Sarah made 6 dozen cupcakes for a party at work. Some of her co-workers, c, each ate 3 cupcakes. Now, there are 45 cupcakes
left. Which equation represents this situation?
OA. (12 x 6)-(c x 3) = 45
OB. (cx 3)-12 = 45
OC. cx 3=45
OD. (12 x 6)- c = 45

Let's let w = the width of the rectangle.  If the length is 10 yards less than 3 times the width, then the length is 3w - 10.

How do we find the area?  Length times width, right?

So, we have w(3w - 10) = 77.  Distributing, we get 3w2 - 10w = 77.

We need to put it all on one side, so we subtract 77 from both sides.

3w2 - 10w - 77 = 0

Now, we have to factor the left side. To do this, we multiply 3(-77) = -231.  What are two factors of -231 that add up to -10? How about -21 and 11?  -21(11) = -231 and -21 + 11 = -10.

This may not be how you are taught, but we are now going to split -10w into -21w + 11w and plug that into our equation.

Sooooo, now we have 3w2 - 21w + 11w - 77 = 0

Next, we are going to look at the first two terms, 3w2 - 21w.  What is common between the two? 3w. Factoring out 3w, we get 3w(w - 7).

Now, the second two terms, 11w - 77. What is common? 11. Factoring out 11, we get 11(w - 7).

Putting all of that together, we now have 3w(w - 7) + 11(w - 7) = 0.

I can explain why and make it more confusing, so I'll just tell you that, since the w - 7 is the same in both parentheses, we keep that as one set of parentheses and combine what's in front into a second set of parentheses.

So, we have (w - 7)(3w + 11) = 0

Lastly, for the left side to equal 0, then either w - 7 and/or 3w + 11 has to equal 0, right?

We pull each out and set them equal to 0.

w - 7 = 0

     w = 7

If we plug in 7, we get (7-7)(3(7) + 11) = (0)(21+11) = 0(32) = 0, which is what we want.

3w + 11 = 0

        3w = -11

          w = -11/3

If we plug -11/3 into the same equation, we'd get 0, again what we want.  However, we can't have a negative length!  Therefore, -11/3 is out as an answer.

Our width is 7.  Since the length is 3w - 10, we plug in 7 and get 3(7) - 10 = 21 - 10 = 11.

Let's check. Length times width = 7(11) = 77. Check!

Answer:

Interest = $720

Balance = $9,720

Step-by-step explanation:

P = $9,000, the principal

r = 8% = 0.08, the interest rate

n = 2, semiannual compounding

After 6 months, the interest is

9000 * 0.08 = $720

The balance after 6 months is

9000 + 720 = $9720

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The student would consume 1,095/24, or 45.625 cases of Mt. Dew per year.

Consume is an action or process of buying or using goods or services. It is the use of a resource, typically money or time, for a specific purpose. It is the purchase of goods or services for personal use or for the use of a family, business or organization. Consumption of goods and services is the basic activity of any economy.

Assuming that there are 365 days in a year, the student would consume 1,095 cases of Mt. Dew per year. This can be calculated by multiplying 3 cans per day by 365 days, resulting in a total of 1,095 cans. Since there are 24 cans per case, the student would consume 1,095/24, or 45.625 cases of Mt. Dew per year.

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The standard deviation of the number of toys donated by juniors is greater than that of seniors.

It is the measure of the dispersion of statistical data. Dispersion is the extent to which the value is in variation.

[tex]\rm \sigma = \sqrt{\dfrac{\Sigma (x_i - \mu)^2}{n}}[/tex]

For the seniors, the mean is given as,

Mean = (5 x 2 + 35 x 2 + .... + 15 x 2) / 10

Mean = 26

Then the standard deviation is given as,

σ = √[(26 - 5)² + (26 - 5)² + (26 - 15)²] / 10

σ = 14.28

For the juniors, the mean is given as,

Mean = (40 x 2 + 25 x 2 + ....... + 40 x 2) / 10

Mean = 26

Then the standard deviation is given as,

σ = √[(26 - 40)² + (26 - 25)² + (26 - 40)²] / 10

σ = 13.19

The standard deviation of the number of toys donated by juniors is greater than that of seniors.

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The complete question is given below.

Answe

Step-by-step explanation:

answer is 9

The 1995 processor when compared to the processor in today's phones is 12 .5 times larger .

To find how much larger the 1995 processor is , you first need to find the area of the processors.

Area of 1995 processor:

= 3. 8 x 2 . 9

= 11. 02 cm ²

Area of 2005 processor :

= 1. 1 x 0. 8

= 0. 88 cm ²

In comparison to the 2009 processor, the 1995 processor is :

= 11. 02 / 0.88

= 12 .5 times larger

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The amount that should be deposited monthly is $286.66.

The monthly deposit is the periodic payment into an investment account that earns interest at a compound rate.

The monthly deposit can be determined using an online finance calculator.

N (# of periods) = 60 months (5 years x 12)

I/Y (Interest per year) = 6%

PV (Present Value) = $0

FV (Future Value) = $20,000

Results:

Monthly Deposit = $286.66

Sum of all periodic deposits = $17,199.36

Total Interest = $2,800.64

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Answer:

slope-5\7 is the answer

Answer:

Choice A (x=9)

Step-by-step explanation:

There are 180 degrees in a triangle, as seen in the picture; the triangle shown is an equilateral triangle meaning all angles are the same; therefore, each side has to be 60 degrees. Therefore the answer we plug into 5x+15 must simplify to 60. So:

5x+15

plug in 9

= 5 (9) + 15

= 45 + 15

= 60

The range of the side of the square is 24 to 31. The interval notation is (24,31).

What is interval notation?

An interval on a number line can be represented using interval notation. It is a method of representing subsets of the real number line, in other words.

Given that, the perimeter of a square must be greater than 96 inches but less than 124 inches.

Inequality form is

96 < P < 124

Where P is the perimeter.

The perimeter of a square is P = 4s, where s is the length of the side.

Putting P = 4s in 96 < P < 124

96 < 4s < 124

Divide by 4:

24 < s < 31

The interval notation is (24,31).

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Step-by-step explanation:

geometric mean theorem for right-angled triangles :

height = sqrt(pq)

where p and q are the parts of side as split by the height of that side.

19.

x = sqrt(4×16) = sqrt(64) = 8

20.

y = sqrt(5×8) = sqrt(40) = 6.32455532...

21.

18 = sqrt(12y)

18² = 12y

324 = 12y

y = 27

22.

10 = sqrt(25x)

10² = 25x

100 = 25x

x = 4

23.

Pythagoras

x² = 5² + height² = 25 + 4×5 = 25 + 20 = 45

x = sqrt(45) = 6.708203932...

24.

Pythagoras

b² = 16² + height² = 256 + 6×16 = 256 + 96 = 352

b = sqrt(352) = 18.76166304...

25.

Pythagoras

27² = 16² + height² = 256 + 16(z - 16) =

= 256 + 16z - 256 = 16z

729 = 16z

z = 729/16 = 45.5625

26.

Pythagoras

x² = (8 - 2)² + height² = 6² + (8 - 2)×2 =

= 36 + 12 = 48

x = sqrt(48) = 6.92820323...

Answer: 90%

Step-by-step explanation:

Step 1: Calculate the total number of marbles in the bag.

3 red + 3 green + 15 yellow + 9 purple = 30 marbles

Step 2: Calculate the number of marbles that are not red.

3 green + 15 yellow + 9 purple = 27 marbles

Step 3: Calculate P(not red).

27/30 = 0.9

Answer: 90%

Answer:

the answer is answer c

Step-by-step explanation:

This simplified form of given expression is: 21952s¹⁵t³/(-8s⁶t¹²) = 21952 / -8 *s¹⁵t³ / s⁶t¹² = 2744 / -1 * s⁹t⁻⁹

An expression or mathematical expression is a finite collection of symbols that is well-formed according to context-dependent norms. In mathematics, an expression is a phrase that has at least two numbers or variables and at least one arithmetic operation. Addition, subtraction, multiplication, or division are all examples of math operations. An expression in mathematics is a collection of numbers, variables, and functions (such as addition, subtraction, multiplication or division etc.) Expressions and phrases are similar in structure.

Here,

Now, we can multiply this result by the original expression raised to the power of 3:

(4s⁵t⁻⁷/−2s⁻²t⁴)³ * (1/(-8s⁶t¹²)) = (4s⁵t⁻⁷)³ / (-8s⁶t¹²)

Finally, we'll simplify the numerator by raising 4s⁵t-7 to the power of 3:

(4s⁵t-7)³ = (4s⁵t)³ * (-7)³ = 64s¹⁵t³ * 343 = 21952s¹⁵t³

Putting it all together, we get the abbreviated version of the given expression: 21952s¹⁵t³/(-8s⁶t¹²) = 21952 / -8 *s¹⁵t³ / s⁶t¹² = 2744 / -1 * s⁹t⁻⁹

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Answer: -.6, 0, .6

Step-by-step explanation: (-1,6) (0,0) (1, .6)

The total cost of a meal costing $32 with 7% sales tax and 18% automatic tip is $40

An equation is an expression that uses mathematical operations to show the relationship between numbers and variables. Types of equations are linear, quadratic, cubic and so on.

The sales tax is 7% and the automatic tip is 18%. If the meal costs $32, hence:

Sales tax = 7% of $32 = 0.07 * 32 = $2.24

Automatic tip = 18% of $32 = 0.18 * 32 = $5.76

The total cost = cost of meal + sales tax + automatic tip

Substituting:

Total cost = $32 + $2.24 + $5.76 = $40

The total cost is $40

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The real roots of the polynomial function are (a) r = -6 and r = 2

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

s(r) = r^5 + 4r^4 - 13r^3 - 10r^2 - 12r + 72

At the real roots of the polynomial function, the following must be true

s(r) = 0

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

Next, we test the options

Option (a)

s(-6) = (-6)^5 + 4(-6)^4 - 13(-6)^3 - 10(-6)^2 - 12(-6) + 72 = 0

s(2) = (2)^5 + 4(2)^4 - 13(2)^3 - 10(2)^2 - 12(2) + 72 = 0

See that s(-6) and s(2) have the values of 0

Hence, the real roots are s = -6 and s = 2

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The value of the angle Z will be 56 degrees.

The angles that the same arc subtends at its circumference are equal. At the circle's centre, two equal chords subtend two equal angles.

The triangle in the centre is an isosceles triangle so the two angles will be 34°.

The third angle will be calculated as:-

Central angle = 180 - 34 - 34

Central angle = 112

The measure of the angle Z will be:-

Z = 112 / 2

Z = 56°

Therefore, the measure of the angle Z suspended outside will be 56 degrees.

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Answer:

hey, what are you asking

Step-by-step explanation:

Answer:

2483 in 8yrs means you multiply the two first

2483

× 8

_____

19864

so 8% of 19864

you have to divide the number by the percentage

o. 8÷ 19864= 2483

The exact value of sinθ = 15.5/23

And, The exact value of cosθ = 17/23

The circle is a closed two dimensional figure , in which the set of all points is equidistance from the center.

We have to given that;

The terminal side of angle θ intersects the unit circle in the first quadrant at x=17/23.

We know that;

The given parameters are represented as;

⇒ (x, y) = ( cos θ , sin θ )

Here, x = 17/23

Hence, We get;

⇒ cos θ = 17/23

Now, Using the following trigonometry identity;

⇒ cos²θ + sin²θ = 1

⇒ (17/23)² + sin²θ = 1

⇒ 289/529 + sin²θ = 1

⇒ sin²θ = 1 - 289/529

⇒ sin²θ = 529 - 289 / 529

⇒ sin²θ = 240/529

⇒ sin θ = √240/529

⇒ sinθ = 15.5 / 23

Thus, The exact value of sinθ = 15.5/23

And, The exact value of cosθ = 17/23

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a) The leash is 12.2 ft long.

b) The diagonal is 7.1m

c) The altitude is 6.1 in

We can see a right triangle here, where the leash is the hypotenuse of that triangle.

Using the Pythagorean's theorem we can write:

leash = √( (10ft)² + (7ft)²)

leash = 12,2 ft

8) Remember that for a square of side length S, we have:

perimeter = 4*S

diagonal = √2*S

We know that the perimeter is 20 meters, then:

20m = 4*S

S = 20m/4 = 5m

Then the diagonal is:

D = √2*5m = 7.1m

9) For an equilateral triangle of sidelength S, the altitude is:

A = √( S² - (S/2)²)

In this case the side length is 7 inches, then:

A = √( (7in)² - (7in/2)²)

A = 6.1 in

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The area of the triangle in terms of 'x' will be (x² + 13x + 28) / 2.

Assume 'h' is the height of the triangle and 'b' be the base of the triangle. Then the area of the triangle is given as,

A = (1/2) × h·b

The area of the triangle is given as,

A = 1/2 [(x + 4)(x + 7)]

Simplify the equation, then we have

A = [(x + 4)(x + 7)] / 2

A = (x² + 7x + 4x + 28) / 2

A = (x² + 13x + 28) / 2

The area of the triangle in terms of 'x' will be (x² + 13x + 28) / 2.

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[A] Under the present cash-only sales policy, the firm's net cash flow every three weeks is:

2,548 units x RM35/unit = RM89,180

2,548 units x RM20/unit = RM50,960

= RM38,220

[B] The firm's immediate (now) net cash flow from adoption of the proposed 3-week credit sales policy is:

0

[C] The firm's net cash flow every 3 weeks from adopting the proposed credit policy is:

2,912 units x RM36/unit = RM105,312

2,912 units x RM22/unit = RM63,904

= RM41,408

[D] The incremental cash flow every 3 weeks arising from switching from the present cash to the proposed credit policy is:

RM41,408 - RM38,220 = RM3,188

[E] The firm's effective 3-week required rate of return from receivables is:

7%/4 = 1.75%

[F] The present value of the perpetual incremental 3-week cash flows arising from switching from the cash to credit policy is:

RM3,188 / (1 + 1.75%) = RM3,147.65

[G] The present value of the costs of switching from cash to credit policy is:

0

[H] The net present value of switching from cash to credit policy is:

RM3,147.65 - 0 = RM3,147.65

[I] The firm should switch from the cash to credit policy as the net present value is positive. The increase in revenue from the increased sales volume outweighs the increased cost of goods sold.

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Answer:

D

Step-by-step explanation:

lateral area = circumference * height

= 2π*r *24

=2π*6*24 =288π yd² = 904

The acceleration of the object when the force on the object changes to 16 N is 4 m/s²

The second law of motion by Newton says that the force is equal to the change in momentum per change in the time. For a constant mass, force equals the mass times acceleration, i.e. F = m x a.

Given here: A force acting on an object.

We know, The formula for force states that the force is equal to mass that is multiplied by the acceleration.

Thus we have the equation as F=m.a

Now in case 1 we have  

20=m×5

m=4 kg

Again in case 2 we have

16 = 4×a

a=4 ms⁻²

Hence, The acceleration of the object when the force on the object changes to 16 N is 4 m/s²

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The expression 48s represents the number of scarves (s) and its per unit  (48).

An expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.

Given that, Emiko makes shibori scarves and sells them for $48 each on a website for handmade goods.

Here, the expression 48s represents the total price of buying s scarves

We need to tell what 48s mean,

So,

48s here is the total cost for buying s scarves,

That mean, if we buy s scarves we will have to pay $48s

Similarly, if we will buy 4 scarves, we will pay = 48 × 4 = $192

For 10 scarves, we will pay = 48 × 10 = $480

Therefore, we can say $48 is the unit price of the scarf.

Hence, the expression 48s represents the number of scarves (s) and its per unit  (48).

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The question was incomplete, so I answered for the question :-

Emiko makes shibori scarves and sells them for 48 each on a website for handmade goods the expression 48s represents the total price of buying scarves what do the parts of the expression 48s represents.

Answer:

Step-by-step explanation:

number of scarves

Price of scarves

The weight of the table in terms of y is 2y

What is an equation?

An equation is a mathematical statement that proves two mathematical expressions are equal in algebra, and this is how it is most commonly used. In the equation 3x + 5 = 14, for instance, the two expressions 3x + 5 and 14 are separated.

Let z be the weight of 1 cupboard

Let x be the weight of 1 table

Z = 5y+6+x

3z+4x=29y+18

=> 4x=29y+18 - 3z

Substitute for z

4x=29y+18 - 3(5y+6+x)

   = 29y+18 -15y-18-3x

4x+3x=14y

=> 7x=14y

=> x=2y

The weight of the table in terms of y is 2y

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The approximation for the population of the bacteria 5 minutes from now is 3506 organisms.

Let's call the current time "t", and the population of the bacteria at time "t" be "P(t)".

So, we have two points on the curve:

(t, P(t)) = (0, 1661), and (t + 9, P(t + 9)) = (9, 3 * 1661) = (9, 4983).

The equation of the line that passes through these two points can be found using the point-slope form of the line:

y - y1 = m(x - x1)

Substituting the points into the equation, we get:

4983 - 1661 = m(9 - 0)

m = (4983 - 1661) / (9 - 0) = 3322 / 9 = 369

So, we have

y = 369x + 1661

For the next 5 minutes, we have

P(t + 5) ≈ y = 369 * 5 + 1661 = 3506 (rounded to the nearest whole number)

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All of three statements about addition, multiplication and division of rational numbers are true.

The square root of any nonperfect square number is an irrational number.

                                   Complex numbers (a + ib)

Real numbers                                                                 Imaginary numbers.

(a + i0)                                                                                      (0 + ib)

Rational numbers               Irrational numbers

(perfect squares)              (non-perfects squares)

Fractions.  

(p/q, q ≠ 0)            

Integers.

(whole nos. -: 0 to ∞)

(negative integers -: - ∞ to - 1)

(positive integers -: 1 to ∞)

The statement adding two rational numbers is a rational number is true.

The statement multiplying two rational numbers is a rational number is true.

The statement if you divide two rational numbers, you’ll always get a rational number is also true.

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The length of AB is 10 cm.

What is the Pythagorean Theorem?

The Pythagorean theorem is a mathematical theorem that states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. It can be expressed as c² = a² + b².

The length of AB can be found using the Pythagorean theorem. The theorem states that in a right triangle, the sum of the squares of the lengths of the two shorter sides equals the square of the length of the hypotenuse (the longest side). In this case, we can form two right triangles, one with sides AD and AC and another with sides BC and AB.

Using the Pythagorean theorem, we have:

AB² = AC² + AD²

AB² = (8²) + (6²)

AB² = 64 + 36

AB² = 100

AB = √(100) = 10

Hence, AB is 10 cm.

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