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gladu [14]
3 years ago
6

Given the two sets, what is A ∩ B ? A = {1, 2, 3, 4, 5, 6} B = {2, 3, 5, 7}

Mathematics
1 answer:
topjm [15]3 years ago
5 0

Answer:

2, 3, 5

Step-by-step explanation:

A∩B means "A intersection B" which includes all elements that are shared in BOTH sets. This would be the middle crossover section of a Venn diagram.

Hence, 2 and 3 and 5 are shared in both sets.

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Simplify the product.<br> ((3x-6)/(x+5))·((2x+10)/(x-5))
cricket20 [7]
I hope this helps you

3 0
3 years ago
G(x)=x+3 and h(x)=2x Find gh(x)
lilavasa [31]

Answer:

2x + 3

Step-by-step explanation:

To find g(h(x)) substitute x = h(x) into g(x), that is

g(2x) = 2x + 3

4 0
3 years ago
"Immediately after a ban on using hand-held cell phones while driving was implemented, compliance with the law was measured. A r
sergiy2304 [10]

Answer:

(a) Null Hypothesis, H_0 : p_1-p_2=0  or  p_1= p_2  

    Alternate Hypothesis, H_A : p_1-p_2\neq 0  or  p_1\neq p_2

(b) We conclude that there is a statistical difference in these two proportions measured initially and then one year later.

Step-by-step explanation:

We are given that a random sample of 1,250 drivers found that 98.9% were in compliance. A year after the implementation, compliance was again measured to see if compliance was the same (or not) as previously measured.

A different random sample of 1,100 drivers found 96.9% compliance."

<em />

<em>Let </em>p_1<em> = proportion of drivers that were in compliance initially</em>

p_2<em> = proportion of drivers that were in compliance one year later</em>

(a) <u>Null Hypothesis</u>, H_0 : p_1-p_2=0  or  p_1= p_2      {means that there is not any statistical difference in these two proportions measured initially and then one year later}

<u>Alternate Hypothesis</u>, H_A : p_1-p_2\neq 0  or  p_1\neq p_2     {means that there is a statistical difference in these two proportions measured initially and then one year later}

The test statistics that will be used here is <u>Two-sample z proportion statistics</u>;

                     T.S.  = \frac{(\hat p_1-\hat p_2)-(p_1-p_2)}{\sqrt{ \frac{\hat p_1(1-\hat p_1)}{n_1} + \frac{\hat p_2(1-\hat p_2)}{n_2}} }  ~ N(0,1)

where, \hat p_1 = sample proportion of drivers in compliance initially = 98.9%

\hat p_2 = sample proportion of drivers in compliance one year later = 96.9%

n_1 = sample of drivers initially = 1,250

n_2 = sample of drivers one year later = 1,100

(b) So, <u><em>the test statistics</em></u>  =  \frac{(0.989-0.969)-(0)}{\sqrt{ \frac{0.989(1-0.989)}{1,250} + \frac{0.969(1-0.969)}{1,100}} }  

                                           =  3.33

<u>Now, P-value of the test statistics is given by;</u>

         P-value = P(Z > 3.33) = 1 - P(Z \leq 3.33)

                                            = 1 - 0.99957 = <u>0.00043</u>

Since in the question we are not given with the level of significance so we assume it to be 5%. Now at 5% significance level, the z table gives critical values between -1.96 and 1.96 for two-tailed test.

<em>Since our test statistics does not 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 </em><u><em>we reject our null hypothesis.</em></u>

Therefore, we conclude that there is a statistical difference in these two proportions measured initially and then one year later.

7 0
3 years ago
Graph f(x) = 2x^4+3 <br> let x = 0, 1, and 2.<br> please show your work
mestny [16]
Sub those points for x
f(x) is the y

(x,y)

so for x=0
f(0)=2(0)^4+3
f(0)=0+3
f(0)=3
(0,3) is a opint

for x=1
f(1)=2(1)^4+3
f(1)=2(1)+3
f(1)=2+3
f(1)=5
(1,5) is another point

for x=2
f(2)=2(2^4)+3
f(2)=2(16)+3
f(2)=32+3
f(2)=35
(2,35) is another point


points are
(0,3)
(1,5)
(2,35)
3 0
3 years ago
ALGEBRAIC EXPRESSION 11. Subtract the sum of 13x – 4y + 7z and – 6z + 6x + 3y from the sum of 6x – 4y – 4z and 2x + 4y – 7. 12.
Naily [24]

Answer:

Explained below.

Step-by-step explanation:

(11)

Subtract the sum of (13x - 4y + 7z) and (- 6z + 6x + 3y) from the sum of (6x - 4y - 4z) and (2x + 4y - 7z).

[(6x - 4y - 4z) +(2x + 4y - 7z)]-[(13x - 4y + 7z) + (- 6z + 6x + 3y) ]\\=[6x-4y-4z+2x+4y-7z]-[13x-4y+7z-6z+6x+3y]\\=6x-4y-4z+2x+4y-7z-13x+4y-7z+6z-6x-3y\\=(6x+2x-13x-6x)+(4y-4y+4y-3y)-(4z+7z+7z-6z)\\=-11x+y-12z

Thus, the final expression is (-11x + y - 12z).

(12)

From the sum of (x² + 3y² - 6xy), (2x² - y² + 8xy), (y² + 8) and (x² - 3xy) subtract (-3x² + 4y² - xy + x - y + 3).

[(x^{2} + 3y^{2} - 6xy)+(2x^{2} - y^{2} + 8xy)+(y^{2} + 8)+(x^{2} - 3xy)] - [-3x^{2} + 4y^{2} - xy + x - y + 3]\\=[x^{2} + 3y^{2} - 6xy+2x^{2} - y^{2} + 8xy+y^{2} + 8+x^{2} - 3xy]- [-3x^{2} + 4y^{2} - xy + x - y + 3]\\=[4x^{2}+3y^{2}-xy+8]-[-3x^{2} + 4y^{2} - xy + x - y + 3]\\=4x^{2}+3y^{2}-xy+8+3x^{2}-4y^{2}+xy-x+y-3\\=7x^{2}-y^{2}-x+y+5

Thus, the final expression is (7x² - y² - x + y + 5).

(13)

What should be subtracted from (x² – xy + y² – x + y + 3) to obtain (-x²+ 3y²- 4xy + 1)?

A=(x^{2} - xy + y^{2} - x + y + 3) - (-x^{2}+ 3y^{2}- 4xy + 1)\\=x^{2} - xy + y^{2} - x + y + 3 +x^{2}- 3y^{2}+ 4xy -1\\=2x^{2}-2y^{2}+3xy-x+y+2

Thus, the expression is (2x² - 2y² + 3xy - x + y + 2).

(14)

What should be added to (xy – 3yz + 4zx) to get (4xy – 3zx + 4yz + 7)?

A=(4xy-3zx + 4yz + 7)-(xy - 3yz + 4zx) \\=4xy-3zx + 4yz + 7 -xy + 3yz - 4zx\\=3xy-7zx+7yz+7

Thus, the expression is (3xy - 7zx + 7yz + 7).

(15)

How much is (x² − 2xy + 3y²) less than (2x² − 3y² + xy)?

A=(2x^{2} - 3y^{2} + xy)-(x^{2} - 2xy + 3y^{2})\\=2x^{2} - 3y^{2} + xy-x^{2} + 2xy - 3y^{2}\\=x^{2}-6y^{2}+3xy

Thus, the expression is (x² - 6y² + 3xy).

7 0
3 years ago
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