Answer:
£19000
Step-by-step explanation:
Discount cost = 5% of 20000 = 5/100 x 20000 = 1000
SO, cost after discount = 20000 - 1000 = 19000
hope this helps
Which of the binomials below is a factor of this trinomial X^2+2x-35
Answer:
A.x+1
Step-by-step explanation:
An experimental population of fruit flies increases according to the law of exponential growth. There were 60 flies after the 2nd day of the experiment and 360 flies after the fourth day. How many flies were there in the original population?
Answer:
There were 10 flies originally
Step-by-step explanation:
Since we have an exponential growth, we will be having a constant percentage of increase and we can set up the increase at any day using the following equation;
V = I(1+r)^d
where V is the number of flies on a particular day
I is the initial number of flies
r is the constant increase in percentage
and d is the number of days.
So we have for the second day;
60 = I(1+r)^2 ••••••(i)
For the fourth day, we have;
360 = I(1+r)^4 ••••••••(ii)
divide equation ii by i; we have;
360/60 = (1+r)^4/(1+r)^2
6 = (1+r)^2
(√6)^2 = (1+r)^2
1 + r = √6
r = √6 - 1
So we can substitute the value of r in any of the equations to get I which is the initial number of flies
Let’s use equation 1
60 = I(1 + r)^2
60 = I(1 + √6 -1)^2
60 = I(√6)^2
60 = 6I
I = 60/6
I = 10 flies
Question 9 - (3 marks available)
By rounding to 1 significant figure, estimate the answers to these questions:
a) 17 * 82
b) 54 x 671
c) 207 x 643
Answer: a) 1,600
b) 35,000
c) 120,000
Step-by-step explanation:
First, round each number to one significant digit (the first digit).
Then multiply them.
a) 17 --> rounds to 20
82 --> rounds to 80
20 x 80 = 2 x 8 with two zeros
= 1 6 0 0
b) 54 --> rounds to 50
671 --> rounds to 700
50 x 700 = 5 x 7 with three zeros
= 3 5 0 0 0
c) 207 --> rounds to 200
643 --> rounds to 600
200 x 600 = 2 x 6 with four zeros
= 1 2 0 0 0 0
Find the constant of variation k for the direct variation.
A . K = -2
B . K = 2
C . K = -0.5
D . K= -1.5
Answer:
K = -2
Step-by-step explanation:
If y varies directly as x, k (constant) can be found by dividing the y-coordinate by the x-coordinate.
[tex]k = \frac{2}{-1} = -2[/tex]
Answer:
B
Step by step explanation
What is the equation of the graph line with in standard form X=-3Y =-3X +Y=-3X-Y= -3
Answer:6
Step-by-step explanation:
An 8-sided fair die is rolled twice and the product of the two numbers obtained when the die is rolled two times is calculated. Draw the possibility diagram of the product of the two numbers appearing on the die in each throw Use the possibility diagram to calculate the probability that the product of the two numbers is A prime number Not a perfect square A multiple of 5 Less than or equal to 21 Divisible by 4 or 6
Answer:
(a)See below
(b)I) 0.125 (ii)0.828125 (iii)0.234375 (iv) 0.625 (v)0.65625
Step-by-step explanation:
When an 8-sided die is rolled twice, the sample space is the set of all possible pairs (a,b) where a is the 1st outcome and b is the 2nd outcome.
The sample space is:
[tex][(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6),(1, 7),(1, 8)\\(2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6),(2, 7),(2, 8)\\(3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6),(3, 7),(3, 8)\\(4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6),(4, 7),(4, 8)\\(5, 1), (5, 2), (5, 3), (5, 4), (5, 5),(5, 6),(5, 7),(5, 8)\\(6, 1), (6, 2), (6, 3), (6, 4)(6, 5),(6, 6),(6, 7),(6, 8)\\(7, 1), (7, 2), (7, 3), (7, 4)(7, 5),(7, 6),(7, 7),(7, 8)\\(8, 1), (8, 2), (8, 3), (8, 4)(8, 5),(8, 6),(8, 7),(8, 8)][/tex]
PART A
The sample space of the product a*b of each pair forms the required possibility diagram.
This is given as:
[tex]1, 2, 3, 4, 5, 6,7,8\\2, 4, 6, 8, 10, 12,14,16\\3,6,9,12,15,18,21,24\\4,8,12,16,20,24,28,32\\5,10,15,20,25,30,35,40\\6,12,18,24,30,36,42,48\\7,14,21,28,35,42,49,56\\8,16,24,32,40,48,56,64[/tex]
PART B
I) A prime number
The number of products that gives prime numbers = 8
The probability that the product is a prime number
[tex]=\dfrac{8}{64}= \dfrac{1}{8}\\=0.125[/tex]
ii) Not a perfect square
Number of products that results in perfect squares =11
The probability that the product is not a perfect square
[tex]=\dfrac{64-11}{64}= \dfrac{53}{64}\\=0.828125[/tex]
iii) A multiple of 5
Number of products that are multiples of 5=15
The probability that the product is a multiple of 5
[tex]=\dfrac{15}{64}\\=0.234375[/tex]
iv) Less than or equal to 21
Number of products which are less than or equal to 21=40
The probability that the product less than or equal to 21
[tex]=\dfrac{40}{64}=\dfrac{5}{8}\\=0.625[/tex]
v) Divisible by 4 or 6
Number of products divisible by 4 or 6= 42
The probability that the product is divisible by 4 or 6
[tex]=\dfrac{42}{64}=\dfrac{21}{32}\\=0.65625[/tex]
Solve for d.
4d – 4 = 5d - 8
Answer:
d = 4
Step-by-step explanation:
4d - 4 = 5d - 8
Add -5d and 4 on both sides.
4d - 5d = - 8 + 4
- 1d = - 4
Divide -1 into both sides.
d = -4/-1
d = 4
Multiply 17/18 by the reciprocal of -289/324.
Answer:
18/17
Step-by-step explanation:
the negative reciprocal of -289/324 is 324/289. When it is multiplied by 17/18 you get 18/17 as the answer.
Answer:
[tex] - 1 \frac{1}{17}[/tex]
Step-by-step explanation:
[tex]Reciprocal \: of \: - \frac{289}{324} = - \frac{324}{289} \\ \\ \frac{17}{18} \times (- \frac{324}{289} ) \\ \\ = \frac{17}{18} \times (- \frac{18 \times 18}{17 \times 17} ) \\ \\ = - \frac{18}{17} \\ \\ = - 1 \frac{1}{17} \\ [/tex]
Triangle ABC is congruent to TriangleA'BC' by the HL theorem. Triangles A B C and A prime B C prime are connected at point B. Angles A prime C prime B and A C B are right angles. The lengths of C prime A prime and C A are congruent. The lengths of A prime B and B A are congruent. What single rigid transformation maps TriangleABC onto TriangleA'BC'? answer options: Triangle ABC is congruent to TriangleA'BC' by the HL theorem. Triangles A B C and A prime B C prime are connected at point B. Angles A prime C prime B and A C B are right angles. The lengths of C prime A prime and C A are congruent. The lengths of A prime B and B A are congruent. What single rigid transformation maps TriangleABC onto TriangleA'BC'? dilation reflection rotation translation
Answer:
B, reflection will be your answer.
Step-by-step explanation:
Congruent triangles have equal measure of corresponding sides and angles.
The single transformation that maps triangle ABC and triangle A'B'C is (b) reflection
From the question, we understand that the triangles are congruent by HL.
HL means hypotenuse legs.
This implies that
The two triangles are right-angled triangleThe length of the hypotenuse of both triangles are equal.Reflecting either of the triangles would map both triangles.
Hence, the single transformation is reflection
Read more about transformation at:
https://brainly.com/question/15469392
0.0995 rounded to 3 decimal places
Answer:
0.100
Step-by-step explanation:
0.0995 has 4 decimal places
5>4 so round up
9 turns to 10, the 1 is "added on" to the number ahead
9 turns to 10 again, the 1 is "added on" to the number ahead
0 turns to 1
you are left with 0.100
Answer:
0.100
Step-by-step explanation:
Three decimal places: 0. 0 / 9 / 9 / 5
Rounding number: 0. 0 / 9 / 9 / 5
Since it is 5, add 1 to the second 9. This will result to 0 while adding 1 to the first 9. Again, this would result to 10 which will add 1 to the next number, 0.
0.1000
Since the question wants you to round three places, you were not told to remove the zeros in those decimal places. So only remove the last 0.
0.100 is the answer
A charity organization is holding a food drive with a goal to collect at least 1,000 cans of food by the end of the month. It currently has 565 cans from donations and is having an event where 87 guests will attend and bring cans. Which solution set represents the number of cans each guest must bring to meet the goal?
A.)
B.)
C.)
D.)
The answer is 5 in a close dot going --->
Which is D.)
The picture is to show how it looks in Plato.
Answer: D.
Step-by-step explanation:
If they already have 565 cans and 87 will bring cans then we could represent it by the inequality
87x + 565[tex]\geq[/tex] 1000 where x is the number of cans each guest much bring to meet the goal. so solve for x.
87x + 565[tex]\geq[/tex] 1000
-565 -565
87x [tex]\geq[/tex] 435
x [tex]\geq[/tex] 5
since we now that x is 5 then A and C can't be answers.
B can't be an answer in this case because 5 is excluded but they actually need at least 1000 bottles so 5 needs to be excluded.
Find the range of value of x for which: x-3/x+3>0
answer x>1/2 (sqrt(21) - 3)
x>0.791288
PLEASE HELP IMAGE ATTACHED!!
Answer:
Step-by-step explanation:
Parallel lines have same slope
19) y = x - 4
m = 1 ; (2, 3 )
Equation: y - y₁ = m(x- x₁)
y - 3 = 1(x - 2)
y - 3 = x -2
y = x - 2 + 3
y = x + 1
20) 2x + 3y = 3
We have to write in y = mx + b form
3y = - 2x - 3
[tex]y=\frac{-2}{3}x-\frac{3}{3}\\\\y=\frac{-2}{3}x-1\\\\m=\frac{-2}{3}[/tex]; (-6, -1)
[tex]y-[-1]=\frac{-2}{3}(x-[-6])\\\\y+1=\frac{-2}{3}(x+6)\\\\y+1=\frac{-2}{3}x+\frac{-2}{3}*6\\\\y+1=\frac{-2}{3}x-4\\\\y=\frac{-2}{3}x-4-1\\\\y=\frac{-2}{3}x-5[/tex]
for perpendicular lines, m2 = -1/m1
21) y = 2x+ 5
m1 = 2
[tex]m_{2}=\frac{-1}{2}[/tex]; (-2,8)
[tex]y-8=\frac{-1}{2}(x-[-2])\\\\y-8=\frac{-1}{2}(x+2)\\\\y-8=\frac{-1}{2}x+2*\frac{-1}{2}\\\\y-8=\frac{-1}{2}x-1\\\\y=\frac{-1}{2}x-1+8\\\\y=\frac{-1}{2}x+7[/tex]
22) x+ 4y = 8
4y = -x + 8
[tex]y=\frac{-1}{4}x+\frac{8}{4}\\\\y=\frac{-1}{4}x+2\\\\m_1=\frac{-1}{4}\\\\m_{2}=4\\\\[/tex]
m2 = 4; (-2,-11)
y - [-11] = 4(x -[-2])
y + 11 = 4 (x + 2)
y + 11 = 4x + 8
y = 4x + 8 - 11
y = 4x - 3
10. Julio is driving to the store. The average distance d, in miles, he travels over t minutes is given by the
function d(t) = 0.5t. What is the value of the function when t = 15?
Answer:
7.5 miles
Step-by-step explanation:
Given the equation d(t) = 0.5t, all you need to do is plug in the value of t.
They're asking what the Function equals, and they're giving you the value of the variable t.
To solve, write the equation d(15) = 0.5(15)
And if you simplify the right side of the equation, you'll find that
d(15) = 7.5
If t represents time, then you can conclude that Julio travels 7.5 miles in the time t, of 15 minutes.
Can somebody help me with this question ?? :)
Answer:
x = 44°
Step-by-step explanation:
Since this is an isosceles triangle, the other angle that isn't defined is also 68°. So, since all the angles add up to 180°,
x + 68(2) = 180
x + 136 = 180
x = 44°
Answer:
44 is the answer
Step-by-step explanation:
13, 15, 17, 19,... describe the pattern in the sequence. Find the next three terms
Answer:
21, 23, 25
Step-by-step explanation:
It adds by x +2 (x being the previous number.)
Answer:
pattern : +2
next three terms : 21, 23, and 25
Find the value of x.
Answer:
x=11 degrees
Step-by-step explanation:
45+4x+1=90
46+4x=90
4x=44
x=11
PLEASE HELP I DONT KNOW WHAT TO DO !! I APPRECIATE IT IF YOU HELP ME !
Answer:
x = ±20
Step-by-step explanation:
x^2 -1=399
Add 1 to each side
x^2 = 399+1
x^2 = 400
Take the square root of each side
sqrt(x^2) = ±sqrt(400)
x = ±20
A model rocket is launched from ground level. Its height, h meters above the ground, is a function of time t seconds after launch and is given by the equation h=-4.9t^2+68.6t What would be the
maximum height, to the nearest meter, attained by the model?
Answer:
240 m to nearest meter.
Step-by-step explanation:
h = -4.9t^2 + 68.6t
We need to convert this to vertex form to find the maximum value of h:
h = -4.9(t^2 - 14t)
h = -4.9[(t - 7)^2 - 49]
h = -4.9(t - 7)^2 + 240.1
So maximum height is when t = 7 and it's 240.1 meters.
Evaluate : -80 - (-15) =
Answer:
-65
Step-by-step explanation:
-80 - -15
Two minuses become plus
= -80+15
Subtract and keep the sign of the higher number
= -(80-15)
= -65
Answer:
I'm glad you asked!
Step-by-step explanation:
[tex]-80-(-15)[/tex]
= [tex]-80-(-15)[/tex]
= [tex]=-80+15[/tex]
[tex]=-65[/tex]
The answer is - [tex]65.[/tex]
Describe the transformation from the parent function of f ( x ) = x 2 to g ( x ) = 6 x 2.(Need answer in less than 2 hours!)
Answer: (b) vertical stretch by a factor of 6
Step-by-step explanation:
Consider h(x) = A(x - h)² + k
A is the vertical stretch by a factor of Ah is the horizontal shift (positive = right, negative = left)k is the vertical shift (positive = up, negative = down)f(x) = x²
g(x) = 6x²
↓
vertical stretch by a factor of 6
Manuel need to say more than $75 for a class trip. he already has $24 and will save an equal amount each week for the next 6 weeks. Which any quality can be used to determine how much money Manuel should save each week?
Answer:
the answer is D!
Step-by-step explanation:
I took that quiz :)
PLEASE HELP ASAP WILL GIVE BRAINLIEST The weight of a box of cereal can vary by one fourth of an ounce and still be sold as a full box. Each box is supposed to contain 18 ounces of cereal. Which graph represents the possible weights of boxes that are overfilled or underfilled and cannot be sold as full boxes?
Answer:
The third option
Step-by-step explanation:
Answer:
It is number 1 because they are asking for over or under 18
Step-by-step explanation:
Hope this helps!
Graph y=−4/7x+1. do this math
Answer:
Use demos or a graphing calc.
Step-by-step explanation:
Answer:
Graph the line using the slope and y-intercept, or two points.
Slope: −4/7
y-intercept: 1
A fair dice is rolled 3 times in a row. The outcomes are shown below. Calculate the probability of all three events occurring. Roll Outcome 1st 5 2nd factor of 6 3rd more than 1
Answer:
5/54
Step-by-step explanation:
probability of the dice being 5 = 1/6
probability of the dice being a factor of 6 = 4/6
probability of the dice being more than 1 = 5/6
1/6 * 4/6 = 4/36
4/36 * 5/6 = 20/216
20/216 simplified to lowest is equal to 5/54
I will mark you brainliest!!!! Determine which region contains the solution to the system.
Answer:
Region B
Step-by-step explanation:
The solution to the system is the point at which the two lines intersect, which would be in Region B.
Set up the problem, but use a calculator to find the number of outcomes for the permutation. Eight horses run a race. In how many ways can the first three finishers turn out?
Explanation:
Label the slots A,B,C for first through third place.
There are 8 choices for slot A, 7 for slot B, and 6 for slot C. We start with 8 and count our way down until we get to the final slot. Then we multiply out those values
8*7*6 = 336
There are 336 ways to select three people from a pool of eight overall.
-----------------
If you want to use the permutation formula, then your steps might look like this
[tex]_n P _r = \frac{n!}{(n-r)!}\\\\_8 P _3 = \frac{8!}{(8-3)!}\\\\_8 P _3 = \frac{8!}{5!}\\\\_8 P _3 = \frac{8*7*6*5!}{5!}\\\\_8 P _3 = 8*7*6\\\\_8 P _3 = 336\\\\[/tex]
Note how the 5! terms cancel out on the second to last step, leaving behind the expression 8*7*6 which was found earlier.
///// PLZZZZZZZZZ HLPPPPPPPPPP MEEEEEEEEEEEEEEEEEE ////// WHAT IS THE SLOPE OF THE BELOW IF NECESSARY ENTER YOUR ANSWER AS A FRACTION IN LOWEST TERMS USING THE SLASH (/) AS THE FRACTION BAR DO NOT ENTER YOUR ANSWER AS A DECIMAL NUMBER OR AN EQUATION.
Answer:
1/6
Step-by-step explanation:
We have two points so we can use the slope formula
m = (y2-y1)/(x2-x1)
= (6-3)/(12 - -6)
= (6-3)/(12+6)
= 3/18
=1/6
Three-fifths of the members of the Spanish club are girls. There are a total of 30 girls in the Spanish club.
Which statements can be used to solve for x, the total number of members in the Spanish club? Select three options
Problem: You do not have an attached picture. Though, I can help you out with this question.
So, three-fifths of the members are girls. There are 30 of girls. We can immediately make an equation using "x".
3/5x=30
3/5x × 5/3=30 × 5/3
x=50
Thus, there are 50 members in total. Though if x is too hard for you, you may substitute it by using another variable.
Variable in here is x.
what is the solution to this inequality x/10+6≥8
Answer:
x ≥ 20
Step-by-step explanation:
First, we want to isolate x. We can start to do that by subtracting 6 to both sides.
x/10≥2
Now, we multiply each side by 10.
x ≥ 20
That's the answer, all values above or equal to 20 are solutions.
Answer:
The answer is x_> 20
Step-by-step explanation: