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3 years ago

Ryan records four numbers from his science homework using scientific notation.

Mathematics

1 answer:

lisabon 2012 [21]3 years ago

8 0

$\large \mathfrak{Solution : }$

The incorrect one is 35 × 10⁵

it can be written as :

$3.5 \times 10 {}^{6}$

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Complete the proof of the identity by choosing the Rule that justifies each step.

Sever21 [200]

<h3>Answer :-</h3>

( 1 - cos²x ) secx

=> sin²x . secx

Here the rule ( rule 1 ) is the first trigonometric identity [ sin²A + cos²A = 1 ] by simplifying we have , [ 1 - cos²A = sin² ] . So here we substituted 1 - cos²x = sin²x .

=> sin²x [ 1/cosx ]

Here the rule ( rule 2 ) is secx = 1/cosx . So here we substituted secx = 1/cosx .

=> sinx [ sinx/cosx ]

Here the rule ( rule 3 ) is sin²x can be written as sinx . sinx , so we get sinx . sinx [ 1/cosx ] next by simplifying , sinx [ sinx/cosx ].

=> sinx tanx

Here the rule ( rule 4 ) is , in the above we got sinx/cosx and here we know that , sinx/cosx = tanx . So we have tan x .

4 0

3 years ago

City health officials will conduct a two-sample t-test for a difference in means to investigate whether

Anvisha [2.4K]

Answer:

The calculated value t = 2.366 > 2.0301 at 0.05 level of significance

The null hypothesis is rejected

There is a difference between the means

Step-by-step explanation:

Step(i):-

Given that the first sample size 'n₁' = 22

Given that the mean of the first sample x₁⁻ = 120

Given that the standard deviation of the sample (s₁) = 20

Given that the mean of the second sample x₂⁻ = 100

Given that the standard deviation of the second sample (S₂) = 30

Step(ii):-

T-test statistic

$t = \frac{x^{-} _{1} -x^{-} _{2} }{\sqrt{S^{2} (\frac{1}{n_{1} }+\frac{1}{n_{2} } ) } }$

where

$S^{2} = \frac{n_{1} S_{1} ^{2}+n_{2} S_{2} ^{2} }{n_{1} +n_{2}-2 }$

$S^{2} = \frac{22( 20)^{2}+ 15(30) ^{2} }{22 +15-2 }$

S² = 637.1428

S = √637.1428 = 25.24168

The standard deviation of the sample 'S' = 25.24168

Step(iii):-

Null Hypothesis:H₀:

There is no difference between the means

Alternative Hypothesis:H₁:

There is a difference between the means

T-test statistic

$t = \frac{x^{-} _{1} -x^{-} _{2} }{\sqrt{S^{2} (\frac{1}{n_{1} }+\frac{1}{n_{2} } ) } }$

$t = \frac{ 120 -100 }{\sqrt{637.14 (\frac{1}{22 }+\frac{1}{15 } ) } }$

t = 2.366

Degrees of freedom

γ = n₁+n₂ -2 = 22+15-2 = 35

t₀.₀₅ = 2.0301

The calculated value t = 2.366 > 2.0301 at 0.05 level of significance

The null hypothesis is rejected

There is a difference between the means

3 0

3 years ago

Read 2 more answers

What's larger 0.75 or 1/2

Brilliant_brown [7]

Okay let's see.. 0.750
1.200
As we see 1 is bigger than 0.So that means 1/2 is bigger.Hope this helps! (;

8 0

3 years ago

Read 2 more answers

Which of the following expression simplifies to 4/15?

uysha [10]

B -2/5+2/3

I'm good with fractions :D

3 0

4 years ago

Solve: z/2 + 26 > 17.5

Sophie [7]

Answer: Z> -17

z/2+26=17.5

We move all terms containing z to the left and all other terms to the right.

+ 0.5z=+17.5-26

We simplify left and right side of the equation.

+ 0.5z=-8.5

We divide both sides of the equation by 0.5 to get z.

z=-17

7 0

3 years ago