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Archy [21]
3 years ago
11

Simplify (3x+2)(x-7)

Mathematics
2 answers:
vovangra [49]3 years ago
8 0
The answer is
3 {x}^{2}  - 19x - 14
first you must multiply or use the FOIL method (First, Outer, Inner, Last)
First you multiply the first terms
(3x)(x)
this gives you 3x^2, then you multiple the outer terms
( - 7)(3x)
this gives you -21x, then you multiply the inner terms
(2)(x)
that gives you 2x, finally you multiply the last terms
(2)( - 7)
that gives you 14, now you combine like terms
- 21x + 2x =  - 19x
now you put all the terms together and end up with your solution
3 {x}^{2}  - 19x - 14

RSB [31]3 years ago
3 0

Remember to follow the FOIL method.

Note that: FOIL = First, Outside, Inside, Last.

Multiply

First: (3x)(x) = 3x²

Outside: (3x)(-7) = -21x

Inside: (2)(x) = 2x

Last: (2)(-7) = -14

-------------------------------------------------------------------------------------------------------------

3x² -21x + 2x -14

Combine like terms

3x² (-21x + 2x) - 14

3x² - 19x - 14

3x² - 19x - 14 is your answer

<em>~Rise Above the Ordinary</em>

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Which statements about the cylinder are true? Select two
Rus_ich [418]

Answer:

The radius of the cylinder is (1/2)x units

The area of the cylinder’s base is (1/4)πx2 square units

The height of the cylinder is 4x units

Step-by-step explanation:

<u><em>The complete question is</em></u>

A cylinder with a base diameter of x units has a volume of πx3 cubic units.

Which statements about the cylinder are true? Check all that apply.

(1) The radius of the cylinder is (1/2)x units.

(2) The radius of the cylinder is 2x units.

(3) The area of the cylinder’s base is (1/4)πx2 square units.

(4) The area of the cylinder’s base is (1/2)πx2 square units.

(5) The height of the cylinder is 2x units.

(6) The height of the cylinder is 4x units

we know that

The volume of the cylinder is equal to

V=\pi r^{2}h

we have

r=\frac{x}{2}\ units ----> the radius is half the diameter

V=\pi x^{3}\ units^3

substitute the given values  in the formula of volume

\pi x^3=\pi (\frac{x}{2})^{2}h

solve for h

simplify

x=(\frac{1}{4})h

h=4x\ units

<u>Verify each statement</u>

(1) The radius of the cylinder is (1/2)x units

The statement is true

see the explanation

(2) The radius of the cylinder is 2x units.

The statement is false

Because, the radius of the cylinder is x/2 units

(3) The area of the cylinder’s base is (1/4)πx2 square units

The statement is true

Because, the area of the cylinder's base is equal to

A=\pi r^{2}

r=\frac{x}{2}\ units

substitute

A=\pi (\frac{x}{2})^{2}

A=\frac{\pi x^2}{4}\ units^2

(4) The area of the cylinder’s base is (1/2)πx2 square units.

The statement is false

Because, the area of the cylinder's base is equal to

A=\frac{\pi x^2}{4}\ units^2

see the part (3)

(5) The height of the cylinder is 2x units.

The statement is false

Because, the height of the cylinder is 4x units (see the explanation)

(6) The height of the cylinder is 4x units

The statement is true

see the explanation

7 0
3 years ago
Consider a population of Pacific tree frogs (Pseudacris regilla). In this population of frogs, a single locus controls the produ
zloy xaker [14]

Answer:

Step-by-step explanation:

Hello!

Use these data to calculate the chi-square statistic. Report your calculated chi-square statistic to two decimal places.

In this example, the study variable is X: genotype of a single locus two allele gene that codes the mating call of tree frogs. Categorized: S₁S₁, S₁S₂, and S₂S₂.

Usually, when you have a sample of observed genotypes of a gene of interest, the goal is to check if these genotypes follow a theoretical model such as the frequency models proposed by Mendel.

In Mendelian genetics, when two heterozygous individuals (Aa, Aa) from the F1 generation are crossed, you expect the next generation (F2) to show the genotypic ratio 1:2:1 ⇒ This model means that out of 4 descendants 1 will have the genotype AA, 2 will have the genotype Aa and 1 will have the genotype aa. Since there is no theoretical model specified I'll use the mendelian ratio 1:2:1.

If this theory applies to the population then we'll expect that the proportion of the first genotype is P(S₁S₁)= 0.25, the second P(S₁S₂)= 0.5 and the third P(S₂S₂)=0.25

To test if the observed genotypes follow the theoretical model you have to apply a Chi-Square Goodness of Fit Test.

For this test the hypotheses are:

H₀:P(S₁S₁)= 0.25; P(S₁S₂)= 0.5; P(S₂S₂)=0.25

H₁: The data is not consistent with the specified distribution.

α: 0.05

Statistic: X^2= sum(\frac{(o_i-e_i)^2}{e_i} )~X^2_{k-1}

Where:

oi: Observed frequency for the i- category

ei: Expected frequency for the i-category

k= number of categories

The rejection region for this test is one-tailed to the right. This is so because if the observed and expected values are too different (the chi-square value will be high) this will mean that the population doesn't follow the theoretical model and thus reject the null hypothesis. If the differences between what's observed and what's expected are small, this will mean that the population follows the theoretical model (and you'll obtain a small chi-square value) and you will not reject the null hypothesis.

The critical value is:

X^2_{k-1; 1 - \alpha }= X^2_{3;0.95}= 7.815

If the statistic is at least 7.815, the decision is to reject the null hypothesis.

If the statistic is less than 7.815, the decision is to not reject the null hypothesis.

Step 1 is to obtain the expected frequencies for each category:

e_i= n*P_i

e_{S_1S_1}= n * P(S_1S_1)= 1341*0.25= 335.25

e_{S_1S_2}= n * P(S_1S_2)= 1341 * 0.5= 670.5

e_{S_2S_2}= n * P(S_2S_2)= 1341*0.25= 335.25

Note: the summatory of the expected frequencies is equal to the total of observations ∑ei= n. If you have doubts about your calculations, you can add them to check it: ∑ei= 335.25 + 670.5 + 335.25= 1341

X^2= (\frac{(987-335.25)^2}{335.25} )+(\frac{(333-670.5)^2}{670.5} )+(\frac{(21-335.25)^2}{335.25} ) = 1731.50

Decision: Reject null hypothesis.

I hope this helps!

3 0
3 years ago
i thought of a number. if i subtract 6 from it and multiply the difference by 4 the result is 36. find the number that i thought
SVEN [57.7K]
Since the difference*4=36, the difference = 9
since the number-6= the difference, the number-6=9
Thus the number is 15
3 0
3 years ago
If total liabilities are 1,000 and total assets are 8000 owner's e q u i t y must be
olga_2 [115]
Total equity is equal to assets - liabilities.

Therefore,

8000 - 1000 = 7000

The owner's equity is $7,000.
5 0
3 years ago
What's the probability a number is odd given that it's an integer between 0 and 11?
Elza [17]
A odd number lie between 0 and 11(0 and 11 not included), it means that total of ten numbers, starting from {1,2,3........,10} form our sample space.

sample space=s={1,2,3....,10}=total 10 numbers
So,
m=total no. of odd numbers{1,3,5,7,9} in our sample space=5 numbers
 
probability that number is odd=p=m/s
p=5/10=0.5
  
8 0
3 years ago
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