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3 years ago

A straight line has the equation 3x - 2y = -4. Find the gradient and the y-intercept.

1 answer:

5 0

Start with the given equation

Subtract from both sides

Multiply both sides by

Distribute

Multiply

Rearrange the terms

Reduce any fractions

So the equation is now in slope-intercept form () where (the slope) and (the y-intercept)

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Suppose an isotope has a half-life of 10 years. If you start with 50 grams of the isotope, how much of it will you have in 10 ye

Goshia [24]

The half life of a decaying substance is defined as the time at which the substance decreases to one-half of its original value. In this case, given hlf-life of 10 years and an original mass of 50 grams, after 10 years, the isotope mass becomes 50*0.5 or 25 grams. Answer is B.

5 0

3 years ago

I need help with #2 please I don’t understand

kipiarov [429]

1. Square
2. Circle
3. Triangle (inside of a square)
4. Pentagon
5. Rectangle

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6 0

4 years ago

Read 2 more answers

A laboratory scale is known to have a standard deviation (sigma) or 0.001 g in repeated weighings. Scale readings in repeated we

weqwewe [10]

Answer:

99% confidence interval for the given specimen is [3.4125 , 3.4155].

Step-by-step explanation:

We are given that a laboratory scale is known to have a standard deviation (sigma) or 0.001 g in repeated weighing. Scale readings in repeated weighing are Normally distributed with mean equal to the true weight of the specimen.

Three weighing of a specimen on this scale give 3.412, 3.416, and 3.414 g.

Firstly, the pivotal quantity for 99% confidence interval for the true mean specimen is given by;

P.Q. = $\frac{\bar X - \mu}{\frac{\sigma}{\sqrt{n} } }$ ~ N(0,1)

where, $\bar X$ = sample mean weighing of specimen = $\frac{3.412+3.416+3.414}{3}$ = 3.414 g

$\sigma$ = population standard deviation = 0.001 g

n = sample of specimen = 3

$\mu$ = population mean

Here for constructing 99% confidence interval we have used z statistics because we know about population standard deviation (sigma).

So, 99% confidence interval for the population mean, $\mu$ is ;

P(-2.5758 < N(0,1) < 2.5758) = 0.99 {As the critical value of z at 0.5% level

of significance are -2.5758 & 2.5758}

P(-2.5758 < $\frac{\bar X - \mu}{\frac{\sigma}{\sqrt{n} } }$ < 2.5758) = 0.99

P( $-2.5758 \times {\frac{\sigma}{\sqrt{n} } }$ < ${\bar X - \mu}$ < $2.5758 \times {\frac{\sigma}{\sqrt{n} } }$ ) = 0.99

P( $\bar X-2.5758 \times {\frac{\sigma}{\sqrt{n} } }$ < $\mu$ < $\bar X+2.5758 \times {\frac{\sigma}{\sqrt{n} } }$ ) = 0.99

99% confidence interval for $\mu$ = [ $\bar X-2.5758 \times {\frac{\sigma}{\sqrt{n} } }$ , $\bar X+2.5758 \times {\frac{\sigma}{\sqrt{n} } }$ ]

= [ $3.414-2.5758 \times {\frac{0.001}{\sqrt{3} } }$ , $3.414+2.5758 \times {\frac{0.001}{\sqrt{3} } }$ ]

= [3.4125 , 3.4155]

Therefore, 99% confidence interval for this specimen is [3.4125 , 3.4155].

6 0

3 years ago

What is the equation of the line that passes through the point (-8,5) and has a slope of -1/4

tresset_1 [31]

Answer:

$y=\frac{-1}{4} x+3\\$

Step-by-step explanation:

$(y-5)=\frac{-1}{4} (x--8)\\(y-5)=\frac{-1}{4} (x+8)\\y=\frac{-1}{4} x-\frac{8}{4}+5 \\y=\frac{-1}{4} x-2+5\\y=\frac{-1}{4} x+3\\$

5 0

3 years ago

Read 2 more answers

Mr. Herrera is going to

Mnenie [13.5K]

Answer:

Mr. Herrera will hike 78 miles on 6th day.

Step-by-step explanation:

Given:

Number of miles Mr. Herrera will hike in 9 days = 117 miles

Total Number of days =9 days

Let us first find the number of miles he will hike in 1 day

By Using Unitary method we get,

Number of miles Mr. Herrera will hike in 1 days= $\frac{117} {9}=13\ miles$

We need to find miles hiked in 6th day.

Number of miles Mr. Herrera will hike on 6th day= Number of miles Mr. Herrera will hike in 1 days $\times$ Number of days = $13 \times 6 =78$

7 0

3 years ago