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3 years ago

Find the greatest common factor of 30 and 105 a. 3 b. 15 c. 30 d. 5

Mathematics

1 answer:

Korvikt [17]3 years ago

5 0

Answer:

Greatest common factor is 15.

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The following data comparing wait times at two rides at Disney are listed below: Position Pirates Splash Mountain Sample Size 32

myrzilka [38]

Answer:

a) $(14.68 -18.77) - 2.39 \sqrt{\frac{11.87^2}{32}+\frac{16.79^2}{30}} =-12.968$

$(14.68 -18.77) + 2.39 \sqrt{\frac{11.87^2}{32}+\frac{16.79^2}{30}} =4.788$

b) $t=\frac{14.68-18.77}{\sqrt{\frac{11.87^2}{32}+\frac{16.79^2}{30}}}}=-1.10$

Step-by-step explanation:

Data given and notation

$\bar X_{A}=14.68$ represent the mean for Pirates

$\bar X_{B}=18.77$ represent the mean for Splash Mountain

$s_{A}=11.87$ represent the sample standard deviation for the sample Pirates

$s_{B}=16.79$ represent the sample standard deviation for the sample Slpash Mountain

$n_{A}=32$ sample size selected for Pirates

$n_{B}=30$ sample size selected for Splash Mountain

$\alpha=0.02$ represent the significance level for the hypothesis test.

t would represent the statistic (variable of interest)

$p_v$ represent the p value for the test (variable of interest)

Part a

The confidence interval would be given by:

$(\bar X_A -\bar X_B) \pm t_{\alpha/2} \sqrt{\frac{s^2_{A}}{n_{A}}+\frac{s^2_{B}}{n_{B}}}$

The degrees of freedom are given by:

$df = n_A +n_B -2 = 32+30-2 = 60$

Since we want 98% of confidence the significance level is $\alpha =1-0.98 =0.02$ and $\alpha/2 =0.01$ , we can find in the t distribution with df =60 a critical value that accumulates 0.01 of the area on each tail and we got:

$t_{\alpha/2}= 2.39$

And replacing we got for the confidence interval:

$(14.68 -18.77) - 2.39 \sqrt{\frac{11.87^2}{32}+\frac{16.79^2}{30}} =-12.968$

$(14.68 -18.77) + 2.39 \sqrt{\frac{11.87^2}{32}+\frac{16.79^2}{30}} =4.788$

Part b

State the null and alternative hypotheses.

We need to conduct a hypothesis in order to check if the means are equal, the system of hypothesis would be:

Null hypothesis: $\mu_{A} = \mu_{B}$

Alternative hypothesis: $\mu_{A} \neq \mu_{B}$

the statistic is given by:

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

t-test: "Is used to compare group means. Is one of the most common tests and is used to determine whether the means of two groups are equal to each other".

Calculate the statistic

We can replace in formula (1) the info given like this:

$t=\frac{14.68-18.77}{\sqrt{\frac{11.87^2}{32}+\frac{16.79^2}{30}}}}=-1.10$

6 0

3 years ago

John wants to make cookies. To make cookies, he need 2 over 3 of a cup of flour per batch of cookies. If John has 4 cups of flou

Mnenie [13.5K]

$\dfrac{2}{3} \text { cups = } 1 \text { batch}$

----------------------------------------------
Find 1 cup :
----------------------------------------------

$1 \text { cup = } 1 \div \dfrac{2}{3} \text { batch}$

$1 \text { cup = } 1 \times \dfrac{3}{2} \text { batch}$

$1 \text { cup = } \dfrac{3}{2} \text { batch}$

----------------------------------------------
Find 4 cups :
----------------------------------------------
$4 \text { cups = } \dfrac{3}{2} \times 4 \text { batch}$

$4 \text { cups = } \6 \text { batches}$

--------------------------------------------------------------------------------------------
Answer: John can make 6 batches with 4 cups of flour.
--------------------------------------------------------------------------------------------

6 0

3 years ago

Given z^3 = 3 + square root 3i which letter represents z

Marianna [84]

The expression that represents the value of z is $\sqrt[3]{3 + i\sqrt 3 }$

<h3>What are complex numbers?</h3>

Complex numbers are numbers that have real and imaginary parts

A complex number (n) is represented as:

$n = a + bi$

From the above expression, we have:

a represents the real part
bi represents the imaginary part

Given that:

$z^3 = 3 + \sqrt 3 i$

Rewrite the above expression as:

$z^3 = 3 + i\sqrt 3$

Take the cube roots of both sides

$z = \sqrt[3]{3 + i\sqrt 3 }$

The letters are not given.

Hence, the expression that represents the value of z is $\sqrt[3]{3 + i\sqrt 3 }$

Read more about complex numbers at:

brainly.com/question/11089283

8 0

2 years ago

Please help me I’ll mark brainiest

Lubov Fominskaja [6]

Answer:

which number

every of them?

8 0

3 years ago

Eloise started to solve a radical equation in this way: Square root of negative 2x plus 1 − 3 = x Square root of negative 2x plu

andreyandreev [35.5K]

Here I copy the steps and indicate where the error is.

Square root of negative 2x plus 1 − 3 = x=> this is the starting equation

√[ - 2x + 1] - 3 = x

Square root of negative 2x plus 1 − 3 + 3 = x + 3 in this step she added 3 to each side, which is fine

Square root of negative 2x plus 1 = x + 3 she made the addtions => fine

Square root of negative 2x plus 1 − 1 = x + 3 – 1 due to plus 1 in inside the square root, this step will not help

Square root of negative 2 x = x + 2 wrong! she cannot simplify - 1 that is out of the square root with +1 that is inside the square root

Then, from here on all is wrong, but she made other additional mistakes.

(Square root of negative 2 x)2 = (x − 4)2 −2x the right side should be (x+2)^2 which is x^2 + 4x +4 not (x-4)^2 - 2x

Later she made a mistake changing the sign of -8x to +8x

Those are the mistakes. Finally, the global error is that she should verify whether the found values satisfied the original equation.

3 0

3 years ago

Read 2 more answers