QUESTION 5
(a) Differentiate the following
(i)
y=e²x - 3e-4x

Answer:

p=2

Step-by-step explanation:

If Benjamin has 25 papayas, given the ratio of papayas to pears as 50:94, he has 47 pears.

The ratio is the numerical relationship that one variable has when compared with another.

The ratio has the same meaning as proportion.

Ratios are represented in percentages, decimals, fractions, or with the ratio sign (:).

Another way to calculate it is to examine the ratio against the number of papayas he has.

Benjamin has 25 papayas, which is half of 50 (25/50).  This means he has half of the pears, which is 47 (94/2).

Papayas = 25

The ratio of papayas to pears = 50:94

For every 50 papayas Benjamin has, he has 94 pears.

The number of pears he has = 47 (25/50 x 94)

Thus, if Benjamin has 25 papayas, given the ratio of papayas to pears as 50:94, he has 47 pears.

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The two values of y after factorizing the given quadratic equation are 0, -0.5

The given equation is quadratic as the order of the equation is 2. In a quadratic equation with a single variable, the variable will have two different values which satisfy the equation. These values of the variable can be real and different, real and equal, or imaginary.

So, there will be two values of y.

Consider the given equation,

10y^2 + 12y = 7y

10y^2 +12y - 7y = 0

10y^2 + 5y = 0

Since the coefficients of y and y^2 are both multiples of 5,

5*(2y^2 + y) = 0

2y^2 + y = 0

Taking y as a common factor,

y*(2y+1) = 0

Now, we get two cases,

y = 0 or 2y + 1 = 0 => y = -(1/2) = -0.5

Therefore, y = 0 or y = -0.5

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The total impact on Jakob's cash flow for the year is C. $6,400.

It should be noted that Jakob received a $1,000-a-year raise in January, sold stocks in March for $6,000 that were originally purchased for $4,000.

The impact will be:

= Raise + Sale of stock - Mortgage

= 1000 + 6000 - 600

= 6400

Therefore, the correct option is C

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Answer:

169,578$

Step-by-step explanation:

If you divide 2 million 5 hundred and 43 thousand 6 hundred and 66 by 15, the answer you would get would be 169,577.733333 (digit 3 goes on and on), but the question says we would need to round it to the nearest dollar. Therefore, the answer is 169,578$!!!

Answer:

An equivalent numerical expression with whole-

number exponent using these laws can be written as:

1) 2² × 2³ = 2^5     => using product of Powers

2) 2² × 3² = (2×3)² = 6²      => using power of a Product

3) (2²)³ = 2^6      => using power of a power

Step-by-step explanation:

First of all, let us understand some terms like;

1) Exponentiation: It is the mathematical process of raising one integer to the power of another. The base is the first integer, while the exponent is the second.

2) Power: A power is a phrase that depicts the same component being multiplied repeatedly.

3) Exponent: The number of times the base is used as a factor is represented by the exponent.

Now, let us understand the 7 Laws of Exponents;

1) a^m × a^n = a^(m+n)   => Product With the Same Bases

2) a^m / a^n = a^(m-n)    => Quotient with Same Bases

3) (a^m)^n = a^(m×n)    => Power Raised to a Power

4) a^n × b^n = (ab)^n    => Product to a Power

5) a^n / b^n = (a/b)^n    => Quotient to a Power

6) a^0 = 1     => Zero Power

7) a^(-m) = 1/a^m    => Negative Exponent Rule

Furthermore, an equivalent numerical expression with whole-

number exponent using these laws can be written as:

1) 2² × 2³ = 2^5     => using product of Powers

2) 2² × 3² = (2×3)² = 6²      => using power of a Product

3) (2²)³ = 2^6      => using power of a power

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Answer:

{-3/2, 3/2}

Step-by-step explanation:

Let's solve your equation step-by-step.

2(|x|)=3

Step 1: Divide both sides by 2.

2(|x|)/2 = 3/2

|x|= 3/2

Step 2: Solve Absolute Value.

|x|= 3/2

We know either x= 3/2 or x=−3/2

x=3/2

(Possibility 1)

x=−3/2

(Possibility 2)

The percent increase in pay was 20%

Maddie's Boutique paid the members of its staff $20 per hour.

and,  the boutique merged with another store, and the staff members started making $24 per hour.

To find the what percent increase in pay ?

Now, According to the question:

Based on the given conditions,

= (24 - 20) ÷ 20

= [tex]\frac{24-20}{20}[/tex]

= 1/5

and, Covert to percentage

= 1/5 x 100

= 20%

Hence, The percent increase in pay was 20%

What is Percentage?

Percentage can be calculated by dividing the value by the total value, and then multiplying the result by 100. The formula used to calculate percentage is :

(value/ total value) x 100%

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The total cost functions are:

total charges for Hertz=32+42x

total charges for Enterprise=24+46x

What does the total rental cost of each company entails?

The total rental cost of each company consists the fixed service charges and the daily charge which can be multiplied by the total of number of days of rental to determine total charges overall.

Hertz:

total charges=32+42x

when x=6 days

total charges=32+(42*6)

total charges=$284

Enterprise:

total charges=24+46x

when x=6 days

total charges=24+(46*6)

total charges=$300

Renting for 4 days:

total charges(Hertz)=32+(42*4)

total charges(Hertz)=$200

total charges(Enterprise)=24+(46*4)

total charges(Enterprise)=$208

savings=$208-$200

savings=$8

The company that charges less when Avery decides to rent car for only 4 days is Hertz and Avery can $8 as result of choosing Hertz

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Answer: $466.

Step-by-step explanation:

Add all the numbers in the graph together, you get 194.

Now, subtract 194 from 660, you get 466. That's how much profit the company makes.

The required generated profit on iPhone 4s is given as $466.2.

The cost price is defined as the is the price of producing something while the selling price is the amount that the buyer pays.

Here,
As of the mentioned data,
Cost of making an iPhone = $193.8
The selling price of the iPhone = $660

Profit is meant how much money is generated from the product besides the product cost price.
Profit  = selling price - cost price
Profit= 660 - 193.9
Profit = $466.2

Thus, the required generated profit on iPhone 4s is given as $466.2.

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Answer:

x≤1

Step-by-step explanation:

The average rate of change of the function from x == -4 to x = 3 is calculated as: -26.

The formula for determining the average rate of change across a given interval of a function is expressed as:

Average rate of change = g(b) - g(a)/b - a.

Given the function, g(x) = -2x³ + 5 to find the average rate of change from x = -4 to x = 3, do the following:

a = -4

g(a) = g(-4) = -2(-4)³ + 5 = -2(-64) + 5 = 128 + 5 = 133

b = 3

g(b) = g(3) = -2(3)³ + 5 = -2(27) + 5 = -54 + 5 = -49

Substitute the values into g(b) - g(a)/b - a:

Average rate of change = (-49 - 133)/(3 - (-4))

Average rate of change = -182/7

Average rate of change = -26

Thus, the average rate of change of the function from x == -4 to x = 3 is calculated as: -26.

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The area of the given circle is 36.298 cm square.

Here, we are given that f is the function that determines the area of a circle (in square cm) that has a radius of r cm.

The area of a circle is given the the formula as follows-

area of a circle = πr^2

⇒ f(r) = πr^2

The value of π is approximately 3.14

⇒ f(r) = 3.14r^2

Now, we are given that the radius of a circle is 3.4 cm.

Thus, its area will be-

f(3.4) = 3.14 × 3.4 × 3.4

= 3.14 × 11.56

= 36.298

Thus, the area of the given circle comes out to be 36.298 cm square.

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Han llenaría 8 tazas con jugo de naranja porque si tomas la mitad de 1 taza de jugo de naranja puedes hacer 2 tazas ahora haz eso 4 veces y obtendrás 8 tazas de jugo de naranja

Reason:

A rational number is a fraction of any two integers, as long as the denominator is nonzero. This applies to the first two answer choices.

Choices C and D are undefined because of the 0 in the denominator. You cannot divide by zero. This rules out the last two choices.

The baseball coach bought each pizza at an approximate cost of $ 10 or an exact cost of $ 10.75.

In this problem we know that a baseball coach spends a total of $ 118.25 on buying 11 pizzas. First, we need to estimate the amount of money spent per each pizza bought, which is found by means of multiplication tables and the supposition of truncation, that is, finding the maximum integer less than or equal to the real total cost.

By direct inspection we find that 10 times the 11 pizzas is equal to $ 110, which is the maximum integer less than or equal to the real total cost. Then, we estimate a cost of $ 10 per each pizza bought. Second, the exact unit cost is found by dividing the total by the number of pizzas:

c = $ 118.25 / 11

c = $ 10.75

In a nutshell, the baseball coach bought each pizza at an approximate cost of $ 10 or an exact cost of $ 10.75.

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The interval at which the function x³ + 3x² - 4x - 12 increases is

x ∈ (- ∞, - 2.5) ∪ (0.5, ∞).

We have,

x³ + 3x² - 4x - 12

We need to draw a graph to see at which interval the graph is increasing.

The graph is given below.

We see that the graph is increasing from x = -∞ to x = -2.5 and from  x = -2.5 it decreases till x = 0.5 and again from x = 0.5 it increases to x = ∞.

So we can write the interval as:

x ∈ (- ∞, - 2.5) and  x ∈ (0.5, ∞)

We can write it as one single interval as:

S = (- ∞, - 2.5) ∪ (0.5, ∞)

Thus the interval at which the function x³ + 3x² - 4x - 12 increases is

x ∈ (- ∞, - 2.5) ∪ (0.5, ∞).

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Answer:

hi can we talk for a while I'm a little alone

The items that you can add with not breaking the weight limit are:

The hair dryer, the souvenir, the boots, the boots and the souvenir, and the hair dryer and the souvenir.

The maximum weight allowed is 50 pounds, and you already have 44.9 pounds, then the weight you can add is:

50lb - 44.9lb = 5.1lb

Now, the items that you have are:

2.5 lb hair dryer.

1.3 lb souvenir.

3.6 lb pair of boots.

The only things that you can't add together are the hair dryer and the boots, because the weight adds up to:

2.5lb + 3.6lb = 6.1lb

Which is more than the 5.1lb left that you have.

Obviuously, you can't take the 3 items.

Then you can add:

The hair dryer, the souvenir, the boots, the boots and the souvenir, and the hair dryer and the souvenir.

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Answer:(0,4)

Step-by-step explanation:

0.95X -0.55X+10-62 ... Step 1: Find Roots solution. X=-4. X = 3. Step 2: Graph ... Write the Domain and Range of the function. Positive.

Answer:

  (c)  inconsistent equation

Step-by-step explanation:

You want to know if the equation -6x+6x-6=2-5 is an identity, conditional, or inconsistent.

The simplified equation, after combining like terms, is ...

  -6 = -3

This is an "inconsistent" equation, always false.

for the two given fractions 3/4 and 1/6 we have:

Here we have two fractions, 3/4 and 1/6, and we want to find the sum, product, and quotient between them.

First let's do the sum:

3/4 + 1/6

We just need to find a common denominator, which can be 12, so we can rewrite it as:

9/12 + 2/12 = 11/12

The sum of the two fractions is 11/12

Now the product, it is, we multiply denominator with denominator and numerator with numerator, we will get:

(3/4)*(1/6) = (3*1)/(4*6) = 3/24 = 1/8

The product between the two fractions is equal to 1/8.

Finally, the quotient, this is:

The product between the first numerator and second denominator, and between the first denominator and second numerator, so the quotient becomes:

(3/4)/(1/6) = (3/4)*(6/1) = (3*6)/(4*1) = 18/4 = 9/2

Then we conclude that for the two given fractions 3/4 and 1/6 we have:

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Answer:2

Step-by-step explanation:

[tex]\frac{14}{5} -5[/tex]

Divide 14 by 2 to get 7.

7−5

Subtract 5 from 7 to get 2.

Answer=2