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3 years ago

Solving Multi-Step Equations

1 answer:

8 0

$1.\\2n+3n+7=-41\\5n=-41-7\\5n=-48\\n=-48:5\\\boxed{n=-9.6}\\------------------\\2.\\2x-5x+6.3=-14.4\\-3x=-14.4-6.3\\-3x=-20.7\\x=(-20.7):(-3)\\\boxed{x=6.9}\\------------------$

$3.\\2z+9.75-7z=5.15\\-5z=5.15-9.75\\-5z=-4.6\\z=(-4.6):(-5)\\\boxed{z=0.92}\\------------------\\4.\\3h-5h+11=17\\-2h=17-11\\-2h=6\\h=6:(-2)\\\boxed{h=-3}\\------------------$

$5.\\2t+8-t=-3\\t=-3-8\\\boxed{t=-11}\\------------------\\6.\\6a-2a=-36\\4a=-36\\a=-36:4\\\boxed{a=-9}\\------------------$

$7.\\3c-8c+7=-18\\-5c=-18-7\\-5c=-25\\c=(-25):(-5)\\\boxed{c=5}\\------------------\\8.\\7g+14-5g=-8\\2g=-8-14\\2g=-22\\g=-22:2\\\boxed{g=-11}\\------------------$

$9.\\2b-6+3b=14\\5b=14+6\\5b=20\\b=20:5\\\boxed{b=4}\\------------------\\10.\\2(a-4)+15=13\\2a-8=13-15\\2a=-2+8\\2a=6\\a=6:2\\\boxed{a=3}\\------------------$

$11.\\7+2(a-3)=-9\\2a-6=-9-7\\2a=-16+6\\2a=-10\\a=-10:2\\\boxed{a=-5}\\------------------\\12.\\13+2(5c-2)=29\\10c-4=29-13\\10c=16+4\\10c=20\\c=20:10\\\boced{c=2}$

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A national grocery store chain wants to test the difference in the average weight of turkeys sold in Detroit and the average wei

Arte-miy333 [17]

Answer:

Calculated value t = 1.3622 < 2.081 at 0.05 level of significance with 42 degrees of freedom

The null hypothesis is accepted .

Assume the population variances are approximately the same

Step-by-step explanation:

Explanation:-

Given data a random sample of 20 turkeys sold at the chain's stores in Detroit yielded a sample mean of 17.53 pounds, with a sample standard deviation of 3.2 pounds

The first sample size 'n₁'= 20

mean of the first sample 'x₁⁻'= 17.53 pounds

standard deviation of first sample S₁ = 3.2 pounds

Given data a random sample of 24 turkeys sold at the chain's stores in Charlotte yielded a sample mean of 14.89 pounds, with a sample standard deviation of 2.7 pounds

The second sample size n₂ = 24

mean of the second sample "x₂⁻"= 14.89 pounds

standard deviation of second sample S₂ = 2.7 pounds

Null hypothesis:-H₀: The Population Variance are approximately same

Alternatively hypothesis: H₁:The Population Variance are approximately same

Level of significance ∝ =0.05

Degrees of freedom ν = n₁ +n₂ -2 =20+24-2 = 42

Test statistic :-

$t = \frac{x^{-} _{1} - x_{2} }{\sqrt{S^2(\frac{1}{n_{1} } }+\frac{1}{n_{2} } }$

where $S^{2} = \frac{n_{1} S_{1} ^{2}+n_{2}S_{2} ^{2} }{n_{1} +n_{2} -2}$

$S^{2} = \frac{20X(3.2)^2+24X(2.7)^2}{20+24-2}$

substitute values and we get S² = 40.988

$t= \frac{17.53-14.89 }{\sqrt{40.988(\frac{1}{20} }+\frac{1}{24} )}$

t = 1.3622

Calculated value t = 1.3622

Tabulated value 't' = 2.081

Calculated value t = 1.3622 < 2.081 at 0.05 level of significance with 42 degrees of freedom

Conclusion:-

The null hypothesis is accepted

Assume the population variances are approximately the same.

6 0

3 years ago

A teacher was interested in knowing the amount of physical activity that his students were engaged in daily. He randomly sampled

klasskru [66]

Answer:

The standard error of the mean is 4.5.

Step-by-step explanation:

As we don't know the standard deviation of the population, we can estimate the standard error of the mean from the standard deviation of the sample as:

$\sigma_{\bar{x}}\approx\frac{s}{\sqrt{n}}$

The sample is [30mins, 40 mins, 60 mins, 80 mins, 20 mins, 85 mins]. The size of the sample is n=6.

The mean of the sample is:

$\bar{x}=\frac{1}n} \sum x_i =\frac{30+40+60+80+20+85}{6}=52.5$

The standard deviation of the sample is calculated as:

$s=\sqrt{\frac{1}{n-1}\sum (x_i-\bar x)^2} \\\\ s=\sqrt{\frac{1}{5}\cdot ((30-52.5)^2+(40-52.5)^2+(60-52.5)^2+(80-52.5)^2+(20-52.5)^2+(85-52.5)^2}\\\\s=\sqrt{\frac{1}{5} *3587.5}=\sqrt{717.5}=26.8$

Then, we can calculate the standard error of the mean as:

$\sigma_{\bar{x}}\approx\frac{s}{\sqrt{n}}=\frac{26.8}{6}= 4.5$

6 0

3 years ago

Generate the nest three terms of each arithmetic sequence shown below.

o-na [289]

Answer:

A)2,6,10

B)2,-6,-18

C)-1,-3,-5

Step-by-step explanation:

A)a1=-2 and d=4

We know that the arithmetic sequence formula is

$a_{n}=a_{1}+(n-1)d$

Now

$a_{2}=a_{1}+(2-1)d$

$a_{2}=a_{1}+(1)d$

Substituting the given value we get

$a_{2}= -2+(1)4$

$a_{2}= -2+4$

$a_{2}= 2$

------------------------------------------

Similarly

$a_{3}=a_{1}+(3-1)d$

$a_{3}=a_{1}+(2)d$

Substituting the given value we get

$a_{3}= -2+(2)4$

$a_{3}= -2+8$

$a_{3}= 6$

-------------------------------------------------

$a_{4}=a_{1}+(4-1)d$

$a_{4}=a_{1}+(3)d$

Substituting the given value we get

$a_{4}= -2+(3)4$

$a_{4}= -2+16$

$a_{4}= 10$

-------------------------------------------------------------------------------------------

B $a_n=a_{(n-1)}-8$ with $a_1=10$

$a_2=a_{(2-1)}-8$

$a_2=a_{1}-8$

Substituting the given value

$a_2= 10-8$

$a_2=2$

---------------------------------------------------------------------

$a_3=a_{(3-1)}-8$

$a_3=a_{2}-8$

Substituting the value

$a_3=2-8$

$a_3= -6$

---------------------------------------------------------------------

$a_4=a_{(4-1)}-8$

$a_4=a_{3}-8$

Substituting the value

$a_4= -6-8$

$a_4= -14$

-------------------------------------------------------------------------------------------

C) $a_1=3, a_2=1$

Here the difference is -2

the arithmetic sequence formula is

$a_{n}=a_{1}+(n-1)d$

Now

$a_{3}=a_{1}+(3-1)d$

$a_{3}=a_{1}+(2)d$

Substituting the value we get

$a_{3}= 3+(2)-2$

$a_{3}= 3-4$

$a_{3}= -1$

------------------------------------------------------------------------------

$a_{4}=a_{1}+(4-1)d$

$a_{4}=a_{1}+(3)d$

Substituting the value we get

$a_{4}= 3+(3)-2$

$a_{4}= 3-6$

$a_{4}= -3$

----------------------------------------------------------------------------------

$a_{5}=a_{1}+(5-1)d$

$a_{5}=a_{1}+(4)d$

Substituting the value we get

$a_{5}= 3+(4)-2$

$a_{5}= 3-8$

$a_{5}= -5$

4 0

3 years ago

Factor the expression completely. 8x -12

maxonik [38]

Answer:

x=1.5

Step-by-step explanation:

You divide 8 by 8 and then -12 by 8. And then you get x=-1.5 because 8 divided by 8 is zero and -12 divided by 8 is -1.5

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3 years ago

How many times can 28 go into 224?? I need it now!!

Paha777 [63]

It can go in 8 times

3 0

3 years ago

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