Stevie and Michael share their profit in a ratio 3:5. Stevie gets £120 more than Michael. How much profit did they make altogether? Please help

Answer:2

Step-by-step explanation:

-5.4+8.2=14/5 and then opposite of -2 3/4 is 2.

Answer: 12 friends.

Step-by-step explanation:

the data we have is:

Mei Su had 80 coins.

She gave the coins to her friends, in such a way that every friend got a different number of coins, then we have that:

The maximum number of friends that could have coins is when:

friend 1 got 1 coin

friend 2 got 2 coins

friend 3 got 3 coins

friend N got N coins

in such a way that:

(1 + 2 + 3 + ... + N) ≥ 79

I use 79 because "she gave most of the coins", not all.

We want to find the maximum possible N.

Then let's calculate:

1 + 2 + 3 + 4 + 5 = 15

15 + 6 + 7 + 8 + 9 + 10 = 55

now we are close, lets add by one number:

55 + 11 = 66

66 + 12 = 78

now, we can not add more because we will have a number larger than 80.

Then we have N = 12

This means that the maximum number of friends is 12.

Answer:

12

Step-by-step explanation:

my

Answer:

The area of the shaded region = (36·π - 72) cm²

The perimeter of the shaded region = (6·π  + 12·√2) cm

Step-by-step explanation:

The given figure is a sector of a circle and a segment of the circle is shaded

We have that since the arc AC subtends an angle 90° at the center of the circle, the sector is a quarter of a circle, which gives;

Area of sector = 1/4×π×r²

As seen the radius, r = AB = 12 cm

∴ Area of sector = 1/4×π×12² = 36·π cm²

The area of the segment AB = Area of sector ABC - Area of ΔABC

Area of ΔABC = 1/2×Base ×Height =

Since the base and the height = The radius of the circle = 12 cm, we have;

Area of ΔABC = 1/2×12×12 = 72 cm²

The area of the segment AB = 36·π cm² - 72 cm² = (36·π - 72) cm²

The area of the shaded region = The area of the segment AB = (36·π - 72) cm²

The perimeter of the shaded region = 1/4 perimeter of the circle with radius r + Line Segment AC

The perimeter of the shaded region =  1/4 × π × 2 × r + √(12² + 12²) = 1/4 × π × 2 × 12 + 12·√2 = (6·π  + 12·√2) cm

Answer:

B. (2, 2)

Step-by-step explanation:

In order for the coordinate to be a solution of the systems of inequalities, it has to be in the shaded region (not on the line since both are dotted). Only B fits in the shaded region.

Answer:

2+2=4

Step-by-step explanation:

2+2=4

good question like if you have two chocolates and your mom gives you two more than there will be 4 and they will be too delicious

i hope this will help you :)

have a great day

Answer:

2+2=4

Step-by-step explanation:

So you take the 2 numbers 2+2 and you use your finger counting to get to 4. It’s really hard mathematics but you’ll get there. Have a great day!

Answer:

C

Step-by-step explanation:

In this question, we are interested in calculating the z-score of a company employee.

Mathematically;

z-score = (x- mean)/SD

where in this case;

x is the value given which turns out to be the annual salary of the employee = 28,000

Mean = 34,000

standard deviation = 4,000

Plugging these values into the equation above, we have;

z-score = (28000-34000)/4000 = -6000/4000 = -1.5

Answer:

c/ -1.5

Step-by-step explanation:

edge 2020

Answer:

proved

Step-by-step explanation:

prove that : (sin^2 θ)/(1+cosθ)=1-cosθ

(sin^2θ)*(1−cosθ)/(1+cosθ)(1+cosθ) =

sin^2Ф)(1-cosФ)/1-cos^2Ф since 1-cos^2Ф=sin^2Ф then:

(sin^2Ф)(1-cosФ)/sin^2Ф =

1-cosФ     (sin^2Ф/sin^Ф=1)

proved

Answer:

Step-by-step explanation:

take it befor delete

Answer:

5x4^10

Step-by-step explanation:

Hope this helps have a nice day :)

Answer:

5. [tex]4^{9}[/tex]

Step-by-step explanation:

There is a common ratio r between consecutive terms, that is

r = 20 ÷ 5 = 80 ÷ 20 = 320 ÷ 80 = 4

This indicates the sequence is geometric with n th term

[tex]a_{n}[/tex] = a . [tex]r^{n-1}[/tex]

Here a = 5 and r = 4 , thus

[tex]a_{10}[/tex] = 5. [tex]4^{9}[/tex]

Answer:

  e/f

Step-by-step explanation:

Common factors in the numerator and denominator cancel.

  [tex]\dfrac{e\times e\times e\times e\times f}{e\times e\times e\times f\times f}=\dfrac{e}{e}\times\dfrac{e}{e}\times\dfrac{e}{e}\times\dfrac{e}{f}\times\dfrac{f}{f}=1\times1\times1\times\dfrac{e}{f}\times1=\boxed{\dfrac{e}{f}}[/tex]

The required simplification of the expression is [tex]\dfrac{e}{f}[/tex].

We have to the given expression, e x e x e x e x f ÷ e x e x e x f x f.

The given expression is simplify in the following steps given below.

Expression; [tex]\dfrac{e \times e \times e \times e \times f}{e \times e \times e \times f \times f}[/tex]

Then,

The simplification of the given expression,

[tex]=\dfrac{e \times e \times e \times e \times f}{e \times e \times e \times f \times f}\\\\[/tex]

Cancel out the same term from denominator and numerator,

[tex]= \dfrac{e}{f} \times \dfrac{e}{f} \times \dfrac{e}{f} \times \dfrac{e}{f} \times \dfrac{f}{f} \\\\= 1 \times 1 \times 1 \times \dfrac{e}{f} \times 1 \\\\= \dfrac{e}{f}[/tex]

Hence, The required simplification of the expression is [tex]\dfrac{e}{f}[/tex]

To know more about Multiplication click the link given below.

https://brainly.com/question/16871801

Answer:

The answer is

Step-by-step explanation:

To find the graph which shows (f + g)(x) we must first find (f + g)(x)

That's

f(x) = - x² + 3x + 5

g(x) = x² + 2x

To find (f + g)(x) add g(x) to f(x)

That's

(f + g)(x) = -x² + 3x + 5 + x² + 2x

Group like terms

(f + g)(x) = - x² + x² + 3x + 2x + 5

We have (f + g)(x) as

(f + g)(x) = 5x + 5

Since (f + g)(x) is linear the graph which shows (f + g)(x) is the last graph

Hope this helps you

Answer:

last graph or D

Step-by-step explanation:

Answer:

3, 6, and 15

Step-by-step explanation:

Notice that if 60 is a multiple, the numbers in question could have the same factors as 60.

So let's look at 60's prime factors:

60 = 2 * 2 * 3 * 5

we also know that 3 is a factor, so the factor 3 must be included in all three options, we also know that 4 is NOT a factor, so both factors 2 cannot be included (but only one of them could).

So, in order to build the lowest possible numbers that verify such conditions, we can use:

3

3 * 2 = 6

since 3 or 2 cannot be repeated, the next smaller would be:

3 * 5 = 15

Answer:

The times are t = 9, t = 10, t = 11 and t = 12

Step-by-step explanation:

For the train to be more than 16 km South and since south is taken as negative,

d(t) > -16

t³ - 9t² + 6t > -16

t³ - 9t² + 6t + 16 > 0

Since -1 is a factor of 16, inserting t = -1 into the d(t), we have

d(-1) = (-1)³ - 9(-1)² + 6(-1)+ 16 = -1 - 9 - 6 + 16 = -16 + 16 = 0. By the factor theorem, t + 1 is a factor of d(t)

So, d(t)/(t + 1) = (t³ - 9t² + 6t + 16)/(t +1) = t² - 10t + 16

Factorizing  t² - 10t + 16, we have

t² - 2t - 8t + 16

= t(t - 2) - 8(t - 2)

= (t -2)(t - 8)

So t - 2 and t - 8 are factors of d(t)

So (t + 1)(t -2)(t - 8) > 0

when t < -1, example t = -2 ,(t + 1)(t -2)(t - 8) = (-2 + 1)(-2 -2)(-2 - 8) = (-1)(-4)(-10) = -40 < 0

when -1 < t < 2, example t = 0 ,(t + 1)(t -2)(t - 8) = (0 + 1)(0 -2)(0 - 8) = (1)(-2)(-8) = 16 > 0

when 2 < t < 8, example t = 3 ,(t + 1)(t -2)(t - 8) = (3 + 1)(3 -2)(3 - 8) = (4)(1)(-5) = -20 < 0

when t > 8, example t = 9,(t + 1)(t -2)(t - 8) = (9 + 1)(9 -2)(9 - 8) = (10)(7)(1) = 70 > 0

Since t cannot be negative, d(t) is positive in the interval 0 < t < 2 and t > 8

Since t ∈ (0, 12]

In the interval 0 < t < 2 the only value possible for t is t = 1

d(1) = t³ - 9t² + 6t = (1)³ - 9(1)² + 6(1) = 1 - 9 + 6 = -2

Since d(1) < -16 this is invalid

In the interval t > 8 , the only possible values of t are t = 9, t = 10.t = 11 and t = 12.

So,

d(9) = 9³ - 9(9)² + 6(9) = 0 + 54 = 54 km

d(10) = 10³ - 9(10)² + 6(10) = 1000 - 900 + 60 = 100 +60 = 160 km

d(11) = 11³ - 9(11)² + 6(11) = 1331 - 1089 + 66 = 242 + 66 = 308 km

d(12) = 12³ - 9(12)² + 6(12) = 1728 - 1296 + 72 = 432 + 72 = 504 km

Answer:

Step-by-step explanation:

Unfortunately, f(x)=(15)x is not an exponential function.  I will assume that you meant

f(x) = 5^x

The second table fits this function.  Note that if x = -2, f(-2) = 5^(-2) = 1/25.

Answer:

6.552×10³×10

6.552×10^3+1

6.552×10^4 is the standard form

i hope this will help you :)

Answer:

Out of 8000 students, 10% take tuition in various subjects before the exam.

10% of 8000 is:

10/100 * 8000 = 800

Among the 800, 40% take tuition in English only and 20% take tuition in Math only.

80 students take tuition in other subjects, therefore, in percentage:

80/800 * 100 = 10%

Therefore, the percentage of students that take tuition in both Math and English is:

100% - (40% + 20% + 10%) = 100% - 70% = 30%

30% of the 800 students take tuition in both subjects. That is:

30/100 * 800 = 240 students

Therefore, among the 8000 students in the district, only 240 take tuition in both English and Math.

In percentage:

240/8000 * 100 = 3%

3% of students take tuition in both English and Math.

In Ratio:

3 : 100

3 out of 100 students take tuition in English and Math.

Answer:

53

Step-by-step explanation:

Explicit Formula: an = a1 + d(n - 1)

Simply plug in your known variables:

an = 8 + 3(n - 1)

Then plug in 16 for n:

a(16) = 8 + 3(16 - 1)

a(16) = 8 + 3(15)

a(16) = 8 + 45

a(16) = 53

Answer:

53

Step-by-step explanation:

an = dn + (a - d)

an = 3n + 8  - 3

an = 3n + 5

Put n as 16 and solve.

3(16) + 5

48 + 5

= 53

Answer:

[tex]\displaystyle y = \frac{1}{5}x+1[/tex]

Or:

[tex]x + 5 = 5y[/tex]

Step-by-step explanation:

We have the function:

[tex]y=5x-5[/tex]

And we want to find its inverse.

To find the inverse of a function, we:

Hence:

[tex]x=5y-5[/tex]

Solve for y. Add:

[tex]\displaystyle x + 5 = 5y[/tex]

Divide:

[tex]\displaystyle y = \frac{x+5}{5}[/tex]

Simplify. Hence:

[tex]\displaystyle y = \frac{1}{5}x+1[/tex]

In conclusion, the inverse function is:

[tex]\displaystyle y = \frac{1}{5}x+1[/tex]

Answer:

B is P(x)=(x-3)^2 +2

C is P(x)=(x-1)^2 -5

Step-by-step explanation:

i think i am right

Answer:

Please find attached the required graph and

Step-by-step explanation:

The values for the information given can be written down as follows;

Time, seconds             Volume mL

0,                                    500

12,                                   450

24,                                  400

36,                                  350

48,                                  300

60,                                  250

72 250

84 250

96 250

108 250

120 250

132 250

144 250

156 250

168 250

180 250

192 250

204 250

216 250

228 250

240 250

252 250

264 250

276 250

288 250

300 250

312 225

324,                                        200

336,                                         175

348,                                         150

360,                                         125

372,                                         100

384,                                         75

396,                                        50

408,                                        25

420,                                        0

Answer:

The population of the city was 25,000 in 1970 and 1983.

Step-by-step explanation:

In order to find the year at which the population was 25,000 we need to make p(t) equal to that number and solve for t as shown below.

[tex]25000 = 14*t^2 + 650*t + 32000\\14*t^2 + 650*t + 7000 = 0\\t^2 + 46.43*t + 500 = 0\\t_{1,2} = \frac{-46.43 \pm \sqrt{(46.43)^2 - 4*1*500}}{2}\\t_{1,2} = \frac{-46.43 \pm \sqrt{155.75}}{2}\\t_{1,2} = \frac{-46.43 \pm 12.48}{2}\\t_1 = \frac{-33.95}{2} = -16.98\\t_2 = \frac{-58.91}{2} =- 29.5[/tex]

Since t = 0 corresponds to the year 2000, then t1 = 1983 and t2 = 1970.

Answer:

Stratified sampling

Step-by-step explanation:

The is a type of sampling in which the population of interest is divided into subpopulations and then each subpopulation is randomly sampled.

In this case study, instead of just doing a random sampling of all students, the research divided the population of all students into subpopulations which includes freshmen, sophomores, juniors and seniors and then she makes a random sampling of each of these subpopulations.

Step-by-step explanation:

Places A and B are 100 km apart on a highway. One car starts from A and another from B at the same time. If the car travel in the same direction at different speeds, they meet in 5 hours. If they travel towards each other, they meet in 1 hour. What are the speeds of the two cars?

Solution :

Let “x km/hr” be the speed of 1st car

Let “y km/hr” be the speed of the 2nd car

Time = Distance/Speed

Speed of both cars while they are traveling in the same direction = (x – y)

Speed of both cars while they are traveling in the opposite direction = (x + y)

5 = 100/(x -y)

x – y = 100/5

x - y = 20

x - y - 20 = 0 ---(1)

1 = 100/(x + y)

x + y = 100

x + y - 100 = 0--b----(2)

x/(100 + 20) = y/(-20 + 100) = 1/(1 + 1)

x/120 = y/80 = 1/2

x/120 = 1/2 y/80 = 1/2

x = 120/2 y = 80/2

x = 60 y = 40

So, the speed of first car = 60 km/hr

Speed of second car = 40 km/hr

Answer:

option B is the correct option.

Solution,

[tex] {(x - 4)}^{2} = 5 \\ [/tex]

x-4=_+√5

X=4_+√5

Hope this helps...

Good luck on your assignment...

Answer:

(x-4)^2 =5

x^2-16=5

x^2=5+16

x^2=21

√x^2=√21

x=√21

Step-by-step explanation :

First of all open the bracket which has square

Secondly change the position of 16

Note: when a number changes its place , the symbol also changes

then when you get the value take the square root on both sides

and you'll get the answer

Answer:

second option

Step-by-step explanation:

Given

[tex]x^{4}[/tex] + 6x² + 5 = 0

let u = x², then

u² + 6u + 5 = 0 ← in standard form

(u + 1)(u + 5) = 0 ← in factored form

Equate each factor to zero and solve for u

u + 1 = 0 ⇒ u = - 1

u + 5 = 0 ⇒ u = - 5

Change u back into terms of x, that is

x² = - 1 ( take the square root of both sides )

x = ± [tex]\sqrt{-1}[/tex] = ± i ( noting that [tex]\sqrt{-1}[/tex] = i ), and

x² = - 5 ( take the square root of both sides )

x = ± [tex]\sqrt{-5}[/tex] = ± [tex]\sqrt{5(-1)}[/tex] = ± [tex]\sqrt{5}[/tex] × [tex]\sqrt{-1}[/tex] = ± i[tex]\sqrt{5}[/tex]

Solutions are x = ± i and x = ± i[tex]\sqrt{5}[/tex]

Answer:

88° and 132°

Step-by-step explanation:

The sum of angles in a pentagon ( a 5-sided shape) is given as

= (5 - 2) 180°

= 540°

The angles ∠EAB and ∠AED are supplementary hence the sum is 180° Therefore,

∠AED + 110 = 180

∠AED = 180 - 110

= 70°

Given that the sum of the angles in a pentagon is 540° then

110 + 70 + 2k + 140 + 3k = 540

5k + 320 = 540

5k = 540 - 320

5k = 220

k = 220/5

= 44°

Hence the angle ∠ABC

= 2 × 44

= 88°

∠CDE

= 3 × 44

= 132°

Answer:

6

Step-by-step explanation:

If 2 of the friends wants to stand beside each other, we can take these 2 friends like 1 option and calculated the number of ways, using the rule of multiplication as:

__ 3_____ * ____2_____ *____1____  =  6

1st place        2nd place        3rd place

Because we have 3 options (2 friends and the friends that are beside each other) for the first place of the picture, 2 options for the second and 1 option for the third.

Answer:

bearing of A from C is - 65.24°

the distance |BC| is 187.84 m

Step-by-step explanation:

given data

girl walks AB = 285 m (side c)

bearing angle B = 78°

girl walks AC = 307 m (side a)

solution

we use here the Cosine Law for getting side b that is

ac² = ab² + bc² - 2 × ab × cos(B)     ...............1

307² = 285² + x²  - 2 × 285 cos(78)

x = 187.84 m

and

now we get here angle θ , the bearing from A to C get by law of sines

sin (θ) = [tex]\frac{187.84}{307} \times sin(78)[/tex]

sin (θ) =  0.5985  

θ = 36.76°

and as we get here angle BAC that is

angle BCA = 180 - ( 36.76° + 78° )

angle BCA = 65.24°

and here  negative bearing of A from C so - 65.24°

Answer:

TRUE

Step-by-step explanation:

Notice that point P is at the center of the circle. Notice also that it is being crossed by two diameters (segments RT and SQ). Then, the central angles RPS and TPQ must be equal because they are opposed by their vertex (center point P). Notice as well that the two triangles formed (triangle SRP, and triangle TPQ) are both isosceles triangles since they have the two sides that are adjacent  to the central angles mentioned above, equal to the circle's radius. Therefore, the sides opposite to the central angles (RS in one triangle, and QT in the other) must be equal among themselves.