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3 years ago

Is there a real number whose square is −1? a. Is there a real number x such that ? b. Does there exist such that x2 = −1?

Mathematics

1 answer:

Sauron [17]3 years ago

5 0

Answer:

a. $x^2=-1$

b.a real number x

Step-by-step explanation:

We are given that statement.

We have to rewrite the given statement using variable or variables.

Statement:Is there a real number whose square is -1.

a.Let x bet the real number

The square of real number x written as $x^2$

According to question

$x^2=-1$

Therefore,

Is there a real number x such that $x^2=-1$

b.Does there exist a real number x such that

$x^2=-1$

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Evaluate : A. <img src="https://tex.z-dn.net/?f=x%5E%7Bx%5E3%7D%3D3" id="TexFormula1" title="x^{x^3}=3" alt="x^{x^3}=3" alig

sdas [7]

Answer:

$x^{x^3} = 3$
log $x^{x^3}$ = log 3
x³ log x = log 3
3x³ log x = 3 log 3
x³ log x³ = log 3³
$x^3^{x^3}$ = 3³
x³ = 3
x = $3^{1/3}$

4ˣ + 6ˣ = 9ˣ
2²ˣ + 2ˣ3ˣ = 3²ˣ

Divide both sides by 2²ˣ

1 + (3/2)ˣ = (3/2)²ˣ

Substitute (3/2)ˣ = t

t² - t - 1 = 0

Solve for t:

t = (1 ± √5)/2

Positive root is considered as (3/2)ˣ can't be negative.

(3/2)ˣ = (1 + √5)/2
x = log [(1 + √5)/2] / log (3/2)
x = 1.18681439028

7 0

2 years ago

What is the answer to 701km-523km445m

mixas84 [53]

You convert it to meters first. So you get 701000m and 523445mYou subtract the values and get this: 177555

So your answer is 177555

Hope this helps :)

8 0

2 years ago

15% converted to a fraction then simplified to lowest terms

mojhsa [17]

Percent means parts out tof 100 so 15%=15/100
divide by 5/5
3/20=lowet terms

4 0

3 years ago

A study is done by a community group in two neighboring colleges to determine which one graduates students with more math classe

stealth61 [152]

Answer:

$t=\frac{(4-3.5)-0}{\sqrt{\frac{1.5^2}{11}+\frac{1^2}{9}}}}=0.890$

The p value for this case would be:

$p_v =P(t_{18}>0.890)=0.193$

The p value is higher than the significance level so then we can conclude that we can FAIL to reject the null hypothesis and then the true mean for group A is not significantly higher than the mean for B

Step-by-step explanation:

Information given

$\bar X_{1}=4$ represent the mean for sample A

$\bar X_{2}=3.5$ represent the mean for sample B

$s_{1}=1.5$ represent the sample standard deviation for A

$s_{2}=1$ represent the sample standard deviation for B

$n_{1}=11$ sample size for the group A

$n_{2}=9$ sample size for the group B

$\alpha=0.1$ Significance level provided

t would represent the statistic

Hypothesis to test

We want to verify if the student who graduates from college A has taken more math classes, on the average, the system of hypothesis would be:

Null hypothesis: $\mu_{1}-\mu_{2} \leq 0$

Alternative hypothesis: $\mu_{1} - \mu_{2}> 0$

The statistic is given by:

$t=\frac{(\bar X_{1}-\bar X_{2})-\Delta}{\sqrt{\frac{s^2_{1}}{n_{1}}+\frac{s^2_{2}}{n_{2}}}}$ (1)

And the degrees of freedom are given by $df=n_1 +n_2 -2=11+9-2=18$

Replacing we got:

$t=\frac{(4-3.5)-0}{\sqrt{\frac{1.5^2}{11}+\frac{1^2}{9}}}}=0.890$

The p value for this case would be:

$p_v =P(t_{18}>0.890)=0.193$

5 0

3 years ago

Apply the distributive property to factor out the greatest common factor of all three terms 14x+21y+7z=

Elenna [48]

Answer:

7(2x+3y+z)

Step-by-step explanation:

14x+21y+7z

Factor out 7

7*2x+ 7*3y+7*z

7(2x+3y+z)

8 0

3 years ago