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ANTONII [103]
3 years ago
11

The number of charter schools is 4 less than twice the number of alternative schools and there are 48 charter schools how many a

lternative schools are in the country
Mathematics
1 answer:
jarptica [38.1K]3 years ago
7 0
Let x = the number of alternative schools.

Therefore, 2x - 4 = 48.
                  2x -4 +4 = 48 + 4
                  2x = 52
                    x = 26

Therefore, there are 26 alternative schools(You could check this answer by substituting x=26 into the equation above.).
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Quadratic Equation Word Problem
Crazy boy [7]
------------------------------------------------------
Define x :
------------------------------------------------------
Let the width be x.

------------------------------------------------------
Find Area of the walkway :
------------------------------------------------------
Area = 30x + 30x + 20x + 20x + 4x²       
Area = 100x + 4x²

------------------------------------------------------
Find cost of the walkway in term of x:
------------------------------------------------------
1m² = $10
100x + 4x² = 10(4x² + 100x)
(100x + 4x²)m = $(40x² + 1000x)

------------------------------------------------------
Find Width of the walkway :
------------------------------------------------------
The budget is $6000

40x² + 1000x = 6000
40x² + 1000x - 6000 = 0
x² + 25x -150 = 0              //Divide by 40 through
(x - 5)(x + 30) = 0             //Factorise
x = 5 or x = -30 (Rejected, width cannot be negative)

------------------------------------------------------
Answer: The width can be 5m wide.
------------------------------------------------------

5 0
3 years ago
Historically, these bolts have an average thickness of 10.1 mm. A recent random sample of 10 bolts yielded these thicknesses:
Akimi4 [234]

Answer:

a) Sample mean = 9.99

Sample standard deviation = 0.3348

b) -1.0389

c) 0.1631

Step-by-step explanation:

We are given the following in the question:

9.7, 9.9, 10.3, 10.1, 10.5, 9.4, 9.9, 10.1, 9.7, 10.3

a) sample mean and standard deviation

Formula:

\text{Standard Deviation} = \sqrt{\displaystyle\frac{\sum (x_i -\bar{x})^2}{n-1}}  

where x_i are data points, \bar{x} is the mean and n is the number of observations.  

Mean = \displaystyle\frac{\text{Sum of all observations}}{\text{Total number of observation}}

Mean =\displaystyle\frac{99.9}{10} = 9.99

Sum of squares of differences = 1.009

S.D = \sqrt{\dfrac{1.009}{9}} = 0.3348

b) observed value of the t-statistic

Formula:

t_{stat} = \displaystyle\frac{\bar{x} - \mu}{\frac{\sigma}{\sqrt{n}} }

Putting all the values, we have

t_{stat} = \displaystyle\frac{9.99 - 10.1}{\frac{0.3348}{\sqrt{10}} } = -1.0389

c) probability of these statistics (or worse) if the true mean were 10.1 mm

Degree of freedom =  n - 1 = 9

Calculating the value from the table

P(x < 9.99) = 0.1631

0.1631 is the the probability of these statistics (or worse) if the true mean were 10.1 mm

8 0
3 years ago
A 15-inch candle burns down in 10 hours. at what rate does the candle burn in inches per hour
Monica [59]

Answer:

5 inches per hour

Step-by-step explanation:

8 0
3 years ago
Read 2 more answers
Find the magnitude of (3,4,9)
mixas84 [53]
The answer is 5 out 5
4 0
3 years ago
The Thomas Supply Company Inc. is a distributor of gas-powered generators. As with any business, the length of time customers ta
Dmitry [639]

Answer:

The answer is below

Step-by-step explanation:

When computing quartile and decile, the data must be arranged in ascending order.

Given the data points:

13 13 13 20 26 26 29 31 34 34 35 35 36 37 38  41 41 41 42 43 46 47 48 49 53 55 56 62 67 82

The numbers are arranged in ascending order. The total number of terms is 30.

a)

First \ quartile(Q_1)=\frac{1}{4}(n+1)^{th}\  term\\\\where\ n=number\ of\ terms. Hence:\\\\Q_1=\frac{1}{4}(30+1)=7.75^{th}\ term=average\ of\ 7th\ and\ 8th\ term=\frac{29+31}{2} =30\\\\Q_1=30\\\\Third \ quartile(Q_3)=\frac{3}{4}(n+1)^{th}\  term\\\\Q_3=\frac{3}{4}(30+1)=23.25^{th}\ term=average\ of\ 23rd\ and\ 24th\ term=\frac{48+49}{2} =48.5\\\\Q_3=48.5

b)

Second \ decile(D_2)=\frac{2}{10}(n+1)^{th}\  term\\\\where\ n=number\ of\ terms. Hence:\\\\D_2=\frac{2}{10}(30+1)=6.2^{th}\ term=average\ of\ 6th\ and\ 7th\ term=\frac{26+29}{2} =27.5\\\\D_2=27.5\\\\\\Eight \ decile(D_8)=\frac{8}{10}(n+1)^{th}\  term=\frac{8}{10}(30+1)=24.8^{th}\ term\\=average\ of\ 24th\ and\ 25th\ term=\frac{49+53}{2} =51\\\\D_8=51

6 0
3 years ago
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