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irina1246 [14]
3 years ago
9

11c - 2d = -2 c + 8d = 8 using the substitution method

Mathematics
1 answer:
Darya [45]3 years ago
4 0
<span>A) 11c - 2d = -2
B) c + 8d = 8
</span><span>B) c  = 8 - 8d then substitute this into A)

</span><span>A) 88 -88d - 2d = -2
A) 90 = 90d
d = 1
c = 0

</span>
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21 feet to 8 yards write a ratio as a fraction in simplest form without any units
Dmitriy789 [7]

We know, 3 feet = 1 yard.

We have to convert feet to yards to calculate the ratio so that the final answer doesn't have any unit.

Therefore, 21 feet = \frac{21 feet}{3 feet}yards = 7 yards

Thus, the ratio

\frac{21feet}{8yards} =\frac{7yards}{8yards} =\frac{7}{8}

The fraction \frac{7}{8} is already in its simplest form.

Therefore, the given ratio as a fraction in the simplest form without any units is \frac{7}{8}

3 0
2 years ago
A journal article reports that a sample of size 5 was used as a basis for calculating a 95% CI for the true average natural freq
oksano4ka [1.4K]

Answer:

Lower = 231.134- 3.098=228.036

Upper = 231.134+ 3.098=234.232

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

\bar X represent the sample mean for the sample  

\mu population mean (variable of interest)

s represent the sample standard deviation

n=5 represent the sample size  

Solution to the problem

The confidence interval for the mean is given by the following formula:

\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}   (1)

And for this case we know that the 95% confidence interval is given by:

\bar X=\frac{233.002 +229.266}{2}= 231.134

And the margin of error is given by:

ME = \frac{233.002 -229.266}{2}= 1.868

And the margin of error is given by:

ME= t_{\alpha/2} \frac{s}{\sqrt{n}}

The degrees of freedom are given by:

df = n-1 = 5-1=4

And the critical value for 95% of confidence is t_{\alpha/2}= 2.776

So then we can find the deviation like this:

s = \frac{ME \sqrt{n}}{t_{\alpha/2}}

s = \frac{1.868* \sqrt{5}}{2.776}= 1.506

And for the 99% confidence the critical value is: t_{\alpha/2}= 4.604

And the margin of error would be:

ME = 4.604 *\frac{1.506}{\sqrt{5}}= 3.098

And the interval is given by:

Lower = 231.134- 3.098=228.036

Upper = 231.134+ 3.098=234.232

6 0
3 years ago
Which equation matches the statement: "The sum of -4x and 2 is 9"??
neonofarm [45]

Answer:

A

Step-by-step explanation:

sum means addition

the problem says sum of -4x and 2 meaning -4x + 2

the word "is" right before 9 means equals 9

6 0
3 years ago
DeSean is sorting his toy car collection. ⅔ of the cars are sports cars. ¼ of the remaining toys are pick up trucks. All of the
user100 [1]

Answer:

Fraction of fire trucks = \frac{1}{4}

Total number of toy cars = 16

Step-by-step explanation:

Fraction of sports car = \frac{2}{3}

Fraction of remaining cars =1-\frac{2}{3}=\frac{3-2}{3} =\frac{1}{3}

So,

Fraction of pick up cars = \frac{1}{4}(\frac{1}{3})=\frac{1}{12}

Therefore,

Fraction of fire trucks = \frac{1}{3}-\frac{1}{12}=\frac{4-1}{12}=\frac{3}{12}=\frac{1}{4}

That is Number of fire trucks = \frac{1}{4} ( Total number of toy cars )

Number of fire trucks = 4

Total number of toy cars = 4(4)=16

3 0
3 years ago
A bar of soap is shaped like a right rectangular prism. The base is a rectangle that is 12 centimeters by 2 centimeters. The hei
evablogger [386]

Answer:

6 cm

Step-by-step explanation:

Volume of a Prism = base area x height =

Base area = length x width =  12 x 2 = 24 cm^2

Volume = 24 x 3 = 72 cm^3

Volume of a pyramid = 1/3( l x w x h)

72 = 1/3( 6x6 x h)

Multiply both sides of the equation by 3

216 = 36 x h

divide both sides by 36

h = 6

8 0
3 years ago
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