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Which system of inequalities is represented by the graph?

asambeis [7]

The system of inequalities that is represented by the graph is option b: {y≥1y−x>0.

What is the inequalities about?

The term inequality is seen in mathematics as a kind of a statement that connote an order type of relationship and it ranges from greater than, greater than or equal to and others.

Note that The shaded area is said to be below the solid line at y=1, so the outcome of the set is said to be partially set up by the inequality .

Hence;

y≥1. . . . . . values of y in the solution set are greater than or equal to 1

The shaded area is seen below the line y=x, so is said to be partially determined by y−x>0.

Learn more about inequalities from

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8 0

2 years ago

Which of the following choices lists the values of the side lengths of a triangle with 45-45-90 degree angles and a hypotenuse =

Gnoma [55]

Answer:

The correct answer is D. 12√2, 12√2, 24.

Step-by-step explanation:

Let's recall that a property of the right triangles 45 - 45 - 90 is that the lengths of the sides of this type of triangles are in the ratio 1 : 1: √2.

Thus, if the hypotenuse is 24 units, the length of the legs is 12√2. We calculated it this way:

24/√2 = x/1

x√2 = 24

x = 24/√2

x = (24 * √2) / (√2 * √2) (For not having a square root in the denominator)

x = 24√2/2

x = 12√2 (Most simplified expression)

The correct answer is D. 12√2, 12√2, 24.

5 0

3 years ago

15 is what percent of 40%

Andrej [43]

15 is 37.5% of 40

Equation: Y = P% * X

P% = Y/X

P% = 15/40

p = 0.375

0.375 × 100 = 37.5%

4 0

4 years ago

Find the value of y given the value of x for y = 3 -4.3x when x = -3

ohaa [14]

Answer:

y = 15.9

Step-by-step explanation:

y = 3 - 4.3x

y = 3 - 4.3(-3)

y = 3 + 12.9

y = 15.9

4 0

4 years ago

Read 2 more answers

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