15-16 find the domain of each function.
15. (b) \(f(x)=\frac{1+x}{e^{\cos x}}\)

Sure, here's a word problem that can be solved using the equation 25 + 0.5x ≠ 60:

Tommy has been saving money in his piggy bank. He started with $25 and has been adding $0.50 each day. He wants to know how many days it will take for his savings to reach $60. Can you help him find the number of days (x) it will take?

Remember, the equation that represents this situation is 25 + 0.5x ≠ 60.

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Answer:

12 sq. units

Step-by-step explanation:

The formula for finding the area of a triangle is a = 1/2bh, or 1/2 times base times height.

To do this, multiply the base (6) and height lengths (4). This gets you 24.

But we're not done. You must then multiply by 1/2, which is the same a dividing by 2/1 or 2. 24/2 = 12. Slap on the unit of measurement and you've got your answer.

Answer:

2(0.4)^-2 = 12.5

Step-by-step explanation:

do math noob

Answer:

p = 43

Step-by-step explanation:

I assume you mean an expression with exponents.

In the future, for a to the n power use a^n.

Recall the following two rules of exponents:

\( x^a \times x^b = x^{a + b} \)

\( (x^a)^b = x^{ab} \)

Now we can answer your question.

\( (x^{22})(x^7)^3 = \)

\(= (x^{22})(x^{21})\)

\( = x^{43} \)

Since

\( x^{43} = x^p \)

then

p = 43

The volume of sphere a is 32π/3 cubic cm, and the volume of sphere b is 256π/3 cubic cm.

What is volume of sphere?

The volume of a sphere is given by the formula:

V = (4/3)πr³

where r is the radius of the sphere, and π (pi) is a mathematical constant approximately equal to 3.14159.

The volume of a sphere can be calculated using the formula:

V = (4/3)π\(r^3\)

where r is the radius of the sphere and π is the mathematical constant pi.

Using this formula, we can find the volumes of spheres a and b as follows:

Volume of sphere a:

V = (4/3)π(\(2^3\)) = (4/3)π(8) = 32π/3 cubic cm

Volume of sphere b:

V = (4/3)π(\(4^3\)) = (4/3)π(64) = 256π/3 cubic cm

Therefore, the volume of sphere a is 32π/3 cubic cm, and the volume of sphere b is 256π/3 cubic cm.

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Answer:

D

Step-by-step explanation:

(5/9)^8

You distribute the exponent 8 to both the 5 and the 9, so D is just 1 step more simplified.

Answer:  The correct option is (D) {5^8}{9^}.

hope this helps. ;)

The probability that Robert is approved on both the written application and the interview is approximately 0.5531

To find the probability that Robert is approved on both the written application and the interview, we can use the formula for conditional probability

P(A and B) = P(B | A) × P(A)

where A and B are events, P(A) is the probability of event A, and P(B | A) is the probability of event B given that event A has occurred.

Let's define the events

A = "Robert is approved on the written application"

B = "Robert is approved by the interview committee"

We know that P(A) = 0.67, and P(B | A) = 0.83. We want to find P(A and B), which represents the probability that both events A and B occur.

Using the formula for conditional probability, we have

P(A and B) = P(B | A) × P(A)

P(A and B) = 0.83 × 0.67

P(A and B) = 0.5531

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Answer: 6 units

Step-by-step explanation:

Since this is just a reflection, the length of A'C' shouldn't be different from the length of AC.

Answer:

A. This data set has two modes. Both 3 and 4 are the modes of the data set.

Step-by-step explanation:

The mode is a statistical measure that represents the most frequently occurring value in a data set. In the given data set, 1 appears once, 2 appears once, 3 appears three times, 4 appears three times, 5 appears once, and 7 appears once. Since both 3 and 4 appear three times, the data set has two modes, which are 3 and 4. Therefore, the correct answer is A: "This data set has two modes. Both 3 and 4 are the modes of the data set." Option B is incorrect because the mode cannot be calculated by taking the average of the values that appear most frequently, and option C is incorrect because the data set does have modes.

Answer: 3,020,000

Step-by-step explanation:

three million twenty thousand

Answer: 3,020,000

Step-by-step explanation: 3,000,000 + 20,000 = 3020000

Answer:

The answer is 59.5.

Step-by-step explanation:

Add 35+70%.

The ounces of soda consumed by an adult next month are examples of a discrete random variable,  False

A discrete random variable are known as counts. This is because it takes on only a countable number of distinct values. This means a random variable can only be considered to be discrete if it can take on values that are countable in an interval, otherwise it can be continuous.

Now on the question of ounces of soda consumed by an adult next month is considered not to be discrete random variable. This is because ounces of soda or volume of soda consumed are countless and infinite in number.  

Hence, the statement that says ounces of soda consumed by an adult next month are an example of a discrete random variable is False.

Choice b(False) is correct.  

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A bin of 50 parts contains 5 that are defective and a sample of 10 parts is selected without replacement, then total 40,753,713 samples contain at least 4 defective parts.

A bin of 50 parts contains 5 that are defective.

A sample of 10 parts is selected without replacement.

Number of samples of size 10 from 50 pieces, at least 4 of which are faulty = Samples with precisely 4 defectives + samples with precisely 5 defects

Number of samples of size 10 from 50 pieces, at least 4 of which are faulty = \(^{5}C_{4}\cdot ^{45}C_{6}+ ^{5}C_{5}\cdot^{45}C_{5}\)

Using the formula \(^nC_{r} = \frac{n!}{r!(n-r)!}\)

Number of samples of size 10 from 50 pieces, at least 4 of which are faulty = \(\frac{5!}{4!(5-4)!}\cdot\frac{45!}{6!(45-6)!}+\frac{5!}{5!(5-5)!}\cdot\frac{45!}{5!(45-5)!}\)

Number of samples of size 10 from 50 pieces, at least 4 of which are faulty = \(\frac{5!}{4!1!}\cdot\frac{45!}{6!39!}+\frac{5!}{5!0!}\cdot\frac{45!}{5!40!}\)

Number of samples of size 10 from 50 pieces, at least 4 of which are faulty = \(\frac{5\times4!}{4!\times1}\cdot\frac{45\times44\times43\times42\times41\times40\times39!}{6\times5\times4\times3\times2\times1\times39!}+1\cdot\frac{45\times44\times43\times42\times41\times40!}{5\times4\times3\times2\times1\times40!}\)

Number of samples of size 10 from 50 pieces, at least 4 of which are faulty = 5 × 15 × 44 × 43 × 7 × 41 + 1 × 9 × 11 × 7 × 41

Number of samples of size 10 from 50 pieces, at least 4 of which are faulty = 40,753,713

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If your height is 5 feet 3 inches and your weight is 120 pounds, then the BMI is 21.23

To calculate your Body Mass Index (BMI), use the following formula:

BMI = weight in kilograms / (height in meters)²

First, convert your height to meters :

5 feet 3 inches = 63 inches

63 inches = 160.02 cm

160.02 cm = 1.6002 meters

Next, convert your weight to kilograms :

120 pounds = 54.43 kg

Now, plug in these values to calculate your BMI:

BMI = 54.43 kg / (1.6002 meters)²

Divide the terms

BMI = 21.23

Therefore, your BMI is approximately 21.23

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Answer:

-7

Step-by-step explanation:

Answer:

Step-by-step explanation:

b

Answer:

0<r<4

Step-by-step explanation:

-8<8-4r<8

Subtract 8 from each side

-8-8<8-4r-8<8-8

-16<-4r<0

Divide by -4, remembering to flip the inequality

-16/-4>-4r/-4>0/-4

4>r>0

Rewriting

0<r<4

Answer:

14-F

15-D

16-A

Step-by-step explanation:

The logarithmic form of the exponential equation 8e^x-5 = 0 is given as follows:

x = ln(5/8).

The exponential function in this problem is defined as follows:

8e^x-5 = 0.

The equation can be sorted isolating the exponential as follows:

8e^x = 5.

e^x = 5/8.

The natural logarithm(symbolized by the ln) is the opposite of the exponential function, hence the logarithmic form of the equation is presented as follows:

ln(e^x) = ln(5/8).

As stated above, the natural logarithm and the exponential functions are inverse functions, meaning that:

ln(e^x) = x.

Thus the logarithmic form of the exponential equation 8e^x-5 = 0 is given as follows:

x = ln(5/8).

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The corresponding horizontal distance (d) covered by the block is: d = v * t

To find the horizontal distance (d) where the block will land on the floor after dropping from a certain height (h), we can use the equations of motion and principles of projectile motion.

The key principle we'll use is that when an object is launched horizontally, its vertical motion is influenced by gravity alone, while its horizontal motion remains uniform.

Let's calculate the value of d for two different heights:

When h = 6.2 m:

The formula to calculate the time taken (t) for an object to fall from a certain height is given by:

h = (1/2) * g * t^2

Solving for t:

t^2 = (2 * h) / g

t^2 = (2 * 6.2) / 9.8

t^2 = 1.264

t ≈ 1.124 seconds

Now, the horizontal distance (d) covered by the block is given by:

d = v * t, where v is the horizontal component of velocity.

Since the block leaves the inclined surface horizontally, the horizontal component of velocity is constant throughout and doesn't change due to gravity.

Therefore, d = v * t.

When h = 3.1 m:

We can use the same approach as above to calculate the time taken (t):

t^2 = (2 * 3.1) / 9.8

t^2 ≈ 0.632

t ≈ 0.795 seconds

And the corresponding horizontal distance (d) covered by the block is:

d = v * t

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Answer:

Its C. or option 3

Step-by-step explanation:

Answer:

Step-by-step explanation:

Assume the Black-Scholes framework for a stock. You are given: i) The current stock price is 40 ii) The stock pays no dividends iii) The expected rate of appreciation is 16% iv) The stock' s volatility is 30% v) The Black-Scholes price of a 6-month 42-strike European call on the stock is 3.22 vi) The continuously compounded risk-free rate is 8% You just bought a 6-month straddle which pays the absolute difference between the stock price after 6 months and 42. Calculate the probability of having a positive profit after 6 months. Possible Answers A Less than 0.35 B At least 0.35 but less than 0.40 c At least 0.40 but less than 0.45 D At least 0.45 but less than 0.50 E At least 0.50

Answer:

C

Step-by-step explanation:

The domain of a function is the span of x-values.

And the range of a function is the span of y-values it covers.

From the graph, we can see that the span of x-values the graph covers goes from x=1 to x=6.

In other words, the domain is all numbers between 1 and 6 including 1 and 6.

In an inequality, this is:

\(1\leq x\leq 6\)

For the range, we can see that the lowest the graph goes is y=1, and the highest it goes is y=7.

So, the range is all numbers in between 1 and 7 including 1 and 7.

In an inequality, this is:

\(1\leq y\leq 7\)

Thus, the correct answer is C.

D is half correct, but the domain and range is flipped, so that may be your mistake. Be more careful next time!

Answer:

in the first one, the rule is y=2x+1

the second rule is y=x/2+1

sorry iont about the 3rd one

Step-by-step explanation:

The annual maintenance collected in 2014 will be $1,750,000.

To calculate the annual maintenance collected in 2014, we need to find the number of customers who will renew their maintenance contract and the number of customers who will pay for maintenance as a percentage of product sales in 2013.

Number of customers renewing maintenance in 2014 = 80% of $2,000,000 = $1,600,000

Number of customers paying for maintenance in 2014 = 75% of $2,000,000 = $1,500,000

So, the total annual maintenance collected in 2014 will be:

$1,600,000 + $1,500,000*10% = $1,750,000

Therefore, the annual maintenance collected in 2014 will be $1,750,000.

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Answer:

39

Step-by-step explanation:

4 cubed is 64 and 64-25 is 39

Good luck!

After solving the given expression, the value obtained for the difference between 4³ and 25 will be equal to 39.

The four basic mathematical operations are the addition, subtraction, multiplication, and division of two or even more integers.

Among them is the examination of integers, particularly the order of actions, which is crucial for all other mathematical topics, including algebra, data organization, and geometry.

As per the given statement in the question,

The difference between 4³ and 25 will be,

4³ = 64

Then,

64 - 25 = 39

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Answer:

$9.95

Step-by-step explanation:

Answer:

its 9.955

Step-by-step explanation:

39.82÷4

by calculator

Answer: its (4f 5) ^3

Step-by-step explanation: