When y varies directly as x and x = 2 when y = 6.
What is the value of x when y = 10

The solution of the trigonometric function sin(x) + 1 = cos(x) in the interval of [0, 2) will be 0.

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

The trigonometric function is given below.

sin(x) + 1 = cos(x)

Simplify the equation, then we have

sin(x) + 1 = cos(x)

(sin(x) + 1)² = cos² (x)

(sin(x) + 1)² = 1 - sin² (x)

sin² (x) + 2sin x + 1 = 1 - sin² (x)

2sin² (x) = 0

sin (x) = sin 0

x = 0

The solution of the trigonometric function sin(x) + 1 = cos(x) in the interval of [0, 2) will be 0.

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You will pay back $100.00

We know that the formula for the compound ineterst:

[tex]A = P(1 +\frac{r}{n})^{nt}[/tex]

where, A = Accrued amount

P = Principal amount

r = interest rate as a decimal

R = interest rate as a percent

r = R/100

n = number of compounding periods

t = time in years

First, convert R as a percent to r as a decimal

r = 5.2/100

r = 0.052 rate per year,

Now we solve the equation for A

[tex]A = P(1 +\frac{r}{n})^{nt}[/tex]

[tex]A = 95\times (1 +\frac{0.052}{2})^{2\times 1}[/tex]

A = 95.00 × (1 + 0.026)²

A = 100.004

A ≈ 100

Therefore, the total amount accrued with compound interest on a principal of $95.00 at a rate of 5.2% per year compounded semi annually is $100.00.

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The simplified form of expression -2.6f +0.7f - 14 - 9 is -1.9f - 23

We know that an expression is nothing but a mathematical statement that consists of at least two terms( variables or constants) along with one algebraic operation.

As we know simplifying an expression means rewriting the same expression in a compact manner with no like terms.

To simplify expressions, we combine all the like terms ; solve all the given brackets, if any.

In the simplified expression, we left with unlike terms which cannot be reduced further.

Consider an expression:

-2.6f +0.7f - 14 - 9

We simplify above expression.

-2.6f +0.7f - 14 - 9

= (-2.6 + 0.7)f - (14 + 9)              .........(combine like terms)

= -1.9f - 23

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Answer:

c

Step-by-step explanation:

it wouldnt just be 9, thats marias books, to get what jim ahs and hers its 9+b

b representing the amount jim read

The required inequality is d + b ≥ 11 representing the possible values for the number of donuts and brownies purchased.

Inequality is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are not equal.

We can represent the number of donuts purchased as d, and the number of brownies purchased as b. The inequality that represents the minimum number of donuts and brownies that must be purchased altogether is:

d + b ≥ 11

This inequality states that the total number of donuts (d) and brownies (b) purchased must be greater than or equal to 11.

This inequality can be represented graphically on a number line, with point 11 being the boundary between the solutions that satisfy the inequality and those that do not.

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The length of the strawberry lace Lucy has is 36cm, and she needs a piece 18mm long for her cake decoration.

To calculate how many pieces of the strawberry lace she needs, we must convert the measurements from centimeters to millimeters.

We can do this by multiplying 36 centimeters by 100 to get the length of the lace in millimeters (36 cm x 100 = 3600 mm). We then divide this number by the length of the desired piece (3600 mm / 18 mm = 200). Therefore, Lucy needs 200 pieces of 18mm long strawberry lace to decorate her cake.

To summarize, the formula used to calculate the number of pieces Lucy needs is:

(Length of lace in millimeters) / (Length of desired piece in millimeters) = Number of pieces needed.

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The fraction of the bag of sugar that Rick's dad pour into the water is 2/3

An equation is an expression that shows the relationship between numbers and variables.

Fractions is a part of a whole number. It is the ratio of two numbers. The top number is the numerator while the bottom number is the denominator. Hence:

Fraction = numerator / denominator

Rick opens a 3-cup bag of sugar. Rick's dad pours 2 cups into the water. Hence:

Fraction of sugar poured into water = amount of sugar poured in water / total amount of sugar

Substituting:

Fraction of sugar poured into water = 2 cups / 3 cups = 2/3

Ricks dad pour 2/3 of the sugar into the water

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Answer: t=2

Step-by-step explanation:

-4t+14= -9t+24

+9t     =+9t

5t+14=24

    -14=-14

5t=10

5t/5       10/5

t=2

Answer: 15.4

Step-by-step explanation: d= [tex]\sqrt{(-18)^{2} - 18^{2}) +((-19)^{2} - 11^{2})\\[/tex]

[tex]\sqrt{361 - 121}[/tex]

[tex]\sqrt{240}[/tex]

15.4

There are 32.1 pounds of meat.

Addition is an operation used in math to add numbers. The result that is obtained after addition is known as the sum of the given numbers. The addition symbol is one of the widely used math symbols. The addition symbol consists of one horizontal line and one vertical line. It is also known as the addition sign or the plus sign (+). The addition formula is the statement that shows an addition fact and is expressed as, addend + addend = sum. This can be understood with the help of the example shown in the figure given below. While adding numbers, if the sum of the addends is greater than 9 in any of the columns, we regroup this sum into tens and ones. Then we carry over the tens digit of the sum to the preceding column and write the ones digit of the sum in that particular column. In other words, we write only the number in 'ones place digit' in that particular column, while taking the 'tens place digit' to the column to the immediate left.

Add up the pounds of meat.

7.75 + 17.85 + 6.5 = 32.1 pounds

Thus, there are 32.1 pounds of meat.

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Nareh should give his brother $80. This means that once they have the same amount of money, Nareh will have $220 and Urch will have $300.

Subtract the amount of money that Urch has from the amount of money that Nareh has:

300 - 220 = 80

Nareh should give his brother $80 so that both of them will have the same amount of money.

Nareh currently has $300 and Urch currently has $220, so Nareh should give Urch $80 in order to make them have the same amount of money. This means that once they have the same amount of money, Nareh will have $220 and Urch will have $300.

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1. The value of n in 3n + 19 = 28 will be 3.

2. The value of b in 34 - 4b = 18 will be 4.

An equation simply has to do with the statement that illustrates the variables given. In this case, it is vital to note that two or more components are considered in order to be able to describe the scenario.

The value of n in 3n + 19 = 28 will be:

3n + 19 = 28

Collect the like terms

3n = 28 - 19

3n = 9

Divide

n = 9 / 3

n = 3.

The value of b in 34 - 4b = 18 will be:

34 - 4b = 18

4b = 34 - 18

4b = 16

Divide.

b = 16 / 4

b = 4

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The speed of the cheetah based on the information provided is 12.85 feet per second.

The speed of a body in movement can be expressed using different units such as:

Based on this, it is necessary to find how much distance the cheetah covers every second by dividing the distance given by the time given as it follows:

Therefore, the speed of the cheetah is 12.85 feet per second

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The average speed is S=2.033 m/s

The speed formula can be defined as the rate at which an object covers some distance. Speed can be measured as the distance traveled by a body in a given period of time.

The unit of speed is a meter/second.

Speed formula can be used to find the speed of objects, given the distance and time taken to cover that distance.

To calculate the average speed we have a general formula:

speed = distance ÷ time.

Given distance=100m

time=49.17 s

Plugging the values in the above formula:

speed=100/49.17

speed=2.033

Therefore, the average speed is 2.033 m/s.

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Serenity is going to invest in an account paying an interest rate of 4.4% compounded continuously therefore Serenity would need to invest $400 to the nearest hundred dollars, for the value of the account to reach $670 in 11 years.

This is the interest on savings calculated on both the initial principal and the accumulated interest from previous periods.

We can solve the problem by :

1+(0.044÷365)= 1.0001205479

Yearly impounding factor, 1.0001205479^365=1.0449795838

For a period of 11 years, maturity factor,1.0449795838^11 = 1.6225043167.

$1 becomes $1.6225043167.

If Maturity value is to be,$670 which is amount to be invested,

670÷ 1.6225043167 = 412.942

To the nearest 100 dollars is $400.

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Answer:

Step-by-step explanation:

The value of α2ββ2α2 is -20. a quadratic polynomial p(x) = 4x2 − 5x − 1, we can calculate the two zeroes, α and β, of the equation.

Given,

p(x) = 4x2 − 5x − 1

α and β are the zeroes of the quadratic polynomial p(x).

Therefore,

α + β = -5/4

and

αβ = 1/4

Therefore,

α2ββ2α2 = (α+β)2αβ = (-5/4)2(1/4) = (-5/4)(-5/4)(1/4) = 25/16 = -20

Given a quadratic polynomial p(x) = 4x2 − 5x − 1, we can calculate the two zeroes, α and β, of the equation. To find the value of α2ββ2α2, we first need to find the sum and product of the two zeroes, which can be done by solving the equation. The sum of the zeroes is -5/4 and their product is 1/4. We can then use these values to calculate the value of α2ββ2α2, which is equal to (-5/4)2(1/4) = 25/16 = -20. Thus, the value of α2ββ2α2 is -20.

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Answer:

A

Step-by-step explanation:

Answer:

$4

Step-by-step explanation:

Given;

Dozen long stemmed roses cost $48

Question:

What is the cost per rose?

Solve:

Based on the given, we can see that it states that a dozen long stemmed roses cost $48.

Knowing that - Dozen = 12

Since, we know that dozen equal 12. Hence, 12 long stemmed roses cost $48.

Now, divide the cost by the amount to find the cost per rose.

Thus,

48 ÷ 12 = 4.

Therefore, the cost per rose is $4.

RevyBreeze

The account balance after eleven years would be ₱14,925.08. Calculate the future value of the account: FV = PV x (1 + r)^n = 820 x (1 + 0.025)^22 = ₱14,925.08. total number of semi-annual periods: 11 years x 2 semi-annual periods per year = 22 semi-annual periods.

The account balance after eleven years would be ₱14,925.08.

1. Calculate the compounded interest rate: 5% per year compounded semi-annually = 2.5% per semi-annual period.

2. Calculate the total number of semi-annual periods: 11 years x 2 semi-annual periods per year = 22 semi-annual periods.

3. Calculate the future value of the account: FV = PV x (1 + r)^n = 820 x (1 + 0.025)^22 = ₱14,925.08.

The account balance after eleven years would be ₱14,925.08.

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Answer

1: 3x-y=0
2: 5x+y= -4
3: y=-x+4

Step-by-step explanation:

Nominal scale- A nominal scale is a discrete classification of data, in which data are neither measured nor ordered but subjects are merely allocated to distinct categories.

Measurements on an interval scale have substantial differences between the values. In other words, the disparities between the scale's points are exact and measurable.

Ratio scales are interval scales where lengths are expressed in relation to a rational zero.

Ordinal scale: a scale where data is presented merely in terms of order of magnitude because there is no accepted method for determining differences.

Since there are 5 categories: Blue, Red, Green, Yellow, Orange, so by the above definition we can say that for this question we would use Nominal scale for measurement.

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Answer:

248 children

296 adults

Step-by-step explanation:

Define the variables:

Given information:

Create a system of equations with the given information and defined variables:

[tex]\begin{cases}\;\;\;\;\:\:\:x+y=544\\1.5x+2y=964\end{cases}[/tex]

Rearrange the first equation to isolate x:

[tex]\implies x=544-y[/tex]

Substitute the found expression for x into the second equation and solve for y:

[tex]\implies 1.5(544-y)+2y=964[/tex]

[tex]\implies 816-1.5y+2y=964[/tex]

[tex]\implies 816+0.5y=964[/tex]

[tex]\implies 0.5y=148[/tex]

[tex]\implies y=296[/tex]

Therefore, 296 adults swam at the public pool.

Substitute the found value of y into the equation for x and solve for x:

[tex]\implies x=544-296[/tex]

[tex]\implies y=248[/tex]

Therefore, 248 children swam at the public pool.

Answer:

To solve the equation:

39 - 3x12²÷24

Step-by-step explanation:

First, we need to simplify the expression inside the parentheses:

12² = 12*12 = 144

Then we can substitute that value into the equation:

39 - 3x144÷24

Next, we can simplify the expression inside the parentheses:

144÷24 = 6

Then we can substitute that value into the equation:

39 - 3x6

Now we can solve the equation by performing the multiplication and subtraction:

39 - 18 = 21

So the solution is 21.

Steps:

1. 12² = 144

2. 144÷24 = 6

3. 39 - 3x6 = 39 - 18 = 21

So, 39-3*12²÷24 = 21

Answer:

36

Step-by-step explanation:

39 - 3 x [tex]12^{2}[/tex] ÷ 24  First simplify the exponent

39 - 3 (12 x12) ÷ 24

39 - 3 x 24 ÷ 24  Next do multiplication and division going from left to right

39 - 72 ÷ 24

39 - 3  Subtract 3

36

The mass of the liquid in the container is 18.17 g, correct to 3 significant figures

Calculate the volume of the container:

Volume = πr2h

Volume = π x (5 cm)2 x 20 cm

Volume = 3,142 cm3

Calculate the total volume of liquid A and B:

Total volume of A and B = 4:11

Total volume of A and B = 4 + 11 = 15 cm3

Calculate the volume of liquid A:

Volume of A = 4/15 x 15 cm3

Volume of A = 4 cm3

Calculate the volume of liquid B:

Volume of B = 11/15 x 15 cm3

Volume of B = 11 cm3

Calculate the mass of liquid A:

Mass of A = Volume of A x Density of A

Mass of A = 4 cm3 x 1.05 g/cm3

Mass of A = 4.2 g

Calculate the mass of liquid B:

Mass of B = Volume of B x Density of B

Mass of B = 11 cm3 x 1.27 g/cm3

Mass of B = 13.97 g

Calculate the total mass of liquid C:

Total mass of C = Mass of A + Mass of B

Total mass of C = 4.2 g + 13.97 g

Total mass of C = 18.17 g

The mass of the liquid in the container is 18.17 g, correct to 3 significant figures.

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Answer: There would be 345 students because 85+200+60=345

Step-by-step explanation: it equal 245

If Ken's pay remains constant, he should expect to earn $69,600 in two years.

In Mathematics, a proportional relationship is a type of relationship that generates equivalent ratios and it can be modeled or represented by the following mathematical expression:

y = kx

Where:

Next, we would determine the constant of proportionality (k) for the data points as follows:

Constant of proportionality, k = y/x

Constant of proportionality, k = 14,500/5

Constant of proportionality, k = 2,900

In two (2) years, Ken's wages is given by:

y = kx

y = 2,900(24)

y = $69,600.

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After clockwise rotation 90°, we obtain vertices of image as (-2, -2), (-3, -6) and (3, -4). Therefore, option D is the correct answer.

Here are the rotation rules: 90° clockwise rotation: (x, y) becomes (y, -x) 90° counterclockwise rotation: (x, y) becomes (-y, x) 180° clockwise and counterclockwise rotation: (x, y) becomes (-x,-y).

Given that, triangle LMN with vertices L(2, -2), M(6, -3) and N(4, 3).

After clockwise rotation 90° we get

Here, L(2, -2) →L'(-2, -2)

M(6, -3) →M'(-3, -6)

N(4, 3) →N'(3, -4)

Therefore, option D is the correct answer.

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