Thompson and Thompson is a steel bolts manufacturing company. Their current steel bolts have a mean diameter of 145 millimeters, and a standard deviation of 6 millimeters. If a random sample of 39 steel bolts is selected, what is the probability that the sample mean would differ from the population mean by less than 0.5 millimeters

Triangle XYZ = UYW

We know that the 2 triangles are similar using angles Theorem

Let us find XZ to determine UY (for confirmation):

To determine XZ, use the Pythagorean Theorem:

[tex]a^{2} + b^{2} = c^{2} \\ OR\\leg^{2} +leg^{2} = Hypotenuse^{2} \\24^{2} + b^{2} = 26^{2} \\576+b^{2} =676\\b^{2} =100\\b=10[/tex]

You can see that XZ = WU

Now find UY= 26

Corresponding angles

Hope it helps!

Hello and Good Morning/Afternoon:

To find the slope of something:

  ⇒ let's consider what the formula of the slope needs

               [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

      ⇒ needs any two points on the line (x₁,y₁) and (x₂,y₂)

Let's get the required information:

Let's solve:

  [tex]Slope = \frac{2-0}{5-0} =\frac{2}{5}[/tex]

Answer: 2/5

Hope that helps!

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Using the given information, the value of Σfd is 800

From the question, we are to determine the value of Σfd

The formula for mean, using the assumed mean method is given by

[tex]\bar x = A + \frac{\sum fd}{\sum f}[/tex]

Where [tex]\bar x[/tex] is the mean

A is the assumed mean

From the given information,

[tex]\bar x = 80[/tex]

[tex]A = 60[/tex]

[tex]\sum f = 40[/tex]

Putting the parameters into the equation, we get

[tex]80 = 60 + \frac{\sum fd}{40}[/tex]

[tex]80-60 = \frac{\sum fd}{40}[/tex]

[tex]20 = \frac{\sum fd}{40}[/tex]

[tex]\sum fd = 20 \times 40[/tex]

[tex]\sum fd = 800[/tex]

Hence, the value of Σfd is 800

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The expression that represents the total amount earned last week $100 + $19t.

The expression is a function of the amount her friend paid for the photoshoot, the hours worked and the wages per hour.

Total pay = (amount earned per hour x total hours worked) + amount paid for photoshoot

($19 x t) + $100

$19t + $100

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It took 1.9 years to pay back the loan.

Interest is the amount of money given or received when a certain sum of amount is received as a loan or given or deposited for investment.

It is given that

Principal amount of loan = $ 8000

Interest paid = $ 600

Rate = 4%

Time Period = ?

Assuming Simple Interest has been applied

I = ( P* R* T) /100

600 = ( 8000 * 4 * T ) / 100

60000 = 8000 * 4 * T

T = 1.875 years

T = 1.9 years rounded to 1 decimal

T = 22.5 months

Therefore it took 1.9 years to pay back the loan.

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Answer: 3

Step-by-step explanation:

test the numbers

Answer:

3

Step-by-step explanation:

first you divide the given number with 11 the remainder you get substract in order to get 0

The probability that a person wins the game is 32.1%

Based on the information given, the following can be depicted. It should be noted that there are 6 sides as well as 4 cards.

Therefore, the numbers on the dice i.e from 1 - 6 will be represented 4 times each. This gives a total of (4 × 6) = 24. There are also 4 cards. The total in sample space will now be:

= 24 + 4 = 28

The frequency table will be such that 28 or more have a relative frequency of 9. Therefore, the probability that a person wins the game will be:

= 9/28 = 32.1%

When you win 25% of the time, this illustrates that the number of products picked will be:

= 25% × 28

= 7 products.

The probability of participants achieving a winning score of 36 or higher in four consecutive attempts will be:

= 1/6⁴ = 1/1296

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Answer:

[tex]\frac{x-3}{2x-3}[/tex]. hole or removable discontinuity at x=2

Step-by-step explanation:

Well generally if you want the simplest form, you factor each the denominator and numerator and then see if you can cancel any of the factors out (because they're in the denominator and numerator)

So let's start by factoring the first equation:

[tex]x^2-5x+6[/tex]

Now let's find what ac is (it's just c since a=1...)

[tex]AC= 6[/tex]

List factors of -6

[tex]\pm1, \pm2, \pm3, \pm6[/tex].

Now we have to look for two numbers that add up to -5. It's a bit obvious here since there isn't many factors, but it's -2 and -3, and they're both negative since 6 is positive, and -5 is negative...

So using these two factors we get

[tex](x-2)(x-3)[/tex]

Ok now let's factor the second equation:

[tex]2x^2-7x+6[/tex]

Multiply a and c

[tex]AC = 12[/tex]

List factors of 12:

[tex]\pm1, \pm2, \pm3, \pm4, \pm6, \pm12[/tex].

Factors that add up to -7 and multiply to 12:

[tex]-3\ and\ -4[/tex]

Rewrite equation:

[tex]2x^2-4x-3x+6[/tex]

Group terms:

[tex](2x^2-4x)+(-3x+6)[/tex]

Factor out GCF:

[tex]2x(x-2)-3(x-2)[/tex]

Rewrite:

[tex](2x-3)(x-2)[/tex]

Now let's write out the equation using these factors:

[tex]\frac{(x-2)(x-3)}{(2x-3)(x-2)}[/tex].

Here we can factor out the x-2 and the simplified form is:

[tex]\frac{x-3}{2x-3}[/tex]

So we can "technically" define f(2) using the most simplified form, but it's removable discontinuity, so it has a hole as x=2. since it makes (x-2) equal to 0 (2-2) = 0.

Answer:

The product is the difference of squares is [tex]$$\left(9c+5\right)\left(9c-5\right)=81{{c}^2}-25$$[/tex]

Step-by-step explanation:

Explanation

[tex]$$\begin{aligned}&(9 c+5)(9 c-5)=(9 c)^{2}-(5)^{2} \\&(9 c+5)(9 c-5)=81 c^{2}-25\end{aligned}$$[/tex]

The maximum amount of supplies that the storage unit can hold is 28 ft³

For us to calculate the volume or amount of space in Evan's prism, we will first of all calculate the volume of rectangular prisms. Formula is;

V = Length × width × height.

We are given;

length = 4 feet

width =  3.5 feet

height of the prism = 2 feet.

Thus;

V = 4 * 3.5 * 2

V = 28 ft³

Thus, the maximum amount of supplies that the storage unit can hold is 28 ft³

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The surface area of the right cone is 602.88 inch².

Given,

        length of radius of the base is = 8 inches

                          the slant height is  =16 inches.

Now using formula ,

the surface area of right circular cone is a right circular cone = πr(r + l)

So,    r = 8 inches  l = 16 inches

put values in  the formula ,

             surface area of right circular cone = 3.14 × 8 ( 8 + 16 )

                                                                       = 3.14 × 8 × 24

                                                                       = 602.88 inch²

Therefore, the surface area of the right cone is 602.88 inch².

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The equation of the line of best fit is y = 50x/3

The missing graph is added as an attachment

From the graph, we have the following points

(x, y) = (0,0) and (3,50)

The equation is then calculated as:

y = (y2 - y1)/(x2 - x1) * (x - x1) + y1

This gives

y = (50 -0)/(3- 0) * (x - 0) + 0

Evaluate

y = 50x/3

Hence, the equation of the line of best fit is y = 50x/3

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And

Answer:

x = 7.41 (nearest hundredth)

y = 9.53 (nearest hundredth)

Step-by-step explanation:

Trigonometric ratios

[tex]\sf \sin(\theta)=\dfrac{O}{H}\quad\cos(\theta)=\dfrac{A}{H}\quad\tan(\theta)=\dfrac{O}{A}[/tex]

where:

From inspection of the triangle:

To find x, use the tan trigonometric ratio:

[tex]\implies \tan 39^{\circ}=\dfrac{6}{x}[/tex]

[tex]\implies x=\dfrac{6}{\tan 39^{\circ}}[/tex]

[tex]\implies x=7.409382939...[/tex]

Therefore, x = 7.41 (nearest hundredth)

To find y, use the sin trigonometric ratio:

[tex]\implies \sin 39^{\circ}=\dfrac{6}{y}[/tex]

[tex]\implies y=\dfrac{6}{\sin39^{\circ}}[/tex]

[tex]\implies y=9.534094374...[/tex]

Therefore, y = 9.53 (nearest hundredth)

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Thus, the rate of change per gallon of gas is 60 miles per gallon.

A motorcycle consumes 5 gallons of gas for 300 miles and 7 gallons for 420 miles.

Rate of change is defined as the change in value with rest to the time is called rate of change.

Now,

Rate of change = Difference B/w volume (i.e. in gallons)  /difference in miles
= 420-300/7-2
= 60 gallons/mile

Thus, The required rate of change per gallon of gas is 60 miles per gallon.

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Answer:

Step-by-step explanation:

Please post a picture of the triangle and the choices.

Answer:

option B is correct.

Explanation:

[tex]\sf Equation : y-4\ =-\frac{2}{3}\left(x+3\right)[/tex]

[tex]\sf \rightarrow y\ =-\frac{2}{3}x-2 + 4[/tex]

[tex]\sf \rightarrow y\ =-\frac{2}{3}x + 2[/tex]

comparing it with slope intercept form "y = mx + b'' where m is slope and b is y-intercept.

Here slope: -2/3 and y-intercept: 2

This means the slope is decreasing and has crosses the y axis at (0, 2)

Answer:

a reflection in the line y=x

Step-by-step explanation:

The inverse relation of an equation is when the x and y are swapped. For this reason it's going to be reflected over the y=x line. You can also use an online graphing tool to show this as well:

Answer:

3√2

Step-by-step explanation:

In a 45-45-90 triangle, the two legs are the same length while the hypotenuse is √2 times larger.

3*√2 = 3√2

The equation regarding the algebraic information that represents the total earnings is y = 22x + 125.

From the information that's given, it can be seen that the expression is:

y = 22x + 125

She earned $555 after working for 15 hours. Therefore, the equation to represent the total earnings will be:

y = 22x + 125.

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1. x = a

2. y = b

3. The slope of a vertical line is undefined..

4. Change in y/change in x (m) or rise/run

5. Rewrite the equation in slope-intercept form to find the value of the y-intercept. The value of x will always be 0.

The equation, y = mx + b, in slope-intercept form, defines a line, where m is the slope and the y-intercept = b.

1. Slopes of vertical lines are always undefined, therefore, for a vertical line that contains (a, b), the equation would be: x = a.

2. Horizontal lines have a slope of 0, therefore, the equation of a horizontal line that contains the point, (a, b), will  be: y = b.

3. The slope of a vertical line is undefined.

4. Two ways of finding the slope if we are given two points on a line are:

Change in y/change in x (m) = y2 - y1 / x2 - x1

or

rise/run

5. If we have an equation in point-slope form, for example, y - 2 = 2(x - 4), rewrite the equation in slope-intercept form and find the value of the y-intercept:

y - 2 = 2x - 8

y = 2x - 8 + 2

y = 2x - 6

The y-intercept = -6, therefore, the coordinates of the y-intercept would be: (0, -6).

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The missing information in the proof is a which is option A.

Given d is the mid point of ab and e is the mid point of ac. Coordinates are point a (2b,2c), point e (ab, c), point c (2a, 0),point b (0,0), point d (b, c).

We have to find the missing proof in the solution.

To find the missing figure we have to just find the distance between point d and point e.

Distance formula for determining the distance between two points on a coordinate plane is given as :

d=[tex]\sqrt{(y_{2} -y_{1} )^{2} +(x_{2} -x_{1} )^{2} }[/tex]

where ([tex]x_{1} ,y_{1} ) (x_{2} ,y_{2} )[/tex] are the coordinates at the end of line.

DE=[tex]\sqrt{(a+b-b)^{2} +(c-c)^{2} }[/tex]

Simplifying this we get:

DE=[tex]\sqrt{(a^{2} +0^{2} }[/tex]

=[tex]\sqrt{a^{2} }[/tex]

=a

Hence the missing proof is a which is the distance or length of DE..

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Answer:

8

Step-by-step explanation:

Midpoint means half point of a certain shape. This means that if all the points of OPQ are midopoints of the bigger triangle, then OPQ has to be half the size of the big triangle. There are two ways to figure this out. The first way is to add all the numbers up to find the perimeter of the big triangle (6+6+4) which is 16. Then, you can do 16/2 to get the perimeter of the smaller triangle which is 8. The other method is to take each value of the bigger triangle and divide them by 2 (6/2, 6/2, 4/2). When you do that, you get (3, 3, 2). Now, you just add those values (3+3+2) which gets you 8 gor the smaller triangle. I hope this helps!

The coordinate of point R is 11/40, so the correct option is C.

On the number line we can see that:

M = -1/4

T = 5/8

There are 5 segments between T and M, and the difference between T and M is:

5/8 - (-1/4) = 5/8 + 2/8 = 7/8

The measure of each segment will be equal to:

m = (7/8)/5 = 7/(8*5) = 7/40

Now, coordinate R is 2 segments to the left of T, so the coordinate of point R is given by:

R = 5/8 - 2*(7/40)

R = 25/40 - 14/40 = 11/40

The correct option is C.

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Answer: 7) Step 1 8) Step

Step-by-step explanation:

The answer to 7 is 11. The error starts in step 1, as you can see youre supposed to do 8 divided by 2 plus 3 times 3 minus 2, instead it seems like 3+3 were added instead of becoming 9 thus the answer becomes 7.

The answer to 8 is also 11. 18-14/2 is 11.

Answer: 14.79

Step-by-step explanation:

[tex]\frac{b}{\sin B}=\frac{a}{\sin A}\\\\a=\frac{b \sin A}{\sin B}\\\\a=\frac{23 \sin 40^{\circ}}{\sin 88^{\circ}}\\\\a \approx 14.79[/tex]

The value of f(19) in the given equation is 55.

The function of a linear equation illustrates a straight line graph and for a given set of input into the function, there is usually a specific output.

Given that:

We are to find the f(x) = 19.

So;

f(19) = 3(19) - 2

f(19) = 57 - 2

f(19) = 55

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Answer:

(-4,-3)

Step-by-step explanation:

Just check each vertex point and move them by instruction, write them down and do elimination and you'll find the answer

Answer:

The population in year 2014 is 41100.

Step-by-step explanation:

In the question, it is given that the city's population is growing linearly. In 2008 , population was 28200 and in 2012 , it is 36800 .

It is required to predict the population in 2014 .

To do so, use the population given in two years as two points on a line and find the equation of population and year. Then, find the population in year 2014 .

Step 1 of 2

The population in 2008 was 28200 and in 2012 it was, 36800 .

The equation relating population and year is,

[tex]$$\begin{aligned}&y-28200=\left(\frac{36800-28200}{2012-2008}\right)(x-2008) \\&y-28200=\left(\frac{8600}{4}\right)(x-2008) \\&y-28200=2150(x-2008)\end{aligned}$$[/tex]

Step 2 of 2

The population in year 2014 can be determined by substituting 2014 for x,

[tex]$$\begin{aligned}&y-28200=2150(2014-2008) \\&y-28200=2150(6) \\&y-28200=12900 \\&y=41100\end{aligned}$$[/tex]

[tex]y=78^{\circ}[/tex] (alternate interior angles theorem)

[tex]x=78^{\circ}[/tex] (alternate segment theorem)

[tex]z=24^{\circ}[/tex] (angles in a triangle add to 180 degrees)