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## Find the first, fourth, and tenth terms of the arithmetic sequence described by the given rule. A(n) = –6 + (n – 1)(6)

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Find the first, fourth, and tenth terms of the arithmetic sequence described by the given rule. A(n) = –6 + (n – 1)(6)

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## The lengths of two sides of a right triangle are 5 inches and 8 inches. What is the difference between the two possible lengths of the third side of the triangle? Round your answer to the nearest tenth.

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If 5 in and 8 in are legs:
hypotenuse = √(5²+8²) = √89 ≈ 9.4 in.

If 5 in is the leg and 8 in is the hypotenuse:
other leg = √(8²-5²) = √39 ≈ 6.2 in.

The difference between the two possible lengths of the third side =
9.4 – 6.2 = 3.2 in.

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## A metal washer is made by cutting out a circle 13.2 mm in diameter from a larger circle. To the nearest tenth, what is the area of the washer?

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A metal washer is made by cutting out a circle 13.2 mm in diameter from a larger circle. To the nearest tenth, what is the area of the washer?

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## A car gets 32 mpg. How many kilometers per gallon is this? Express your answer rounded to the nearest tenth of a kilometer per gallon.

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A car gets 32 mpg. How many kilometers per gallon is this? Express your answer rounded to the nearest tenth of a kilometer per gallon.

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## N the right triangle above, a= 9.9 and c= 12.4 Find the value of b, rounded to the nearest tenth.

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N the right triangle above, a= 9.9 and c= 12.4 Find the value of b, rounded to the nearest tenth.

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## What's one tenth of 7,000

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What’s one tenth of 7,000

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## DEF, FE= 13 and M<=34. Find DF to the nearest tenth

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DEF, FE= 13 and M<=34. Find DF to the nearest tenth

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## 22. The tangent of an angle is 7.5. What is the measure of the angle to the nearest tenth?

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22. The tangent of an angle is 7.5. What is the measure of the angle to the nearest tenth?

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## Find P(Y|B) from the information in the table. | X | Y |Z | total a | 8 | 80 | 40 | 128 b | 6 | 34 | 45 | 85 c | 23 | 56 | 32 | 111 total | 37 | 170 | 117 | 324 To the nearest tenth, P(Y|B) =____

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P(Y|B) reads ‘Probability of event Y happening given event B is happening’. This is a conditional probability and the formula is given as

P(Y|B) = P(Y∩B) / P(B)

From the table, P(Y∩B) = 34/324 and P(B) = 85/324

Hence,
P(Y|B) = (34/324) ÷ (85/324) = 34/85

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## Eric drove his fishing boat into a large cove and dropped the anchor in 52 feet of water the anchor descends at a constant rate of 3.8 feet per second, how long will it take for the anchor to hit the bottom of the lake? Round your answer to the nearest tenth If of a second if necessary.

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Eric drove his fishing boat into a large cove and dropped the anchor in 52 feet of water the anchor descends at a constant rate of 3.8 feet per second, how long will it take for the anchor to hit the bottom of the lake? Round your answer to the nearest tenth If of a second if necessary.

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## Round 1.41 to the nearest tenth

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Round 1.41 to the nearest tenth

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## Find the area of the figure. Round to the nearest tenth if necessary.

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So I went ahead and divided up the figure so that you would understand what I’m going to tell you. Let’s start with the red rectangle.

The distance from point R to point I is 6 units and the distance from Point R to point S is 5 units. 6*5 = 30 so that red rectangle has an area of 30 units

Now let’s calculate triangle AVI. Area of a triangle is Base * Height. The base is 1 and the height is 5 which means the area of triangle AVI is 5.

Next, triangle ALT. From Point A to point L is 4 unit. From Point L to point T is 3 units. 4*3 is 12. So triangle ALT has an area of 12.

Triangle TSI. From Point T to point L is 3 units. From Point L to X is 2. Triangle TSI has an area of 6.

Now we add all of them up. 30+5+12+6 = 53. In total, RSTUV has an area of 53

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## Find the area of the shaded region. Round answers to the nearest tenth. Assume all inscribed polygons are regular.

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We can calculate for the area of the shaded region by 1)
calculating the area of circle, 2) calculating for area of triangle, and 3)
calculating for area of the segment below the triangle. Then subtract 2 and 3
from 1.

1) Area of circle, Ac = π r^2

Ac = π (6)^2

Ac = 113.10

2) Area of triangle, At

The triangle is an equilateral triangle with angles on each
corner equal to 60 degrees. Meanwhile, the 3 angles at the center is 120
degrees each since a circle is 360 degree. We know that the radius (line from
centerpoint to corner) is equivalent to 6. Using the cosine law, we can calculate
for the length of one side.

s^2 = 6^ + 6^2 – 2 (6) (6) cos 120

s^2 = 108

s = 10.4

Since this is an equilateral triangle therefore all sides
are equal. The area for this is:

At = (sqrt3 / 4) * s^2

At = 46.77

3) Area of segment, As is given as:

As = [ (r^2) / 2 ] ( θ rad – sin θ )

As = [(6^2) / 2] (120 * π / 180 – sin 120)

As = 22.11

Therefore the area of shaded region is:

A = 113.10 – 46.77 – 22.11

A = 44.22

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## Find the volume of the cone. Use 3.14 for p. Round to the nearest tenth.

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Find the volume of the cone. Use 3.14 for p. Round to the nearest tenth.

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## The Mendes family bought a new house 8 years ago \$129,000. The new house is now worth \$186,000. Assuming a steady rate of growth, what was the yearly rate of appreciation? Round your answer to the nearest tenth of a percent (1.2% etc) ******PLEASE HELP****

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So assuming simplet interest

find the change to find the interest
change=186000-129000=57000

simple interest=time times rate times principal
time is in years (8)
rate is in decimal
principal is amount invested (129000)

so
interest is 57000
57000=(8)(r)(129000)
57000=1032000r
divide both sides by 1032000
0.05523255813953488372093023255814=r
or
5.523255813953488372093023255814%
rounded
5.5%

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## To the nearest tenth, what is the area of a circle with circumference 35.6 centimeters?A. 100.9 cm2B. 211.8cm2C. 316.8cm2D. 403.4cm2

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To the nearest tenth, what is the area of a circle with circumference 35.6 centimeters?A. 100.9 cm2B. 211.8cm2C. 316.8cm2D. 403.4cm2

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## A circle has a central angle measuring 7pi/6 radians that intersects an arc of length 18 cm. What is the length of the radius of the circle? Round your answer to the nearest tenth. Use 3.14 for pi. 3.7 cm 4.9 cm 14.3 cm 15.4 cm

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You need to determine the number of ways in which 30 competitors from 50 can qualify. First, you have to realize that the order is irrelevant, that is: it is the same competitor_1, competitor _2, competitor _3 than competitor_3, competitor_2, competitor_1, or any combination of those three competitors.

So, the number of ways is which 30 competitors from 50 can qualify is given by the formula of combinations, which is:

C (m,n) = m! / (n! * (m -n)! )

=> C (50,30) = 50! / (30! (50 – 30)! ) = (50!) / [30! (50 – 30)!] = 50! / [30! 20!] =

= 47,129,212,243,960 different ways the qualifiying round of 30 competitors can be selected from the 50 competitors.

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## .736 rounded to the nearest tenth

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Answer:

Option C – BD=76 cm

Step-by-step explanation:

Given : You are designing a diamond-shaped kite. you know that AD = 44.8 cm, DC = 72 cm, and AC = 84.8 cm.

To find : How long BD should it be?

Solution :

First we draw a rough diagram.

The given sides were AD = 44.8 cm, DC = 72 cm and AC = 84.8 cm.

According to properties of kite

Two disjoint pairs of consecutive sides are congruent.

So, AD=AB=44.8 cm

DC=BC=72 cm

The diagonals are perpendicular.

So, AC ⊥ BD

Let O be the point where diagonal intersect let let the partition be x and y.

AC= AO+OC

AC=   …….[1]

Perpendicular bisect the diagonal BD into equal parts let it be z.

BD=BO+OD

BD=z+z

Applying Pythagorean theorem in ΔAOD

where H=AD=44.8 ,P= AO=x , B=OD=z

………[2]

Applying Pythagorean theorem in ΔCOD

where H=DC=72 ,P= OC=y , B=OD=z

…………[3]

Subtract [2] and [3]

……….[4]

Add equation [1] and [4], to get values of x and y

Substitute x in [1]

Substitute value of x in equation [2], to get z

We know, BD=z+z

BD= 38.06+38.06

BD= 76.12

Nearest to whole number BD=76 cm

Therefore, Option c – BD=76 cm is correct.

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## What is the molality of a solution containing 5.0 moles of solute in 3.2 kg of solvent? Round to the nearest tenth.

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This problem is to apply Roult’s Law.

Roult’s Law states that the vapor pressure, p, of a solution of a non-volatile solute is equal to the vapor pressure of the pure solvent, Po solv, times the mole fraction of the solvent, Xsolv

p = Xsolv * Po sol

X solv = number of moles of solvent / number of moles of solution

The solvent is water and the solute (not volatile) is glycerin.

Number of moles = mass in grams / molar mass

mass of water = 132 ml * 1 g/ml = 132 g

molar mass of water = 18 g/mol

=> number of moles of water = 132 g / 18 g/mol = 7.33333 mol

mass of glycerin = 27.2 g

molar mass of glycerin:, C3H8O3: 3 * 12 g/mol + 8 * 1 g/mol + 3*16 g/mol = 92 g/mol

number of moles of glycerin = 27.2g / 92 g/mol = 0.29565

total number of moles = 7.33333 moles + 0.29565 moles = 7.62898 moles

=> X solv = 7.33333 / 7.62898 = 0.96125

=> p = 0.96125 * 31.8 torr ≈ 30.57 torr ≈ 30.6 torr.

Answer: 30.6 torr

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## A planet orbiting a distant star has been observed to have an orbital period of 0.76 Earth years at a distance of 1.2 AU. What is the mass of the star the planet is orbiting? Round your answer to the nearest tenth.

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Answer:

1) Water has very high specific heat.

2) It expands when it freezes

3) ability to dissolve in ionic substances

4) Water molecules at the surface experience fewer hydrogen bonds than water molecules within the liquid.

Explanation:

1) Water molecules due to their high specific heat , undergo relatively less increase in temperature after absorbing heat. So they prevent their adjoining area to experience sharp increase in temperature.

2) Water is an example which expands on freezing. In it , large spaces are left between molecules when it cools. It happens because hydrogen bonds prevent any two molecules to come very close thereby  creating gaps. This gap is filled up when ice melts , which results in overall reduction in volume of water.

3) Uneven distribution of charge results in water molecules becoming polar in nature . A polar substance  can be dissolved in polar solvents only.

4) It is due to property of surface tension. Property  of surface tension results due to molecules of water near the surface experiencing a  net downward  force due to hydrogen bonds . It is due to fewer hydrogen bonds made by them.

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## Find m angle F round the answer to the nearest tenth

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You need to determine the number of ways in which 30 competitors from 50 can qualify. First, you have to realize that the order is irrelevant, that is: it is the same competitor_1, competitor _2, competitor _3 than competitor_3, competitor_2, competitor_1, or any combination of those three competitors.

So, the number of ways is which 30 competitors from 50 can qualify is given by the formula of combinations, which is:

C (m,n) = m! / (n! * (m -n)! )

=> C (50,30) = 50! / (30! (50 – 30)! ) = (50!) / [30! (50 – 30)!] = 50! / [30! 20!] =

= 47,129,212,243,960 different ways the qualifiying round of 30 competitors can be selected from the 50 competitors.

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## If a = 4 units and b = 3 units, the length of the diagonal of the outside square rounded to the nearest tenth is

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Answer:  The correct option is (C). 10 = square root of the quantity of x minus 8 all squared plus y minus 9 all squared

Step-by-step explanation:  Given that the segment AB has point A located at (8, 9). The distance from A to B is 10 units.

We are to select the correct option that could be used to calculate the coordinates for point B.

Let, (x, y) be the co-ordinates of point B.

According to distance formula, the distance between two points (a, b) and (c, d) is given by

Therefore, the distance between the points A(8, 9) and B(x, y) is given by

Since, distance between A and B is 10 units, so

d = 10.

Therefore,

Thus, the correct statement is

10 = square root of the quantity of x minus 8 all squared plus y minus 9 all squared.

Option (C) is correct.

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## What’s the nearest tenth of 54.3

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Answer:

Option C – BD=76 cm

Step-by-step explanation:

Given : You are designing a diamond-shaped kite. you know that AD = 44.8 cm, DC = 72 cm, and AC = 84.8 cm.

To find : How long BD should it be?

Solution :

First we draw a rough diagram.

The given sides were AD = 44.8 cm, DC = 72 cm and AC = 84.8 cm.

According to properties of kite

Two disjoint pairs of consecutive sides are congruent.

So, AD=AB=44.8 cm

DC=BC=72 cm

The diagonals are perpendicular.

So, AC ⊥ BD

Let O be the point where diagonal intersect let let the partition be x and y.

AC= AO+OC

AC=   …….[1]

Perpendicular bisect the diagonal BD into equal parts let it be z.

BD=BO+OD

BD=z+z

Applying Pythagorean theorem in ΔAOD

where H=AD=44.8 ,P= AO=x , B=OD=z

………[2]

Applying Pythagorean theorem in ΔCOD

where H=DC=72 ,P= OC=y , B=OD=z

…………[3]

Subtract [2] and [3]

……….[4]

Add equation [1] and [4], to get values of x and y

Substitute x in [1]

Substitute value of x in equation [2], to get z

We know, BD=z+z

BD= 38.06+38.06

BD= 76.12

Nearest to whole number BD=76 cm

Therefore, Option c – BD=76 cm is correct.

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## Find the volume of each figure to the nearest tenth. Show your work.

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Find the volume of each figure to the nearest tenth. Show your work.

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## Jared has to go to school. After school, he needs to stop at the grocery store before heading home. Jared’s school is 5.8 miles from his house at 40° north of east. The grocery store is 2.6 miles from his house at 10° west of north. How far is Jared’s school from the grocery store? Round the answer to the nearest tenth. A. 3.8 miles B. 4.6 miles C. 5.0 miles D. 6.4 miles

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You need to determine the number of ways in which 30 competitors from 50 can qualify. First, you have to realize that the order is irrelevant, that is: it is the same competitor_1, competitor _2, competitor _3 than competitor_3, competitor_2, competitor_1, or any combination of those three competitors.

So, the number of ways is which 30 competitors from 50 can qualify is given by the formula of combinations, which is:

C (m,n) = m! / (n! * (m -n)! )

=> C (50,30) = 50! / (30! (50 – 30)! ) = (50!) / [30! (50 – 30)!] = 50! / [30! 20!] =

= 47,129,212,243,960 different ways the qualifiying round of 30 competitors can be selected from the 50 competitors.

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