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3 years ago

The designers of drink cartons must consider the length of the straw required so that it will reach the bottom

Mathematics

2 answers:

Lady_Fox [76]3 years ago

8 0

Answer:

the answer is right above me

daser333 [38]3 years ago

4 0

Answer:

<em>The length of the straw is 13.53 cm</em>

Step-by-step explanation:

<u>Rectangular Prism</u>

A rectangular prism or cuboid is a box-shaped object. It has six flat faces and all angles are right angles. And all of its faces are rectangles.

If the straw must reach into the diagonally opposite corners of the base of the carton, then its minimum length is calculated by:

$d^2= a^2+b^2+c^2$

Where a,b, and c are the dimensions of the cuboid. The image shows the dimensions of the drink carton: a=6 cm, b=10 cm, c=4 cm (order is not important), thus:

$d^2= 6^2+10^2+4^2=36+100+16=152$

$d=\sqrt{152}$

d= 12.33 cm

The straw must stick out of the carton by an additional 1.5 cm, thus the total length of the straw is: 12.33 + 1.5 = 13.53 cm

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Find the values of x and y if (x+2,y)=(3,4).

gogolik [260]

Answer:

x = 1 and y = 4

Step-by-step explanation:

Solution,

(x+2,y) = (3,4)

Now,

Comparing corresponding elements,

x+2 = 3 , y = 4

or, x = 3 - 2 , y = 4

or, x = 1 , y = 4

Therefore, the value of x is 1 and y is 4.

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4 years ago

The price of a notebook was $3.55 yesterday. today, the price fell to $3.30 . find the percentage decrease. round your answer to

Paul [167]

30 % because 55 - 30 is 25 and the nearst tenth is 30

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3 years ago

The following information was obtained from matched samples. Individual Method 1 Method 2 1 7 5 2 5 9 3 6 8 4 7 7 5 5 6 Refer to

kykrilka [37]

Answer:

$p_v =2*P(t_{(8)}$

c. should not be rejected

Step-by-step explanation:

1) Data given and notation

The data given is:

Method 1 : 7,5,6,7,5

Method 2: 5,9,8,7,6

$\bar X_{1}=6$ represent the mean for the method 1

$\bar X_{2}=7$ represent the mean for the method 2

$s_{1}=1$ represent the sample standard deviation for the method 1

$s_{2}=1.58$ represent the sample standard deviation for the method 2

$n_{1}=5$ sample size selected for the Consultant A

$n_{2}=5$ sample size selected for the Consultant B

$\alpha=0.05$ represent the significance level for the hypothesis test.

t would represent the statistic (variable of interest)

$p_v$ represent the p value for the test (variable of interest)

State the null and alternative hypotheses.

We need to conduct a hypothesis in order to check if the mean for the difference is equal to 0, the system of hypothesis would be:

Null hypothesis: $\mu_{1}- \mu_{2}=0$

Alternative hypothesis: $\mu_{1} - \mu_{2}\neq 0$

If we analyze the size for the samples both are less than 30 so for this case is better apply a t test to compare means, and the statistic is given by:

$t=\frac{\bar X_{1}-\bar X_{2}}{\sqrt{\frac{s^2_{1}}{n_{1}}+\frac{s^2_{2}}{n_{2}}}}$ (1)

t-test: "Is used to compare group means. Is one of the most common tests and is used to determine whether the means of two groups are equal to each other".

Calculate the statistic

We can replace in formula (1) the info given like this:

$t=\frac{6-7}{\sqrt{\frac{1^2}{5}+\frac{1.58^2}{5}}}=-1.195$ (1)

P-value

The first step is calculate the degrees of freedom, on this case:

$df=n_{1}+n_{2}-2=5+5-2=8$

Since is a two sided test the p value would be:

$p_v =2*P(t_{(8)}$

Conclusion

If we compare the p value and the significance level given $\alpha=0.05$ we see that $p_v>\alpha$ so we can conclude that we have enough evidence to FAIL to reject the null hypothesis. So the best option would be:

c. should not be rejected

3 0

3 years ago

Write two equivalent fractions for 10 to 3

saw5 [17]

20/6 because 20 x 3 = 6 x 10 = 60. 309 is equivalent to 10/3 because 30 x 3 = 9 x 10 = 90.
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7 0

3 years ago

What is the length of segment AB?

Scorpion4ik [409]

Point A is at (12,12)

Point B is at (48,24)

Use the distance formula √((x2-x1)^2 + (y2-y1)^2)

Length = √((48-12)^2 + (24-12)^2)

Length = √(36^2 + 12^2)

Length = √(1296 + 144)

Length = √1440

The answer is E.

5 0

3 years ago