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3 years ago

Solve using the appropriate method a-3b=33 b+6=2a

Mathematics

1 answer:

Varvara68 [4.7K]3 years ago

6 0

Answer:

1= -6b=a

Step-by-step explanation:

a-3b=33b+6=2a

+3b +3b

a=36b+6=2a

-6 -6

a -6=36b=2a

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

-6 -6

a= -6b=2a

This is the work and the answer

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How many quart are in a gallon

Alexandra [31]

Answer:

There are 4 quarts in 1 gallon.

Step-by-step explanation:

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3 years ago

Liam is deciding which of two gyms to join. Each gym charges a monthly rate plus one-time membership fee. Liam correctly wrote a

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3 years ago

Cable Strength: A group of engineers developed a new design for a steel cable. They need to estimate the amount of weight the ca

KatRina [158]

Answer:

95% confidence interval for the mean breaking strength of the new steel cable is [763.65 lb , 772.75 lb].

Step-by-step explanation:

We are given that the engineers take a random sample of 45 cables and apply weights to each of them until they break. The mean breaking weight for the 45 cables is 768.2 lb. The standard deviation of the breaking weight for the sample is 15.1 lb.

Since, in the question it is not specified that how much confidence interval has be constructed; so we assume to be constructing of 95% confidence interval.

Firstly, the Pivotal quantity for 95% confidence interval for the population mean is given by;

P.Q. = $\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }$ ~ $t_n_-_1$

where, $\bar X$ = sample mean breaking weight = 768.2 lb

s = sample standard deviation = 15.1 lb

n = sample of cables = 45

$\mu$ = population mean breaking strength

Here for constructing 95% confidence interval we have used One-sample t test statistics as we don't know about population standard deviation.

So, 95% confidence interval for the population mean, $\mu$ is ;

P(-2.02 < $t_4_4$ < 2.02) = 0.95 {As the critical value of t at 44 degree

of freedom are -2.02 & 2.02 with P = 2.5%}

P(-2.02 < $\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }$ < 2.02) = 0.95

P( $-2.02 \times {\frac{s}{\sqrt{n} } }$ < ${\bar X-\mu}$ < $2.02 \times {\frac{s}{\sqrt{n} } }$ ) = 0.95

P( $\bar X-2.02 \times {\frac{s}{\sqrt{n} } }$ < $\mu$ < $\bar X+2.02 \times {\frac{s}{\sqrt{n} } }$ ) = 0.95

95% confidence interval for $\mu$ = [ $\bar X-2.02 \times {\frac{s}{\sqrt{n} } }$ , $\bar X+2.02 \times {\frac{s}{\sqrt{n} } }$ ]

= [ $768.2-2.02 \times {\frac{15.1}{\sqrt{45} } }$ , $768.2+2.02 \times {\frac{15.1}{\sqrt{45} } }$ ]

= [763.65 lb , 772.75 lb]

Therefore, 95% confidence interval for the mean breaking strength of the new steel cable is [763.65 lb , 772.75 lb].

3 0

3 years ago

write the equation of the line that is perpendicular to the line y = 2x 2 and passes through the point (6, 3). a. y = 2x 6 b. y

Nataliya [291]

For perpendicular lines, m1m2 = -1 or m2 = -1/m1.
Line y = 2x + 2 has a slope of 2, hence required slope is -1/2
Required equation is y - y1 = -1/2(x - x1)
y - 3 = -1/2(x - 6)
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5 0

3 years ago

Find the real solution for:

Advocard [28]

Answer:

none of the above

Step-by-step explanation:

p^3 = 125

Rewrite 125 as 5^3

p^3 = 5^3

Take the cube root of each side

(p^3) ^ (1/3) = ( 5^3) ^ (1/3)

p = 3

6 0

3 years ago