To solve the inequality 4x < 8, you would divide both sides of the inequality by 4.

I WILL GIVE BRAINLIEST

Katen [24]

Answer:

40 square inches

step-by-step explanation:

The new club sticker is in the shape of a triangle

It has a height of 8 inches

And a base of 10 inches

Area of a triangle is given by: $\frac{1}{2}$ × base × height

Area of the triangular club sticker = $\frac{1}{2}$ × 10 inches × 8 inches = 40 square inches.

8 0

3 years ago

Help me understand this question!

Ivan

Answer:

AB = 24, BC = 6

Step-by-step explanation:

Let, the length be a and breadth be b.

So, 2(a + b) = 60 => a + b = 30

(PQR) and (ABC) are similar.

So, a/8 = b/2

2a = 8b

2(30 - b) = 8b

60 - 2b = 8b

10b = 60

b = 6

So, a = 24

[If there's any problem with the solution, please inform me]

3 0

4 years ago

If the rate of the boat in still water is 27 mph, and the rate of the current of a river is x mph, what is the rate of the boat

BigorU [14]

Answer:

a)27-x

b)27+x

Step-by-step explanation:

when a boat travels in the same direction as the current is downstream-->speeds the boat. If the rate of the boat in still water is 27 mph and the rate of the current of a river is x mph, the rate of the boat when the boat is going downstream is 27+x

when a boat travels against the current is upstream-->slow down. If the rate of the boat in still water is 27 mph and the rate of the current of a river is x mph, the rate of the boat when the boat is going upstream is 27-x

6 0

3 years ago

The bacterial strain Acinetobacter has been tested for its adhesion properties. A sample of five measurements gave read- ings of

oksian1 [2.3K]

Answer:

Part a

We need to conduct a one tailed test

We need to conduct a hypothesis in order to check if the mean is higher than 2.5, the system of hypothesis would be:

Null hypothesis: $\mu \leq 2.5$

Alternative hypothesis: $\mu > 2.5$

Part b: Calculate the statistic

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

$z=\frac{3.372-2.5}{\frac{0.66}{\sqrt{5}}}=2.954$

Part c :P-value

Since is a one sided test the p value would be:

$p_v =P(z>2.954)=0.0016$

Conclusion

If we compare the p value and the significance level assumed $\alpha=0.01$ we see that $p_v$ so we can conclude that we have enough evidence to reject the null hypothesis, we can conclude that the true mean is higher than 2.5 at 1% of signficance.

Step-by-step explanation:

a. Should the alternative hypothesis be one-sided or two-sided?

b. Test the hypothesis that the mean adhesion is 2.5 dyne-cm².

c. What is the P-value of the test statistic?

Data given and notation

Data: 2.69, 5.76, 2.67, 1.62 ,4.12

We can calculate the sample mean with this formula:

$\bar X= \frac{\sum_{i=1}^n X_i}{n}$

$\bar X=3.372$ represent the sample mean

$\sigma=0.66$ represent the population standard deviation

$n=5$ sample size

$\mu_o =2.5$ represent the value that we want to test

$\alpha=0.01$ 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)

Part a: State the null and alternative hypotheses.

We need to conduct a one tailed test

We need to conduct a hypothesis in order to check if the mean is higher than 2.5, the system of hypothesis would be:

Null hypothesis: $\mu \leq 2.5$

Alternative hypothesis: $\mu > 2.5$

If we analyze the size for the sample is < 30 but we know the population deviation so 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".

Part b: Calculate the statistic

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

$z=\frac{3.372-2.5}{\frac{0.66}{\sqrt{5}}}=2.954$

Part c :P-value

Since is a one sided test the p value would be:

$p_v =P(z>2.954)=0.0016$

Conclusion

If we compare the p value and the significance level assumed $\alpha=0.01$ we see that $p_v$ so we can conclude that we have enough evidence to reject the null hypothesis, we can conclude that the true mean is higher than 2.5 at 1% of signficance.

8 0

3 years ago

Which is the simplified form of r^-7 + s^-12

makkiz [27]

Answer:

The simplified form of r^-7 + s^-12 is ----> 1/r^7 + 1/s^12

Step-by-step explanation:

3 0

3 years ago