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3 years ago

Factorise fully 3x+18

Mathematics

1 answer:

Nana76 [90]3 years ago

5 0

Find the Greatest Common Factor (GCF)

GCF = 3

Factor out the GCF. (Write the GCF first, and then in parenthesis, divide each term by the GCF)

3(3x/3 + 18/3)

Simplify each term in parenthesis

= 3(x + 6)

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A peony plant with red petals was crossed with another plant having streaky petals. A geneticist states that 75% of the offsprin

Strike441 [17]

Answer:

The sample data confirm the geneticist's prediction that 75% of the offspring from this cross will have red flowers.

Step-by-step explanation:

A Chi-square goodness of fit test can be used to test the claim made by the geneticist.

The hypothesis is defined as:

H₀: There is no difference between the observed and expected value,i.e. p₁ < 0.75.

Hₐ: There is a significant difference between the observed and expected value, i.e. p₁ > 0.75.

The test statistic is:

$\chi^{2}=\sum \frac{(O-E)^{2}}{E}$

Consider the tables attached below.

The value of the test statistic is:

$\chi^{2}=\sum \frac{(O-E)^{2}}{E}=25.8133$

The critical value is:

$\chi^{2}_{\alpha, k-1}=\chi^{2}_{0.01, 1}=6.635$

*Use a Chi-square table.

The critical region is:

$\chi^{2}\geq 6.635$

The test statistic value of 25.8133 lies in the critical region.

The null hypothesis is rejected at 1% level of significance.

Conclusion:

As the null hypothesis is rejected it can be concluded that 75% of the offspring from this cross will have red flowers.

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3 years ago

Suppose You walk from school and travel 3 blocks east then 6 blocks west then 11 blocks east again how far are and in which dire

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You are 8 blocks east from the school

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3 years ago

Compare the decimals 9,135.40 and 9,135.4.

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C is correct because both are the same numbers but they are different by significant figures.

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3 years ago

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3 years ago

An icicle with a diameter of 15.5 centimeters at the top, tapers down in the shape of a cone with a length of

Helga [31]

Answer:

Step-by-step explanation:

Note: I will leave the answers as fraction and in terms of pi unless the question states rounding conditions to ensure maximum precision.

From the question, we can tell it is a inversed-cone (upside down)

Volume of Cone = $\pi r^{2} \frac{h}{3}$

a) Given Diameter , d = 15.5cm and Length , h = 350cm,

we first find the radius.

$r = \frac{d}{2} \\=\frac{15.5}{2} \\=7.75cm$

We will now find the volume of the cone.

Volume of cone $\pi (7.75)^{2} \frac{350}{3} \\= \frac{168175\pi }{24}$

We know the density of ice is 0.93 grams per $1cm^{3}$

$1cm^{3} =0.93g\\\frac{168175\pi }{24} cm^{3} =0.93(\frac{168175\pi }{24} )\\= 20473 g$ (Nearest Gram)

b) After 1 hour, we know that the new radius = 7.75cm - 0.35cm = 7.4cm

and the new length, h = 350cm - 15cm = 335cm

Now we will find the volume of this newly-shaped cone.

Volume of cone = $\pi (7.4)^{2} \frac{335}{3} \\= \frac{91723\pi }{15} cm^{3}$

Volume of cone being melted = New Volume - Original volume

= $\frac{168175\pi }{24} -\frac{91723\pi }{15} \\= \frac{35697\pi }{40} cm^{3}$

c) Lets take the bucket as a round cylinder.

Given radius of bucket, r = 12.5cm (Half of Diameter) and h , height = 30cm.

Volume of cylinder = $\pi r^{2} h\\=\pi (12.5)^{2} (30)\\=\frac{9375\pi }{2} cm^{3}$

To overflow the bucket, the volume of ice melted must be more than the bucket volume.

Volume of ice melted after 5 hours = $5(\frac{35697\pi }{40} )\\=\frac{35697\pi }{8} cm^{3}$

See, from here of course you are unable to tell whether the bucket will overflow as all are in fractions, but fret not, we can just find the difference.

Volume of bucket - Volume of ice melted after 5 hours

= $\frac{9375\pi }{2} -\frac{35697\pi }{8 } \\=\frac{1803\pi }{8}cm^{3}$

from we can see the bucket can still hold more melted ice even after 5 hours therefore it will not overflow.

4 0

2 years ago

Factorise fully 3x+18​

Factorise fully 3x+18