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3 years ago

4x - 2y = -20 7x + 2y = -2

Mathematics

1 answer:

Brut [27]3 years ago

8 0

Answer:

(-2, 6)

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS
Equality Properties

Algebra I

Solving systems of equations using substitution/elimination
Solving systems of equations by graphing

Step-by-step explanation:

Step 1: Define systems

4x - 2y = -20

7x + 2y = -2

Step 2: Rewrite systems

4x - 2y = -20

Add 2y to both sides: 4x = 2y - 20
Divide 4 on both sides: x = 1/2y - 5

Step 3: Redefine systems

x = 1/2y - 5

7x + 2y = -2

Step 4: Solve for y

Substitution

Substitute in x: 7(1/2y - 5) + 2y = =-2
Distribute 7: 7/2y - 35 + 2y = -2
Combine like terms: 11/2y - 35 = -2
Add 35 to both sides: 11/2y = 33
Isolate y: y = 6

Step 5: Solve for x

Define original equation: 7x + 2y = -2
Substitute in y: 7x + 2(6) = -2
Multiply: 7x + 12 = -2
Subtract 12 on both sides: 7x = -14
Divide 7 on both sides: x = -2

Step 6: Graph systems

Check the system.

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3 years ago

An engineer is comparing voltages for two types of batteries (K and Q) using a sample of 37 type K batteries and a sample of 58

Olegator [25]

Answer:

Hypothesis Test states that we will accept null hypothesis.

Step-by-step explanation:

We are given that an engineer is comparing voltages for two types of batteries (K and Q).

where, $\mu_1$ = true mean voltage for type K batteries.

$\mu_2$ = true mean voltage for type Q batteries.

So, Null Hypothesis, $H_0$ : $\mu_1 = \mu_2$ {mean voltage for these two types of

batteries is same}

Alternate Hypothesis, $H_1$ : $\mu_1 \neq \mu_2$ {mean voltage for these two types of

batteries is different]

The test statistics we use here will be :

$\frac{(X_1bar-X_2bar) - (\mu_1 - \mu_2) }{s_p\sqrt{\frac{1}{n_1}+\frac{1}{n_2} } }$ follows $t_n__1 + n_2 -2$

where, $X_1bar$ = 8.54 and $X_2bar$ = 8.69

$s_1$ = 0.225 and $s_2$ = 0.725

$n_1$ = 37 and $n_2$ = 58

$s_p = \sqrt{\frac{(n_1-1)s_1^{2}+(n_2-1)s_2^{2} }{n_1+n_2-2} } = \sqrt{\frac{(37-1)0.225^{2}+(58-1)0.725^{2} }{37+58-2} }$ = 0.585 Here, we use t test statistics because we know nothing about population standard deviations.

Test statistics = $\frac{(8.54-8.69) - 0 }{0.585\sqrt{\frac{1}{37}+\frac{1}{58} } }$ follows $t_9_3$

= -1.219

At 0.1 or 10% level of significance t table gives a critical value between (-1.671,-1.658) to (1.671,1.658) at 93 degree of freedom. Since our test statistics is more than the critical table value of t as -1.219 > (-1.671,-1.658) so we have insufficient evidence to reject null hypothesis.

Therefore, we conclude that mean voltage for these two types of batteries is same.

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Answer:

Step-by-step explanation:

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3 years ago

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IRINA_888 [86]

Answer:

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Step-by-step explanation:

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2 years ago

When the sum of twice a number and 4 is tripled the result is 72?

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Hope This Helps You!
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3 years ago