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sashaice [31]
2 years ago
14

Bob is having a party and want to order some cake. there will be 57 guest and he wants to make sure that everyone gets a slice o

f cake. he wants to pay as little as possible for the cakes and for them to be the same size. First cake 20cm, serve 12 people and cost £13.50, second cake 25cm, serve 20 people and cost £18.75
Mathematics
1 answer:
Dafna1 [17]2 years ago
4 0
To find out which cake is better for the price, we need to multiply the cake amounts by how many cakes of that kind we need. You need 5 20cm cakes, so we multiply 5 by the price of the 20cm cake (13.50) to get $67.50. You need 3 25cm cakes, so 3 x 18.75 = 56.25.

20cm cake: $67.50
25cm cake: $56.25

Answer: The 25cm cake is cheaper for more people.
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This rectangular frame is made from 5 straight pieces of metal.
Aneli [31]

Answer:

Total weight = 70.5 kg

Step-by-step explanation:

Rectangular frame is made from 5 straight pieces of metal. One of them goes through the diagonal of the rectangle.

2 pieces form the length of the rectangular frame, hence, they have a length of 12 m each

2 pieces from the width of the rectangular frame, hence, they a length of 5 m each

To find the length of the diagonal, we can use Pythagoras Theorem:

Hypotenuse² = Base² + Perpendicular²

Hypotenuse² = 5² + 12²

Hypotenuse² = 169²

Hypotenuse = 13

Hence, the length of the piece of metal placed at the diagonal is 13cm

Find the sum of all lengths of the metal pieces.

Total length = 12 + 12 + 5 + 5 + 13

Total length = 47 m

Total weight = 1.5 × Total length

Total weight = 1.5 kg/m × 47m

Total weight = 70.5 kg

7 0
1 year ago
Express as a sum: 4.5–8.3–2<br> i will give you brianily if you get it rite
olchik [2.2K]

Answer:

-5.8

Step-by-step explanation:

4.5–8.3–2

-3.8 -2

-5.8

4 0
2 years ago
Read 2 more answers
Of the 500 sample households in the previous exercise, 7 had three or more large-screen TVs. (a) The percentage of households in
likoan [24]

Answer:

a) The percentage of households in the town with three or more largescreen TVs is estimated as :

The best estimation for the population proportion is :

\hat p=\frac{7}{500}=0.014

And that represent the 1.4%.

b) And the 95% confidence interval would be given (0.00370;0.0243).

And the % would be between 0.37% and 2.43%.

Step-by-step explanation:

Data given and notation  

n=500 represent the random sample taken    

X=7 represent the households with three or more large-screen TVs

\hat p=\frac{7}{500}=0.014 estimated proportion of households with three or more large-screen TVs

\alpha=0.05 represent the significance level (no given, but is assumed)    

z would represent the statistic (variable of interest)    

p= population proportion of households with three or more large-screen TVs

Part a

The percentage of households in the town with three or more largescreen TVs is estimated as :

The best estimation for the population proportion is :

\hat p=\frac{7}{500}=0.014

And that represent the 1.4%.

Part b

Yes is possible. We hav that np>10 and n(1-p)>10 so we have the assumption of normality to find the interval.

The confidence interval would be given by this formula

\hat p \pm z_{\alpha/2} \sqrt{\frac{\hat p(1-\hat p)}{n}}

For the 95% confidence interval the value of \alpha=1-0.95=0.05 and \alpha/2=0.025, with that value we can find the quantile required for the interval in the normal standard distribution.

z_{\alpha/2}=1.96

And replacing into the confidence interval formula we got:

0.014 - 1.96 \sqrt{\frac{0.014(1-0.014)}{500}}=0.00370

0.014 + 1.96 \sqrt{\frac{0.014(1-0.014)}{500}}=0.0243

And the 95% confidence interval would be given (0.00370;0.0243).

And the % would be between 0.37% and 2.43%.

4 0
2 years ago
Describe the transformation f(x) = √x + 1 − 5 in words. The parent function f(x) = √x has been shifted 1 unit and 5 units.
KATRIN_1 [288]

Answer:

The translation is 1 unit to the left and 5 units down

Step-by-step explanation:

we have

g(x)=\sqrt{x+1}-5

f(x)=\sqrt{x} -----> parent function

we know that

The transformation

f(x)-----> g(x) has the following rule

(x,y)-------> (x-1,y-5)

That means

The translation is 1 unit to the left and 5 units down

see the attached figure to better understand the problem

6 0
2 years ago
Read 2 more answers
A puppy finds a rawhide bone and begins to pull it with a force, Ft. The free-body diagram is shown. A free body diagram with 4
Drupady [299]

Answer:

  • <em><u> It begins to move toward the right</u></em>

Explanation:

The given information can be summarized in this way:

  • First force vector: Fg = - 8N (vertical down)
  • Second force vector: Ft = 6N (horizonal right)
  • Third force vector: FN = 8N (vertical up)
  • Fourth vector: Ff = - 4N (horizontal left)

Following Newton's second law, net force equal mass times acceleration:

  • Net force = mass × acceleration

To predict the motion, you apply Newton's second law in each direction (vertical and horizontal)

  • <u>Vertical force balance:</u>

        Net vertical force = 8N - 8N = 0. This means there is not motion in the vertical direction.

  • <u>Horizontal force balance:</u>

         Net horizontal force = 6N - 4N = 2N. This means there is a net force of 2N to the right, which lets you predict that the bone starts to accelerate to the right; this is, the bone begins to move toward the right.      

6 0
2 years ago
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