How to write repeating decimals as fractions

Answer:

first brand 55 gallons

second brand 95 gallons

Step-by-step explanation:

The solution of the linear equations y = 4x − 19.4 and y = 0.2x − 4.2 will be (4, -3.4). Then the correct option is A.

The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.

The equations are given below.

y = 4x − 19.4      ...1

y = 0.2x−4.2      ...2

From equations 1 and 2, then we have

4x - 19.4 = 0.2x - 4.2

3.8x = 15.2

x = 4

Then the value of the variable 'y' will be calculated as,

y = 4 (4) - 19.4

y = 16 - 19.4

y = - 3.4

The solution of the linear equations y = 4x − 19.4 and y = 0.2x − 4.2 will be (4, -3.4). Then the correct option is A.

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The answer is D 2,024,657

Answer:

A

Step-by-step explanation:

0.365 x 739,000= 269,735

Answer: B. 0.45

Step-by-step explanation:

From the given table, the total number of students = 137

The number of students are sophomores =35+42=77

Let A be the event that students are sophomores.

Then probability that students are sophomores is given by  :

[tex]\text{P(A)}=\dfrac{77}{137}[/tex]

The number of sophomores who attended the jazz concert = 35

Let B be the event that students attended the jazz concert .

The probability that students attended the jazz concert and are sophomores is given by  :

[tex]\text{P(A and B)}=\dfrac{35}{137}[/tex]

Now, the probability of that the student attended the jazz concert, given that the students is sophomore is given by :-

[tex]P(B|A)=\dfrac{\text{P(A and B)}}{\text{P(A)}}\\\\=\dfrac{\dfrac{35}{137}}{\dfrac{77}{137}}\\\\\\=\dfrac{35}{77}=0.454545454545\approx0.45[/tex]

Answer:

(0.55, 0.75)

Step-by-step explanation:

The range can be estimated to be 6 standard deviations wide.  Therefore, the standard deviation is:

σ = (0.72 - 0.42) / 6

σ = 0.05

The margin of error is ±2σ, so:

ME = ±0.10

Therefore, the interval estimate is:

(0.65 - 0.10, 0.65 + 0.10)

(0.55, 0.75)

The standard deviation is a measure of a collection of values' variance or dispersion. The interval estimate of the true population proportion is (0.55, 0.75).

The standard deviation is a measure of a collection of values' variance or dispersion. A low standard deviation implies that the values are close to the set's mean, whereas a high standard deviation shows that the values are spread out over a larger range.

A.) The range is around 6 standard deviations broad. As a result, the standard deviation is:

σ = (0.72 - 0.42) / 6

σ = 0.05

B.) Because the margin of error is ±2σ, therefore, we can write,

Margin Of Error = (±0.05)×2 = ±0.10

C.) The interval can be estimated as,

Interval = 0.65±0.10

             = 0.65-0.10, 0.65+0.10

             = 0.55, 0.75

Hence, the interval estimate of the true population proportion is (0.55, 0.75).

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Answer:

(√5)/2

Step-by-step explanation:

In the attached figure, we have labeled the circumcenter point D and the incenter point E. The points of tangency of the incircle with sides AB, BC and CA are labeled G, H, and F, respectively.

The distances from any vertex to the two points of tangency from that vertex are the same. So, AG = FA, BG = BH, and CF = CH. If we call the radius of the incircle "r", then we have ...

AG = FA = r, BG = BH = 3-r, CF = CH = 4-r

so the side length BC is ...

BC = BH +CH = (3-r) +(4-r) = 7-2r

We already know that side length BC is 5, so ...

5 = 7 -2r

r = (7 -5)/2 = 1

Of course, the circumcenter of a right triangle is the midpoint of the hypotenuse, so the circumradius "R" is 5/2 = 2.5.

The formula for the distance between the two centers is ...

d = √(R(R -2r)) = √(2.5(2.5 -2)) = √1.25 = (√5)/2

_____

Comment on this answer

We have used a formula for the center-to-center distance found using a web search. The attached diagram shows the coordinates of the two centers, so the distance can be found from those. It is the same.

Answer:

What is the area AA of each section of the circle?

Give your answer in terms of pi.

A = 25πm²

Step-by-step explanation:

Given the radius of the circle to be 10

The question is to find area of each sections of the circle .

The formula for calculating the area of a circle is area equals to πr²

A = πr²

Given r = 10m

The next step is to substitute the values into the equations  

A = π (10m)²

A = 100πm²

Since the circle is divided into 4 equal sections, we need to find the area of each sections by dividing the complete area of the circle by 4

Therefore,  

A = 100πm²/4  

A = 25πm²

Answer:

25π[tex]m^{2}[/tex]

Step-by-step explanation:

Answer:

-2(2x +5)² = -8x² -40x -50

Step-by-step explanation:

Evaluate from the inside out, according to the order of operations.

  h(g(f(x))) = h(g(2x +5)) = h((2x +5)²) = -2(2x +5)² = -2(4x² +20x +25)

  = -8x² -40x -50

I personally prefer the factored form, but that is not considered "simplified."

Answer:

67.1

Step-by-step explanation:

we need to use trig to work this out

(Soh Cah Toa)

The answer will be 67.11461952384143

to nearest tenth its

67.1

Answer:

x = 67.1°

Step-by-step explanation:

Cos(x) = Adj./Hypo.

Cos(x) = 28/72

Cos(x) = 0.3889

x = 67.1°

Answer:

162.43

Step-by-step explanation: I hope its helps it's been a couple of years since I have done geometry

Answer:

the total area of the octagon is 8(20.3 in²), or 162.4 in²

Step-by-step explanation:

A regular octagon has 8 pie-shaped sections.  Each is triangle of height 7 in and base 5.8 in.

Thus, the area of each such section is, by A = (1/2)(b)(h(),

A = (1/2)(5.8 in)(7 in) = 20.3 in².

There are 8 such sections.  

Thus, the total area of the octagon is 8(20.3 in²), or 162.4 in²

Answer:

525

Step-by-step explanation:

Answer:

80 ft²

Step-by-step explanation:

The area of the path is equal to the area of the overall square minus the area of the garden.

Area of a square is the side length squared:

A = s²

The overall square has a side length of 12 feet.  The side length of the garden is 12 - 2 - 2 = 8 feet.  So the area of the path is:

A = 12² - 8²

A = 144 - 64

A = 80

The area of the path is 80 ft².

Answer:

not geometric

Step-by-step explanation:

A geometric series is one where the nth term is multiplied by a common ratio to get the n+1 term.

1    1/2   1/4     1/8       1/16 .....

is a geometric series. the fourth term (1/8) is multiplied by 1/2 to get 1/16.

The series you have been given is not geometric.  It reduces to

1/3   1/4   1/5    1/6 which does not give you a common number to multiply the nth term to get to the n+1 term.  

Answer:

[tex]\frac{6}{\pi }[/tex] or 1.9099

Step-by-step explanation:

Look for y values at each of those given values of "x" and apply the slope formula.  When x = pi. y = -1 so the coordinate is [tex](\pi,-1)[/tex].  When x = 3pi/2, y = 2 so the coordinate is [tex](\frac{3\pi }{2},2)[/tex]

Plug those values into the slope formula:

[tex]\frac{2-(-1)}{\frac{3\pi }{2}-\pi}[/tex]

You need a common denominator of pi:

[tex]\frac{3}{\frac{3\pi-2\pi}{2} }=\frac{3}{\frac{\pi }{2} }[/tex]

Do the math on that to get a slope of [tex]\frac{6}{\pi } =1.9099[/tex]

1: 107

2: 73

3; 123

4: 62

5: 116

6: 16

7: 92

The missing angle measures in the hexagon are:

∠5 = 116°

∠4 = 62°

∠3 = 123°

∠2 = 73°

∠6 = 16°

∠7 = 92°

∠1 = 107°

A hexagon is a six-sided polygon, whose sum of interior angles equals 720°.

∠5 = 180 - 54 = 116° (supplementary angles)

∠4 = 180 - 118 = 62° (supplementary angles)

∠3 = 180 - 57 = 123° (supplementary angles)

∠6 = 180 - 164 = 16° (supplementary angles)

∠7 = 180 - 88 = 92° (supplementary angles)

∠1 = 720 - 116 - 118 - 123 - 164 - 92 = 107° (sum of interior angles in a hexagon )

∠2 = 180 - 107 = 73° (supplementary angles)

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Answer:

x = 3

Step-by-step explanation:

By rearranging the equations,

y = 6 - 3x

y = x - 6

x - 6 = 6 - 3x

4x - 6 = 6

4x = 12

x = 3

Answer:

x = 3

Step-by-step explanation:

Follow the elimination method like so:

3x + y = 6            The Ys cross each other out.

x - y = 6               Add to get:

4x = 12

4x = 12               Divide to get:

4       4

x = 3

Hope this helps! :)

Answer:

S(t) = 2 - 0.25*t

Step-by-step explanation:

A lake near the Arctic Circle is covered by a 2-meter-thick sheet of ice during the cold winter months.

When spring arrives, the warm air gradually melts the ice, causing its thickness to decrease at a constant rate.

S(t) denote the ice sheet's thickness S ( measured in meters) as a function of time (measured in weeks).

Therefore the equation formed will be linear.

The equation will be of the form y = mx + b

Here S(t) = mt + b

Here m is the slope which is the rate at which ice is melting.

Putting t = 0

S(t) = 2

Putting t = 3,

S(t) = 1.25

Therefore, m*0 + b = 2 or, b = 2

and 3m + b = 1.25

or, 3m = 1.25 - 2 = -0.75

or, t = -0.25

Hence, function's formula = S(t) = -0.25*t + 2

i.e. S(t) = 2 - 0.25*t

Answer:

y = 2 - 0.25x

Step-by-step explanation:

A lake near the Arctic Circle is covered by a 2-meter-thick sheet of ice during the cold winter months.

When spring arrives, the warm air gradually melts the ice, causing its thickness to decrease at a constant rate.

S(t) denote the ice sheet's thickness S ( measured in meters) as a function of time (measured in weeks).

Therefore the equation formed will be linear.

The equation will be of the form y = mx + b

Here S(t) = mt + b

Here m is the slope which is the rate at which ice is melting.

Putting t = 0

S(t) = 2

Putting t = 3,

S(t) = 1.25

Therefore, m*0 + b = 2 or, b = 2

and 3m + b = 1.25

or, 3m = 1.25 - 2 = -0.75

or, t = -0.25

Hence, function's formula = S(t) = -0.25*t + 2

i.e. S(t) = 2 - 0.25*t

Answer:

at the most 308 pounds

Step-by-step explanation:

Given

Weight of each sack = 364 pounds

Weight of Kevin = w = 150 pounds

Weight that lift can take = 2000 pounds

In order to find the weight of sacks that can be put into the elevator we have to subtract the weight of Kevin from the capacity of the lift.

So, actual weight of sacks that can be taken =[tex]2000-150[/tex]

= 1850 pounds

As 6 sacks have to be taken, to find the weight of one sack

Required weight of one sack = [tex]\frac{1850}{6}[/tex]

= 308.33 pounds

So, each sack has to weigh at the most 308 pounds ..

The correct option is a. at the most 308 pounds. Each sack should weigh at most 308 pounds to ensure that the elevator's weight limit is not exceeded when Kevin is in the elevator with six sacks.

To determine the weight each sack can be so that the elevator capacity is not exceeded, we must consider the total weight limit of the elevator and the weight of Kevin.

 The elevator has a capacity of 2,000 pounds. Kevin weighs 150 pounds, and he will be riding the elevator with the sacks. Therefore, the total weight available for the sacks is:

 2,000 pounds (elevator capacity) - 150 pounds (Kevin's weight) = 1,850 pounds.

 If six sacks are to be taken at a time, we divide the total available weight by the number of sacks to find the maximum weight each sack can have:

1,850 pounds / 6 sacks = 308.333... pounds.

Since the weight of each sack must be a whole number, we round down to the nearest whole number, which is 308 pounds. This ensures that the elevator's capacity is not exceeded.

Therefore, This allows for a small margin of error in the weight of the sacks, which is safer and more practical than having the sacks weigh exactly 308 pounds each.

Answer:

Step-by-step explanation:

1. a) spread is the range which is given as Max(S)- Min(S)

Colin =

[tex]3,9,9,14,15,16,17,20,21\\\\range=21-3=18\\\\[/tex]

Jezebel=

[tex]=4,5,8,10,11,14,20,20,26\\\\range=26-4=22[/tex]

Jezebel had a greatest spread.It was 22 while for Colin was 18

2. a) The middle 50% of the game sold is the difference between the third quartile and first quartile of the data

Colin=

[tex]=3,9,9,14,15,16,17,20,21\\\\median=15\\\\lower half=3,9,9,14\\\\\\Q1=(9+9) /2 =9\\\\\\Upper half= 16,17,20,12\\\\\\Q3=(17+20)/2 = 18.5\\[/tex]

⇒The middle 50% = Q3-Q1 = 18.5- 9 = 9.5

Jezebel

[tex]=4,5,8,10,11,14,20,20,26\\\\\\=lower half= 4,5,8,10\\\\\\upper half=14,20,20,26\\\\\\Q1=(5+8)/2 = 6.5\\\\Q3= (20+20)/2 = 20[/tex]

⇒The middle 50% = Q3-Q1 = 20-6.5 = 13.5

Colin had the least spread of 9.5 as compared to Jezebel who had 13.5

c)The answers in part 2a and 2 b tels us that the middle section that contained 50% of the scores was more in Jezebel record than in Colin records.

Answer:

Part 42) The surface area of the sphere is [tex]SA=795.8\ ft^{2}[/tex]

Part 43) The surface area of the sphere is [tex]SA=1,781.6\ m^{2}[/tex]

Part 44) The scale factor is [tex]\frac{19}{9}[/tex]

Step-by-step explanation:

Part 42) What is the surface area of a sphere with a circumference of 50 feet round the answer to the nearest 10th

step 1

Find the radius of the sphere

The circumference is equal to

[tex]C=2\pi r[/tex]

we have

[tex]C=50\ ft[/tex]

assume

[tex]\pi =3.14[/tex]

substitute and solve for r

[tex]50=2(3.14)r[/tex]

[tex]r=7.96\ ft[/tex]

step 2

Find the surface area of the sphere

The surface area of the sphere is equal to

[tex]SA=4\pi r^{2}[/tex]

substitute the value of r

[tex]SA=4(3.14)(7.96)^{2}[/tex]

[tex]SA=795.82\ ft^{2}[/tex]

round to the nearest 10th

[tex]795.82=795.8\ ft^{2}[/tex]  

Part 43) The volume of a sphere is 2254 pi m^3. What is the surface of the sphere to the nearest 10th?

step 1

Find the radius of the sphere

The volume of the sphere is equal to

[tex]V=\frac{4}{3}\pi r^{3}[/tex]

we have

[tex]V=2,254\pi\ m^{3}[/tex]

substitute and solve for r

[tex]2,254\pi=\frac{4}{3}\pi r^{3}[/tex]

Simplify

[tex]1,690.5=r^{3}[/tex]

[tex]r=11.91\ m[/tex]

step 2

Find the surface area of the sphere

The surface area of the sphere is equal to

[tex]SA=4\pi r^{2}[/tex]

substitute the value of r

[tex]SA=4(3.14)(11.91)^{2}[/tex]

[tex]SA=1,781.6\ m^{2}[/tex]

Part 44) What is the scale factor of a cube with a volume of 729 m^3 to a cube with a volume of 6859?

we know that

If two figures are similar, then the ratio of its volumes is equal to the scale factor elevated to the cube

so

Let

z -----> the scale factor

x ----> the volume of the larger cube

y ----> the volume of the smaller cube

[tex]z^{3}=\frac{x}{y}[/tex]

we have

[tex]x=6,859\ m^{3}[/tex]

[tex]y=729\ m^{3}[/tex]

substitute

[tex]z^{3}=\frac{6,859}{729}[/tex]

[tex]z=\frac{19}{9}[/tex]

[tex](\frac{6,859}{729})[/tex]

- D is the midpoint of AB, E is the midpoint of BC

Answer: A. Given

I left off DB||FC because that's not given.  But we can construct it.

Construct line through C parallel to AB.  Extend DE to intersect and call the meet F.

- DB || FC

By Construction

----

- Angle B congruent to angle FCE

Answer: D. Alternate Interior Angles

We have transversal BC across parallel lines AB and CF, so we get congruent angles ABC and FCB aka FCE

- angle BED congruent to angle CEF

Answer: H. Vertical angles are congruent

When we get lines meeting like this we get the usual congruent and supplementary angles.

- Triangle BED congruent to Triangle CEF

Answer: F. Angle Side Angle

We have BE=CE, DBE=FCE, BED=CEF

- DE congruent to FE and DB congruent to FC

Answer: C. CPTCTF

Corresponding parts ...

- AD congruent to DB and DB congruent to FC therefore AD congruent to FC

Answer: E. Transitive Property of Congruent

Things congruent to the same thing are congruent

- ADFC is a parallelogram

Answer: G.  AD and FC are congruent and parallel

Presumably this is a theorem we have already established.

- DE || AD

Answer: B. Definition of a parallelogram

Answer:

  31.25

Step-by-step explanation:

The initial term is 25 and the common ratio is 5/25 = 1/5. The formula tells you the sum is ...

  25/(1 -1/5) = 25/(4/5) = 31.25

If we factor 25 from the sum, we have

[tex]\displaystyle 25\left(1+\dfrac{1}{5}+\dfrac{1}{25}+\ldots\right)=25\sum_{i=0}^\infty \left(\dfrac{1}{5}\right)^i = 25 \dfrac{1}{1-\frac{1}{5}} = 25\dfrac{1}{\frac{4}{5}}=25\cdot \dfrac{5}{4} = \dfrac{125}{4}[/tex]

[tex]-(x^2+24x+144)=12y+12...[/tex]Answer:

(-12, 8)

Step-by-step explanation:

The standard form of this parabola, the one we can use to determine the vertex coordinates and the value of p is:

[tex](x-h)^2=4p(y-k)[/tex]

where h and k are the coordinates of the vertex and p is the distance between the vertex and the focus.  We need that p value to determine how far above the vertex the focus is.  In this case, the focus will lie on the same x-coordinate as the focus, we just need to find how far that distance away is.  That requires us to do some algebraic gymnastics on that original equation.  Putting it into vertex form.

Begin by multiplying everything by 12 to get rid of the pesky fraction:

[tex]12y=-x^2-24x-12[/tex]

Now we need to complete the square.  The easiest way to do this is to have just the x terms on one side of the equals sign and everything else on the other side, so we will add 12 to both sides:

[tex]-x^2-24x=12y+12[/tex]

The leading coefficient when you complete the square has to be a positive 1; ours is a negative 1, so factor out the negative:

[tex]-(x^2+24x)=12y+12[/tex]

The rules for completing the square are as follows:  Take half the linear term (ours is a 24), square that half, then add it into the parenthesis.

Half of 24 is 12 so

[tex]-(x^2+24x+144)=12y+12[/tex]

BUT...since this is an equation, if we add something to one side we have to add it to the other side too.  BUT we didn't just add in a 144, we have to take into account the -1 sitting outside the parenthesis that will not be ignored. So we didn't add in 144, we added in -1(144) which is -144.

[tex]-(x^2+24x+144)=12y+12-144[/tex]

What we have done on the left by completing the square is to create a perfect square binomial.  Rewriting it as such and combining like terms on the right:

[tex]-(x+12)^2=12y-132[/tex]

Don't forget the purpose of this is to find the value of p.  We're almost there.  On the right, factor out a 12:

[tex]-(x+12)^2=12(y-11)[/tex]

From this we can determine the coordinates of the vertex and the value of p.  The vertex sits at (-12, 11).  

The equation for p is 4p = 12 so p = 3

That means that the focus is 3 units below the vertex on the same x coordinate.  The focus then is at (-12, 8)

Final answer:

A rectangle and a rhombus both have opposite sides that are parallel and their interior angles add up to 360 degrees. They differ in that a rectangle has four right angles and a rhombus has four congruent sides, which are not necessarily attributes they share unless they are both squares.

Explanation:

Both a rectangle and a rhombus share some properties as they are both quadrilaterals. Firstly, the opposite sides are parallel in both shapes. Secondly, the angle measures add to 360° which is a property of all quadrilaterals. However, they differ in other aspects; a rectangle has four right angles, whereas a rhombus generally does not unless it's a square. A rhombus has four congruent sides, and a rectangle does not unless it's a square. Therefore, the correct selections based on their commonalities are that the opposite sides are parallel and their angle measures add up to 360°.

Answer:

[tex] 19\sqrt{7} [/tex]

Step-by-step explanation:

[tex] 25\sqrt{7} - 2\sqrt{63} = [/tex]

[tex] = 25\sqrt{7} - 2\sqrt{9 \times 7} [/tex]

[tex] = 25\sqrt{7} - 2\sqrt{9} \sqrt{7} [/tex]

[tex] = 25\sqrt{7} - 2\times 3 \sqrt{7} [/tex]

[tex] = 25\sqrt{7} - 6 \sqrt{7} [/tex]

[tex] = 19\sqrt{7} [/tex]

Answer:

C [tex]x=\frac{4}{3}[/tex]

Step-by-step explanation:

The given logarithmic equation is:

[tex]\log_{3x+4}(4096)=4[/tex]

We rewrite in exponential form; to get;

[tex]4096=(3x+4)^4[/tex]

We rewrite the LHS as a certain natural number exponent 4.

[tex]8^4=(3x+4)^4[/tex]

The exponents are the same, hence the bases must also be the same.

[tex]\implies 3x+4=8[/tex]

[tex]\implies 3x=8-4[/tex]

[tex]\implies 3x=4[/tex]

Divide both sides by 3;

[tex]\implie x=\frac{4}{3}[/tex]

The correct answer is C

Answer:

Step-by-step explanation:

The directions tell you what to do and give an example. That work is to be repeated 15 more times. The work is tedious, at best. I found it slightly less tedious to enter the 64 numbers into a spreadsheet and let it do the sums. See the attached for the result.

At the bottom of the array are the sums of columns. At the right are the sums of rows. The upper right and lower left numbers are the sums of the corresponding diagonals.

The "pattern" is that the sums are all -6, which is what you expect from a magic square.

The length of diagonal EK is sqrt(5^2 + 4^2) ≈ 6.403m

Hence perimeter = 2*(12 + 6.403) → 36.8 m (to the nearest tenth of a metre)

The perimeter of the cross-section is 36.8 m.

Given that the length of diagonal EK is

[tex]\sqrt{(5^2 + 4^2) }[/tex]

≈ 6.403m

Thus, the perimeter would be

2*(12 + 6.403)

→ 36.8 m.

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[tex]\bf \textit{vertex of a horizonal parabola, using f(y) for "x"} \\\\ x=\stackrel{\stackrel{a}{\downarrow }}{a}y^2\stackrel{\stackrel{b}{\downarrow }}{+b}y\stackrel{\stackrel{c}{\downarrow }}{+c} \qquad \left(f\left(-\cfrac{ b}{2 a}\right)~~~~ ,~~~~ -\cfrac{ b}{2 a} \right) \\\\[-0.35em] \rule{34em}{0.25pt}[/tex]

[tex]\bf 2x+y^2=0\implies 2x=-y^2\implies x=\cfrac{-y^2}{2}\implies x=\stackrel{\stackrel{a}{\downarrow }}{-\cfrac{1}{2}}y^2\stackrel{\stackrel{b}{\downarrow }}{+0}y\stackrel{\stackrel{c}{\downarrow }}{+0} \\\\\\ -\cfrac{b}{2a}\implies -\cfrac{0}{2\left(-\frac{1}{2} \right)}\implies 0\qquad therefore\qquad (f(0)~~,~~0)\implies \stackrel{vertex}{(0,0)}[/tex]

you can see it this way, x = -(1/2)y² is just a horizontal parabola opening to the left-hand-side, the -1/2 is just a stretch transformation of the parent function x = y², but as much as it stretches, their vertex is the same, at the origin.

I don’t know what the answer is I wish I could help

The answer is y=56.2x-112.4