A laboratory table is two meters long. What is its length in millimeters? and in centimeters

Abel planned for a garden to be 42 m long but found that it needs to be 24 m long to fit in his backyard. He found the change of

Tom [10]

Question:

Abel planned for a garden to be 42 m long but found that it needs to be 24 m long to fit in his backyard. He found the change of scale below.

$\frac{42m}{7}/{\frac{24m}{7} = \frac{6}{4}$

Which is Abel’s error?

Abel should have written the ratio as $24 metres/7 metres$

Abel should have written the ratio as $24 metres/42 metres$

Abel should have divided both numbers by 6.

Abel should have divided both numbers by 4.

Answer:

Abel should have divided both numbers by 6.

Step-by-step explanation:

Given

Measured Length of backyard = 42m

Actual Length of backyard = 24m

Measured Ratio: $\frac{42m}{7}/{\frac{24m}{7} = \frac{6}{4}$

Required

Error in calculation of measured ratio

From Abel's calculation:

It can be observed that He divided both numbers by 7

Though 42/7 = 6 but that's not so for 24/7

24/7≠4;

Instead 24/7 = 3.43 (Approximated)

To get the actual ration, he has to divide both numbers by the highest common factor

The common factors of 42 and 24 include 2,3,6 of which the highest is 6

Hence; HCF of 42 and 24 = 6

So, we can conclude that the error in his calculation is having not dividing both numbers by 6

7 0

3 years ago

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A 34-foot pole casts a 30-foot shadow. At the same time, a nearby tree casts a 24-foot shadow. How tall is the tree?

artcher [175]

Answer:

27.2 ft

Step-by-step explanation:

Let's set up a ratio that represents the problem:

Object's Height (ft) : Shadow (ft)

Substitute with the dimensions of the 34 foot pole and its 30 foot shadow.

34 : 30

Find the unit rate:

The unit rate is when one number in a ratio is 1.

Let's make the Shadow equal to one by dividing by 30 on both sides.

Object's Height (ft) : Shadow (ft)

34 : 30

/30 /30

1.13 : 1

Now, let's multiply by 24 on both sides to find the height of the tree.

Multiply:

Object's Height (ft) : Shadow (ft)

1.13 : 1

x24 x24

27.2 : 24

Therefore, the tree is 27.2 feet tall.

7 0

2 years ago

What is the radius of a sphere with a volume of 4.5π cubic centimeters?

Snowcat [4.5K]

V=(4/3)pir^3
4.5pi=(4/3)pir^3
divide both sides by pi
4.5=(4/3)r^3
times 3/4 both sides
3.375=r^3
cube root both sides
1.5=r
radius is 1.5cm

3 0

2 years ago

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Which steps can be used in order to determine the solution to Negative 1.3 + 4.6 x = 0.3 + 4 x?

Mars2501 [29]

Answer:

x=8/3 OR 2.7

Step-by-step explanation:

-1.3+4.6x=0.3+4x

4.6x-4x=0.3+1.3

0.6x=1.6

x=1.6/0.6=8/3

x=8/3 OR 2.7

Hope this helps!

4 0

2 years ago

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National data indicates that 35% of households own a desktop computer. In a random sample of 570 households, 40% owned a deskt

Elan Coil [88]

Answer:

Yes, this provide enough evidence to show a difference in the proportion of households that own a desktop.

Step-by-step explanation:

We are given that National data indicates that 35% of households own a desktop computer.

In a random sample of 570 households, 40% owned a desktop computer.

Let p = population proportion of households who own a desktop computer

SO, Null Hypothesis, $H_0$ : p = 25% {means that 35% of households own a desktop computer}

Alternate Hypothesis, $H_A$ : p $\neq$ 25% {means that % of households who own a desktop computer is different from 35%}

The test statistics that will be used here is One-sample z proportion statistics;

T.S. = $\frac{\hat p-p}{{\sqrt{\frac{\hat p(1-\hat p)}{n} } } } }$ ~ N(0,1)

where, $\hat p$ = sample proportion of 570 households who owned a desktop computer = 40%

n = sample of households = 570

So, test statistics = $\frac{0.40-0.35}{{\sqrt{\frac{0.40(1-0.40)}{570} } } } }$

= 2.437

Since, in the question we are not given with the level of significance at which to test out hypothesis so we assume it to be 5%. Now at 5% significance level, the z table gives critical values of -1.96 and 1.96 for two-tailed test. Since our test statistics doesn't lies within the range of critical values of z so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region due to which we reject our null hypothesis.

Therefore, we conclude that % of households who own a desktop computer is different from 35%.

3 0

2 years ago