Find the value of sin D rounded to the nearest hundredth, if necessary.
E90°

F
E√13

E
D√87

Answer:

The time value, at the end of the fifth year, of a 5-year annuity that pays $200 every month, starting from the beginning of the second month, when the continuously compounded interest rate is 9.959%, is $11,828. To calculate this, we can use the formula A = PMT x [((1 + r)n - 1) / r], where PMT is the payment amount, r is the continuously compounded interest rate, and n is the number of payments. In this case, PMT = $200, r = 0.09959, and n = 60. Plugging these values into the formula, we get A = $200 x [((1 + 0.09959)60 - 1) / 0.09959] = $11,828.

Answer:

it's already rounded to the nearest hundredth

Step-by-step explanation:

because there is no numbers after the hundredth.

If a variable needs to be eliminated, to solve -7x - 10y = -83 4x - 10y = 16, the correct first step is to:

Subtract to eliminate y.

In order to solve a system of linear equations, we can use elimination method. The goal of elimination method is to simplify the system of equations by making one of the variables disappear or equal to zero.

Here, the system of equations is:

To eliminate one of the variables, we can add or subtract the equations so that one of the coefficients cancels out.

In this case, we want to eliminate y. We can do that by subtracting the first equation from the second equation.

When we subtract the first equation from the second equation, the y-term will cancel out because the coefficients are the same:

--------- (subtract the two equations)

11x = 99

Now, we only have one variable, x, and we can easily solve for it:

x = 9

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The zeros of the function f(x) = x^4 - x² - 2 are given as follows:

+/-squareroot of 2, +/- i

The function for this problem is defined as follows:

f(x) = x^4 - x² - 2

The zeros are the values of x for which:

f(x) = 0.

Applying the transformation y = x², the function can be reduced to a quadratic function as follows:

y² - y - 2 = 0.

Hence:

(y - 2)(y + 1) = 0.

Meaning that the solutions for y are given as follows:

Then the solutions for x are given as follows:

Meaning that the third option is correct.

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348 are the total number of customers visited the theatre.

Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data.

Given that at a cinema, films are shown on screen 1 and screen 2

screen 2 customers pay full price or child price

There are three times as many customers in screen 1.

68 customers paid child price in screen 1

In screen 1 the number of customers are 87

In screen 2 the number of customers are three times the screen 1.

87×3=261 in screen 2.

72 are full in screen 1.

53 are in child of screen 2

208 in screen 2 full screen

261+87=348

Hence, 348 are the total number of customers visited the theatre.

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By algebra properties and trigonometric formulas, the trigonometric equation sin α + cos α is equal to √7 / 2.

In this problem we find the definition of trigonometric equation, whose value must be found by means of algebra properties and trigonometric formulas. First, write the entire formula:

sin α + cos α

Second, square the formula:

(sin α + cos α)² = sin² α + 2 · sin α · cos α + cos² α

Third, simplify the formula and clear sin α + cos α:

(sin α + cos α)² = 1 + 2 · sin α · cos α

sin α + cos α = √(1 + 2 · sin α · cos α)

Fourth, find the value of the resulting trigonometric equation:

sin α + cos α = √[1 + 2 · (3 / 8)]

sin α + cos α = √7 / 2

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Answer: 16 grasses, 41 weeds, and 51 trees

Step-by-step explanation:

You can use a variable for the different pollen sources. Use g for grass, w for weeds, and t for trees. w=3g-7.  t=3g+3.  g+w+t=108. In that last equation, you can substitute other values for w and t. g+(3g-7)+(3g+3)=108. combine like terms to get, 7g-4=108. This equation simplifies to g=16. Substitute 16 for g in the first 2 equations, and find that w=41, and t=51.

(Sorry if my explanation didn't make sense)

Answer:

The equation need to solve this problem is y=a(b)^x

a= the starting value

b= the rate of change

x= the time

to get the rate of change do the following:

add 1 to the percentage of change (only if value is growing)

subtract the percentage from one (only if value is decaying)

Since the printer is depreciating it is a decay.

The rate of change for this problem is showed below.

1-0.05

0.95 is the rate of change.

Below is the equation for the problem.

y=35000(0.95)^4 Work the problem.

Y=35000(0.814506250

Y=28507.71875 Since we are working with money we round to two decimal places.

The printer's value after four years is $28,507.72.

Answer:Yes

because there were at least 10 "successes" and at least 10 "failures" in the sample

Step-by-step explanation:

Answer:

20% or 0.2

Step-by-step explanation:

→ 32 ÷ 160

common factor

→ = ⅕

convert the number

→ = 20% or 0.2

hope this helps!

Answer: g(x) - h(x) = (-3x^2 + 2x - 6) - (-4 - x) = -3x^2 + 3x - 2.

Step-by-step explanation: The expression g(x) - h(x) can be found by subtracting h(x) from g(x).

g(x) = -3x^2 + 2x - 6

h(x) = -4 - x

So,

g(x) - h(x) = (-3x^2 + 2x - 6) - (-4 - x) = -3x^2 + 3x - 2.

The fruit salad recipe requires 1/3 cup of strawberries and the smoothie recipe requires 3/4 cup of strawberries. So in total, 1/3 + 3/4 = 5/12 cup of strawberries are required for both recipes.

Now we know that Cindy and Borling are both making the recipes. So we need to multiply the 5/12 cup of strawberries by 2 to find out how many cups of strawberries are needed for both of them.

5/12 cup * 2 = 10/12 cup or 5/6 cup of strawberries.

Now if two more friends are joining them, we need to multiply the 5/6 cup of strawberries by 4 to find the total number of cups of strawberries required for all 4 of them.

5/6 cup * 4 = 2 and 1/6 cups.

So in total, 2 and 1/6 cups of strawberries would be required for both girls and two of their friends.

Answer:

Find x.

1/3+3/4=x

4/12+9/12=x

13/12=x

1 1/12 cups of strawberries for one person.

3*1 1/12=3 1/4

Step-by-step explanation:

The equation of the set of algebra tiles is x + 8 = 12.

Algebra tiles are mathematical manipulatives that help students comprehend the principles of algebra and strategies to think algebraically. For introductory algebra pupils at the level of elementary school, middle school, high school, and college, these tiles have been demonstrated to offer solid examples.

Given set,

x 1 1 1 1 1 1 1 1 = 1 1 1 1 1 1 1 1 1 1 1 1

the set has one positive x and eight positive units,

the equation is x + 8.

and on the right side of the equation, there are 12 positive units,

equation is x + 8 = 12

Hence the equation s x + 8 = 12.

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Answer:

x + 8 = 12.

Step-by-step explanation:

in case you need it (x=4)

Your daughter is 7 years old.

Let "x" be your age.

According to the statement, your age is 34. Thus, x= 34.

Let "y" be the age of your daughter.

According to the statement, your daughter's age is given by the following equation:

[tex]2y+20=x\\ \\2y+20=34[/tex]

[tex]2y+20-20=34-20\\ \\2y=14[/tex]

[tex]\frac{2y}{2} =\frac{14}{2} \\ \\y=7[/tex]

Let's see if number 7 makes the original condition be true.

So, you are 20 years older than twice your daughter's age. Let's multiply your daughter○s age by 2 and add 20, it should return your age (34).

[tex]2(7)+20=\\ \\14+20=\\ \\34[/tex]

That's correct, it means that 7 is the correct answer.

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The value of function f' (x)=28 and G' (x)=63

    x           f(x)       g(x)      f' (x)       g' (x)
      1            3           2          4            6

      2            1           3          5             7
      3             2          1          7             9        


                                       
F(X)=f(f(x))

F' (X)=(F' (f(x)) x F' (x)⇒ (chain rule)

F' (1)=F' (F(1)x f' (1))

=f' (3) x f' (1)   (( ∵  f(1)=3))

=7 x 4        (∵f' (3)=7, f' (1)=4))

=28

G(x)=g(g(x))

G' (x)=g' (g(x) X  g' (x) ⇒   (chain rule)

G' (2)=g' (g(2) x g' (2)

=g' (3) x g' (2)     (∵g(2)=3))

=9x7        ((∵g' (3)=9, g' (2)=7))

=63


The chain rule is a formula in calculus that expresses the derivative of the composition of two differentiable functions f and g in terms of f and g's derivatives.
d/dx(f(g(x)=f'(g(x)g'(x).


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The value of angle A and C is 14° and 121° respectively

A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry. A triangle with vertices A, B, and C is denoted \triangle ABC. In Euclidean geometry, any three points, when non-collinear, determine a unique triangle and simultaneously, a unique plane.

The sum of angle in a triangle is 180°

Therefore 45+6x-5+x-7 = 180

collect like terms

45-5-7+6x+x =180

33+7x = 180

7x = 180 - 33

7x = 147

x = 147/7

x= 21

therefore the value of angle A = ( 21-7) = 14°

and angle C = 6(21) - 5

C = 126-5

C = 121°

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Answer: 0

Step-by-step explanation:

Step 1: Substitute the a as 6.

Step2: 5*(a) =5*6, which equals 30

Step 3: 5(6) - 30= 0

The dimensions of the square is [tex]\frac{30}{9+4 \sqrt{3}}[/tex] and equilateral triangle is [tex]& \frac{10 \sqrt{3}}{9+4 \sqrt{3}}[/tex] that produce a minimum total area.

The sum of the perimeter of an equilateral triangle and a square is 10

Differentiation is a derivative of the value of an independent variable that can be used to measure features of an independent variable per unit change.

The objective is to find the dimensions of the equilateral triangle and square that produce a minimum total area.

Consider,

⇒4a+3b=10

⇒4a=10-3b

⇒a=[tex]\frac{10-3b}{4}[/tex]

The total area of the circle and square is,

[tex]A=a^2+\frac{\sqrt{3}}{4} b^2[/tex]

Substitute the value of a in the formula,

[tex]$$\begin{aligned}A & =\left(\frac{10-3 b}{4}\right)^2+\frac{\sqrt{3}}{4} b^2 \\& =\frac{100-60 b+9 b^2}{16}+\frac{\sqrt{3}}{4} b^2 \\& =\frac{100-60 b+9 b^2+4 \sqrt{3} b^2}{16} \\& =\frac{100-60 b+(9+4 \sqrt{3}) b^2}{16}\end{aligned}$$[/tex]

Differentiate the total area and equate with 0 ,

[tex]$$\begin{aligned}\frac{d A}{d r} & =\frac{0-60+2(9+4 \sqrt{3}) b}{16} \\0 & =\frac{0-60+2(9+4 \sqrt{3}) b}{16} \\\end{aligned}$$[/tex]

[tex]0-60+2(9+4 \sqrt{3}) b & =0 \\2(9+4 \sqrt{3}) b & =60[/tex]

And,

b[tex]=\frac{30}{9+4 \sqrt{3}}[/tex]

Substitute the value of b in the value of a,

[tex]$$\begin{aligned}a & =\frac{10-3\left(\frac{30}{9+4 \sqrt{3}}\right)}{4} \\& =\frac{90+40 \sqrt{3}-90}{4(9+4 \sqrt{3})} \\& =\frac{40 \sqrt{3}}{4(9+4 \sqrt{3})} \\& =\frac{10 \sqrt{3}}{9+4 \sqrt{3}}\end{aligned}$$[/tex]

a[tex]& =\frac{10 \sqrt{3}}{9+4 \sqrt{3}}[/tex]

Therefore, the dimensions of the square is [tex]\frac{30}{9+4 \sqrt{3}}[/tex] and equilateral triangle is [tex]& \frac{10 \sqrt{3}}{9+4 \sqrt{3}}[/tex] that produce a minimum total area.

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a. Linearly dependent. Notice that u = 3w, so w can be written as a scalar multiple of u, meaning the set is linearly dependent.

b. Linearly independent. The vectors are not scalar multiples of each other, meaning they are linearly independent.

c. Linearly dependent. Notice that v = -2u, so v can be written as a scalar multiple of u, meaning the set is linearly dependent.

d. Linearly independent. The vectors are not scalar multiples of each other, meaning they are linearly independent.

e. Linearly dependent. If (ui, u2, ..., um) is a set of vectors in R" and n < m, then the set is linearly dependent. This means that the set of vectors {u, v, w} is linearly dependent as n = 2 and m = 3.

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Answer:

-18

Step-by-step explanation:

missing 1 question means losing 3 points so if we mutliply the amout of questions he missed, 6, times the points yoy lose per question,3, we get 18.

The explicit formula for aₙ is a formula for the nth term of this sequence aₙ = 8n + 17.

What is the explicit formula?

The explicit formulae for L-functions are relations between sums over the complex number zeroes of an L-function and sums over prime powers, introduced by Riemann for the Riemann zeta function.

The formula for the nth term of this sequence is a_n = 8n + 17.

This means that each term in the sequence is equal to 8 multiplied by the position of the term (n) plus 17.

For example, the first term (n = 1) is 25, which can be calculated as 8 * 1 + 17 = 25.

The second term (n = 2) is 33, which can be calculated as 8 * 2 + 17 = 33, and so on.

hence, the explicit formula for aₙ is a formula for the nth term of this sequence is aₙ = 8n + 17.

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Answer:

To find the probability that both a randomly selected male student and a randomly selected female student are smokers, we can use the formula for conditional probability: P(A and B) = P(A) * P(B|A), where A is the event that the male student is a smoker and B is the event that the female student is a smoker.

First, we need to find the probability that a randomly selected male student is a smoker:

P(A) = (number of male smokers) / (total number of male students) = 63 / (63 + 147) = 63/210

Next, we need to find the probability that a randomly selected female student is a smoker, given that the male student is a smoker:

P(B|A) = (number of female smokers and male smokers) / (number of male smokers) = 70 / 63

Finally, we can find the probability that both students are smokers by multiplying these two probabilities together:

P(A and B) = P(A) * P(B|A) = (63/210) * (70/63) = 0.09

So the probability that both a randomly selected male student and a randomly selected female student are smokers is 0.09 or 9%.

Step-by-step explanation:

Contrapositive represents the implication of conditional statement to the logical statement if p then q to be false where as contradiction we prove that our supposition is false that implies the given condition is true.

Comparison in the proof of contrapositive and contradiction:

Contrapositive represents the hypothesis is true that implies conclusion is also true or the conclusion is false that implies hypothesis is also false.

Example of contrapositive: For any integer a , b a + b ≥ 17 , a≥9 , b≥ 9.

Using contrapositive :

If a < 9 , b < 9 then a + b < 17

a < 9, b < 9 consider a ≤8 , b≤8

a + b = 8 + 8

        = 16

        < 17

It proves a < 9 , b < 9 then a + b < 17 implies ,when  a≥9 , b≥ 9 then

a + b ≥ 17 .

Contradiction : Here we suppose the statement which is against the required statement and prove it wrong which implies our given statement is true.

Example: For any integer a, a²  is even then a is even .

Here we assume a is an odd integer then prove it wrong.

Therefore, comparing contrapositive and contradiction provides contrapositive is conditional to logical and contradiction required to our supposition is wrong.

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The equations that have the same solution are:

2.3p – 10.1 = 6.49p – 4

230p – 1010 = 650p – 400 – p

23p – 101 = 65p – 40 – p

Options B, C, and D are the correct answer.

Solutions are the values of an equation where the values are substituted in the variables of the equation and make the equality in the equation true.

We have,

2.3p - 10.1 = 6.5p - 4 - 0.01p

2.3p - 6.5p + 0.01p = 10.1 - 4

2.31p - 6.5p = 6.1

-4.19p = 6.1

p = -6.1/4.19

p = -1.5

Now,

Solve for p.

2.3p – 10.1 = 6.4p – 4

2.3p - 6.4p = 10.1 - 4

-4.1p - 6.4

p = -6.4/4.1

p = -1.6

2.3p – 10.1 = 6.49p – 4

2.3p - 6.49p = 10.1 - 4

-4.19p = 6.1

p = -1.5

230p – 1010 = 650p – 400 – p

230p - 649p = 1010 - 400

-419p = 610

p = -1.5

23p – 101 = 65p – 40 – p

23p - 64p = 101 - 40

-41p = 61

p = -1.5

2.3p – 14.1 = 6.4p – 4

2.3p - 6.4p = 14.1 - 4

-4.1p = 10.1

p = 2.5

Thus,

Equations that have the same solution

2.3p – 10.1 = 6.49p – 4

230p – 1010 = 650p – 400 – p

23p – 101 = 65p – 40 – p

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Answer:

  (a) 5.78%

  (b) $10,594.63

  (c) 5.95%

Step-by-step explanation:

You want the annual rate, the 1-year balance, and the effective yield on an account in which $10,000 is deposited, and the value doubles in 12 years.

The compound interest formula is ...

  A = Pe^(rt)

where P is the amount invested at annual rate r for t years, and A is the account balance.

Solving for r, we have ...

  ln(A/P)/t = r

The account value will have doubled when A/P = 2, so the rate is ...

  r = ln(2)/12 ≈ 0.057762 ≈ 5.78%

The annual rate is about 5.78%.

The balance after 1 year is ...

  A = 10000·e^(ln(2)/12·1) = 10000·2^(1/12) = 10594.63

The balance after 1 year will be $10,594.63.

The APR (r) will be ...

  A = P(1 +r)^t

  10594.63 = 10000(1 +r)¹

  r = 10594.63/10000 -1 = 0.059463 ≈ 5.95%

The effective yield is about 5.95%.

The three methods are used to select a sample from a larger population in order to make inferences about the population as a whole.

Probability-proportional-to-size sampling is a method where the probability of an item being selected is proportional to its size. In this case, the size is represented by the dollar amount of the sale.

Systematic selection involves selecting items at regular intervals. In this case, the starting point is 13 and the interval is 30. Every 30th item is selected, starting from the 13th item.

The starting dollar is $17,240 and the interval is $220,000. Every item with a sales amount that falls within the interval is selected with a probability proportional to its size.

The random-number table selection technique involves using a random number table to select items. The last four digits of the invoice number are used to determine which item is selected.

The selection process starts at row (0004) and column (01) and continues across the row and then down to the next row.

The probability of an item being selected in each method differs and is important in ensuring a representative sample is obtained.

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The solution to the system of equations is x = (y + 2) / 3 and y = 2.5.

Equations are mathematical statements that express the relationship between two or more variables. An equation typically consists of an equal sign, two expressions containing the variables, and the equals sign is used to show that the two expressions on either side of it are equal in value. Equations are used to solve problems, make predictions, and describe patterns.

Let's start by solving for x in the first equation:

y = 3x - 2

Add 2 to both sides of the equation:

y + 2 = 3x

Divide both sides of the equation by 3:

(y + 2) / 3 = x

Now that we've solved for x, we can substitute x into the second equation.

y = x + 2

Substitute (y + 2) / 3 for x:

y = (y + 2) / 3 + 2

Simplify the left side of the equation:

y = (y + 2 + 3) / 3

Multiply both sides of the equation by 3:

3y = (y + 5)

Subtract y from both sides of the equation:

2y = 5

Divide both sides of the equation by 2:

y = 5 / 2

y = 2.5

Therefore, the solution to the system of equations is x = (y + 2) / 3 and y = 2.5.

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Answer:

$5

Step-by-step explanation:

Let the cost of a children's ticket be x.

The cost of an adults ticket would be x + 3. (adult ticket costs $3 more than a children's ticket.)

200 adult tickets would cost 200(x+3), and 100 children's ticket would cost 100x.

The combined costs of children's ticket and adult would be 200(x+3) + 100x.

Using these information, the equation: 200(x+3) + 100x = 2100 can be formed.

200(x+3) + 100x = 2100

200x + 600 + 100x = 2100

300x = 1500

x = 5

The children's ticket cost $5.

Double check.

200*8 + 100*5 = 2100.

Answer:

  f'(-3.5) ≈ 0.8292

  f'(2) ≈ 5.277

  f'(4) ≈ 10.34

Step-by-step explanation:

You want the approximate derivative of f(x) = 8·1.4^x using h=0.001 at x = {-3.5, 2, 4}.

The derivative is approximated by the formula ...

  [tex]f'(x)\approx\dfrac{f(x+h)-f(x)}{h}\\\\f'(x)\approx\dfrac{f(x+0.001)-f(x)}{0.001}\qquad\text{for $h=0.001$}\\\\f'(x)\approx\dfrac{8\cdot1.4^{x+0.001}-8\cdot1.4^x}{0.001}\qquad\text{using the given $f(x)$}[/tex]

The calculation for different values of x is tedious, but not difficult.

For example, ...

  f'(-3.5) = (8·1.4^-3.499 -8·1.4^-3.5)/0.001 = (2.4648358 -2.4640066)/0.001

  = 0.0008292/0.001

  f'(-3.5) = 0.8292

The remaining f'(x) values are shown in the attached table in the column f₁(x₂).

__

Additional comment

When function evaluation is repeated for different values, it is usually convenient to let a calculator or spreadsheet do the math. You can enter the formula once and have it evaluated as many times as you need.

The formula shown can be simplified to f'(x) ≈ 8000(1.4^(x+.001) -1.4^x), reducing the tedium by a small amount. The second attachment shows a different calculator using this formula.