Suppose 15% of x equals 20% of y. What percentage of x is y?


A 5

B 35

C 75

D 133 1/3

E 300

Answer:

Step-by-step explanation:

x + 46 = 90

x = 44

m<4 = 44

The rate of change of the annual u.s. factory sales in 2000 is 7.7 billion dollars per year

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

s(t) = 0.12t² − t + 5.7

In 2000, we have the value of t to be

t = 2000 - 1990

Evaluate

t = 10

So, we have

s(10) = 0.12 * 10² − 10 + 5.7

Evaluate

s(10) = 7.7

Hence, the rate in 2000 is 7.7 billion dollars per year

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Question

the rate of change of annual u.s. factory sales (in billions of dollars per year) of consumer electronic goods to dealers from 1990 through 2001 can be modeled as s(t) = 0.12t2 − t + 5.7 billion dollars per year

Calculate the rate of change in 2000

The no-arbitrage price today of a 5-year $1,000 US Treasury note with a 2% coupon rate and a 4.25% yield to maturity is approximately $908.44, closest to option B: $900.53.

To determine the no-arbitrage price of a 5-year $1,000 US Treasury note with a coupon rate of 2% and a yield to maturity (YTM) of 4.25%, we can use the present value of the future cash flows.First, let's calculate the annual coupon payment. The coupon rate is 2% of the face value, so the coupon payment is ($1,000 * 2%) = $20 per year.The yield to maturity of 4.25% is the discount rate we'll use to calculate the present value of the cash flows. Since the coupon payments occur annually, we need to discount them at this rate for five years.

Using the present value formula for an annuity, we can calculate the present value of the coupon payments:PV = C * (1 - (1 + r)^-n) / r,

where PV is the present value, C is the coupon payment, r is the discount rate, and n is the number of periods.

Plugging in the values:PV = $20 * (1 - (1 + 0.0425)^-5) / 0.0425 = $85.6427.

Next, we need to calculate the present value of the face value ($1,000) at the end of 5 years:PV = $1,000 / (1 + 0.0425)^5 = $822.7967.

Finally, we sum up the present values of the coupon payments and the face value:No-arbitrage price = $85.6427 + $822.7967 = $908.4394.

Rounding to the penny, the no-arbitrage price is $908.44, which is closest to option B: $900.53.

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The instructional context can greatly impact learning with educational technology. In a study with a digital learning game, it was found that the instructional context influences student engagement and motivation. This, in turn, affects their learning outcomes.

The study examined the design of the game, the teacher's role, and the classroom environment. By optimizing these factors, the researchers found that students were more likely to be actively engaged and achieved better learning outcomes.

Therefore, the instructional context plays a crucial role in leveraging the potential of educational technology for effective learning.

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Certainly! Here's the solution to find the equation of the cubic polynomial with zeros at 0, 1, and 2:

Since the zeros of the polynomial are 0, 1, and 2, we can express the polynomial in factored form as:

\( \sf f(x) = (x - 0)(x - 1)(x - 2) \\\)

Simplifying the expression, we get:

\( \sf f(x) = x(x - 1)(x - 2) \\\)

Expanding the product, we have:

\( \sf f(x) = (x^2 - x)(x - 2) \\\)

Using the distributive property, we can further simplify:

\( \sf f(x) = (x^3 - 2x^2 - x^2 + 2x) \\\)

Combining like terms, we get:

\( \sf f(x) = (x^3 - 3x^2 + 2x) \\\)

Therefore, the equation of the cubic polynomial with leading coefficient 1 and zeros at 0, 1, and 2, in standard form, is:

\( \sf f(x) = x^3 - 3x^2 + 2x \\\)

\(\huge{\mathfrak{\colorbox{black}{\textcolor{lime}{I\:hope\:this\:helps\:!\:\:}}}}\)

♥️ \(\large{\underline{\textcolor{red}{\mathcal{SUMIT\:\:ROY\:\:(:\:\:}}}}\)

Answer:

64

Step-by-step explanation:

It is hard to explain in writing. Because all of the sides are semetrical then whatever mesurment that is on one side, will be on the other. So for example, if there is 12in on one side, the other side will be 12in too. If the top of the letter is 3in, then so are the rest of the parts that are the same size. When you figure out all of the lengths of the sides then you add them up.

I hope this helps.

If it didn't then plz tell me what I need to clarify :)

Answer:

1

Step-by-step explanation:

\( {6}^{2} - 7(8 + 6 - {3}^{2})\)

Using BODMAS we'll have to solve what is in the bracket first

\( = {6}^{2} - 7(14 - 9) \\ = {6}^{2} - 7(5) \\ \)

Multply -7 by 5 still using the rule of BODMAS

\( = {6}^{2} - 35 \\ = 36 - 35 \\ = 1\)

Answer: B. statistic

Step-by-step explanation: A characteristic, usually a numerical value, which describes a sample, is called a statistic.

The expression is simplified to s = -5/ 4

Algebraic expressions are expressions composed of terms, variables, constants, factors and coefficients.

They are also made up of mathematical operations such as addition, subtraction, multiplication, division, etc

Given the expression;

42 = 14{ 4 + 4/ 5s}

Divide both sides by 14

42/14  = 14{ 4 + 4/ 5s}/14

3 = 4 + 4/ 5s

3 =   20 + 4s/5

cross multply

15 = 20 + 4s

collect like terms

15 - 20 = 4s

-5 = 4s

Make 's' the subject

s = -5/ 4

Thus, the expression is simplified to s = -5/ 4

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The flowerbed is 48.75 feet away from the hive.

In accordance with the statement, the bee flies at constant speed from a hive to a flowerbed, stays in the flowerbed and flies back to the hive, also at constant speed. We assume that the bee has travelled the same distance in the first and third stages.

20 = 15 · t₁ + 10 + 10 · t₂    (1)      

15 / t₁ = 10 / t₂                    (2)

By (2):

15 · t₂ = 10 · t₁

In (1):

10 = 15 · t₁ + 100 / 15 · t₁

10 = (65 / 3) · t₁

t₁ = 6 / 13 min

And:

t₂ = 4 / 13 min

Finally, the distance between the flowerbed and the hive is:

d = 15 / (4 / 13)

d = 48.75 ft

The flowerbed is 48.75 feet away from the hive.

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GURL IM STUCK ON THAT TOO Step-by-step explanation:

The domain of each composite function is as follows:

f(g(x)): The domain is all real numbers.

g(f(x)): The domain is all real numbers except x ≠ 1.

f(g(x)): The domain is all real numbers except x ≠ 0.

For the composite function f(g(x)), we substitute g(x) into f(x) to get f(g(x)) = 2(4x) + 3 = 8x + 3. Since this is a linear function, the domain is all real numbers.

For the composite function g(f(x)), we substitute f(x) into g(x) to get g(f(x)) = (3x - 1)^2 = 9x^2 - 6x + 1. The square of a real number is always non-negative, so there are no restrictions on the domain of g(f(x)). Hence, the domain is all real numbers.

For the composite function f(g(x)), we substitute g(x) into f(x) to get f(g(x)) = 3/(4x - 1). However, we need to consider the denominator of this function. For the expression 4x - 1 to be defined, we must have 4x - 1 ≠ 0, which implies x ≠ 1/4. Therefore, the domain of f(g(x)) is all real numbers except x ≠ 1/4.

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Answer:

(7, 8)

Step-by-step explanation:

We know

Point A is located at (5,8) and is translated two units to the right.

Translate to the right mean the x will increase; in this case, it translated two units to the right meaning the x will increase b 2.

So, the coordinate of A will be at (7, 8)

Answer:

7.2 miles

Step-by-step explanation:

52-16= 36

36/5= 7.2

Using monthly payment formula, the Smith Family's total monthly payment is approximately $2,360.99.

To calculate the total monthly payment for the Smith Family, we need to consider the mortgage payment, insurance, property tax, and HOA fees.

1. Mortgage Payment:

The loan amount is the house price minus the down payment:

$350,000 - $70,000 = $280,000.

To calculate the monthly mortgage payment, we need to determine the interest rate and loan term. Since you mentioned it's a 15-year loan, we'll assume an interest rate of 4% (which can vary depending on market conditions and the borrower's credit).

We can use a mortgage calculator formula to calculate the monthly payment:

M = P [i(1 + i)ⁿ] / [(1 + i)ⁿ⁻¹]

Where:

M = Monthly mortgage payment

P = Loan amount

i = Monthly interest rate

n = Number of months

The monthly interest rate is the annual interest rate divided by 12, and the loan term is 15 years, which is 180 months.

i = 4% / 12 = 0.00333 (monthly interest rate)

n = 180 (loan term in months)

Plugging in the values into the formula:

M = $280,000 [0.00333(1 + 0.00333)¹⁸⁰] / [(1 + 0.00333)¹⁸⁰⁻¹]

Using a calculator, the monthly mortgage payment comes out to be approximately $2,014.99.

2. Insurance:

The monthly insurance payment is given as $66.

3. Property Tax:

The monthly property tax payment is given as $230.

4. HOA Fees:

The HOA fees are stated as $600 per year. To convert this to a monthly payment, we divide by 12 (months in a year): $600 / 12 = $50 per month.

Now, let's add up all these expenses:

Mortgage payment: $2,014.99

Insurance: $66

Property tax: $230

HOA fees: $50

Total monthly payment = Mortgage payment + Insurance + Property tax + HOA fees

Total monthly payment = $2,014.99 + $66 + $230 + $50

Total monthly payment = $2,360.99

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The Recurrence Relation T(n) for T(n) = 2n.T(n-1) + 12 2 is:

T(n) = 2n * 2(n-1) * 2(n-2) * ... * 2(1) * T(0) = 2^n * n! * T(0).

To solve the given recurrence relation T(n) = 2n * T(n-1) + 12, we can use iteration or expansion methods. Let's use the expansion method to find an explicit formula for T(n).

Expanding the recurrence relation, we have:

T(n) = 2n * (2(n-1) * T(n-2) + 12) + 12

= 2n * 2(n-1) * T(n-2) + 2n * 12 + 12

= 2n * 2(n-1) * (2(n-2) * T(n-3) + 12) + 2n * 12 + 12

By continuing this process, we can observe a pattern. Each term in the expansion will be of the form 2n * 2(n-1) * 2(n-2) * ... * 2(1) * T(0), where T(0) is the initial term.

The number of factors of 2 will depend on the value of n. We can see that for each term, the number of factors of 2 is n! (n factorial). Therefore, the explicit formula for T(n) is:

T(n) = 2n * 2(n-1) * 2(n-2) * ... * 2(1) * T(0) = 2^n * n! * T(0).

In this case, T(0) represents the initial term of the sequence. Without knowing its value, we cannot provide a specific numerical solution. However, the above formula provides a general expression for T(n) in terms of n and T(0), satisfying the given recurrence relation.

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Answer:

he can make 6 goodie bags

Step-by-step explanation:

We want to find the dimensions of the poster such that the area of the whole poster is minimized .These are: Length = 325.2cm and

Width = 17cm

We can assume that the poster is a rectangle, and we know that a rectangle of length L and width W has an area:

A = L*W

Here we do know that the top and bottom margins are 9 cm each.

The side margins are 6cm each.

Then the measures of the printed areas are:

W' = W - 2*6cm = W - 12cm

L' = L - 2*9cm = L - 18cm

And we know that the area of the printed part is 1536 cm^2, then we can write:

A'  = (W - 12cm)*( L - 18cm) = 864 cm^2

      W*L - 12cm*L - 18cm*W + 216cm^2 = 1536 cm^2

      W*L = 12cm*L + 18cm*W + 1320cm^2

And W*L is equal to the area, so what we need to minimize is:

A =  12cm*L + 18cm*W + 1320cm^2

Here we can see that the dependence of the area is larger on W than on L, so what we need to minimize is W.

We will take the smallest value of W such that the given margins are allowed.

That value would be such that:

W - 12cm > 0

W > 12cm

this could (and to be strict, should) be something like 16.0001cm, but let's use 17cm just to use whole numbers, we will get:

W = 17cm

Then to get the length we solve:

W*L = 12cm*L + 18cm*W + 1320cm^2

17cm*L = 12cm*L + 18cm*17cm + 1320cm^2

5cm*L = 1560cm^2

L = 325.2cm

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P = 90 is the solution for the given equation.

Given: Qd=95−4

PQs=5+P

To find Qd if P=5:

Put P = 5 in the equation

Qd=95−4P

Qd = 95 - 4 x 5

Qd = 75

So, Qd = 75.

To find P if Qs = 20:

Put Qs = 20 in the equation

Qs = 5 + PP

= Qs - 5P

= 20 - 5P

= 15

So, P = 15.

To solve Qd=Qs, substitute Qd and Qs with their respective values.

Qd = Qs

95 - 4P = 5 + P

Subtract P from both sides.

95 - 4P - P = 5

Add 4P to both sides.

95 - P = 5

Subtract 95 from both sides.

- P = - 90

Divide both sides by - 1.

P = 90

Thus, P = 90 is the solution for the given equation.

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Answer:

bro i got a B+ in math tooo!!!!!!!!

Step-by-step explanation:

yeah tell them!

Answer:

It's a low A and your working on bringing it up

Step-by-step explanation:

To evaluate the given integral, we need to plug in the limits of integration, which are 0 and 4, into the antiderivative of the integrand.

The antiderivative of 4/5 t^3 - 3/4 t^2 + 2/5 t is:

(4/5) * (t^4/4) - (3/4) * (t^3/3) + (2/5) * (t^2/2) + C

where C is the constant of integration.

Now, plugging in the limits of integration:

[(4/5) * (4^4/4) - (3/4) * (4^3/3) + (2/5) * (4^2/2)] - [(4/5) * (0^4/4) - (3/4) * (0^3/3) + (2/5) * (0^2/2)]

Simplifying this expression, we get:

(256/5 - 64 + 16/5) - (0 - 0 + 0)

= 240/5

= 48

Therefore, the value of the given integral is 48.

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To evaluate the integral ∫[0, 4] (4/5t^3 - 3/4t^2 + 2/5t) dt, we can use the power rule of integration.

Applying the power rule, we can integrate each term of the polynomial separately:

∫ (4/5t^3) dt = (4/5) * (1/4) * t^4 + C1 = t^4/5 + C1

∫ (-3/4t^2) dt = (-3/4) * (1/3) * t^3 + C2 = -t^3/4 + C2

∫ (2/5t) dt = (2/5) * (1/2) * t^2 + C3 = t^2/5 + C3

Adding the constants of integration, we can write the complete integral:

∫[0, 4] (4/5t^3 - 3/4t^2 + 2/5t) dt = (t^4/5 + C1) - (t^3/4 + C2) + (t^2/5 + C3)

To evaluate the definite integral between the limits 0 and 4, we substitute the upper limit (4) and lower limit (0) into the expression:

[(4^4/5 + C1) - (4^3/4 + C2) + (4^2/5 + C3)] - [(0^4/5 + C1) - (0^3/4 + C2) + (0^2/5 + C3)]

Simplifying the expression further, we get:

[(1024/5 + C1) - (0 + C2) + (16/5 + C3)] - [(0 + C1) - (0 + C2) + (0 + C3)]

Since the constants of integration cancel out, we are left with:

[(1024/5) - (0) + (16/5)] - [(0) - (0) + (0)]

= 1024/5 + 16/5

= 1040/5

= 208

Therefore, the value of the integral ∫[0, 4] (4/5t^3 - 3/4t^2 + 2/5t) dt is 208.

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The inequality that represents relationship the number of video games of Phillip and Emily is 18 + r < 30.

What are types of symbols to connect two expressions?

There are two types symbols that connect two expressions. One is known as equal sign and another one is inequality. There are various symbol under inequality and they are less than, greater than, less than or equal, greater than or equal.

Given that Phillip has 18 video games. Emily has r video games.

The number of video games that Phillip and Emily have is 18 + r.

Also given that together, Phillip and Emily have a combined total of less than 30 video games.

Thus 18 + r < 30

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Answer:

5.67811 x 10^5 liters/second * 3.15576 x 10^7 seconds/year

= (5.67811 x 3.15576) x (10^5 x 10^7) litres/year (Using the product of powers property of exponents)

= 179,523,225,360 litres/year

Answer: 179,523,225,360

Step-by-step explanation:

Let's start solving the expression using the product to sum formulae.

Here's the given expression,

\[\sin \frac{x}{3} \cos \frac{2 x}{3}+\cos \frac{x}{3} \sin \frac{2 x}{3}\]

Using the product-to-sum formula,

\[\sin A \cos B=\frac{1}{2}[\sin (A+B)+\sin (A-B)]\]

Applying the above formula in the first term,

\[\begin{aligned}\sin \frac{x}{3} \cos \frac{2 x}{3} &= \frac{1}{2} \left[\sin \left(\frac{x}{3}+\frac{2 x}{3}\right)+\sin \left(\frac{x}{3}-\frac{2 x}{3}\right)\right] \\&= \frac{1}{2} \left[\sin x+\sin \left(-\frac{x}{3}\right)\right]\end{aligned}\]

Using the product-to-sum formula,

\[\cos A \sin B=\frac{1}{2}[\sin (A+B)-\sin (A-B)]\]

Applying the above formula in the second term,

\[\begin{aligned}\cos \frac{x}{3} \sin \frac{2 x}{3}&= \frac{1}{2} \left[\sin \left(\frac{2 x}{3}+\frac{x}{3}\right)-\sin \left(\frac{2 x}{3}-\frac{x}{3}\right)\right] \\ &= \frac{1}{2} \left[\sin x-\sin \left(\frac{x}{3}\right)\right]\end{aligned}\]

Substituting these expressions back into the original expression,

we have\[\begin{aligned}\sin \frac{x}{3} \cos \frac{2 x}{3}+\cos \frac{x}{3} \sin \frac{2 x}{3} &= \frac{1}{2} \left[\sin x+\sin \left(-\frac{x}{3}\right)\right]+\frac{1}{2} \left[\sin x-\sin \left(\frac{x}{3}\right)\right] \\ &=\frac{1}{2} \sin x + \frac{1}{2} \sin x - \frac{1}{2} \sin \left(\frac{x}{3}\right)\\ &= \sin x - \frac{1}{2} \sin \left(\frac{x}{3}\right)\end{aligned}\]

Therefore, the given expression can be written in terms of a single trigonometric function as:

\boxed{\sin x - \frac{1}{2} \sin \left(\frac{x}{3}\right)}

Hence, the required expression is \sin x - \frac{1}{2} \sin \left(\frac{x}{3}\right). The solution is complete.

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Answer:

What is a mean?

A mean is the average of all the numbers in a data set.

How can I find mean?

to find mean you add up all the numbers in the data set; and divide them by the amount of numbers there are.

103+3+41+7=154

154÷4=38.5

The mean is 38.5

Answer: Let's solve this problem step by step.

First, let's assume the salaries of An and B to be 5x and 3x, respectively, where x is a common multiplier.

According to the given information, they save Rs. 2600 and Rs. 1800, respectively. Since savings come from the remaining portion of their incomes after spending, we can calculate their expenditures as follows:

For An:

Income of An = Salary of An + Savings of An

Income of An = 5x + 2600

For B:

Income of B = Salary of B + Savings of B

Income of B = 3x + 1800

Now, let's consider the proportion of their expenditures. It is given that the proportion of their expenditures is 9:5. So, we can write the following equation:

(Expenditure of An)/(Expenditure of B) = 9/5

Since expenditure is the complement of savings, we have:

[(Income of An - Savings of An)] / [(Income of B - Savings of B)] = 9/5

Substituting the previously derived expressions for income, we get:

[(5x + 2600 - 2600)] / [(3x + 1800 - 1800)] = 9/5

Simplifying the equation, we have:

5x / 3x = 9/5

Cross-multiplying, we get:

5 * 3x = 9 * 3x

15x = 27x

Subtracting 27x from both sides, we have:

0 = 12x

This implies that x = 0, which is not a valid solution. Therefore, there seems to be an error or inconsistency in the given information or equations. Please recheck the problem statement or provide additional information to help resolve the issue.

Answer:

4 Hours

Step-by-step explanation:

Since the equation is:

y = 9x + 16

You have to find x

This is the logical way:

52-16 = 36 because thats the starting fee

So 36 divided by 9 equals 4

You do that because 9 is the charge per hr

So he rented it for 4 hours.

Hope this helps:)

The third line shows the solutions to n > 0.

The correct option is third line.

A horizontal line with uniformly spaced numerical increments is referred to as a number line.

The way the number on the line can be replied will depend on the numbers on the line.

The number's intended use is described in the question that goes with it, such as when graphing a point.

Locating numbers, comparing numbers, fractions and mixed numbers, decimals, integers, absolute value, addition, subtraction, inequalities, multiples, common denominators, and other mathematical concepts may all be taught using number lines, which are incredibly versatile manipulatives.

We have a number-line.

To find the number line that shows the solution, n > 0:

n is greater than 0.

At 0, there is an open dot circle.

And the line should be extended toward positive infinity.

Therefore, third line is required number line.

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Answer:

13

Step-by-step explanation:

it will be B because it find the missing side you need to do the pythagorean theorem