.5x−6=x+0.05 Which number is equal to the value of x?

Given that tan theta = -4/7, and 270° < theta < 360°, what is the exact value of sec theta

aleksley [76]

Answer:

sec Θ = $\frac{\sqrt{65} }{7}$

Step-by-step explanation:

Using the trigonometric identity

sec²Θ = tan²Θ + 1

Since 270° < Θ < 360° ← that is fourth quadrant, then

sec Θ > 0, thus

sec²Θ = (- $\frac{4}{7}$ )² + 1 = $\frac{16}{49}$ + 1 = $\frac{65}{49}$ , then

sec Θ = $\sqrt{\frac{65}{49} }$ = $\frac{\sqrt{65} }{7}$

6 0

2 years ago

Translate the Verbal phrase into a Math Expression: Four more than twice a number

alukav5142 [94]

Answer:

2x+4 or 4+2x

Step-by-step explanation:

3 0

3 years ago

100 POINTS + BRAINLIEST !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!11 Solve x³ - 9x^(1.5) + 8 = 0

VLD [36.1K]

Answer:

x=1, x=4

Step-by-step explanation:

3 0

2 years ago

Read 2 more answers

Solve the system of elimination -2x+2y+3z=0 -2x-y+z=-3 2x+3y+3z=5

Dahasolnce [82]

Answer:

x = 1 , y = 1 and z = 0

Step-by-step explanation:

-2x+2y+3z=0 ------(1)

-2x-y+z=-3 --------(2)

2x+3y+3z=5 ---------(3)

To find the values of x,y and z

(3) - (2)⇒ 2y + 4z = 2

y + 2z = 1 --------(4)

(1) - (2)⇒ 3y +2z =3 ---(5)

(5) - (4)⇒ 2y = 2

y = 1

Substituting the value of y in (4) we get z =0

Substituting the value of y and z in (1) we get x = 1

Therefore x = 1 , y = 1 and z = 0

5 0

3 years ago

4.One attorney claims that more than 25% of all the lawyers in Boston advertise for their business. A sample of 200 lawyers in B

AleksAgata [21]

Answer:

$z=\frac{0.315 -0.25}{\sqrt{\frac{0.25(1-0.25)}{200}}}=2.123$

$p_v =P(Z>2.123)=0.0169$

The p value obtained was a very low value and using the significance level given $\alpha=0.05$ we have $p_v$ so we can conclude that we have enough evidence to reject the null hypothesis, and we can said that at 5% of significance the proportion of lawyers had used some form of advertising for their business is significantly higher than 0.25 or 25% .

Step-by-step explanation:

1) Data given and notation

n=200 represent the random sample taken

X=63 represent the lawyers had used some form of advertising for their business

$\hat p=\frac{63}{200}=0.315$ estimated proportion of lawyers had used some form of advertising for their business

$p_o=0.25$ 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 more than 25% of all the lawyers in Boston advertise for their business:

Null hypothesis: $p\leq 0.25$

Alternative hypothesis: $p > 0.25$

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:

$z=\frac{0.315 -0.25}{\sqrt{\frac{0.25(1-0.25)}{200}}}=2.123$

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 right tailed test the p value would be:

$p_v =P(Z>2.123)=0.0169$

The p value obtained was a very low value and using the significance level given $\alpha=0.05$ we have $p_v$ so we can conclude that we have enough evidence to reject the null hypothesis, and we can said that at 5% of significance the proportion of lawyers had used some form of advertising for their business is significantly higher than 0.25 or 25% .

8 0

3 years ago