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3 years ago

Evaluate 2(x + 1) - 3 when x = 6.

Mathematics

1 answer:

alexandr1967 [171]3 years ago

4 0

Evaluate 2(x + 1) - 3 when x = 6.

First, plug in x value.

2(6 + 1) -3 ParenthesisEMDAS

2(7) - 3 PEMultiplyDAS

14 - 3 PEMDASubtract

11 ←

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Which of the following points are more than 5 units from the point P(−2, −2)? Select all that apply. A A (2, 1) B B (4, −1) C C

netineya [11]

The distance between any 2 points P(a,b) and Q(c,d) in the coordinate plane, is given by the formula:

 $|PQ|= \sqrt{ (a-c)^{2} + (b-d)^{2}}$

Using this formula we calculate the distances |PA|, |PB|, |PC|, |PD| and |PE| and compare to 5.

$|PA|= \sqrt{ (-2-2)^{2} + (-2-1)^{2}}= \sqrt{16+9}= \sqrt{25}=5$

$|PB|= \sqrt{ (-2-4)^{2} + (-2+1)^{2}}= \sqrt{36+1}= \sqrt{37} \approx 6$

$|PC|= \sqrt{ (-2-2)^{2} + (-2+3)^{2}}= \sqrt{16+1}= \sqrt{17}\approx4$

$|PD|= \sqrt{ (-2+6)^{2} + (-2+6)^{2}}= \sqrt{16+16}= \sqrt{32}\ \textgreater \ \sqrt{25}=5$

$|PE|= \sqrt{ (-2+5)^{2} + (-2-1)^{2}}= \sqrt{9+9}= \sqrt{16}=4$

Answer: B and D

3 0

3 years ago

A local minimum of a function is its: A) smallest value of the function over its entire domain. B) largest value of the function

Hunter-Best [27]

Answer:

Step-by-step explanation:

7 0

3 years ago

Find the values of x when y=1

kirill [66]

Answer:

$x=1+\sqrt{5}, 1-\sqrt{5}$

Step-by-step explanation:

$x^{2} -2x-4=0$
$(x-1)^{2} -1-4=0$
$(x-1)^{2} -5=0$
$(x-1)^{2} =5$
$x-1=\sqrt{5} ,-\sqrt{5}$
$x=1+\sqrt{5} , 1-\sqrt{5}$

FINAL ANSWER

$x=1+\sqrt{5} , 1-\sqrt{5}$

In Decimal Form (Rounded to 3 significant figures)

x≈-1.24, 3.24

6 0

4 years ago

Read 2 more answers

Jackson spends 214 hours painting 212 pictures. He spends the same amount of time painting each picture. How much time, in hours

Wewaii [24]

1 hour and 7 1/2 minutes per picture
2 1/4 = 60 * 2 = 120 + 15 = 135/2= 67.5 = 1 hour and 7 1/2 minutes

3 0

3 years ago

GreenBeam Ltd. claims that its compact fluorescent bulbs average no more than 3.24 mg of mercury. A sample of 25 bulbs shows a m

amm1812

Answer:

Null hypothesis: $\mu \leq 3.24$

Alternative hypothesis: $\mu > 3.24$

Step-by-step explanation:

1) Previous concepts and data given

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

A right tailed test (sometimes called an upper test) is when the alternative hypothesis statement contains a greater than (>) symbol.

$\bar X=3.29$ represent the sample mean

s represent the sample standard deviation

n represent the sample selected

$\alpha$ significance level

State the null and alternative hypotheses.

We need to conduct a hypothesis in order to check if the mean for fluorescent bulbs is no more than 3.24 mg of mercury, the system of hypothesis would be:

Null hypothesis: $\mu \leq 3.24$

Alternative hypothesis: $\mu > 3.24$

IIf we know the population deviation we can apply a z test to compare the actual mean to the reference value, and the statistic is given by:

$z=\frac{\bar X-\mu_o}{\frac{\sigma}{\sqrt{n}}}$ (1)

z-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".

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4 years ago