Write the point-slope form of the equation of the line through the given point with the given
slope.
3) through: (5, 1), slope
=
1
5

The probability that it takes at most 1 hour of machining time to produce a randomly selected component  is  0.04074

we are provided  with  the  independent  time which are 15, 20, and 30 min and the respective standard deviations which are 2, 1, and 1.8 min.So the total  mean X= 15+20+30 =65, as we know that

Variance = ( standard deviation )²

=> Variance = 2² + 1² + 1.8² = 8.24

since standard deviation = √variance

=>Standard deviation = 2.87

so the z score = X -mean /standard deviation

since here X = 1 hour = 60 mintues

z = 60-65/2.87 =  -1.74216

So the probability, P( z≤ -1.74216) = 0.04074

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The slope of the given line in the graph is 0.

What is slope?

 The steepness and direction of a line are measured by its slope. Any two points along the line can be used to calculate it. A line's steepness is determined by its slope. In mathematics, slope is determined by "rise over run" (change in y divided by change in x). The Slope, also known as the Gradient, of a straight line displays how steep the line is. The change in y coordinate relative to the change in x coordinate is known as the slope of an object.

Here the given graph points are,

[tex](x_1-y_1)=(1,1)\\(x_2,y_2)=(4,1)[/tex]

Using slope formula ,

=> slope m = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

=> slope m = [tex]\frac{1-1}{4-1}[/tex]

=> slope m = 0/3

=> slope m=0.

Therefore slope of the line is 0.

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Assume the account pays a nominal annual interest of r% compounded quarterly, the value of the interest rate (r) is equal to 7.87%.

Mathematically, compound interest can be calculated by using this formula:

A(t) = P(1 + r/n)^{nt}

Where:

Substituting the given parameters into the formula, we have;

1.6(3,818) = 3,818(1 + r/8)^{8 × 6}

1.6 = (1 + r/8)^{48}

Taking the 48th root of both sides of the equation, we have:

[tex]\sqrt[48]{1.6} = \sqrt[48]{(1 + \frac{r}{8} )^{48} }[/tex]

1.00983983823726 = 1 + 0.125r

0.125r = 1.00983983823726 - 1

0.125r = 0.00983983823726

Interest rate, r = 0.00983983823726/0.125

Interest rate, r = 0.0787

Interest rate, r = 7.87%

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The angle the road makes is 3.43°

What is an angle?

An angle is a shape created by two rays that share a terminus and are referred to as the angle's sides and vertices, respectively. Angles created by two rays are in the plane where the rays are located. The meeting of two planes also creates angles. We refer to these as dihedral angles.

Here, we have

A 6% downgrade means that for every 100 units of horizontal run.

The vertical height decreases by 6 units.

The grade has a downward angle of

tan⁻1(6/100) = 3.43°

Hence, the angle the road makes is 3.43°

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The point slope form of the equation is = P2 = (11, 2)

acc to our question-

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The minimum cost will be 1091 units.

Define Vertex Formula.

When the graph crosses its symmetry axes, the vertex formula aids in determining the vertex coordinate of a parabola. The vertex point is often represented by (h, k).

We are aware that a parabola's conventional equation is y=ax²+bx+c. The vertex in this case should be near the base of the U-shaped curve if the coefficient of x² is positive. The vertex should be at the peak of the U-shaped curve if the coefficient of x² is negative.

Given expression is,

C = 70,000 - 120x + 0.055x²

For this equation, the graph will be parabola opening upward.

For that, the vertex will be the minimum cost

x = (-b) / 2a

Here, a = 0.055 , b = -120

Now, plug in the values and find 'x'

minimum cost (x) = ( -(-120) ) / ( 2 * 0.055 )

                            = 120 / 0.11

                            = 120 / 0.11

                            = 1090.90  or 1091 units

Therefore, the minimum cost will be 1091 units.

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The cost per dog treat is 0.55 dollars

How to determine this,

The cost of 8 dog treats is 4.40 dollars

And the number of 1 dog treat is x dollar

x dollar=4.40 dollars×1 dog treat/8 dog treats

x=0.55 dollar per one dog treat

To complete the table,

For 18 dog treats

when 1 dog treat is 0.55 dollar

18 dog treats is x dollar

x=18 dog treats×0.55 dollar/1 dog treat

x=9.9dollars

For 25 dog treats,

when 1 dog treat is 0.55 dollar

for 25 dog treats is x dollar

x=25 dog treats×0.55 dollar/1 dog treat

x=13.75 dollars

For 6.05 dollars,

when 1 dog treat is 0.55 dollar

x dog treat is 6.05 dollars

x=6.05 dollars×1 dog treat/0.55 dollar

x=11 dog treat

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Answer:

Step-by-step explanation: 0.55

The two values of x is x = 3 and x = 5/2 of the equation 2x²– 11x + 15 = 0 i.e, the option(a) and option(d)

What is a Quadratic equation ?

A second-degree equation of the form ax² + bx + c = 0 is known as a quadratic equation in mathematics. Here, x is the variable, c is the constant term, and a and b are the coefficients. Since x is a second-degree variable, this quadratic equation has two roots, or solutions.

The given expression is ,

2x²– 11x + 15 = 0

Solve the equation and find roots

2x² - 6x - 5x + 15 = 0

Take common elements out

2x(x - 3) - 5(x - 3) = 0

we get the brackets same that means we're on right way,

(2x - 5) (x - 3) = 0

split the values into two and find values,

2x - 5 = 0            and        x - 3 = 0

2x = 5                               x = 3

x = 5 / 2

Hence, the  values of x is x = 3 and x = 5/2 of the equation 2x²– 11x + 15 = 0 i.e, the option(a) and option(d)

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Answer:

  (B)  A line from (0, 0) going through (41, 36.49) where the x-axis is labeled Weight (in pounds) and the y-axis is labeled Cost (in dollars)

Step-by-step explanation:

You want a description of the graph showing the proportional dependency of cost on weight if a couple of (weight, cost) points are (25, 22.25) and (41, 36.49).

The independent variable is weight, so the x-axis will be labeled Weight (in pounds). The dependent variable is cost, so the y-axis will be labeled Cost (in dollars). The two given points can be plotted on the graph.

The description from the available answer choices is ...

A line from (0, 0) going through (41, 36.49) where the x-axis is labeled Weight (in pounds) and the y-axis is labeled Cost (in dollars)

<95141404393>

The mean recurrence interval between earthquakes of this magnitude range over the previous 30 years essentially has been 4.769230 in a basically sort of big way in a subtle way.

Given, the earthquake's magnitude literally basically is between 6.0 and 7.0 in a very definitely big way, or so they for all intents and purposes thought. occurrences = 2 earthquakes

Duration: 30 years

particularly Mean Earthquake Recurrence Interval,

T=(n+1) / m

Where m = 6+7 / 2 = 6.5 , n = 30

T = ( 30+1)/6.5

   = 31/6.5

   = 4.769230

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The probability that the sample mean would differ from the population mean by greater than 0.5 millimeters is 1

From the question, the given parameters about the distribution are

The standard deviation is the square root of variance

So, we have

Standard deviation = 6

The z-score is calculated using the following formula

z = (x - mean value)/standard deviation

Substitute the given parameters in the above equation

z = (0.5 - 127)/6

Evaluate

z = -21.08

The probability is then calculated as:

P(x > 0.5) = P(z > -21.08)

From the z table of probabilities, we have;

P(x < 0.5) = 1

Hence, the probability is 1.0

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Step-by-step explanation:

The formula D = 401t + 5940 can be used to approximate the total average credit card debt in a U.S. household (in dollars) t years after 1995. Use this formula to predict what the total average credit card debt will be in the year 2028.

2028 - 1995 = 33 years, so t = 33

D = 401t + 5940

D = 401(33) + 5940

D = 13,233 + 5940  

D = 19,173

Answer: In the year 2028, the total average credit card debt for a U.S. household will be $19,173

Answer: Diverge Reasoning I took the test

The jar of chemicals contains 176 grams of zinc.

Using ratio and proportion to calculate the amount of zinc. Let us assume the mass of zinc to be x. Equating the ratios.

4 : 11 = x : 484

Rewriting the equation in terms of x

x = (484 × 4) ÷ 11

Performing multiplication in numerator on Right Hand Side of the equation to find the value of x

x = 1936 ÷ 11

Performing division on Right Hand Side of the equation to find the value of x

x = 176

Thus, the mass of zinc is 176 grams.

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Step-by-step explanation:

A. total mass = 9 + (x × 1.2)

B. 21 - 9 = 12kg

12 ÷ 1.2 = 10 articles.

hope it helps. :)

The correct option is  a.) a questionnaire, used as observing the relationship between independent variable as well as a dependent variable is the goal of a quantitative research technique known as employed as.

Quantitative methods place an emphasis on accurate measurements or the statistical, quantitative, or numerical evaluation of information gathered through surveys, polls, and other types of research, as well as the manipulation of statistical data that has already been obtained using computing methods.

Quantitative research involves gathering numerical information and using it to understand a specific event or generalise it across groups of individuals.

Its primary attributes are:

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The area of a circle is 12πx-60π unit².

By examining the given figure, there are two circles i.e the small circular hole and the bigger circle. Since the small is a hole then we have to subtract its area from the area of the bigger circle.

Given:

radius of small circle(r₂) = x+2

radius of bigger circle(r₁) = x+8

The formula of Area(A) = πr²

Area of the figure = A₁ - A₂

                             =  πr₁² - πr₂²

                             =  π(x+8)²- π(x+2)²

                             = π(x²+16x+64) -  π(x²+4x+4)

                             =  x²π+16πx+64π - x²π-4πx-4π

                            =   12πx-60π unit squared

Therefore,  the area of the circle is 12πx-60π unit squared. So the 2nd option is the answer.

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The ratios of lines to pages are proportional in both books.

From the information, in In one book, there are 15 lines per page.

In another book, there are 90 lines in every 6 pages. Therefore, the number of lines per page will be:

= Number of line / Number of page

= 90 / 6

= 15 lines per page

Therefore since they're the same for both books as we got 15 lines, they're proportional.

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The correct selling price of the item has being solved as $20.04 The error that the manager has made is $12.04

Given that there is a markup, the item that is being sold for 12 dollars would be affected by the percentage of the mark up.

This mark up is a 67% markup

This would be solved as

12$ + 67% of 12$

= $12 + 8.04

= $20.04

Hence the correct selling price is $20.04

Next we would have to find the likely error that the manager has made

= $20.04- ​$8

= $12.04

The likely error of the manager is $12.04

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Answer:

I'm pretty sure the answer would be >

Answer: |-8|>-2

Step-by-step explanation:

Because of the lines on both sides of the "-8" you don't pay attention to the "-" sign. That is because this is an absolute value sign. So instead you would read that as 8 ? -2 and which of course 8 is clearly greater

Hope this helps ;)

Please find attached the graph of the image of ΔIJK following a translation transformation of (-17, 5), and a reflection across the line y = 5

A transformation is an operation that changes the location, size and shape of geometric figures.

The coordinates of the vertex of ΔIJK are; I(14, 8), J(8, 5), K(14, 2)

The translation transformation is 17 units left and 5 units up = T₍₋₁₇, ₅₎

The location of the vertices of the image of ΔIJK following the translation transformation are;

[tex]I(14,\, 8)\ \underset{\longrightarrow}{T_{(-17,\, 5)}}\ I'(-3,\, 13)[/tex]

[tex]J(8, 5)\ \underset{\longrightarrow}{T_{(-17,\, 5)}}\ j'(-9,\, 10)[/tex]

[tex]K(14, 2)\ \underset{\longrightarrow}{T_{(-17,\, 5)}}\ K'(-3,\, 7)[/tex]

The coordinates of a point following a reflection across the line y = 1 are as follows;

The coordinates of the vertices of the image I'J'K' relative to the line y = 1 are;

I'(-3, 13), Relative point I'(-3, 12)

J'(-9, 10) has a relative point at (-9, 9)

K'(-3, 7) has a relative point (-3, 6)

The coordinates of the vertices of the reflected image are therefore;

(x, y)  [tex]\underset{\longrightarrow}{R_{y = 1}}[/tex]  (x, -(y - 1))

Which gives;

I'(-3, 12)  [tex]\underset{\longrightarrow}{R_{y = 1}}[/tex] I''(-3, -12 + 1) = I''(-3, -11)

J'(-9, 9) [tex]\underset{\longrightarrow}{R_{y = 1}}[/tex] I''(-9, -9 + 1) = I''(-9, -8)

k'(-3, 6)  [tex]\underset{\longrightarrow}{R_{y = 1}}[/tex] k''(-3, -6 + 1) = k''(-3, -5)

Please find attached the image of the ΔIJK following the translation and reflection transformation

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Answer:

the label are marked by numbers

I think so ya is does you just need to tell your teacher if you don't understand

When the directrix is at x = 5 and  point in the vertex is at h = 2. Then P would be -3

In the equation of parabola, P is defined as the distance between the directrix and the vertex

The vertex is defined by the points V ( h, k )

h is for the x coordinate

k is for the y coordinate

when the directrix is given in the x, we solve for P using h

P = h - point given for directrix

P = 2 - 5

P = -3

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-68 as a quotient of integers is -680/10.

The given integer is -68.

In arithmetic, a quotient is a quantity produced by the division of two numbers. The quotient has widespread use throughout mathematics, and is commonly referred to as the integer part of a division, or as a fraction or a ratio.

Here, -68/1

Multiply 10 to both the numerator and denominator, we get

= -680/10

= -68

Therefore, -68 as a quotient of integers is -680/10.

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Simply put, probability is the likelihood that something will occur.When we don't know how an event will turn out, we can discuss the likelihood or likelihood of several outcomes.Statistics is the study of events that follow a probability distribution.

I clarify this because the question uses plural “drawing white socks”. Ok, in our language practice one does usually say socks instead of sock because they usually come in pair.

If it means 1 draw of 1 sock then the probability is 6out of 21. Or about 28.57%

But if it is to draw twice with one sock being drawn in each draw to get a pair of white socks then the probability is 6/21 * /20 = 30/420 = 1/14 or about 7.14%

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At the end of the first round, the total time is 648 seconds ( option E )

An average is the result that you get when you add two or more numbers together and divide the total by the number of numbers you added together.

For example, if there are 10 students in a class with ages 10, 11, 12, 10, 10,12,12,10,11,12 their average age will be( 10+ 11+12+10+10+12+12+10+11+12)/10

for Mariam her average time is 76 which means her total time is 76× 2= 152

for Jake and Rafael their average time is 84 which means their total time is 84×4= 336

for Sam,his average time is 80 which means is total time is 80×2= 160

therefore the total time spent by the 4 students is 152+336+160=648seconds

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Answer:

as shown in underline ^^

Step-by-step explanation:

Fill in the missing words:

When a solid mixes with a liquid and becomes part of the liquid it dissolves.

A solid that dissolves in a liquid is soluble.

A solid that does not dissolve in a liquid is insoluble.