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3 years ago

Help me on this math question

Mathematics

2 answers:

Maksim231197 [3]3 years ago

8 0

The answer is evaluate

Korolek [52]3 years ago

3 0

To evaluate an algebraic expression, you have to substitute a number for each variable and perform the arithmetic operations. In the example above, the variable x is equal to 6 since 6 + 6 = 12. If we know the value of our variables, we can replace the variables with their values and then evaluate the expression.

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Given parallelogram MNOP, MA = x + 5, AO = y + 2, PA = 3x and AN = 2y

erma4kov [3.2K]

Answer:

The values of x and y are x = 6 and y = 9

Step-by-step explanation:

MNOP is a parallelogram its diagonal MO and PN intersected at point A

In any parallelogram diagonals:

Bisect each other
Meet each other at their mid-point

In parallelogram MNOP

∵ MO and NP are its diagonal

∵ MO intersect NP at point A

- Point A is the mid-point pf them

∴ MO and NP bisect each other

∴ MA = AO

∴ PA = AN

∵ MA = x + 5

∵ AO = y + 2

- Equate them

∴ x + 5 = y + 2 ⇒ (1)

∵ PA = 3x

∵ AN = 2y

- Equate them

∴ 2y = 3x

- Divide both sides by 2

∴ y = 1.5x ⇒ (2)

Now we have a system of equations to solve it

Substitute y in equation (1) by equation (2)

∴ x + 5 = 1.5x + 2

- Subtract 1.5x from both sides

∴ - 0.5x + 5 = 2

- Subtract 5 from both sides

∴ - 0.5x = -3

- Divide both sides by - 0.5

∴ x = 6

- Substitute the value of x in equation (2) to find y

∵ y = 1.5(6)

∴ y = 9

The values of x and y are x = 6 and y = 9

4 0

3 years ago

Polymer composite materials have gained popularity because they have high strength to weight ratios and are relatively easy and

Brums [2.3K]

Answer:

$t=\frac{51.6-48}{\frac{1.1}{\sqrt{10}}}=10.349$

$p_v =P(t_9>10.349)=1.34x10^{-6}$

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 reject the null hypothesis, and the the actual mean is significantly higher than 48 MPa at 5% of significance.

Step-by-step explanation:

1) Data given and notation

$\bar X=51.6$ represent the sample mean

$s=1.1$ represent the standard deviation for the sample

$n=10$ sample size

$\mu_o =48$ represent the value that we want to test

$\alpha=0.05$ 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 score is higher than 48, the system of hypothesis would be:

Null hypothesis: $\mu \geq 48$

Alternative hypothesis: $\mu > 48$

We don't know the population deviation, so for this case is better apply a t test to compare the actual mean to the reference value, and the statistic is given by:

$t=\frac{\bar X-\mu_o}{\frac{\sigma}{\sqrt{n}}}$ (1)

t-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:

$t=\frac{51.6-48}{\frac{1.1}{\sqrt{10}}}=10.349$

Calculate the P-value

First we find the degrees of freedom:

$df=n-1=10-1=9$

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

$p_v =P(t_9>10.349)=1.34x10^{-6}$

Conclusion

5 0

3 years ago

In ΔABC shown below, ∠BAC is congruent to ∠BCA: Triangle ABC, where angles A and C are congruent Given: Base ∠BAC and ∠ACB are c

Morgarella [4.7K]

1. Definition of bisector
2. ASA congruence theorem or ASA Postulate

6 0

3 years ago

Read 2 more answers

Patrick buys 12 bunches of bananas for $9 what will he pay for 8 bunches of bananas

larisa [96]

$12b.......9\$ \\ 8b.........x \\\\ x=\frac{8*9}{12}=\frac{72}{12} \\\\ \boxed{x=5\$}$

5 0

3 years ago

Put the fractions in order starting with the smallest to the largest

stiks02 [169]

Answer:

21/40, 17/20, 29/40, 3/4, 4/5

Step-by-step explanation:

21/40 = 10.5/20

29/40 = 14.5/20

17/20 = 13.5/20

3/4 = 15/20

4/5 = 16/20

7 0

3 years ago