At Handy Hardware Shop's annual spring-cleaning sale, every ratchet set in the shop gets marked down. Austin purchased 2 ratchet sets during the sale: one for himself and one to give to his dad on Father's Day. Each ratchet set cost $8 less than its full price. He paid a total of $56. What is the cost of each ratchet set at full price?

Answer:

y = 2x - 11

Step-by-step explanation:

Perpendicular lines have negative reciprocal slopes—multiplying the slopes of two lines results in a product of -1.

Given the linear equation,  x + 2y - 12 = 0, and the other point, (6, 1):

Convert the given linear equation into its slope-intercept form:

x + 2y - 12 = 0

Subtract x from both sides:

x - x + 2y - 12 = - x  0

2y - 12 = -x

Next, add 12 to both sides of the equation:

2y - 12 + 12 = -x + 12

2y = -x + 12

Divide both sides by 2 in order to isolate y:

y = - ½x + 6

Since the slope of the given equation is - ½, then the other line perpendicular to it must have a slope of 2:

Let m₁ =  - ½

     m₂ = 2

     m₁ × m₂ = -1

     -½ ×  2  = -1

Hence, the slope of the other line, m₂ = 2. Next, using the slope of the other line, m₂ = 2, and the other given point, (6, 1), substitute these values into the slope-intercept form to solve for the y-intercept, (b):

y = mx + b

1 = 2(6) + b

1 = 12 + b

1 - 12 = 12 - 12 + b

-11 = b

Thus, the y-intercept of the other line is b = -11.

Therefore, the linear equation of the line that is perpendicular to x + 2y - 12 = 0 is:

As a proof, attached is the graph of both equations, where it shows that they are perpendicular from each other.    

Write out the equation:

4x + 5 = 21

Subtract 5 from both sides:

4x = 16

Divide both sides by 4:

X = 4

The number is 4

Using the t-distribution, it is found that the 95% t-confidence interval for the population mean weight of newborn mice with snipped tails is (42157, 42843).

The interpretation is: The researchers are 95% confident that the true population mean weight of newborn mice with snipped tails is between the upper and lower limits of the confidence interval.

We are given the standard deviation for the sample, which is why the t-distribution is used to solve this question.

The information given is:

Sample mean of [tex]\overline{x} = 42500[/tex].

Sample standard deviation of [tex]s = 6068[/tex].

Sample size of [tex]n = 1200[/tex].

The confidence interval is:

[tex]\overline{x} \pm t\frac{s}{\sqrt{n}}[/tex]

The critical value, using a t-distribution calculator, for a two-tailed 95% confidence interval, with 1200 - 1 = 1199 df, is t = 1.96.

The interval is:

[tex]\overline{x} - t\frac{s}{\sqrt{n}} = 42500 - 1.96\frac{6068}{\sqrt{1200}} = 42157[/tex]

[tex]\overline{x} + t\frac{s}{\sqrt{n}} = 42500 + 1.96\frac{6068}{\sqrt{1200}} = 42843[/tex]

The 95% t-confidence interval for the population mean weight of newborn mice with snipped tails is (42157, 42843).

The interpretation is that we are 95% sure that the population mean weight is in this interval, hence:

The researchers are 95% confident that the true population mean weight of newborn mice with snipped tails is between the upper and lower limits of the confidence interval.

A similar problem is given at https://brainly.com/question/25417022

Answer:

woah amazing

Step-by-step explanation:

Answer:

ok so a is 1b b is 5 c is 57 d is 97

Answer:

x=-2/5

Step-by-step explanation:

Answer:

n=300

Step-by-step explanation:

Answer:

yea its the thing you eat your food on at breakfast lunch dinner etc.

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

3 4 5 6

The sample mean weight, from this random sample of 135 pigs, fall within the confidence interval. (Option A: yes)

Suppose that we have:

Then the confidence interval is obtained as

[tex]\overline{x} \pm Z_{\alpha /2}\dfrac{\sigma}{\sqrt{n}}[/tex]

[tex]\overline{x} \pm Z_{\alpha /2}\dfrac{s}{\sqrt{n}}[/tex]

For this case, we work with sample standard deviation(you can choose even population standard deviation, it won't matter as both are not given here).

We're provided that:

Since the formula for limits of confidence interval is:

[tex]\overline{x} \pm Z_{\alpha /2}\dfrac{s}{\sqrt{n}} = \overline{x} \pm 1.645\dfrac{s}{\sqrt{135}}[/tex]

That has:

[tex]\text{Lower limit} = 75 = \overline{x} - 1.645\dfrac{s}{\sqrt{135}}\\\\\text{Upper limit} = 90 = \overline{x} +1.645\dfrac{s}{\sqrt{135}}\\\\[/tex]

Thus, we get:

Adding both the equations, we get:

[tex]165 = 2\overline{x}\\\\\overline{x} = 82.5 \: \rm pounds[/tex]

That is between 75 and 90 pounds.

Thus, the sample mean weight, from this random sample of 135 pigs, fall within the confidence interval. (Option A: yes)

Learn more about confidence interval for large samples here:

https://brainly.com/question/13770164

Answer:

  the correct choice is marked

Step-by-step explanation:

The lengths will form a right triangle if the squares of the two shortest legs total the square of the longest. The square of a root is the number under the radical, so you're looking to see if the two smallest numbers under the radicals total the largest number under the radical.

  A: 22 +88 = 110 . . . . . a right triangle

  B: 66 +99 = 165 ≠ 176 . . . . an obtuse triangle

  C: 22 +110 = 132 ≠ 121 . . . . an acute triangle

  D: 66 +77 = 143 ≠ 154 . . . . an obtuse triangle

_____

Additional comment

The largest angle is opposite the longest side. If the longest side is too long for the triangle to be a right triangle, then the opposite angle is larger than 90°, and the triangle is obtuse. If the longest side is too short for a right triangle, then the triangle is acute.

Answer:

you are correct

Step-by-step explanation:

brainliest pls

Answer:

x = 4 + sqrt 5

x = 4 - sqrt 5

Step-by-step explanation:

(X-4)^2 = 5

X - 4 = + - sqrt 5

X = 4 + sqrt 5 and

X = 4 - sqrt 5

Answer:

Step-by-step explanation:

Take the square root of each side of the equation to set up the solution for x

[tex](x-4)^{2*\frac{1}{2} } =[/tex] ±[tex]\sqrt{5}[/tex]

Remove the perfect root factor x - 4 under the radical to solve for x.

x - 4 = ±[tex]\sqrt{5}[/tex]

The complete solution is the result of both the positive and negative portions of the solution.

First, use the positive value of the ± to find the first solution.

[tex]x-4=\sqrt{5}[/tex]

Add 4 to both sides of the equation.

[tex]x=\sqrt{5} +4[/tex]

Next, use the negative value of the ± to find the second solution.

[tex]x-4=-\sqrt{5}[/tex]

Add 4 to both sides of the equation.

[tex]x=-\sqrt{5} +4[/tex]

The complete solution is the result of both the positive and negative portions of the solution.

[tex]x=\sqrt{5} +4,-\sqrt{5} +4[/tex]

Answer:

first blank: 16

second blank: 4

third blank: -8

fourth blank: -20

Step-by-step explanation:

hope this helps and I hope you can rate my answer!

Answer:

6300 kg is equivalent to 6.3·10^5 g

Step-by-step explanation:

Convert 6300 kg TO g in standard form.  Recall that 1000 g = 1 kg.

                                        1000 g

Multiplying 6300 kg by ------------- results in 63·10^4, or 6.3·10^5

                                           1 kg

6300 kg is equivalent to 6.3·10^5 g.

Answer:

6 large Boxes 2 Small boxes

Step-by-step explanation:

400 - 800 - 1200 - 1600 - 2000 - 2400

   1        2         3           4       5           6

50 - 100

1       2    

2 is 1/3 of 6

2400 + 100 + 2500

Answer:

I do believe that the answer is true

Step-by-step explanation:

Answer: TRUE

Step-by-step explanation: A bill of rights is a list of the most important rights belonging to the citizens of the country. It is the declaration and enumeration of a person's right and privileges even the government must respect that.

Answer: Option 1 & 2

Step-by-step explanation:

Just answered the question

Answer:

81x^4+216x^3+216x^2+96x+16

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

Step-by-step explanation:

9(2g - h) = ...

= (9•2g) + (9•(-h))

= 18g - 9h

Answer:

Perimeters of Similar Figures

of their perimeters is equal to the ratio of their corresponding side lengths.

Step-by-step explanation:

Answer:

here it is

Perimeter is the distance around a two dimensional shape, a measurement of the distance around something; the length of the boundary.

Answer:

7.77

Step-by-step explanation:

Answer:

40%

Step-by-step explanation:

To find the percentage, set up a proportion!

12/30 = x/100

Now cross multiply!

30 · x = 30x

12 · 100 = 1,200

You are left with:

30x = 1,200

Divide both sides by 30...

And you get....

x = 40

The mixture is 40% lysol!

I hope this clears up any confusion you may have had :D

Answer:

um there are 3 1/2 forties in two hours and 20 minutes. Did this answer your question?

Step-by-step explanation:

2 hours 20 minutes= 140 minutes

140/40=3 1/2

Answer:

14/11

Step-by-step explanation:

The cardinal number for the set is 5.

The size of a finite set (even comprehended as its cardinality) exists calculated by the number of elements it has. Remember that counting the number of elements in a set amounts to creating a 1-1 correspondence between its elements and the numbers in {1,2,...,n}.

The cardinal number (or cardinality) of set A, represented by n(A), exists as the number of distinct elements in set A

Since set A contains 5 distinct elements, then:

n(A) = 5

Therefore, the cardinal number for the set is 5.

To learn more about cardinality of a set

https://brainly.com/question/23976339

#SPJ2

Answer:

It's dilate

Step-by-step explanation:

Because it changed in size and if it would to be translation the same size would be the same just different amount of spaces between the shapes.

800 women because

2500 divided by 5 = 500 children

then.......2500 minus 500 children minus 1200 men is a balance of 800 women.