For a total accumulated amount of $3688.86, a principal of $2000, and a time period of 5 years, use the compound interest formula to find r, if interest is compounded
monthly.
r=

Answer:

14/16 or 7/8.

Step-by-step explanation:

We know the total champions is 30. There are 16 boys, so to find the number of girls we can do 30-16. This gives us 14. Now we know that there are 16 boys and 14 girls, and the question is asking for the ratio of champions who are girls to the number who are boys. This means the ratio would simply be 14 to 16, for every 14 girls there are 16 boys. You can simply this ratio to 7 to 8, meaning for every 7 girls there are 8 boys.

Answer:

acbs

Step-by-step explanation:

Answer: 1139

Step-by-step explanation:

-137+854=717

717-84=633

633+506=1139

Answer:

Step-by-step explanation:

Inequality represents number of months (m) it will take Gabriela to save at least $5,600 is m ≥ 6.

As given in the question,

Amount Gabriela plans to save to buy a car = at least $5,600

Amount she already has = $2500

Amount she needs to save at least = $(5600 -2500)

                                                          =$3100

Plans to save each month =$500

Inequality to represents the number of months to save at least $5600

m ≥ 3100/500

⇒ m ≥ 6

Therefore, inequality represents number of months (m) it will take Gabriela to save at least $5,600 is m ≥ 6.

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The value of x in the given expression 8 = x over 2.5 minus 6 is (-1/8)^(2/7)

What is Algebraic expression ?

Algebraic expressions are the idea of expressing numbers using letters or alphabets without specifying their actual values. The basics of algebra taught us how to express an unknown value using letters such as x, y, z, etc. These letters are called here as variables. An algebraic expression can be a combination of both variables and constants. Any value that is placed before and multiplied by a variable is a coefficient.

given expression is :

-8 = x^(2.5-6)

Now, solving for x by transferring power of x to -1/8 that will become -8 to the power (2/7) :

-8 = x^(-3.5)

-8 = 1/x^(3.5)

x^(3.5) = -1/8

x^(7/2) = -1/8

x = (-1/8)^(2/7)

Therefore, the value of x in the given expression is (-1/8)^(2/7)

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Answer: I hope this helps.

Step-by-step explanation:

Answer:

all the correct answers are the correct answers of

Step-by-step explanation:

step by step explanation no needed because answer already answered okay there answer needed.

The missing number so that the equation has no solutions is -7/3.

The equation given is represented by:

x+1 = -2x–6

It should be noted that we just have to find the value of x. This will be

x+1 = -2x–6

x + 2x = -6 - 1

3x = -7

x = -7/3

Therefore, the value of x is -7/3.

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Sales of Statin on January 1, 2008 was 22.2 billion dollars; and the year that the Statin sales reached 25.6 billion dollars was in 2010.

Given:

S = 1.7 x + 5.2 .............................. (1)

Sales of statin on January 1, 2008 can be calculated as follows:

x = 2008 - 1998 = 10

Substituting x = 10 into equation (1), we have:

S = (1.7 * 10) + 5.2

S = 17 + 5.2

S = 22.2

The answer above implies that sales of Statin on January 1, 2008 was 22.2 billion dollars.

The year that the Statin sales reached 25.6 billion dollars can be calculated as follows:

S = 25.6

Substituting S = 25.6 into equation (1) and solving for x, we have:

25.6 = 1.7x + 5.2

25.6 - 5.2 = 1.7x

20.4  = 1.7x

x = 20.4 / 1.7

x = 12

Therefore, we have:

The year Statin sales reached 25.6 billion = 1998 + x = 1998 + 12 = 2010

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The sales of Statin on January 1, 2008 is 22.2 billion dollars and the year statin sales reached 25.6 billion was in 2010

Linear functions are equations that has a leading degree of 1.

Given the expression that represents amount of sales, S , of statin (in billions of dollars) x years after January 1, 1998 as;

S = 1.7 x + 5.2

For the sales of statin on January 1, 2008, this is calculated as

x = 2008 - 1998 = 10years

Substitute x = 10 into the given equation to have;

S = 1.7(10) + 5.2

S = 17 + 5.2

S = 22.2

Therefore the sales of Statin on January 1, 2008 is 22.2 billion dollars.

For the year that the Statin sales reached 25.6 billion dollar;

S(x) = 25.6

Substituting S = 25.6 into the equation

25.6 = 1.7x + 5.2

1.7x = 25.6 - 5.2

1.7x = 20.4

x = 12

Hence the year statin sales reached 25.6 billion was in 2010

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The equation, in point-slope form, that represents the distance of Byron from home is: A. y - 4 = -6(x - 1/2).

An equation can be written in point-slope form, where m represents the slope and (a, b) represents a point on the line, as: y - b = m(x - a).

From the given information describing Bray's distance from home after some time, we have the following parameters:

Substitute m = -6 and (a, b) = (1/2, 4) into y - b = m(x - a):

y - 4 = -6(x - 1/2)

Therefore, the equation, in point-slope form, that represents the distance of Byron from home is: A. y - 4 = -6(x - 1/2).

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We need to prove

(1 + cos a)(1 - sec a) = -sin a tan a

LHS

= (1 + cos a)(1 - sec a)

= 1 -sec a + cos a - cos a sec a

= 1 - sec a + cos a - cos a (1/cos a)

= 1 - sec a + cos a - 1

= cos a - sec a

= cos a - 1/cos a

= [tex]\frac{cos^{2}a - 1}{cos a}[/tex]

We know that [tex]sin^{2}a+ cos^{2}a = 1[/tex],

Then [tex]1 - cos^{2}a = sin^{2} a[/tex]

        [tex]cos^{2}a - 1 = -sin^{2}a[/tex]

= [tex]-\frac{sin^2a}{cos a}[/tex]

= [tex]-\frac{(sina)(sina)}{cosa}[/tex]

=[tex]- (sin a)(\frac{sin a}{cosa} )[/tex]

We know that tan a = sin a / cos a

= - sin a tan a

= RHS

                                        LHS = RHS

                                     Hence Proved

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Answer:

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Answer:

Length of the rectangle = 43 inches

Width of the rectangle= 20 inches

Step-by-step explanation:

Answer:

8.30

Step-by-step explanation:

19.92 / 2.40 = 8.30

8.30 is the amount per pound.

Answer: 8.30

Step-by-step explanation: We know that Paula Paid 19.92$ for 2.4 pounds

Price of 1 Walnut = 19.92 ÷ 2.4 = 8.30

The two numbers that are (1/16) away from -(1/5) are -(11/80) and -(21/80).

A fraction is a way to describe a part of a whole. such as the fraction ¼ can be described as 0.25.

The two numbers that are 1/16 away form -(1/5) can be found by adding 1/16 to -(1/5) and subtracting 1/16 from -(1/5). Therefore, we can write,

-(1/5) + (1/16) = -(11/80)

-(1/5) - (1/16) = -(21/80)

Hence, the two numbers that are (1/16) away from -(1/5) are -(11/80) and -(21/80).

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Applying the distance formula to find the base and height of the triangle, the area of the triangle is calculated as: 17.85 units².

Area of triangle = 1/2(base)(height).

The base of triangle QRS is QS.

The height of triangle QRS is RT.

Use the distance formula [tex]\sqrt{(y_2 - y_1)^2 + (x_2 - x_1)^2}[/tex] to find the length of QS and RT:

Q(2, 4) = (x1, y1)

S(8, -2) = (x2, y2)

QS = √[(8−2)² + (−2−4)²]

QS = √72

QS ≈ 8.5 units

R(6, 6) = (x1, y1)

T(3, 3) = (x2, y2)

RT = √[(3−6)² + (3−6)²]

RT = √18

RT ≈ 4.2 units

Area of triangle QRS = 1/2(8.5)(4.2)

Area of triangle QRS = 1/2(35.7)

The area of triangle QRS = 17.85 units²

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11*21+11*19+17*18/3=746/3=248.3

A): 2013 = 149.32

Find difference of: 194.31

2014 = 194.31 149.32

= 44.99

2015 Total Will Be:

B):

149.32 + 25 = 174.32

(2013)

(B) (A)

The system of inequalities is,

The total hours will be X+Y≤4.

The total amount she can earn 8.5X + 10Y ≤ 22.85.

First let us assume that she work 7 days in the week.

If she works for 28 hours a week, Then the hours of work done by her in a day will be,

28hours/7days

Per day working hours are 4 hours per day.

now, if she has to earn at least 160$ a week. Then, the amount she has to earn in one day will be 160$/7days,

Amount needed to be earned in one day is 22.85$,

Now, if she work for X hours as cashier, then she can work Y hours as florist.

The total hours for which she can can be represented by,

X+Y≤4

The amount she will earn in one day can be represented by the inequality,

8.5X + 10Y ≤ 22.85.

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The personal expense that the Penders spent more on than they had budgeted is:

Credit Cards & Pocket Money to the tune of $ 23.75 (Option C)

A budget is an estimate of revenue and costs for a given period of time that is generally created and re-evaluated on a regular basis. Budgets may be created for an individual, a group of individuals, a company, a government, or almost anything else that generates and spends money.

The budgeted amount for Credit Card was $50. Total amount spent was $60. Hence the excess amount spent is $10.

The budgeted amount for Pocket money was $80. Total amount spent was $93.75. Hence the excess amount spent is $13.75.

Hence total amount spend over budget is $23.75

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Answer:

S₆ = - 364

Step-by-step explanation:

the sum to n terms of a geometric series is

[tex]S_{n}[/tex] = [tex]\frac{a_{1}(r^{n}-1) }{r-1}[/tex]

where a₁ is the first term and r the common ratio

here a₁ = 2 and r = [tex]\frac{a_{2} }{a_{1} }[/tex] = [tex]\frac{-6}{2}[/tex] = - 3 , then

S₆ = [tex]\frac{2((-3)^{6}-1) }{-3-1}[/tex]

    = [tex]\frac{2(729-1)}{-4}[/tex]

   = [tex]\frac{2(728)}{-4}[/tex]

   = [tex]\frac{1456}{-4}[/tex]

  = - 364

The function f(x) = cos x crosses the x-axis at x₁ = - 0.5π and x₂ = - 1.5π.

Cosine function is a function bounded between - 1 and 1 and whose period is 2π, all the values of x such that the cosine function crosses the x-axis is described by the following expression:

cos x = 0        (1)

Then, by inverse trigonometric functions:

x = cos⁻¹ 0

x = 0.5π ± π · i, where i is a non-negative integer.

If we know that i = 1 and i = 2, then the values of x within the interval [- 2π, 0] are, respectively:

x₁ = - 0.5π, x₂ = - 1.5π

The function f(x) = cos x crosses the x-axis at x₁ = - 0.5π and x₂ = - 1.5π.

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Step-by-step explanation:

supplementary angles are two angles that are together 180°.

they don't have to be adjacent, but the fact that the 2 angles can be placed "randomly" in a scenario is rarely used, except maybe for intersection angles of a line with parallel lines.

a linear pair are 2 angles that are truly adjacent (neighbors, touching each other) that are together 180°.

so, our original statement is

if 2 angles are supplementary, then the angles are a linear pair.

that by itself is (as described) not true in all cases. angles can be non-adjacent (and therefore not a linear pair) and still be supplementary.

so the original statement is false.

(a)

the inverse is

if 2 angles are not supplementary, then the angles are not a linear pair.

that is true.

as per the definition, linear pair angles are a true subset of supplementary angles (every linear pair is a pair of supplementary angles, but not every pair of supplementary angles is a linear pair).

so, if they are not a member of the set of supplementary angles, they cannot be a member of a subset either.

(b)

the converse is

if 2 angles are a linear pair, then the angles are supplementary.

that is true.

because linear pair angles are a true subset of supplementary angles. if something is a member of a subset, it is also a member of any superset.

(c)

the contrapositive is

if 2 angles are not a linear pair, then the angles are not supplementary.

that is false.

as described, linear angles are a true subset of supplementary angles. so, an element can be outside a subset but still inside a superset.

like in the original example, 2 angles across intersected parallel lines can be supplementary, but they are not a linear pair.

Answer:

X+Y-3

Step-by-step explanation:

I don’t know what X/Y is, but “three less than” means you need to subtract 3 from the sum of X+Y

Answer:

32

Step-by-step explanation:

do 4 divided by 1/8

if you flip the fraction it will become 4/1 × 8/1 = 32

The Coefficient of x^2  in algebraic Expression 2x^4 + x^2 -x +7 will be 1.

What is Algebraic expression ?

Algebraic expressions are the idea of expressing numbers using letters or alphabets without specifying their actual values. The basics of algebra taught us how to express an unknown value using letters such as x, y, z, etc. These letters are called here as variables. An algebraic expression can be a combination of both variables and constants. Any value that is placed before and multiplied by a variable is a coefficient.

Given algebraic  Expression is :

2x^4 + x^2 -x +7

Now,

The coefficient is the constant term multiplied with the variable.

Therefore, here the Coefficient of of x^2 will be 1.

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