THE QUESTION IS IN THE PICTURE

Answer:

not sure but i think the answer is 9.40

Step-by-step explanation:

We want to see which pair of sets is disjoint, this is, see which pair of sets does not share any element.

The correct option is: E = {even numbers} and F = {odd numbers}

So we only need to see which one is the pair of sets that does not share any element, so we can analyze the given options and see if we can find a number that belongs to both sets.

1) X = {rational numbers} and Y = {whole numbers}

Any whole number is also a rational number, for example:

2 = 4/2

So we can write the number 2 as a quotient of two integers, then we can see that these sets share elements.

2) P={multiples of 2} and Q={multiples of 3}

The number 6 is a multiple of both 2 and 3, thus the number 6 belongs to bot sets, then the sets are not disjoint.

3) G={multiples of 5} and H={multiples of 10}

10 is a multiple of 10 and 5, so the number 10 belongs to both sets, thus the sets are not disjoint.

4) E={even numbers} and F={odd numbers}

We define the even numbers as the ones divisible by 2, while the odd numbers are those that are not divisible by 2. Then by definition, there is no even number that is also odd.

Then we can see that these two sets are disjoints, and this is the correct option.

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The overall logarithmic function pertaining to f(x) exists within the stated domain of (0,1)U(1,infinity), whilst featuring a range of "all real numbers".

A logarithmic function's domain is all positive real numbers except 0, as the logarithm of 0 is undefined. From our given table, we conclude that x values consist solely of positive powers of 5; this yields the following domain condition: x > 0 and x ≠ 1.

The range of a logarithmic function comprises every element in the set of real numbers. Despite observing y-values between -3 and 3 in our table, the potential for logarithmic functions to approach negative infinity when x approaches 0, long with the tendency to lean towards positive infinity as x approaches infinitely large values renders the range to encompass all real numbers.

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The value of x will remain 0 after evaluating the expression.

The expression (y > 0) && (1 > x++) involves two conditions connected by the logical AND operator &&. For the entire expression to be true, both conditions must be true.

In this case, y is assigned the value of 0, and therefore, the condition y > 0 will evaluate to false. Since the first condition is false, the second condition 1 > x++ will not be evaluated, because even if it were true, the entire expression would still be false.

Since the entire expression is false, the increment operation x++ will not be executed, and the value of x will remain 0.

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The cost of plain wrapping paper is $13 and the cost of holiday wrapping paper is $18

Chloe:

Number of plain wrapping paper sold = 2

Number of holiday wrapping paper sold = 10

Total income = $206

Eduardo:

Number of plain wrapping paper sold = 3

Number of holiday wrapping paper sold = 5

Total income = $129

Let x represent the cost of plain wrapping paper and y represent the cost of holiday wrapping paper:

Formulating the equations:

2x+10y = 206-----(1)

3x+5y = 129------(2)

Multiplying (2) with 2 and subtracting with (1) we get:

2x+10y = 206

6x+10y = 258

4x = 52

x = 13

So cost of plain wrapping paper is $13

holiday wrapping paper = $18

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In the first limit, lim(x->0) (1 - cos(2x))/(7x), the type of indeterminate form is 0/0. By applying L'Hopital's Rule, we can find the limit by differentiating the numerator and denominator with respect to x.

(a) For the limit lim(x->0) (1 - cos(2x))/(7x), we have an indeterminate form of 0/0. To apply L'Hopital's Rule, we differentiate the numerator and denominator with respect to x:

Numerator: d(1 - cos(2x))/dx = 0 - (-2sin(2x)) = 2sin(2x)

Denominator: d(7x)/dx = 7

Now, we evaluate the limit of the ratio of the derivatives:

lim(x->0) (2sin(2x))/7

Since sin(2x)/x approaches 1 as x approaches 0, we can substitute the limit:

lim(x->0) (2sin(2x))/7 = (2 * 1)/7 = 2/7

Therefore, the limit of (1 - cos(2x))/(7x) as x approaches 0 is 2/7.

(b) For the limit lim(x->∞) √(ln(x)), we have an indeterminate form of ∞ * 0. However, L'Hopital's Rule is not applicable in this case as it is specifically used for the indeterminate forms 0/0 and ∞/∞. Therefore, we cannot evaluate this limit using L'Hopital's Rule. Other methods, such as using properties of limits or algebraic manipulations, may be needed to find the limit in this case.

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a) The percentage increase in sales from 2004 to 2014 for Company A was 21.25%.

b) The company that had the most sales per worker in 2014 was Company A.

The percentage increase refers to the amount of increase (that is the difference between the current value and the initial value) divided by the initial value, multiplied by 100.

Percentage increases are determined as the quotients of division operations, which are multiplied by 100 to express the value in percentage terms.

a) Percentage increase in sales from 2004 to 2014 for Company A:

Sales increase = $68 ($388 - $320)

Percentage increase = 21.25% ($68/$320 x 100)

b) Sales per Worker in 2014:

Company A = $121,250 ($388,000,000/3,200)

Company B = $89,062.50 ($57,000,000/640)

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                    Company A                                      Company B

              Sales        Number of Workers        Sales       Number of Workers

           ($ millions)                                        ($ millions)

2004      $320               2,960                        $48                   605

2014         388               3,200                           57                   640

(b) Which company had the most sales per worker in 2014. Company A or Company B?

Answer:

The right answer is:

(a) $30.78

(b) $360

(c) 2.339%

Step-by-step explanation:

The given values are:

At $36.30 per share,

Purchased = 300 shares

At $22.50 per share,

Purchased = 200 shares

Per share dividend,

= $0.72

Now,

(a)

The average price per share will be:

=  \(\frac{(300\times 36.30)+(200\times 22.50)}{300+200}\)

=  \(\frac{10,890+4,500}{500}\)

=  \(\frac{15,390}{500}\)

=  \(30.78\) ($)

(b)

The annual dividend will be:

=  \(0.72\times Number \ of \ shares\)

=  \(0.72\times 500\)

=  \(360\) ($)

(c)

The average annual yield will be:

=  \(\frac{Dividend \ per \ share}{Average \ cost}\times 100\)

=  \(\frac{0.72}{30.78}\times 100\)

=  \(2.339\)%

Answer:

(3x - 7)(2x + 3)

Step-by-step explanation:

Multiply 6 by -21, which gets you -126.

Now, we have to find 2 factors that multiply to -126 and add to -5.

These two factors will be -14 and 9.

Now, we can group by putting the 2 factors in place of -5x

6x² + 9x - 14x - 21

Then, we can factor out a common value in both halves of the expression:

3x(2x + 3) - 7(2x + 3)

Now, we can split this into 2 factors:

(3x - 7)(2x + 3)

Answer:How much interest will I earn in a CD? It depends on the interest rate the bank offers and how long the CD's term is. Here's an example: $5,000 invested in a 3-year CD with a 0.80% APY would earn about $120 by the end of the term.

Step-by-step explanation:

Answer: $ 91.50.

Step-by-step explanation:

Let x be the original price.

Since discount is applied before tax.

New price = (Original price - Discount)-Tax rate (Original price - Discount)

, where Discount = Discount rate x Original price.

Substituting values, we get

\(62.28=(x-0.25x)-0.0925(x-0.25x)\)

\(62.28=(0.75x)-0.0925(0.75x)\)

\(62.28=0.75x-0.069375x\)

\(62.28=0.680625x\)

\(x=\frac{62.28}{0.680625}\)

\(x=91.50\)

Hence, the original price was  $ 91.50.

Answer:

see explanation

Step-by-step explanation:

Consecutive angles of a parallelogram are supplementary, thus

∠ M + ∠ N = 180 , substitute values

3x + 8x - 40 = 180, that is

11x - 40 = 180 ( add 40 to both sides )

11x = 220 ( divide both sides by 11 )

x = 20

Thus

∠ M = 3x = 3(20) = 60°

∠ N = 8x - 40 = 8(20) - 40 = 160 - 40 = 120°

Answer:

34 inches

Step-by-step explanation :

54/360 X 20

Answer:

y= 1x+6

Step-by-step explanation:

The value of the expression tan(-5π/6) can be determined using trigonometric properties and  identities.

First, let's consider the unit circle. The angle -5π/6 is measured in the clockwise direction from the positive x-axis. In this position, the reference angle is π/6, which is the positive angle formed with the x-axis.

The tangent function (tan) is defined as the ratio of the sine (sin) of an angle to the cosine (cos) of the angle. Using the reference angle π/6, we can determine the value of tan(π/6) as the ratio of sin(π/6) to cos(π/6). sin(π/6) equals 1/2, and cos(π/6) equals √3/2. Therefore, tan(π/6) is (1/2) divided by (√3/2), which simplifies to 1/√3 or √3/3. Since tan is an odd function, tan(-5π/6) is equal to the negative of tan(5π/6). Therefore, tan(-5π/6) has the same value as -√3/3.

In conclusion, the value of tan(-5π/6) is -√3/3, which means that the tangent of the angle -5π/6 is negative and equal to the ratio of -√3 to 3.

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The acceleration the car must achieve, according to the mean value theorem, is 60 mi/h²2.

To find the acceleration of the car using the mean value theorem:

At 2:00 PM, the car's speedometer reads 30 mph.

At 2:10 PM, the car's speedometer reads 40 mph.

The mean value theorem states that if a function is continuous on a closed interval [a, b] and differentiable on the open interval (a, b), then there exists at least one value c in the open interval (a, b) such that:

f'(c) = (f(b) - f(a)) / (b - a)

consider time as the independent variable (t) and speed as the dependent variable (s).

s(2:00 PM) = 30 mph (let's denote it as s(a))

s(2:10 PM) = 40 mph (let's denote it as s(b))

The time interval between these two readings is 10 minutes or 1/6 hour. Therefore, a = 2:00 PM and b = 2:10 PM.

The mean value theorem to find the acceleration. The acceleration represents the derivative of the speed with respect to time to find s'(c), where c is the time at which the car achieves the average speed.

The mean value theorem formula,

s'(c) = (s(b) - s(a)) / (b - a)

Substituting the given values:

s'(c) = (40 mph - 30 mph) / (1/6 h)

Simplifying:

s'(c) = 10 mph / (1/6 h)

To get the acceleration in mi/h²,  to divide by the time unit squared. Since mph is a unit of speed, to divide by hours squared.

s'(c) = (10 mph / (1/6 h)) ×(1/1 h²)

s'(c) = (10 mph × 6 h) / (1 h²)

s'(c) = 60 mph / h

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Answer:

3 7/10

Step-by-step explanation:

8 4/5 - 5 1/10

8 8/10 - 5 1/10

8 - 5 = 3       8/10 - 1/10 = 7/ 10

3 7/10

there are no values of a and b that would make y = aeʳ + be³r not a solution to the equation. This is because when we substitute the function y = aeʳ + be³r, its derivatives y' and y'' into the differential equation,

To verify that y = aeʳ + be³r, where a, b ∈ ℝ, is a solution to the differential equation y'' - 4y' + 3y = 0, let's follow the given steps:

a. find y' and y'' by taking the derivatives of y = aeʳ + be³r with respect to r:

y' = a(eʳ) + b(3e³r)y'' = a(eʳ) + b(9e³r)

Note that a and b are constants, not variables .

b. Now, substitute y, y', and y'' into the differential equation y'' - 4y' + 3y = 0:

y'' - 4y' + 3y = (a(eʳ) + b(9e³r)) - 4(a(eʳ) + b(3e³r)) + 3(a(eʳ) + b(e³r))

              = (a - 4a + 3a)eʳ + (9b - 12b + 3b)e³r               = 0eʳ + 0e³r

              = 0

Since the equation simplifies to 0, we have shown that y = aeʳ + be³r, y', and y'' satisfy the given differential equation.

Now, let's address the additional question:

Are there any values of a, b that would make y = aeʳ + be³r not a solution to the equation?

No,the equation is satisfied for any values of a and b. Thus, the given form of y is indeed a valid solution to the differential equation for all real values of a and b.

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Answer:

-40

Step-by-step explanation:

h(x) = -7(6) +2

-42+2 = -40

Answer: -40

Step-by-step explanation:

-7x6+2= -40

hope this helps!!

Answer:

45

Step-by-step explanation:

Answer:

45

Step-by-step explanation

Juan has just completed a 15 kilometer race in 20 minutes.  What was his average speed in kilometers per hour?

Solution

First, 15 kilometers is a distance, so

       d  =  15

Next, we are given 20 minutes and we are asked to present the speed in kilometers per hour rather than kilometers per minute.  We need to convert 20 minutes to hours.  Since there are 60 minutes per hour, we divide by 60 to find out how many hours it took

t  =  20 minutes / 60 minutes per hour =  1/3 hours

Now we can use the d=rt equation:

15  =  (r)(1/3)

If we multiply both sides

(3)(5)  =  (r)(1/3)(3)  or  r  =  45

Juan's average speed was 45 kilometers per hour.

The dimensions of the box that minimize the surface area where x is the length of each side of the base and y is the height of the box are 8 cm x 8 cm x 2 cm.

To design a rectangular box with a square base and an open top, we need to determine the dimensions of the box that will minimize the surface area.

Let x be the length of each side of the base and y be the height of the box. The volume of the box must be 128 cm, so we can write the equation as x^2y=128.

Using the volume equation, we can solve for y in terms of x: y=128/x^2. Substituting this into the surface area equation, we get:

A=2x^2+4x(128/x^2)=2x^2+512/x.

We can find the critical points by taking the derivative and setting it to zero: A'(x)=4x-512/x^2=0.

Solving for x, we get x=8 cm. Substituting this into the volume equation, we get y=2 cm.

Therefore, the dimensions of the box that minimize the surface area are 8 cm x 8 cm x 2 cm.

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Answer:

1 inch represents 11 feet.

Step-by-step explanation:

Actual length is 363 feet

Scale model is 33 inches.

So, the scale factor is \(\frac{33}{363}\)

Simplify it, we get \(\frac{1}{11}\)

It means the scale factor is 1 inch for 11 feet.

That's 1 inch represents 11 feet.

Answer:

its going to be option D

Step-by-step explanation:

i promise im right

This can be expressed in this form:

1/2x - 18.

The time it take riders to pass over the hill and reach ground level is 111.19 seconds .

Given :

the roller coaster's height expressed by the equation below;

h = -0.067t^2 + 7t + 50

where

t is the time in seconds

The driver will hit the ground at the point where h = 0

Substitute

-0.067t^2 + 7t + 50 = 0

Multiply through  by -1

0.067t^2 - 7t +-50 = 0

Factorize :

On factorizing, the positive value of "t" is 111.19 seconds

Hence the time it take riders to pass over the hill and reach ground level is 111.19 seconds

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Answer:

if Clara's father were to put all of the ties in a bowl, shuffle them, and pick a tie, then the chance of getting a plaid one would be a more significant percentage than the blue and green ties. let's say he will have a 40%  chance to make it simple.

The probability of choosing a plaid tie at random is 2/9.

It is a branch of mathematics that deals with the occurrence of a random event.

The total number of ties that Clara's father has is:

total = 6 + 2 + 16 + 3 = 27

The number of plaid ties is:

plaid = 6

Therefore, the probability of choosing a plaid tie at random is:

plaid/total = 6/27 = 2/9

Hence, the probability of choosing a plaid tie at random is 2/9.

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The probability that the student owns 3 pets is 0.0272.

Poisson distribution is a type of probability distribution that is often used in the analysis of events that are rare. A Poisson distribution can be used to estimate the probability of a given number of events occurring in a fixed time or space when the average rate of occurrence is known.

The parameter of a Poisson distribution is the average rate of occurrence of the event in question. It is equal to the expected value and the variance of the distribution.The number of pets that a randomly selected student owns has a Poisson distribution with parameter 0.8.

Therefore,λ = 0.8.

The probability that the student owns 3 pets is given by;

P(X=3) = (λ³ * e^-λ) / 3!

P(X=3) = (0.8³ * e^-0.8) / 3!

P(X=3) = (0.512 * 0.4493) / 6

P(X=3) = 0.0272

Therefore, the probability that the student owns 3 pets is 0.0272.

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If the triangles are similar but no congruent, then the triangles have different size, thus the only correct option is the dilation (first option).

We know that two figures are congruent if the figures have the same shape and size, while two figures are similar only if have the same shape (but the figures can have different size).

Here we know that the triangles are similar but no congruent, so the triangles must have different size. From the given transformations, the only one that changes the size is the first option, a dilation.

And for example, if we apply a dilation AND the other transformations, then we still will get a similar figure, but if we apply a reflection/rotation/translation alones, we will get a congruent triangle.

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The expected value of the winnings from this game is $3.24.

To find the expected value of the winnings, we multiply each payout by its corresponding probability and then sum up the results. Let's calculate it step by step:

Payout ($) Probability Payout x Probability

2 0.64 1.28

4 0.18 0.72

6 0.12 0.72

8 0.04 0.32

10 0.02 0.20

Now, let's sum up the values in the "Payout x Probability" column:

1.28 + 0.72 + 0.72 + 0.32 + 0.20 = 3.24

Therefore, the expected value of the winnings from this game is $3.24.

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