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Savatey [412]
3 years ago
10

Each batch of Mrs. Crawley’s Toffee makes 14 pieces of toffee. If sandy needs 8 dozen pieces of toffee, how many batches does sh

e have to make?
Mathematics
2 answers:
Klio2033 [76]3 years ago
8 0
To solve this question first find how many pieces are in 8 dozens. 1 dozens equals 12 so to find 8 dozens multiply 12 by 8. This gives you 96. 12 dozens=96 pieces. Now divide 96 by 14 to find out how many batches Sandy has to make. 96 divided by 14 is 7, the answer is rounded up. Therefore, Sandy has to make 7 batches.
Phantasy [73]3 years ago
6 0
7 batches of cookies 14 x 7=98 whereas sandy needs 12 x 8=96 ,so 7 batches would be perfect
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Answer:

what are the coordinates

Step-by-step explanation:

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2 years ago
A researcher wishes to be 95% confident that her estimate of the true proportion of individuals who travel overseas is within 3%
andre [41]

Answer:  a) 683   b) 1067

Step-by-step explanation:

The confidence interval for population proportion is given by :-

p\pm z_{\alpha/2}\sqrt{\dfrac{p(1-p)}{n}}

a) Given : Significance level :\alpha=1-0.95=0.05

Critical value : z_{\alpha/2}}=\pm1.96

Margin of error : E=0.03

Formula to calculate the sample size needed for interval estimate of population proportion :-

n=p(1-p)(\dfrac{z_{\alpha/2}}{E})^2\\\\=0.2(0.8)(\dfrac{1.96}{0.03})^2=682.951111111\approx683

Hence, the required sample size would be 683 .

b) If no estimate of the sample proportion is available then the formula to calculate sample size will be :-

n=0.25(\dfrac{z_{\alpha/2}}{E})^2\\\\=0.25(\dfrac{1.96}{0.03})^2=1067.11111111\approx1067

Hence, the required sample size would be 1067 .

3 0
3 years ago
If x=2 calculate : x2*x
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5 0
3 years ago
Solve with cramer's rule x+2y+3z=11, 2x+y+2z=10, 3x+2y+z=9
nalin [4]

Answer:

x = 2 , y = 0 , z = 3

Step-by-step explanation:

Cramer's rule is a rule through which we can find the solution of linear equation.

we have the three linear equations as

x+2y+3z=11

2x+y+2z=10

3x+2y+z=9

AX=B  

A: coefficient matrix

X= unknown vectors(x,y,z)

D = values of the linear equation (11 , 10 , 9)

now we find the determinant of the given linear equation

determinant of the matrix will be

A = \left[\begin{array}{ccc}1&2&3\\2&1&2\\3&2&1\end{array}\right]  = 1(1-4) - 2(2-6) + 3(4 - 3)

                    = 1(-3) - 2(-4) + 3(1)

                    = -3+8+3 = 8

also D\neq 0

so the determinant is Non zero we can apply Cramer's rule

we will be replacing the first column of the coefficient matrix A with the values of D

by replacing the first column we will get the value of the variable 'x'

Dx =  \left[\begin{array}{ccc}11&2&3\\10&1&2\\9&2&1\end{array}\right]   = 11(1-4) -2(10-18) + 3(20-9) = -33+16+33 = 16

x = \frac{Dx}{D}  = \frac{16}{8} = 2

similarly

Dy = \left[\begin{array}{ccc}1&11&3\\2&10&2\\3&9&1\end{array}\right] = 1(10-18) -11(2-6) + 3(18 -30) = -8 +44 -36 = 0

y = \frac{Dy}{D} = 0

Dz= \left[\begin{array}{ccc}1&2&11\\2&1&10\\3&2&9\end{array}\right] = 1(9 - 20) -2(18 - 30) + 11(4 -3) = -11 +24 +11 = 24

z = \frac{Dz}{D} = \frac{24}{8} = 3

so we have the solution as

x = 2 , y = 0 , z = 3

Therefore the solution for the given linear equations is (2,0,3).

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Answer:

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Step-by-step explanation:

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2 years ago
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