Alice, Bernice, and Carol have £600 altogether. The ratio of Alice’s money to Bernice’s money is 3:7. Carol has £60 more than Alice. What is the amount of money each girl got?

Answer:

3 : 7 =>

Anna = $180

Raman = $420

1 : 4 =>

Anna = $120

Raman = $480

Step-by-step explanation:

Shares when ratio is 3 : 7

Anna : Raman = 3 : 7

Sum of ratio 10

Anna's share=

                   [tex]\frac{3}{10} \times 600 = \$ 180[/tex]

Raman 's share=

                  [tex]\frac{7}{10} \times 600 = \$ 420[/tex]

Shares when ratio is 1 : 4

Anna : Raman = 1 : 4

Sum of ratio = 5

Anna 's share =

                   [tex]\frac{1}{5} \times 600 = \$ 120[/tex]

Raman's share =

                  [tex]\frac{4}{5} \times 600 = \$ 480[/tex]

Answer:

True

Step-by-step explanation:

The formula to convert Fahrenheit degrees to Celcius degrees is [tex]C=5/9*(F-32)[/tex]

Answer:

D

Step-by-step explanation:

notice how everything goes up by 3? that's a sequence.

Answer:

C

Step-by-step explanation:

For any point (x, y) on the parabola the focus and directrix are equidistant

Using the distance formula

[tex]\sqrt{x^2+(y-5)^2}[/tex] = | y + 5 | ← square both sides

x² + (y - 5)² = (y + 5)² ← expand parenthesis on both sides

x² + y² - 10y + 25 = y² + 10y + 25 ( subtract y² - 10y + 25 from both sides )

x² = 20y

Answer:

i think 88

Step-by-step explanation:

(it's been a while since I've done this so I'm not too sure it's correct)

The formula we need to use is

2πr(angle/360)

we need the radius (r)

To get r we need angle AES

180-80= 100

using the equation from before

88=2πr*(100/360)

raidus: 50.42

Then to get the length CD we need angle DEC

180-80=100

2π*50.42*(100/360)=88

there probably was some kind of shortcut we could've used to figure this out faster but whatever

Answer:

I don't know.

Answer:

It's (-3, -2)

I did the math, don't worry

Answer:

c=13 and a=20

Step-by-step explanation:

Here you need to use the Pythagoras theorem :

c²=a² + b²

c = √a² + b²

c = √(12)²+(5)²

c= √144+25

c = √169

c = 13

2) c²=a²+b²

    b= √c²-b²

    b= √(29)²-(21)²

    b = √400

    b = 20

In 2 you change your formula just so that it can be easier and just calculate your length straight forward but you can also just do it in the original equation

Answer:

x = 15 , x = 2

Step-by-step explanation:

[tex]x^2 -17x + 30 =0\\\\x^2 -2x-15x +30=0\\\\x(x-2)-15x(x-2) =0\\\\(x-15)(x-2)=0\\\\[/tex]

x = 15 , x = 2

Answer:

7/5 is the scale factor

Step-by-step explanation:

Answer:

Step-by-step explanation:

let the speed of Landon=x

speed of Eduardo=x+9

5x+5(x+9)=135

divide by 5

x+x+9=135/5=27

2x+9=27

2x=27-9

2x=18

x=18/2=9

speed of Landon=9 mph

speed of Eduardo=9+9=18 mph

Answer:

C. 8

Step-by-step explanation:

Options

A. 5

B. 6

C. 8

D. Can't say without knowing the number of participants

Number of sweet distributed = Total number of sweets - left over sweets

= 1025 sweets - 1 left over sweet

= 1024 sweets

Number of participants = Number of sweets distributed / number of sweets given to each participant

A. 5

Number of participants = Number of sweets distributed / number of sweets given to each participant

= 1024 /5 Sweets

= 204.8 participant

B. 6

Number of participants = Number of sweets distributed / number of sweets given to each participant

= 1024/6

= 170.67 participant

C. 8

Number of participants = Number of sweets distributed / number of sweets given to each participant

= 1,024/8

= 128 participant

D. Can't say without knowing the number of participants

From the options given, the number of sweets given away to each participant could be 8

Number of sweets given to each participants is 32.

Since, A sports teacher had 1025 sweets and he had one sweet left after distributing.

So, number of sweets he distributing is, [tex]1025-1=1024[/tex]

Since, distributing these equally amongst all the participants

Therefore, number of sweets given to each participants is, [tex]=\sqrt{1024}=32[/tex]

So, total number of participants is 32 and number of sweets given to each participants is 32.

Learn more about square root here:

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Answer:

1:1 because they ate the same amount both weeks

Answer:

489.40 cm³

Step-by-step explanation:

Since the cross section is parallel to their respective bases, hence:

Area of the cylinder cross section = area of the circular base = πr²

where r is the radius of the cylinder base.

Area of other cross section = area of rectangle base = 3.8 cm * 8.1 cm

Since both cross sections have same area, hence:

Area of cylinder cross section = Area of rectangle base

πr² = 8.1 * 3.8

r² = 9.8

r = 3.1 cm

Volume of the cylinder = πr²h = π(3.1)²(15.9) = 489.40 cm³

Answer:

y = 6x - 19

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = 6x - 4 ← is in slope- intercept form

with slope m = 6

Parallel lines have equal slopes , then

y = 6x + c ← is the partial equation

To find c substitute (3, - 1) into the partial equation

- 1 = 18 + c ⇒ c = - 1 - 18 = - 19

y = 6x - 19 ← equation of parallel line

Step-by-step explanation:

B) opposite sides are congruent !!!!!!

Answer:

Multiply the numerator by the numerator and the denominator by the demoninator.

Step-by-step explanation:

Answer:

Nope, to multiply two fractions = numerator × numerator / denominator × denominator

Step-by-step explanation:

For Example:

[tex]\frac{5}{3}[/tex] × [tex]\frac{8}{2}[/tex]

Multiply 5 by 8

40

Multiply 3 by 2

6

Result: [tex]\frac{40}{6}[/tex]

Finally Simplify

[tex]\frac{40}{6} =[/tex] [tex]40[/tex] ÷ 6 = [tex]6\frac{4}{6}[/tex] or 6.6 as a decimal

Answer:

1

Step-by-step explanation:

Answers:

========================================================

Explanations:

8) Positive r values always go with positive regression slopes. The r value will likely not equal the slope, but they share the same sign.

------------------------------

9) The data set isn't given so I'm not sure. But it seems like your teacher just wants to know a hypothetical situation in which r value will produce the best fit. That would be r = -0.95 since we're the furthest from zero. The closer you are to r = 1 or r = -1, the better the fit.

------------------------------

10) The blue regression line, aka line of best fit, is fairly close to all of the data points. Also, the blue line has a positive slope. This means r is fairly close to 1. So that's why we go with r = 0.9

------------------------------

11) The general equation is y = mx+b. We simply replace x,y with x1,y1.

------------------------------

12) When considering y = mx+b, the m is the slope. I'm not entirely sure where the m comes from, but I've read some sources that say 'm' somehow represents 'mountain' which involves slopes. This could have simply been a memorization tool and not the actual reason why m was chosen to be the slope.

As an example, y = 2x+5 has slope 2.

------------------------------

13) The b in y = mx+b is the y intercept. It's the initial value.

It always occurs when x = 0 since

y = mx+b

y = m*0+b

y = b

Meaning the point (0,b) is the location of the y intercept.

For example, y = 2x+5 has y intercept 5 located at the point (0,5).

Answer:

I need more information to answer this. Please provide more context

Step-by-step explanation:

SOHCAHTOA

SIN: Opposite/hypo

COS: Adj/Hyp

TAN: Opp/Adj

Answer:

I think it is of the last option

Answer:

15×5 =75

Step-by-step explanation:

1 inch reprsnt 5

Answer:

84%

Step-by-step explanation:

each liter is 1000 cubic centimetre, so you have a total density of 3000, but instead think of 3 liters being 100% density and think of alcohol as 80% density, there are 4 times at much 80% than 100% liquid.

with 3 liters of alcohol, 3 liters of water is now 90% density or 0.9 gram per centimetre. add another 3 liters and it is 2/3, so the grams per centimetre would be 8.66667 or 8 2/3's

if you add another 3 liters, THEN it is 85%

add 12 liters in total and the final answer 84%

Answer:

D

8x^2-12x+5

thanx for youer sug

Answer:

[tex]8x^2-12x+5[/tex]

Step-by-step explanation:

This is the same as saying h(g(x)). All you do is take the g(x) equation and plug that in for x in the h(x) equation.

h(x) = 4x+1                                           Plug in g(x) equation for x

h(g(x)) = [tex]4(2x^2-3x+1)+1[/tex]                Distribute the 4 and simplify

h(g(x)) = [tex]8x^2-12x+5[/tex]  

Answer:

6cm

Step-by-step explanation:

Area of the trapezoid = Area of the square + Area of the triangle

Area of the square= Area of the trapezoid - Area of the triangle

Area of the square= 60 - 24

Area of the square= = 36 square metres

Since Area of the square= L²

L is the length of the side of the square

L² = 36

L = √36

L = 6cm

Hence the required length is 6cm

Answer:

option c is the correct answer

Answer:

a. P(x = 5) = 0.24

b. P(x ≥ 6) = 0.43

c. P(x < 4)= 0.14

Step-by-step explanation:

According to the Question,

⇒We use Binomial Probability Formula

[tex]P(X = x ) = \frac{n!}{x!((n-x)! } * p^{x} * (1-p)^{n-x}[/tex]

Where, p=0.52 & n=10

a. The probability that the number of U.S. adults who have very little confidence in newspapers is ​exactly​ five . So, (x=5)

Thus, [tex]P(X = 5 ) = \frac{10!}{5!((10-5)! } * 0.52^{5} * (1-0.52)^{10-5}[/tex]

On Solving Above Equation we get,

P(5)=0.2441 ≈ 0.24

b. The probability that the number of U.S. adults who have very little confidence in newspapers is at least 6 . So, (x≥6)

Then,

P(x≥6) = P(6)+P(7)+P(8)+P(9)+P(10)

P(x≥6) = [tex]\frac{10!}{6!((10-6)! } * 0.52^{6} * (1-0.52)^{10-6}[/tex] + [tex]\frac{10!}{7!((10-7)! } * 0.52^{7} * (1-0.52)^{10-7}[/tex] +[tex]\frac{10!}{8!((10-8)! } * 0.52^{8} * (1-0.52)^{10-8}[/tex] + [tex]\frac{10!}{9!((10-9)! } * 0.52^{9} * (1-0.52)^{10-9}[/tex]+[tex]\frac{10!}{10!((10-10)! } * 0.52^{10} * (1-0.52)^{10-10}[/tex]

On solving above equation we get,

P(x≥6) =  0.4270 ≈ 0.43

c. The probability that the number of U.S. adults who have very little confidence in newspapers is less than 4 . So, (x<4)

Then,

P(x < 4)=P(3) + P(2)+P(1)+P(0)

P(x<4) = [tex]\frac{10!}{3!((10-3)! } * 0.52^{3} * (1-0.52)^{10-3}[/tex] + [tex]\frac{10!}{2!((10-2)! } * 0.52^{2} * (1-0.52)^{10-2}[/tex]+ [tex]\frac{10!}{1!((10-1)! } * 0.52^{1} * (1-0.52)^{10-1}[/tex] + [tex]\frac{10!}{0!((10-0)! } * 0.52^{0} * (1-0.52)^{10-0}[/tex]

On solving we get,

P(x < 4)= 0.1410 ≈ 0.14  

The graph of the function f ( x ) = x² - 2x + 3 is plotted

Graphs behave differently at various x-intercepts. Sometimes the graph will cross over the x-axis at an intercept. Other times the graph will touch the x-axis and bounce off.

Identify the even and odd multiplicities of the polynomial functions' zeros.

Using end behavior, turning points, intercepts, and the Intermediate Value Theorem, plot the graph of a polynomial function.

The graphs cross or are tangent to the x-axis at these x-values for zeros with even multiplicities. The graphs cross or intersect the x-axis at these x-values for zeros with odd multiplicities

Given data ,

Let the function be represented as A

Now , the value of A = f ( x )

f ( x ) = x² - 2x + 3   be equation (1)

Now , the function is a parabolic equation with the vertices at ( 1 , 2 )

Therefore , the function is f ( x ) = x² - 2x + 3  and the graph is plotted

Hence , the parabolic function is f ( x ) = x² - 2x + 3

To learn more about equation of graph of polynomials click :

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Answer:

The population of town A = 18,000

The population of town B = 15,000

The population of town C = 20,000

Step-by-step explanation:

Given;

A:B = 6:5

B:C = 3:4

total population = 53,000

A + B + C = 53,000

[tex]\frac{A}{B} = \frac{6}{5} \\\\A = \frac{6B}{5} \\\\\Also;\\\\\frac{B}{C} = \frac{3}{4} \\\\C = \frac{4B}{3} \\\\then;\\\\\frac{6B}{5} +B+ \frac{4B}{3} = 53,000\\\\multiply \ through \ by \ "15"\\\\18B + 15B + 20B = 795,000\\\\53B = 795,000\\\\B = \frac{795,000}{53} \\\\B = 15,000[/tex]

Now solve for A and C;

[tex]A = \frac{6 \times 15,000}{5} = 18,000\\\\C = \frac{4 \times 15,000}{3} = 20,000[/tex]

3/5×(-3)/10 + 1/15 - 3/5×1/5 =  -7/30 ≅  -0.2333333

I hope this helps!