Let f and g be the functions given by #f(x)=1+sin(2x)# and #g(x)=e^(x/2)#. Let R be the region in the first quadrant enclosed by the graphs of f and g. How do you find the area?

Answer:

y = 6.7

x = 8

Step-by-step explanation:

3^2 + 6*2 = y

√9 + 36 = y

6.7 = y

10^2 = 6^2 + x

100 = 36 + x

100 (-36) = 36 (-36) +x

√64 = x

8 = x

9514 1404 393

Answer:

Step-by-step explanation:

The function has a positive leading coefficient (1/3) and is of odd degree (3). These conditions mean the sign of the end behavior of the function will match the sign of x.

  x → ∞, m(x) → ∞

  x → -∞, m(x) → -∞

I think positive since is rising ....

Answer:

total number of brown sugar cubes = 3

total number of white sugar cubes = 1

total number of sugar cubes = total no of brown sugar cubes + total no of white sugar cubes = 3 + 1 = 4

probability to select one brown sugar cube = total number of brown sugar cube / total number of sugar cube = 3/ 4

therefore the probability of selecting a brown sugar cube is 3/4 or 0.75

The equation -5x + y = 2 in slope-intercept form is y = 5x + 2.

The line with m as the slope, m and c as the y-intercept is the graph of the linear equation y = mx + c. The values of m and c are real integers in the slope-intercept form of the linear equation.

To write these equations in slope-intercept form, we need to isolate y on one side of the equation.

-5x + y = 2

Adding 5x to both sides, we get:

y = 5x + 2

Therefore, the equation -5x + y = 2 in slope-intercept form is y = 5x + 2.

Learn more about slope intercept on:

brainly.com/question/9317111

#SPJ9

The formula for the volume of a cone is:

V = (1/3)πr²h

where r is the radius of the base, h is the height of the cone, and π is pi.

In this case, the slant height is given as 17 cm, which we can use with the radius to find the height of the cone using the Pythagorean theorem:

h² = s² - r²

h² = 17² - 8²

h² = 225

h = 15

Now that we have the height, we can plug in the values for r and h into the formula for the volume:

V = (1/3)π(8²)(15)

V = (1/3)π(64)(15)

V = (1/3)(960π)

V = 320π

Therefore, the volume of the cone is 320π cubic cm. Answer: 320π.

Answer:

648 is your answer

Step-by-step explanation:

hope this helps!!

Answer:

216

Step-by-step explanation:30-12=18 so 18 x 12=216 hope that helped

Answer:

2x^2+1=5-2x

2x^2+1-5+2x

2x^2-4+2x=0

x^2-2+x=0

x^2+x-2=0

(x+2)(x-1)

x1= -2

x2= 1

Answer:

\(2x^2+1=5-2x2x^2+1-5+2x2x^2-4+2x=0x^2-2+x=0x^2+x-2=0(x+2)(x-1)x1= -2x2= 1\)

Step-by-step explanation:

I hope this helps and have a good day!

Answer:

What connects to what.

Step-by-step explanation:

"Vertices is the plural of the word vertex, which is the point at which two or more lines/edges meet. " QRS is like "1,2,3. " Not sure if this is what you mean??

Answer:

E

Step-by-step explanation:

3/10 + 1/10 = 4/10

simplify 4/10

4/2 and 10/2

ANSWER = 2/5

Answer:

0.527

Step-by-step explanation:

From the question,

The sequence is Geometry Progression (G.P)

Tₙ = arⁿ⁻¹.......................... Equation 1

Where n = number of term, a = first term, r = common ratio

Given: n = 7, a = 6, r = 2/3

Substitute these values into equation 1

T₇ = 6(2/3)⁷⁻¹

T₇ = 6(2/3)⁶

T₇ = 6(64/729)

T₇ = 384/729

T₇ = 0.527

Hence, the 7th term of the sequence is 0.527

There are nine 3 number combinations that add up to 19

From the question, we have the following parameters that can be used in our computation:

Summation = 19

Combinations = 3

Using the above as a guide, we have the following:

The combinations of three numbers that add up to 19 are:

(1, 9, 9), (2, 6, 11), (3, 5, 11)

(3, 6, 10), (4, 4, 11), (4, 5, 10)

(5, 5, 9)

These are all the combinations of three positive integers that add up to 19.

Read more about numbers at

https://brainly.com/question/10853762

#SPJ1

Answer:

about 1.6090405507426917 years (round this)

Step-by-step explanation:

This question requires reverse thinking. This type of problem is usually presented like 13,500 people are there to start with and it increases by 6.5 yearly, how much will it be in a year? But this time we have to find the years and we have the end population value.

First write equation:

13,500(0.065)^x = 27000

Simplify by dividing:

0.65^x = 0.5

*Use property of log (for isolating x):

x(log(0.65)) = log(0.5)

Isolate x:

x = log(0.5)/log(0.65)

x = 1.6090405507426917

*the reason why we did log was because we need the x to not be in an exponent for but to be normal. So log makes us able to write it like that. Same works with ln or natural log. For continuously compounding or continuously depreciating you would use ln.

Answer:

U B = 100.5

Step-by-step explanation:

the upper bound of the size of the television screen= 95.5 since it is corrected to the nearest 5 then the U B =100.5 cm

The upper bound of the size of the television screen is 100.5 cm

The conversion of the size of the television screen to the nearest 5cm from the initial size of 95 cm is = 100 cm.

Now, the upper bound of the size of the television screen which is 100 is can be determined by the addition of a half value to 100 cm:

i.e.

= (1/2) + 100 cm

= 0.5 + 100 cm

= 100.5 cm

Therefore, we can conclude that the upper bound of the size of the television screen is 100.5 cm

Learn more about nearest value here:

https://brainly.com/question/16382026?referrer=searchResults

Before we start, let's plot the graph of the hyperbola:

The problem wants the distance across the base of the base, we can see that at y = 0 (base) the "vases" touches x = 2.935. that's the distance between the center of the base and the end of it, looking at the image we can see that basically, it's the distance between the x-intercept, we know that half of the distance is 2.935, then the distance is

Therefore, the correct answer is 5.87 inches, distance between x-intercept

Answer:

number 1

1       1000 grams

2      2000 grams

5        5000 grams

8         8000 grams

10          10000 grams

Step-by-step explanation:

now 2

1 grams    1000

3 grams      3000

4 grams       4000

6 grams       6000

9 grams       9000

that is all i know please mark me the brainiest

Answer:

\(\frac{3}{2}\)

Step-by-step explanation:

let n be the number , then

\(\frac{1}{3}\) n = \(\frac{1}{2}\) ( multiply both sides by 3 )

n = 3 × \(\frac{1}{2}\) = \(\frac{3}{2}\)

We have shown that there are elements m, n ∈ S with m - n divisible by 16.

Answer:Let's consider the remainders of elements of S when divided by 16. These remainders can only be integers between 0 and 15, so there are only 16 possible remainders. However, we have 17 elements in S, so by the Pigeonhole Principle, at least two of these elements must have the same remainder when divided by 16. Let's call these elements m and n. Since they have the same remainder when divided by 16, their difference must be divisible by 16. In other words, m - n is divisible by 16. Therefore, we have shown that there are elements m, n ∈ S with m - n divisible by 16.

Learn more about Elements

brainly.com/question/13025901

#SPJ11

(a) The rate of change of the sound pressure with respect to time is approximately 0.0694 dB/second.

(b) The rate of change of the sound pressure at r = 1 second is 0 dB/second.

(a) The rate of change of the sound pressure with respect to time (dp/dt), we can use the chain rule. The given formula for sound pressure is P = 10 log(W/W₀), where W is the sound power and W₀ is the reference threshold.

Given:

W = 7.2 Watts (sound power)

dW/dt = 0.5 Watts/second (rate of change of sound power with respect to time)

Using the chain rule, we have:

dp/dt = (dP/dW) × (dW/dt)

The derivative of P with respect to W can be found by differentiating the logarithmic function:

dP/dW = 10 × (1/W) × (dW/dt)

Substituting the given values:

dp/dt = 10 × (1/W) × (dW/dt)

= 10 × (1/7.2) × 0.5

= 0.0694 dB/second

Therefore, the rate of change of the sound pressure with respect to time is approximately 0.0694 dB/second.

(b) Given:

W = 1² + 1 + 1

t = 3 seconds

To find the rate of change of the sound pressure at t = 3 seconds (dp/dt), we need to differentiate the formula for sound pressure with respect to time.

Using the chain rule, we have:

dp/dt = (dP/dW) × (dW/dt)

The derivative of P with respect to W is:

dP/dW = 10 × (1/W)

The derivative of W with respect to t can be found by differentiating the given formula:

dW/dt = d/dt (1² + 1 + 1)

= 0

Substituting the values:

dp/dt = (dP/dW) × (dW/dt)

= 10 × (1/3) × 0

= 0

Therefore, the rate of change of the sound pressure at t = 3 seconds is 0 dB/second.

(c) Given:

W = cos(0.2)

r = 1 second

To find the rate of change of the sound pressure at r = 1 second (dp/dt), we need to differentiate the formula for sound pressure with respect to time.

Using the chain rule, we have:

dp/dt = (dP/dW) × (dW/dt)

The derivative of P with respect to W is:

dP/dW = 10 × (1/W)

The derivative of W with respect to t can be found by differentiating the given formula:

dW/dt = d/dt (cos(0.2))

= 0

Substituting the values:

dp/dt = (dP/dW) × (dW/dt)

= 10 × (1/cos(0.2)) × 0

= 0

Therefore, the rate of change of the sound pressure at r = 1 second is 0 dB/second.

To know more about rate of change click here :

https://brainly.com/question/32023967

#SPJ4

a. The probability that a randomly selected person will have a white blood cell count between 6000 and 10,000 is approximately 0.7272.

b. Approximately 7.78% of people have white blood cell counts in the elevated range (>10,500).

c. The probability that a randomly selected person has a white blood cell count below 4500 is approximately 0.0436.

To answer these questions regarding the distribution of white blood cell counts, we will use the Normal distribution with a mean of 7500 and a standard deviation of 1750. Let's calculate the probabilities using this information.

a. To find the probability that a randomly selected person will have a white blood cell count between 6000 and 10,000, we need to calculate the area under the Normal curve between these two values.

Using technology or a table, we find the z-scores for both values:

For 6000:

z1 = (6000 - 7500) / 1750

z1 ≈ -0.857

For 10000:

z2 = (10000 - 7500) / 1750

z2 ≈ 1.429

Using the z-scores, we can calculate the probability as the difference between the cumulative probabilities at z2 and z1:

P(6000 < x < 10000) = P(z1 < z < z2)

Using the Normal distribution table or technology, we find the cumulative probabilities:

P(z < -0.857) ≈ 0.1950

P(z < 1.429) ≈ 0.9222

P(6000 < x < 10000) ≈ P(z < 1.429) - P(z < -0.857)

P(6000 < x < 10000) ≈ 0.9222 - 0.1950

P(6000 < x < 10000) ≈ 0.7272

Therefore, the probability that a randomly selected person will have a white blood cell count between 6000 and 10,000 is approximately 0.7272.

b. To find the percentage of people with white blood cell counts over 10,500 (elevated range), we need to calculate the probability of having a value greater than 10,500.

Using the z-score:

z = (10500 - 7500) / 1750

z ≈ 1.429

P(x > 10500) = 1 - P(z < 1.429)

P(x > 10500) = 1 - 0.9222

P(x > 10500) ≈ 0.0778

Therefore, approximately 7.78% of people have white blood cell counts in the elevated range (>10,500).

c. To find the probability that a randomly selected person has a white blood cell count below 4500, we calculate the cumulative probability up to that value.

Using the z-score:

z = (4500 - 7500) / 1750

z ≈ -1.714

P(x < 4500) = P(z < -1.714)

Using the Normal distribution table or technology, we find:

P(z < -1.714) ≈ 0.0436

Therefore, the probability that a randomly selected person has a white blood cell count below 4500 is approximately 0.0436.

learn more about "probability ":- https://brainly.com/question/25839839

#SPJ11

The gravitational potential energy gained by the group of skydivers before jumping is 4,410 kJ.

Gravitational Potential Energy (GPE) is estimated as;

GPE = m×g×h              

In which

m = mass of parachuting outfit (kg)

g = acceleration due to gravity (m/s²)

h = height (meters)

Put the values in the formula.

GPE = 90× 9.8× 5000

GPE = 4,410,000‬ joules

GPE = 4,410 kJ

Thus, the gravitational potential energy gained by the group of skydivers before jumping is 4,410 kJ.

To know more about the Gravitational Potential Energy, here

https://brainly.com/question/3120930

#SPJ4

Answer:

3(3) + 0.75(2) = (3 + 0.75)x

Step-by-step explanation:

The cost per pound of the mixture is the total cost divided by the total weight.

3 lb granola at $3 per lb has a cost of 3(3)

0.75 lb of raisins at $2 per lb has a cost of 0.75(2)

The total cost is 3(3) + 0.75(2)

The mixture has an unknown cost per lb, so we call it x.

When you multiply the cost per lb of the mix by the total weight, you get the total cost.

Total weight of mix: 3 + 0.75

Cost per lb of mix: x

Total cost of mix: (3 + 0.75)x

Above, we know the total cost is 3(3) + 0.75(2)

We set these two amounts equal to get our equation.

3(3) + 0.75(2) = (3 + 0.75)x

Answer: 3(3) + 0.75(2) = (3 + 0.75)x

To determine which population is furthest from the mean, we would need specific population data to compare. Without the actual population data, it is not possible to provide a specific answer.

The population that is furthest from the mean would typically be the population with the largest deviation or difference from the mean. Deviation is a measure of how far individual values in a population are from the mean. Therefore, to determine which population is furthest from the mean, we would calculate the deviations of each population from their respective means and compare them.

The population with the largest deviation, or the population whose values are the farthest from the mean, would be considered the population furthest from the mean. However, without the specific population data, it is not possible to determine which population is furthest from the mean

Learn more about population data here:

https://brainly.com/question/24846692

#SPJ11

A triangle with an area of 108 square feet has a base length and height equal to 24 feet and 9 feet, respectively.

Given that the cross-section of the lean-to shelter is in the shape of a triangle, its area is the area of a triangle.

A = 1/2bh

where b is the length of the base

h is the height

If the base of the triangle is 6​ feet more than twice its height, then we have b = 6 + 2h.

A = 1/2bh

A = 1/2(6 + 2h)(h)

A = h^2 + 3h

If the area of the triangle is 108 square feet, then

A = h^2 + 3h

108 = h^2 + 3h

h^2 + 3h - 108 = 0

Getting the roots of the polynomial.

h^2 + 3h - 108 = 0

(h - 9)(h + 12) = 0

h = 9     ;     h = -12

Since h must be a positive number, h = 9 feet.

Substitute the value of h in the equation for b.

b = 6 + 2h

b = 6 + 2(9)

b = 6 + 18

b = 24 feet

Learn more about base and height of triangle here: https://brainly.com/question/28318761

#SPJ4

The value of probability that a customer wins a prize is,

⇒ 12.5%

We have to given that;

A jewelry store has each customer spin a spinner with 8 equal sections numbered 1, 1, 1, 2, 2, 3, 3, 4 to win a free bracelet.

And, Customers who spin a 4 win.

Now, We have;

Total outcomes = 8

And, Possible outcomes for who spin a 4 win is,

⇒ 1

Hence, The value of probability that a customer wins a prize is,

⇒ 1 / 8

⇒ 1/8 x 100%

⇒ 12.5%

Thus, The value of probability that a customer wins a prize is,

⇒ 12.5%

Learn more about the probability visit:

https://brainly.com/question/13604758

#SPJ1

Answer: C

Step-by-step explanation:

For our unknown value x, the opposite side = 10 and the adjacent side = 18, using this information you can use SOH CAH TOA.

TOA refers to opposite over adjacent, which would be

tan x = 10/18.

Hope this helps!

The number 71.38 can be written in word form as "seventy-one and thirty-eight hundredths." The correct answer is option D.

In decimal notation, the number 71.38 can be broken down into its whole number and decimal parts. The whole number part is 71, and the decimal part is 0.38.

In a decimal number, the digits to the right of the decimal point represent fractions of a whole. Each digit to the right of the decimal point has a place value that is a power of 10.

In word form, the decimal part 0.38 is read as "thirty-eight hundredths." Therefore, when combined with the whole number 71, the correct word form is "Seventy-one and thirty-eight hundredths."

Therefore option D is the correct answer.

Learn more about the whole number:

https://brainly.com/question/9879870

#SPJ11

Answer:

Step-by-step explanation:

get all x terms on one side, giving you 3^x=10

Then, the simple rule is y=b^x becomes x=logb(base)y

b is 3, x is x, and y is 10

logbase3(10)=x

Answer:

d; y - 1 = 4/5(x + 2)

Step-by-step explanation:

the equation for a point-slope form line is y - y1 = m(x - x1)

plug in the points and you will get your answer

y - 1 = 4/5(x + 2)

that is your answer