5.

emmasim [6.3K]

Get the b all alone on one side of the inequality. To do this, we can divide both sides by 5.

5b / 5 ≤ -15 / 5
b ≤ -3

So, that means b has to be less than or equal to -3.

In interval notation it would look like [-3, -∞)

In a set builder notation: {x | x ∈ R, x ≤ -3}

Which is read as the set of all x, such that, x is a member of the real numbers and x is less than or equal to -3.

6 0

3 years ago

Read 2 more answers

Someone help me, will be giving brainliest, thanks. this is due today. just one question.

Inessa [10]

Answer:

8,-6

Step-by-step explanation:

x^2 -6x +8 = 0

(x-4)(x-2)

3 0

2 years ago

In a poll of 1000 adults in July 2010, 540 of those polled said that schools should ban sugary snacks and soft drinks. Complete

erastova [34]

Answer:

$z=2.53$

$p_v =P(z>2.53)=0.0057$

The p value obtained was a very low value and using the significance level given $\alpha=0.05$ we have $p_v$ so then we have enough evidence to reject the null hypothesis, and we can say that at 5% of significance, the proportion of adults who support a ban on sugary snacks and soft drinks is more than 0.5 or 50%.

Step-by-step explanation:

1) Data given and notation

n=1000 represent the random sample taken

X=540 represent the adults that said that schools should ban sugary snacks and soft drinks

$\hat p=\frac{540}{1000}=0.54$ estimated proportion of adults that said that schools should ban sugary snacks and soft drinks

$p_o=0.5$ is the value that we want to test

$\alpha=0.05$ represent the significance level

Confidence=95% or 0.95

z would represent the statistic (variable of interest)

$p_v$ represent the p value (variable of interest)

2) Concepts and formulas to use

We need to conduct a hypothesis in order to test the claim that majority of adults (more than 50%) support a ban on sugary snacks and soft drinks, the system of hypothesis are:

Null hypothesis: $p\leq 0.5$

Alternative hypothesis: $p > 0.5$

When we conduct a proportion test we need to use the z statistic, and the is given by:

$z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}$ (1)

The One-Sample Proportion Test is used to assess whether a population proportion $\hat p$ is significantly different from a hypothesized value $p_o$ .

3) Calculate the statistic

Since we have all the info requires we can replace in formula (1) like this:

$z=\frac{0.54 -0.5}{\sqrt{\frac{0.5(1-0.5)}{1000}}}=2.53$

4) Statistical decision

It's important to refresh the p value method or p value approach . "This method is about determining "likely" or "unlikely" by determining the probability assuming the null hypothesis were true of observing a more extreme test statistic in the direction of the alternative hypothesis than the one observed". Or in other words is just a method to have an statistical decision to fail to reject or reject the null hypothesis.

The significance level provided $\alpha=0.05$ . The next step would be calculate the p value for this test.

Since is a one side right tailed test the p value would be:

$p_v =P(z>2.53)=0.0057$

So the p value obtained was a very low value and using the significance level given $\alpha=0.05$ we have $p_v$ so then we have enough evidence to reject the null hypothesis, and we can say that at 5% of significance, the proportion of adults who support a ban on sugary snacks and soft drinks is more than 0.5 or 50%.

7 0

3 years ago

Preston drew a blueprint of an additional room he is planning to add to his house. On the blueprint, 2 centimeters is equal to 3

Sidana [21]

1 cm = 1.5 feet
9 feet / 1.5 = 6 cm 12 feet / 1.5 = 8 cm B. 6 cm by 8 cm

8 0

3 years ago

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Given that tan θ ≈ −0.087, where 3 2 π < θ < 2 , π find the values of sin θ and cos θ.

elena-s [515]

Answer:

sin θ ≈ -0.08667
cos θ ≈ 0.99624

Step-by-step explanation:

Straightforward use of the inverse tangent function of a calculator will tell you θ ≈ -0.08678 radians. This is an angle in the 4th quadrant, where your restriction on θ places it. (To comply with the restriction, you would need to consider the angle value to be 2π-0.08678 radians. The trig values for this angle are the same as the trig values for -0.08678 radians.)

Likewise, straightforward use of the calculator to find the other function values gives ...

sin(-0.08678 radians) ≈ -0.08667

cos(-0.08678 radians) ≈ 0.99624

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<em>Note on inverse tangent</em>

Depending on the mode setting of your calculator, the arctan or tan⁻¹ function may give you a value in degrees, not radians. That doesn't matter for this problem. sin(arctan(-0.087)) is the same whether the angle is degrees or radians, as long as you don't change the mode in the middle of the computation.

We have shown radians in the above answer because the restriction on the angle is written in terms of radians.

_____

<em>Alternate solution</em>

The relationship between tan and sin and cos in the 4th quadrant is ...

$\cos{\theta}=\dfrac{1}{\sqrt{1+\tan^2{\theta}}}\\\\\sin{\theta}=\dfrac{\tan{\theta}}{\sqrt{1+\tan^2{\theta}}}$

That is, the cosine is positive, and the sign of the sine matches that of the tangent.

This more complicated computation gives the same result as above.

4 0

3 years ago