The diameter of the lead in a pencil p must be within 0.01 millimeters of 1 millimeter

Part a: translation: (x,y) ---> (x + 1, y - 8); D'(3, -1), E'(8, -2),  F'(4, -8), G'(-1, -7).

Part b: reflection : in the x axis :D'(2,-7), E'(7,-6), F'(3,0) and G'(-2,-1).

In geometry, a translation is a transfer that occurs either laterally to the left or right as well as vertically up or down.

It may also consist of a mix of the two. Instead, you should evaluate the coordinates of the important locations in the first and second figures if you need must describe a translation. The number of units that have been moved horizontally, vertically, and in which directions are noted verbally.

Given that:

Part a: translation: (x,y) ---> (x + 1, y - 8)

D(2,7) -> D'(2 + 1, 7 - 8) = D'(3, -1)

E(7,6) -> E'(7+ 1,6- 8) = E'(8, -2)

F(3,0) -> F'(3+ 1,0- 8)  = F'(4, -8)

G(-2,1) -> G'(-2+ 1,1- 8) = G'(-1, -7)

Thus, the coordinates of D'E'F'G' -  D'(3, -1), E'(8, -2),  F'(4, -8), G'(-1, -7).

Part b: reflection : in the x axis

vertices D(2,7), E(7,6), F(3,0) and G(-2,1).

value of x will remain same, but y get negative.

(x,y) -- (x, -y)

D'(2,-7), E'(7,-6), F'(3,0) and G'(-2,-1).

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Correct question:

Parallelogram DEFG with vertices D(2,7), E(7,6), F(3,0) and G(-2,1):

a: translation: (x,y) ---> (x + 1, y - 8)

b: reflection : in the x axis

Answer:

scale factor = [tex]\frac{1}{2}[/tex]

Step-by-step explanation:

the side corresponding to WX is EH

the scale factor is the ratio of corresponding sides, image to original, so

scale factor = [tex]\frac{EH}{WX}[/tex] = [tex]\frac{2}{4}[/tex] = [tex]\frac{1}{2}[/tex]

A Organic shape is one that does not have an identifiable name. While still flat, 2-D enclosed areas, these shapes are more "freeform" and might resemble things that we see in nature.

Geometric shapes are well-defined, regular shapes described by mathematical formulas, including circles, squares, triangles, and rectangles. Symmetrical shapes exhibit mirror-like symmetry, like butterflies or snowflakes.

Organic shapes  appear in natural objects like leaves or rocks; they are flowing and curvilinear in form, with varying size, proportions, and contours. Organic shapes are free from strict rules and symmetry, often used in art.

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You have to apply the outside exponent to each piece inside the parentheses.

[tex]\begin{aligned}\left(2a^2\right)^3 &=(2)^3\cdot\left(a^2\right)^3\\[0.5em]&=8 a^6\end{aligned}[/tex]

You have to apply the outside exponent to each piece inside the parentheses.

[tex]\begin{aligned}\left(2a^2\right)^3 &=(2)^3\cdot\left(a^2\right)^3\\[0.5em]&=8 a^6\end{aligned}[/tex]

Answer:

f = -15

Step-by-step explanation:

Use algebra to solve!

f/3 + 22 = 17

f/3 = 17 - 22 (bring 22 to the other side, this changes the sign from plus to minus)

f/3 = -5 {because 17-22 = (-5)}

f = (-5) (3) {to eliminate 3 from the denominator of f, you do the opposite of division which is multiplication, so -5 times 3}

therefore, f = -5

You can also check this answer by putting it back into the original equation, -15/3 is -5 and then -5 + 22 = 17.

Step-by-step explanation:

The narrowest definition of the number -2 is that it is an integer that is less than zero and has an absolute value of 2. In other words, it is the additive inverse of the number 2, and can be written as "-2 = -1 * 2".

Answer:

[tex]\frac{15}{(x-7)*(x+3)} = \frac{3/2}{x-7} + \frac{-3/2}{x+3}[/tex]

Step-by-step explanation:

Set up the partial fraction decomp:

[tex]\frac{15}{(x-7)*(x+3)} = \frac{A}{x-7} + \frac{B}{x+3}\\[/tex]

Multiply across:

[tex]15 = (\frac{A}{x-7} + \frac{B}{x+3})*(x+3)*(x-7)\\15 = A(x+3) + B(x-7)\\[/tex]

You can do this two ways from this point, you can plug in values for x to solve for A and B individually or set up a system of equations to find A and B

[tex]15 = Ax + 3A + Bx -7B\\Ax + Bx = 0\\3A - 7B = 15\\[/tex]

From the first equation we can see that A = -B, plugging into the second equation we get that

-10B = 15, so therefore B = -3/2 and because of the first equation A = 3/2 giving us our answer

Area of a circle is given by

[tex]\text{A} = \pi \times r^2[/tex]

We need to know the radius

[tex]\text{r} = \dfrac{\text{d}}{2}[/tex]

[tex]\text{r} = \dfrac{\text{74}}{2}[/tex]

[tex]\text{r} = 37 \ \text{mm}[/tex]

The radius is 37 mm and pi = 3.14

[tex]\text{A} = 3.14 \times (37)^2[/tex]

[tex]\text{A} = \boxed{\bold{4298.66 \ \bold{mm}^2}}[/tex]

a) The vector parametric equation for the helical path is r(t) = <28cos(12πt), 28sin(12πt), 5t*12>, where t is the parameter and 0 ≤ t ≤ 1.

b) You walked a total distance of 840π feet.

a) To find the vector parametric equation for the helical path, we first note that the spiral staircase makes 6 complete revolutions as we climb from the bottom to the top. This means that as we climb 60 feet, we will make 6 full revolutions around the z-axis. Since the radius of the spiral is 28 feet, we can use the equation for a helix to describe our path.

r(t) = <28cos(θ), 28sin(θ), ht>

where θ is the angle of rotation around the z-axis and h is the height we have climbed. We know that we make 6 full revolutions, or 12π radians, as we climb from the bottom to the top, so we can substitute θ = 12πt. We also know that we climb 60 feet in one hour, so our height function is h(t) = 5t*12.

Thus, our vector parametric equation for the helical path is r(t) = <28cos(12πt), 28sin(12πt), 5t*12>, where t is the parameter and 0 ≤ t ≤ 1.

b) To find the distance we walked, we need to integrate the magnitude of the velocity vector over the interval [0,1].

The velocity vector is the derivative of the position vector:

v(t) = < -336πsin(12πt), 336πcos(12πt), 60>

The magnitude of the velocity vector is:

|v(t)| = sqrt((-336πsin(12πt))^2 + (336πcos(12πt))^2 + 60^2) = 336π

Thus, the distance we walked is:

distance = ∫|v(t)|dt from 0 to 1 = ∫336π dt from 0 to 1 = 336π(1-0) = 336π

Therefore, we walked a total distance of 840π feet.

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The area of the shaded region on the actual triangle is: 2/16 = 1/8 inches²

So the answer is (B) 1/8 inches².

The size of a two-dimensional surface or region, such as a floor's surface, a painting's face, or the contours of a piece of land, is measured in terms of area.

It represents the amount of space that is enclosed or occupied by the surface or region under consideration and is typically measured in square units, such as square metres or square feet.

The area of the shaded region on the actual triangle is related to the area of the shaded region on the map by the square of the scale factor. In this case, the scale factor is 1 inch = 1/4 square inches, so the square of the scale factor is:

(1/4)² = 1/16

This means that the area of the shaded region on the actual triangle is 1/16th the area of the shaded region on the map.

The area of the shaded area on the map is 2 inches², matching the area of the triangle on the map, which is 2 inches²

Therefore, the shaded area on the actual triangle has the following area:

2/16 = 1/8 inches².

Therefore, the response is (B) 1/8 inches².

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Option B is the correct answer: chocolate-peanut butter cups and chocolate-caramel bites.

Xzavier should choose the two candies with the highest price per pound to maximize his spending.

The prices per pound are as follows:

$13.88 for chocolate-covered cashews

$11.46 for chocolate-covered peanut butter cups

$9.62 for Chocolate-Caramel Bites

$8.24 for Gourmet Gummy Bears

Chocolate-covered Cashews and Chocolate-Peanut Butter Cups are the two chocolates with the highest per-pound pricing.

As a result, Xzavier purchased a half-pound of Chocolate-covered Cashews and a half-pound of Chocolate-Peanut Butter Cups.

Option B is the correct answer: chocolate-peanut butter cups and chocolate-caramel bites.

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Answer:

14 grams = 14,000 milligrams

Step-by-step explanation:

since multiply the grams by 1000 will convert it to milligrams

Jake measured a hotel and made a scale drawing, the length of the room in the drawing is 24 inches.

If the scale of the drawing is 8 inches : 7 feet, this means that for every 8 inches in the drawing, there are 7 feet in real life.

To find out length of the room is in the drawing, we need to set up a proportion:

8 inches / 7 feet = x inches / 21 feet

where x is the length of the room in the drawing.

We can cross-multiply and solve for x:

8 inches × 21 feet = 7 feet × x inches

168 inches = 7 feet × x inches

Dividing both sides by 7, we get:

24 inches = x

Therefore, the length of the room in the drawing is 24 inches.

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Sasha will deposit $450 at 6% simple interest. The formula for calculating the balance of an account with simple interest is given by A = P(1 + rt), where A is the final amount, P is the initial principal balance, r is the annual interest rate (expressed as a decimal), and t is the time in years.

In this case, the initial principal balance P is $450, the annual interest rate r is 6% or 0.06 as a decimal, and the time t is 2 years. Plugging these values into the formula gives us:

A = 450(1 + 0.06 * 2)

Evaluating this expression gives us a final amount of approximately $477 in the account after two years.

Sasha will deposit the rest of her money ($850 - $450 = $400) at 2% compounded annually. The formula for calculating the balance of an account with annual compounding is given by A = P(1 + r/n)^(nt), where A is the final amount, P is the initial principal balance, r is the annual interest rate (expressed as a decimal), n is the number of times the interest is compounded per unit time (per year in this case), and t is the time in years.

In this case, the initial principal balance P is $400, the annual interest rate r is 2% or 0.02 as a decimal, n is 1 since it’s compounded annually, and the time t is 2 years. Plugging these values into the formula gives us:

A = 400(1 + 0.02/1)^(1 * 2)

Evaluating this expression gives us a final amount of approximately $416.16 in the account after two years.

Therefore, there will be approximately $60.84 more money in Sasha’s account at 6% simple interest than at 2% compounded annually after two years.

Answer:

4,500.00 rupees

Step-by-step explanation:

The quantity of Willow's books that are mysteries would be = 125 books.

To calculate the quantity of books that are mysteries the following is carried out.

The total number of books that willow has = 225 books

The total number of books that are mysteries = 5/9 of 225

That is ;

= 5/9 × 225/1

= 1125/9

= 125 books.

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The probability of the event is 4/13 when the odds in favor of the event are 4 to 9.

When the odds in favor of an event are given as a ratio of "a to b", the probability of the event can be calculated as:

Probability of the event = a / (a + b)

In this case, the odds in favor of the event are 4 to 9.

Therefore, we have:

a = 4 (the number of favorable outcomes)

b = 9 (the number of unfavorable outcomes)

Substituting these values into the formula, we get:

Probability of the event = 4 / (4 + 9)

Probability of the event = 4 / 13

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a)There are 286 ways to select any three people from the group of 13.

b)There are 35 ways to select three women from the group of seven women.

c) The probability that the selected group consists of all women is 0.122 or approximately 12.2%

What is probability?

Probability is the measure of the likelihood or chance that an event will occur, expressed as a number between 0 (impossible) and 1 (certain), or as a percentage between 0% and 100%. It is used to quantify uncertainty and make predictions in various fields such as mathematics, statistics, physics, engineering, economics, and social sciences

a. The total number of ways to select three people from a group of 13 is given by the combination formula,

C(13, 3) = 13! / (3! × (13 - 3)!) = 286

Therefore, there are 286 ways to select any three people from the group of 13.

b. The number of ways to select three women from a group of seven women is given by the combination formula,

C(7, 3) = 7! / (3! × (7 - 3)!) = 35

Therefore, there are 35 ways to select three women from the group of seven women.

c. To find the probability that the selected group consists of all women, we need to find the number of ways to select three women from the group of seven women and divide it by the total number of ways to select three people from the group of 13:

P(all women) = C(7, 3) / C(13, 3) = 35 / 286 = 0.122

Therefore, the probability that the selected group consists of all women is 0.122 or approximately 12.2%.

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Answer:

Pretty sure it’s A, D, A

Step-by-step explanation:

The area of the triangle is 22 miles square

From the question, we have the following parameters that can be used in our computation:

The triangle

Where we have

Base = 11 miles

Height = 4 miles

using the above as a guide, we have the following:

Area = 1/2 * Base * Heigt

substitute the known values in the above equation, so, we have the following representation

Area = 1/2 * 11 * 4

Evaluate

Area = 22 miles square

hence, the area is 22 miles square

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The Dimensions of the tent are: Base of triangular face (b): 4.46 ft, Height of triangular face (0.5b): 2.23 ft, Length of tent (b + 1): 5.46 ft.

With two triangular bases and three rectangular sides, a triangular prism is a three-dimensional geometric form. The rectangular faces link the matching edges of the bases, which are connected by the parallel triangular bases. This produces a form with a triangular cross-section along the prism's length. The distance between the vertices of the triangle bases is referred to as the length, whereas the height of the prism is the perpendicular distance between the bases.

Given:

Volume of tent = [tex]63 ft^3[/tex]

Let's assume the base of the triangular face of the tent is "b" feet. The height of the triangular face is half of the base, so it would be "0.5b" feet.

The length of the tent is given to be 1 foot more than the base, so the length would be "b + 1" feet.

Mathematically, the volume of a triangular prism can be given by:

[tex]Volume = (1/2) * base * height * length[/tex]

Substituting the given values and rearranging the formula to solve for "b":

[tex]63 = (1/2) * b * (0.5b) * (b + 1)\\126 = b^2 * (0.5b) * (b + 1)\\0.5b^3 + 0.5b^2 - 126 = 0[/tex]

Solving this cubic equation, we get "b ≈ 4.46" (rounded to two decimal places).

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The correct options are -  A. In the period in which the corresponding sales are recorded, records the expected bad debt expenditure. and C. Reports accounts receivable at the estimated amount of cash to also be collected on the balance sheet.

The measure that the company uses to set aside money for its bad debts or uncollectible accounts is known as the allowance method of accounting. This accounting technique reflects the accrual basis.

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Correct question:

The allowance method of accounting for bad debts has the following advantages over the direct write-off method including: (You may select more than one answer. ):

A. Records estimated bad debts expense in the period when the related sales are recorded.

B. Records estimated bad debts expense when the account receivable is determined to be uncollectible.

C. Reports accounts receivable on the balance sheet at the estimated amount of cash to be collected

D. Reports sales on the income statement at the estimated amount of cash to be collected

The journal entry for the given information is below:

Journal entries:    

S.no. Accounts title andd explanations Debit $ Credit $

a. Accounts receivable   2500

Service revennue    2500

b. Cash account   2000

Service revenue    2000

c. Cash account   500

Unearned service revenue   500

d. Accounts receivabale  1500

Cash account    1500

e. Rent Payable   500

Cash account    500

f. Rent expenses   750

Rent payable    750

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Scores between 23 & 59 will give Paul a C for the semester (an average between 70 and 79).

The sum of the scores on the first three, hundred point tests

= 82 + 88 + 87 = 257.

The total score required in four 100-point tests to get an average score of 70 = 70X4= 280.

The total score required in four 100-point tests to get an average score of 79 = 79X4= 316.

Therefore, the score on the fourth test should be between (280-257) & (316-57) i.e, 23 & 59 to get an average score of 70 & 79.

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The geometric sequence in the list of options is A. 3, 12, 48, . . .

A geometric sequence is a sequence of numbers in which each term after the first is found by multiplying the previous term by a fixed number.

A. 3, 12, 48, . . . is a geometric sequence because each term is obtained by multiplying the previous term by 4.

B. 3, 1, . . . is not a geometric sequence because there is no fixed ratio between terms.

C. 0, 1, 3, 9, . . . is not a geometric sequence because the ratio between terms is not constant.

D. 3, 6, 12, 21, . . . is not a geometric sequence because the ratio between terms is not constant.

Therefore, the only geometric sequence is A. 3, 12, 48, . . .

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Answer:

3, 12, 48, . . .

Step-by-step explanation:

got it right

The value of tan (2∅) in the right triangle is  - 960 / 644.

A right angle triangle is a triangle that has one of its angles as 90 degrees. The sum of angles in a triangle is 180 degrees.

Therefore, the triangle is a right angle triangle because it follows the Pythagoras's principle as follows:

c² = a² + b²

where

Therefore,

15² + 8² = 17²

Let's find ∅ using trigonometric ratios,

tan ∅ = opposite / adjacent

tan ∅ = 15 / 8

Therefore,

tan 2∅ = 2 tan ∅ / 1 - tan² ∅

tan 2∅ = 30 / 8 ÷ 1 - (15 / 8)²

tan 2∅ = 30 / 8 ÷ 1 - 225 / 64

tan 2∅ = 15 / 4 ÷  64 - 225/ 64

tan 2∅ = 15 / 4 ÷ -161 / 64

tan 2∅ = 15 / 4 × 64 / -161

tan 2∅ =  - 960 / 644

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The value of tan (2∅) in the right triangle is  - 960 / 644.

A right angle triangle is a triangle that has one of its angles as 90 degrees. The sum of angles in a triangle is 180 degrees.

Therefore, the triangle is a right angle triangle because it follows the Pythagoras's principle as follows:

c² = a² + b²

where

Therefore,

15² + 8² = 17²

Let's find ∅ using trigonometric ratios,

tan ∅ = opposite / adjacent

tan ∅ = 15 / 8

Therefore,

tan 2∅ = 2 tan ∅ / 1 - tan² ∅

tan 2∅ = 30 / 8 ÷ 1 - (15 / 8)²

tan 2∅ = 30 / 8 ÷ 1 - 225 / 64

tan 2∅ = 15 / 4 ÷  64 - 225/ 64

tan 2∅ = 15 / 4 ÷ -161 / 64

tan 2∅ = 15 / 4 × 64 / -161

tan 2∅ =  - 960 / 644

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Step-by-step explanation:

distance / rate = time                s = plane speed    w = wind speed

Flying with wind       1053 / ( s+ w) = 1.75

                                   solve for s = 601.714 -w

Flying against wind  1053 / (s-w) = 2.75       sub in for s (above)

                                  1053 / ( 601.714 - w   -w )  = 2.75

                                          solve for w = 109.27 mi/hr  

sub this 'w'  into one of the equations to solve for 's'

          1053 / ( s + 109.273) = 1.75      shows   s = 492.44  mi/hr

Answer:

(a) 3581 N

(b) 6.1 kJ

(c) 4.5 kJ

(d) 74.6%

Step-by-step explanation:

(a) To lift the piano straight up, we need to counteract the force of gravity acting on it. The force required can be calculated using the formula F = mg, where F is the force, m is the mass of the piano, and g is the acceleration due to gravity. So, F = (230 kg) x (9.81 m/s^2) = 3581 N.

(b) The work done in lifting the piano is given by the formula W = Fd, where W is the work done, F is the force required to lift the piano, and d is the height to which the piano is lifted. So, W = (3581 N) x (1.7 m) = 6.1 kJ.

(c) Using a ramp reduces the force required to lift the piano. The force required can be calculated using the formula F = mg sinθ, where θ is the angle of inclination of the ramp. We are given that the force required is 300 N and the length of the ramp is 15 m. So, sinθ = F/mg = 300/(230 x 9.81) = 0.1416. Therefore, θ = sin^-1(0.1416) = 8.13 degrees. The work done using the ramp can be calculated using the formula W = Fd, where d is the height to which the piano is lifted. Using trigonometry, we can find that the height to which the piano is lifted is 1.53 m. So, W = (300 N) x (15 m) x sin 8.13 degrees = 4.5 kJ.

(d) The efficiency of the ramp is the ratio of the work output to the work input, expressed as a percentage. The work output is the same as the work done using the ramp, which is 4.5 kJ. The work input is the same as the work done when lifting the piano straight up, which is 6.1 kJ. So, the efficiency of the ramp is (4.5/6.1) x 100% = 74.6%.