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1 year ago

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50% of all the cakes Lucy bakes that week were party cakes 1-5 fruit cakes and remainder were sponge cakes what percentage of ca

kes were sponge cakes

1 answer:

Stells [14]1 year ago

4 0

30% were sponge cakes because you do 1/5=0.2 or20%+50%=70% and 100%-70%=30% so 30% is your answer.

You might be interested in

Abel and Cedric will share a total of $180. Abel will receive half as much as Cedric. What amount. in dollars, will Cedric recei

Black_prince [1.1K]

Answer:

Cedric's share=$120

Abel's share=$60

Step-by-step explanation:

Abel will receive half as much as Cedric

Let

Cedric's share=x

Abel's share = 1/2 of x

Total money=$180

x + 1/2x = 180

2x+x/2 =180

3/2x=180

Divide both sides by 3/2

x= 180÷3/2

=180 × 2/3

=360/3

=120

Therefore,

Cedric's share = x = 120

Abel's share=1/2x

=1/2 × 120

=120/2

=60

Cedric's share=$120

Abel's share=$60

4 0

1 year ago

Match the x-coordinates with their corresponding pairs of y-coordinates on the unit circle.

jeka57 [31]

<span>y=+- square root 5 over 3

y^2 + x^2 = 1 => x^2 = 1 - y^2 = 1 - 5/9 = 4/9 => x = +/- 2/3

Answer: x = +/- 2/3

y=+- square root 7 over 3

y^2 + x^2 = 1 => x^2 = 1 - y^2 = 1 - 7/9 = 2/9 => x = +/- (√2) / 3

Answer: x = +/-(√2)/3

y=+- 3 over 3

x^2 = 1 - y^2 = 1 - 3/9 = 1 - 1/3 = 2/3 => x = +/-(√2/3)

Answer: x = +/-√(2/3)

y=+- 2 square root 2 over 2

= y = +/- 2(√2) /2 = √2 ...... these y-coordinates are out of the unit circle, then there is not a corresponding x - coordinate for them.

</span>

5 0

1 year ago

In a USA TODAY/Gallup Poll, respondents favored Barack Obama over Mitt Romney in terms of likeability, 61% to 32% (Los Angeles T

dybincka [34]

Answer:

a) percentage of respondents that favored neither Obama nor Romney in terms of likeability = 7%

b) For a given survey of 500, the number of respondents that favored Obama than Romney is 145.

Step-by-step explanation:

Given that none of those surveyed can favour the two candidates at the same time,

n(Universal set) = n(U) = 100%

n(Obama) = n(O) = 61%

n(Romney) = n(R) = 32%

n(That favour Obama and Romney) = n(O n R) = 0%

To calculate for the number that favour neither of the candidates

n(O' n R')

n(U) = n(O) + n(R) + n(O n R) + n(O' n R')

100 = 61 + 32 + 0 + n(O' n R')

n(O' n R') = 100 - 93 = 7%

b) For a given survey of 500, how many more respondents favored Obama than Romney?

Number of those surveyed that favour Obama = 61% of 500 = 305

Number of those surveyed that favour Romney = 32% of 500 = 160

Difference = 305 - 160 = 145

5 0

1 year ago

A piece of rubber tubing maintains a cylindrical shape as it is stretched. At the instant that the inner radius of the tube is 2

professor190 [17]

Answer:

the rate of change in volume is dV/dt = 4π mm³/s = 12.56 mm³/s

Step-by-step explanation:

since the volume V of a cylinder is related with the height H and the radius R through:

V = πR²*H

then the change in time is given by the derivative with respect to time t

dV/dt = (∂V/∂R)*(dR/dt) + (∂V/∂H)*(dH/dt)

the change in volume with radius at constant height is

(∂V/∂R) = 2*πR*H

the change in volume with height at constant radius is

(∂V/∂H) = πR²

then

dV/dt = 2π*R*H *(dR/dt) + πR²*(dH/dt)

replacing values

dV/dt = 2π* 2 mm * 20 mm * (-0.1 mm/s) + π (2 mm) ²* 3 mm/s = 4π mm³/s

dV/dt = 4π mm³/s = 12.56 mm³/s

7 0

1 year ago

One of the vertices of △PQR is P(2, −1). The midpoint of PQ is M(3, 0). The midpoint of QR is N(5, 3). Show that MN || PR and MN

VLD [36.1K]

Answer:

<em>See the proof below</em>

Step-by-step explanation:

Given the following coordinates

P(2, −1)

Midpoint of PQ M(3, 0)

We can get the coordinate point Q using the midpoint formula;

M(X,Y) = (x1+x2/2, y1+y2/2)

X = x1+x2/2

3 = 2+x2/2

6 = 2+x2

x2 = 6-2

x2 = 4

Y = y1+y2/2

0 = -1+y2/2

0 = -1 + y2

y2 = 0+1

y2 = 1

<em>Hence the coordinate of Q is (4, 1)</em>

Next is to get the coordinate of R

Given the midpoint of QR to be N(5, 3)

(5,3) = (4+x2/2, 1+y2/2)

5 = 4+x2/2

10 = 4+x2

x2 = 10-4

x2 = 6

1+y2/2 = 3

1+y2 = 6

y2 = 6-1

y2 = 5

<em>Hence the coordinate of R is (6,5)</em>

<em></em>

Given the coordinates M(3, 0) and N(5, 3)

Slope is expressed as:

m = y2-y1/x2-x1

m = 3-0/5-3

m = 3/2

Slope of MN = 3/2

Get the slope of PR

Given the coordinates P(2, −1) and R (6,5)

Slope of PR = 5-(-1)/6-2

Slope of PR = 5+1/4

Slope of PR = 6/4 = 3/2

<em>Since the slope of MN is equal to that of PR, hence MN is parallel to PR i.e MN || PR</em>

<em></em>

To show that MN = 1/2PR, we will have to take the distance between M and N and also P and R first as shown:

For MN with coordinates M(3, 0) and N(5, 3)

MN = √(x2-x1)²+(y2-y1)²

MN = √(5-3)²+(3-0)²

MN = √2²+3²

MN = √13

Get the length of PR where P(2, −1) and R (6,5)

PR = √(6-2)²+(5+1)²

PR = √4²+6²

PR = √16+36

PR = √52

PR = √4*13

PR = √4*√13

PR = 2√13

Since MN = √13

PR = 2MN

Divide both sides by 2

PR/2 = 2MN/2

PR/2 = MN

Hence MN = 1/2 PR (Proved!)

8 0

1 year ago