Find the value of 3 + 5 × (2 − 1).

The triangle shown below has an area of 121212 units^2 <br> 2<br> squared.<br> Find xxx.

dalvyx [7]

Answer:

4

Step-by-step explanation:

Let's set up an equation using the formula for the area of a triangle.

Hint #22 / 3

\begin{aligned} \text{Area of a triangle} &= \dfrac12 \cdot \text{base} \cdot \text{height}\\\\ 12&= \dfrac12 \cdot 6 \cdot x \\\\ 12&= 3x \\\\ \dfrac{12}{\blueD{3}}&= \dfrac{3x}{\blueD{3}} ~~~~~~~\text{divide both sides by } {\blueD{ 3}}\\\\ \dfrac{12}{\blueD{3}}&= \dfrac{\cancel{3}x}{\blueD{\cancel{3}}}\\\\ x &=\dfrac{12}{\blueD{3}}\\\\ x &=4\end{aligned}

Area of a triangle

12

3

12

3

12

x

=

2

1

⋅base⋅height

=

2

1

⋅6⋅x

=3x

=

3

3x

divide both sides by 3

=

3

x

=

3

12

=4

5 0

2 years ago

From generation to generation, the mean age when smokers first start to smoke varies. However, the standard deviation of that ag

Jlenok [28]

Answer:

If we compare the p value and the significance level given for example $\alpha=0.05$ we see that $p_v$ so we can conclude that we to reject the null hypothesis, and the the actual mean starting age of smokers is significantly lower than 19.

Step-by-step explanation:

1) Data given and notation

$\bar X=18.1$ represent the mean age when smokers first start to smoke varies

$s=1.3$ represent the standard deviation for the sample

$\sigma=2.1$ represent the population standard deviation

$n=37$ sample size

$\mu_o =5.7$ represent the value that we want to test

$\alpha$ represent the significance level for the hypothesis test.

t would represent the statistic (variable of interest)

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

State the null and alternative hypotheses.

We need to conduct a hypothesis in order to determine if the mean starting age is at least 19, the system of hypothesis would be:

Null hypothesis: $\mu\geq 19$

Alternative hypothesis: $\mu < 19$

We know the population deviation, so for this case is better 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".

Calculate the statistic

We can replace in formula (1) the info given like this:

$z=\frac{18.1-19}{\frac{2.1}{\sqrt{37}}}=-2.607$

Calculate the P-value

Since is a one-side lower test the p value would be:

$p_v =P(z$

Conclusion

If we compare the p value and the significance level given for example $\alpha=0.05$ we see that $p_v$ so we can conclude that we to reject the null hypothesis, and the the actual mean starting age of smokers is significantly lower than 19.

4 0

2 years ago

Find the first, fourth, and eighth terms of the sequence. A(n) = –3 • 2^n–1

Sphinxa [80]

A(n) = –3 • 2⁽ⁿ⁻¹⁾

for n = 1 , A₁ = -3.(2)⁰ = -3
for n = 2 , A₂ = -3.(2)¹ = -6
for n = 3 , A₃ = -3.(2)² = -12
for n = 4 , A₄ = -3.(2)³ = -24
...........................................
for n = 8 , A₈ = -3.(2)⁷ = -384

4 0

2 years ago

Triangles ABC, EDC, and EFG are similar triangles. The measures of the three interior angles of triangle EFG are °, °, and °.

Misha Larkins [42]

Because of the vertical angles theorem, BAC becomes 50°. And angle B is 180-(50+30)=100.

If all 3 triangles are similar, the angles of triangle EFG are 30°, 50°, 100°

4 0

2 years ago

Read 2 more answers

Which equation below shows a correct first step for solving 3x = -12

Wewaii [24]

The answer is A. You just solve each one and you would find that it would be the same as 3x=-12.

5 0

2 years ago