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3 years ago

Use the substitution method to solve the system of equations.Choose the correct ordered pair.

Mathematics

1 answer:

Nat2105 [25]3 years ago

5 0

Hope this helps!
Source: Myself, I am a Senior in High school in Pre-calculus

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Solve with solution...no spam answers pls

Agata [3.3K]

Let's analyze Hannah's work, step-by-step, to see if she made any mistakes.

In Step 1, Hannah wrote $\dfrac{d}{dx} (-3+8x)$ as the sum of two separate derivatives $\dfrac{d}{dx}(-3)+ \dfrac{d}{dx} (8x)$ using the sum rule.

This step is perfectly fine.

In Step 2, $\dfrac{d}{dx}(8x)$ was kept as it is, and $\dfrac{d}{dx}(-3)$ was rewritten as $0$ using the constant rule.Indeed, according to the constant rule, the derivative of a constant number is equal to zero.

This step is perfectly fine.

In Step 3, $\dfrac{d}{dx} (8x)$ was rewritten as $\dfrac{d}{dx}(8) \dfrac{d}{dx}(x)$ supposedly using the constant multiple rule.

The problem is that according to the constant multiple rule, $\dfrac{d}{dx}(8x)
$ should be rewritten as $8 \dfrac{d}{dx}(x)$ and not as $\dfrac{d}{dx}(8)\dfrac{d}{dx}(x)$ .

Therefore, Hannah made a mistake in this step.

6 0

3 years ago

Read 2 more answers

What are the excluded values of x for x+4/-3x2+12x+36

grin007 [14]

Answer:

x = - 2, x = 6

Step-by-step explanation:

The denominator of the rational expression cannot be zero as this would make the expression undefined.

Equating the denominator to zero and solving gives the values that x cannot be.

Solve

- 3x² + 12x + 36 = 0 ( divide through by - 3 )

x² - 4x - 12 = 0 ← in standard form

(x - 6)(x + 2) = 0 ← in factored form

Equate each factor to zero and solve for x

x - 6 = 0 ⇒ x = 6

x + 2 = 0 ⇒ x = - 2

x = - 2 and x = 6 ← are the excluded values

5 0

3 years ago

Identify the null hypothesis, alternative hypothesis, test statistic, P-value, conclusion about the null hypothesis, and final c

Black_prince [1.1K]

Answer:

The test statistic value Z = 4.64 > 1.96 at 0.05 level of significance

Null hypothesis is rejected

Alternative hypothesis is accepted

Test the claim that the proportion of all children in the town who suffer not from asthma is 11%

Step-by-step explanation:

Step(i):-

Given sample size 'n' = 167

Given data In a sample of 167 children selected randomly from one town, it is found that 37 of them suffer from asthma.

Sample proportion

$p^{-} = \frac{x}{n} = \frac{37}{167} = 0.2215$

Given Population proportion 'P' = 11% = 0.11

Step(ii) :-

Null Hypothesis : H₀ : p = 11

Alternative Hypothesis H₁: p≠11

Test statistic

$Z = \frac{p^{-} -P }{\sqrt{\frac{P Q}{n} } }$

$Z = \frac{0.2215 -0.11 }{\sqrt{\frac{0.11 X 0.89}{167} } }$

Z = 4.64

step(iii)

Critical value Z = 1.96

The calculated value Z = 4.64 > 1.96 at 0.05 level of significance

Null hypothesis is rejected

Alternative hypothesis is accepted

Conclusion:-

Test the claim that the proportion of all children in the town who suffer not from asthma is 11%

4 0

3 years ago

The new school and my parents ordered me for my birthday cost $140.00 They were not happy that they had to pay 5% shipping fee w

ExtremeBDS [4]

5% of 140 is 7 so the answer is $147

3 0

2 years ago

A news site offers a subscription that costs $28.50 for 6 months. What is the unit price per month.

crimeas [40]

Divide the total cost by the amount of months
28.5 divided by 6=4.75

7 0

3 years ago