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2 years ago

Use the Distributive Property to multiply. 2(b – 7)

Mathematics

2 answers:

mr Goodwill [35]2 years ago

8 0

Answer:

2b - 14

Step-by-step explanation:

2(b – 7)

2b - 14

alexandr402 [8]2 years ago

7 0

Answer:

$2b-14$

Step-by-step explanation:

Using the distributive property, $2(b-7)$ can be written as $(2\cdot b)-(2\cdot7)$ which solved/simplified is $2b-14$

Man, it's late! Well, hope this helped you out and answered your question!

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Ashley mixes two types of soft drinks with different types of concentration: one soft drink has 20% sugar and the other drink ha

ICE Princess25 [194]

Answer:

Sugar concentration of the mixed soft drink will be 32.5%.

Step-by-step explanation:

Sugar concentration of first drink = 20%

Volume of first soda = 250 ml

Sugar in first soda = 20% of 250 ...... (1)

Sugar concentration of second drink = 45%

Volume of second soda = 250 ml

Sugar in second soda = 45% of 250 ...... (2)

Let $x\%$ be the sugar concentration in resultant mixture.

Volume of mixture = 250 + 250 = 500 ml

Sugar in mixture = $x\%$ of 500 ml ...... (3)

Total sugar concentration (Adding (1) and (2)) and equating it to equation (3):

20% of 250 + 45% of 250 = $x\%$ of 500

$\Rightarrow \dfrac{20}{100} \times 250 + \dfrac{45}{100} \times 250 = \dfrac{x}{100} \times 500\\\Rightarrow 2 \times x = 65\\\Rightarrow x = 32.5\%$

Hence, Sugar concentration of the mixed soft drink will be 32.5%.

8 0

2 years ago

Let the following sample of 8 observations be drawn from a normal population with unknown mean and standard deviation:

Vikentia [17]

Answer:

$\= x = 18.5$ , $\sigma = 5.15$

$15.505 < \mu < 21.495$

$14.93 < \mu < 22.069$

Step-by-step explanation:

From the question we are are told that

The sample data is 21, 14, 13, 24, 17, 22, 25, 12

The sample size is n = 8

Generally the ample mean is evaluated as

$\= x = \frac{\sum x }{n}$

$\= x = \frac{ 21 + 14 + 13 + 24 + 17 + 22+ 25 + 12 }{8}$

$\= x = 18.5$

Generally the standard deviation is mathematically evaluated as

$\sigma = \sqrt{\frac{\sum (x- \=x )^2}{n}}$

$\sigma = \sqrt{\frac{\sum ((21 - 18.5)^2 + (14-18.5)^2+ (13-18.5)^2+ (24-18.5)^2+ (17-18.5)^2+ (22-18.5)^2+ (25-18.5)^2+ (12 -18.5)^2 )}{8}}$

$\sigma = 5.15$

considering part b

Given that the confidence level is 90% then the significance level is evaluated as

$\alpha = 100-90$

$\alpha = 10\%$

$\alpha = 0.10$

Next we obtain the critical value of $\frac{ \alpha }{2}$ from the normal distribution table the value is

$Z_{\frac{ \alpha }{2} } = 1.645$

The margin of error is mathematically represented as

$E = Z_{\frac{ \alpha }{2} } * \frac{\sigma }{\sqrt{n} }$

=> $E =1.645 * \frac{5.15 }{\sqrt{8} }$

=> $E = 2.995$

The 90% confidence interval is evaluated as

$\= x - E < \mu < \= x + E$

substituting values

$18.5 - 2.995 < \mu < 18.5 + 2.995$

$15.505 < \mu < 21.495$

considering part c

Given that the confidence level is 95% then the significance level is evaluated as

$\alpha = 100-95$

$\alpha = 5\%$

$\alpha = 0.05$

Next we obtain the critical value of $\frac{ \alpha }{2}$ from the normal distribution table the value is

$Z_{\frac{ \alpha }{2} } = 1.96$

The margin of error is mathematically represented as

$E = Z_{\frac{ \alpha }{2} } * \frac{\sigma }{\sqrt{n} }$

=> $E =1.96 * \frac{5.15 }{\sqrt{8} }$

=> $E = 3.569$

The 95% confidence interval is evaluated as

$\= x - E < \mu < \= x + E$

substituting values

$18.5 - 3.569 < \mu < 18.5 + 3.569$

$14.93 < \mu < 22.069$

8 0

3 years ago

The question is on the picture I took. If you can please help me :)

Monica [59]

i forgot tho

Step-by-step explanation:

5 0

3 years ago

Perform the multiplication FOR THIRTY POINTS! (x^2)/(3) multiplied by (x^2-x-6)/(x^2-6x+9)

Oxana [17]

Answer:

(x^3+2x^2)/(3x-9)

Step-by-step explanation:

3 0

3 years ago

|x-5|=3 Whats x? please help?

finlep [7]

Answer:

x = 8 or x = 2

Step-by-step explanation:

We know x - 5 = 3 or x - 5 = -3.

Possibility 1:

Step 1: Add 5 to both sides.

$x-5+5=3+5$
$x=8$

Possibility 2:

Step 1: Add 5 to both sides.

$x-5+5=-3+5$
$x=2$

Step 2: Check if both solutions apply to original equation.

$|8-5|=3$
$|3|=3$
$3=3$
$|2-5|=3$
$|-3|=3$
$3=3$

3 0

2 years ago

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