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ella [17]
2 years ago
10

Rob is making a scale model of the Solar System on the school field. He wants the distance from the Sun to Jupiter to be 8 metre

s on his scale model. The real distance from the Sun to Jupiter is 7.8 × 10 8 kilometres. Find the scale of the model. Give your answer in the form 1 : n , where n is written in standard form.
Mathematics
1 answer:
ANEK [815]2 years ago
3 0

Answer:

1 : 9.75 * 10⁷

Step-by-step explanation:

To find n, we have to divide the real distance by the scale distance. This is 7.8 * 10⁸ / 8 = 0.975 * 10⁸ = 9.75 * 10⁷ which means that the ratio is 1 : 9.75 * 10⁷.

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Hilda adds 5 to a number, then multiplies the sum by negative 2. The result is 6. Write an equation to find the number, x.
adell [148]
The equation would be x+5*-2=6.

The result of that equation would be x=16
7 0
2 years ago
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Charlotte is redecorating the master bedroom in her house. She has already purchased a new bedroom set and also plans to paint t
jasenka [17]

Answer:

a. 30%

b. $893.59

c.

\frac{(351.10-x)}{893.59}\times 100\%

Step-by-step explanation:

a. Given that the carpet costs $427.35, the labor costs $212.52 and other flooring supplies costs $75.

#To get the  percent of the flooring bill that will go towards the cost of labor:

\%  labor\ cost=\frac{labor \ cost}{Total \ flooring \ cost}\times 100\%\\\\=\frac{212.52}{427.35+212.52+75}\times 100\%\\\\=\frac{212.52}{714.87}\times 100\%\\\\=29.73\%\approx30\%

Hence, labor costs 30% of the total flooring costs.

b.The total flooring costs is :

F_c=212.52+427.35+75\\\\=714.87

Given that she spends 25% more on furniture than on flooring, we multiply the flooring cost by 125% to get the furniture costs:

Furniture \ Cost= Flooring \ C\ost \times 125%\\\\=714.87\times 1.25\\\\=893.59

Hence, she spends $893.59 on furniture.

c.To get what percentage of  furniture cost was the night stand.

-Given the total furniture cost is $893.59:

Let x be the cost of the dresser and y the cost of the nightstand;

x+y=Furniture\  cost -Bed \ cost\\\\x+y=893.59-558.49=351.1\\\\y=351.1-x

The percentage is then calculated as:

\% cost \ of \ nightstand=\frac{cost \ of \ nighstand}{Furniture \ Cost}\times 100\%\\\\=\frac{351.10-x}{893.59}\times 100\%\\\\=\frac{(351.10-x)}{893.59}\times 100\%

Hnece the percentage cost of the night stand is \frac{(351.10-x)}{893.59}\times 100\%

7 0
2 years ago
What is the domain of the given function? <br> {(3,-2), (6, 1), (-1,4), (5,9), (-4,0)}
grandymaker [24]

Answer:

D = { -4,-1,3,5,6}

Step-by-step explanation:

The domain is the x values  or the inputs

D = { 3,6,-1,5,-4}

We normally put them in order from smallest to largest

D = { -4,-1,3,5,6}

4 0
2 years ago
During April of 2013, Gallup randomly surveyed 500 adults in the US, and 47% said that they were happy, and without a lot of str
Brilliant_brown [7]

Answer:

number of successes

                 k  =  235

number of failure

                 y  = 265

The   criteria are met    

A

    The sample proportion is  \r p  =  0.47

B

    E =4.4 \%

C

What this mean is that for N number of times the survey is carried out that the which sample proportion obtain will differ from  the true population proportion will not  more than 4.4%

Ci  

   r =  0.514 = 51.4 \%

 v =  0.426 =  42.6 \%

D

   This 95% confidence interval  mean that the the chance of the true    population proportion of those that are happy to be exist within the upper   and the lower limit  is  95%

E

  Given that 50% of the population proportion  lie with the 95% confidence interval  the it correct to say that it is reasonably likely that a majority of U.S. adults were happy at that time

F

 Yes our result would support the claim because

            \frac{1}{3 } \ of  N    < \frac{1}{2}  (50\%) \ of \  N  , \ Where\ N \ is \ the \  population\ size

Step-by-step explanation:

From the question we are told that

     The sample size is  n  = 500

     The sample proportion is  \r p  =  0.47

 

Generally the number of successes is mathematical represented as

             k  =  n  *  \r p

substituting values

             k  =  500 * 0.47

            k  =  235

Generally the number of failure  is mathematical represented as

           y  =  n  *  (1 -\r p )

substituting values

           y  =  500  *  (1 - 0.47  )

           y  = 265

for approximate normality for a confidence interval  criteria to be satisfied

          np > 5  \ and  \ n(1- p ) \ >5

Given that the above is true for this survey then we can say that the criteria are met

  Given that the confidence level is  95%  then the level of confidence is mathematically evaluated as

                       \alpha  = 100 - 95

                        \alpha  = 5 \%

                        \alpha  =0.05

Next we obtain the critical value of  \frac{\alpha }{2} from the normal distribution table, the value is

                 Z_{\frac{ \alpha }{2} } =  1.96

Generally the margin of error is mathematically represented as  

                E =  Z_{\frac{\alpha }{2} } *  \sqrt{ \frac{\r p (1- \r p}{n} }

substituting values

                 E =  1.96 *  \sqrt{ \frac{0.47 (1- 0.47}{500} }

                 E = 0.044

=>               E =4.4 \%

What this mean is that for N number of times the survey is carried out that the proportion obtain will differ from  the true population proportion of those that are happy by more than 4.4%

The 95% confidence interval is mathematically represented as

          \r p  - E <  p  <  \r p  + E

substituting values

        0.47 -  0.044 <  p  < 0.47 +  0.044

         0.426 <  p  < 0.514

The upper limit of the 95% confidence interval is  r =  0.514 = 51.4 \%

The lower limit of the   95% confidence interval is  v =  0.426 =  42.6 \%

This 95% confidence interval  mean that the the chance of the true population proportion of those that are happy to be exist within the upper and the lower limit  is  95%

Given that 50% of the population proportion  lie with the 95% confidence interval  the it correct to say that it is reasonably likely that a majority of U.S. adults were happy at that time

Yes our result would support the claim because

            \frac{1}{3 }  < \frac{1}{2}  (50\%)

 

3 0
2 years ago
Sheri’s cab fare was $32, with a 20% gratuity and no taxes. Sheri wrote a check to the cab driver for $40.
stira [4]

Yes, $40 is a reasonable amount to pay for the cab fare.

<em><u>Explanation</u></em>

Sheri’s cab fare was $32 and the percentage of gratuity is 20%

So, the amount of gratuity will be: \$32* 20\% = \$32*0.20= \$6.40

Thus, <u>the fare of the cab including the gratuity</u> will be:  \$32+\$6.40 = \$38.40

As Sheri wrote a check to the cab driver for $40 , it means she paying ($40 - $38.40) or <u>$1.60 more to the cab driver</u>. So, the $40 check is a reasonable amount to pay for the cab fare.

5 0
2 years ago
Read 3 more answers
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