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3 years ago

Simplify quantity x squared plus 5 x plus 6 end quantity over quantity x plus 2

Mathematics

2 answers:

Aleksandr-060686 [28]3 years ago

8 0

Answer:

Step-by-step explanation:

Given

$\frac{x^2+5x+6}{x+2}$

Factor the numerator

x² + 5x + 6 = (x + 2)(x + 3) , thus

= $\frac{(x+2)(x+3)}{x+2}$

Cancel the factor (x + 2) on the numerator and denominator, leaving

= x+ 3 → c

noname [10]3 years ago

5 0

Answer:

C. x+3

Step-by-step explanation:

Simplifying

x²++5x+6/x+2

Firstly we need to factorize the numerator to have;

x²+5x+6

x²+3x+2x+6

(x²+3x)+(2x+6)

x(x+3)+2(x+3)

x+2(x+3)

The equation will now become;

(x+2)(x+3)/x+2

= x+2 will cancel out x+2 to have x+3 left which is the required function

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Measurements of the sodium content in samples of two brands of chocolate bar yield the following results (in grams):

Tpy6a [65]

Answer:

98% confidence interval for the difference μX−μY = [ 0.697 , 7.303 ] .

Step-by-step explanation:

We are give the data of Measurements of the sodium content in samples of two brands of chocolate bar (in grams) below;

Brand A : 34.36, 31.26, 37.36, 28.52, 33.14, 32.74, 34.34, 34.33, 29.95

Brand B : 41.08, 38.22, 39.59, 38.82, 36.24, 37.73, 35.03, 39.22, 34.13, 34.33, 34.98, 29.64, 40.60

Also, $\mu_X$ represent the population mean for Brand B and let $\mu_Y$ represent the population mean for Brand A.

Since, we know nothing about the population standard deviation so the pivotal quantity used here for finding confidence interval is;

P.Q. = $\frac{(Xbar -Ybar) -(\mu_X-\mu_Y)}{s_p\sqrt{\frac{1}{n_1} +\frac{1}{n_2} } }$ ~ $t_n__1+n_2-2$

where, $Xbar$ = Sample mean for Brand B data = 36.9

$Ybar$ = Sample mean for Brand A data = 32.9

$n_1$ = Sample size for Brand B data = 13

$n_2$ = Sample size for Brand A data = 9

$s_p = \sqrt{\frac{(n_1-1)s_X^{2}+(n_2-1)s_Y^{2} }{n_1+n_2-2} }$ = $\sqrt{\frac{(13-1)*10.4+(9-1)*7.1 }{13+9-2} }$ = 3.013

Here, $s^{2}_X$ and $s^{2} _Y$ are sample variance of Brand B and Brand A data respectively.

So, 98% confidence interval for the difference μX−μY is given by;

P(-2.528 < $t_2_0$ < 2.528) = 0.98

P(-2.528 < $\frac{(Xbar -Ybar) -(\mu_X-\mu_Y)}{s_p\sqrt{\frac{1}{n_1} +\frac{1}{n_2} } }$ < 2.528) = 0.98

P(-2.528 * $s_p\sqrt{\frac{1}{n_1} +\frac{1}{n_2}$ < $(Xbar -Ybar) -(\mu_X-\mu_Y)$ < 2.528 * $s_p\sqrt{\frac{1}{n_1} +\frac{1}{n_2}$ ) = 0.98

P( (Xbar - Ybar) - 2.528 * $s_p\sqrt{\frac{1}{n_1} +\frac{1}{n_2}$ < $(\mu_X-\mu_Y)$ < (Xbar - Ybar) + 2.528 * $s_p\sqrt{\frac{1}{n_1} +\frac{1}{n_2}$ ) = 0.98

98% Confidence interval for μX−μY =

[ (Xbar - Ybar) - 2.528 * $s_p\sqrt{\frac{1}{n_1} +\frac{1}{n_2}$ , (Xbar - Ybar) + 2.528 * $s_p\sqrt{\frac{1}{n_1} +\frac{1}{n_2}$ ]

[ $(36.9 - 32.9)-2.528*3.013\sqrt{\frac{1}{13} +\frac{1}{9}$ , $(36.9 - 32.9)+2.528*3.013\sqrt{\frac{1}{13} +\frac{1}{9}$ ]

[ 0.697 , 7.303 ]

Therefore, 98% confidence interval for the difference μX−μY is [ 0.697 , 7.303 ] .

4 0

2 years ago

Judy uses 7.5 pints of blue paint and white paint to paint her bedroom walls. 1/4 of this amount is blue paint, and the rest is

lianna [129]

Answer:

5.625 pints

Step-by-step explanation:

refer to pic

8 0

2 years ago

What is the area of a regular nonagon (9 sides) with side length of 15 cm and apothem of 20.6 cm? Round the answer to the neares

Triss [41]

We know that

<span>The nine radii of a regular Nonagon divides into 9 congruent isosceles triangles
</span>therefore
[the area of <span>a regular nonagon]=9*[area of isosceles triangle]

</span>[area of isosceles triangle]=b*h/2------> 15*20.6/2----> 154.5 cm²
so
[the area of a regular nonagon]=9*[154.5]------> 1390.5 cm²

the answer is
1390.5 cm²

5 0

2 years ago

Write the linear equation that gives the rule for this table.

MAVERICK [17]

Answer:

The linear equation that gives the rule for this table will be:

y=x+25

Step-by-step explanation:

Taking two points from the table

(2, 27)

(3, 28)

Finding the slope between two points

$\mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}$

$\left(x_1,\:y_1\right)=\left(2,\:27\right),\:\left(x_2,\:y_2\right)=\left(3,\:28\right)$

$m=\frac{28-27}{3-2}$

$m=1$

We know the slope-intercept form of linear equation is

$y=mx+b$

where m is the slope and b is the y-intercept

substituting the point (2, 27) and m=1 in the slope-intercept form to determine the y-intercept 'b'

$y=mx+b$

27 = 1(2)+b

27-2 = b

b = 25

Now, substituting m=1 and b=25 in the slope-intercept form to determine the linear equation

y=mx+b

y=1(x)+25

y=x+25

Thus, the linear equation that gives the rule for this table will be:

y=x+25

4 0

2 years ago

Please help me with this

pogonyaev

ANSWER
x= 46

EXPLANATION
To solve this problem you need to remember that a straight line is 180°. This figure is basically a straight line split in two, so 134°+x=180°. You can also subtract 134 from 180 to get 46.

4 0

2 years ago