A group of students is arranging squares into layers to create a project. The first layer has 4 squares. The second layer has 8 squares. Which formula represents an arithmetic explicit formula to determine the number of squares in each layer?

Answer: Brian invested $16000 in Fund B .

Step-by-step explanation:

Let x be the amount Brian invested in Fund B.

Given, The $8000 that he invested in Fund A returned a 4% profit. The amount that he invested in Fund B returned a 1% profit.

i.e. profit on Fund A = 4% of 8000 = 0.04 ×8000 = $320

Profit on Fund B = 1% of x = 0.01x

Together they earn 1% profit, i.e. Combined profit = 2% of (8000+x)

= 0.02(8000+x)

As per question,

Combined profit=Profit on Fund A+Profit on Fund B

[tex]\Rightarrow\ 0.02(8000+x) =320+0.01x\\\\\Rightarrow\ 0.02(8000) +0.02x=320+0.01x\\\\\Rightarrow\ 160+0.02x=320+0.01x\\\\\Rightarrow\ 0.02x-0.01x=320-160\\\\\Rightarrow\ 0.01x=160\\\\\Rightarrow\ x=\dfrac{160}{0.01}\\\\\Rightarrow\ x=16000[/tex]

Hence, Brian invested $16000 in Fund B .

Answer:

0

Step-by-step explanation:

Notice that the last factor is null (9×0)

So the result will be null since any number that is multiplied by 0 equals 0.

Answer:

24 and 36

Step-by-step explanation:

2x + 3x = 60

5x = 60

x = 12

Dawn has 2(12) = 24

Jackson has 3(12) = 36

Step-by-step explanation:

To find the number of baseball cards each person received we must first find the total parts

That's

2 + 3 = 5

For Dawn

Dawn's part is 2

We have

2/5 × 60

For Jackson

Jackson's part is 3

That's

3/5 × 60

Hope this helps you

Answer:

29.5 mm

Step-by-step explanation:

We are told that the average monthly rainfall for 6 months was 28.5 mm.

Thus, total for the 6 months = 28.5 × 6 = 171 mm

Now, we are told that it rained 1 mm extra each month.

So extra for the six months = 1 × 6 = 6mm

New total for 6 months = 171 + 6 = 177 mm

So, new average for 6 months = 177/6 = 29.5 mm

Answer:

4a

Step-by-step explanation:

4a

the top and right are a-b, but you have to add the b’s back in, so really all sides are a

a+a+a+a=4a

Answer: 4a

Step-by-step explanation: perimeter is the length of all sides added together. Every length is given combine like variables and you will get 4a+2b-2b. 2b-2b is 0 which leaves you with 4a

Answer:

A = 62.35 cm²

Step-by-step explanation:

Use the area formula A = [tex]\frac{\sqrt{3}a^2}{4}[/tex], where a is the side length.

Plug in the values:

A = [tex]\frac{\sqrt{3}(12^2)}{4}[/tex]

A = [tex]\frac{\sqrt{3}(144)}{4}[/tex]

A = 62.35 cm²

Answer:

-1

Step-by-step explanation:

3/2 * (-22/33)

Simplify by dividing the second fraction by 11

3/2 * (-2/3)

Rewriting

3/3 * (-2/2)

-1/1

Answer:

-1

Step-by-step explanation:

(a/b)(c/d) = (a*c)(

(3/2)(-22/33)

(3*-22)/(2*33) = -66/66 = -1

Answer:

Step-by-step explanation:

Hello, please consider the following.

The "vertex form" is as below.

[tex]y=a(x-h)^2+k\\\\\text{Where (h, k) is the vertex of the parabola.}\\[/tex]

Let's do it!

[tex]f(x)=\dfrac{1}{2}x^2+3x-2\\\\f(x)=\dfrac{1}{2}\left(x^2+3*2*x\right) -2\\\\f(x)=\dfrac{1}{2}\left( (x+3)^2-3^2\right)-2\\\\f(x)=\dfrac{1}{2}(x+3)^2-\dfrac{9}{2}-\dfrac{4}{2}\\\\f(x)=\dfrac{1}{2}(x+3)^2-\dfrac{9+4}{2}\\\\\large \boxed{\sf \bf \ \ f(x)=\dfrac{1}{2}(x+3)^2-\dfrac{13}{2} \ \ }[/tex]

Thank you.

Answer:

239 ft².

Step-by-step explanation:

Let P represent the price for tiling.

Let S represent the size of the room.

From the question,

Price (P) varies directly as the size (S) i.e

P & S

P = KS

Where K is the constant of proportionality.

Next, we shall determine the value of K as follow

Price (P) = $ 4224

Size (S) = 264 ft²

Constant of proportionality (K) =?

P = KS

4224 = K × 264

Divide both side by 264

K = 4224/264

K = 16

Finally, we shall determine the size of the kitchen that will cost $ 3824 for tiling.

This is illustrated below:

Price (P) = $ 3824

Constant of proportionality (K) = 16

Size (S) =?

P = KS

3824 = 16 × S

Divide both side by 16

S = 3824/16

S = 239 ft²

Therefore, the size of the kitchen is 239 ft².

Answer:

Step-by-step explanation:

Let S be the sample space, n(S) = 60

a) Let A be the event that the selected athlete uses

s less than a minute, n(A) = 59

The probability that a randomly selected athlete uses less a minute,  P(A) = n(A)/n(S) = 59/60 = 0.9833

b) 1 - 0.9833 = 0.0167

c)  1 - 1 = 0

Answer:

B. Congruent - SSS

Step-by-step explanation:

Since, corresponding sides of both the triangles are congruent. Hence, both the triangles are congruent by SSS Postulate.

ΔMNO ≅ ΔPQR due to Congruent-SSS

Two triangles are said to be congruent if their corresponding sides and angles are equal.

Given:

In ΔMNO and ΔPQR

Side ME=Side PQ

Side NO=Side QR

Side MO=Side PR

MNO ≅PQR

Since, corresponding sides of both the triangles are congruent.

So, both the triangles are congruent by SSS Postulate.

Hence , ΔMNO ≅ ΔPQR

learn more about of congruent triangles

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Answer:

[tex]\boxed{0.15}[/tex]

Step-by-step explanation:

Part 1: Solve for the total amount of marbles

To solve for the probability of certain events, a population is needed to derive this information from. In order to find this population, add up the amounts of each marble.

8 + 14 + 12 = 34 marbles

Part 2: Determine the probabilities

Now, given the amounts of marbles, simply multiply the ratios of blue marbles to total marbles and the ratio of clear marbles to total marbles to get the combined probability.

[tex]\frac{12}{34}*\frac{14}{33} = \frac{28}{187} \approxeq 0.1497 \approxeq 0.15 * 100 = 15[/tex]

The probability of these events occurring simultaneously is 15%.

Answer:

(5, 2)

Step-by-step explanation:

(5, 6) go down 4 units means subtract 4 from the y

(5, 2)

The point to end up will be (5, 2).

What is Coordinates?

A pair of numbers which describe the exact position of a point on a cartesian plane by using the horizontal and vertical lines is called the coordinates.

Given that;

In the first quadrant you start at (5, 6 ) and move 4 units down.

Now,

Since, In the first quadrant you start at 5, 6 and move 4 units down.

Hence, The end up point = (5, 6 - 4)

                                       = (5, 2)

Thus, The point to end up will be (5, 2).

Learn more about the coordinate visit:

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Answer:

about 72 dollars

Step-by-step explanation

"about" tells us to round our numbers. Therefore, 7.8 becomes 8. As each pound is $8.99, we multiply the two and get 71.92, which is "about" 72.

Answer:

$72

Step-by-step explanation:

To find the cost, multiply the price per pound by the number of pounds.

8.99(7.8)

= 70.12

This is closest to $72

2^1 would be the answer.

2^2 x 2^3 is 32

2^4 is 16

32/16 is 2

2^1 is 2 so the answer is 2^1

Answer:

2¹

Step-by-step explanation:

When multiplying exponents of the same base, you can simply add the exponents together so 2² * 2³ = 2⁽²⁺³⁾ = 2⁵. When dividing exponents of the same base, you can simply subtract the exponents so 2⁵ / 2⁴ = 2⁽⁵⁻⁴⁾ = 2¹.

Answer:

WY= 25

XY= 23

VZ=36

so,

WY/XY = YZ/VZ

25/23 = YZ/25 (then do cross multiply)

25×25 = 23 × YZ

625= 23 × YZ

625/23= YZ

27,17= YZ

#i'm indonesian

#hope it helps.

Answer:

[tex]\huge \boxed{13.04}[/tex]

Step-by-step explanation:

The triangles are congruent, we can use ratios to solve.

WY/XY = (WY+YZ)/VZ

Let the length of YZ be x.

25/23 = (25+x)/35

Cross multiply.

23(25+x) = 25 × 35

575 + 23x = 875

Subtract 575 from both sides.

575 + 23x - 575 = 875 - 575

23x = 300

Divide both sides by 23.

(23x)/23 = 300/23

x = 13.0434782609...

We have:

h - height

b = 2h - base

A = 36 - area

so:

[tex]A=\frac{1}{2}\cdot b\cdot h\\\\A=\frac{1}{2}\cdot 2\cdot h \cdot h\\\\A=h^2\\\\36=h^2\quad|\sqrt{(\dots)}\\\\\boxed{h=6}[/tex]

Answer:

2(5x - 4)(x + 1)

Step-by-step explanation:

10x^2 + 2x − 8 =

First, factor out the GCF of all terms which is 2.

= 2(5x^2 + x - 4)

5x^2 factors into 5x and x.

= 2(5x      )(x       )

-4 factors into -4 and 1, -1 and 4, and -2 and 2. Use the set of two factors in the proper positions that will give the middle term.

= 2(5x - 4)(x + 1)

Answer:

[tex]\large \boxed{2(5x-4)(x+1)}[/tex]

Step-by-step explanation:

[tex]10x^2 + 2x - 8[/tex]

Rewrite 2x as 10x - 8x.

[tex]10x^2 + 10x-8x - 8[/tex]

Factor out the two groups.

[tex]10x(x+1)-8(x+1)[/tex]

Take x+1 as a common factor.

[tex](10x-8)(x+1)[/tex]

Factor 10x - 8.

[tex]2(5x-4)(x+1)[/tex]

Answer:

the equilibrium expected growth rate is 6.65%

Step by step Explanation:

We were given stock sold per share of $32.50

Dividend per share =$1.25

Required Return rate = 10.5%

Then we can calculate Percentage of Dividend for share as;

dividend of br. 1.25 per share at the end of the year (D1=br.1.25)

= 1.25×100= 125

Let the dividend percentage = y

stock sold per share × y= 125

125= 32.50y

y = 125/32.50

y= 3.85

y= 3.85*100%

Then the Dividend percentage = 3.85%

Growth rate=(required rate of return -Dividend percentage)

= 10.5 - 3.85 = 6.65

Therefore, the equilibrium expected growth rate is 6.65%

[tex]\dfrac{x}{6}-7=-4\\\dfrac{x}{6}=3\\x=18[/tex]

Answer:

x = 18

Step-by-step explanation:

x/6 - 7 = -4

Add 7 to each side

x/6 - 7+7 = -4+7

x/6 = 3

Multiply each side by 6

x/6 *6 = 3*6

x = 18

Answer:

It is a unit of radius that is radius of 1. Thus, the distant to the middle to any edge is always 1.

Step-by-step explanation:

Answer:

1. GH

2. a

Step-by-step explanation:

Perpendicular: When 2 lines meet at 90 degrees

1. It is line segment GH because AB and GH meet at a 90 degree angle (since there is a box at angle GHF indicating that it is 90 degrees)

2. It has to be a units because it is a rectangle where the top and bottom are congruent and the sides are too

This is a rectangle since AB and CD are parallel and GH can be a transversal line, according to same side interior angles theorem EGH is a also 90 degrees. That means FEG is 90 degrees too because then the quadrilateral will add up to 360 degrees

Answer:

Option a. Y=3x

Step-by-step explanation:

Let us use cross multiplication method.

Let the cost of 1 magazine be x.

No. of copies                               Cost

1)50                                                $150

2)1                                                      x

50x=150 x 1               equation(1)

x=150/50

x=$3

Now see equation (1),

150=50x

150=50 x 3

Here let us represent the cost as y and no. of copies as x.

Y=3x

Therefore, a. Y=3x is the right answer.

Thank you!

Answer:  Yes. The sales tax is 5% which equals $4.20 for $84

Step-by-step explanation:

[tex]\dfrac{0.60}{12}=0.05\qquad \rightarrow 5\%\\\\\\\dfrac{1.20}{24}=0.05\qquad \rightarrow 5\%\\\\\\\dfrac{1.80}{36}=0.05\qquad \rightarrow 5\%\\\\\\\dfrac{2.40}{48}=0.05\qquad \rightarrow 5\%[/tex]

The sales tax rate is proportional for the values in the table.

$84 x 0.05 = $4.20

The sales tax on a purchase of $84 is $4.20

Answer:

x=1

Step-by-step explanation:

subtract 38 from both sides:

7x=7

divide both sides by 7 to isolate x:

x=1

HOPE THIS HELPS!!!! :)

Answer:

[tex]\huge\boxed{A)\ 7.618\times10^{-6}}[/tex]

Step-by-step explanation:

The scientific notation:

[tex]a\cdot10^n[/tex]

where

[tex]1\leq a<10;\ n\in\mathbb{Z}[/tex]

We have

[tex]761.8\times10^{-8}[/tex]

We need to move the decimal point two places to the left.

[tex]\underbrace{(7.618\times10^2)}_{=761.8}\times10^{-8}=7.618\times(10^2\times10^{-8})[/tex]

use

[tex]a^n\cdot a^m=a^{n+m}[/tex]

[tex]=7.618\times10^{2+(-8)}=7.618\times10^{-6}[/tex]

Answer:

a

Step-by-step explanation:

Answer:

The point (-2, 4) is not a solution of the linear equation, 5·y =  3·x + 18

Please find attached the required graph of the linear equation 5·y =  3·x + 18 written in the form y = 3/5·x + 18/5

Step-by-step explanation:

The given equation is 5·y = 3·x + 18, from which we have;

y = 3/5·x + 18/5

To draw the graph, we generate for vales of y corresponding to values of x as follows;

x,      y

-6,    0

-5,    0.6

-4,    1.2

-3,    1.8

-2,    2.4

-1,      3

0,      3.6

1,       4.2

2,      4.8

3,      5.4

4,       6

5,       6.6

6,       7.2

7,        7.8

8,        8.4

9,        9

10,      9.6

11,       10.2

12,      10.8

13,      11.4

14,       12

15,      12.6

16,      13.2

Therefore, when y = 0, x = -6, when x = 0, y = 3.6, when x = -2, y = 2.4, when y = 4, x = -2, x = 6

Therefore, the point (-2, 4) is not a solution of the linear equation, 5·y =  3·x + 18

Answer: Infinitely many solutions

Step-by-step explanation:

There are many solutions because the lines lies on top of each other.

i dont know the exact answer but its not  

One solution

Two solutions

so its most likely

Infinitely many solutions

Answer:

The answer is

Step-by-step explanation:

To find the slope passing through two points we use the formula

Where

m is the slope

( x1 , y1) and ( x2 , y2) are the points

From the question the points are

(-8,-3) and (2, 3)

So the slope is

Hope this helps you

Answer:

The length of the bridge is 72 cm

Step-by-step explanation:

In order to find the length of bridge, we have to apply distance formula which is D = S × T where S represents speed and T is time :

[tex]d = s \times t[/tex]

[tex]let \: s = 18,t = 4[/tex]

[tex]d = 18 \times 4[/tex]

[tex]d = 72 \: cm[/tex]

The length of the bridge is 11 cm .

When an object moves in a straight line at a steady speed, we can calculate its speed if we know how far it travels and how long it takes. This equation shows the relationship between speed, distance traveled and time taken:

Speed is distance divided by the time taken.

For example, a car travels 30 kilometers in 2 hours.

Its speed is 30 ÷ 2 = 15km/hr.

Formula used :

Distance  = Speed * Time

Time = Distance / Speed

Speed = Distance / Time

According to the question

Length of train = 61 cm

Speed of train = 18 cm/s

Time taken to cross the bridge = 4 seconds

In this length traveled by train = length of train + Length of bridge

( as time given is to completely cross platform )

Therefore,

length traveled by train = 61 + Length of bridge

formula used

Distance  = Speed * Time

61 + Length of bridge =  18 * 4

61 + Length of bridge = 72

Length of bridge  = 72 - 61

Length of bridge  = 11 cm

Hence, the length of the bridge is 11 cm .

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