within the mean)
1 - 0.8413 = 0.1587
= 0.16
Answer:
A. 16%
Step-by-step explanation:
Hope that this helps. peace and love
What is the solution to the equation 2 (4 minus 3 x) + 5 (2 x minus 3) = 20 minus 5 x? x = –13 x = StartFraction 5 Over 4 EndFraction x = StartFraction 13 Over 2 EndFraction x = 3
Answer:
8 - 6x + 10x - 15 = 20 -5x
8 + 4x - 15 = 20 - 5x
8 - 15 = 20 - 9x
6 = 20 - 9x
-14 = -9x
divide by -9 .736
Step-by-step explanation:
The solution of the equation 2 (4 – 3x) + 5 (2x – 3) = 20 – 5x will be 3. Then the correct option is D.
What is the solution of the equation?The solution of the equation means the value of the unknown or variable.
The equation is given below.
2 (4 – 3x) + 5 (2x – 3) = 20 – 5x
Simplify the equation, we have
2 (4 – 3x) + 5 (2x – 3) = 20 – 5x
8 – 6x + 10x – 15 = 20 – 5x
9x = 27
x = 3
Then the correct option is D.
More about the solution of the equation link is given below.
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Which equation can be used to represent the statement?
Half of a number minus seven is one and five-tenths.
o 3+x=15
0 1 x - 15-7
07-12-15
Answer:
Read below.
Step-by-step explanation:
x will represent the number
[tex]\frac{1}{2} x-7=1\frac{5}{10} \\\\\frac{1}{2} x-7=1\frac{1}{2}\\\\x-14=3\\\\x=17[/tex]
I don't know you answer choices because they don't really make sense but change them and I'll edit this. Or it could already be one in my working.
Emanuel used the calculations below to find the product of the given fractions. (Three-fifths) (StartFraction 4 over 9 EndFraction) (Negative one-half) Step 1 StartFraction (3) (4) (negative 1) over (5) (9) (negative 2) EndFraction Step 2 StartFraction negative 12 over negative 90 EndFraction Step 3 StartFraction 12 over 90 EndFraction Step 4 StartFraction 2 over 15 EndFraction In which step did his first error occur? help asap
Answer:
Emanuel did a mistake in her first step.
Step-by-step explanation:
The given expression is
[tex]\left(\dfrac{3}{5}\right)\left(\dfrac{4}{9}\right)\left(-\dfrac{1}{2}\right)[/tex]
Emanuel solve this problem but she did a mistake in her first step. She distributes negative sign with 1 and 2 both which is incorrect. We can write negative sign with either 1 or 2 but not both.
Correct steps are:
Step 1:
[tex]\dfrac{(3)(4)(-1)}{(5)(9)(2)}[/tex]
Step 2:
[tex]\dfrac{-12}{90}[/tex]
Step 3:
[tex]-\dfrac{2}{15}[/tex]
Therefore, she did a mistake in her first step.
Answer:
a
Step-by-step explanation:
M is the midpoint of AB¯. Find the coordinates of B given A(–2, 1) and M(4, 3).
Answer:
B (10, 5)
Step-by-step explanation:
We simply set the midpoint equal to each of its respective variable equation in [tex]m = (\frac{x1+x2}{2},\frac{y1+y2}{2} )[/tex]
Step 1: Solve x
4 = (-2 + x)/2
8 = -2 + x
x = 10
Step 2: Solve y
3 = (1 + y)/2
6 = 1 + y
y = 5
Put it in coordinates and we have our final answer!
Answer:
B(10,5)
Step-by-step explanation:
You already have A and M so you just find the difference and add it to M. That is my way of getting the answer. I am taking the Honors Geometry class in 6th grade.
A helicopter flies 665 feet above ground. What is the measure of the angle of depression from the helicopter to the girl’s line of sight? Round to the nearest degree. 23° 25° 65° 67°
Answer:
67°
Step-by-step explanation:
Given:
Height of helicopter from the ground, x = 665 feet
Distance from the helicopter to the girl's line of sight(opposite) = 665ft - 5 ft = 600 ft
Horizontal distance(adjacent) = 280 ft
To find the angle of depression, use the formula:
[tex] tan y = \frac{x}{y} [/tex]
Solve for y:
[tex]y = tan^-^1 (\frac{x}{y})[/tex]
[tex]y = tan^-^1 (\frac{660}{280}) = 67.01[/tex]
Angle of depression = 67°
Answer:
67 degrees
Step-by-step explanation:
ALL THE POINTS!! (01.01 LC) What is the rational number equivalent to 3 point 12 with a bar over 12? (1 point) 3 and 4 over 33 3 and 8 over 33 3 and 10 over 39 3 and 5 over 39
Answer:
A is the answer
Step-by-step explanation:
Answer:
a
Step-by-step explanation:
find the circumference
Answer:
37.68 ft
Step-by-step explanation:
d = 2r = 2*6 = 12
so C = 3.14 * 12 = 37.68 ft
Sue and Cath have $20 left for a cab fare home. The cab fare is $3 per mile plus a $2 fixed charge. What is the maximum number of miles they will be able to travel in the cab?
Answer:
6 hours
Step-by-step explanation:
There is a direct fee of 2 dollars, so 20-2=18. Then, to figure out how many hours you can go, divide 18/3, which is 6.
You can drive 6 hours.
Hope this helps!
SOMEONE HELP ASAP! IM STUCKKKKKK
Answer: B) increasing for x < -4/3 and x > 4/3
decreasing for -4/3 < x < 4/3
Step-by-step explanation:
Graph the equation and follow the curve from left to right. If you are going up, it is increasing. If you are going down, it is decreasing.
Refer to the image below. Red is increasing. Blue is decreasing.
The vertices are at: x = -4/3 and x = 4/3
Can someone please help……
Answer:
first option
Step-by-step explanation:
I don't know how to explain
The total surface area of a right circular cone with the slant height 25cm is 704 sq. cm . Find the volume of the cone.
HELP PLEASE !!!
Answer:
area=πr√{h^2+r^2}
area=704cm^2, Height(h) =25cm
therefore,
by solving, πr√{h^2+r^2}=704cm^2
you will get value of r.
now, volume=πr^2×h/3
putting all values answer will come
Step-by-step explanation:
Find the measure of angle P.
Answer:
80°
Step-by-step explanation:
Inscribed angle QRP is half the measure of intercepted arc QP, so is ...
∠R = 90°/2 = 45°
The sum of angles in a triangle is 180°, so angle P is ...
∠P = 180° -55° -45°
∠P = 80°
The work accomplished by two people working on
the same task for the same amount of time but at
different rates is given by the equation w = riturit.
When solving this equation for t, which of the
following steps would not be algebraically
correct?
W-r1t = r2t
w = t(r1+ r2)
w= r1r2t
Answer:
w = r1r2t is the correct answer which would be the letter C. This is the one that is not algebraically correct.
Step-by-step explanation:
When solving this equation for t the step w= r₁r₂t would not be algebraically correct.
What is a linear equation?It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.
The following are the basic principles and steps to summarize any linear algebra statement:
Erase all packaging symbols, such as parenthesis and parenthesis, by dividing factors.
Using the exponent rule, grouping can be rule out if the words contain decimals.
To merge words, omit or add similar pictures.
It is given that,
The work accomplished by two people working on the same task for the same amount of time but at different rates is given by the equation,
w=r₁t+r₂t
Taking t common,
w=(r₁+r₂)t
Rearrange the equation as
t=w / (r₁+r₂)
Thus, when solving this equation for t the step w= r₁r₂t would not be algebraically correct.
Learn more about the linear equation here:
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Choose the equation that represents the graph below:
8
6
4
ND
No
6 8
-8 -6 -4 -2
- 2 +
-4 +
-6
02
Answer:
y=4/3 x + 4
Step-by-step explanation:
You know the y intercept is 4, since it is shown on the picture.
Then to figure out the slope, you divide the difference of the y-coordinates of 2 points on a line by the difference of the x-coordinates of those same 2 points.
So that means 4 divided by 3.
2. Emma is playing a game with two fair dice.
She needs to score 5, using both dice, to win the
game.
What's the probability she will win the game?
Answer:
The required probability is:
[tex]\dfrac{1}{9}[/tex]
Step-by-step explanation:
It is given that Emma has two fair dice.
To win, she needs to score 5 using both dice.
Cases, where she can have 5:
{(1,4), (4,1), (2,3), (3,2)}
Let the event be A that she gets a score = 5
Total number of favorable cases, n(A) = 4
Total number of cases for throw of 2 dice, n(S) = 36
These are:
{
(1,1) (1,2) (1,3) (1,4) (1,5) (1,6)
(2,1) (2,2) (2,3) (2,4) (2,5) (2,6)
(3,1) (3,2) (3,3) (3,4) (3,5) (3,6)
(4,1) (4,2) (4,3) (4,4) (4,5) (4,6)
(5,1) (5,2) (5,3) (5,4) (5,5) (5,6)
(6,1) (6,2) (6,3) (6,4) (6,5) (6,6)
}
Formula for probability of an event E is given as:
[tex]P(E) = \dfrac{\text{Number of favorable cases}}{\text {Total number of cases}}[/tex]
or
[tex]P(E) = \dfrac{\text{n(E)}}{\text {n(S)}}[/tex]
Using the above formula, the required probability:
[tex]P(A) = \dfrac{\text{n(A)}}{\text {n(S)}}\\\Rightarrow \dfrac{4}{36}\\\Rightarrow \dfrac{1}{9}[/tex]
So, the required probability is [tex]\dfrac{1}{9}[/tex].
Calculate the correct solution to the equation -5x = -45 a) x = -9 b) x = 9 c)x = 1/9 d)x = -1/9
Answer:
X=9Solution,
[tex] - 5x = - 45 \\ or \: x = \frac{ - 45}{ - 5} \\ x = 9[/tex]
hope this helps...
Good luck on your assignment...
Answer:
Option B
Step-by-step explanation:
=> -5x = -45
Dividing both sides by -5
=> x = 9
What is the value of x? Enter your answer in the box. x =
Answer:
By using the given information in the diagram, the value of x is 20.
Step-by-step explanation:
From looking at the diagram, the triangles appear to be similar. This means that they are going to have the same ratios between each side.
We are given two measurements on one side of the triangle, 11 and 121. We can find the ratio of these sides by dividing 121 by 11.
121 ÷ 11 = 11
So, the ratio between the two triangles is 11 which means that the ratio for the rest of the sides of the triangle is going to have a ratio of 11. Knowing this, we can turn this into a equation to find the value of x.
[tex]\frac{121}{11} = \frac{5x+10}{10}[/tex]
Cross multiply the terms.
1210 = 55x + 110
Subtract 110 from both sides of the equation.
1210 - 110 = 55x + 110 - 110
1100 = 55x
Divide 55 from both sides of the equation.
1100/55 = 55x/55
20 = x
So, the value of x is 20.
Which graph shows the solutions to x^2+3x-1 ≥ 0
Answer:
if i'm not mistaken the answer is B
Answer:
Ans for the solution is B
There are 20 wild pigs on an island and the number of pigs doubled each year for the past 5 years how would one describe the graph of this model
Answer:
There are 640 pigs after 5 years.
Step-by-step explanation:
if it doubles each year the first year it doubles it is 40 then the second 80 third 160 fourth 320 and fifth 640.
graph it by having the X axis the years and the Y axis do it by 40s
What is the area of the parallelogram if each square is 1 square foot? a. 12 ft ³ b. 12 ft ² c. 12 d. 12 feet
Answer:
12 ft² :)
Step-by-step explanation:
Area of a parallelogram = base * height
4 * 3 = 12
Area of the parallelogram = 12 ft²