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eduard
2 years ago
14

In a certain county, the number of Charter Schools is eight less than twice the number of Alternative Schools. We know that ther

e are 36 Charter Schools in the county. How many Alternative Schools are in the county?
Mathematics
1 answer:
kipiarov [429]2 years ago
5 0

The solution would be like this for this specific problem:

Since the number of charter schools is eight less than twice the number of alternative schools, then it’s:

<span>2x - 8 </span><span>
<span>and then
<span>2x - 8 = 36 </span>
<span>2x = 44 </span>
x = 22 </span></span>

So there are 22 Alternative Schools in the county. I am hoping that this answer has satisfied your query and it will be able to help you in your endeavor, and if you would like, feel free to ask another question.

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A local sorority sold hot dogs and bratwursts at the spring fling picnics. The first day they sold 8 dozen hot dogs and 13 dozen
Sergeu [11.5K]

Answer: Cost of each hot dog and bratwursts would be $1.1 and $1.35 each.

Step-by-step explanation:

Since we have given that

Cost of each dozen hot dogs be 'x'.

Cost of each dozen bratwursts be 'y'.

The first day they sold 8 dozen hot dogs and 13 dozen bratwursts for $316.20.

So, the equation would be

8x+13y=\$316.20

.The second day they sold 10 dozen hot dogs and 15 dozen bratwursts for a total of $375.00.

So, the equation would be

10x+15y=\$375.00\\\\2x+3y=\$75

So, the equations becomes

8x+13y=316.20--------------(2)\\\\(2x+3y=75)\times 4\\\\\implies 8x+12y=300------------(1)

So, by elimination method, we get that

8x+13y=316.20\\\\(-)8x+(-)12y=(-)300\\\\--------------\\y=\$16.20

Put the value of y in the eq(1), we get that

2x+3y=75\\\\2x+3(16.20)=75\\\\2x+48.6=75\\\\2x=75-48.60\\\\2x=26.4\\\\x=\dfrac{26.4}{2}\\\\x=\$13.2

Hence, the cost of hot dogs would be \dfrac{13.2}{12}=\$1.1

And the cost of bratwursts would be \dfrac{16.2}{12}=\$1.35

4 0
2 years ago
The radius of the circular lens of a magnifying glass is 4 centimeters.
Nadusha1986 [10]

Answer: 50.24 square centimeters.

Step-by-step explanation:

Given: The radius of the circular lens of a magnifying glass = 4 centimeters

The area of a circle is given by :-

\text{Area}=\pi r^2, where r is the radius of the circle.

Then the area of the circular lens of a magnifying glass is given by :-

\text{Area}=\pi (4)^2=(3.14)(16)=50.24\text{ square centimeters }

Hence, the area of the circular lens of a magnifying glass = 50.24 square centimeters.

5 0
2 years ago
93 27 14 what is next in the sequence?
Assoli18 [71]

Answer:

4

Step-by-step explanation:

9×3=27

2×7=14

1×4=4

nice logic

6 0
2 years ago
1. In a batch of 10 items, we wish to extract a sample of 3 without replacement. How many
svetlana [45]

Answer:

1) 120

2) E (Z) = 12 and Variance of Z = 90

a) 5 liters

Step-by-step explanation:

1. We can find this by suing combinations.

Here n= 10 and r= 3 so n C r

= 10 C 3= 120

2. E(X) = 8 and E(Y) = 3

Z = 2X - 3Y +5

E(Z ) = 2 E (X) - 3(E)(Y) +5   ( applying property for mean)

       = 2(8) - 3(3)+ 5 = 16+5-9= 21-9= 12

V(X) = 9 and V(Y) = 6.

V(Z) = E(Z )²-  V(X) *V(Y)   (applying property for Variance for two variables )

        = 144- 54= 90

3. 55 liters contain adulterated milk in 7: 4.

So it contains 4/ 11*55= 20 liters of water

But we want to make it a ratio of 7:6

the water will be 6/13 *55= 25.38 when rounded gives 25 liters of water

So 25- 20 = 5 liters must be added to make it a ratio of 7:6

6 0
2 years ago
The mean hourly wage for employees in goods-producing industries is currently $24.57 (Bureau of Labor Statistics website, April,
sweet-ann [11.9K]

Answer:

a. H_{0}: μ = $24.57

H_{a}: μ ≠ $24.57

b. 0.12

c. we fail to reject the null hypothesis since p ≈0.12 > 0.05

d. we fail to reject the null hypothesis since z ≈-1.6 > -1.96

Step-by-step explanation:

a)

H_{0}: μ = $24.57

H_{a}: μ ≠ $24.57

b)

To compute p value, we need to calculate z-score of $23.89 per hour. in the distribution assumed under null hypothesis

z-score can be calculated as follows:

\frac{X-M}{\frac{s}{\sqrt{N} } } where

  • X= $23.89
  • M is the mean value under null hypothesis ( $24.57)
  • s is the sample standard deviation ($2.40)
  • N is the sample size (30)

Putting the numbers in the formula we get

\frac{23.89-24.57}{\frac{2.40}{\sqrt{30} } } ≈ −1,5518

The corresponding p-value is <em>two tailed </em>and  ≈ 0.12

c)

since p ≈0.12 > 0.05 <em>we fail to reject the null hypothesis.</em>

d)

Critical value for the 0.05 significance level in two tailed test is :

c(z)=-1.96 Since z≈ −1,6 >-1.96, it is not in the critcal region, therefore <em>we fail to reject the null hypothesis. </em>

7 0
2 years ago
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