Which ratio forms a proportion with 18/27 ?

Look at the prime factorization. If all the factors have powers that are multiples of 6, then the number is a square and a cube. If they are multiples of 3, then a cube; if multiples of 2, then a square.

1000 = 2³·5³ . . . . a perfect cube

4 = 2² . . . . a perfect square

120 = 2³·3·5 . . . . none of the above (not a square or a cube)

36 = 2²·3² . . . . a perfect square

100 = 2²·5² . . . . a perfect square

49 = 7² . . . . a perfect square

125 = 5³ . . . . a perfect cube

25 = 5² . . . . a perfect square

Answer: Z.

Step-by-step explanation:

They want you to figure formula then find right graph, but do it fastest way. If it doubles each year, graph can't be straight line, eliminate Y.

A(0) has to be $5, eliminate W. A(1) has to be double A(0), eliminate X. Check: Z shows A(1) is 10, A(2) is 20.

Answer:

The equation is A(x) = 5(2)ˣ and the graph is Graph Z.

Step-by-step explanation:

Equations on compounding interest (which this essentially is) are of the form

A(x) = p(1+r)ˣ, where p is the amount of principal, r is the interest rate and x is the amount of time.

Since Stella begins with $5, the principal is 5.

Since the amount of money doubles each year, this means we add an extra 100%; this makes r equal to 1.

This gives us the equation

A(x) = 5(1+1)ˣ = 5(2)ˣ

This graph will not be linear, as there is not a constant rate of change (there are different amounts added every year).

She begins with $5.  This means the y-intercept of the graph will be 5.

After 1 year, the amount of money doubles; this makes it 10.  The only graph that is not linear and goes through (0, 5) and (1, 10) is graph Z.

Answer:

Acute

Step-by-step explanation:

The last angle is 71 which is less than 90

Answer:

acute triangle

Step-by-step explanation:

The sum of the two angles given is more than 90°, so the remaining angle is less than 90°. All angles are acute angles, so the triangle is an acute triangle.

Answer:

31) Second number line

32) False

33) x>2

Step-by-step explanation:

31) Since -6<x has only < sign but no = sign, it will be an open dot on top of -6.

Since x≤2 has = sign, it will be a closed dot on top of 2.

So, second number line is the correct option.

32) x < -5 represents all the numbers to the left of -5 on a number line like -6,-7,-8,-9 etc.

Since 4 is on the right side of -5 on the number line, it won't be a solution of the inequality x < -5.

33) x+3 > 5

Subtracting 3 from both the sides of the inequality, we have

x + 3 -3 > 5 - 3

Cancelling out the +3 and -3 from the left side, we have

x > 2

1. The 2nd number line represents the inequality.

Explanation:

In words, the inequality reads "negative six is less than x, which is less than or equal to two". On the number line, the open circle at negative six means that -6 is not a solution to the inequality: -6 < x. The point at positive two means that positive two is a solution to the inequality: x ≤ 2. Therefore, all numbers greater than -6 and less than or equal to +2 are solutions to the inequality. This is shown on the second number line.

2. False

Explanation:

In words, the inequality reads "x is less than negative five". This means that all numbers less than -5 are solutions to the inequality. Positive four is not less than negative five, so it is not a solution to the inequality.

3. x > 2

Explanation:

To solve the inequality, we have to move all the terms that do not contain x to one side. This inequality is simple because it only requires one step: subtraction.

Solve for x: x + 3 > 5

1. Subtract 3 from both sides to get x by itself:

x + 3 - 3 > 5 - 3

2. Simplify

x > 2

Answer:

63 tons

Step-by-step explanation:

The problem statement asks for the tons of hay removed from the first pit. It is convenient to let a variable (x) represent that amount. This is said to be 3 times the amount removed from the second pit, so that amount must be x/3.

The amount remaining in the first pit is 90-x.

The amount remaining in the second pit is 75 -x/3.

Since the first pit remaining amount is half the second pit remaining amount, we can write the equation ...

... 90 -x = (1/2)(75 -x/3)

... 180 -2x = 75 -x/3 . . . . multiply by 2

... 105 - 2x = -x/3 . . . . . . subtract 75

... 315 -6x = -x . . . . . . . . multiply by 3

... 315 = 5x . . . . . . . . . . . add 6x

... 63 = x . . . . . . . . . . . . . divide by 5

63 tons of hay were taken from the first pit.

_____

Check

After removing 63 tons from the first pit, there are 27 tons remaining. After removing 63/3 = 21 tons from the second pit, there are 54 tons remaining. 27 is half of 54, so the answer checks OK.

Answer:

$12.47

Step-by-step explanation:

The total charge was ...

... $13.28 +14.25 = $27.53

The change from 2 $20 bills is ...

... 2 × $20 - 27.53 = $40.00 -27.53 = $12.47

The total cost of lunch is $27.53. Ana paid with two $20 bills, which equals $40.00. After Ana gave the two $20 bills, she received $12.47 in change.

The subject area of this question is mathematics, specifically arithmetic involving decimal numbers. To solve this, we first add together the costs of the two lunches, which are $14.25 and $13.28, that result in $27.53. Ana initially pays with two $20 bills, which sums up to $40.00. Now, we subtract the total cost of the lunches from the amount Ana paid with. So, $40.00 - $27.53 gives us $12.47. This tells us that Ana received $12.47 in change back after paying for lunch.

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Divide y by x:

150/10 = 15

135/9 = 15

30 /2 = 15

They all equal 15

This means the constant of proportionality would be y = 15x

The answer is C.

Answer:

Option C is correct

y = 15x

Step-by-step explanation:

Direct variation states that:

[tex]y \propto x[/tex]          ......[1]

then, the equation is in the form of:

[tex]y=kx[/tex], where k is the constant of variation.

From the given table :

consider any points;

x = 9 and y = 135

Substitute these in [1] we have;

[tex]135 = 9k[/tex]

Divide both sides by 9 we have;

15 = k

or

k = 15

then, the equation we have; y = 15x

Therefore,  the constant of proportionality for the table and write in the form y = kx is, y = 15x

Answer:

8√2

Step-by-step explanation:

4√2 + 7√2 - 3√2 = (√2)(4 + 7 - 3) = 8√2

Recognize that √2 is a common factor and simply add its coefficients.

[tex]4\sqrt2+7\sqrt2-3\sqrt2=(4+7-3)\sqrt2=\boxed{8\sqrt2}\\\\Answer:\ \boxed{\text{8\ square root of 2}}[/tex]

Answer:

(3, 8)

Step-by-step explanation:

For x = 3,

. . . y = 2^x

. . . y = 2^3 = 2·2·2 = 8

This is represented by the ordered pair (x, y) = (3, 8).

Answer:

(3,8)

Step-by-step explanation:

Since the answer choices are given we can plug the "x" value and see if it returns the y-value given in the ordered pair (x,y) and so:

[tex]y=2^x[/tex]

Let's use the ordered pair (3,8) meaning that when x=3 y =8 and so:

[tex]y=2^3=2\times2\times2=8[/tex]

[tex]y=8[/tex]

This is correct and so this is a solution, since the solution is unique when x=3 y is always going to return an 8.

Answer:

D

Step-by-step explanation: 153 divided by 3 = 51

Answer:

D. 153

Step-by-step explanation:

Which number is divisible by 3?

A number is divisible by 3 if you add all the digits and it is divisible by e.

A. 35

3+5 = 8

8/3  has a remainder so it is not divisible by 3

B. 133

1+3+3 = 7

7/3 has a remainder so it is not divisible by 3

C. 103

1+0+3 =4

4/3 has a remainder so it is not divisible by 3

D. 153

1+5+3 =9

9/3 =3  153 is divisible by 3

Answer:

60% increase

Step-by-step explanation:

Percentage increase = (new - old)/ old * 100

We know the new = 4.00

old = 2.50

Lets substitute the values in

Percentage increase = (4-2.5)/2.5 *100

                                   = 1.5/2.5 * 100

                                     =.6*100

                                    =60%

Answer:

C) 115 feet

Step-by-step explanation:

Assuming your setup is correct and the question is asking the height, given that the length of the slant rope is 150 ft, you find x by multiplying the equation by 150:

... 150*sin(50°) = x ≈ 115 ft

Almost any on-line calculator will compute this value. If you don't specifiy the angle is degrees, you will need to verify that it is properly interpreted. (It may be interpreted as radians. Different calculators make different assumptions.)

The Google or Bing search boxes are pretty reliable calculators. Usually * is suitable as the multiplication indicator, and / works for division. They follow the order of operations rigorously, so parentheses are needed for numerators, denominators, and exponents when more than a single number is involved.

_____

There are on-line equation solvers, too. I've found them to be more fussy and less useful. One likes to give irrational results as the ratio of two (large) integers, for example.

Answer:

115 feet

Step-by-step explanation:

Given : A hot-air balloon is tied to the ground with two taut ropes. One rope is directly under the balloon and makes a right angle with the ground. The other rope forms an angle of 50º with the ground.

To Find: What is the height x, to the nearest foot, of the balloon?

Solution:

We are given a set up :

[tex]sin 50 ^{\circ}=\frac{x}{150}[/tex]

Using scientific calculator find the value of sin 50

0.76604

[tex]0.76604=\frac{x}{150}[/tex]

[tex]0.76604 \times 150=x[/tex]

[tex]114.906=x[/tex]

Hence the height of the balloon is 115 feet.

Option C is correct.

Answer:

$3,659.82

Step-by-step explanation:

Adding to the checkbook those debits and credits not already there brings its balance to ...

... $3045.58 +651.84 -37.60 = $3659.82

Adjusting the bank's balance by the deposits and checks not already there brings its balance to ...

... $4262.92 +220.05 -325.50 -497.65 = $3659.82

Thus, the reconciled accounts will agree on the balance $3659.82.

The reconciled balance for Gregory Co. was $3,659.82 after accounting for all transactions including deposits, outstanding checks, credited note, and bank charges.

The question involves reconciling the checkbook balance with the bank statement balance for Gregory Co. To reconcile the bank balance with the checkbook balance, we need to account for any transactions that have not been reflected in one or the other. We start with the bank statement balance and adjust it for outstanding checks and deposits not reflected on the statement.

Answer:

r = -0.9997  

Step-by-step explanation:

A statistics calculator gives the value

r = -0.9997

You can see in the graph below that it represents an excellent negative correlation between x and y.

Every point appears to be exactly on the regression line .

It represents a linear positive correlation between x and y −0. 999.

Given

The table shows Britney's distance, in miles, from her destination after different time intervals in hours:

Time (hours) (x) 2 4 1 3 6 5 7

Distance from destination (miles) (y) 1,000 880 1,060 940 760 820 690

A number between +1 and −1 is calculated so as to represent the linear interdependence of two variables or sets of data.

Then,

The correlation coefficient for the data, and what does it represent is;

It represents no correlation between x and y.

Hence, it represents a linear positive correlation between x and y −0. 999.

To know more about the correlation coefficient click the link given below.

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Answer:

D. The inequality has an equal sign it

Step-by-step explanation:

We use solid lines whenever the inequality contains [tex]\leq[/tex] or [tex]\geq[/tex]. That means it contains an equal sign which means the boundary line is inclusive.

On the other hand when the inequality does not have an equal sign in it we use a dashed line to indicate that all values on the boundary line are not inclusive.

That is we use a dashed or broken line for the boundary line of an inequality whenever it contains [tex]\:<\: or \:>\:[/tex].

The correct answer is D

Answer:

The percent increase was 48.7.

Step-by-step explanation:

The absolute increase in enrollment is 1084 - 729 = 355. This corresponds to a relative increase of 355/729=0.487 (relative to Aug 2017). The proportion 0.487, expressed in percent: 48.7%

Depending on your current method to exercise, you could solve this using the proportionality method: 355/729 = x/100, then cross-multiply and solve for x. Same thing.

Nicole has already spent 17 dollars, and will spend c more dollars, for a total of [tex] 17+c [/tex] dollars.

We want this total to be more than 30, so we have

[tex] 17+c>30 [/tex]

Solving this inequality for c yields

[tex] c > 13 [/tex]

The question asks about the additional amount Nicole will need to spend to exceed a total of $30. Given she has already spent $17, the inequality c > 13 represents the additional amount, in dollars, Nicole must spend to meet this requirement. Therefore, Nicole must spend more than $13.

The question is about calculating the possible additional spending of Nicole in order to ensure her total spent will exceed $30. Nicole has already spent $17. As per the condition, set up the inequality which indicates that Nicole will spend more than $30. It's mentioned that we can use c for the additional amount Nicole will spend. Therefore:

17 + c > 30

This inequality can be solved for c by subtracting 17 from both sides:

c > 30 - 17

So,

c > 13

This means Nicole will have to spend more than $13 additionally to ensure her total spending is more than $30.

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x = 77.56 cm

y = 69.71 cm

The mnemonic SOH CAH TOA reminds you that ...

... Cos = Adjacent/Hypotenuse

so ...

... cos(64°) = (34 cm)/x

... x = (34 cm)/cos(64°) ≈ 77.56 cm

___

It also reminds you ...

... Tan = Opposite/Adjacent

so ...

... tan(64°) = y/(34 cm)

... (34 cm)·tan(64°) = y ≈ 69.71 cm

5.3

The mnemoic SOH CAH TOA reminds you that ...

... Tan = Opposite/Adjacent

... tan(24°) = x/12

Then multiplying by 12 gives ...

... 12·tan(24°) = x = 5.34274 ≈ 5.3

$450

Each year, the amount of interest earned is ...

... 4.5% × $5000 = $225

After 2 years, a total of ...

... $225 × 2 = $450

has been transferred.

_____

Comment on percentages

Of course, you know that 4.5% = 4.5/100 = 45/1000 = 0.045.

You can think of the % symbol as a fancy (shorthand) way to write /100. (Likewise, the ‰ symbol means /1000.)

Answer:

0.48

Step-by-step explanation:

The problem at hand

[tex]500 = (2)(10^{5x})[/tex]

First divide out 2 on both side of the = sign

[tex]500 = (2)(10^{5x})[/tex]

[tex]\frac{500}{2} = \frac{(2)(10^{5x})}{2}[/tex]

[tex]250 = 10^{5x}[/tex]

Now take the base 10 log on each side of the = sign

[tex]\log_{10} (250) = \log_{10} (10^{5x})[/tex]

Now move the exponent to the left like so

[tex]\log_{10} (250) = 5x \log_{10} (10)[/tex]

Rule you need to know. [tex]\log_a (a) = 1[/tex]

[tex]\log_{10} (250) = 5x (\log_{10} (10))[/tex]

[tex]\log_{10} (250) = 5x(1)[/tex]

[tex]\log_{10} (250) = 5x[/tex]

Now divide 5 from both sides of the equation

[tex]\frac{\log_{10} (250)}{5} = \frac{5x}{5}[/tex]

[tex]\frac{\log_{10} (250)}{5} = x[/tex]

[tex]x = \frac{\log_{10} (250)}{5}[/tex]

[tex]x = 0.4795880017[/tex]

Round to nearest hundredths

[tex]x = 0.48[/tex]

Side Note:

You could approach this problem in a different manner.

For instance, we could have done the following

[tex]x = \frac{\log_{10} (250)}{5(\log_{10} (10))}[/tex]

Also, you did not have to use log with a base 10. You could have used the natural log, which is [tex]\ln_e (x)[/tex]

[tex]x = \frac{\ln_{e} (250)}{5(\ln_{e} (10))}[/tex]

Solving the equation gives 0.48 when rounded to the nearest hundredth.

To solve the equation [tex]500 = (2)(105x)[/tex] , we will first isolate the exponential term. The steps are as follows:

Divide both sides of the equation by 2 to get 250 = 105x.

Take the common logarithm (log) of both sides of the equation to get [tex]log(250) = log(105x).[/tex]

Using logarithmic properties, we have log(250) = 5x log(10)

Now we simplify further since log(10) is 1, so log(250) = 5x.

Divide both sides by 5 to solve for x, which gives [tex]x = log(250) / 5.[/tex]

Using a calculator with a LOG button, we find log(250) approximately equals 2.39794 and, therefore, x is approximately 0.47959 when rounded to five decimal places.

However, we are asked to round x to the nearest hundredth, so the final answer is x = 0.48.

Answer:

2.4 * 10^1

Step-by-step explanation:

Divide the two numbers. 4.8 * 10^3 = 4800

4800/200 = 24

Put into scientific notation

24 = 2.4 * 10^1

4.8 * 10^3 is 24 (2.4*10^1) times greater than 200

The total amount raised by the school is 24 times greater than the amount raised by Graham's class.

The amount raised by Graham's class is $200.

The total amount raised by the school is [tex]4.8 * 10^3.[/tex]

To find the number of times greater the total amount raised by the school is compared to Graham's class, we need to divide the total amount raised by the school by the amount raised by Graham's class.

So, we divide 4.8 * 10^3 by 200 to find the number of times greater the total amount raised by the school is compared to Graham's class.

Therefore,

[tex]= 4.8 * 10^3/ 200[/tex]

[tex]= 2.4 * 10^1.[/tex]

Therefore, the total amount raised by the school is 24 times greater than the amount raised by Graham's class.

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Answer:

A. 49°

Step-by-step explanation:

∠O is the other base angle (along with ∠Q) of the isosceles triangle OPQ. Base angles of an isosceles triangle have the same measure.

Answer: First prism has the greatest volume.

Step-by-step explanation:

Since we have given that

Volume of prism = Length × Breadth × Height

So, we need to find the greatest volume, for which we find volumes of all figures:

1) Volume of prism would be

[tex]5\times 7\times 5\\\\=175\ cm^3[/tex]

2) Volume of prism would be

[tex]10\times 3\times 4\\\\=120\ cm^3[/tex]

3) volume of prism would be

[tex]7\times 7\times 3\\\\=147\ cm^3[/tex]

4) Volume of prism would be

[tex]5\times 3\times 7\\\\=105\ cm^3[/tex]

Hence, first prism has the greatest volume.

The volume of the prism with the Greatest volume is 250cm³

The volume of a prism is calculated by multiplying the prism's base area by its height. Mathematically expressed as

V = Base Area×Height

, it represents the space enclosed within the prism.

Since the prism is a cuboid, then

V = l × w × h

Where h is the height , l is the length and w is the width.

V = 5 × 5 × 10

V = 250 cm³

The volume of the prism is 250cm³

Answer:

See below for the graph.

Step-by-step explanation:

A circle or ellipse can be defined using the same sort of equation. Here, we have chosen to use the formulation ...

... ((x -a)/p)^2 +((y -b)/q)^2 -1 = 0

This will be the general form of the equation for an ellipse with center (a, b) and semi-axes p and q, in the x- and y-directions, respectively. When the axes are the same length, the ellipse is a circle.

By defining the function ...

... c(a, b, p, q, x, y) = ((x -a)/p)^2 +((y -b)/q)^2 -1

we can use the same function for all of the circles/ellipses in the figure. The parabola has vertex (0, -6) and a vertical scale factor of -1, so it can be formulated using the vertex form:

... y = k(x -a)^2 +b . . . . . for vertex (a, b) and vertical scale factor k.

_____

The equations

Parabola is a plane curve. The iconic character can be made with the following equation as given below,

We need to draw 3 circles, an ellipse and a parabola, in order to get the desired digram.

For a circle, we only need to know the radius of the circle and the center of the circle,

1. The head(red circle)

The head of the circle is drawn from the origin of the coordinate, while the radius can be found by dividing the length between the points where the circle cuts the x-axis.

[tex]Radius =\dfrac{6-(-6)}{2} = 6[/tex]

Equation of the circle face,

[tex]\text{Equation of the circle face} => {(x-0)^2+(y-0)^2} = 6^2[/tex]

2. The Left Eye (Blue Circle)

3. The Right Eye (Green Circle)

Similarly for the eyes of the diagram,

The right eye = [tex](x-2)^{2}+(y-2)^{2}=1^{2}[/tex]

The left eye = [tex](x+2)^{2}+(y-2)^{2}=1^{2}[/tex]

4.  The Mouth (Purple Ellipse)

The equation of the parabola can be written as,

(x/3)² +(y+2)² -1 = 0

5. The Body (Black Parabola)

The parabola can be made using the equation,

Equation of a parabola

y = a(x-h)² + k

where,

(h, k) are the coordinates of the vertex of the parabola in form (x, y);

a defines how narrower is the parabola, and the "-" or "+" that the parabola will open up or down.

Therefore, the equation for the body,

Equation of the parabola = [tex]y = -(x-0)^2 -6[/tex]

Learn more about Parabola:

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9. AM ≅ AT

10. x=3, y=5

AH being the perpendicular bisector of MT means MH ≅ TH. Then ΔAHM ≅ ΔAHT by SAS, and by CPCTC.

... SAS — side-angle-side: if two adjacent sides and the included angle of a triangle are congruent to their corresponding sides and angles in another triangle, the two triangles are congruent.

... CPCTC — Corresponding Parts of Congruent Triangles are Congruent

___

Using the result of problem 9 as a guide, you can say that ...

... 2x = x+3 ⇒ . . . . (subtract x from both sides)

... y +4 = 2y -1 ⇒ . . . . (add 1-y to both sides)

about 0.380435 hours . . . approximately 22 minutes 49.6 seconds

Start with this equation ...

... 10.5 hours = 27.6 miles

And divide both sides by 27.6

... 10.5/27.6 hours = 1 mile

... 0.380435 hours = 1 mile

Answer:

C. 26 + 11 - S

Step-by-step explanation:

She had 26 shells

She collected 11 more shells ( that is addition)

26 + 11

Then she gave S shells away ( that is subtraction)

26+11-S

She has 26+11-S

Answer:

C. 26 + 11 - S

Step-by-step explanation: