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jasenka [17]
3 years ago
10

John sells plain cakes for $8 and decorated cakes for $12. On a particular day, John started with a total of 100 cakes, and sold

all but 4. His sales that day totaled $800.
He sold ___
plain cakes and ____
decorated cakes that day.
Mathematics
2 answers:
qaws [65]3 years ago
6 0

x+ y =  96   →     y = 96 - x     (1)

And the price per plain cake * the number he sold + price of the decorated cake * the number he sold = total sales

So

8x + 12y = 800    (2)

Subbing (1) into (2), we have that

8x + 12 (96 - x)  = 800   simplify

8x + 1152 - 12x  = 800       

-4x + 1152 = 800    subtract 1152 from both sides

-4x  = -352     divide both sides by -4

x = 88   = the number of plain cakes he sold

And 96 - x =  96 - 88  = 8   = the number of decorated cakes he sold

VikaD [51]3 years ago
3 0

Answer:

He sold 88 plain cakes and he decorated 8 cakes.

Step-by-step explanation:

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In a restaurant, the proportion of people who order coffee with their dinner is p. A simple random sample of 144 patrons of the
mote1985 [20]
<h2>Answer with explanation:</h2>

Given : In a restaurant, the proportion of people who order coffee with their dinner is p.

Sample size : n= 144

x= 120

\hat{p}=\dfrac{x}{n}=\dfrac{120}{144}=0.83333333\approx0.8333

The null and the alternative hypotheses if you want to test if p is greater than or equal to 0.85 will be :-

Null hypothesis : H_0: p\geq0.85   [ it takes equality (=, ≤, ≥) ]

Alternative hypothesis : H_1: p  [its exactly opposite of null hypothesis]

∵Alternative hypothesis is left tailed, so the test is a left tailed test.

Test statistic : z=\dfrac{\hat{p}-p}{\sqrt{\dfrac{p(1-p)}{n}}}

z=\dfrac{0.83-0.85}{\sqrt{\dfrac{0.85(1-0.85)}{144}}}\\\\=-0.561232257678\approx-0.56

Using z-vale table ,

Critical value for 0.05 significance ( left-tailed test)=-1.645

Since the calculated value of test statistic is greater than the critical value , so we failed to reject the null hypothesis.

Conclusion : We have enough evidence to support the claim that p is greater than or equal to 0.85.

8 0
3 years ago
Benito made punch with 26 ounces of grape juice, 38 ounces of apple juice, and 52 ounces of lemon sparkling water. Then he made
natita [175]
  26
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+52
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6 0
3 years ago
A bag contains y fruits. A box can hold 4 times as many fruits as the bag.
sashaice [31]
Y = 8

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3 0
3 years ago
In a right triangle ABC, CD is an altitude, such that AD=BC. Find AC, if AB=3 cm, and CD= 2 cm.
konstantin123 [22]

Consider right triangle ΔABC with legs AC and BC and hypotenuse AB. Draw the altitude CD.

1. Theorem: The length of each leg of a right triangle is the geometric mean of the length of the hypotenuse and the length of the segment of the hypotenuse adjacent to that leg.

According to this theorem,

BC^2=BD\cdot AB.

Let BC=x cm, then AD=BC=x cm and BD=AB-AD=3-x cm. Then

x^2=(3-x)\cdot 3,\\ \\x^2=9-3x,\\ \\x^2+3x-9=0,\\ \\D=3^2-4\cdot (-9)=9+36=45,\\ \\\sqrt{D}=\sqrt{45}=3\sqrt{5},\\ \\x_1=\dfrac{-3-3\sqrt{5} }{2}0.

Take positive value x. You get

AD=BC=\dfrac{-3+3\sqrt{5} }{2}\ cm.

2. According to the previous theorem,

AC^2=AD\cdot AB.

Then

AC^2=\dfrac{-3+3\sqrt{5} }{2}\cdot 3=\dfrac{-9+9\sqrt{5} }{2},\\ \\AC=\sqrt{\dfrac{-9+9\sqrt{5} }{2}}\ cm.

Answer: AC=\sqrt{\dfrac{-9+9\sqrt{5} }{2}}\ cm.

This solution doesn't need CD=2 cm. Note that if AB=3cm and CD=2cm, then

CD^2=AD\cdot DB,\\ \\2^2=AD\cdot (3-AD),\\ \\AD^2-3AD+4=0,\\ \\D

This means that you cannot find solutions of this equation. Then CD≠2 cm.

8 0
3 years ago
Read 2 more answers
Please help!!!!!
sergeinik [125]

-8.1

Step-by-step explanation:

\frac{ - 4}{9} x + 2.4 = 6

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<em>- 4x + 21.6 = 54</em>

<em>Take </em><em>2</em><em>1</em><em>.</em><em>6</em><em> </em><em>away</em><em> </em><em>from</em><em> </em><em>both</em><em> </em><em>sides</em>

<em>- 4x = 32.4</em>

<em>Divide</em><em> </em><em>by </em><em>-</em><em>4</em>

<em>x =  - 8.1</em>

8 0
2 years ago
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