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2 years ago

Solve the simultaneous equation 5x-4y=10. X+2y=9

Mathematics

1 answer:

professor190 [17]2 years ago

4 0

Step-by-step explanation:

<h2>using ELIMINATION method</h2>

10x-8y=20

4x+8y=36

14x=56

x=56/14

x=4

10(4)-8y=20

40-8y=20

-8y=20-40

-8y=-20

y=-20/-8

y=2.5

<h2>MARK ME BRAINLIEST PLS!!</h2>

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REY [17]

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A. 3

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Solve for r.

4r - 6 = 30
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D. 9
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Solve for u.

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3 years ago

The sum of three consecutive natural numbers is 1251 find the numbers

valentinak56 [21]

Numbers are 416, 417 and 418

<u>Step-by-step explanation:</u>

Step 1:

Let the numbers be x, x + 1 and x + 2. Given that their sum is 1251.

⇒ x + x + 1 + x + 2 = 1251

⇒ 3x + 3 = 1251

⇒ 3x = 1248

⇒ x = 416

Step 2:

Find the other numbers.

⇒ x + 1 = 417 and x + 2 = 418

8 0

3 years ago

6. Santiago Diaz Granados played an arcade game that cost 25 tokens per game. In six games, Santiago won 0 tokens, 10 tokens, 50

Pavel [41]

-- To play the six games, <span>Santiago Diaz Granados spent

(6 x 25) = 150 tokens.

-- As a result of his skill, experience, talent, steady hand, nerves
of steel, superior hand-eye coordination, and superb reflexes, </span><span>
Santiago Diaz Granados won</span>

(0 + 10 + 50 + 0 + 5 + 10) = 75 tokens.

-- At the end of the 6th game, <span>Santiago Diaz Granados was behind
the curve.
After spending 150 tokens and winning 75 tokens, </span><span>Santiago Diaz Granados
was down by (150 - 75) = 75 tokens since he arrived at the arcade.
Any true friend could look at the choices, could see that choice-B is
the correct one, and could advise </span><span>Santiago Diaz Granados to cash in
whatever he had left, accept his losses, return to his home, and live
to fight another day.

Viva </span><span>Santiago Diaz Granados ... </span><span>un verdadero héroe de su pueblo. Viva !</span>

3 0

3 years ago

Help. rhombus JKLM is shown below. Find m<KLM

pantera1 [17]

Answer: It's 76 (sorry, I answered it wrong!)

Step-by-step explanation:

In a rhombus, the diagonals split the angles into two equal parts. If one part of the angle is 38, then the other part is 38. Add up both of them, and you'll get the entirety of angle L, which is 76.

6 0

3 years ago

23. A certain type of gasoline is supposed to have a mean octane rating of at least 90. Suppose measurements are taken on of 5 r

Nostrana [21]

Answer:

a) $p_v =P(Z$

b) Since $p_v$ we can reject the null hypothesis at the significance level given. So based on this we can commit type of Error I.

Because Type I error " is the rejection of a true null hypothesis".

c) $P(\bar X >90)=1-P(Z$

$1-P(Z$

d) For this case we need a z score that accumulates 0.02 of the area on the right tail and 0.98 on the left tail and this value is z=2.054

And we can use this formula:

$2.054=\frac{90-89}{\frac{0.8}{\sqrt{n}}}$

And if we solve for n we got:

$n = (\frac{2.054 *0.8}{1})^2=2.7 \approx 3$

Step-by-step explanation:

Previous concepts and data given

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

We can calculate the sample mean and deviation with the following formulas:

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

$s=\sqrt{\sum_{i=1}^n (X_i -\bar X)^2}{n-1}$

$\bar X=88.96$ represent the sample mean

$s=1.011$ represent the sample standard deviation

n=5 represent the sample selected

$\alpha$ significance level

State the null and alternative hypotheses.

We need to conduct a hypothesis in order to check if the mean is less than 90, the system of hypothesis would be:

Null hypothesis: $\mu \geq 90$

Alternative hypothesis: $\mu < 90$

If we analyze the size for the sample is < 30 and we don't know the population deviation so is better apply a t 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:

$z=\frac{88.96-90}{\frac{0.8}{\sqrt{5}}}=-2.907$

Part a

P-value

First we need to calculate the degrees of freedom given by:

$df=n-1=5-1 = 4$

Then since is a left tailed test the p value would be:

$p_v =P(Z$

Part b

Since $p_v$ we can reject the null hypothesis at the significance level given. So based on this we can commit type of Error I.

Because Type I error " is the rejection of a true null hypothesis".

Part c

We want this probability:

$P(\bar X$

The best way to solve this problem is using the normal standard distribution and the z score given by:

$z=\frac{x-\mu}{\frac{\sigma}{\sqrt{n}}}$

If we apply this formula to our probability we got this:

$P(\bar X >90)=1-P(Z$

$1-P(Z$

Part d

For this case we need a z score that accumulates 0.02 of the area on the right tail and 0.98 on the left tail and this value is z=2.054

And we can use this formula:

$2.054=\frac{90-89}{\frac{0.8}{\sqrt{n}}}$

And if we solve for n we got:

$n = (\frac{2.054 *0.8}{1})^2=2.7 \approx 3$

7 0

3 years ago