What is the next step in using the distributive property to solve this equation?

The following table lists the masses, in grams, of the nine planets (including dwarf planet Pluto). Use the data to choose the c

Marrrta [24]

The ratio between the masses of Jupiter and Venus is

$\dfrac{1.989\cdot 10^{30}}{4.869\cdot 10^{27}}$

We can separate the coefficient and the powers of ten:

$\dfrac{1.989\cdot 10^{30}}{4.869\cdot 10^{27}}=\dfrac{1.989}{4.869}\cdot \dfrac{10^{30}}{10^{27}}$

Use the exponent rule

$\dfrac{a^b}{a^c}=a^{b-c}$

to simplify the powers of 10:

$\dfrac{10^{30}}{10^{27}}=10^3$

So, the ratio is

$\dfrac{1.989}{4.869}\cdot 10^3\approx 0.4\cdot 10^3=400$

So, Jupiter has a mass that is approximately 400 times greater than Venus's.

4 0

3 years ago

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A recipe submitted to a magazine by one of its subscribers’ states that the mean baking time for a cheesecake is 55 minutes. A t

EastWind [94]

Answer:

$t=\frac{59.4-55}{\frac{3.239}{\sqrt{10}}}=4.296$

The degrees of freedom are given by:

$df=n-1=10-1=9$

The p value for this case is given by:

$p_v =P(t_{(9)}>4.296)=0.001$

And for this case the p value is lower than the significance level so we have enough evidence to reject the null hypothesis and then we can conclude that true mean is higher than 55.

Step-by-step explanation:

Information given

We have the following data: 54 55 58 59 59 60 61 61 62 65

The sample mean and deviation can be calculated with the following formulas:

$\bar X = \frac{\sum_{i=1}^n X_i}{n}$

$s=\sqrt{\frac{\sum_{i=1}^n (X-i -\bar x)^2}{n-1}}$

$\bar X=59.4$ represent the sample mean

$s=3.239$ represent the sample standard deviation

$n=10$ sample size

$\alpha=0.05$ represent the significance level

t would represent the statistic

$p_v$ represent the p value

System of hypothesis

We want to test if the true mean is higher than 55, the system of hypothesis would be:

Null hypothesis: $\mu \leq 55$

Alternative hypothesis: $\mu > 55$

Replacing the info given we got:

$t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}$ (1)

And replacing the info given we got:

$t=\frac{59.4-55}{\frac{3.239}{\sqrt{10}}}=4.296$

The degrees of freedom are given by:

$df=n-1=10-1=9$

The p value for this case is given by:

$p_v =P(t_{(9)}>4.296)=0.001$

And for this case the p value is lower than the significance level so we have enough evidence to reject the null hypothesis and then we can conclude that true mean is higher than 55

8 0

4 years ago

Adam uses coconut milk for the dessert. The coconut milk is in a can but he doesn’t know how much the can holds. The can is 12 c

BartSMP [9]

Given:
Diameter = 8 cm
Height = 12 cm
Value of pi = 3

radius is 1/2 of the diameter. r = 8cm/2 = 4cm
Volume = π r² h
V = 3 * (4cm)² * 12 cm
V = 3 * 16cm² * 12 cm
V = 576cm³

Volume of the can is 576cm³. It is also the amount of milk inside the can.COMMENTS REPORT

4 0

3 years ago

Which sequences are geometric? Select 3 options.

Andrei [34K]

A,B,D are your answers :)

9 1

3 years ago

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Number 3 pls 2 day of CMM pls help

STALIN [3.7K]

Answer:MODEL SOFTWARE ACCURACY

Brown & Sharpe 12.22.10 PC-DMIS 2.5+3.0L/1000 microns

Brown & Sharpe 7.10.7 PC-DMIS 1.9+4.0L/1000 microns

† Factory machine specification for accuracy: L = Length in mm of the feature to be checked Download CMM Linecard

Step-by-step explanation:

6 0

4 years ago