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stellarik [79]
3 years ago
15

For the expression y + 6 - 3, determine the coefficient for the variable term.

Mathematics
1 answer:
Darya [45]3 years ago
4 0

Answer:

3

Step-by-step explanation:

Determine the coefficient of y+ 6 - 3 in the binomial expansion y+ 3(2-1)  

3(2+-1) + y = + 3(2) - (3)^-1   = 3

= y + 6 - 3   = y+3

remember to add a minus sign before every second term then a plus.

Now we see that in the term where y is in factor 3 as asked in the question (this is the term  2(3), the coefficient is therefore 3.

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To determine the number of trout in a​ lake, a conservationist catches 180 ​trout, tags them and throws them back into the lake.
GaryK [48]
The ratio of the trout with tags that are caught and the total trout with tags is first calculated.

     r = 12 trout / 180 trout = 1/15

Then, we divide the number of trouts caught without tag by the value obtained above.

     N = (48 - 12) / (1/15) = 540

Then, we add the number obtained above and 180.
     T = 540 + 180 = 720

ANSWER: 720
3 0
3 years ago
A rectangular piece of wood is 12 centimeters longer than it is wide. A strip 1 centimeter wide is cut off all around. This decr
denis-greek [22]

Answer:

Length 37 cm, width 25 cm.

Step-by-step explanation:

Let the original dimensions be length x and width x - 12 cms.

The new dimensions will be length (x - 2) and width (x - 12 - 2) = x-14 cm.

So , from the areas, we have:

x(x - 12) - (x - 2)(x - 14) = 120

x^2 - 12x  - (x^2 - 16x + 28) = 120

-12x + 16x - 28 = 120

4x = 148

x = 37 cms

So the length was 37 cm and the width was 37-12 = 25 cm.

7 0
3 years ago
In a study of cereal leaf beetle damage to oats, researchers measured the number of beetle larvae per stem in small plots of oat
PSYCHO15rus [73]

Answer:

At 0.05 level of significance, there is no difference in the mean number of larvae per stem. This supports the scientist's claim.

(d) H0: MeanMalathion - MeanNoMalathion equals 0

H1: MeanMalathion - MeanNoMalathion not equals 0

Step-by-step explanation:

Test statistic (t) = (mean 1 - mean 2) ÷ sqrt[pooled variance (1/n1 + 1/n2)]

Let the difference between the two means be x and the pooled variance be y

n1 = 5, n2 = 12

t = x ÷ sqrt[y(1/5 + 1/12)] = x ÷ sqrt(0.283y) = x ÷ 0.532√y = 1.88x/√y

Assuming the ratio of x to √y is 0.5

t = 1.88×0.5 = 0.94

n1 + n2 = 5 + 12 = 17

degree of freedom = n1 + n2 - 2 = 17 - 2 = 15

significance level = 0.05 = 5%

critical value corresponding to 15 degrees of freedom and 5% confidence interval is 2.131

The test is a two-tailed test because the alternate hypothesis is expressed using not equal to.

The region of no rejection of the null hypothesis lies between -2.131 and 2.131

Conclusion

Fail to reject the null hypothesis because the test statistic 0.94 falls within the region bounded by the critical values.

The scientist's claim is right.

A null hypothesis is a statement from a population parameter which is either rejected or accepted (fail to reject) upon testing. It is expressed using the equality sign.

An alternate hypothesis is also a statement from a population parameter which negates the null hypothesis and is accepted if the null hypothesis is rejected. It is expressed using any of the inequality signs.

3 0
3 years ago
In triangle PQR, PR = 23mm, QR = 39mm, and m<R = 163 degrees. Find the area of the triangle to the nearest tenth.
Schach [20]

Answer: 131.1287 square mm (approx)

Step-by-step explanation:

The area of a triangle,

A=\frac{1}{2} \times s_1\times s_2\times sin \theta

Where s_1 and s_2 are adjacent sides and \theta is the include angle of these sides,

Here PR and QR are adjacent sides and ∠R is the included angle of these sides,

Thus, we can write,

s_1 = PR= 23\text{ mm}, s_2=QR=39\text{ mm} and \theta = 163^{\circ},

Thus, the area of the triangle PQR,

A=\frac{1}{2} \times 23\times 39\times sin163^{\circ}

A=\frac{262.257419136}{2} = 131.128709568\approx 131.1287\text{ square mm}

5 0
3 years ago
A box can had a maximum of 60 comic books.If comic books are bundled together in groups of 8, write and solve an inequality to f
Reika [66]

Answer: the maximum number of bundles of comic books that the box can carry is 7

Step-by-step explanation:

Let x represent the maximum number of bundles of comic books that the box can carry.

If comic books are bundled together in groups of 8, then the total number of comic books in x bundles of comic books would be 8x.

A box can hold a maximum of 60 comic books. Therefore, the inequality to find the maximum number of bundles of comic books that the box can carry is

8x ≤ 60

x ≤ 60/8

x ≤ 7.5

8 0
3 years ago
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