The blueprint specifications for a machined part call for its thickness to be 3.145 in.

with a tolerance of +-0.010 in. Find the limit dimensions of the part?

Answer:

[tex]A_{new}=(-3,0)\\B_{new}=(0,-1)\\C_{new}=(1,-4)\\D_{new}=(-3,-5)[/tex]

Step-by-step explanation:

Looking at the diagram, you can see and determine the following points, write them down:

A=(-1,4)

B=(2,3)

C=(3,0)

D=(-1,-1)

Translating 2 units left means x changes by (-2)

Translating 4 units down means y changes by (-4)

Old Point + Point Change = New Point

[tex]A_{old}+T=A_{new}\\A_{old}=(-1,4)\\T=Translation=(-2,-4)\\A_{old}+T=(-1,4)+(-2,-4) = A_{new}=(-3,0)[/tex]

[tex]B_{old}=(2,3)\\C_{old}=(3,0)\\D_{old}=(-1,-1)\\T=(-2,-4)\\B_{new}=(2,3)+(-2,-4)=(0,-1)\\C_{new}=(3,0)+(-2,-4)=(1,-4)\\D_{new}=(-1,-1)+(-2,-4)=(-3,-5)[/tex]

The distance from the fence to the edge of the garden using the center as reference point is 4 1/2 feet.

Given data

garden 14 1/2 feet long and 8 3/4 feet wide

Fence 23 1/2 feet long and 17 3/4 feet wide

We assume:

the fence has no thickness,

the distance considered is in the side of the length

the reference point for the distance is the center

Therefore:

Using the mid points we solve as follows:\

garden length / 2 - fence length / 2

= ( 23 1/2 ) / 2 - ( 14 1/2 ) / 2

= 11.75 - 7.25

= 4.5

= 4 1/2 feet

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Step-by-step explanation:

that's why it is so important to always write also the units a number represent.

and for a fully nice scientific notation you write also at least 1 digit after the decimal point.

(a) 6.0 × 10²⁴ kg

(b) 4.0 × 10² g

now,

1 kg = 1000 g ("kilo" means 1000)

so, in order to be able to compare the 2 numbers, you have to bring both numbers to the same unit. either both to kg or both to g.

6.0 × 10²⁴ kg = 6.0 × 10²⁴ × 1000 g = 6.0 × 10²⁷ g

or

4.0 × 10² g = 4.0 × 10² / 1000 kg = 4.0 × 10^-1 kg

once you have both showing the same unit, you can truly compare them.

The two numbers that you would subtract to find the interquartile range (IQR) of the set of values are: A. 22 - 18.

The interquartile range (IQR) = Upper quartile (Q3) = lower quartile (Q1).

Given the data set, 17, 21, 19, 23, 16, 22, 19, 20, 24, 18, we have the following:

Upper quartile (Q3): 22 (center of the second half of the data)

Lower quartile (Q1): 18 (the middle/center of the first part of the data)

Interquartile range (IQR) = 22 - 18

Interquartile range (IQR) = 4

Therefore, the two numbers that you would subtract to find the interquartile range (IQR) of the set of values are: A. 22 - 18.

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One person took a loan A monthly payment is $530.65. An interest rate is 5.90%. APR is over 29 years. The present value of a loan is 100.69.

Given that,

One person took a loan

A monthly payment is $530.65

An interest rate is 5.90%

APR is over 29 years.

We have to find the present value of a loan

The formula for present value of a loan is

The present value (PV) formula is used in finance to determine the present worth of money received in the future. The compound interest formula serves as the foundation for the present value formula (PV formula). The formula for compound interest is,

PV = [tex]\frac{FV}{(1+\frac{r}{n)} ^{nt}}[/tex]

Where,

PV=present value

FV=future value

r= rate of interest

n=When frequently the amount compounds

t=time

Given FV=$530.65

r= 5.90% =0.059

t=29 years

n=1(Due to the amount's annual compounding).

PV=[tex]\frac{530.65}{(1+\frac{0.059}{1})^{1\times29} }[/tex]

PV=[tex]\frac{530.65}{(1+0.059)^{29}}[/tex]

PV=[tex]\frac{530.65}{(1.059)^{29}}[/tex]

PV=[tex]\frac{530.65}{5.27}[/tex]

PV=100.69

Therefore, The present value of a loan is 100.69.

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A number in which value of 3 is ten times greater than the value of 3 is 375,786.

Here,

We have to find a number in which the value of the 3 is ten times greater than the value of the 3 in 135,864.

What is Place value?

Place value can be defined as the value represented by a digit in a number on the basis of its position in the number.

Now,

The value of 3 in 135,864 is 30,000.

And, We want to write a number that is ten times greater than 30,000.

Hence, We have to write any other number in which the value of 3 is 300,000.

Since, There are infinitely many numbers that we can write.

Some numbers are:

375,786

2,345,576

9,387,988  ........  and so on.

Therefore, A number in which value of 3 is ten times greater than the value of 3 is 375,786.

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Answer:

area is 3.14 r2

Step-by-step explanation:

here r = 5 inch

area = 3.14 × 25

so 78.5 in2

Answer:

B) x ≥ –2 or x < 5

Step-by-step explanation:

We can immediately rule out A) All real numbers, since that will almost never be true for an inequality like this. We can also rule out C) 2 ≤ x < 5, since this is not a compound inequality.

Let's see if B) x ≥ –2 or x < 5 works by plugging in an x value greater than -2 and then, plugging in an x value less than 5.

Plug -1 into x

–4(-1) + 1 ≤ 9

4 + 1 ≤ 9

Combine like terms

5 ≤ 9

This is true, 5 is less than 9, so x ≥ –2 works.

Plug 4 into x

4∕5 + 2 < 3

Combine like terms

2.8 < 3

This is true, 2.8 is less than 3.

It can't be D) no solution now that B works, so B) x ≥ –2 or x < 5 is your answer.

Take care and Have a lovely rest of your day! :)

Answer:

15-(6+7)

Step-by-step explanation:

Answer:

15 - (6+7)

Step-by-step explanation:

The scientist should use 90 ounces of 35 percent solution and 120 ounces of water.

Percent is defined as the amount for a hundred units. Percentage is calculated by dividing the given amount by the total amount and multiplying by 100.

Let the scientist uses x ounces water.

Therefore the 35 percent solution is 210 - x.

Therefore the amount of salt in the 35 percent solution is 0.35 (210 - x )

The resulting mixture contains 15 percent salt.

Amount of salt = 15% of 210 =0.15 × 210 = 31.5 ounces.

Now 31.5 = 0.35 ( 210 - x )

or, 90 = 210 - x

or, x = 120 ounces

Therefore the 35 percent solution needed = 210 - 120 =90 ounces

Hence the scientist should use 90 ounces of 35 percent solution and 120 ounces of water.

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Answer:

  $2367

Step-by-step explanation:

You want to know how to figure the 12% tax due on the amount that falls in the bracket $9876 to 29600.

Tax tables are often written in a somewhat misleading way. This one seems to tell you

  0 to 9875 . . . . 10% tax rate

  9876 to 29600 (and up to 40,125) . . . . 12% tax rate

What this means is that every dollar between (and including) the 9876th dollar and the 29600th dollar will have a $0.12 tax applied. It is figured by subtracting 9875 from the amount that falls in this bracket, and multiplying that difference by 12%.

  (29600 - 9875) × 12%

  = 19725 × 0.12

  = 2367 . . . . . . . . tax due on the amount in the 9876 to 29600 bracket

If your taxable amount is $29,600, the total tax due is ...

  (amount in first bracket) × 10% + (amount in second bracket) × 12%

  = 9875 × 0.10 + (29600 -9875) × 0.12

  = 987.50 +2367.00

  = $3,354.50 . . . . . . . . . . . total due on $29,600

__

Additional comment

It can be easier to write a new tax table that simplifies the computation. For taxable amounts up to $40,125, this table can be simplified to ...

Using this last entry for $29,600, we find the total tax due to be ...

  $29,600 × 0.12 - 197.50

  = $3,552.00 -197.50

  = $3,354.50 . . . . . . . same as above.

The amount $197.50 is (12% -10%)×9875.

Along the same lines, the rest of the tax table can be simplified to ...

It turns out that the tax due is the maximum of the values computed using these equations. (You don't actually have to know what bracket applies to your income. Knowing the bracket does simplify the process by choosing the applicable formula.)

Note that this is a tax table for 2020. The rates for 2021 are different.

Using the continuity concept, the functions are classified as follows:

1) Continuous.

2) Continuous.

3) Discontinuous.

A function f(x) is continuous at x = a if it is defined at x = a, and:

[tex]\lim_{x \rightarrow a^-} f(x) = \lim_{x \rightarrow a^+} f(x) = f(a)[/tex]

For functions 1 and 2, the functions are given by simple definitions, hence they are continuous, the limits and the numeric value will al be equal.

In item 3, the function will be discontinuous. This is because the function [x] returns the greatest integer less than x, hence:

Thus:

Due to different lateral limits, the function is not continuous at x = 2.

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The number sentence is 5 - 7 and temperature at midnight is equal to -2°F .

What is algebra ?

Algebra is a branch of mathematics that deals with various symbols and the arithmetic operations such as addition , subtraction , etc.

The temperatures are given at different time of a day. It is given that the final temperature was the temperature that existed at midnight. Firstly temperature rise between 6 AM and 3PM by 11° from - 6 °F at 6 AM and then between 3PM and midnight it fell by 7°.

So , we can show these variations as follows :

At 6AM temperature = - 6 °F

Between 6AM and 3 PM temperature rose by 11° , so temperature at 3 PM will be :

= - 6 + 11

= 5 °F

Between 3PM and midnight the temperature fell by 7° , so the number sentence will be :

= 5 - 7

And the temperature at midnight will be :

= -2°F

Therefore , the number sentence is 5 - 7 and temperature at midnight is equal to -2°F .

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The distance of Neptune from the sun than Mercury will be B. Subtract the distances by getting the same power of 10: (4.5 x 10^10) - (5.8 x 10^7)-(4.5 x 10^10)-(.0058 x 10^10) = 44.99 x 10/10km.

From the information, Mercury is 5.8 x 10^7 km from the sun and Neptune is 4.5 x 10^10 km from the sun.

It should be noted that since we want to find the difference, therefore, we've to subtract.

Therefore, distance of Neptune from the sun than Mercury will be Subtract the distances by getting the same power of 10: (4.5 x 10^10) - (5.8 x 10^7)-(4.5 x 10^10)-(.0058 x 10^10) = 44.99 x 10/10km.

In conclusion, the correct option is B.

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Answer:

x = 2 - 5[tex]\sqrt{3}[/tex], x = 2 + 5[tex]\sqrt{3}[/tex]

Step-by-step explanation:

x² - 4x = 71

to complete the square

add ( half the coefficient of the x- term )² to both sides

x² + 2(- 2)x + 4 = 71 + 4

(x - 2)² = 75 ( take the square root of both sides )

x - 2 = ± [tex]\sqrt{75}[/tex] = ± 5[tex]\sqrt{3}[/tex] ( add 2 to both sides )

x = 2 ± 5[tex]\sqrt{3}[/tex]

then

x = 2 - 5[tex]\sqrt{3}[/tex] , x = 2 + 5[tex]\sqrt{3}[/tex]

To find the average height over each coaster, we must first add the height of each one together

109+135+115+365+126 = 850

Now divide 850 by the total amount of coasters, 5

850
-------     =  170 Feet
 5

Since the amusement park claimed their average height was 170 ft, it is not misleading. It is a good strategy because it is an honest statistic, which gives the amusement park more liability.

Answer:

18/5 which also equals 3 3/5 would be the answer

Answer:

140

Step-by-step explanation:

→ Find an expression for the area

6x × x = 6x²

→ Equate to area

6x² = 600

→ Solve

x = 10

→ Find length and width

Length = 60 and width = 10

→ Find perimeter

60 + 60 + 10 + 10 = 140

Step-by-step explanation:

you can ask questions for clarification

The coordinate of B is (1,-3)

In coordinate system mid point is the point which is exactly at the middle

The coordinates of point A are (5,1)

The coordinate of  mid point M are (3,-1)

It is to be noted that mid point divides both sides in the ratio 1:1

We are required to find the coordinates of point B

Let the coordinates of B be (x,y)

For mid points, section  formula further simplifies to

m's x coordinate= (a's x coordinate + b's x coordinate)/2

m's y coordinate = (a's y coordinate + b's y coordinate)/2

therefore,

3 = (5+x)/2

6=5+x

x=6-5 =1

-1 = (1+y)/2

-2 =1+y

y=-3

Hence the coordinates of B are (x,y) which is (1,-3)

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Answer:

  10.770

Step-by-step explanation:

You want the distance between points (-12,20) and (-22,16) using the distance formula.

The distance formula gives you the distance (d) between points (x1, y1) and (x2, y2).

  d = √((x2 -x1)² +(y2 -y1)²)

For the given points, the distance is ...

  d = √((-22-(-12))² +(16 -20)²) = √((-10)² +(-4)²) = √(100+16)

  d = √116 = 2√29 ≈ 10.770330

The distance between the given points is about 10.77 units.

Answer:

Answer for this question is C because, 1 input has 2 outputs. And that's why C doesn't represent a function.

The coordinates of the midpoint M of the line segment VW are M = (5, 6)

In this question,

We have been given a line segment having endpoints V(7, 2) and W(3, 10)

We need to find the coordinates of the midpoint M of the line segment VW.

We know that the midpoint of points (x1, y1) and (x2, y2) is

M = (x1 + x2 / 2, y1 + y2 / 2)

Using midpoint formula,

M = ((7 + 3) / 2, (2 + 10) / 2)

M = (10/2, 12/2)

M = (5, 6)

Therefore, the coordinates of the midpoint M of the line segment VW are M = (5, 6)

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The missing values are x = 45, t = 90, n = 60, p = 75, m = 30, s = 15, k = 135, w = 30, f = 60 and y = 45.

Herein we have a geometrical system formed by six triangles, one of them is a equilateral triangle and other one is a right triangle. By geometry we know that the sum of the measures of a triangle is equal to 180°, the angles in a equilateral triangle have the same measure and one of the angles in a right triangle is a right angle.

Then, we have following system of linear equations:

t = 90                              (1)

t + 2 · x = 180                  (2)

3 · n = 180                       (3)

2 · p + m = 180                (4)

p + f + y = 180                 (5)

(t + 5) + w + n = 180        (6)

s + k + m = 180                (7)

x + n + p = 180                (8)

f + w = 90                        (9)

m + n = 90                      (10)

p + s = 90                        (11)

By (1) and (2):

x = 45

By (3):

n = 60

By (8):

p = 180 - 45 - 60

p = 75

By (4):

m = 180 - 2 · 75

m = 30

By (11):

s = 90 - 75

s = 15

By (7):

k = 180 - 15 - 30

k = 135

By (6) and (1):

w = 180 - 60 - 90

w = 30

By (9):

f = 90 - 30

f = 60

By (5):

y = 180 - 75 - 60

y = 45

The missing values are x = 45, t = 90, n = 60, p = 75, m = 30, s = 15, k = 135, w = 30, f = 60 and y = 45.

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Similar triangles are triangles which have the same corresponding angle measures and proportional side lengths. The value of x is 17.5.

Similar triangles are triangles which have the same corresponding angle measures and proportional side lengths.

Let PQ be the line between RS and RT.

Now PQR and RST are similar triangles.

RT/RP=RS/RQ

14/8=x/10

Use cross multiplication

14(10)=8x

140=8x

Divide both sides by 8.

17.5=x

Therefore x is 17.5.

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A line segment has two endpoints, whereas a ray has one endpoint and extends infinitely in the other direction, and a line extends infinitely in both directions.

The image of the transformation on the graph are (7, -7), (7, -2) and (-1, -14)

The graph represents the given parameter

On the graph, we have the coordinates of the triangle to be

(3, 1), (3, 6) and (-5, -6)

The transformation rule is given as

Translated 4 units to the right, and 8 units down.

Mathematically, the transformation rule is given as

(x, y) = (x + 4, y - 8)

When the above transformation rule is applied to the coordinates of the triangle, we have

(3 + 4, 1 - 8), (3 + 4, 6 - 8) and (-5 + 4, -6 - 8)

Evaluate the sum and the difference

So, we have

(7, -7), (7, -2) and (-1, -14)

Next, we plot the image of the transformation on the graph

See attachment for the image of the transformation of the triangle on the graph

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The length of the rectangular wall of a barn is 7 and the width is 17 feet

Area of the rectangular wall of a barn = 119 square feet

Length of the wall of the barn = width of barn + 10 feet

Let the width of the wall of the barn be x feet

So, the length of the wall of the barn will be x + 10 feet

The area of the rectangular wall of the barn is given by:

Area of the rectangular wall of the barn = Length of the barn * Width of the barn

119 = x*(x+10)

119 = x^2 +10x

0 = x^2 +10x - 119

Using splitting the middle term method

0 = x^2 + 17x - 7x - 119

0 = x(x + 17) - 7(x + 17)

x = 17 or 7.

Since the width is 10 feet more than the length

Therefore, the length of the rectangular wall of a barn is 7 and the width is 17 feet

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Answer:

Option A

Step-by-step explanation:

When adjacent sides and angle between the adjacent sides are given, then,

 [tex]\sf \boxed{\text{\bf Area of Parallelogram = a*b * $Sin \ \theta$}}[/tex]

Here, a and b are the adjacent sides and [tex]\sf \theta[/tex] is the angle between them.

a = 16 cm ;  b = 30 cm ; [tex]\sf \theta = 45^\circ[/tex]

Area of parallelogram =  16 * 30 * Sin 45

                                     [tex]\sf = 16 * 30 * \dfrac{\sqrt{2}}{2}\\\\= 8*30*\sqrt{2}\\\\= 240\sqrt{2} \ sq.cm[/tex]

Answer:

a) 0

b) 1000

Step-by-step explanation:

revenue = R = 9x

cost = C = 3x + 6000

profit = P = R - C

(a)

P = R - C

P = 9x - (3x + 6000)

P = 9x - 3x - 6000

P = 6x - 6000

For 1000 pens, x = 1000.

P = 6(1000) - 6000

P = 6000 - 6000

P = 0

Answer: 0

(b)

R = C

9x = 3x + 6000

6x = 6000

x = 6000/6

x = 1000

Answer: 1000