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Slav-nsk [51]
3 years ago
11

Simon and Greg shared pencils in the ratio 7:5. If Simon gives away 30 pencils and Greg gets 30 more pencils, they will have the

same number of pencils. How many did each of them have in the beginning?
Mathematics
1 answer:
Nutka1998 [239]3 years ago
8 0
7/5=s/g multiply both sides by g

7g/5=s  multiply both sides by 5/7

g=5s/7

We are then told that:

g+30=s-30  subtract 30 from both sides

g=s-60, and from earlier g=5s/7, and g=g so we can say:

s-60=5s/7  multiply both sides by 7

7s-420=5s  subtract 5s from both sides

2s-420=0  add 420 to both sides

2s=420 divide both sides by 2

s=210, and since g=s-60

g=150

So Simon had 210 pencils and Greg had 150 pencils.

Check..

s:g=210:150=7:5

and

s-30=g+30

210-30=150+30

180=180
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The diameters of bolts produced in a machine shop are normally distributed with a mean of 5.71 millimeters and a standard deviat
Harlamova29_29 [7]

Answer:

The bolts with diameter less than 5.57 millimeters and with diameter greater than 5.85 millimeters should be rejected.

Step-by-step explanation:

We have been given that the diameters of bolts produced in a machine shop are normally distributed with a mean of 5.71 millimeters and a standard deviation of 0.08 millimeters.    

Let us find the sample score that corresponds to z-score of bottom 4%.  

From normal distribution table we got z-score corresponding to bottom 4% is -1.75 and z-score corresponding to top 4% or data above 96% is 1.75.

Upon substituting these values in z-score formula we will get our sample scores (x) as:

z=\frac{x-\mu}{\sigma}

-1.75=\frac{x-5.71}{0.08}

-1.75*0.08=x-5.71

-0.14=x-5.71

-0.14+5.71=x-5.71+5.71

5.57=x

Therefore, the bolts with diameters less than 5.57 millimeters should be rejected.

Now let us find sample score corresponding to z-score of 1.75 as upper limit.

1.75=\frac{x-5.71}{0.08}

1.75*0.08=x-5.71

0.14=x-5.71

0.14+5.71=x-5.71+5.71

5.85=x  

Therefore, the bolts with diameters greater than 5.85 millimeters should be rejected.

7 0
3 years ago
Polk elementary school has three classes for each grade level kindergarten through fifth grade if there is an average of 27 stud
olga2289 [7]
So there are 6 different grade levels with 3 classes in each. So 6*3 = 18 classes total. 

<span>If there are approximately 27 children in each class, than 27*18 = ? your answer.</span>
4 0
3 years ago
Which expression is equal to 45 x 4-7: 4-27 4° 4-4 (45) (4-2) 45 : 4-9​
horsena [70]

Answer: 173: -432° - 16196: -5

Step-by-step explanation: Simplify your expression and there is your answer.  

4 0
3 years ago
10) The temperature recorded at 12 noon was 15°C above zero. If it decreases at the rateof 3°C per hour until midnight, at what
aalyn [17]

Answer:

at 8 pm the temperature will be -9 degrees. and at midnight the temperature will be negitive twenty one(-21) degrees

Step-by-step explanation:

the start time is 12 pm and finish is 12 am and every hour your going to subtract 3 from the given degree so 15-3= 12 , 12-3=9 ect.

6 0
3 years ago
Find a nonzero vector orthogonal to the plane through the points: ????=(0,0,1), ????=(−2,3,4), ????=(−2,2,0).
ser-zykov [4K]

Answer:

The nonzero vector orthogonal to the plane is <-9,-8,2>.

Step-by-step explanation:

Consider the given points are P=(0,0,1), Q=(−2,3,4), R=(−2,2,0).

\overrightarrow {PQ}==

\overrightarrow {PR}==

The nonzero vector orthogonal to the plane through the points P,Q, and R is

\overrightarrow n=\overrightarrow {PQ}\times \overrightarrow {PR}

\overrightarrow n=\det \begin{pmatrix}i&j&k\\ \:\:\:\:\:-2&3&3\\ \:\:\:\:\:-2&2&-1\end{pmatrix}

Expand along row 1.

\overrightarrow n=i\det \begin{pmatrix}3&3\\ 2&-1\end{pmatrix}-j\det \begin{pmatrix}-2&3\\ -2&-1\end{pmatrix}+k\det \begin{pmatrix}-2&3\\ -2&2\end{pmatrix}

\overrightarrow n=i(-9)-j(8)+k(2)

\overrightarrow n=-9i-8j+2k

\overrightarrow n=

Therefore, the nonzero vector orthogonal to the plane is <-9,-8,2>.

8 0
3 years ago
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